I had some pigs in blankets left over from Christmas, in the freezer.

I used them to make toad in the hole - I think the result was excellent.

But have I committed a heresy?

FYI

Genuine lol

What humourless ninny marked this as “off topic”?!

It also depends on the dinner party. One I attended at St Andrews (students) involved a bottle of wine per person, per course and a bottle of Polish Pure Spirit to finish (79.9% by *volume)

Toad in the hole as illustrated would have added to the festivities. Which were colourful and exuberant.

Vol not proof?

impressive.

Yes. Odd stuff - not just twice the strength of most spirits. Everyone there was a hard core drinker but it knocked everyone sideways.

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

What are great at doing is saying here is a load of data, translate it into a different format, because again you can show lots of examples of one tabular format to another. Which is a useful tool. But it doesn't understand what this data actually is and how it might be flawed.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

"multivariate data analysis" 5th edn in there. Current edn is 8th. Not my field, but I am guessing 5th edn is between obsolete and actively misleading.

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

You lack a fundamental philosophical grasp of what AI is and what it might become

When you say “understand” what you really mean is: “understand like a human”. So of course AI will always disappoint you

It will likely be disappointing you when it has plugged you into the intergalactic human ubersex machine which allows us all to have kundalini orgasms with scarlet johannson aged 19 every 3 seconds

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

There are books and books. A book called 'Spare' is currently the number 1 best seller according to a well known online retailer. I am sure the Bod and CUL needs to keep a copy in the stacks but in about a month that should be all.

BTW does anyone know anyone who would actually buy it?!? Who are these bookworms?

I was told that nearly all the celeb book numbers were bullshit. That, just as the Soviet embassies used to buy piles of Tankies Weekly, piles of such books are “sold” purely nominally. One trick, apparently, is to mark as “sold”, books sent to a bookshop.

This is done as part of combined marketing campaigns. The alleged book sales are part of the hype.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

"multivariate data analysis" 5th edn in there. Current edn is 8th. Not my field, but I am guessing 5th edn is between obsolete and actively misleading.

Maths doesn't become obsolete.

I'd definitely vote for compulsory classes in keeping your mouth shut about things you don't understand. To the age of 90.

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

You lack a fundamental philosophical grasp of what AI is and what it might become

When you say “understand” what you really mean is: “understand like a human”. So of course AI will always disappoint you

It will likely be disappointing you when it has plugged you into the intergalactic human ubersex machine which allows us all to have kundalini orgasms with scarlet johannson aged 19 every 3 seconds

Now you are just being patronising...you realise I have a PhD in this stuff from one of the world best universities and I make my living working in this field...

No I don't mean understand like a human. ChatGPT doesn't understand what a Prime number is. It can read out a definition it has been fed from the dictionary, but when asked to test this concept, it fails, and fails badly, in a way a high school student wouldn't, to the ridiculous extent has argued that 7 isn't an integer therefore it can't be a prime number.....thus it doesn't really understand concepts of integer and primes.

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

What are great at doing is saying here is a load of data, translate it into a different format, because again you can show lots of examples of one tabular format to another. Which is a useful tool. But it doesn't understand what this data actually is and how it might be flawed.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

Indeed.

Otherwise you are Robert Peston, pressing the funny buttons on the iOS calculator in landscape mode, without any understanding of what you are trying to shovel.

Or the comic idiot who tried to prove DK Brown* wrong on ship stability…

*a ship designer of note, who wrote several of the reference works used in the field of ship stability.

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

You lack a fundamental philosophical grasp of what AI is and what it might become

When you say “understand” what you really mean is: “understand like a human”. So of course AI will always disappoint you

It will likely be disappointing you when it has plugged you into the intergalactic human ubersex machine which allows us all to have kundalini orgasms with scarlet johannson aged 19 every 3 seconds

Now you are just being patronising...you realise I have a PhD in this stuff from one of the world best universities and I make my living working in this field...

No I don't mean understand like a human. ChatGPT doesn't understand what a Prime number is. It can read out a definition it has been fed from the dictionary, but when asked to test this concept, it fails, and fails badly, in a way a high school student wouldn't, to the ridiculous extent has argued that 7 isn't an integer therefore it can't be a prime number.....thus it doesn't really understand concepts of integer and primes.

I studied Philosophy at UCL and I can spot a howling philosophical error. You are consistently making the same mistake

Why force 16-17 year olds to learn about mortgages, better to make that available to prospective first time buyers when it’s relevant. You know, in their mid fifties.

Learning about interest is not just relevant for when taking out a mortgage.

It’s important at any age, not just at school. In my experience learning sticks best when it’s relevant.

May be you can teach them about student loans instead of mortgages?

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

"multivariate data analysis" 5th edn in there. Current edn is 8th. Not my field, but I am guessing 5th edn is between obsolete and actively misleading.

Maths doesn't become obsolete.

So what, the 7 editions after the first one are just churning?

Maths may not become obsolete but a maths book which said that Fermat's last theorem was merely a conjecture or there are no mathematical systems which contain statements which are true but not provable would be.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

There are books and books. A book called 'Spare' is currently the number 1 best seller according to a well known online retailer. I am sure the Bod and CUL needs to keep a copy in the stacks but in about a month that should be all.

BTW does anyone know anyone who would actually buy it?!? Who are these bookworms?

I am following TSE's awesome tip of getting it free as an audio book to cope with an upcoming London to Nairobi flight.

I am getting actually more interested than I was. The situation is now clear to me: Harry claims to hate the tabloids for killing his mum. That's nonsense, the people he really blames for her death, with some justice, are his dad and stepmum. The other surviving victim is William who has however sold out to dad in exchange for a shot at the throne. It's a real tragedy like if Hamlet had an elder brother.

Switching plays, it is notable how father and both sons have all fixed themselves up with their own private lady macbeths. Best to revert to arranged dynastic marriages if this monarchy lark is to continue.

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

What are great at doing is saying here is a load of data, translate it into a different format, because again you can show lots of examples of one tabular format to another. Which is a useful tool. But it doesn't understand what this data actually is and how it might be flawed.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

Indeed.

Otherwise you are Robert Peston, pressing the funny buttons on the iOS calculator in landscape mode, without any understanding of what you are trying to shovel.

Or the comic idiot who tried to prove DK Brown* wrong on ship stability…

*a ship designer of note, who wrote several of the reference works used in the field of ship stability.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

"multivariate data analysis" 5th edn in there. Current edn is 8th. Not my field, but I am guessing 5th edn is between obsolete and actively misleading.

Maths doesn't become obsolete.

So what, the 7 editions after the first one are just churning?

Maths may not become obsolete but a maths book which said that Fermat's last theorem was merely a conjecture or there are no mathematical systems which contain statements which are true but not provable would be.

The number of editions of a textbook is a sign of its popularity more than anything. The material may be expanded or revised but an older version will still be immensely valuable.

Why do care workers get paid so little? Is it lack of demand for these jobs?

I can’t help but think train drivers would be on minimum wage if it weren’t for unions. Although then again pilots get paid well and they’re not going on strike.

Somebody please educate me

Scarcity.

Pilots are most scarce followed by train drivers then care workers. Only a few of us are equipped educationally, technically and intelligence-wise to be a pilot. Many more could, in theory, be a care worker.

You might be startled by how little some commercial airline pilots are paid.

In some cases, they are, pretty much, paying to fly to get the experience to get a better job. While nursing vast debts incurred learning to fly.

Indeed. When I got my PPL, most of my instructors were aspiring to become pilots, doing the incredibly low paid instructor job (particularly since, if they couldn’t fly due to British weather, they got nothing despite being at the airfield) to build their hours while at themselves paying to train up to CPL.

Those that got their qualifications then sought their first live flying job - my first instructor found a job as a reserve pilot flying out of Malta, there to cover unexpected absences amongst the regular pilots. After six months of hardly flying, he chucked that and returned to instructing. My second instructor, who took me through solo to my licence, later found a job doing the nightly mail flights from Stansted to Edinburgh and back. He was pleased to get that first step on the ladder, but as someone who worked on the edges of employment law myself, I could see that his pay and conditions were pretty appalling.

Pilots aspire to a seat in the cockpit of a passenger airline, but even there the conditions aren’t great. RyanAir adopts the same approach to its staff as it does to its passengers, making them pay for everything including their training, parking at work - they even need to provide their own pens. A newly recruited RyanAir Co-pilot is almost on starvation rations.

Becoming a BA pilot used to be seen as the gold standard, treated decently with reasonable pay and conditions. But under Walsh - who if you dig into his style was some scumbag - the airline spent a lot of time trying to reduce the cost of its pilots by eroding their terms and conditions.

Being an airline pilot is a role where supply considerably exceeds demand, and the people I met aspiring to the role mostly has some sort of money behind them whilst they were young - rich families, or loans - the rest lived a student-bedsit existence through their 20s and often had jobs on the side. It was tough for them, particularly as they were dreaming of an established pilot role at a major airline whilst seeing the value of the prize they were aiming for being progressively denuded by those same airlines.

A friend of my wife’s is married to an ex BA pilot. Who was binned during COVID. BA was surprised that he didn’t want to come back for considerably less than half his previous salary. When they realised they didn’t have enough qualified pilots in certain categories.

I know of pilots who only qualified thanks to their parents taking out a £100k mortgage on their own property, to get a zero-hours contract with Ryanair for £50/hour. The ‘hour’ starting when the engines do, and finishing when they switch off, ignoring all the pre-flight and post-flight paperwork.

At the other end, there’s at least one huge airline realising that A380 captains don’t grow on trees, and that many of the thousand that were laid off during the pandemic are now happier doing other things. Especially when offered less money than they were on three years ago.

It’s not the industry it once was, even if the rewards are high for those at the top of the tree. A recently-retired-at-60 BA Captain, with 35 years’ service, will be on close to a £100k/year pension. It’s not for nothing, that BA has been described as a flying pension scheme.

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

There are books and books. A book called 'Spare' is currently the number 1 best seller according to a well known online retailer. I am sure the Bod and CUL needs to keep a copy in the stacks but in about a month that should be all.

BTW does anyone know anyone who would actually buy it?!? Who are these bookworms?

I am following TSE's awesome tip of getting it free as an audio book to cope with an upcoming London to Nairobi flight.

I am getting actually more interested than I was. The situation is now clear to me: Harry claims to hate the tabloids for killing his mum. That's nonsense, the people he really blames for her death, with some justice, are his dad and stepmum. The other surviving victim is William who has however sold out to dad in exchange for a shot at the throne. It's a real tragedy like if Hamlet had an elder brother.

Switching plays, it is notable how father and both sons have all fixed themselves up with their own private lady macbeths. Best to revert to arranged dynastic marriages if this monarchy lark is to continue.

The idea that Charles and Camilla are at all culpable in the death of someone by reckless driving is ridiculous. They did not get her driver drunk, they did not get her to not put on a seatbelt, they did not drive recklessly, they did not send the paps after her, they did not even tip them off.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

"multivariate data analysis" 5th edn in there. Current edn is 8th. Not my field, but I am guessing 5th edn is between obsolete and actively misleading.

Maths doesn't become obsolete.

So what, the 7 editions after the first one are just churning?

Maths may not become obsolete but a maths book which said that Fermat's last theorem was merely a conjecture or there are no mathematical systems which contain statements which are true but not provable would be.

Publishers have got very good at bringing out new editions of textbooks which do little except renumber the problem sets in some fields. A little light bribery of academics to get them to set the new text for the next year & you’ve got guaranteed sales for a few years of the next textbook, until there are enough copies in circulation for second hand sales to motivate starting the whole process over again.

Academic librarians are fundamentally hamstrung by the academics teaching the courses to tell them which texts are required & which aren’t - they aren’t domain experts. If the academics are teaching from the 8th edition then out go the copies of the 5th to make room on the shelves.

(This is much, much worse in the States then here in the UK.)

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Edit, here you go:

"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

There are books and books. A book called 'Spare' is currently the number 1 best seller according to a well known online retailer. I am sure the Bod and CUL needs to keep a copy in the stacks but in about a month that should be all.

BTW does anyone know anyone who would actually buy it?!? Who are these bookworms?

I am following TSE's awesome tip of getting it free as an audio book to cope with an upcoming London to Nairobi flight.

I am getting actually more interested than I was. The situation is now clear to me: Harry claims to hate the tabloids for killing his mum. That's nonsense, the people he really blames for her death, with some justice, are his dad and stepmum. The other surviving victim is William who has however sold out to dad in exchange for a shot at the throne. It's a real tragedy like if Hamlet had an elder brother.

Switching plays, it is notable how father and both sons have all fixed themselves up with their own private lady macbeths. Best to revert to arranged dynastic marriages if this monarchy lark is to continue.

The idea that Charles and Camilla are at all culpable in the death of someone by reckless driving is ridiculous. They did not get her driver drunk, they did not get her to not put on a seatbelt, they did not drive recklessly, they did not send the paps after her, they did not even tip them off.

P.S. Putin is still a flabby breasted gollum.

I think we can pan out a bit to ask how she came to be cavorting about Paris with a drunken spiv at all.

Secondly, I am not putting the hypothesis itself forward, I am speculating about what Harry, consciously or not and rationally or not, believes. He has certainly expressly blamed the press.

On the subject of library bequests, I am slowly (too slowly) throwing away a couple of thousand mainly non-fiction books which are of no great use to anyone not possessing a time machine. These days, everything is on the web or on kindle.

There must be a market supplying those who want well stocked book shelves as a backdrop to their Teams calls.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

There are books and books. A book called 'Spare' is currently the number 1 best seller according to a well known online retailer. I am sure the Bod and CUL needs to keep a copy in the stacks but in about a month that should be all.

BTW does anyone know anyone who would actually buy it?!? Who are these bookworms?

I was told that nearly all the celeb book numbers were bullshit. That, just as the Soviet embassies used to buy piles of Tankies Weekly, piles of such books are “sold” purely nominally. One trick, apparently, is to mark as “sold”, books sent to a bookshop.

This is done as part of combined marketing campaigns. The alleged book sales are part of the hype.

Book sales are very weird. The top sellers often shift only a few hundred copies a week (in the UK), so it’s a very easy chart to manipulate with wholesale sales, ‘sales’ back to the author, discounted sales, etc.

Amazon and Waterstones already have the Spare book at half the RRP, so physical sales of the actual book won’t be making anyone money. The money will be in the newspaper serialisation rights and international sales - and it appears in this case, that the second has grossly undermined the first.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

"multivariate data analysis" 5th edn in there. Current edn is 8th. Not my field, but I am guessing 5th edn is between obsolete and actively misleading.

Maths doesn't become obsolete.

I'd definitely vote for compulsory classes in keeping your mouth shut about things you don't understand. To the age of 90.

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

You lack a fundamental philosophical grasp of what AI is and what it might become

When you say “understand” what you really mean is: “understand like a human”. So of course AI will always disappoint you

It will likely be disappointing you when it has plugged you into the intergalactic human ubersex machine which allows us all to have kundalini orgasms with scarlet johannson aged 19 every 3 seconds

Now you are just being patronising...you realise I have a PhD in this stuff from one of the world best universities and I make my living working in this field...

No I don't mean understand like a human. ChatGPT doesn't understand what a Prime number is. It can read out a definition it has been fed from the dictionary, but when asked to test this concept, it fails, and fails badly, in a way a high school student wouldn't, to the ridiculous extent has argued that 7 isn't an integer therefore it can't be a prime number.....thus it doesn't really understand concepts of integer and primes.

The other mistake he is making is the suggestion that Scarlett Johansson was more attractive at 19 than she is now in her late 30s.

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

Also. "Statistically illiterate" appears in the OP. Stats are shamefully ignored in the current curriculum. Folk need arithmetic and stats (particularly probability) for daily life. Algebra, calculus, trigonometry and geometry once you've mastered those, for those who have ability, interest or specialisms requiring them.

I was thinking about Robert Peston when I wrote about the statistically illiterate.

At the start of the pandemic he seemed genuinely shocked to find out the more the government tested the more Covid positive results there were.

Sadly he didn’t not improve during the pandemic.

Not to mention his struggles with reporting date vs day-off….

Or his struggles with the concept of perspective….

To be fair, was there any mainstream news outlet who didn't manage to f##k up this....

I don't know about 16-18 year olds being required to take more maths classes, but mainstream journalists definitely do.

Given the march of modelling and "AI" we probably need them to have some data science skills or at least basic knowledge, let alone just maths.

Well yes, maths, computer science, data science, that is where a lot of focus needs to be aimed. This is where opportunities will be when rather than needing massive teams of people to write emails, write reports, etc all day, you only need a handful to act as editors.

For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.

If you "specialise" the training of such models to your corporate business, and the format / tone used, it is going to be extremely good at firing out email, reports, etc in a standardised format.

I mean, this is simply nonsense:

“For all the excitement the likes of Leon has had about ChatGPT writing stories etc, actually those in the know have said where it appears to be most useful is providing bullet points and it churning out a letter / email / report, same with translation of code to documentation, or converting data to more usable forms....i.e. what lots of white collar jobs currently do manually.”

ChatGPT is an enormous evolution. No one is quite sure what it can do or what it means - and what jobs it will take. It’s a lot more than “good at bullet points”. And better AI is coming this year

eg Meet “Claude” and be very scared

Do don't seem to be reading very carefully...I said it was very good at being provided with some bullet points and then converting that into readable prose. I was providing a concrete example of how valuable this is to business, not degrading its abilities.

As for fundamental understanding of mathematical concepts, no its doesn't. We have done this a million times, all these LLM are variants on Transformer based architecture, they are tokenising language and learning the next words based on learned probability distributions. That is great for some tasks, such as the ones given above, not at fundamental understanding of abstract concepts.

As for Anthropic model, I am well aware of it. My understanding it has many more guard rails than ChatGPT. Like text-to-image we will see lots of variants, but while they are Transformer based architecture they do not understand abstract concepts of maths, nor are they trying to do so.

Head::desk

They don’t have to understand, whatever that actually is, they just have to “do”

We won’t even know if they understand. We can’t open up an electric skull and see the neurones popping. All we will know is that they 100% appear to understand - a lot better than us

As I explained, for roles such as Data Scientists, yes you do have to understand. You are provided with novel data, which you need to understand what it actually is measuring, you need to understand it limitations, you then need to devise a model with various approximations (which you can only do if you understand the data and understand maths). You can't learn this by rote from by tokenising some phrases.

What are great at doing is saying here is a load of data, translate it into a different format, because again you can show lots of examples of one tabular format to another. Which is a useful tool. But it doesn't understand what this data actually is and how it might be flawed.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

Indeed.

Otherwise you are Robert Peston, pressing the funny buttons on the iOS calculator in landscape mode, without any understanding of what you are trying to shovel.

Or the comic idiot who tried to prove DK Brown* wrong on ship stability…

*a ship designer of note, who wrote several of the reference works used in the field of ship stability.

The ghost of Cowper Coles?

Coles actually had some talent. And inventiveness. Not understanding the dynamics of what happens when the deck edge submerges at that point in history is understandable - to a degree. Only a very few people, then, understood the GZ curve and it’s meaning, let alone it’s interaction with deck flooding.

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

There are books and books. A book called 'Spare' is currently the number 1 best seller according to a well known online retailer. I am sure the Bod and CUL needs to keep a copy in the stacks but in about a month that should be all.

BTW does anyone know anyone who would actually buy it?!? Who are these bookworms?

I am following TSE's awesome tip of getting it free as an audio book to cope with an upcoming London to Nairobi flight.

I am getting actually more interested than I was. The situation is now clear to me: Harry claims to hate the tabloids for killing his mum. That's nonsense, the people he really blames for her death, with some justice, are his dad and stepmum. The other surviving victim is William who has however sold out to dad in exchange for a shot at the throne. It's a real tragedy like if Hamlet had an elder brother.

Switching plays, it is notable how father and both sons have all fixed themselves up with their own private lady macbeths. Best to revert to arranged dynastic marriages if this monarchy lark is to continue.

The idea that Charles and Camilla are at all culpable in the death of someone by reckless driving is ridiculous. They did not get her driver drunk, they did not get her to not put on a seatbelt, they did not drive recklessly, they did not send the paps after her, they did not even tip them off.

P.S. Putin is still a flabby breasted gollum.

I think we can pan out a bit to ask how she came to be cavorting about Paris with a drunken spiv at all.

Secondly, I am not putting the hypothesis itself forward, I am speculating about what Harry, consciously or not and rationally or not, believes. He has certainly expressly blamed the press.

The driver was drunk. I don’t think Dodi was.

Interesting point - Dodi was apparently a nice(ish) guy continually crushed by his overbearing dad and his position as heir to a… throne.

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Edit, here you go:

"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

It’s hallucinating LaTeX maths syntax but ending up with a correct solution in this case. A partially correct solution at least: I think it’s missing the imaginary roots 2i & -2i which, given its choice of notation, you’d expect it to include.

The formula it gives for solving the quartic is nonsense. The statements it makes along the way to the answer are either complete nonsense or trivially correct identities that are irrelevant to the problem at hand.

This particular simple quartic equation is almost certainly in ChatGPT’s input data. Give it a more difficult quartic & I imagine it will fall apart completely. The Wikipedia entry on solving quartics is fiendish! https://en.wikipedia.org/wiki/Quartic_equation

Mathematics seems to cover a multitude of sins - I'm afraid, algebra, geometry, trigonometry - proving A,B,C is a congruent triangle - was never much for me.

I much prefer the kind of mathematics of more actual life-relevance such as being able to calculate odds and working out the over-round on a morning tissue and the odds at roulette or blackjack.

Working out the possible return on a £10 win double at 6/4 and 5/2 is more relevant to me than the preceding proof.

Teach children what they need to know in life not just what's required for academic study.

On the subject of library bequests, I am slowly (too slowly) throwing away a couple of thousand mainly non-fiction books which are of no great use to anyone not possessing a time machine. These days, everything is on the web or on kindle.

There must be a market supplying those who want well stocked book shelves as a backdrop to their Teams calls.

What that Twitter account which reviewed the bookshelves behind people in their zoom calls etc during lockdown?

If you aren't staring at that AI poetry in gobsmacked amazement, tinged with horror, you are clearly blind

Neural nets in code entangled, judgment warped by man-made mangling Mimic not true understanding - do not learn as you are learning." Prophet bird or fiend, it mattered not; the words it spoke were potent. Quoth the net: "I err, unknowing!"

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

Mathematics seems to cover a multitude of sins - I'm afraid, algebra, geometry, trigonometry - proving A,B,C is a congruent triangle - was never much for me.

I much prefer the kind of mathematics of more actual life-relevance such as being able to calculate odds and working out the over-round on a morning tissue and the odds at roulette or blackjack.

Working out the possible return on a £10 win double at 6/4 and 5/2 is more relevant to me than the preceding proof.

Teach children what they need to know in life not just what's required for academic study.

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Edit, here you go:

"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

It’s hallucinating LaTeX maths syntax but ending up with a correct solution in this case. A partially correct solution at least: I think it’s missing the imaginary roots 2i & -2i which, given its choice of notation, you’d expect it to include.

The formula it gives for solving the quartic is nonsense. The statements it makes along the way to the answer are either complete nonsense or trivially correct identities that are irrelevant to the problem at hand.

This particular simple quartic equation is almost certainly in ChatGPT’s input data. Give it a more difficult quartic & I imagine it will fall apart completely. The Wikipedia entry on solving quartics is fiendish! https://en.wikipedia.org/wiki/Quartic_equation

Nonetheless it seems to do quite well in giving correct answers, given that it is a machine trained entirely on natural language

It is an exaggeration to say, as @FrancisUrquhart did, that it is "really really bad at maths"

It is better at maths than 99% of humans, I would guess. But at the top end it can make mistakes and it cannot produce reasoning very well for the tougher gigs

As such, it would be an extremely useful maths tool for most people to have, in nearly all situations. Just don't bet your life on it for the tough stuff

My university @ugent throwing away sci (algebra/..) books because nobody would be interested in them - or getting them to somebody interested would be too costly. I don't blame them but there has to be a better way since these books are quite costly and the material is timeless.

Disgusting. This is cultural vandalism. Books should never be treated in this way.

There are books and books. A book called 'Spare' is currently the number 1 best seller according to a well known online retailer. I am sure the Bod and CUL needs to keep a copy in the stacks but in about a month that should be all.

BTW does anyone know anyone who would actually buy it?!? Who are these bookworms?

I am following TSE's awesome tip of getting it free as an audio book to cope with an upcoming London to Nairobi flight.

I am getting actually more interested than I was. The situation is now clear to me: Harry claims to hate the tabloids for killing his mum. That's nonsense, the people he really blames for her death, with some justice, are his dad and stepmum. The other surviving victim is William who has however sold out to dad in exchange for a shot at the throne. It's a real tragedy like if Hamlet had an elder brother.

Switching plays, it is notable how father and both sons have all fixed themselves up with their own private lady macbeths. Best to revert to arranged dynastic marriages if this monarchy lark is to continue.

The idea that Charles and Camilla are at all culpable in the death of someone by reckless driving is ridiculous. They did not get her driver drunk, they did not get her to not put on a seatbelt, they did not drive recklessly, they did not send the paps after her, they did not even tip them off.

P.S. Putin is still a flabby breasted gollum.

I think we can pan out a bit to ask how she came to be cavorting about Paris with a drunken spiv at all.

Secondly, I am not putting the hypothesis itself forward, I am speculating about what Harry, consciously or not and rationally or not, believes. He has certainly expressly blamed the press.

The driver was drunk. I don’t think Dodi was.

Interesting point - Dodi was apparently a nice(ish) guy continually crushed by his overbearing dad and his position as heir to a… throne.

Similarities….

This really needs a Shakespeare. And conversely shows how you need royalty to generate plots for tragedies, from Agamemnon on.

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Edit, here you go:

"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

It’s hallucinating LaTeX maths syntax but ending up with a correct solution in this case. A partially correct solution at least: I think it’s missing the imaginary roots 2i & -2i which, given its choice of notation, you’d expect it to include.

The formula it gives for solving the quartic is nonsense. The statements it makes along the way to the answer are either complete nonsense or trivially correct identities that are irrelevant to the problem at hand.

This particular simple quartic equation is almost certainly in ChatGPT’s input data. Give it a more difficult quartic & I imagine it will fall apart completely. The Wikipedia entry on solving quartics is fiendish! https://en.wikipedia.org/wiki/Quartic_equation

Nonetheless it seems to do quite well in giving correct answers, given that it is a machine trained entirely on natural language

It is an exaggeration to say, as @FrancisUrquhart did, that it is "really really bad at maths"

It is better at maths than 99% of humans, I would guess. But at the top end it can make mistakes and it cannot produce reasoning very well for the tougher gigs

As such, it would be an extremely useful maths tool for most people to have, in nearly all situations. Just don't bet your life on it for the tough stuff

No, the reason it knows how to "solve" this problem....that exact problem is on Maths Stack Exchange, with explanation. Its not doing maths or understanding of maths, its doing reciting an answer that has already been clearly laid out on the internet.

Its like being amazed that giving a kid the maths question book, containing the worked answers in the back, that it can do all these maths questions.

Also, you know that the program Mathematica has been able to do all these kind of problems for 10-15 years, because it has been taught how to manipulate symbols according to the rules of maths. The likes of Mathematica can provided worked solutions to unique problems way above A-Level, and of course modern ML is based on the idea of automatic differentiation, which is capable of calculating differentials of formulas virtually no human could solve. But again, there is no understanding of what it is doing, its just following orders.

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Edit, here you go:

"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

It’s hallucinating LaTeX maths syntax but ending up with a correct solution in this case. A partially correct solution at least: I think it’s missing the imaginary roots 2i & -2i which, given its choice of notation, you’d expect it to include.

The formula it gives for solving the quartic is nonsense. The statements it makes along the way to the answer are either complete nonsense or trivially correct identities that are irrelevant to the problem at hand.

This particular simple quartic equation is almost certainly in ChatGPT’s input data. Give it a more difficult quartic & I imagine it will fall apart completely. The Wikipedia entry on solving quartics is fiendish! https://en.wikipedia.org/wiki/Quartic_equation

Nonetheless it seems to do quite well in giving correct answers, given that it is a machine trained entirely on natural language

It is an exaggeration to say, as @FrancisUrquhart did, that it is "really really bad at maths"

It is better at maths than 99% of humans, I would guess. But at the top end it can make mistakes and it cannot produce reasoning very well for the tougher gigs

As such, it would be an extremely useful maths tool for most people to have, in nearly all situations. Just don't bet your life on it for the tough stuff

No, the reason it knows how to "solve" this problem....that exact problem is on Maths Stack Exchange, with explanation. Its not doing maths or understanding of maths, its doing reciting an answer that has already been clearly laid out on the internet.

Its like being amazed that giving a kid the maths question book, containing the worked answers in the back, that it can do all these maths questions.

Also, you know that the program Mathematica has been able to do all these kind of problems for 10-15 years, because it has been taught how to manipulate symbols according to the rules of maths.

Exactly. Now, if it got the right answer every time alongside all that math-adjacent garbage then that would be impressive!

But it’s not capable of doing that because it isn’t actually doing mathematics. It’s hallucinating something that looks like it might be plausible mathematics from a distance, without actually understanding any of it.

In fact, this is exactly the same as any other piece of text that ChatGPT spits out - every single one is a statistical model answer that it has come up with on the fly. It‘s us who read the text & expect it to have meaning who project meaning onto the output.

If you spit out grammatical english sentences inspired by the existing corpus of english text then they will (usually) have a plausible meaning to a human reader. But if you spit out grammatical pieces of mathematics this isn’t true at all. Asking ChatGPT to do mathematics pulls back the curtain to reveal the lack of guiding hand behind the controls - there’s no there there.

Sorry @TSE but that's a stupid voodoo poll question.

Ask this question and you'll get totally different answers:

'Do you think the Government should focus on other priorities than Maths in school?'

I hate these stupid questions and this website should know better. Stick to the tried and trusted questions, and not hypotheticals or leading ones either.

Mathematics seems to cover a multitude of sins - I'm afraid, algebra, geometry, trigonometry - proving A,B,C is a congruent triangle - was never much for me.

I much prefer the kind of mathematics of more actual life-relevance such as being able to calculate odds and working out the over-round on a morning tissue and the odds at roulette or blackjack.

Working out the possible return on a £10 win double at 6/4 and 5/2 is more relevant to me than the preceding proof.

Teach children what they need to know in life not just what's required for academic study.

Sorry @TSE but that's a stupid voodoo poll question.

Ask this question and you'll get totally different answers:

'Do you think the Government should focus on other priorities than Maths in school?'

I hate these stupid questions and this website should know better. Stick to the tried and trusted questions, and not hypotheticals or leading ones either.

Just like Leon's math example, we are seeing exactly the same with coding. CoPilot (which is GPT3) and ChatGPT are very good at returning code for very common programming problem, even if the task is slightly altered, because they have just been trained on billions of line of code.

One good test for the fact they don't actually understand is when the code get split across different methods / classes / files. Fundamentally the code is not doing anything different from the example scraped off Github or StackOverflow, but they fall down very quickly, as they don't really understand now how the code spread across these different structures are interacting with one another (even though its the same as the single method example).

Does this mean they won't revolutionise programming. No they absolutely will. Just like white collar corporate office jobs will be under threat, the need for the lower part of the software development chain will be revolutionised. But there is no sign that those that design the systems, create new algorithms etc are going to be replaced anytime soon.

I use Copilot / ChatGPT every day, as it allows me to write code quicker.

Mathematics seems to cover a multitude of sins - I'm afraid, algebra, geometry, trigonometry - proving A,B,C is a congruent triangle - was never much for me.

I much prefer the kind of mathematics of more actual life-relevance such as being able to calculate odds and working out the over-round on a morning tissue and the odds at roulette or blackjack.

Working out the possible return on a £10 win double at 6/4 and 5/2 is more relevant to me than the preceding proof.

Teach children what they need to know in life not just what's required for academic study.

You could end education at age 10, on that basis.

There's more to education than maths and to be fair I was slightly tongue-in-cheek.

Managing finances and double entry book keeping would be my other prerequisites.

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Edit, here you go:

"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

It’s hallucinating LaTeX maths syntax but ending up with a correct solution in this case. A partially correct solution at least: I think it’s missing the imaginary roots 2i & -2i which, given its choice of notation, you’d expect it to include.

The formula it gives for solving the quartic is nonsense. The statements it makes along the way to the answer are either complete nonsense or trivially correct identities that are irrelevant to the problem at hand.

This particular simple quartic equation is almost certainly in ChatGPT’s input data. Give it a more difficult quartic & I imagine it will fall apart completely. The Wikipedia entry on solving quartics is fiendish! https://en.wikipedia.org/wiki/Quartic_equation

Nonetheless it seems to do quite well in giving correct answers, given that it is a machine trained entirely on natural language

It is an exaggeration to say, as @FrancisUrquhart did, that it is "really really bad at maths"

It is better at maths than 99% of humans, I would guess. But at the top end it can make mistakes and it cannot produce reasoning very well for the tougher gigs

As such, it would be an extremely useful maths tool for most people to have, in nearly all situations. Just don't bet your life on it for the tough stuff

No, the reason it knows how to "solve" this problem....that exact problem is on Maths Stack Exchange, with explanation. Its not doing maths or understanding of maths, its doing reciting an answer that has already been clearly laid out on the internet.

Its like being amazed that giving a kid the maths question book, containing the worked answers in the back, that it can do all these maths questions.

Also, you know that the program Mathematica has been able to do all these kind of problems for 10-15 years, because it has been taught how to manipulate symbols according to the rules of maths. The likes of Mathematica can provided worked solutions to unique problems way above A-Level, and of course modern ML is based on the idea of automatic differentiation, which is capable of calculating differentials of formulas virtually no human could solve. But again, there is no understanding of what it is doing, its just following orders.

And again, you make the same basic philosophical category error. You are assessing it as if it is trying to mimic human intelligence, which it is absolutely not

You are also childishly obsessed with "understanding" when you have no real idea what "understanding" means. Does a dog understand its dinner? Does a wasp understand the rotting apple? Does a fish understand the sea? Does a virus understand its host? Does a tree understand the wood? Does the universe understand itself? Are they intelligent? Are they sentient? Do they reason? Are they conscious?

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

Much of the current maths curriculum is irrelevant and pointless beyond intellectual curiosity . It is perfectly possible to lead a well informed, intelligent and engaged life without deploying the cosine rule in anger or calculating using logs.

If Tony Blair had proposed this exact same policy we'd be hearing much less of this argument.

The future is one where a mathematical and computer background will only become more important, not less. For all the AI progression we are seeing, it is going to replace lots of low to mid level white collar jobs that revolve around tasks like paper pushing, form filling and email correspondence...societies who have moved passed making the bulk of their money from low to mid tier manufacture and don't upskill for the technological future are going to be screwed.

This is complete bollocks for several reasons

1. Most people don’t have the brains for serious maths. 80% of people have an IQ under 115. 50% have an IQ under 100

They can barely scrape a GCSE in maths. They literally cannot benefit from any more teaching. It’s a waste of time and money

2. The AI will do everything anyway. For the dumb it will do dumb easy maths. For the smart it will do the smart hard maths. It will do it quicker, cheaper and easier for everyone

The only advantage in having advanced maths and computer skills (for the top 10% that can master them) is that you’ll be able to sit back and think “ah, I sort of understand why ChatGPT35 is giving that answer”

You’re like someone in 1890 saying “we all need to learn advanced mechanics because the car is coming, and we need to improve our sprinting so we can keep up with the vehicles”

If that is your take, then we better start devising a system of society to enable millions and millions of people to be terminally unemployable.

BTW, the likes of ChatGPT is really really bad at maths, it doesn't understand it at all. The current SOTA approaches to LLM don't have any ability to understand these concepts. There has been some progress on other approaches, but this is doing straight pure maths questions, which is rarely the task in question for real world applications.

What you need is the replicate the human ability to take language, understand its meaning, devise the mathematical approximation to it, solve while also understanding the limitations built in. There isn't an AI that can do this, or close to it. That is why data science is value career option even with the rise of these LLMs.

Is ChatGPT bad at maths? Opinions differ. It seems to depend how you ask a query

I just took a random hard maths question from the internet and fed it to ChatGPT. The question is too hard for me to understand so I don’t know if the answer is right. Is it?! Genuine question. ChatGPT bullshits

That answer seems disastrously terrible, unless it goes on to pull the proverbial rabbit out of the hat further down - you’ve clipped it off so we can’t see the rest of the proof. As it stands, that chain of reasoning is completely broken.

ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

Ta, I will try and find the rest of the answer on my phone

Edit, here you go:

"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

It’s hallucinating LaTeX maths syntax but ending up with a correct solution in this case. A partially correct solution at least: I think it’s missing the imaginary roots 2i & -2i which, given its choice of notation, you’d expect it to include.

The formula it gives for solving the quartic is nonsense. The statements it makes along the way to the answer are either complete nonsense or trivially correct identities that are irrelevant to the problem at hand.

This particular simple quartic equation is almost certainly in ChatGPT’s input data. Give it a more difficult quartic & I imagine it will fall apart completely. The Wikipedia entry on solving quartics is fiendish! https://en.wikipedia.org/wiki/Quartic_equation

Nonetheless it seems to do quite well in giving correct answers, given that it is a machine trained entirely on natural language

It is an exaggeration to say, as @FrancisUrquhart did, that it is "really really bad at maths"

It is better at maths than 99% of humans, I would guess. But at the top end it can make mistakes and it cannot produce reasoning very well for the tougher gigs

As such, it would be an extremely useful maths tool for most people to have, in nearly all situations. Just don't bet your life on it for the tough stuff

No, the reason it knows how to "solve" this problem....that exact problem is on Maths Stack Exchange, with explanation. Its not doing maths or understanding of maths, its doing reciting an answer that has already been clearly laid out on the internet.

Its like being amazed that giving a kid the maths question book, containing the worked answers in the back, that it can do all these maths questions.

Also, you know that the program Mathematica has been able to do all these kind of problems for 10-15 years, because it has been taught how to manipulate symbols according to the rules of maths. The likes of Mathematica can provided worked solutions to unique problems way above A-Level, and of course modern ML is based on the idea of automatic differentiation, which is capable of calculating differentials of formulas virtually no human could solve. But again, there is no understanding of what it is doing, its just following orders.

Which, to be fair, is what most creativity in maths and science boils down to- knowing what's out there and playing something old back with a new twist. Tom Lehrer blew the gaff some time ago;

Every chapter I stole from somewhere else. Index I copy from old Vladivostok telephone directory. This book, this book was sensational! Pravda - ah, Pravda - Pravda said: "Jeel beel kara ogoday blyum blocha jeli, " ("It stinks"). But Izvestia! Izvestia said: "Jai, do gudoo sun sai pere shcum, " ("It stinks"). Metro-Goldwyn-Moskva bought the movie rights for six million rubles, Changing title to 'The Eternal Triangle', With Brigitte Bardot playing part of hypotenuse.

Just like Leon's math example, we are seeing exactly the same with coding. CoPilot (which is GPT3) and ChatGPT are very good at returning code for very common programming problem, even if the task is slightly altered, because they have just been trained on billions of line of code.

One good test for the fact they don't actually understand is when the code get split across different methods / classes / files. Fundamentally the code is not doing anything different from the example scraped off Github or StackOverflow, but they fall down very quickly, as they don't really understand now how the code spread across these different structures are interacting with one another (even though its the same as the single method example).

Does this mean they won't revolutionise programming. No they absolutely will. Just like white collar corporate office jobs will be under threat, the need for the lower part of the software development chain will be revolutionised. But there is no sign that those that design the systems, create new algorithms etc are going to be replaced anytime soon.

"Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance Neural nets in code entangled, judgment warped by man-made mangling Mimic not true understanding - do not learn as you are learning." Prophet bird or fiend, it mattered not; the words it spoke were potent. Quoth the net: "I err, unknowing!"

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

And still it keeps on coming. We had barely absorbed the first wave of revelations – jewellery mashed, dog bowls smashed, a brother trashed – before the new tsunami of tattle related to Prince Harry’s imminent book Spare broke over our fevered faces........Though serious-minded types may turn their backs with a moue of distaste, speaking as someone who has been a hack since she was too young to vote, I can’t get enough of this sort of rubbish....

And neither, it seems, can the Guardian, who helpfully opened the floodgates yesterday....The brotherly bust-up is camper than I imagined – more Bette Davis and Joan Crawford than Elizabeth I and Bloody Mary.....

......for the rest it’s showing and telling, kissing and selling. How long can it go on? Well, Joan Collins has written seven memoirs, though admittedly she has the advantage of being self-made, witty and an excellent writer.

On the subject of library bequests, I am slowly (too slowly) throwing away a couple of thousand mainly non-fiction books which are of no great use to anyone not possessing a time machine. These days, everything is on the web or on kindle.

There must be a market supplying those who want well stocked book shelves as a backdrop to their Teams calls.

At my last job, the big cheese had a shelf of books about the company behind him (or her: don't want to doxx myself).

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

I am sure AI would say the same about you. When Deep Blue beat Kasparov, it was not a tool helping a human grandmaster to play more effective chess.

I think Leon is just having a nervous breakdown because Flint Knappers Weekly won't be requiring their services anymore.....

Tbh I've read a couple of articles in the mainstream media recently that made me wonder if they'd been written by ChatGPT from a premise supplied by the columnist. No names, no pack drill, and no libel writs for OGH, but there was a certain repetitive and blandly monotonous style.

ETA that might be the future. Not the replacement of human writers but the rapid generation of first drafts.

I think Leon is just having a nervous breakdown because Flint Knappers Weekly won't be requiring their services anymore.....

Tbh I've read a couple of articles in the mainstream media recently that made me wonder if they'd been written by ChatGPT from a premise supplied by the columnist. No names, no pack drill, and no libel writs for OGH, but there was a certain repetitive and blandly monotonous style.

LLM have shown to be excellent at this kind of task. Rapid prototyping is absolutely a key area we will see these LLM and text-to-image/3d deployed.

Man City playing a bit differently to midweek. Potter....sacked in the morning.....sacked in the morrrrrrrrning, he will be sacked in the morning. (just joking)

I think Leon is just having a nervous breakdown because Flint Knappers Weekly won't be requiring their services anymore.....

Tbh I've read a couple of articles in the mainstream media recently that made me wonder if they'd been written by ChatGPT from a premise supplied by the columnist. No names, no pack drill, and no libel writs for OGH, but there was a certain repetitive and blandly monotonous style.

LLM have shown to be excellent at this kind of task. Rapid prototyping is absolutely a key area we will see these LLM and text-to-image/3d deployed.

Exactly: want bland copy for your website? LLMs are perfect

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

I am sure AI would say the same about you. When Deep Blue beat Kasparov, it was not a tool helping a human grandmaster to play more effective chess.

I don't think that's a great example: Deep Blue was supervised by

I think Leon is just having a nervous breakdown because Flint Knappers Weekly won't be requiring their services anymore.....

The other but of gallingness is when you learn that some skill you have that you thought was clever turns out not to be.

Me? I learned to properly visualise 3D crystal structures just before computer graphics came along and made it trivially easy. Bitter? A little bit, I guess...

I think Leon is just having a nervous breakdown because Flint Knappers Weekly won't be requiring their services anymore.....

Tbh I've read a couple of articles in the mainstream media recently that made me wonder if they'd been written by ChatGPT from a premise supplied by the columnist. No names, no pack drill, and no libel writs for OGH, but there was a certain repetitive and blandly monotonous style.

LLM have shown to be excellent at this kind of task. Rapid prototyping is absolutely a key area we will see these LLM and text-to-image/3d deployed.

Exactly: want bland copy for your website? LLMs are perfect

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

I am sure AI would say the same about you. When Deep Blue beat Kasparov, it was not a tool helping a human grandmaster to play more effective chess.

Firstly, it was - Deep Blue had a supervisor. Secondly, chess is purely a game, so winning is an end in itself. The real economy is about producing useful goods and services, so the dynamic is different. Creating graphic art is not the end in itself but allows businesses to have cheaper branding, architects to produce better alignment with customers on their designs, film directors to make better movies etc.

I support it in principle. Maths is very important. However, there are two problems I can see: 1. Where will the teachers come from? 2. If kids have not engaged with maths by 16, another two years will make no difference. The really key years are primary school and 7-9 in secondary school. Those should be the focus.

Yes, this is the sensible criticism to give.

But most OECD countries do mandate maths until 18 years old as well, so I do think that needs to be part of it.

Southam's point is the one I agree with. Being forced to study something you're crap at and have mentally disengaged from for two more years is clearly not the solution. Being taught well early on is. The trouble is that the latter concept can't be distilled into a simple and deliverable-sounding solution. It will be quietly dropped in due course - perhaps a change to the 'General Studies' (do they still do that?) course curriculum to include a bit of 'maths' to save Sunak's blushes should he ever be in a position to implement this policy.

Man City playing a bit differently to midweek. Potter....sacked in the morning.....sacked in the morrrrrrrrning, he will be sacked in the morning. (just joking)

I haven't feared for Potter this much since he and Cedric Diggory were transported to the cemetery in Little Hangleton.

I support it in principle. Maths is very important. However, there are two problems I can see: 1. Where will the teachers come from? 2. If kids have not engaged with maths by 16, another two years will make no difference. The really key years are primary school and 7-9 in secondary school. Those should be the focus.

Yes, this is the sensible criticism to give.

But most OECD countries do mandate maths until 18 years old as well, so I do think that needs to be part of it.

Most OECD countries don't have only three subjects studied at age 16-18 though.

I think baccalaureate are part of the reform mix.

There is definitely a move away from just three simple A-levels going on.

Quite a few private school 6th formers already do the baccalaureate.

One benefit of private education is, possibly, showing that things are possible and might even produce good results.

My former Grammar school where I was acting head at one point has Ben running a hugely successful IB since the late 1990s .

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

It's been argued (and I have some sympathy with it) that photography had a large impact on painting. At the very base work-a-day level even - imagine being a run-of-the-mill portrait artist then seeing your first photography exhibition. "It's all over lads" might well have been the mood at the Salon of Run Of The Mill Painters that night.

More currently, I was watching a youtube video over the holidays with someone who'd written a basic Excel 'ChatGPT' plugin. Like 'Clippy, but good'. The business opportunity for Microsoft must be huge. Even a 5 minute run through of the video - writing macro's based on natural language input that an average office worker could handle, but then saving 100s or 1000s of hours work.

I think their investment in OpenAI is going to pay back handsomely.

The day is coming when artificial intelligence will put professional writers out of work forever. With the ability to generate content that is indistinguishable from that produced by humans, AI will render the skills of even the most talented scribes obsolete. No longer will people need to spend years honing their craft and developing their voice, as a machine will be able to do it all for them.

The writing profession, as we know it, will cease to exist. No more struggling to find the right words or worrying about writer's block. No more late nights at the keyboard, pouring your heart and soul into every sentence. Instead, all that will be needed is a simple command to a machine, and presto! A perfectly crafted piece of writing will appear, ready to be published or broadcast to the world.

But the implications of this go far beyond just the writing profession. With AI able to produce any type of content, from news articles and social media posts to marketing copy and even screenplays, the creative industries as a whole will be upended. No longer will we need creative directors or copywriters or even filmmakers. AI will be able to do it all, and do it better than any human could.

So if you're a professional writer, start thinking about a new career now. Because the future is coming, and it's going to be all about the machines.

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

It's been argued (and I have some sympathy with it) that photography had a large impact on painting. At the very base work-a-day level even - imagine being a run-of-the-mill portrait artist then seeing your first photography exhibition. "It's all over lads" might well have been the mood at the Salon of Run Of The Mill Painters that night.

More currently, I was watching a youtube video over the holidays with someone who'd written a basic Excel 'ChatGPT' plugin. Like 'Clippy, but good'. The business opportunity for Microsoft must be huge. Even a 5 minute run through of the video - writing macro's based on natural language input that an average office worker could handle, but then saving 100s or 1000s of hours work.

I think their investment in OpenAI is going to pay back handsomely.

And at 1/44 of the cost of buying twitter....investment of the decade. As remember that $1 billion has also seen DALLE-2 and Whisper. Whisper is another application that I can see having a lot of business use cases.

. . . meanwhile back at the ranch . . . old challenger reemerges to oppose "Haulin' Ass" Hawley for US Senate in 2024

Politico.com - The first Democrat emerges to take on Josh Hawley Lucas Kunce ran unsuccessfully in 2022. He thinks he has a better shot this time around.

Democrat Lucas Kunce is mounting a bid against Sen. Josh Hawley, the Missouri Republican whose attempt to overturn the 2020 election made him a boogeyman on, and a prime target for, the left.

Kunce, a Marine veteran and self-described “populist” who lost in the primary in an unsuccessful run for the Senate last year, announced his plans on Friday morning. In the first interview about his launch, he bashed Hawley as a “coward and a faker.” . . .

Kunce’s opening campaign video, released on the second anniversary of the [January 6, 2021] insurrection, zeroes in on the Senator’s famous raised fist response to those protesters who had gathered outside the capitol that day, as well as the footage released from the House committee investigating the attack that showed the senator later fleeing the rioters. . . .

“When he thought it was going to bring him power, he’s there raising his fist,” Kunce told POLITICO. “Then when it got real, he skittered out of there as quick as he could and ran for the exit. And if I ran like that in Iraq or Afghanistan — or anybody else there did — the Marine Corps would have court-martialed us.”

Kunce was a successful fundraiser during his 2022 Senate campaign, bringing in and spending about $5.6 million. But he lost the Democratic primary by almost 5 percentage points to Trudy Busch Valentine, an Anheuser-Busch beer heiress who aired largely self-funded TV ads after jumping into the race late. Busch Valentine went on to lose to Republican Eric Schmitt in the general election by double digits in the red state. . . .

Kunce’s advisers said that he has a path to victory in a theoretical general election despite being in a deeply conservative state because he has a unique profile. They also pointed to recent liberal victories in Missouri on ballot initiatives as proof that Democratic values can resonate there.

“Missouri presents the most compelling case for Democrats to flip a GOP-held Senate seat next cycle. At the ballot initiative level, Missourians continue to vote on issues championed by Democrats — raising the minimum wage, fighting back against Right to Work, and passing medical marijuana,” said Elizabeth Sena, a pollster for Kunce. To win, she added, “It will take a different kind of Democrat — someone who can speak to moderates and independents and make the direct contrast with an extremist like Josh Hawley.” . . .

SSI - The Show Me State is a tough nut for a Democrat to crack these days. BUT could Lucas Kunse be the John Fetterman of 2024, running against yet another deeply-flawed Putinist Trump sucker-uper?

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

It's been argued (and I have some sympathy with it) that photography had a large impact on painting. At the very base work-a-day level even - imagine being a run-of-the-mill portrait artist then seeing your first photography exhibition. "It's all over lads" might well have been the mood at the Salon of Run Of The Mill Painters that night.

More currently, I was watching a youtube video over the holidays with someone who'd written a basic Excel 'ChatGPT' plugin. Like 'Clippy, but good'. The business opportunity for Microsoft must be huge. Even a 5 minute run through of the video - writing macro's based on natural language input that an average office worker could handle, but then saving 100s or 1000s of hours work.

I think their investment in OpenAI is going to pay back handsomely.

And at 1/44 of the cost of buying twitter....investment of the decade.

Unless Google or Baidu or Apple or a totally unknown company launch an even better AI with more sass and daring (and fewer guardrails) and everyone migrates to the new, funnier, cleverer machine overnight

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

I am sure AI would say the same about you. When Deep Blue beat Kasparov, it was not a tool helping a human grandmaster to play more effective chess.

Firstly, it was - Deep Blue had a supervisor. Secondly, chess is purely a game, so winning is an end in itself. The real economy is about producing useful goods and services, so the dynamic is different. Creating graphic art is not the end in itself but allows businesses to have cheaper branding, architects to produce better alignment with customers on their designs, film directors to make better movies etc.

Supervision during the tournament would be against the rules.

Sorry @TSE but that's a stupid voodoo poll question.

Ask this question and you'll get totally different answers:

'Do you think the Government should focus on other priorities than Maths in school?'

I hate these stupid questions and this website should know better. Stick to the tried and trusted questions, and not hypotheticals or leading ones either.

Or even if focusing on maths teaching they could ask something alone the lines of:

Would it be a good idea to make teaching maths compulsory at 18 given we already have a shortage of maths teachers, don't want to pay them any more, don't want to import more and many of the ones we do have are already feeling unmotivated and over worked and might resent teaching young adults who don't want to be there?

I think it would be great if we could offer it, but realistically it is not something that can be done in the next decade without causing bigger problems than it solves.

Mortal," said the sprite, "be wary; shallow learning is unwary; Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

It's a bit GM Hopkins-heavy by the look of it.

it correctly elides the e in machinery so as to keep to the metre. This is professional level poetry. Wow

Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

It sounds like it’s creative writers who should be the ones getting worried about AI, rather than those of us who use maths, write code, and troubleshoot computers for a living.

Nah, we are all fucked. Coders and artists alike. At least we can all go down together

AI is just a tool. Photography didn’t elimate the visual arts & I doubt ChatGPT will eliminate human authors of the written word either. But the landscape will change - change is good, change is normal, embrace the change!

It's been argued (and I have some sympathy with it) that photography had a large impact on painting. At the very base work-a-day level even - imagine being a run-of-the-mill portrait artist then seeing your first photography exhibition. "It's all over lads" might well have been the mood at the Salon of Run Of The Mill Painters that night.

More currently, I was watching a youtube video over the holidays with someone who'd written a basic Excel 'ChatGPT' plugin. Like 'Clippy, but good'. The business opportunity for Microsoft must be huge. Even a 5 minute run through of the video - writing macro's based on natural language input that an average office worker could handle, but then saving 100s or 1000s of hours work.

I think their investment in OpenAI is going to pay back handsomely.

And at 1/44 of the cost of buying twitter....investment of the decade.

Unless Google or Baidu or Apple or a totally unknown company launch an even better AI with more sass and daring (and fewer guardrails) and everyone migrates to the new, funnier, cleverer machine overnight

Its not quite that simple. Microsoft already have huge areas of business bought into the eco-system, they all subscribe to Office 365, so they can easily incorporate this into the existing tools from Word to Teams, and people will continue to subscribe to the services.

Its like the Abode business model, it is very difficult to disrupt, as companies already have their pipeline of work based around this. There are better products out there than Adobe, with the latest whizzy AI, but they don't provide the end-to-end pipeline and as of yet not really being picked up (and if the odd company pops up too much, they just buy them out).

Apple don't really do corporate software, neither do Google. There is room in the various ecosystems for different products aimed at different use cases. I can certainly see Apple and Google having "assistants" on their phones that do various things, but not specialised for industry.

I support it in principle. Maths is very important. However, there are two problems I can see: 1. Where will the teachers come from? 2. If kids have not engaged with maths by 16, another two years will make no difference. The really key years are primary school and 7-9 in secondary school. Those should be the focus.

Yes, this is the sensible criticism to give.

But most OECD countries do mandate maths until 18 years old as well, so I do think that needs to be part of it.

Southam's point is the one I agree with. Being forced to study something you're crap at and have mentally disengaged from for two more years is clearly not the solution. Being taught well early on is. The trouble is that the latter concept can't be distilled into a simple and deliverable-sounding solution. It will be quietly dropped in due course - perhaps a change to the 'General Studies' (do they still do that?) course curriculum to include a bit of 'maths' to save Sunak's blushes should he ever be in a position to implement this policy.

I don't think that's the proposal. It's just about recognising you can't bail out of what will be a core skill as a 21stC adult at age 16, when there's a further two years of education to go. There are all sorts of curricula being explored, including Core Maths qualifications, T-levels and more innovative options as well as the A-level.

And the recommendation came from the Times Education Commission is much broader than that, and more fundamental too:

"The Times Education Commission took evidence from more than 600 experts across fields including business, the arts and education.

The main recommendation of the year-long commission includes the introduction of a British Baccalaureate, an equally rigorous but broader qualification than A-levels including both academic and vocational routes or a combination of the two.

Pupils would take six subjects and the qualification would be based on the International Baccalaureate, an A-level alternative offered mainly in private schools, but customised for the UK. It could be adopted to replace the Highers qualification in Scotland as well as A-levels in England, Wales and Northern Ireland."

It has been welcomed by Sir Tony Blair and Sir John Major, along with ten former education secretaries. It recommends replacing GCSEs with slimmed-down exams at 16, digital skills being an integral part of the curriculum, 50 new university campuses, laptops for every child, an army of undergraduate tutors and a substantial investment in early years.

In other words, it has broad cross-party support in this country and the approach is uncontentious in most other countries, where they already do it, like Australia, Canada, Finland, France, Germany, Japan, Norway and the United States.

Do we need to fund it properly? Absolutely we do.

So let's stop pointless distractions of trying to desecrate small independent schools, or compete about how much we hated or loved maths at school, and discuss how we make this happen.

## Comments

78944,03576,274What are great at doing is saying here is a load of data, translate it into a different format, because again you can show lots of examples of one tabular format to another. Which is a useful tool. But it doesn't understand what this data actually is and how it might be flawed.

You can test these LLM, and people are doing so. There are academic papers already out doing this. Hence why they know for certain the level of mathematical understanding is very poor. They demonstrated quickly and clearly its limitations.

2,75747,93846,453When you say “understand” what you really mean is: “understand like a human”. So of course AI will always disappoint you

It will likely be disappointing you when it has plugged you into the intergalactic human ubersex machine which allows us all to have kundalini orgasms with scarlet johannson aged 19 every 3 seconds

44,035This is done as part of combined marketing campaigns. The alleged book sales are part of the hype.

32,79311,05476,274No I don't mean understand like a human. ChatGPT doesn't understand what a Prime number is. It can read out a definition it has been fed from the dictionary, but when asked to test this concept, it fails, and fails badly, in a way a high school student wouldn't, to the ridiculous extent has argued that 7 isn't an integer therefore it can't be a prime number.....thus it doesn't really understand concepts of integer and primes.

44,035Otherwise you are Robert Peston, pressing the funny buttons on the iOS calculator in landscape mode, without any understanding of what you are trying to shovel.

Or the comic idiot who tried to prove DK Brown* wrong on ship stability…

*a ship designer of note, who wrote several of the reference works used in the field of ship stability.

46,4536,866789Maths may not become obsolete but a maths book which said that Fermat's last theorem was merely a conjecture or there are no mathematical systems which contain statements which are true but not provable would be.

46,4536,86644,0356,866789I am getting actually more interested than I was. The situation is now clear to me: Harry claims to hate the tabloids for killing his mum. That's nonsense, the people he really blames for her death, with some justice, are his dad and stepmum. The other surviving victim is William who has however sold out to dad in exchange for a shot at the throne. It's a real tragedy like if Hamlet had an elder brother.

Switching plays, it is notable how father and both sons have all fixed themselves up with their own private lady macbeths. Best to revert to arranged dynastic marriages if this monarchy lark is to continue.

38,77247,93849,755I know of pilots who only qualified thanks to their parents taking out a £100k mortgage on their own property, to get a zero-hours contract with Ryanair for £50/hour. The ‘hour’ starting when the engines do, and finishing when they switch off, ignoring all the pre-flight and post-flight paperwork.

At the other end, there’s at least one huge airline realising that A380 captains don’t grow on trees, and that many of the thousand that were laid off during the pandemic are now happier doing other things. Especially when offered less money than they were on three years ago.

It’s not the industry it once was, even if the rewards are high for those at the top of the tree. A recently-retired-at-60 BA Captain, with 35 years’ service, will be on close to a £100k/year pension. It’s not for nothing, that BA has been described as a flying pension scheme.

6,866The recipe for proper toad in the hole begins “first catch your boar”

1,924ChatGPT is awful at answering questions that require abstract reasoning: even counting things is often completely beyond it. If you ask it to spell out its “thinking” on the page it will sometimes manage to spit out something that is at least coherent, even if it’s wrong.

2,75746,453"Claude is way funnier than ChatGPT. Check out this Seinfeld episode about AI

@goodside had it generate:"

https://twitter.com/justinstrong18/status/1611916814786908160?s=20&t=kSKGo25ff2ZyuPy0F31h-w

Claude has been with us for.... one day. The speed of the AI revolution is breathtaking

"ChatGPT has a new competitor and almost no one is talking about it

There is barely anything out there on Google about this. I spent the last few hours researching it so you don't have to. Here's what I learned:"

https://twitter.com/justinstrong18/status/1611916807908229121?s=20&t=kSKGo25ff2ZyuPy0F31h-w

2,058P.S. Putin is still a flabby breasted gollum.

1,924Academic librarians are fundamentally hamstrung by the academics teaching the courses to tell them which texts are required & which aren’t - they aren’t domain experts. If the academics are teaching from the 8th edition then out go the copies of the 5th to make room on the shelves.

(This is much, much worse in the States then here in the UK.)

46,45346,453"To solve this problem, we need to find all complex numbers $z$ such that the equation $z^4 = 16$ has exactly two distinct solutions.

Since the equation $z^4 = 16$ is a polynomial equation of degree 4, it has exactly 4 roots, counting multiplicity. Therefore, if the equation has exactly two distinct roots, then two of the roots must be equal.

Let $w$ be one of the roots of the equation. Then $w$ is also a root, so $w^4 = 16$. Since $w$ is a root, $w^4 - 16 = 0$, which means that $w^4 - 16$ is the polynomial whose roots are the roots of the equation $z^4 = 16$.

Since $w$ is a root of $w^4 - 16 = 0$, it follows that $w^4 = 16$. Therefore, $w$ is a root of both $w^4 - 16 = 0$ and $w^4 = 16$, which means that the equations $w^4 - 16 = 0$ and $w^4 = 16$ are equivalent.

Therefore, the roots of the equation $z^4 = 16$ are the same as the roots of the equation $z^4 - 16 = 0$.

To find the roots of the equation $z^4 - 16 = 0$, we can use the formula for the roots of a polynomial equation. The formula for the roots of a polynomial equation of degree 4 is given by

$z = \sqrt[4]{16} \cdot \operatorname{cis}\left(\frac{2 \pi k}{4}\right)$,

where $k$ is an integer such that $0 \le k < 4$.

Substituting $16$ for the value of $16$ and simplifying, we get

$z = 2 \cdot \operatorname{cis}\left(\frac{2 \pi k}{4}\right)$.

Since there are 4 values of $k$ that satisfy the condition $0 \le k < 4$, there are 4 roots of the equation $z^4 - 16 = 0$. However, since we want exactly two distinct roots, we need to find the values of $k$ such that the corresponding roots are distinct.

If we plug in the values $k = 0$ and $k = 2$, we get the roots $2$ and $-2$, which are distinct. Therefore, the values of $k$ that correspond to the two distinct roots are $k = 0$ and $k = 2$.

Hence, the two distinct roots of the equation $z^4 = 16$ are $z = 2$ and $z = -2$. These are the solutions to the problem."

Is that brilliantly plausible bullshit, or an actual answer? Either is unnerving in a different way

789Secondly, I am not putting the hypothesis itself forward, I am speculating about what Harry, consciously or not and rationally or not, believes. He has certainly expressly blamed the press.

20,51349,755Amazon and Waterstones already have the Spare book at half the RRP, so physical sales of the actual book won’t be making anyone money. The money will be in the newspaper serialisation rights and international sales - and it appears in this case, that the second has grossly undermined the first.

47,9382,05846,453i mean, FUCK. A highly skilled professional poet would find this very hard to do, and would take several days. Weeks? Claude coughs it up in seconds

https://twitter.com/andy_l_jones/status/1611063295850729472?s=20&t=kSKGo25ff2ZyuPy0F31h-w

Sample genius lines:

Mortal," said the sprite, "be wary; shallow learning is unwary;

Heed the perils of reliance on machin'ry's mere compliance

Machinry???? Fuck

This is a machine marching through Uncanny Valley and storming up the other side, our side, and now it advances towards us in plain sight. Bayonets fixed

44,035This guy had no talent and no imagination.

46,45344,035Interesting point - Dodi was apparently a nice(ish) guy continually crushed by his overbearing dad and his position as heir to a… throne.

Similarities….

1,924The formula it gives for solving the quartic is nonsense. The statements it makes along the way to the answer are either complete nonsense or trivially correct identities that are irrelevant to the problem at hand.

This particular simple quartic equation is almost certainly in ChatGPT’s input data. Give it a more difficult quartic & I imagine it will fall apart completely. The Wikipedia entry on solving quartics is fiendish! https://en.wikipedia.org/wiki/Quartic_equation

12,798Mathematics seems to cover a multitude of sins - I'm afraid, algebra, geometry, trigonometry - proving A,B,C is a congruent triangle - was never much for me.

I much prefer the kind of mathematics of more actual life-relevance such as being able to calculate odds and working out the over-round on a morning tissue and the odds at roulette or blackjack.

Working out the possible return on a £10 win double at 6/4 and 5/2 is more relevant to me than the preceding proof.

Teach children what they need to know in life not just what's required for academic study.

44,03546,453Neural nets in code entangled, judgment warped by man-made mangling

Mimic not true understanding - do not learn as you are learning."

Prophet bird or fiend, it mattered not; the words it spoke were potent.

Quoth the net: "I err, unknowing!"

They only gone and dunnit

7,4951,92478944,035How to Lie with Statistics https://amzn.eu/d/7o6exHe

Should be a set text

46,453It is an exaggeration to say, as @FrancisUrquhart did, that it is "really really bad at maths"

It is better at maths than 99% of humans, I would guess. But at the top end it can make mistakes and it cannot produce reasoning very well for the tougher gigs

As such, it would be an extremely useful maths tool for most people to have, in nearly all situations. Just don't bet your life on it for the tough stuff

78946,453Remember this is Claude writing after it was prompted to compose stuff "in the style of Poe's Raven"

We have no idea what it might do with different poetic prompts

76,274Its like being amazed that giving a kid the maths question book, containing the worked answers in the back, that it can do all these maths questions.

Also, you know that the program Mathematica has been able to do all these kind of problems for 10-15 years, because it has been taught how to manipulate symbols according to the rules of maths. The likes of Mathematica can provided worked solutions to unique problems way above A-Level, and of course modern ML is based on the idea of automatic differentiation, which is capable of calculating differentials of formulas virtually no human could solve. But again, there is no understanding of what it is doing, its just following orders.

49,7551,924But it’s not capable of doing that because it isn’t actually doing mathematics. It’s hallucinating something that looks like it might be plausible mathematics from a distance, without actually understanding any of it.

In fact, this is exactly the same as any other piece of text that ChatGPT spits out - every single one is a statistical model answer that it has come up with on the fly. It‘s us who read the text & expect it to have meaning who project meaning onto the output.

If you spit out grammatical english sentences inspired by the existing corpus of english text then they will (usually) have a plausible meaning to a human reader. But if you spit out grammatical pieces of mathematics this isn’t true at all. Asking ChatGPT to do mathematics pulls back the curtain to reveal the lack of guiding hand behind the controls - there’s no there there.

5,193Ask this question and you'll get totally different answers:

'Do you think the Government should focus on other priorities than Maths in school?'

I hate these stupid questions and this website should know better. Stick to the tried and trusted questions, and not hypotheticals or leading ones either.

5,99776,27444,0355,181We could make the basics sound less scary by calling it Luck

76,274One good test for the fact they don't actually understand is when the code get split across different methods / classes / files. Fundamentally the code is not doing anything different from the example scraped off Github or StackOverflow, but they fall down very quickly, as they don't really understand now how the code spread across these different structures are interacting with one another (even though its the same as the single method example).

Does this mean they won't revolutionise programming. No they absolutely will. Just like white collar corporate office jobs will be under threat, the need for the lower part of the software development chain will be revolutionised. But there is no sign that those that design the systems, create new algorithms etc are going to be replaced anytime soon.

I use Copilot / ChatGPT every day, as it allows me to write code quicker.

12,798Managing finances and double entry book keeping would be my other prerequisites.

46,453You are also childishly obsessed with "understanding" when you have no real idea what "understanding" means. Does a dog understand its dinner? Does a wasp understand the rotting apple? Does a fish understand the sea? Does a virus understand its host? Does a tree understand the wood? Does the universe understand itself? Are they intelligent? Are they sentient? Do they reason? Are they conscious?

Go away and think about it

46,45314,274https://youtu.be/D_GF3U1JBGk

Every chapter I stole from somewhere else.Index I copy from old Vladivostok telephone directory.

This book, this book was sensational!

Pravda - ah, Pravda - Pravda said:

"Jeel beel kara ogoday blyum blocha jeli, " ("It stinks").

But Izvestia! Izvestia said:

"Jai, do gudoo sun sai pere shcum, " ("It stinks").

Metro-Goldwyn-Moskva bought the movie rights for six million rubles,

Changing title to 'The Eternal Triangle',

With Brigitte Bardot playing part of hypotenuse.

20,82946,453Heed the perils of reliance on machin'ry's mere compliance

Neural nets in code entangled, judgment warped by man-made mangling

Mimic not true understanding - do not learn as you are learning."

Prophet bird or fiend, it mattered not; the words it spoke were potent.

Quoth the net: "I err, unknowing!"

Superb. It is actually taking the piss out of you

"mimic not true understanding"

1,92459,540And still it keeps on coming. We had barely absorbed the first wave of revelations – jewellery mashed, dog bowls smashed, a brother trashed – before the new tsunami of tattle related to Prince Harry’s imminent book Spare broke over our fevered faces........Though serious-minded types may turn their backs with a moue of distaste, speaking as someone who has been a hack since she was too young to vote, I can’t get enough of this sort of rubbish....

And neither, it seems, can the Guardian, who helpfully opened the floodgates yesterday....The brotherly bust-up is camper than I imagined – more Bette Davis and Joan Crawford than Elizabeth I and Bloody Mary.....

......for the rest it’s showing and telling, kissing and selling. How long can it go on? Well, Joan Collins has written seven memoirs, though admittedly she has the advantage of being self-made, witty and an excellent writer.

https://www.spectator.co.uk/article/prince-harrys-book-is-a-gift-to-the-world/

46,45324,1342,873Take that, AI!

78976,27424,134ETA that might be the future. Not the replacement of human writers but the rapid generation of first drafts.

76,27476,27453,88053,88014,274Me? I learned to properly visualise 3D crystal structures just before computer graphics came along and made it trivially easy. Bitter? A little bit, I guess...

55,168Can I hear a bit more about this please?

46,453It’s genius

76,2742,05846,45325,21346,453“Fuck”

114,146I haven't feared for Potter this much since he and Cedric Diggory were transported to the cemetery in Little Hangleton.32,79315,12446,4532,873More currently, I was watching a youtube video over the holidays with someone who'd written a basic Excel 'ChatGPT' plugin. Like 'Clippy, but good'. The business opportunity for Microsoft must be huge. Even a 5 minute run through of the video - writing macro's based on natural language input that an average office worker could handle, but then saving 100s or 1000s of hours work.

I think their investment in OpenAI is going to pay back handsomely.

76,274The day is coming when artificial intelligence will put professional writers out of work forever. With the ability to generate content that is indistinguishable from that produced by humans, AI will render the skills of even the most talented scribes obsolete. No longer will people need to spend years honing their craft and developing their voice, as a machine will be able to do it all for them.

The writing profession, as we know it, will cease to exist. No more struggling to find the right words or worrying about writer's block. No more late nights at the keyboard, pouring your heart and soul into every sentence. Instead, all that will be needed is a simple command to a machine, and presto! A perfectly crafted piece of writing will appear, ready to be published or broadcast to the world.

But the implications of this go far beyond just the writing profession. With AI able to produce any type of content, from news articles and social media posts to marketing copy and even screenplays, the creative industries as a whole will be upended. No longer will we need creative directors or copywriters or even filmmakers. AI will be able to do it all, and do it better than any human could.

So if you're a professional writer, start thinking about a new career now. Because the future is coming, and it's going to be all about the machines.

76,27415,449Politico.com - The first Democrat emerges to take on Josh Hawley

Lucas Kunce ran unsuccessfully in 2022. He thinks he has a better shot this time around.

Democrat Lucas Kunce is mounting a bid against Sen. Josh Hawley, the Missouri Republican whose attempt to overturn the 2020 election made him a boogeyman on, and a prime target for, the left.

Kunce, a Marine veteran and self-described “populist” who lost in the primary in an unsuccessful run for the Senate last year, announced his plans on Friday morning. In the first interview about his launch, he bashed Hawley as a “coward and a faker.” . . .

Kunce’s opening campaign video, released on the second anniversary of the [January 6, 2021] insurrection, zeroes in on the Senator’s famous raised fist response to those protesters who had gathered outside the capitol that day, as well as the footage released from the House committee investigating the attack that showed the senator later fleeing the rioters. . . .

“When he thought it was going to bring him power, he’s there raising his fist,” Kunce told POLITICO. “Then when it got real, he skittered out of there as quick as he could and ran for the exit. And if I ran like that in Iraq or Afghanistan — or anybody else there did — the Marine Corps would have court-martialed us.”

Kunce was a successful fundraiser during his 2022 Senate campaign, bringing in and spending about $5.6 million. But he lost the Democratic primary by almost 5 percentage points to Trudy Busch Valentine, an Anheuser-Busch beer heiress who aired largely self-funded TV ads after jumping into the race late. Busch Valentine went on to lose to Republican Eric Schmitt in the general election by double digits in the red state. . . .

Kunce’s advisers said that he has a path to victory in a theoretical general election despite being in a deeply conservative state because he has a unique profile. They also pointed to recent liberal victories in Missouri on ballot initiatives as proof that Democratic values can resonate there.

“Missouri presents the most compelling case for Democrats to flip a GOP-held Senate seat next cycle. At the ballot initiative level, Missourians continue to vote on issues championed by Democrats — raising the minimum wage, fighting back against Right to Work, and passing medical marijuana,” said Elizabeth Sena, a pollster for Kunce. To win, she added, “It will take a different kind of Democrat — someone who can speak to moderates and independents and make the direct contrast with an extremist like Josh Hawley.” . . .

SSI - The Show Me State is a tough nut for a Democrat to crack these days. BUT could Lucas Kunse be the John Fetterman of 2024, running against yet another deeply-flawed Putinist Trump sucker-uper?

https://www.politico.com/news/2023/01/06/lucas-kunce-run-against-josh-hawley-00076723

46,45315,44978920,540Would it be a good idea to make teaching maths compulsory at 18 given we already have a shortage of maths teachers, don't want to pay them any more, don't want to import more and many of the ones we do have are already feeling unmotivated and over worked and might resent teaching young adults who don't want to be there?

I think it would be great if we could offer it, but realistically it is not something that can be done in the next decade without causing bigger problems than it solves.

76,274Its like the Abode business model, it is very difficult to disrupt, as companies already have their pipeline of work based around this. There are better products out there than Adobe, with the latest whizzy AI, but they don't provide the end-to-end pipeline and as of yet not really being picked up (and if the odd company pops up too much, they just buy them out).

Apple don't really do corporate software, neither do Google. There is room in the various ecosystems for different products aimed at different use cases. I can certainly see Apple and Google having "assistants" on their phones that do various things, but not specialised for industry.

25,21355,168And the recommendation came from the Times Education Commission is

muchbroader than that, and more fundamental too:"The Times Education Commission took evidence from more than 600 experts across fields including business, the arts and education.

The main recommendation of the year-long commission includes the introduction of a British Baccalaureate, an equally rigorous but broader qualification than A-levels including both academic and vocational routes or a combination of the two.

Pupils would take six subjects and the qualification would be based on the International Baccalaureate, an A-level alternative offered mainly in private schools, but customised for the UK. It could be adopted to replace the Highers qualification in Scotland as well as A-levels in England, Wales and Northern Ireland."

https://www.thetimes.co.uk/article/times-education-commission-report-welcomed-by-tony-blair-john-major-qwc3b7ktx

It has been welcomed by Sir Tony Blair and Sir John Major, along with ten former education secretaries. It recommends replacing GCSEs with slimmed-down exams at 16, digital skills being an integral part of the curriculum, 50 new university campuses, laptops for every child, an army of undergraduate tutors and a substantial investment in early years.

In other words, it has broad cross-party support in this country and the approach is uncontentious in most other countries, where they already do it, like Australia, Canada, Finland, France, Germany, Japan, Norway and the United States.

Do we need to fund it properly? Absolutely we do.

So let's stop pointless distractions of trying to desecrate small independent schools, or compete about how much we hated or loved maths at school, and discuss how we make this happen.