# Re: GPT4 + Mathematica

`Allan Snyder's research group has done these experiments:`
```
http://www.centreforthemind.com/publications/SavantNumerosity.pdf

http://www.centreforthemind.com/images/savantskills.pdf

Saibal

On 03-04-2023 01:10, Brent Meeker wrote:
```
```That's fascinating.  I had not heard to the magnetic
stimulation/inhibition experiments.  Have you a reference?

Brent

On 4/2/2023 2:58 PM, smitra wrote:
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While GPT hooked up to Mathematica may greatly improve its performance, I would not be impressed when judging that in  terms of approaching human level cognition.
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```
A long time ago I was teaching a statistical mechanics class, the students had to do a certain calculation for homework that involved doing the series expansion of 1/sinh(x) to order x. I was shocked to see that none of the students could do it. But some did come up with the right answer, they had shown some failed attempts and then wrote that they used Mathematica and Mathematica says that the answer is  1/x - x/6 ...
```
```
The students couldn't do it because they could not use the Taylor expansion formula due to the singularity at x = 0. Most  students had not bothered to think about how to bypass that problem, otherwise at least a few would have written down the correct derivation:
```
```
1/sinh(x) = 1/(x + x^3/6 +...) = 1/x 1/(1 + x^2/6 + ...) = 1/x (1 - x^2/6 + ...) = 1/x - x/6 +...
```

```
Now, I do think that GPT is a great leap forward, I don't want to downplay the progress made. But I'm quite skeptical about the idea that such systems are approaching human level cognition. The human brain is an enormously powerful system, but we don't have free access to use the power of our brains to do whatever we want. For example, most people cannot multiply two 5 digit numbers in their head, but a simple pocket calculator has no problems with that task.
```
```
However, some autistic savants do have more of a privileged access to use the power of the our brains to do arithmetic. Some of them can do calculations that most other people cannot do. In certain tests involving magnetic stimulation or inhibition of certain brain parts performed on ordinary people, it has been shown that people can temporarily gain certain abilities that they normally don't have. For example, if you look at a screen with a few hundreds dots on it, can you count the number of displayed dots in one second? Most people can't, some autistic savants can do this. But in the experiment with magnetic stimulation or inhibition, the test subjects were also able to do this.
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When we are consciously using our brains doing complicated things e.g. mathematics, then we are using our brains in an extremely inefficient way. If we could have an artificial brain similar to our brain but one which is completely dedicated to doing mathematics instead of what our brains are dedicated to do, then it would be enormously better at math than we are. It's then likely that something like the brain of a lizard that is fully dedicated to math would already completely outclass the world's best mathematicians. Perhaps even the brain of insects could perform at the same level of most mathematicians when fully dedicated to doing math.
```
Saibal

On 28-03-2023 23:32, John Clark wrote:
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```Apparently I'm not the only one who has become obsessed with the
developments in AI that have occurred in the last few weeks, Stephen
```
Wolfram, the man who developed Mathematica, started Wolfram Alpha, and
```wrote the book A New Kind Of Science about cellular automation, has
```
given two very interesting interviews on the subject.  Wolfram wrote a
```plug-in to connect GPT4 with Mathematica because calculation was the
one thing that GPT4 was not very good at but Mathematica is superb at
```
it; he describes the experience as  "poking at an alien intelligence".
```
GPT + Wolfram: The Future of AI is Here! [1]

GPT, AI, and AGI with Stephen Wolfram [2]

John K Clark    See what's on my new list at  Extropolis [3]

9eq

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