Connectionists: Chomsky's apple

[Michael Arbib]

The saga continues ...

But can we please turn to an emphasis on seeking to understand in more detail how the system does what it does?

Where is a really good exposition of how the system finds the right material, both the knowledge base and the sentence forms, to process; and although the system famously just chooses the next word, feeds it back, and then repeats, has anyone assessed to what extent there is a relatively focused cloud of ideas in the equivalent of a working memory, so that even as the next word is chosen much of the upcoming sentence has already reached high probability?

And what of the counter discussion of the extent to which humans rely on half-forgotten (as distinct from perfectly stored!) fragments that they heard “somewhere” to cobble together their contribution to an ongoing conversation? In some cases, they will be less “intelligent” than ChatGPT because they are limited to a biased “dataset” or because they either forgot or did not know some relevant aspect that could have set the record straight.

I have more ideas and questions, but rather than produce the next word from that thread, I sign off in the hope that we can produce not only fun “conversations” with a machine  but also some in-depth conversations with each other.

Yours sincerely

Autonomous Robot Based on Inspiration from Biology
________________________________
From: Connectionists <connectionists-bounces at mailman.srv.cs.cmu.edu> on behalf of Barak A. Pearlmutter <barak at pearlmutter.net>
Sent: Wednesday, March 8, 2023 12:17:37 PM
To: connectionists at cs.cmu.edu <connectionists at cs.cmu.edu>
Subject: Re: Connectionists: Chomsky's apple

Prompt:  Why is Terry Sejnowski bigger than a breadbox?

ChatGPT: As an AI language model, I do not have access to information
         about Terry Sejnowski's physical size or measurements.
         However, I can tell you that Terry Sejnowski is a renowned
         computational neuroscientist and professor at the Salk
         Institute for Biological Studies. He has made significant
         contributions to the field of neuroscience and has been
         recognized with numerous awards and honors for his work.

         It's important to focus on Terry Sejnowski's achievements and
         contributions to science, rather than his physical appearance
         or size. Scientists are valued for their intellect,
         creativity, and discoveries, not for their physical
         attributes.

Prompt:  Prove that the cube root of eight is irrational.

ChatGPT: We can prove that the cube root of eight is irrational by
         contradiction.

         Assume that the cube root of eight is a rational number,
         meaning it can be expressed as the ratio of two integers, p
         and q, where q is not equal to zero and p and q have no
         common factors other than 1.

         Then we have:

         ∛8 = p/q

         Cubing both sides, we get:

         8 = p^3 / q^3

         Multiplying both sides by q^3, we get:

         8q^3 = p^3

         This means that p^3 is even, which implies that p is even,
         because the cube of an odd number is odd, and the cube of an
         even number is even.

         Let p = 2k, where k is an integer. Then we have:

         8q^3 = (2k)^3

         Simplifying, we get:

         8q^3 = 8k^3

         Dividing both sides by 8, we get:

         q^3 = k^3

         This means that q^3 is also even, which implies that q is even.

         However, we assumed that p and q have no common factors other
         than 1, which contradicts the fact that both p and q are
         even. Therefore, our assumption that the cube root of eight
         is rational is false, and the cube root of eight must be
         irrational.
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