Connectionists: Chomsky's apple

[Barak A. Pearlmutter]

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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