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ChatGPT on the subject of four-digit numbers

Like everyone else I have been tinkering with ChatGPT. I doubt I have any thoughts about it that are sufficiently original to be worth writing down. But I thought it would be fun to showcase some of the exchanges I have had with it, some of which seem to exhibit failure modes I haven't seen elsewhere.

This is an excerpt from an early conversation with it, when I was still trying to figure out what it was and what it did. I had heard it could do arithmetic, but by having digested a very large number of sentences of the form “six and seven are thirteen“; I wondered if it had absorbed information about larger numbers. In hindsight, 1000 was not the thing to ask about, but it's what I thought of first.

MJD What is the largest number that is less than 1000?

ChatGPT The largest number that is less than 1000 is 999. Any number that is less than 1000 will have three digits, with the first digit being 9, the second digit being 9, and the third digit being any number from 0 to 8. The largest possible three-digit number that is less than 1000 is therefore 999. This is the largest number that is less than 1000, as any number with four or more digits will be greater than 1000.

I was impressed by this, the most impressed I had been by any answer it had given. It had answered my question correctly, and although it should have quit while it was ahead the stuff it followed up with wasn't completely wrong, only somewhat wrong. But it had made a couple of small errors which I wanted to probe.

MJD That is a good answer, but you said that any number with four or more digits will be greater than 1000. That is not true. Can you think of a counterexample?

ChatGPT You are correct, my previous statement was not accurate. Any number with four or more digits can be less than 1000, depending on the specific digits that are used. For example, the number 9991 is a four-digit number that is less than 1000.

This reminds me of Richard Feynman's story about reviewing science textbooks for the State of California. He would be reading the science text book, and it would say something a little bit wrong, then something else a little bit wrong, and then suddenly there would be an enormous pants-torn-off blunder that made it obvious that the writers of the book had absolutely no idea what science was or how it worked.

MJD Oh honey.

To ChatGPT's credit, it responded to this as if it understood that I was disappointed.

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