The different answers are a clue to the real problem. ChatGPT isn’t designed to provide factual answers to factual questions. In the words of James McGrath, it’s not the computer from Star Trek:
OpenAI has emphasized from the outset what Chat-GPT is. It emulates human speech patterns. It does this remarkably well. They have been very clear what it is not. It is not a search engine. It is not designed, as it shuffles language into new patterns, to preserve and convey things that humans would identify as factual answers to our questions. It does not understand what you are saying nor what it is saying, and thus has no capacity to identify facts in the enormous sample of human text that serves as its basis for its own generated text.
You know how someone would address the computer on Star Trek and ask it for information? You can do that, and Chat-GPT will answer in something more like human speech than the computer on Star Trek. But because it does not provide information and has no capacity to do so other than accidentally on occasion as a byproduct of shuffling textual patterns that have information woven into them, it made things up.
McGrath wondered about John the Baptist’s statement that he wasn’t worthy to carry Jesus’ sandals, so the religion prof asked a few questions to ChatGPT:
Please list all references to someone carrying sandals in ancient Jewish literature.
Thank you, these are very helpful. Are there others outside the Bible?
Who might carry someone else’s sandals in the ancient Mediterranean world?
As you can see, even though I never asked about John the Baptist, Chat-GPT had in its textual corpus more mentions of John the Baptist together with strap and sandal than probably all other references combined. It told me what I already knew, that this is traditionally interpreted as a sign of humility. It invented a quote from the Dead Sea Scrolls and mentioned Geza Vermes, not because it is trying to pretend to know but because these kinds of words are in relevant text from which it shuffled and reorganized. It doesn’t know it is lying, even though it seems as though it is intentionally trying to make made-up information seem authentic. Can something that isn’t a self-aware person lie? But by virtue of how it designed, when it does what it was designed to, it ends up imitating human speech as though it were the speech of an untrustworthy person prone to fabrication. It weaves in details that make what it says sound plausible not because it has a desire to deceive (it has no desire whatsoever) but because details that are correct happen to show up as it creatively shuffles what others have put in text for with related key words.
So please, for the love of all that’s holy, stop quoting ChatGPT at us. I’d like to see the mods ban it, frankly.
I keep forgetting you’re a math guy, as well as @mitchellmckain.
I thought this article was fascinating and it seems to answer the questions posed above. I’ll leave that judgment to the more mathematically educated, so please weigh in. If you have any interest in the history of mathematics, the article is definitely a must read. For the rest of us, I’ll post some TL/DR screenshots as a half-baked summary.
(Okay, in hindsight I went nuts on the screenshots, but the article’s a freebie so cut me some slack.)
https://www.cantorsparadise.com/the-nature-of-infinity-and-beyond-a05c146df02c
One for @Mervin_Bitikofer
Edit: Missed this one. Sorry, Merv
The conclusion seems to refute this quote that Mike found:
The different answers are also not contradictory. The sense was placed differently, “is not strictly a fact finding algorithm” and “one of my primary functions…”
Some of us find ChatGPT helpful and amusing. If you don’t that’s fine. Are you aware BioLogos did a podcast asking ChatGPT questions with a person reading the responses?
Any human reader can tell the difference. The original answer essentially agreed with my premise, and the next agreed with yours. That AI isn’t designed to sort out truth from error or to judge the quality of the sources it draws upon.
It’s helpful and amusing to a point, but I’ve seen it used here as if it were a definitive answer when it’s not even as trustworthy as the much-maligned Wikipedia, which at least cites its sources. At best it’s a source of potential misinformation masquerading as “fact,” but that’s not the worst of it. The point of the BL Forum is conversation. It’s not conversation to pose a question to an AI bot and post the answer. I’m interested in dialogue with actual people, but when ChatGPT proliferates across every thread, it starts to defeat the purpose of the Forum and discourage people from participating.
As are some other ChatGPT remarks, this is off-topic, but it does have its functions if used selectively. I haven’t fact-checked this, but it is easily done:
I don’t recall seeing ChatGPT used here by anyone blindly, but if you are referring to something I posted, I feel like you are exaggerating or misreading how I included it.
This thread began with some interesting quotes ChatGPT pulled as examples of people who had written about how the immediate effect of an uncaused cause will appear to come from nothing.
I’m doubtful a single quote captured the sense of this phenomenon
Essentially? If a father says he is not strictly a dad, he is not agreeing with someone who said he is not a dad.
Thanks for this article, Jay. I was looking for just this very thing earlier today and was only finding things that were way too philosophically technical. This will help.
This was something I shared with Jay on the subject the last time it came up. I think it opens up a topic that is often shrouded in high minded sophistry:
“It is to be presumed, for example, that there are an infinite collection of trios in the world, for if this were not the case the total number of things in the world would be finite, which, though possible, seems unlikely. In the third place, we wish to define “number” in such a way that infinite numbers may be possible; thus we
must be able to speak of the number of terms in an infinite collection, and such a collection must be defined by intension, i.e. by a property common to all its members and peculiar to them.” Betrand Russell, Introduction to Mathematical Philosophy
If the natural numbers are unlimited, then the number of natural numbers is undefined. This is a simple tautology.
The real value of aleph-0 can still be defined as it is found in relation to aleph-1 and not the number of natural numbers.
The more I think about this, the less I see how the math changes by referring to these Aleph ‘numbers’ as non-numerical values.
I understand how the natural and real numbers cannot be put in corresponding relationships. I also get a sense of wonder, as if we are touching on a basic premise of reality when X can be considered as a discrete value representing 4 dimensions, and yet it is ‘smaller’ than the reals between 0 and 0.000001.
(X<---->non-X) > (X, X+1, X+2…)
Edit: I found the previous comment to @Jay313 and wanted to highlight the part I shared with him by placing it in bold type.
If we’re talking “measureable” then I think the process would eventually run up against the issue of whether or not the universe is pixelated, i.e. whether there is a shortest possible distance. But if by “measureable” what is meant is “enumerable” then this is correct.
The more simplistic the manner in which a question is asked, the less value ChatGPT’s response will have. If you asked (as I did) for a discussion of infinity with respect to numerical value, the result would be a discussion of both sides of the issue and a conclusions that depending on the matter in question infinity can be treated either way (though there are infinities that cannot be treated as numerical values).
Actually ChatGPT is wrong on this: it is possible for a man to be a legal bachelor in one jurisdiction while being married in another, so that in effect he is actually a “married bachelor” in common terms because he is both (ChatGPT got really lawyer-like in arguing against this, though, not at all acknowledging the common use of terms but insisting on precise dictionary definitions).
It’s a question of paramount importance whether natural space or spacetime can be infinitely divided and yet the question is also impossible to empirically determine.
Even so, if spacetime is made up of parts, like a kind of superfluid, would not those parts or pixels necessarily bear a kind of meta relation?
Enumerable means countable. Maybe that’s not the right word as the real numbers or values are uncountable between 0 and 1.
No? Why not? It may not be possible as a mathematical function, but it certainly is as an iterative one.
The relation of A and nonA vary, so that it is not a contradiction in the sense you propose. Good counterexample.
Ah, but you can ask it to cite sources! So far with my questions that has made for shorter, crisper answers because rather than try to be exhaustive it finds some example sources and works from them.
Now I’m wondering whether there are “more” points on the graph of an algebraic function than on the x-axis it can be projected onto.
(I just know I’m going to wake up with a headache because my brain won’t leave this one alone.)
The pixilation comes with finitude, not measurability. This is the difference between analog and digital, as well as using the frets on a guitar, rather than bending the string. At any point in the bending, one could take measurements of the length of the string, the tension on it, its thickness and the length of the soundwaves it produces. Measurement doesn’t affect the transition from note to note, even at an infinitely fine granularity.
I was just thinking in terms of analog capabilities. E.g. Just as there are infinitely many reals between zero and one (uncountable infinity - and a possible Aleph-1 pending any proof of the continuum hypothesis; thanks for that, @heymike3 and @mitchellmckain), in the same way there are an infinite number of positions (ignoring Planck’s constant and other actual practical limitations) for an analog volume knob on a stereo system. And yet, I can “turn through” every last one of those uncountable positions (without skipping any of them - again - ignoring Planck space limitations) just by turning the knob - i.e. - making a point travel along the number line. No numbers are skipped. Hence my homespun descriptor for this as a ‘traversible’ infinity. But one can make no such sweep or traverse over all the points in a flat planar region, such as a single square unit of area. One would need to switch to a line segment to do any equivalent sweep of an area. Or switch to an area unit to do a sweep of a cubic unit of space. So I was just wondering aloud if that was a way of distinguishing between those uncountable infinities.
Obviously I have no formal study of any of this under my belt - which is why I’m just shooting in the dark here.