Overall I would say no, because it can make big mistakes, but it seems to be able to somehow adapt to new knowledge, after processing its data exabytes. Let me give you a couple of examples.
- First, a basic mistake it made:
You
And mathematically, as functions on the real axis, is their behavior very different or similar? Are both peaked functions that tend to zero as the value of the variable increases or do their behaviors bear little similarity?
ChatGPT
Mathematically, both the sinc and Gaussian functions have similar behaviors in that they are both smooth functions that tend to zero as the independent variable moves infinitely further away on the real axis. However, there are differences in their specific forms and how quickly they tend to zero. Sinc Function: The sinc function has a bell shape and is defined as sinc(x)=sin(πx)/πx. It vanishes for x=0 and has additional zeros at =±1,±2,…x=±1,±2,…. As ∣x∣ increases, the sinc function tends to zero, but its convergence is relatively slow, since the presence of zeros prevents a rapid decay
...
You
I think you are wrong. The sinc function that you have sent does not vanish at x=0 (its value at the origin is 1). On the other hand, the Gaussian always takes positive values and decreases monotonically. For me it is a big difference. Don't you agree?
ChatGPT
My apologies for the confusion and thanks for pointing it out. You are correct in your observation. The sinc function, in fact, does not vanish at x=0 (its value is 1 at that point), and presents oscillations as ∣x∣ increases, which makes it not smooth in the sense of having continuous derivatives in all orders.
- Next, a situation in which it seems to be able to adapt to new knowledge:
You
But the Gaussian and Lorentzian representations do not need to be convolved with test functions in the Schwartz space (as distributions) to get the same result, they can be integrated together with any continuous function and produce the same result as they do with test functions. Only the sinc function or similarly problematic representations need to be restricted to the Schwartz space to become equal to the others. Did you know that? Do you think that this mathematical restriction is fair to the Gaussian and Lorentzian? In this sense, maybe we are talking about different categories of delta functions.
ChatGPT
Yes, you're correct in pointing out a subtle yet crucial distinction. The Gaussian and Lorentzian representations of the Dirac delta function indeed have a special property that allows them to be integrated with a broader class of functions, not necessarily limited to the Schwartz space, and still produce the same result. This property is a consequence of the fact that these representations are entire functions of t and have certain regularity properties.
I would be curious to know your opinion/experience, if only because AI will soon become widespread.
It can be generally useful as a basic source of knowledge if used correctly. Like any tool, a large language model should be used cautiously; as you say, ChatGPT can make some big mistakes, so blindly believing everything it spits out is not a good idea. However, this is no different to using a computer to do research by solving mathematical problems numerically, e.g. WolframAlpha or simulation software. These tools can also have limitations or errors, and they require careful verification and validation. Therefore, using AI as a learning tool requires responsibility and critical thinking, but avoiding AI altogether for fear of its flaws would also hinder scientific progress.
Dear Matthew J. P. Hodgson,
Many thanks for your answer, especially because it comes from a well-versed source. I personally agree with you. If I may quote your words, the fact that users could be "blindly believing everything it spits out" is my top concern, and the reason for raising this discussion. Because "critical thinking" may or may not be among the average user's/layperson's/student's main skills when it comes to acquiring scientific knowledge.
We are still using November 2022's release of ChatGPT, and it will obviously be upgraded with upcoming versions. But the fact that ChatGPT seems to have big flaws in some scientific areas, despite the many pros it has, makes me worry, due to its user friendliness.
In other words, Wikipedia is not perfect, but is a pretty decent source of basic scientific knowledge, free from big flaws and pseudo-sience. If ChatGPT or similar AIs end up replacing Wikipedia as one of the main sources of basic scientific knowledge for undergraduates/laypeople, should we be concerned?
You're very welcome – I appreciate your thought-provoking questions!
I agree that the accessibility of LLMs like ChatGPT is concerning for science, both because of the misinformation they can spread and their potential to overwhelm scientific publishers with bogus papers.
I think the takeaway is that AI has the potential to bring positive changes to science, but it must be used responsibly. Developers, too, need to be mindful of the broader implications of their creations.
Thanks again, your replies are as thought-provoking and enlightening!
As someone with a scientific background who happens to work in software development, I can't but subscribe your words that “Developers, too, need to be mindful of the broader implications of their creations.” And let me add that not only them, but also everyone else involved in designing, developing, testing and making these LLMs available.
Issues like the Bogdanov affair are far more likely to take place now, using these tools, which as you accurately indicate, should be another point of concern (for both publishers and readers).
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