I've decided we're at something more like the cyborg scientist.

What do I mean? People are wondering if you can just do science with AI. Can AI build the next iteration of itself? Can AI be used to come up with math conjectures or at least prove or disprove conjectures that we have? People certainly think so, including Terrence Tao of Fields Medal renown and some other major mathematicians whom I will not name for privacy reasons.

I wanted to do an experiment. Could I get AI to write a decent paper for me? I had tried in the past to get it to come up with a good paper idea, and it had failed terribly. AI lacks creativity even now. But math is filled with rules than AI could memorize, and coding is filled with rules that AI has memorized, so I attempted to get AI (in particular, Claude) to write an entire paper with only about 15 prompts.

My past relationship with AI has been that it helps, but does not supplant. Information theory identities needed to be double-checked and corrected due to major hallucinations for a paper on bacterial chemotaxis. Factors of two had to be checked for a theoretical connection between memory and regularization when training neural networks. So I assumed that actually, AI would need a lot of handholding and would be unable to produce a decent paper all by itself.

To give it its best shot, I chose an easier research project. The application was novel (pharmaceutical manufacturing), but the theoretical ideas were well-known. Basically, it had to do with turning the control theory patent that I mentioned in a prior blog post into a paper that was readable. All I had to show was that closed-loop control beat open-loop control in theory and sometimes in practice, something that is straightforward and well-known but just not well-known in pharmaceutical manufacturing.

Not only was this an experiment about what AI could do these days; I was also just too tired to write. I prompted Claude to write the paper, with prompts that ranged from requests for code and figures and LaTeX files to genuine asks of the AI chatbot to produce results. In about 15 prompts, I had everything, including a bibliography, with minimal effort. Don't get me wrong-- I still have to check over the math and code. And the writing is, at times, atrocious. There are run-on sentences everywhere. I don't think AI could have come up with the paper idea, a permanent weakness of AI (as it lacks creativity). But the AI-assisted paper is totally fine, and only a few modifications were made in getting it to its final form.

Actually, the original abstract raised some questions because it didn't tough on AI enough, but a slightly modified abstract (the cyborg scientist abstract) was given a 50% discount on open access publication fees.

It is insane what AI can do nowadays. This paper is as close as you can get to AI slop without being AI slop.

If this paper gets in, it will make me very scared for the future of science and humanity. In the future, will a math PhD simply involve a year of prompting an AI chatbot? How close will future graduate students and researchers come to AI scientists who simply sit there and monitor AI chatbots doing all our work? It is already uncomfortable to be at this level of cyborg scientist, where AI is so involved in writing the paper that it seems like the paper is Claude's rather than mine.

I don't know if the paper will get accepted or if it will get the discount that I'm asking for (so I don't have to scrape together funds to publish an AI paper) but I will let you know how things progress.

Right now, I feel like we're fucked as researchers. In 100 years, someone with my job will just be asking AI to produce a paper that they check. This is the Golden Age of AI, despite its gloom, before we slip into the years in which AI replaces our brains. All of our brains.

I had this idea in high school, but I've never seen it in the literature, so here it is. It could really improve resolution for far-away objects. I did it as a high school science fair project and was too near-sighted to try and publish it.

So, have you heard of Pendry's perfect lens? All lenses have to deal with the diffraction limit. Light waves are composed of the traveling waves that everyone talks about and evanescent waves, which nobody talks about. These decay exponentially in amplitude as you move from the light-emanating object. Nobody could do anything about it, but if you can't reconstruct these evanescent waves, you're limited to a resolution that's about the wavelength of the light, modulo a few details. Then came along negative refractive index materials. A negative refractive index material, which means you have negative permittivity and negative permeability, allows you to reconstruct the evanescent waves as well. From this, they built Pendry's perfect lens. Its problem is not its resolution; its problem as a practical matter is that the object distance plus the image distance must be the thickness of the lens.

Forget that negative refractive index materials are lossy and dispersive. That's a whole set of other practical problems, because the refractive index must be exactly -1 for Pendry's perfect lens to work out. But imagine trying to make a very good lens for observing stars and realizing that it has to be the thickness of a galaxy.

My idea was simple: combine lasing materials with negative refractive index materials in a rectangle with mirrors that force you to go through a lens that is effectively the length of the galaxy because you've gone around the rectangle so many times. If you were clever enough about the design, you could maybe get the evanescent waves to reconstruct and get the traveling waves to reconstruct as well. My design was that you'd have mirrors that reflect light in a constant rectangle, around and around; the mirrors would be diagonal at the corners of the rectangle. There would be a lasing material whose refractive index (I determined, probably wrongly because I was in high school) would have to be exactly 3, so that every single time the light went through the lossy negative refractive index material, it would get rejuvenated by the lasing material and refocus so that the traveling waves would reconstruct. You could go through the thickness of the galaxy's worth of negative refractive index materials if it just means that you're going in a loop with mirrors that reflect the light making sure that it keeps amplifying the evanescent waves and keeping the traveling waves enough. When you want an image, you move one of the mirrors so that an image can be reconstructed, swinging one mirror out of the beam path lets that pass exit toward the image plane instead of looping again.

In other words, Pendry's needed thickness becomes time in the rectangular loop. And as we know, light travels very fast.

This lens probably wouldn't have much ability to reconstruct beyond the diffraction limit for anything but a very limited range of wavelengths, but I don't think anyone's proposed it yet, so here it is.