Igor Zaika

In Italy, one of the hobbies for older men is “Umarell”. Retired men who enjoy watching construction sites while giving unsolicited advice

Having studied symmetry my whole adult life, I have come to the belief that we don’t fully know why symmetry is so important in physics. It may be more than one reason. Or it may be one reason. We aren’t there yet to be able to call it. We don’t even fully know what it is. We dont even know if symmetry and redundancy are different, equivalent or exactly the same thing. We dont know if Supersymmetry is a symmetry. We cant say easily what E8 is a symmetry of other than things made from E8. If you were simply to change the definite article at the beginning of this post, it instantly becomes a great point. If you leave it, it remains a fascinating boast. Either way, it’s great food for thought. Thx.

There is a shape in mathematics that can hold a finite amount of paint, yet would require an infinite amount of paint to coat its surface. It is called Gabriel’s Horn. Imagine rotating the curve y=1/x around the x-axis. The result is a long, tapering surface that stretches infinitely, like a tunnel that never ends. Here’s where the paradox appears. The volume of this shape converges—if you add up all its infinitesimal slices, the total stops growing. In other words, you can completely fill it with a finite amount of paint. But the surface area diverges. No matter how far you go along the horn, there is always more surface to cover. The outer “skin” keeps extending, demanding more paint without end. So while you could pour paint inside and fill it entirely, you would never finish painting the outside. This is not a trick, but a consequence of how infinity behaves. The radius shrinks quickly enough for the volume to remain finite, yet not fast enough to keep the surface area from growing without bound. It reveals a deeper truth: infinity does not simply mean “very large”—it means unending. And sometimes, the infinite can exist within the finite in ways that defy our intuition, even while remaining perfectly consistent in mathematics.

Happy Friday from Steilacoom Wa!

The reason symmetry is so important in physics is because symmetry is a highly effective compression operator. If a system is invariant under some symmetry, you only need to explain one axis of it. Scientific models represent the systematic exploitation of the universe's internal redundancies through symbolic logic.

Judging by my tl there is a growing gap in understanding of AI capability. The first issue I think is around recency and tier of use. I think a lot of people tried the free tier of ChatGPT somewhere last year and allowed it to inform their views on AI a little too much. This is a group of reactions laughing at various quirks of the models, hallucinations, etc. Yes I also saw the viral videos of OpenAI's Advanced Voice mode fumbling simple queries like "should I drive or walk to the carwash". The thing is that these free and old/deprecated models don't reflect the capability in the latest round of state of the art agentic models of this year, especially OpenAI Codex and Claude Code. But that brings me to the second issue. Even if people paid $200/month to use the state of the art models, a lot of the capabilities are relatively "peaky" in highly technical areas. Typical queries around search, writing, advice, etc. are *not* the domain that has made the most noticeable and dramatic strides in capability. Partly, this is due to the technical details of reinforcement learning and its use of verifiable rewards. But partly, it's also because these use cases are not sufficiently prioritized by the companies in their hillclimbing because they don't lead to as much $$$ value. The goldmines are elsewhere, and the focus comes along. So that brings me to the second group of people, who *both* 1) pay for and use the state of the art frontier agentic models (OpenAI Codex / Claude Code) and 2) do so professionally in technical domains like programming, math and research. This group of people is subject to the highest amount of "AI Psychosis" because the recent improvements in these domains as of this year have been nothing short of staggering. When you hand a computer terminal to one of these models, you can now watch them melt programming problems that you'd normally expect to take days/weeks of work. It's this second group of people that assigns a much greater gravity to the capabilities, their slope, and various cyber-related repercussions. TLDR the people in these two groups are speaking past each other. It really is simultaneously the case that OpenAI's free and I think slightly orphaned (?) "Advanced Voice Mode" will fumble the dumbest questions in your Instagram's reels and *at the same time*, OpenAI's highest-tier and paid Codex model will go off for 1 hour to coherently restructure an entire code base, or find and exploit vulnerabilities in computer systems. This part really works and has made dramatic strides because 2 properties: 1) these domains offer explicit reward functions that are verifiable meaning they are easily amenable to reinforcement learning training (e.g. unit tests passed yes or no, in contrast to writing, which is much harder to explicitly judge), but also 2) they are a lot more valuable in b2b settings, meaning that the biggest fraction of the team is focused on improving them. So here we are.

New paper from Hendrik Bessembinder just analyzed 100 years of stock market data. And it's shocking. Out of nearly 30,000 stocks analyzed... just 30 companies generated ~44% of all wealth created. 👀

I trained an LLM from scratch on pre-1900 text to see if it could come up with quantum mechanics and relativity. While the model is too small to do meaningful reasoning, it has glimpses of intuition. When given observations from past landmark experiments, the model can declare that “light is made up of definite quantities of energy” and even suggest that gravity and acceleration are locally equivalent. I’m releasing the dataset + models and leave this as an open problem to the research community. I also include what this project has taught me about intelligence in a mini essay linked below. 🧵(1/n)

Vibe coding is more addictive than any video game ever made (if you know what you want to build).