Dirac's my Prof, but von Neumann, my favorite?

When you read articles or books on the history of physics you always find some passage that mentions the name von Neumann. This man, John von Neumann, appears to be on another level and probably is the person you have in mind when someone says "oh, he's an Einstein!"¹. For more on his life and work, see the MacTutor biography and the Institute for Advanced Study page. So I spent the last hour reading up on him and just want to quickly capture what this guy was able to do.

Figure 1. John von Neumann (public domain)

Childhood

He was born in 1903 in Budapest, Hungary; all his family details are there as well, very interesting. At an early age it was clear he was a prodigy. He could divide 8-digit numbers in his head and memorize books by age 6, then by age 8 he was fluent in ancient Greek. He was a sponge for knowledge, and because his parents were wealthy they always had tutors to aid his talents. His profile says that by age 10 he was doing college level math and basically was a genius.

College

I don't know much about the universities in Hungary, but at age 17 he goes to study at the University of Budapest and then continues on at universities in Berlin and Zurich. He gets his PhD in mathematics at 22 and then also gets a degree in engineering because he can. Then he starts to work in areas of quantum mechanics and basically provides the mathematical foundations for what Heisenberg and Schrödinger had proposed; he makes QM a rigorous theory [1]. Okay, he is 23 now and just getting started.

Out in the wild

Gets interested in mathematical models of strategy and invents the new field of game theory. He proves the minimax theorem [2], a fundamental result that shows how to make optimal decisions when opponents are trying to beat you. Turns out that things like poker, war, economics, all the same math. With Oskar Morgenstern he later writes the book that launches the field [3]. Von Neumann publishes it casually.

Gets invited to America to work at the Institute for Advanced Study (IAS) in Princeton. Becomes the youngest professor at IAS. Has a nice neighbor called Albert Einstein who is considered the smartest person alive but I'd wager von Neumann in raw brain-compute is superior, as many who knew both seem to have indicated.

John von Neumann becomes the man that people bring their unsolved problem to, the one they have been working on for months. He then proceeds to solve it while they are still explaining the problem and what they have tried. He was the kind of guy who would be completing their proofs before they finished describing the paper they were working on. Mathematicians start collecting "von Neumann stories" and everyone has one; a legend is born and he keeps pumping out impactful content.

Starts to work on ergodic theory, operator theory, and lattice theory. Publishes dozens of foundational papers that would be a career for a normal person in my view. But for von Neumann it's just another working day at IAS.

Interestingly he was not like our Prof. Dirac, not a hermit; he was known for his social skills and ability to party. He is a legend in many ways. Also known for liking to drink and tell impolite jokes, not a good driver, and many car crashes. Everyone, even the best, has flaws. In general von Neumann is a liked man.

The war years

John von Neumann becomes a U.S. citizen and then, as one would expect given his intellect and the looming threat of war, is recruited to join the Manhattan Project. He helps design the implosion mechanism for the atomic bomb and calculates the explosive lenses needed. His math helps build Fat Man, the bomb that destroys Nagasaki. Not sure how this made von Neumann feel or how he thought about the devastation of the bomb.

He continues with work on the hydrogen bomb, which turns out to be even more destructive. You see it just as math. He decides computing and computers are going to be the future and works on the ENIAC and EDVAC computers. He writes the "First Draft of a Report on the EDVAC" [4], which describes the von Neumann architecture that is still used in computers today. Every computer since uses this architecture. Basically von Neumann invented the modern design for every laptop, phone, server, etc. that exists today. Thank you Prof. von Neumann.

Post-war years

He starts to think about self-replicating machines and cellular automata [5]. Basically the precursor of Conway's Game of Life and cellular automata. He starts to think about the future and predicts nanotechnology and AI decades early.

Surprisingly, in his early fifties he is diagnosed with bone cancer, probably from radiation exposure at nuclear tests. He dies at 53. So what did he achieve in only 53 years?

• Quantum mechanics foundations
• Game theory
• Von Neumann architecture (i.e., computers)
• cellular automata
• Nuclear power
• Theories in economics, meteorology, biology

From reading about von Neumann: things like Einstein had deeper intuition and Gödel had purer logic, but nobody was faster than von Neumann. The smartest people of the 20th century clearly saw him as uniquely different.

Footnotes

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1. There's no doubt Einstein was a very brilliant thinker and one of a kind, but he probably was so influential for his creative and abstract thought rather than his strong foundational knowledge and analytical ability, although he obviously is at the top of the distribution for that as well. ↩

References

[1] J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.

[2] J. von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. 100 (1928) 295--320. https://doi.org/10.1007/BF01448847

[3] J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, 1944.

[4] J. von Neumann, First Draft of a Report on the EDVAC, IEEE Ann. Hist. Comput. 15 (1993) 27--75. https://doi.org/10.1109/85.238389

[5] J. von Neumann, A.W. Burks, Theory of Self-Reproducing Automata, University of Illinois Press, Urbana, 1966.

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Origins of Morality

Note to Reader

This post discusses views on morality and philosophy that some may find personally challenging. Its best to read as an open discussion and not as a challenge to the reader. Additionally, I'm not formally trained at all in any of these topics and the post was drafted approximately 2 years ago and represents my thinking at that time.

Sometimes I think about life and society in ways that make me really think about deep philosophical questions. One such topic is the origins of morality. A while back (~2 years or so) I had an intriguing discussion with a family member about the origins of morality. The seed for the discussion was the ongoing conflicts in the world and how different groups of people view what is "right" and what is "wrong".

So what was the take? Well, my family member posited that morality must be absolute for humanity to continue to exist. I take the contrary view that morality is subjective (i.e., relative) in all circumstances.

Before moving forward, I need to define what is meant by moral absolutism and moral relativism. You can of course get more details on the exact topic by going through the reference links, but let me first start with moral absolutism.

Moral Absolutism

The main guiding feature of moral absolutism is that certain actions are intrinsically right or wrong, regardless of context or consequences. This means there should be, at minimum, one principle that ought never be violated. An example is unjustified killing of a person. Here the "unjustified" refers to an absolute understanding of what constitutes an unjust cause.

My objection to this is there must be some seed of comprehension that leads to this "absolute understanding", but where does one derive from first principles the "absolute" nature of the morality? It is unclear that such a process is possible without some faith, credence, or belief in a "higher power" or a governing entity. This, however, leads to a dilemma because it is not provable (in terms of logic) that such a seed of truth exists. In my view, all we can assume is that groups of people over time develop ideas and concepts that tend to be beneficial in societies, and thus this acts as the seeds of truth to validate or confirm their self-derived view as "absolute". Religion is one such example of a seed of truth that is used to justify the "absolute" nature of morality. Many groups of humans have developed religions and they converge on some top-level principles that, in my view, happen because the net value in general benefits all the most.

I should add some additional discussion on a related view of "moral universalism", which argues that some moral principles apply universally to all individuals regardless of group or society. Unlike absolutism, universalism allows for some flexibility in application and does not necessarily claim that moral principles are completely context-independent. However, it maintains that there are objective moral truths that hold across all groups of people.

I believe my family member was taking the vantage point of moral absolutism, not universality. Both, in my opinion, are difficult to justify, but universality would require that one takes the sentiment that moral principles apply universally, though with some contextual flexibility. Absolutism, in contrast, simply requires some guiding or seeding principle that certain actions are intrinsically right or wrong. Thus one's axiom could be:

"I believe a higher power exists, and this divine entity mandates that unjust killing is wrong."

There are two problems here that I find:

1. What if you don't believe in this "higher-power" and moreover you can't prove with logic or observation the existence or divinity of such entity?
2. Assume you do believe; clearly defining "unjust" in the nuance of every possible circumstance is exceedingly difficult. We do not really know how unjust something is because it's always relative to the context of the situation and previous experiences.

Moral Relativism

In contrast, moral relativism posits that all of morality is subjective and is a matter of lived experiences and environment. If that's the case, how are morals seeded in an individual? How does society birth morality? I argue that this is simply a result of the local social dynamics between humans and their environments.

We clearly see this with the diversity of cultures and religions across the world. What some might view as morally bankrupt, others may view as the commandments of their deity or elders. There is no right or wrong in an absolute sense, but rather in a local, relative sense.

But then you may ask: "Then why is it that most human groups have converged towards the idea that murder¹ is fundamentally wrong?"

For which I would argue, there is a natural ranking of emerged morality within human social groups and murder seems to be one that continually occurs. Most likely due to the mutual benefit among members of those groups who maximize their self-objective function (i.e., survival) by agreeing on a set of conditions (i.e., morals/ethics) where one of them is don't murder each other. This usually is codified through religion. An analogy I think of from physics is we see this kind of behavior with, say, spin-glass systems; entropy would drive these systems to have a state of disordered spins (think of murdering each other which gives you advantage because of less competition for resources), but yet due to high energy penalty (i.e., you might get murdered too!) of such configuration, the spins self-arrange into ordered states (i.e., don't murder each other because although I(we) don't benefit as much in short term, I(we) do in the long term because we live longer and have progeny).

My Stance

So it's probably apparent from the tone above that I'm a staunch relativistic moralist. The reason being is, I don't see how you get to absolutism without a "higher-power"² or governing entity. However, if one goes with absolutism, the debate between an absolutist and a relativist is dead on arrival because the axiomatic difference, i.e., one says god exists, the other does not, and no proof can be given to the other side. As for arguing absolutism through governing physical laws, well it's possible one can argue these laws of morality exist, but again it's hard to see how you get there; your best bet is to try and argue it through physics and complexity theory, but my gosh that is a challenging burden of proof for one to steelman.

Thus I stand by my view that morality is subjective. In the grand scheme of things, if we are lucky, there might be by happenstance a convergence of morals that align well with many groups of people. With globalism this could be more likely; however, with the rise of nationalism it might appear that one group is immoral beyond belief, but in reality it's just a perspective that we're not attuned to. So while many will disagree about what is right and wrong with events going on around the world, it's because of moral relativism and nothing more. It is simply a matter of relative perspective.

Footnotes

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1. Note that murder is specific to intentional malice killing. So killing and murder are not synonyms. ↩

2. Here I use "higher power" broadly to refer to any governing entity, principle, or force that is above human comprehension or ability; not necessarily a deity or god. This could include divine entities, but also abstract principles, natural laws, or any authority that transcends individual human understanding or capability. ↩

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LCSM Dataset

Early last year I started playing around with the CrystaLLM package, which I've also mentioned in previous posts, to gauge the utility of these generative tools for structure creation. CrystaLLM is a autoregressive model that generates crystal structures by condition and populating a CIF format document [1]. So what it is doing is writing the CIF file given the chemistry and optional spacegroup and/or unit replicate factor. I'm not going to go into the technical details of the architecture of the model and training data here as thats a whole post I need to do on generative AI for structures. The main thing is I used my newish personal Desktop with a RTX 5070Ti to do the inference and ended up with about 7,889 structures that are distinct¹. It did take quite some time to configure CrystaLLM and generate the structures², since I enabled/modified the code to verify that the CIF files were valid and matched the target symmetry spacegroup.

In addition to using CrystaLLM to generate the structures, I decided before hand that I would wrap in a labeling step that would compute the total energy, forces, and stress of the crystal structures. I decided why not use ensemble of pre-trained foundation models that are on matbench discovery to do this. For no particular reason other than ones that I was familiar with, I selected seven foundation models to label each structure. This produced the final dataset of 7,889 structures each labeled by the seven foundation models, yielding a ASE database of 53,749 entries.

Figure 1. Element Distribution

Figure 2. Spacegroup Distribution

The resulting distribution of elements and what fraction associated with binary, ternary, quaternary, and quinary can be see in Figure 1. From my perspective the element and component distributions seem reasonable. I also looked at the spacegroup distribution, as shown in Figure 2, I'm less familiar with what to expect but again seems reasonable that majority are orthorhombic or tetragonal.

For now, due to limited personal time, I decided I would make the dataset available on Zenodo upon request since I don't think I'll have much time on weekends to work on the analysis aspect I was hoping to do with the dataset. Eventually by the end of the year I will create a blog post³ on the dataset and analysis. The main question I was trying to answer is can the foundation model ensemble variance across the pre-trained foundation models serve as a proxy for epistemic uncertainty to identify which unknown/novel CrystaLLM-generated crystal structures are physically legitimate versus incorrect? This would require also considering that the foundation models are trained on mostly the same datasets and therefore systematic biases or shared epistemic limitations might exist within all the models. This means that ensemble agreement could reflect a false positive in epistemic knowledge, potentially limiting the extent to which ensemble variance purely reflects epistemic uncertainty about novel structures.

The zenodo entry, which I call Labeled Synthetic Crystal Material (LSCM) dataset [2], can be found here. If you would like to obtain the dataset, I kindly ask you request it via the zenodo entry and I will be happy to provide access. The dataset is in a ASE sqlite3 format. I'm not providing any guarantees on the quality as this is a raw dataset generated purely by the workflow using CrystaLLM and ASE calculators for foundation models model checkpoints. As to whether I'll add to the dataset in the future, probably not as it ties up my GPU considerably and need to use it for other stuff.

Footnotes

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1. The generated structures are distinct within the dataset, i.e. no replicating chemistries+spacegroup, but I haven't yet checked them against the training datasets and known structures in databases like ICSD or COD. ↩

2. I think I started this running on my personal machine in March 2025 and stopped running things in July 2025, but this was not continuous process, I really only ran things on the weekends. ↩

3. If the analysis results turn out to be particularly important and impactful, for example, several generated structures are legit and unknown, then I would probably waver more to writing a formal research paper. This would of course require a lot more time and effort since I would probably have to do some DFT calculations and scour the literature. Could be LLM tools make this feasible to where it actually becomes a viable option for me to do on my own time. ↩

References

[1] L.M. Antunes, K.T. Butler, R. Grau-Crespo, Crystal structure generation with autoregressive large language modeling, Nature Communications. 15 (2024). https://doi.org/10.1038/s41467-024-54639-7.

[2] S. Bringuier, Labeled Synthetic Crystal Material Dataset, (2026). https://doi.org/10.5281/zenodo.18135201.

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