The Universal Pattern Popping Up in Math, Physics and Biology (2013) | Hacker News Reader

The Universal Pattern Popping Up in Math, Physics and Biology (2013)

quantamagazine.org

144 pointskerim-ca54 comments

Not sure why you have to read 3/4 of the article to get to a _link_ to a pdf which _only_ has the _abstract_ of the actual paper:

N. Benjamin Murphy and Kenneth M. Golden* (golden@math.utah.edu), University of Utah, Department of Mathematics, 155 S 1400 E, Rm. 233, Salt Lake City, UT 84112-0090. Random Matrices, Spectral Measures, and Composite Media.

From the abstract:

In this lecture we will discuss computations of the spectral measures of this operator which yield effective transport properties, as well as statistical measures of its eigenvalues.

So a lecture and not a paper, sadly.

heres's a corresponding video: https://www4.math.duke.edu/media/index.html?v=3d280c1b658455...

"We consider composite media with a broad range of scales, whose effective properties are important in materials science, biophysics, and climate modeling. Examples include random resistor networks, polycrystalline media, porous bone, the brine microstructure of sea ice, ocean eddies, melt ponds on the surface of Arctic sea ice, and the polar ice packs themselves. The analytic continuation method provides Stieltjes integral representations for the bulk transport coefficients of such systems, involving spectral measures of self-adjoint random operators which depend only on the composite geometry. On finite bond lattices or discretizations of continuum systems, these random operators are represented by random matrices and the spectral measures are given explicitly in terms of their eigenvalues and eigenvectors. In this lecture we will discuss various implications and applications of these integral representations. We will also discuss computations of the spectral measures of the operators, as well as statistical measures of their eigenvalues. For example, the effective behavior of composite materials often exhibits large changes associated with transitions in the connectedness or percolation properties of a particular phase. We demonstrate that an onset of connectedness gives rise to striking transitional behavior in the short and long range correlations in the eigenvalues of the associated random matrix. This, in turn, gives rise to transitional behavior in the spectral measures, leading to observed critical behavior in the effective transport properties of the media."

Well I'm not sure why I have to dig my way past this comment to find the substantive discussion.

Quanta is not doing hypey PR research press releases, these are substantive articles about the ongoing work of researchers.

>The data seem haphazardly distributed, and yet neighboring lines repel one another, lending a degree of regularity to their spacing

Wow, that kind of reminds me of the process of evolution in that it seems so random and chaotic at the most microscopic scales but at the macroscopic, you have what seems some semblance of order. The related graph also sprung to mind just how very like organisms repel (less tolerance to inbreeding) but at the same time species breed with like species and only sometimes stray from that directive. What is the pattern that underlies how organisms determine production or conflict with other organisms and can we find universality in it?

I guess it's called "universality" for a reason. I suppose if we look hard enough, we'll see it in more things. I read the article and I'm hoping some brilliant minds out there can dissect musical tastes in the same way. I'd love to see if it could relate to what we find harmonious in music and what we find desynchronous via different phase, frequency and amplitude properties.

> I guess it's called "universality" for a reason.

> I'm hoping some brilliant minds out there can dissect musical tastes

There has to be some reason there are "Top 10" listings for video games, music, art, tv, movies, anime, vacation destinations, toys, interior designs, historical buildings in NYC, et. al.

Certainly there is a great deal of variance in the order and membership of these lists, but you do find a lot in common. Without some underlying pattern or bias, I don't think we'd see this in so many places so consistently.

I am fairly convinced there is something to do with biological efficiency around information theory that drives our aesthetic preferences.

Today I was thinking about how observing the macroscopic is not a neutral process, it involves processing more and more information the further you zoom out. Perhaps there's something about these "zooming out" kinds of processes that resembles the law of large numbers but more broadly?

This spacing reminds me of Turing patterns, or activator/inhibitor systems, but I'm gobsmacked that this occurs in random matrices.

Maybe also heap fragmentation

This is interesting, do you have a link to any research about this?

No, it is a hypothesis I formulated here after reading the article. I did a quick check on google scholar but I didn't hit any result. The more interesting question is, if true, what can you do with this information. Maybe it can be a way to evaluate a complete program or specific heap allocator, as in "how fast does this program reach universality". Maybe this is something very obvious and has been done before, dunno, heap algos are not my area of expertise.

Today I thought a lot about this topic and was also trying to find connections to computation. Seems like "computational entropy" could be a useful bridge in the sense that to derive a low entropy output from a high entropy input, it seems intuitively necessary that you'd need to make use of the information in the high entropy input. In this case you would need to compute the eigenvalues, which requires a certain wrestling with the information in the matrices. So even though the entries of the matrices themselves are random, the process of observing their eigenvalues/eigenvectors is has a certain computational complexity involved with processing and "aggregating" that information in a sense.

I realize what I'm saying is very gestural. The analogous context I'm imagining is deriving blue noise distributed points from randomly distributed points: intuitively speaking it's necessary to inspect the actual distributions of the points in order to move the points toward the lower entropy distribution of blue noise, which means "consuming" information about where the points actually are.

The "random song" thing is similar: in order to make a shuffle algorithm that doesn't repeat, you need to consume information about the history of the songs that have been played. This requirement for memory allows the shuffle algorithm to produce a lower entropy output than a purely random process would ever be able to produce.

So hearing that a "purely random matrix" can have these nicely distributed eigenvalues threw me off for a bit, until I realized that observing the eigenvalues has some intrinsic computational complexity, and that it requires consuming the information in the matrix.

Again, this is all very hunchy, I hope you see what I'm getting at.

Interesting, I did not know that colors-of-noice was related to this, what you say sounds conceptually very similar to how Maxwell's demon connects thermodynamics to information theory.

Well, I'm talking about a kind of point sampling technique specifically when I refer to "blue noise" in this case.

Thanks for the reflection though. I'm definitely gonna be thinking about the physical thermodynamics stuff differently after digging into this.

didn't realize this post got traction, it seems like it was HN pooled, I came across this article and related topics after trying to search what would be rigorous and closest to the phenomenon of the unreasonable effectiveness of mathematics by wigner, renormalization groups were the closest that I came across, the reason why the post title doesn't match the story title is likely due to the story being switched to a more detailed article I considered posting, the title is from a quanta video covering universality, linked below

- https://www.quantamagazine.org/the-universal-pattern-popping...

- https://www.quantamagazine.org/tag/universality/

- https://en.wikipedia.org/wiki/Universality_class

- https://en.wikipedia.org/wiki/Renormalization_group

-https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...

The article has a graphic contrasting a "Random" distribution vs. a "Universal" distribution vs. a "Periodic" distribution. I'm guessing the "Random" distribution is actually a Poisson distribution, as that arises naturally in several cases.

But the big question is, does this "Universal" distribution match up to any well known probability distribution? Or could it be described by a relatively simple probability distribution function?

Just a layman: the graphic suggested to me that you might take the lines and their deviation from a periodic distribution. The random distribution is clearly further from periodic, the universal one closer. I wondered if there was some threshold that determined random vs. universal.

I think you mean a Poisson process rather than a Poisson distribution. The Poisson distribution is a discrete distribution on the non-negative integers. The Poisson process’s defining characteristic is that the number of points in any interval follows the Poisson distribution.

There have been a large variety of point processes explored in the literature, including some with repulsion properties that give this type of “universality” property. Perhaps unsurprisingly one way to do this is create your point process by taking the eigenvalues of a random matrix, which falls within the class of determinantal point processes [1]. Gibbs point processes are another important class.

[1] https://en.wikipedia.org/wiki/Determinantal_point_process

2013 But still cool

There is the well known problem that "random" shuffling of songs doesn't sound "random" to people and is disliked.

I wonder if the semi-random "universality" pattern they talk about in this article aligns more closely with what people want from song shuffling.

It's not that a random shuffling of songs doesn't sound random enough, it's that certain reasonable requirements besides randomness don't hold. For example, you'd not want hear the same track twice in a row, even though this is bound to happen in a strictly random shuffling.

If the list of songs is random shuffled, you can only hear the same song twice if there is a duplicate or if you've cycled through the whole list. That's why you shuffle lists instead of randomly selecting list elements.

Random shuffling of songs usually refers to a randomized ordering of a given set of songs, so the same song can’t occur twice in a row if the set only contains unique items. People don’t usually mean an independent random selection from the set each time.

You could think of it as wanting your desire to hear the song again build up to a sufficient level to make it worth a relisten, sort of how a bus driver might want potential passengers to accumulate at a bus stop before picking them up, and therefore delay arrival. Very plausible to me that a good music randomization would have similar statistics if you phrase it right.

>For example, you'd not want hear the same track twice in a row, even though this is bound to happen in a strictly random shuffling.

Why would it be? A random shuffling of a unique set remains a unique set.

It's only when "next song is picked at random each time from set" which you're bound to hear the same song twice, but that's not a random playlist shuffling (shuffling implies the new set is created at once).

a new ordering, not a new set

Same difference...

(yes, you're technically correct)

Or when the set repeats, and the random order puts songs from the end of the first ordering of the set into the beginning of the second ordering of the set, so you quickly hear them twice.

Thank you for reading and understanding the article

Song shuffling has been broken for ages now. It used to work correctly, like shuffling and dealing a deck of cards, only reshuffling and redealing when the entire deck has been dealt (or the user initiates a reshuffle).. Now it's just randomly jumping around a playlist, sometimes playing the same song more than once before all the songs are played once. I have a feeling that money is involved somehow, as with everything else that's been enshittified.

Yeah I suspected something to do with CDN cost efficiency.

Another point in case: Life only exists in liquids, not in solids (too much structure) and not in gases (too much chaos).

In fact one could argue that this is a definition of an interesting system: It has to strike a balance between being completely ordered (which is boring) and being completely random (which is also boring).

What's with all the spammy comments?

https://pmc.ncbi.nlm.nih.gov/articles/PMC11109248/

DNA as a perfect quantum computer based on the quantum physics principles.

The Physics models tend to shake out of some fairly logical math assumptions, and can trivially be shown how they are related.

"How Physicists Approximate (Almost) Anything" (Physics Explained)

https://www.youtube.com/watch?v=SGUMC19IISY

If you are citing some crank with another theory of everything, than that dude had better prove it solves the thousands of problems traditional approaches already predict with 5 sigma precision. =3

What does “5 sigma precision equals 3” mean?

=3 is a cat face[1] smiley, the period preceding it ends the sentence.

[1]: https://en.wikipedia.org/wiki/List_of_emoticons

> The pattern was first discovered in nature in the 1950s in the energy spectrum of the uranium nucleus, a behemoth with hundreds of moving parts that quivers and stretches in infinitely many ways, producing an endless sequence of energy levels. In 1972, the number theorist Hugh Montgomery observed it in the zeros of the Riemann zeta function(opens a new tab), a mathematical object closely related to the distribution of prime numbers. In 2000, Krbálek and Šeba reported it in the Cuernavaca bus system(opens a new tab). And in recent years it has shown up in spectral measurements of composite materials, such as sea ice and human bones, and in signal dynamics of the Erdös–Rényi model(opens a new tab), a simplified version of the Internet named for Paul Erdös and Alfréd Rényi.

Are they also cranks? Seems it at least warrants investigation.

>Are they also cranks?

That is a better question. =3

This isn't crank stuff, and operates on different kinds of problems/scales than "grand unified theory" type cranks. This is about emergent statistical order in complex interacting systems of sufficient size, not about the behaviors of the individual particles or whatever.

Universality broadly construed is well understood since the 70s. Particular universality classes are newer and will likely continue to be discovered, but they all come to be in a qualitatively similar way.

If anyone has genuine interest, this review from shortly after the clarifying development of renormalization group theory might be a nice place to start: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.46....

I'm going to go out on a limb and say you posted this accidentally on the wrong thread somehow, but this isn't (at all) a theory of everything, nor is it some crank producing anything.

Eg https://arxiv.org/abs/0906.0510

See the authors- in terms of contemporary mathematics they are pretty much as far from a crank as it's possible to be. Universality seems to be some sort of intrinsic characteristic of the distribution of eigenvalues of certain types of random matrices which crop up all over the place. That seems interesting and the work is serious academic work (as you can see from the paper I linked) and absolutely doesn't deserve the sort of shallow dismissal you have applied.

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