[HN Gopher] The Universal Pattern Popping Up in Math, Physics an...
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       The Universal Pattern Popping Up in Math, Physics and Biology
       (2013)
        
       Author : kerim-ca
       Score  : 138 points
       Date   : 2026-01-23 05:49 UTC (5 days ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | anthk wrote:
       | https://pmc.ncbi.nlm.nih.gov/articles/PMC11109248/
       | 
       | DNA as a perfect quantum computer based on the quantum physics
       | principles.
        
       | cosmic_ape wrote:
       | 2013 But still cool
        
       | dist-epoch wrote:
       | 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.
        
         | pegasus wrote:
         | 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.
        
           | jonathanstrange wrote:
           | 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.
        
           | nkrisc wrote:
           | 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.
        
           | topaz0 wrote:
           | 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.
        
           | coldtea wrote:
           | > _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).
        
             | lacunary wrote:
             | a new ordering, not a new set
        
               | coldtea wrote:
               | Same difference...
               | 
               | (yes, you're technically correct)
        
             | sejje wrote:
             | 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.
        
         | blurbleblurble wrote:
         | Thank you for reading and understanding the article
        
         | stronglikedan wrote:
         | 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.
        
           | mcmoor wrote:
           | Yeah I suspected something to do with CDN cost efficiency.
        
       | readingnews wrote:
       | 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.
        
         | magicalhippo wrote:
         | 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.
        
         | troelsSteegin wrote:
         | 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."
        
         | blurbleblurble wrote:
         | 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.
        
       | Joel_Mckay wrote:
       | 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
        
         | nkrisc wrote:
         | What does "5 sigma precision equals 3" mean?
        
           | magicalhippo wrote:
           | =3 is a cat face[1] smiley, the period preceding it ends the
           | sentence.
           | 
           | [1]: https://en.wikipedia.org/wiki/List_of_emoticons
        
         | kitd wrote:
         | _> 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, Krbalek and Seba 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
         | Erdos-Renyi model(opens a new tab), a simplified version of the
         | Internet named for Paul Erdos and Alfred Renyi._
         | 
         | Are they also cranks? Seems it at least warrants investigation.
        
           | Joel_Mckay wrote:
           | >Are they also cranks?
           | 
           | That is a better question. =3
        
         | topaz0 wrote:
         | 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.
        
           | topaz0 wrote:
           | 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.
        
             | topaz0 wrote:
             | 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....
        
         | seanhunter wrote:
         | 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.
        
       | FjordWarden wrote:
       | Maybe also heap fragmentation
        
         | redleader55 wrote:
         | This is interesting, do you have a link to any research about
         | this?
        
           | FjordWarden wrote:
           | 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.
        
             | blurbleblurble wrote:
             | 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.
        
               | FjordWarden wrote:
               | 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.
        
               | blurbleblurble wrote:
               | 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.
        
       | blurbleblurble wrote:
       | What's with all the spammy comments?
        
       | 0134340 wrote:
       | >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.
        
         | bob1029 wrote:
         | > 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.
        
         | blurbleblurble wrote:
         | 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?
        
       | wduquette wrote:
       | 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?
        
         | JKCalhoun wrote:
         | 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.
        
         | CrazyStat wrote:
         | 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
        
       | cjohnson318 wrote:
       | This spacing reminds me of Turing patterns, or
       | activator/inhibitor systems, but I'm gobsmacked that this occurs
       | in random matrices.
        
       | Lichtso wrote:
       | 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).
        
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