[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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