On learning the quasicrystalline nature of prime numbers

It is wholly hilarious that I got to this point in studying prime numbers before I learned of the quasicrystalline nature of prime numbers, which was discovered by Freeman Dyson while in idle conversation with Hugh Montgomery over lunch one day in the early 1970s. I knew of the legendary conversation, but first learned of it well before I had an overall grasp of where prime numbers and the Riemann Hypothesis sit in relation to the rest of mathematics. And long before I began to understand what an eigenvalue is. I remember thinking “I’ve got to learn what eigenvalues are.” (The famous quote happened at the mention of 1 – [(sin pi*u)/(pi*u)]2, when Dyson said: ‘Hey, that’s the density of the pair correlation of eigenvalues of random matrices in the Gaussian Unitary Ensemble.’)

So I knew that Freeman Dyson had made a keen observation that mentioned eigenvalues, but didn’t know it was related to quasicrystals, didn’t remember it was related to randomness, didn’t know it was related to prime numbers, and at the time I learned of it, didn’t know what an eigenvalue was, each of which I have studied independently from a number of different directions as I make my peripatetic walk through mathematics over the past decade and a half. Until today.

Today, while working and idly watching yet another video on the Riemann Hypothesis (on the theory that I usually learn at least one new thing by looking at something familiar from another angle), I was startled by the reference to the connection to the conversation with Freeman Dyson.

Oh, that conversation was related to prime numbers? Cool! How did I miss that?

I quickly searched on the topic and pulled up a couple dozen webpages, each of which looks quite fascinating, and a quick skim of the first few has already got lightbulbs going off over my head.

Alas, got work to do, so I’ll reserve deeper comments for the future, but right now I’m just laughing out louad at myself for taking this long to discover that my intuitive hunch about the physics of prime numbers was already worked out decades ago. (I’ve encountered other “physics of prime numbers” theories from time to time, but none this credible.)

0. But wait — before I go — this is also the second major reference to the crystalline nature of That Which Underlies Everything. I long held a faint “no that can’t be true” intuitive hunch that the nature of the primordial substance out of which everything is created (desire? aether? consciousness? definitely not strings) is crystalline in nature. It probably is rooted in “the sea of glass like crystal” which is before the throne of God, but it appears from time to time in thought experiments on the nature of Everything, only to be quickly dismissed because crystals in my mind are rigid, unmoving, and this doesn’t strike me as an apt description of God, or heaven, which to me are the quintessence of motion, energy, life, action.

1. Oops, I guess I’m actually talking about the “first major reference” in my experience to the crystalline nature of That Which Underlies Everything, because the second one is in Schrodinger’s small book What Is Life described beautifully in a chapter of another book I’m reading about quantum biology. I discovered this only a few weeks ago (he was describing DNA a decade before it was discovered as “an aperiodic crystal),” and this made the crystalline nature of the prime substance more likely. My thought experiments stopped dismissing the crystal structure so quickly.

2. And then, a few days ago, while searching on the meaning of the word “tensor” because I’ve fallen in love with how it is a better tool for understanding measurement than the ridiculously flawed Euclidian approach, I discover to my jaw-dropping astonishment that the person who first used the term in the way it is commonly used today was Woldemar Voigt, an expert in crystals. Crystals? I thought tensors flowed, do crystals flow? A lot fell into place when I discovered this, and new questions about the nature of crystals began to form.

So now it’s not a matter of letting the underlying crystal structure remain a little longer in thought experiments… it’s a matter of beginning to devote entire thought experiments to the  underlying crystal structure.

3. And now… prime numbers are crystalline?

Wow. Here we go.

I know I’ve stumbled upon these insights in the past, just never saw them. Three independent references out of the blue in as many weeks lends an aura of grace to the adventure. It is part of the human condition that we are presented with deep insights continually, but are only able to see them when we’re looking. I’m excited to see what comes next.

Well the whole point of this post was to pull together in a single place a bunch of URLs that I will now start reading in earnest, so here we are, a few of the most interesting ones that appeared during the preliminary search:

https://www.math.columbia.edu/~woit/wordpress/?p=1506
https://www.ias.edu/ideas/2013/primes-random-matrices <– this one looks good all the way through
http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/dyson.htm
https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture
https://golem.ph.utexas.edu/category/2013/06/quasicrystals_and_the_riemann.html
https://www.americanscientist.org/article/the-spectrum-of-riemannium
https://news.ycombinator.com/item?id=6541886
https://www.dartmouth.edu/~chance/chance_news/recent_news/primes_part3.pdf (PDF)
https://mathoverflow.net/questions/54501/riemann-zeta-function-connection-to-quantum-mechanics
https://www.wired.com/2013/02/math-and-nature-universality/
http://guava.physics.uiuc.edu/~nigel/courses/563/Essays_2008/PDF/lyon.pdf (PDF)
http://www.ams.org/publicoutreach/math-history/prime-chaos.pdf (PDF)
https://icerm.brown.edu/materials/Abstracts/sp-s13-w3/Random_Matrix_theory_and_the_zeros_of_the_Riemann_zeta-function_]_Brian_Conrey,_American_Institute_of_Mathematics.pdf (PDF)
https://arxiv.org/pdf/1305.3342.pdf (PDF)
https://www.seedmagazine.com/content/article/prime_numbers_get_hitched/
https://math-frolic.blogspot.com/2013/05/riemann-dyson-montgomery-quasi-crystals.html
https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/sym1010064.pdf (PDF)
https://www.vice.com/en_us/article/4x3me3/quasicrystals-are-natures-impossible-matter
https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0020448

There, that ought to be enough to get started… now, back to work.

Reads article about a rogue process

Reads article about a rogue process in Windows related to Microsoft Store. Reads enough of the article to recognize it’s a component he never uses, so can be safely disabled. Opens commnd prompt, uses it to invoke regedit to edit registry to disable the subprocess that is most suspicious, leaving the client-facing one intact, because it hosts commonly-used programs. Leaves regedit open for a couple days in case something got broken. Archives the article locally in case there is an issue with the tweak. Blogs about it. Goes to sleep.

First qutrit teleportation! Complex high-dimensional quantum states go from zero to infinity in one nanosecond

I knew there was a link between pure logic and the real world, and I knew it was through a window we call infinity, but I had no idea that physical “teleportation” of quantum states would be where ternary logic touches the physical world.

The first qutrit had a single digit beyond normal binary quantum teleportation, but now that we’ve broken that barrier, it will be easy to explain to people how the qutrit is not just the addition of another “it” to the “bit” concept, but the addition of a whole “infinity.”

As in, an entire mappable 3-D landscape, not unlike the physical world.

More later as the epiphany coheres.


 

Wow, everyone is writing about this. So glad to see:

https://science.slashdot.org/story/19/08/23/2212204/complex-quantum-teleportation-achieved-for-the-first-time

https://phys.org/news/2019-08-complex-quantum-teleportation.html

https://www.popularmechanics.com/technology/a28798458/quantum-teleportation/

https://arxiv.org/ftp/arxiv/papers/1906/1906.09697.pdf

https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.123.070505

https://medium.com/@teodorteofilov/first-three-dimensional-quantum-teleportation-achived-for-the-first-time-b99157252a78

On group dynamics and critical thinking

A friend told me a story recently, and it so purely reveals a dynamic we do not often see clearly, I’m delighted to discover it. I think it is quite a profound insight. He is a member of an online group discussing a new cryptocurrency, one of many hundreds of similar groups, each of which is in a tiny ecosystem within the larger ecosystem of cryptocurrencies. Each of these smaller groups is usually led by a charismatic and/or brilliant innovator, with a core team surrounded by advocates and on the periphery, detractors.

The leader of the group one day asked him privately in a casual and friendly manner why he was so consistently hostile and negative in discussions. Since he was having fun overall, he was surprised that anyone could say this. Curious, he pulled a few other people aside one by one and asked them if he seemed hostile or negative to them. Most of them would not answer the question directly! But in their vague and wordy answers he was able to see hints that they did perceive him that way, just couldn’t say it. Finally one gave a direct answer: “No! I love your contributions, they’re great, bringing up real concerns that we all need to think about.”

As he pondered this paradox of contradictory opinions, it occurred to him that the people who perceived him as hostile were fully invested in this single cryptocurrency, while he was involved in numerous other similar discussions on all levels of the larger ecosystem.

To sum: people who thought he was hostile could not say so directly nor could they perceive him objectively. They were seeing “only the good” possibilities of their given crypto, and thus found his reasonable questions and comments to be attacks. On the other side, people who thought his insights were good and useful did not see that he was hostile or negative.

Thinking about this dynamic a bit, this appears to explain a dynamic in conversations with people who have and do not have critical thinking. I believe this is a description of something that happens in almost every group ever, but not often is it probed so concisely. As a fan of Rene Girard’s thoughts on scapegoats, I think it goes quite deep. There are many more insights buried in this gem. I’m sure there are experts who know all about this particular dynamic and recognize it immediately, but for me, it’s really insightful about the nature of people who never learned to think critically, and something I will think about for some time to come.

It appears that people who do not have critical thinking skills are only seeing part of the picture. They invest all their trust in someone who sees more of the picture, and then defend that other person with all their ability. Thus, they see anyone who is not doing the exact same thing as a threat to the whole group. On the other hand, people who do have critical thinking skills are more able to trust their own judgments and therefore do not invest as much trust in others, and thus see things more on neutral terms. They do not have a need to be defensive, so they aren’t, at least not in this dynamic (I’ve seen critical thinkers who were defensive, but it happened on very principled lines, not personal.)

This is related to binary vs ternary thinking, and of course the scapegoat mechanism, but this is enough for now, leaving that analysis for another day.

A conspiracy theory must involve Laniakean red strings somehow to be legit

What’s up with the maze of red strings that somehow defines the crazy consipiracy-theorist in the movies? It’s a meme that shows up often. I personally think the image is beautiful — I mean the Platonic meme itself — not the actual screenshots from scenes in movies. Such complexity! Such multidimensional beauty! Looking like a miniature fractal version of the Laniakean shape of the universe, or the wiring diagram of a part of the brain itself, these scenes have always won my heart, and shaped how I see the character from that point forward. I’m drawn in.

Getting data into Twilio parsed variable

It took several attempts, but I eventually found out why I could not access the value of a “parsed” variable within Twilio Studio while using the HTTP Widget. Someone else may encounter this error, so here’s how I resolved it. The following 3 attempts are screenshots from the log viewer built in to the studio.

1. This one is incorrect because it sends content_type “text/html.” Notice there isn’t even a “parsed” variable, as seen in the next screenshot. This is because Twilio only parses variables from Content Type “application/json”.

2. This one is incorrect because the JSON string is quoted. We correctly sent “application/json” but quoted the JSON. In other words, do not send “{JSON}” but rather, send {JSON}.

3. This one is finally correct. We get a parsed variable.

Here is the PHP code which correctly generated the variable:

<?php
$data = array("caller-exists"=>1);
header('Content-Type: application/json');
echo json_encode($data);
?>

Compile and Install FreeSWITCH 1.8.2 onto Ubuntu 18.4.2 LTS

This closely follows the excellent and very concise instructions at another site: “FreeSWITCH 1.8.2 on Ubuntu 18.4 LTS“. I found a few unexpected twists and turns before it was working, so I’ve put this information together to help others who encounter these or similar issues.

Dependencies

Starting on a freshly installed Ubuntu Server 18.4 (32bit), install these packages:

apt-get install --yes build-essential pkg-config uuid-dev \
zlib1g-dev libjpeg-dev libsqlite3-dev libcurl4-openssl-dev \
libpcre3-dev libspeexdsp-dev libldns-dev libedit-dev libtiff5-dev \
yasm libopus-dev libsndfile1-dev unzip

Compiling FreeSWITCH

Download the FreeSWITCH sources from here: https://files.freeswitch.org/freeswitch-releases/

Find the latest version, then use wget to pull the file into your /usr/src folder, which is where things like this usually happen:

cd /usr/src
wget https://files.freeswitch.org/freeswitch-releases/freeswitch-1.8.6.zip

When the file completes downloading, expand it, then move into the newly created folder:

unzip freeswitch-1.8.6.zip
cd freeswitch-1.8.6

In the file modules.conf I needed to comment two lines, so I opened it up in an editor: nano modules.conf and modified these lines by adding the comment character:

#languages/mod_lua

and

#applications/mod_signalwire

because attempting to compile FreeSWITCH with Lua or SignalWire threw errors. Once these were commented in modules.conf, compilation worked. (If you need to use these modules, there are better guides for you than this one):

./configure && make

If you see errors while compiling, you can either install missing packages or comment out any module that is throwing the error. After you make the change, re-start compilation by including a “make clean” like this:

./configure && make clean && make

After a successful compilation, you’ll see a screen like the following:

It’s time to install FreeSWITCH. The following command does it. The default location this will install into: /usr/local/freeswitch

sudo make install

Set Owner and Permissions

This summarizes the instructions at: https://freeswitch.org/confluence/display/FREESWITCH/Debian+Post-Install+Tasks

Create user ‘freeswitch’, add it to group ‘freeswitch’. Change owner and group of the freeswitch installation:

cd /usr/local
groupadd freeswitch
adduser --quiet --system --home /usr/local/freeswitch --gecos "FreeSWITCH open source softswitch" --ingroup freeswitch freeswitch --disabled-password
chown -R freeswitch:freeswitch /usr/local/freeswitch/
chmod -R ug=rwX,o= /usr/local/freeswitch/
chmod -R u=rwx,g=rx /usr/local/freeswitch/bin/*

Configure FreeSWITCH as systemd Service

Place the following configuration in a file at: /etc/systemd/system/freeswitch.service

[Unit]
Description=freeswitch
After=syslog.target network.target local-fs.target

[Service]
; service
Type=forking
PIDFile=/usr/local/freeswitch/run/freeswitch.pid
PermissionsStartOnly=true
; blank ExecStart= line flushes the list
ExecStart=
ExecStart=/usr/local/freeswitch/bin/freeswitch -u freeswitch -g freeswitch -ncwait -nonat -rp
TimeoutSec=45s
Restart=on-failure
; exec
WorkingDirectory=/usr/local/freeswitch/bin
User=root
Group=daemon
LimitCORE=infinity
LimitNOFILE=100000
LimitNPROC=60000
;LimitSTACK=240
LimitRTPRIO=infinity
LimitRTTIME=7000000
IOSchedulingClass=realtime
IOSchedulingPriority=2
CPUSchedulingPolicy=rr
CPUSchedulingPriority=89
UMask=0007

[Install]
WantedBy=multi-user.target

Note that this working systemd file came from the URL in the previous section. There are other examples online, but several didn’t work for me; this one did. To create the file, you could type cat >> /etc/systemd/system/freeswitch.service and paste the preceding text in, then close the file with CTRL-D. Or you could use vi or nano to create the file. Once the file is in place, start the service as described in the next section.

Starting and Confirming Service

Reload the service engine, then start the service:

systemctl daemon-reload
service freeswitch start

Use service freeswitch status to confirm it is running. When it is running reliably, you can “enable” it so it will run when the system boots up.

systemctl enable freeswitch.service

Reboot the machine, and then ensure service is running after reboot:

ps -aux|grep free

You should see that is a running process, if all went well.

 

The Greek subject lives in the excluded middle of binary logic

Well, well, well. I am delighted to find yet another piece of private intuition has a respectable home already existing in the public domain. I’ve been working on this insight for years, but not able to put it into words well enough to relay it to others coherently. Much to my delight, I find that Schrödinger already had the same observation, and saw it more clearly than me, though apparently not many realized the importance of what he was saying.

I was reading an article about the rather interesting angle on a new quantum theory called “Quantum Bayesianism” when I came across the following quote. I screenshotted and annotated it immediately, as I do with such things.

As you may know, I’ve been studying ternary logic for a long time now, and have written often about a particular tiny flaw in binary logic, which first arose in Greek thought. I’ve been able to trace the flaw within mathematics and logic back to Aristotle and Euclid’s original “dimensionless point” concept. They had a good reason for defining this — on the surface, it appears to solve a certain problem with measurement and everything works intuitively once you accept the fact that math exists in a different world than common everyday reality. But the assumption causes other problems, which took centuries to identify because Euclid and Aristotle’s insights worked so well.

The flaw is cleverly hidden, but once you see it, you begin to see it everywhere because… it is everywhere. It is hidden by being embedded in the definition of binary logic — not in its postulates or axioms, but deeper, in its first underlying assumption. Although it is plainly right in front of us, we don’t understand that, in order to accept it as true, we have to accept the existence of something that doesn’t exist… and this is where things begin to go wrong.

I knew that the logical flaw had huge consequences, because so much is dependent upon this form of logic (for one example, as is well known, computers operate at their most fundamental level using this logic). But I had a hard time figuring out what was the valuable thing being left out of binary logic, partly because I was using binary logic to contemplate binary logic. It was years before I even realized I was doing this, and began seeking to understand ternary logic on its own terms. It was still more years before I was beginning to make real breakthroughs in this area. I’m not smart enough to figure this out myself as if I were someone like C. S Peirce. Rather, I’m better at seeing a paradox when it is exposed by others (who usually have no idea how it’s related to the structure of binary logic), and then contemplating it. I do this one piece at a time, slowly building an internal database of seemingly unrelated pieces that each show a different facet of this problem.

Now I see this one, and it’s a big one. In order to make binary logic work, we have to move the stuff that normally fits into the “excluded middle” (i.e. whatever naturally exists between True and False) somewhere, because it no longer fits in the excluded middle. Until now, I thought the shift was a subtle one, where we simply started subtly emphasizing how we related to some things and de-emphasizing others, with effects that grew incrementally over time (very hard to research), but now I see we shifted ourselves* out of logic and math. And we lost track of the shift. We began thinking of the world as an external system, contemplated by a subject which had no relation to the external object except as an observer discovering “laws” and “principles” which guide the external world (and by extension, ourselves). In fact, we are very much actors who are intimately involved in what we’re contemplating. Only in the past century have we discovered quantum physics which forced us to put our consciousness back in to the mix of things. However, we are continually baffled by this realization because we’ve become so accustomed to thinking that… well… that we don’t exist, except as abstract observers of the world.

*This point is unfinished because I have other things I need to do now, but I think the point about judgment in this StackExchange article is relevant here. Did ancient Greeks shift the act of judgment? I think we did, and Frege noticed this when he made logic more rigorous.

Ternary logic and a coin toss

Discovered a quick way to illustrate the value of ternary over binary logic. Think of a coin toss. Although it might take millions of times, there is a tiny possibility that the coin could land on its edge. What do you call this result, in the binary world of heads or tails?

This is a crude example (and it can be described with binary logic if you add one layer of abstraction), but it effectively shows how ternary logic can explain things more holistically than binary. It doesn’t convey the true nature of the “third pole” either, but it does give a place to introduce that topic.

A better example would involve reference to infinity. It took me a long time to understand how infinity is embedded in ternary logic but excluded from binary. Seeing how prevalent it is is in quantum theory, I’m convinced our understanding of “probability” can be expanded to do this, but that is outside the scope of a simple example. Nevertheless, I’m pleased as punch to have a simple way of opening a conversation on this subject to others now.

Unitarity and locality are linked to time and space

Just figured out that unitarity and locality are linked to time and space, respectively. I’ve known for a while now that time is a purely mental thing which has no physical existence outside of the present moment (which is empirically proven in several ways, for those new to the idea). As a consequence, I’ve been intuiting what it looks like if space completely collapses to a comparatively tiny now (in space that would be… “here?”) like this also, but not making much progress. Then today I discovered a controversial theory in the mathematics of quantum physics which operates “without unitarity or locality.” Googling these revealed that these are two mathematical measures related to time and space. Oh, I see. From what I can tell, unitarity is a mathematical way of talking about time. Locality, it’s pretty easy to understand how it’s related to space.

So, Aha! It is possible for there to be things that exist without reference to time and space both. These things can be mathematically described, and this is one of the things quantum physics studies and knows well, even though it’s new to me.

But… how in the world am I going to wrap my head around the concept of no space? No time makes sense to me finally — time is literally all an intricately-linked illusion in our minds — but no space is… well… what holds everything together if it is not space? If space is merely a perception, how do we share space between us so seamlessly, as if we’re all in the same (quantum mechanical) dream simultaneously? I can believe that time has been an unfurling of space through a seive of, uh, serial nows, but how do I do this with space? Oh this stuff breaks my brain, but I will keep on thinking about it any way.

https://en.wikipedia.org/wiki/Unitarity_(physics)

And, while I’m here, some related links that I went through while figuring this out, these are the better ones of the crowd:

Woit: Physicists Discover Geometry Underlying Particle Physics
http://www.math.columbia.edu/~woit/wordpress/?p=6260

Unitarity Principle of Quantum Mechanics
https://sureshemre.wordpress.com/2014/03/08/unitarity-principle-of-quantum-mechanics/

Information Loss as a Foundational Principle for the Second Law of Thermodynamics
https://www.researchgate.net/publication/1861558_Information_Loss_as_a_Foundational_Principle_for_the_Second_Law_ofThermodynamics

Amplituhedron (For the Rest of Us)
http://sciexplorer.blogspot.com/2015/08/amplituhedron-for-rest-of-us.html

The Sacred, Spherical Cows of Physics
Theoretical physics milks symmetry to power its newest tool.
http://nautil.us/issue/13/symmetry/the-sacred-spherical-cows-of-physics