#bayesian stuff

[art-of-mathematics]

Title: "Non-linear regression in a blurry cloud of (un-) certainty"

Date: 2023/06/12 - Size: DIN A4

Collage made with torn pieces of paper, printed background paper (top is rather dark night sky, bottom is mererly clouds in pastel-colors)

I resized and printed the non-linear regression visualisation/illustration and put it on top of the watercolour background paper.

I included a scrap piece of paper with the title of the picture and have torn it with a spiral-shaped jag at the bottom, which I bent around the top part of the non-linear regression illustration.

[max1461]

I think a good chunk of my symptoms are PTSD. They've got a whole Bayesian theory of PTSD here. So my plan is to try and not do all that stuff, you know. They think my brain got its priors fucked and is interpreting things wrong, so I'm going to try to not do that.

[rayssyscourse]

subjective reality anon - I'd love to see those articles :)

absolutely!!!! there was one other person in the reblogs who asked for them too, if I can find them again I'll tag them lol

Quantum superposition - https://scienceexchange.caltech.edu/topics/quantum-science-explained/quantum-superposition

Qbism - https://www.quantamagazine.org/quantum-bayesianism-explained-by-its-founder-20150604/

Perception based on prior assumptions - https://www.quantamagazine.org/brains-speed-up-perception-by-guessing-whats-next-20190502/

https://www.quantamagazine.org/to-be-energy-efficient-brains-predict-their-perceptions-20211115/

Double-slit experiment (famous experiment proving quantum superposition and the decoherence of it) -

https://plus.maths.org/content/physics-minute-double-slit-experiment-0

Observer interference - https://www.researchgate.net/publication/326795653_The_Observer_Effect

https://bigthink.com/starts-with-a-bang/measuring-reality-affect-observe/#:~:text=That%20pattern%20persists%20even%20if,really%20does%20affect%20the%20outcome.

you'll notice this in the links, but one site I really like is called Quanta Magazine--they report on other branches of science too, but their quantum physics stuff is particularly good, and I find it to be really digestible considering how complex the topics are, lol. Enjoy!!

also--a couple things I don't have on hand but might be useful to look up are the Heisenberg uncertainty principle and quantum entanglement :)

[mellifiedman]

I don't think I should have to figure out permutations and Bayesian probabilities and stuff like that when it's nice outside. They should make an exception

[uququ]

possible i fundamentally misunderstand its actual application but bayesian reasoning seems fundamentally ridiculous as a day-to-day decisionmaking tool. like, you're just picking some numbers basically arbitrarily & doing math on them, not only is there no way that's actually more effective than just thinking about stuff but also it imbues you with a false confidence in the objectivity of your views! what's the point!

[expfcultragreen]

To be precise,

....apes aren't monkeys and monkeys arent apes. "Ape" isnt a suborder of "monkey" or whatever, theyre all in the dry nose cladistic group but that group includes a bunch of stuff, it isnt a thing of "monkey" being an umbrella term that encompasses apes, its a thing of them both being under an umbrella (dry nose + nostrils down-and-forward) that only some monkeys are under. Apes evolved from a monkeylike ancestor a really long time ago, as did the modern monkeys around them; monkeys arent proto-apes, theyre derived from the same extinct primate as apes.

....Im just thinking tangentially about how old primates as a group are....like.......pre-continental drift/breakup old, so cool. The ones on this side of the planet have been evolving in isolation from the others for so fucking long....you know only the central/south american ones have prehensile tales....pretty jealous personally

Following the emergence of Simiformes in Africa, Platyrrhini split from Catarrhini during the Eocene when New World monkeys dispersed to South America, likely by rafting on mats of vegetation across the Atlantic Ocean. The Atlantic is estimated to have been possibly 1,000 km (600 mi) narrower, based on estimates from the expansion of the Atlantic mid-ocean ridge formation processes (2.5 cm/1 in per year.) It is also possible that during this rafting process, there were a number of islands between Africa and South America which have since been submerged.

Bayesian estimates of divergence time using "conservative but realistic fossil constraints" have indicated the most recent common ancestor of new world monkeys to have existed between 27-31 million years ago

Most recent common ancestor with what? Catarrhines in general? Whatever, silly wikipedia, make me infer go ahead

1000km closer 27-31mya, so cool.....picture it, a fruiting tree on an eroding coastal or riverine bank.....while loaded down with foraging proto-platyrrhines, it collapses into the drink and with enough high-moisture food to last across the mini-atlantic, away theyre swept, never to return

[darkmaga-returns]

After a week, I think it’s clear that Donald Trump was not engaging in hyperbole when he told the libs: “we will do things to you that have never been done before.” What an incredible line! What a comedian! What a prophet! Many such cases.

Poetry is just a line that sticks in your head—and while bad politics is bad poetry, good politics is good poetry. Politics and religion are brothers; and comedy is the cousin of both. Every prophet is a comedian. Every comedian is a prophet. This is Hallmark stuff—everyone should know it.

I was talking to a very worried lib a couple of months before the election. I was like: dude, remember that full-page huge-point headline in the Times? “WHEN DONALD TRUMP SAYS… [long list of hyperbolic threats to libs and libbery] BELIEVE HIM.”

I was like: Trump University? Trump Steaks? And, let’s not forget, for the intellectual right of 2017—the great Ann Coulter’s epic literary fumble, “In Trump We Trust”?

As a writer, after 2020, the idea of trusting Trump to execute (as opposed to his talents as a comedian, prophet, etc) was like… it was like putting your savings in TrumpCoin. Has the man changed? Do men change? And yet—

All the Bayesian logic went one way. A bullet went another. So did history. So much for Hari Seldon. Somehow, as too often happens, I was wrong, but not exactly surprised.

[ramrodd]

Great-Grandpa Joe | Ex-Presidents Salute Jimmy Carter | Denmark Claps Ba...

COMMENTARY:

The Problem: Part 1 and 2 of 2 These wildfires reflect two distopian consequenc3es of Project 2025 and Christian Nationalism, The inability of the LAx fire fighters to contain the fires is a direct consequence of the "starve the beast" agenda of Grover Norquist and the Supply Side economics of Project 2025 that has diver453e capital from the general welfare to finance the tax subsidies for the Standford-Silicon Valley axis of Oligarchs like Elon Musk, Mark Zuckerberg, Peter Thiel, Jeff Bezos and, of course Donald Trump. The scorthed earth left by these wildfires is a metric for the financing of the executive compensation of Project 2025 Fortune 500 CEOs wo oppose DEI performance technology, However, the spark for these wildfires and extreme weather associated with it and since at least 1997, when GW Bush began to enlarge his body count on the Texas death row as part of his hupermasculity campaign for the White House is the spiritual warfare being conducted by the Pro-Life, Proud boy Calvinism of the Christian Natinalism The  constant social agitation and deliberate polarization by the Pro-Life Evangelicals assocaiated with New Gingrich's GOPAC poltical strategy based on Trotsky's insurgence process he copied from the anti-war strategy of the campus radicals during the 60 is driving the spritiual warfare that manifests as extreme weather. Now, you either believe this JEsus shit or your don't, but the collective will of the people  directly influences the output of the Demiurrge associated with Genesis1:2. also known as The spriti of God. When the storm clouds began to glock out the sun at noon during Jesus's crucifixtion decrived in Mark 15:33 was a weather system that was feeding on the grief and anguish of the Jesus Followers in Jerusalem for Passover when they learned of the arrest and crucifixion of jesus after the God Spell, Dead Head celebration of the prosession form Jericho which officially began whenBlind Bartimaeus Receives His Sight in Mark 10and ends with the Triumphal Entry of Palm Sunday in Mark 11 turns to sorrow, fear and angerm at noon on Good Griday, You either believe this shit or your don't  I am here to say it is absolutely true, The Demiurge is an actual phenomena in the global ecology of Mother Earth and is capture perfect in Forbidden Planet as the Plannetary Force that feeds of the Id of mankind, It loves lynch mobs, WWE cage matches, and the Olypic Games when the Olypic Flame is buring, If you want to believe Bart "Giggles" Ehrman, Jimmy Tabor and the Jesus Seminar taht it is all mythism, you are disarming your self against the malevolent potential of Genesis 1:2. The power of the Arc of the Covenant and the power that flows out of Jesus to heal the woman with the chronic hemorage in Mark 5:25 - 34 is what Gnostic religons try to control by logic and it was probaly as gnostic assassination the unleached the micro burst that sank the super yacht  Bayesian, Some evil wizard has actuall agency over this stuff, but the extreme weather that triggered the LAX wildfires is part of the spirutal warfare being warged by the Proud Boy Calvinism of  Christian Nationalism as the Pro-Life element of Pro=Ject 2024. The Holy Spirit has agency over the Spirit of God and can manipulate the Demurge  like a house hold appliance withou the unintended consequences of gnostic intervention. When Jesus said the only unforgivable sin is to deny the Holy Spirit, what He meant was to emply him consciously to domesticate the not-sentient Spirit of God. Phe Pro-Choice Liberation Gospel of Cornelius and N.T. Wrught;s versuib if Oaykube Tgeikigt represents a Druid Chritology that easily neutralizes Part Ehrman's Chaple Hill Campus Crusade for Apostasy and the bogus Pro-Life Salvation Gosple of Christian Nationalism,  Be like Jesus and submit to the Epicuriean Equity of Socrates or the Stoic Equity of a well regulated militia and the authoiry of Matthew 8L9 and let nature do the rest.

[positively-knotted]

Fuck it, full list + review:

First year

Linear Algebra: easy, boring.

Group theory: marginally harder, significantly more interesting.

Real analysis: one of the hardest, but only because you do it right at the start. Really one you only appreciate once it's over.

Probability: I really enjoyed this actually - not too hard if you're ok at analysis.

Statistics: it's like they took probability and took out the interesting parts.

Intro calculus: mostly very very boring, but some neat problems I guess. Also badly named, this means intro to differential equations.

Multivariable calculus: honestly one of the easiest courses I've taken. Slightly more interesting than intro.

Fourier analysis: terrible course, only taught for applied people. Everyone else should be allowed to wait until they've done functional analysis.

Geometry: mostly linear algebra tbh, with some random calculus problems thrown in. Fine, but felt very thrown together.

Dynamics. This was the hardest course I ever took. Wtf was happening. How did I get a first in this. I had no idea what I was meant to do at any point.

Algorithms: can you learn an algorithm and apply it by hand? Then you can pass this course!

Second year:

More linear algebra: Spectral theorem is useful, otherwise by far the easiest second year course.

Ring theory: vital for any pure mathematician. The course was very hard, but mostly because the lecturer was the kind of person to define a subring as "an injective morphism" to second years. Modules are cool tho.

Complex analysis: also very very hard, but mostly because it was badly taught. I see why people like it; I didn't.

Measure theory: the end of real analysis! Nice to finally define an integral, and definitely nicer arguments than other analysis courses. Overall fun if tricky.

Metric spaces: sick. It was taught by Ben Green. Need I say more?

Topology: I am doing a PhD in topology, so very biased. You spend a lot of time doing fairly boring analysis-y stuff, but the payoff is great.

More differential equations: this was fantastically taught and actually very fun, although partly because I was good at it. That said, actually solving the damn things wasn't always that fun compared to the theory.

More probability: Markov chains are cool and also just easier than everyone thinks they're going to be? Ended up being my best second year exam somehow lol, but fairly mid-tier for interest.

More statistics: I only took this because I felt I should know Bayesian stats. I have forgotten Bayesian stats.

Quantum theory: did you know that everything is a Hilbert space? And do you know your trig identities? If yes, you might like this course! More seriously, this is just "intro to Lie algebra representation theory" but they don't tell you that.

Short courses (more group theory, number theory, projective geometry, multivariable analysis): these courses were badly designed so no comment

Third year

Representation theory: sick. Do this. It's just algebra but done better.

Commutative algebra: ill. is how I felt. Don't do this. Well do it's very important in pure maths but make sure you find a good teacher. You probably should do it though I guess.

Galois theory: everyone interested in pure maths should do this, but personally I hated it. I do not care sufficiently about polynomials.

Algebraic number theory: if you care about numbers, this is cool. I found it fairly easy/boring since it wasn't aimed at people who'd done as much algebra as I had, but was nice to see.

Surfaces: a weird sort of intro to classical differential geometry, focusing on smooth surfaces and Riemann surfaces. It was nice and very easy, but the course was very weirdly designed imo. Other unis also seem to have similar courses though, which confuses me, since I feel it makes more sense to just teach general manifolds then Riemannian geometry, and use surfaces as simple examples throughout.

Algebraic curves: massive overlap with surfaces since both needed Riemann surfaces but neither was a prereq for the other. Then also covered all of projective geom, and rushed through the interesting stuff. Having now relearnt it though, it's super cool and I would recommend to everyone pure or not.

Baby AlgTop: basically Ch0+1 of Hatcher, dealing with cell complexes and the fundamental group. Everyone should know what the fundamental group is, but tbh I don't think everyone needs to sit through a course that proves the simplicial approximation theorem.

Functional Analysis: quite easy if you have finally internalised the lessons that undergrad analysis was trying to teach you, very hard if not. Basically did everything you've already seen more generally, imo should be compulsory.

More Functional Analysis: this time it's topology! Seriously though. Do it if you like topology, otherwise just trust people.

More quantum theory: this time it was "intro to Lie group representation theory". Then it became perturbation theory and I stopped going.

Master's year:

All of these reviews will be useless because the masters I did was weird.

Homological algebra: why was this taught before category theory??? Useful tool, but a hard course. Especially before category theory.

Category theory: should be compulsory for pure mathematicians. Also should be an undergrad course, since all my other masters courses assumed you knew basic category theory. (And so did some 3rd year algebra courses).

Algebraic geometry: I dropped it after 3 lectures bc the lecturer was bad. But if you have a good lecturer, maybe it might not be? Im unconvinced.

Proper Algebraic topology: the classic course covering Ch2+3 of Hatcher. If you like pictures and sign errors you should do it. If not, you probably still should.

Manifolds: this could also be an undergrad course tbh. Do you love vector bundles? You should love vector bundles. I love vector bundles. De Rham cohomology is underwhelming though, sorry @lipshits-continuous.

Lie groups: I think there is no good way to teach Lie groups to geometers. At least to me. I have absolutely no idea how I got 70% in this exam I did not deserve it.

Riemannian geometry: my best exam ever I think, somehow. It's kinda just analysis, except for geometers so there's much more handwaving and fewer δs. It's pretty boring at points, but the interplay between topology and curvature is fascinating imo.

Low-dimensional topology: this is now my PhD, but also the course was atrocious. Do with that what you will.

Uhh that was a good use of time while I waited for my rice to cook

Math enthusiasts of tumblr. What math subjects have you studied and which ones were your favorite? Which ones were your least favorite? Which ones were the hardest?

[tropylium]

Seen recently: a very interesting example clearly formalizing a type of complaint I would have about Bayesian inference. It's a kinda simple process if we take priors and posteriors as point probabilities, but if we try and model also uncertainty… then it's the modelling of tail risk that will dominate what actually happens with unexpected information.

You can probably see how this will in practice couch out to reticient disagreements about all sorts of stuff; if A thinks that say a terrorist attack is a statistical one-off fluke event from a thin tail, while B thinks it represents simply a usual instance of a relatively thick tail, they're going to end up with noticably different conclusions — even if we assumed them to be perfectly rational agents who agree about every observable fact about the issue.

Made all the worse by the fact that, by definition, tails are what we receive little information about and thus, in many situations, must rely on priors instead.

[max1461]

In most applications I think Bayesian reasoning is not that useful in everyday life, but I do think it would be pretty effective a strategy for like, planning the perfect murder. When people talk about committing the perfect murder they always come up with all this elaborate stuff like "oh we're gonna dissolve the body, blah blah", but the thing is, a ton of murderers don't get caught, and there are widely available statistics on every conceivable type of murder and just how likely it is to get solved. By going through all these statistics, you could not only plot a murder with a very low probability of getting caught, but get a quantitative estimate of just how likely you are to get caught and rationally weigh that against the expected pay off.

Someone should write a ratfic whodunit about this.

[captainmdhridoyhossain-blog]

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[montecarloedexistence]

A Bad attempt at explaining Asteroseismology

So, starting off, it’s Asteroseismology. Not Astroseismology. Be careful not to forget the e, otherwise you’ll struggle to find relevant papers Which is exactly what happened to me when I was looking for resources for my summer project.

Anyways I’ve got to start summarizing my work for a report so I thought I’d write it out here in a tumblr post, and then edit this to be more formal in the LaTeX document.

So, Asteroseismology. It’s basically looking at stars for Surface Oscillations, and trying to figure out the internal structure. How does that work you might ask?

Well, surfaces of stars oscillate for LOTS of reasons. But as the surface expands and contracts, the luminosity of the star changes, and with nicer and nicer telescopes, you can start measuring them with extreme precision.

Now the surface of a star can expand and contract for many reasons. Cepheid Variable Stars for instance, they’ve got their atmospheres acting up like a 4 stroke engine and they pulsate over time.

But most stars don’t do that. They’ve got a generally turbulent atmosphere, where the plasma behaves in Extremely weird ways. (Look up the Solar Magnetohydrodynamics for that). But you’ve got Plasma, which is basically a whole bunch of charges, moving around randomly. Now the random movements of charges makes more magnetic fields which move the plasma in more weird ways. Which sometimes leads to explosions. And like setting off an Explosion on the surface of the earth leads to seismic waves, similar process happens and you’ve got waves propagating through the star.

These sources of the waves are pretty random, but happen all the time. Smart people call that Stochastic Oscillations.

Now, the structure of the star can be broken into three regions largely.

The Atmosphere. Basically Gas and Plasma. Energy moves around through Convection

The Radiative Zone: Basically the energy moves around through Radiation. The gravity here is so strong the gas molecules are held together like it's basically a solid.

The Core: This is where the energy generation happens. It's still under EXTREME pressure and basically solid, but you've still got stuff moving around enough to fuse elements to make energy.

Now, we have an explosion, and waves traveling through the star. And the inside of the star is basically like a solid sphere. So you've got Waves traveling in 3d Space, with the boundary conditions being a sphere. Some waves constructively interfere, some destructively interfere, and you're just left with a few resonant frequencies that oscillate and can be easily detected.

Now the resonant frequencies that oscillate will change depending on the internal constitution of the stars.

How is research generally conducted here?

Well, you take a supercomputer and build a model of a Star, with Pressure, Temperature and density at each layer, varying the composition at the center of the star. And then you model how the observed resonant frequencies will change with the different internal compositions.

Once you build like a LOT of such models, you then look at what you've observed of a star, it's temperature, radius, brightness and resonant frequencies, and you use Bayesian Statistics and tell "Okay, given these properties you see on the surface, and these many models we've got, it is LIKELY the inside of the star is going to have this composition."

So yeah, that's about what I learned this summer, without using any maths on here. I think I have a better idea on what to put in the report now.

Pls wish me luck on writing the report now kthanxbie

[bambamramfan]

It's always fun when my replies prove for me "some people are absurdly upset about this." You should read them.

Bruh if you can't tell those images are AI at first glance that says a lot about you...

To be clear, I consider this "debate" so far beneath discussion that it's just a joke. But it's also my rule of thumb that "the side who avoids mentioning the object level is the one to be skeptical of." Ie., if someone says "it's unbelievable what will get you canceled these days" and an opponent actually quotes the offense, well, there's a good Bayesian prior for who was acting more egregiously.

So here's one of the stills

No, I could not "tell at first glance" that was AI. Now, some people on twitter inform me that when you know what to look for - asymmetry in the eyes, etc - it becomes obvious. But it sure wasn't obvious to me, especially if it was a split second during a movie (caveat, I have yet to see the movie.)

But even as I agree "AI art = bad", this shows how much the anti movement is becoming puritanical and obsessed. They sound just like the TERF's who say it's obvious how an image of any particular transwoman is not a """real""" woman - and both groups are wrong half the time, lumping original art and slightly mannish ciswomen in with the "fake" stuff they hate so much. And then it becomes a sin merely not to see what is "obvious" to the paranoiacs.

Or maybe I am blind and the above image is obvious to anyone, enough to ruin their movie going experience. I guess that makes my ignorance blissful.

It says a lot about me.

"Late Night with the Devil" is a horror movie releasing tomorrow about a 70's late night show that has been highly anticipated by the indie film scene.

That is, until reviewers discovered that 3 title cards during the movie were AI generated art. (I couldn't tell myself when I saw the images, but if you look closely enough the telltale signs are there.) Now the same people who were championing it, are boycotting it. I'm not kidding.

These are from the same community that if you ask about a movie by Roman Polanski, Woody Allen, or Harvey Weinstein, talk about "separating the art from the artist." I'm not calling them hypocrites - these are apples to oranges - but the scale of the difference is very funny.

I'm not a fan of AI art, at least in its current incarnation, which promises to replace quality, adequately paid art with industrial slop at a mass scale. I get drawing a line and trying to defend the line.

If anything, it reminds me of tumblr and fan fiction communities. The way the sharpest knives in identity politics aren't out for Republicans and white men and grey tribers - no these days they are wielded against authors who have five intersectional flags but offend against a sixth. Because you can't hurt the mega-establishment, but you can hurt the queer POC author next door.

Which just makes the insular progressive communities hellscapes without proportionality.

No enemies but the in-in-in-in-in-group.

[art-of-mathematics]

Interesting... One of my approaches to correct my cognitive processing via metacognition are very similar... The concept I could finally map fairly detailled some weeks ago, and reading articles on Quantum Bayesian Optimization now. .. well, I see very similar patterns, even with incredible amount of detail considered in both realm...

Emergent properties of error-correction algorithms in non-linear dynamical information systems (as form of self-organization)... could explain the similarity between cognition's underlying non-linear processing patterns - and quantum computing/ quantum information flows / quantum logic in general.

[max1461]

you know what? honestly. everybody thinks its some XYZ because of society, and shit, and expectations. I say "well it's Q" and because of society, and expectations, and social scripts, and bayesian priors, and WHATEVER, people think "oh, Q must be XYZ". well it isn't. at least I don't think. you don't know me, you're guessing, and you're guessing wrong. I'm not like that, that's not the thing going on with me, I'm completely different than all that stuff your imagining. it's a totally different thing. whatever.