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I cringe whenever an old person asks a young person "What do you want to do in life?" As if the answer could ever be simple. I’m sure I can’t remember everything I ever thought I might want to do but failed to. (And I’d guess it’s the same for most people.) Each of the above represents a potential alternative history now, and at the time, a superposition.




In the Public Encyclopedia’s (present) discussion of the hypothetical existence of a magnetic monopole

http://upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Em_monopoles.svg/1000px-Em_monopoles.svg.png

in nature, among the possible fundamental particles, exemplifies both (and maybe >2) “sides” in the debate over what probability means:

Magnetism in bar magnets and electromagnets does not arise from magnetic monopoles, and in fact there is no conclusive experimental evidence that magnetic monopoles exist at all in the universe.

Since Dirac’s 1931 paper[8] , several systematic monopole searches have been performed. Experiments in 1975[10] and 1982[11] produced candidate events that were initially interpreted as monopoles, but are now regarded as inconclusive.[12]Therefore, it remains an open question whether or not monopoles exist.

Further advances in theoretical particle physics, particularly developments in grand unified theories and quantum gravity, have led to more compelling arguments[which?] that monopoles do exist. Joseph Polchinski, a string-theorist, described the existence of monopoles as "one of the safest bets that one can make about physics not yet seen”.[13]These theories are not necessarily inconsistent with the experimental evidence. In some theoretical models, magnetic monopoles are unlikely to be observed, because they are too massive[why?] to be created in particle accelerators, and also too rare in the Universe to enter a particle detector with much probability.[13] (According to these models, there may be as few as one monopole in the entire visible universe.[14])

http://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Em_dipoles.svg/1000px-Em_dipoles.svg.png

Here are a few potential explanations of how one is to arrive at a probability number:

  • opinion — it’s just Joseph Polchinski’s opinion
  • frequentism — Europeans never observed a black swan before exploring the New World, therefore black swans have 0% chance of existing.
  • frequentism + how hard you’ve searched — the probability comes attached with a confidence number. If you’ve stayed within the city limits of Minneapolis your entire life, you should attach a low confidence to your search for tarantulas the size of your head. But we’ve tried very hard to find monopoles, and haven’t. So a “more confident” zero on that one.
  • Dutch Books — could we arbitrage Joseph Polchinski’s “sure thing” bet?
  • authority, credibility, expertise — who exactly is this Joseph Polchinski character, anyway? And who says he’s such an expert? Is he an interested party? I don’t believe what vested interests and biased sources say, even if it happens to be true.
  • propensity — good gravy, I don’t even get to invoke the famous “coin has an innate propensity to tend to certain heads/tails ratio” because it would get us nowhere in terms of “Do monopoles have a propensity to exist or not?”. Anyway propensity merely passes the buck even in the cases where it does make sense.
  • reason & facts — there is no conclusive evidence that monopoles exist, yet they haven’t been proven impossible. I will withhold my opinion and it would be unreasonable to assign a probability mass to either alternative. We’re simply somewhere ∈ [0%, 100%] at this time.
  • model strength — some of these models sound suspect. It’s constructed “just so” that there’s only one monopole in the universe? Very convenient for you, when you want to say monopoles exist and we just haven’t seen them yet. Pull the other one!

image
All of the stochastic maths is done with the Kolmogorov axioms, i.e. it’s done with measure spaces with a fixed | finite | constant measure (= 100% of the probability mass) without connecting that to “how likely” a one-off event is. (Much like some maths you could pass off as financial modelling “is just" the theory of martingales = fair repeated bets.) But it needn’t have be called “likelihood”, it could have been “fuzzy truthiness” or “believability” or “motions of a fixed-volume-but-infinitely-divisible liquid”. As Cosma Shalizi puts it here:

Probabilities are numbers that tell us how often things happen.

Mathematicians are anxious to get on with talking about ergodicity, Markov transition matrices, and large-deviations theory. What you’re seeing in this block quote is the handoff between mathematicians and philosophers—essentially the mathmos say “You take it from here to the firm foundation” and philosophers, so far, haven’t been able to.

 

Is there a problem in practice due to not having a sound foundation on our concept of probability? Yes. It’s not secure to move forward with the rear flank uncovered. The lax attitude toward probability and “We’ll do the best with what we can” lets us make up numbers for the {pessimistic, neutral, optimistic} scenarios of our forecasting spreadsheets.

Think about when some consequential decision by a powerful group depends on the value of one parameter. It could be

  • the likelihood of Floridian home prices decreasing by more than 5% in a year,
    image
  • the likelihood of [foreign country X] attacking "us" in response to Y,
  • the likelihood of RHIC creating a strangelet and swallowing the world in a minisecond,
  • the likelihood of construction on the new power plant going over budget,
  • the likelihood of borrowing rates staying this low for another 5 years,
    image
  • the likelihood of real GDP rising at least 2%/year during the next 10 years,
  • the likelihood of our borrowing rate quadrupling
    image
  • the likelihood that your college degree will “be worth it” to you
  • the likelihood of this whole startup thing actually working.
    http://paulgstacey.files.wordpress.com/2010/09/startup_financing_cycle.png

and I get to either rely on

  • historical data (“home prices have always gone up before”, “we haven’t seen any problems with financial derivatives yet”, “correlation with a Gaussian copula has always worked so far”),
  • reason and facts (and multiply an endless debate among the experts),
  • or gut (throw in some numbers that sound pessimistic, optimistic, and neutral, and we’ll see how the forecast behaves).

We got nuthin’.




A tiny portion of Doug Hofstadter’s “semantic network”.
via jewcrew728, structure of entropy

hi-res




The origins of mass & the feebleness of gravity by Frank Wilczek

tl,dr:

  • dark matter & dark energy
  • "Even though protons, neutrons, and electrons comprise only 3% of the universe’s mass as a whole, I hope you’ll agree that it’s a particularly significant part of the mass." lol
  • "Just because you can say words and they make sense grammatically doesn’t mean they make sense conceptually. What does it mean to talk about ‘the origin of mass’?”
  • "Origin of mass" is meaningless in Newtonian mechanics. It was a primitive, primary, irreducible concept.
  • Conservation is the zeroth law of classical mechanics.
  • F=MA relates the dynamical concept of force to a kinematic quantity and a conversion factor (mass).
  • rewriting equations and they “say” something different
  • the US Army field guide for radio engineers describes “Ohm’s three laws”: V=IR, I=V/R, and a third one which I’ll leave it as an exercise for you to deduce”
  • m=E/c²
  • Einstein’s original paper Does the inertia of a body depend on its energy content? uses this ^ form
  • You could go back and think through Einstein’s problem (knowing the solution) in terms of free variables. In order to unite systems of equations with uncommon terms, you need a conversion factor converting a ∈ Sys_1 to b ∈ Sys_2.
  • Min 13:30 “the body and soul of QCD
    http://www.lightnessofbeingbook.com/LOBColorPlates/images/Plate01_ThreeJet.jpg
    http://www.fnal.gov/pub/today/images11/CMSResult042211figure1.jpg
    image
    img_lrg/jet.jpg not found

  • Protons and neutrons are built up from quarks that are moving around in circles, continuously being deflected by small amounts. (chaotic initial value problem)
  • supercomputer development spurred forward by desire to do QCD computations
  • Min 25:30 “The error bounds were quite optimistic, but the pattern was correct”
  • A model with two parameters that runs for years on a teraflop machine.
  • Min 27:20 The origin of mass is this (N≡nucleon in the diagram): QCD predicts that energetic-but-massless quarks & gluons should find stable equilibria around .9 GeV:
    Full-size image (27 K)

    http://www.yorku.ca/lewisr/images/Yspectrum.png
    image
    Or said alternately, the origin of mass is the balance of quark/gluon dynamics. (and we may have to revise a bit if whatever succeeds QCD makes a different suggestion…but it shouldn’t be too different)
  • OK, that was QCD Lite. But the assumptions / simplifications / idealisations make only 5% difference so we’ll still explain 90% of the reason where mass comes from.
  • Computer ∋ 10^27 neutrons & protons
  • The supercomputer can calculate masses, but not decays or scattering. Fragile.
  • Minute 36. quantum Yang-Mills theory, Fourier transform, and an analogy from { a stormcloud discharging electrical charge into its surroundings } to { a "single quark" alone in empty space would generate a shower of quark-antiquark virtual pairs in order to keep a balanced strong charge }
  • Minute 37. but just like in QM, it “costs” (∃ a symplectic, conserved quantity that must be traded off against its complement) to localise a particle (against Heisenberg uncertainty of momentum). And here’s where the Fourier transform comes in. FT embeds a frequency=time/space=locality tradeoff at a given energy (“GDP" in economic theory). The “probability waves" or whatever—spread-out waveparticlequarkthings—couldn’t be exactly on top of each other, they’ll settle in some middle range of the Fourier tradeoff.
  • "quasi-stable compromises"
  • This is similar to how the hydrogen atom gets stable in quantum mechanics. Coulomb field would like to pull the electron on top of the proton, but the quantum keeps them apart.
    http://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Bohr-atom-PAR.svg/500px-Bohr-atom-PAR.svg.png
    http://upload.wikimedia.org/wikipedia/commons/a/a4/HydrogenOrbitalsN6L0M0.png
  • "the highest form of musicality"
  • Quantum mechanics uses the mathematics of musical notes (vibrating harmonics).
  • Quantum chromodynamics uses the mathematics of chords, specifically triads since 3 colour forces act on each other at once.
    image
    image
  • Particles are nothing more than stable tradeoffs that can be made between localisation costs (per energy) from QM and colour forces.
  • (Aside to quote Wikipedia: “Mathematically, QCD is a non-Abeliangauge theory based on a local (gauge) symmetry group called SU(3).”)

  • Minute 40. Because the compromises can’t be evened out exactly due to quanta, there’s some leftover energy. It’s the same for a particular kind of quark-gluon interaction (again, because of the quanta). The .9 GeV overshoot | disbalance | asymmetry in some particular quark-gluon attempts to balance creates the neutrons and protons. And that’s the origin of mass.

Minute 42. Feebleness of gravity.

  • (first of all, gravity is weak—notice that a paperclip sticks to a magnet rather than falling to the floor)
  • (muscular forces are the result of a lot of ATP conversions and such. That just happens to be even weaker—but if you think of how far removed those biochemical electropulses and cell fibres are from the fundamental foundation, maybe that’s not so surprising.)
  • Gravity is 40 orders of magnitude weaker than the electrical force. Not forty times, forty orders of magnitude.
  • Planck’s vision; necessary conversion; a theory of the universe with only numbers.
  • The Planck distance, even for nuclear physicists, is about 20 orders of magnitude too small.
  • The clunkiness of Planck’s constants mocks dimensional analysis. “If you measure natural objects in natural units, you should get something of the order of unity”.
  • "If you agree that the proton is a natural object and the Planck scale is a natural unit, you’d be off by 18 orders of magnitude".
  • Suppose gravity is a primitive. Then the question becomes: “Why is the proton so light?” Which now we can answer. (see above)
    http://www.grin.com/object/external_document.243440/7414ac37090135af37b2813c60318981_LARGE.png
    http://www-cdf.fnal.gov/physics/new/qcd/diphoton_2012/diphoton_xsec_10fb/plots/TXSec_massQLSSV01_07Jun12.gif
    http://cms.web.cern.ch/sites/cms.web.cern.ch/files/styles/large/public/field/image/Fig3-MassFactSoBWeightedMass.png
  • Simple physics (local interactions, basic = atomic = fundamental = primitive behaviours) should occur at Planck scales. (More complex behaviours then should “emerge” out of this reduction.)
  • So that should be, in terms of energy & momentum, 10^18 proton masses, where the fundamental interactions happen.
  • The value of the quark-gluon interaction at the Planck scale. “Smart” dimensional analysis says the quantum level that makes protons from the gluon-quark interactions then gets us to ½, “which I hope you’ll agree is a lot closer to unity than 10^−18”.
  • Minute 57. “A lot of what we know about the deep structure of the Standard Model is summarised on this slide”
  • weak force causes beta decay
  • standard model not so great on neutrino masses
  • SO(10)’s spinor representation has all the standard model’s symmetries as subgroups
  • Minute 67. Trips my regression-analysis circuits. Slopes & intercepts. Affine!
  • Supersymmetry would have changed the clouds and made everything line up real nicely. (The talk was in 2004 and this week, in 2012, the BBC reported that SuSy was kneecapped by the latest LHC evidence.)
  • "If low-energy supersymmetry turns out to be false, I’ll be very disappointed and we’ll have to think of something else."

(Source: mit.tv)




For most people, this:
time-dependent Schrödinger equation
is indistinguishable from this:
Ἐν ἀρχῇ ἦν ὁ λόγος, καὶ ὁ λόγος ἦν πρὸς τὸν θεόν
In both cases, the layperson needs an interpreter.

…[I]t takes years of dedicated study before scientific truth in its truest, mathematical and symbolic forms can be understood. The rest of us rely on experts to explain it, someone who has seen and understood the truth and can dumb it down for us….

The Last Psychiatrist




Life is meaningless, unless you believe otherwise.




Am I a good person? Deep down, do I even really want to be a good person, or do I only want to seem like a good person so that people (including myself) will approve of me? Is there a difference? How do I ever actually know whether I’m bullshitting myself, morally speaking?

David Foster Wallace, Consider the Lobster and Other Essays

Front Cover

(via untilasinglesolitonsurvives)

 

I regard the above quandary as philosophical chaff. Not the kind you separate from the wheat, but the stuff a fighter pilot throws behind his ship to confuse and distract the enemy.

If you go to the soup kitchen, do you expect to see a guy there happily doing the chores because he enjoys helping others — or a dour-faced pissed off person who hates helping others, but does it just because that’s what he’s supposed to do. I’d expect the former.

The right definition of altruism is first-order altruism: if you enjoy helping others.

 

OTOH, the white saviour industrial complex is not helping anybody but themselves. “I work at a non-profit! We do something patronising & impractical & don’t I sound like a good person?!” may be a sign of selfishness, but that’s kind of obvious, right? Anyone can tell if someone is working at a non-profit as a status job, or is concentrating on effective execution, by the way they talk about it. Did they found this non-profit? Did they happen to mention how they speak French and have travelled all over the world at the same time? Ok, then.

As far as donating to non-profits: I freely admit that I do so to assuage my guilt for being born lucky. So what? I don’t think people receiving the aid felt patronised by that. So what’s the harm and what would be the “pure” motivation for giving anyway? If you give to an effective organisation that’s what matters.

There’s nothing wrong with feeling good (or even superior) about your choice to do so. If you fed a hundred starving people every day for a year least year, guess what, you are better than me. I look up to you and expect you to look down on me. Of course charities know that the product they’re selling to donors is good feelings, so like anyone pidiendo your plata they are going to pitch you. Well, do your homework and at least find out how much of the benefits go to White People.

Regarding the good feelings from donating money, here’s an interesting thought experiment. What if, instead of donating money to Médecins Sans Frontières, you looked up a random name in Lagos and wired them $100 US = 16,279 Naira. According to this estimate that would be like two weeks to a month’s salary at a good big store job, or 20 expat croissants = 50 breads.

File:Naira notes.jpg

Would you feel good about that? How good? Maybe you could repeat it 10 times, or 100, if you are well off. Is 50 breads going to change someone’s life? Is this where you buy a suit and a shave for a homeless guy and suddenly he’s a self-sufficient success? No, it’s much more like if you paid two months’ rent for someone working in the service sector in the OECD. It’s not going to be life-transforming (and when people receive life-transforming amounts of money, does it transform their lives in a good way?) but it’s quite a decently nice thing to do for someone. The life of one person is going to be quite easier for a while. Are you going to worry about favouritism with your whitey Superquid? Not really, it’s too small to make that much of a difference.

So whatever money donated to a non-profit has to be calibrated against something like that. Even if you bought a million dollar water purification system or a road or something, it’s not going to save the world. But it is a nice thing to do and maybe your kindness can be multiplied by three if you take advantage of some currency weakness. (And of course, if 100 million rich people did the same thing it would have 8 orders of magnitude greater effect/spread. But that is like creating a worldwide market versus being one customer. One customer doesn’t matter.)

It’s pretty much the same scale as the rest of life (maybe bonus 1 order of magnitude in case of vast currency differences). Picture a rich white man supporting several people (wife & kids) for 20 years on his big salary. That takes his entire dedication. And someone who can support a mistress or 5 kids in big-city lifestyle is extremely wealthy. Now consider that as a donor you’re not going to take people into your fold and make them your life, but instead are sending one-off payments (subtract 2 orders of magnitude) that hopefully don’t hamper your fun times too much (subtract 2-3 orders of magnitude). Yes, it’s nice, and yes, it’s even better if most rich people do it. But no, it’s not going to transform 100,000,000 lives — that is too many orders of magnitude above one person’s power.

Finally: I don’t pretend to understand poverty. I am a fallible human and I’m sure anyone who end-benefits from my donation doesn’t think of me or other donors as superheroes. I judge anyone who reads books/magazine articles and then tries to act like they know about “Africa" or "development" or whatever. Rich expats who live in developing countries always have a different opinion, surely more informed, but I’m not sure if the view-from-the-mansion is totally trustworthy either. Bill Easterly, a development economist, says nobody has really figured it out and the best you can do in donating money is try to make sure it [1] does no harm, [2] isn’t wasted. You are not going to socially transform jack. I think accepting my own fallibility, ignorance, and selfish impulses is a critical part of the honesty that makes me not a patronising, egotistical Saviour. Yes, I’m aggrandising myself in saying this.

(Source: entropy-entropy)




What is mathematics? It’s neither physical nor mental, it’s social. It’s part of culture, it’s part of history.

It’s like law, like religion, like money, like all those other things which are very real, but only as part of collective human consciousness. That’s what maths is.

Reuben Hersh, interviewed by John Brockman

emphasis mine. via davidaedwards

(Source: edge.org)




from “On Self-Referential Sentences” by Douglas Hofstadter, originally in Scientific American (January 1981), reprinted in Metamagical Themas (1985)
via crystilogic




The ontological commitment of a sentence is whatever must be among the values of bound variables for the sentence to come out as true.

Willard van Orman Quine

I bring up this quotation not to agree or disagree with Quine, but just to point out the connection between everyday language and mathematics. The connection is well-known in some circles — like,  anyone for whom the phrase “possible world semantics” rings fifty different bells.

If you’re not schooled in such stuff, just notice this: Quine is talking about regular declarative sentences in natural languages, yet using the word “variables”.

One reasonable conclusion to draw is that, through the machinations of Analytical-Philosophy-Of-Language, the reach of mathematics can extend very, very far. How useful is stuff, anyhow? What if mathematics appeared in every declarative sentence you wrote or uttered?

(Source: supervenes)