Posts tagged with mass

@tdhopper posted his self-measurements of weight loss

image

a few months back. I recently decided also that I wanted to lose fat-weight—the infamous “I could stand to be a few kilos lighter”—and I think I came up with a more productive way of thinking about my progress: I’m not going to look at the scale at all. I’m just going to count calorie estimates from the treadmill estimator or use online calculators for how much is burned by running / swimming — and calories burned is the only thing I will use: no attempts at eating less.

 

Also, instead of thinking in terms of weight I’m going to think in terms of volume. Here are some pictures of people holding 5 pounds of fat (2¼ kilos):

http://www.realfitnesscoaching.com/wp-content/uploads/2013/09/100_3417.jpg

http://weblogs.sun-sentinel.com/features/health/theskinny/blog/fatblob.jpg

As you can see this is a large fraction of a person’s flesh, if their BMI is in the healthy range.

I’m not so fat that I have tens of litres of fat making up my body. Rather if I look at myself and visually “remove 2 litres” that “looks” like it would be very substantial—such a huge volume that, of course it would take weeks of diligent exercise!

But as we know from Mr Hopper’s posts (or I know it from my own experience of weighing myself), the noise is louder than the signal.

The magnitude of daily variation swamps the magnitude of “fundamental” progress.

 

The goal of counting kcal burned and thinking in terms of volume is to make both the goals and the progress feel more visceral. Everybody knows how to lose weight, the problem is just that one doesn’t do it. Other than simply increasing self-discipline or increasing the mental energy I put towards this goal (neither of which I want to do).

  1. More accurate measurement of my small-scale progress and
  2. Choosing meaningful goals in the first place—not a number grabbed out of the air (“five kilos”—why five?), but rather imagine how much volume has left my muffin-top and how much volume is left—whilst still carrying with me the “larger numbers” associated with kcal fat-loss, than the “small numbers” which characterise litres (gallons ~ 8 lbs) of fat loss.

Here’s my mathematical model of why this is hard in the first place:

  • I take about 100 measurements at roughly the same time but not exactly timepoints <- 1:1e2 + rnorm(1e2,sd=1)
    image
  • the natural variation in weight, in the unit scale of [kcal stored by fat] is on the order of kilos daily.variation <- 1e5 * sin( runif(1,min=-pi/2,max=pi/2) + timepoints)
    image
  • even if I subtracted off my daily fluctuation pattern (Mr Hopper does this by weighing himself at the same time every day), there are apparently other noise factors on the order of half a kilo or perhaps .1 kilo other.variation <- 1e4 * sin( runif(1,min=-pi/2,max=pi/2) + timepoints)
    image

  • the “underlying phenomenon” I’m trying to measure is perhaps on the order of .01 kilos lost per day. Let’s say I lose 1 kilo in 3 weeks, that would be 8000 kcal if I’m good. (i.e., I actually do my workouts and I don’t eat a compensatory extra 8000± kcal). I could model the underlying fat loss as a step function to be more truthful but I’ll use a linear model, saying I lose 100 kcal per measurement (supposing I measure 3 times a day) rather than 700 kcal every time I work out, which is not once a day (that would be the step function). But the catch is, I’m not sure if I’m compensating by eating more. My statistical task is to estimate B, in other words to distinguish if I’m losing weight or not, and how fast I’m losing it (in kcal units, leaving the conversion 8000 kcal ~ 1 kilo as an afterthought), from the signal-swamped data. B<-rnorm(1,mean=100,sd=50); trend<-−B*timepoints
  • Now my job is to estimate B. Is it even positive? (i.e. am I actually losing weight?) In R I just made the variable so I could print(B) but the point is to model why it’s hard to do this from my real data, which is the sum data <- daily.variation   +   other.variation   - B*timepoints
    image
  • This is why I like my idea: measurements of kcal burned on the treadmill is 1000 times more precise than measurements of my bodyweight.

So my overall system is to do “chunks” of 7000 kcal = 1 kilo of fat or 3500 kcal =1 pound of fat. I can stand to do 500–700 kcal per cardio session—about an hour. (I also do an extra +1 kcal for every minute it took me to penalise for low speed: exercise crowds out normal metabolism.) Then it becomes a “long count” up to 3500 or up to 7000. That means 5 cardio sessions (of 770 kcal each) to get up to 1 pound of fat-loss, 7 wimped-out cardio sessions (of 550 kcal each) to reach a pound, and so on. It’s easy enough to “count to 5”. This system makes each one of the 5 be significantly large at the order of magnitude appropriate to convert kcal of exercise to litres of body volume.




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)




Why the scientists aren&#8217;t combining data from two experiments to get 5-sigma evidence (= &#8220;proof&#8221;) for the Higgs boson

The Higgs field was postulated nearly 50 years ago, the LHC was proposed about 30 years ago, the experiments have been in design and development for about 20 years, and we’ve been taking data for about 18 months. Rushing to get a result a few weeks early [would be dumb].


The reason we have two experiments at the LHC looking for the Higgs boson is because if one experiment makes a discovery then the other experiment can confirm or refute the discovery. This is why we have both D0 and CDF, both Belle and BaBar, both ATLAS and CMS, both UA2 and UA1

Why the scientists aren’t combining data from two experiments to get 5-sigma evidence (= “proof”) for the Higgs boson

The Higgs field was postulated nearly 50 years ago, the LHC was proposed about 30 years ago, the experiments have been in design and development for about 20 years, and we’ve been taking data for about 18 months. Rushing to get a result a few weeks early [would be dumb].

The reason we have two experiments at the LHC looking for the Higgs boson is because if one experiment makes a discovery then the other experiment can confirm or refute the discovery. This is why we have both D0 and CDF, both Belle and BaBar, both ATLAS and CMS, both UA2 and UA1


hi-res




As every sci-fi geek knows, matter may travel faster than the speed of light as long as its mass is imaginary (a multiple of √−1). A so-called tachyon would not overturn special relativity—and it would provide a handy way of resolving any conflicts in a given Star Trek plot.

  • 14th Law of How to Write Star Trek: Whenever you’ve written yourself into a hole, instead of re-writing the show so that it’s better, simply make characters issue the word “tachyon” several times toward the end. Everything is magically resolved, returning all aspects of life to the way the show started with no long-term consequences for the characters—which by the way is a great lesson to teach to young adults—and then Spock or Data has an “a-ha!” moment wherein he throws around jargon to further justify the deus ex machina.

The only problem with tachyons, as any sci-fi geek can attest, is that “imaginary” mass is pure fiction! How could anything weigh an imaginary amount?

 

Well, I’m not sure that tachyons do exist—although if someone wants to post some arXiv links to relevant papers that would be awesome—but, I will say that “imaginary mass” isn’t that ridiculous of a concept.

As Tristan Needham said in the best book about complex numbers ever, the “imaginary” descriptor only reflects the historical prejudice against √−1.

Do imaginary numbers exist? No. But neither do counting numbers. Numbers are linguistic entities that humans communicate with. Sort of like how trees, flowers, bushes, shrubs, brambles, and vines all exist in nature, but those classifications, concepts, words, groupings are human-language mental constructs. “Five” doesn’t “exist” per se, but mathematical models built with the-thing-that-satisfies-the-properties making five five, do wonderfully at prediction of physics experiments.

Anyway, imaginary numbers exist just as much as other numbers. Just like rational numbers, they’re generated by an operation that comes up as a matter of course in algebra. And algebra seems to have something to do with nature. God knows why. (ohh! which way did I mean it?!)

So I’m not saying imaginary mass exists, but here are some good ways to think about imaginary numbers.

  • imaginary numbers are twisted numbers
  • imaginary numbers are phase-shifted like a sine wave versus a cosine wave
  • an imaginary current heats up a wire but does no useful work

If the mass of a particle is an imaginary number, then … that might help you make sense of tachyons.

 

Nerdy side note: E=MC² is not the real equation to describe the conversion of energy into matter or vice-versa.

  • E=MC² tells you how to convert stationary matter into energy.
  • The real equation is E² = [mc²]² + [pc]².
  • (p is momentum.)
  • (Notice that the real equation is of the form A²+B²=C². i.e., Energy is the hypotenuse (C) to the triangle sides B=mc² and A=p•c)

You can casually start/interrupt conversations with this knowledge the next time you attend a kegger / black-tie affair. Doing so will win handsome glances from potential sex partners. Also, there is a 0% chance that anyone will think you’re an insufferable know-it-all.