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Posts tagged with science

What is the world made of?…There are twelve basic building blocks.

Six of these are quarks—- they go by the interesting names of up, down, charm, strange, bottom and top. (A proton, for instance, is made of two up quarks and one down quark.) The other six are leptons—- these include the electron and its two heavier siblings, the muon and the tauon, as well as three neutrinos.

There are four fundamental forces in the universe: gravity, electromagnetism, and the weak and strong nuclear forces. Each of these is produced by fundamental particles that act as carriers of the force…: …photon…graviton…eight…gluons…three…W+, … W- , … Z.

The behavior of all of these particles and forces is described with impeccable precision by the Standard Model, with one notable exception: gravity.

Alberto Güijosa




Lawrence Krauss, author of A Universe from Nothing lecturing on cosmology.

  • Don’t really agree with or like his monolithic straw-man representation of “religion” versus “science” at minute 6. “Religion pretends to know all the answers” .


    Sub-i, sub-j, larry. There are many religions and many sciences.
  • Minute 14. Edwin Hubble’s original data! straight-line plot through a bunch of dispersed points. “That’s why we know he was a great scientist” — nobody laughed in the tape, but I did — “he knew that he should draw a straight line through a cloud of points”. I also love it when people take the time to go through an old paper, pull things out, and present them anew.
  • I have never understood the business of standard candles. To me it seems like you have two degrees of freedom (distance and brightness), only one of which can be knocked out by the measurement of apparent brightness.

    So say we figure out a “standard candle” — a star with a particular colour signature that tells us “The star is at X phase of its life, is made up of Z, and such stars always shine at a constant brightness of 1 for Q million years.”

    But still — how do we know that our theory is right? How do we know, know, know that  it’s really brightness of 1? It’s not like we can triangulate. And it’s certainly not like we’ve been there and seen it first-hand.
  • I had the same problem in a discussion with a geologist a few months ago. I sometimes get the sense that working scientists are so immersed in the practical fact that, yes, for all intents and purposes we know X to be true, that they’re not willing to step back to an abstract, philosophical level and say: “Well, if you really keep pulling on the threads, there are assumptions at the bottom of everything, so yes, we really don’t absolutely know X to be the case. However, Philosophical Prig, we don’t really know we’re not living in The Matrix either! So hush up and get back to doing something relevant.” But that’s the kind of answer I really want to hear: no, we don’t know know know, but for all practical purposes, yes we know.
  • Minute 15. How old is the universe? So Hubble got the answer wrong in 1929, and it was obviously wrong. “Scientists don’t know what they’re doing”

    But I had the same reaction to people talking about dark matter in the 90’s. “What is this stuff we call dark matter? Or dark energy?” As I understood it at the time, “dark matter” just represented a 90% fudge factor in astronomical measurements. It could be that gravity or quarks or anything else about the laws of physics is simply different in other parts of the universe. And how would we rule out that hypothesis? We just rule it out by assuming that the laws of Nature are the same everywhere, because that’s what we’ve assumed for the last few hundred years and it’s always worked out. Straight-line extrapolation to “That assumption must be true now and everywhere” despite that we’re now talking about multiple galaxies so unimaginably far away.
  • Minute 18:30 “This is a Hubble plot, much better than Hubble’s plot. It was made after the discovery that on a log-log plot, everything is a straight line.” Again, no laughs, but I thought that was hilarious.
  • Calculations that estimate the total energy in all vacuums add up to 10^28 times the observed mass of the universe. Whoops.
  • Dark matter here on Earth? Let’s go down into the mines and measure it. (By the way, where would the physicists be if those evil resource-extraction companies in Lead, South Dakota hadn’t negotiated with the legal entities that be and drilled into the Earth’s crust? Way to play it as it lies, Sandia Labs. #scruples)
  • Flat, closed, or open universe? (also why are these the only three options?) Well, we only observe 30% of the mass thta would be required to make the universe flat.
  • A gigantic, gigantic, um, really gigantic triangle — to measure the curvature of the universe.
  • That’s what those microwave-background radiation detecting balloons in Antarctica have been doing.
  • There’s always something there, even when there’s nothing. (see this video of the quantum fields flickering about in empty space)
  • 90% of the mass of a proton is due to the vacuum. (not delta spikes, more like 1/x or exp(−x) integrals.) Therefore your mass is 90% due to quantum fluctuations around the zero point energy.
  • The universe also has a net total energy of 0. Hence the possibility of “a universe from nothing” (our universe needn’t have a Creator since there is enough mass/energy in the physical vacuum that those virtual fluctuations could have acted as a Prime Mover).
  • 70% + 30% = 100%
  • Making our place in the Universe even less special. “Regular” matter—the stuff we observe—is only a 1% pollution in the uniform dark-energy / dark-matter background of the universe.
  • Deep-future scientists (like in a few billion years) won’t be able to observe other galaxies. Measuring the universe, they will observe (correctly) that their galaxy is the only one around, and that there is nothing but empty, eternal space around them.
  • So they will be “Lonely and ignorant, but dominant. Of course those of us who live in the United States are already used to that.”





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Categorial decomposition of Galilean spacetime.

Sean Carroll tells us that it was Galileo who first si rese conto che motion can be separated into:

  • motion in the x direction — ẋ or x′[t]
  • motion in the y direction — ẏ or y′[t]
  • motion in the z direction — ż or z′[t]

and, importantly, that physical laws should be the same for all the 360° × 360° orthonormal choices of (x,y,z). It was Galileo’s idea that you can draw axes, that forces can be decomposed onto those axes, and that forces along one axis behave independently of each other.

For example if you kick a football, it goes forward x′[t], chips up y′[t], and bends left z′[t]. If you kicked it off a cliff, it would retain its exact same forward x'[t] speed even after it dropped y<0 below the plane of the cliff at an ever increasing speed. (NB: That’s not actually true, which is why we say “in a vacuum”.)

 

The traditional way to talk about a path γ is talking in tuples:

  • First, you have some points
  • Then, you have a 3-basis.
  • Then, you have an interval.
  • If you want to talk about kicking the ball, you would probably call the ball a point, say “there is” a vector space tangent to the ball, and your single kick of the ball constitutes a single force-vector applied (instantaneously) to the point, I mean ball. “Then” — by which I mean “at higher values of t∈interval” — the ball “is” chipped up in the air, “then” back on the ground.
  • The path γ is any member of the product (pairing) of 3-basis with interval.

path γ ∈ time × space*

* space in the geographer’s sense; the casual, not mathematical, sense of the word space. Lawvere calls mathematical space a “universe” … like the theoretical universe that the theory lives in

All of this “you have” — it’s a violation of E′. The “false subject” in English sentences that start with “There are” is repeated over, and over, and over again in mathematics (hence the invention of the symbol ∃).

 

Now cometh F William Lawvere, 3 centuries later, with a conceptual breakthrough.

path γ : time → space

The categoryists use labelled dots and labelled arrows to sketch concepts. So in pictures 2 and 3 you can see projection arrows splitting 3-space into a 2-plane (ground) and a 1-line (air). (Arrows sometimes seem backwards in category theory. Galileo projects 3D onto 1D + 2D, so something like “coprojection” would be the natural piecing together of independent sub-motions to get the full picture.)

And the Galileo example is just meant to be a shared thing we can all discuss. But this same thought-pattern — categorial decomposition — I can use on non-chalkboard things from my life as well. Gottman-style 2-eqn relationship dynamics; speculating about some economics in the news; love triangles; the deeper you plant this seed, the more places you see it.

(Source: amazon.com)










Even if science is hellish on the scientists, isn’t it important for society?

Perhaps. But likely not. Science merely offers power — the use of that power for good or evil is out of the hands of scientists.

And as it stands, we have the power to … cure malaria or end world hunger. In a final sense, we simply choose not to. Becoming a scientist will not give you control over how your technology is used. [I]f anything, it is an abdication from [that] responsibility.

Just ask Oppenheimer.

Keith Yost

(Source: tech.mit.edu)




Change Minds and Grow the Economy

Random thought. If end-of-life health care costs eat up 33% of US health care spending = $850 billion, then that means that if you could make people less afraid of dying and more willing to accept it, you would save = make a colossal amount of money. (In fact $850bn = roughly ten years of revenues of US President Obama’s optimistic projection if he raises taxes on the richest Americans.)

In other words, changing people’s attitudes could add 10% to the GDP of the biggest economy in the world.

Random thought #2. If we’re interested in maximising utility across the economy rather than increasing production levels, then perhaps the most important field of research is not bioengineering but the psychology of satisfaction. If you could figure out how to make people appreciate the things they have and not covet the things others have, then gross utility would shoot way up. How much? Billions? Maybe even on the order of the entire economy itself?




Without science, explaining why there is something rather than nothing requires explaining every leaf, rock, beetle and star.

Cosmology and evolutionary theory pare the explanation requirement down … we might have to explain only a physical law or three, and everything else … can follow naturally. … [I]t might be that we don’t have to explain why there is matter and energy, perhaps not even why there is three-dimensional space and time or why physical constants have the values they have.

It is also possible, although harder to conceive, that we could explain everything down to nothing: no physical laws, only logic. Putting that another way, it might be that naive mental pictures of nothing are logically impossible.

Aaron C. Brown, reviewing Why There is Something Rather than Nothing by Lawrence Krauss




[I]n the late 1920’s and early 1930’s…. There were lots of deep thoughts [in economics], but a lack of quantitative results. … It is usually not of very great practical or even scientific interest to know whether the [causal] influence [of some factor] is positive or negative, if one does not know anything about the strength.


But much worse is the situation when an [outcome] is determined by many different factors at the same time, some factors working in one direction, others in the opposite directions. One could write long papers about so-called tendencies explaining how this … might work…. But what is the … total net effect of all the factors? This question cannot be answered without measures of … strength….

Trygve Haavelmo

Bank of Sweden pseudo-Dynamite Prize Laureate 1989, for work in econometrics

(Source: nobelprize.org)




Tachyons

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.




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70 Plays • Download

10:20 “These molecules, in a weird way, have been waiting — all this time — for us to understand them—to get to know them.”

11:30 ”All the attention that we paid to the water would be repaid with beauty.”

11:40 ”How is it that we can all be walking around, pretending that we aren’t going to die? … All of us are walking on a thin sheet of glass, with cracks in it. And I was the only one that noticed.”

(Source: radiolab.org)




[T]he question of what “really” exists pervades the sciences and human thought in general.

The belief that the infinite does not really exist goes back at least to Aristotle. Parrnenides even questioned the reality of plurality and change. (Einstein’s vision has much in common with Parmenides). Towards the end of the nineteenth century an acrimonious exchange took place between Kronecker and Cantor regarding the reality of the actual (as opposed to potential) infinite. Kronecker claimed that only the finite integers really exist and all else is merely the work of man.

Cantor countered that the essence of mathematics was its freedom and that he had attained a larger vision than Kronecker had who could not see the infinite. Most mathematicians have followed Cantor and found his paradise a more beautiful and alluring universe.

…. But this seeing is not explained by modus ponens. In his beautiful book Proofs and Refutations, Lakatos (1976) has shown that the mathematical process itself is dialectical and not Euclidean. At all times our ideas are formally inconsistent. But inconsistency, while still recognized as a pathology, is no longer seen to be a fatal disease. If we come across a contradiction, we localize it, isolate it, and try to cure it. But we have to get over our neurotic phobias concerning this disease and recognize it as inseparable from life itself.
David A Edwards

(Source: math.uga.edu)




3-D fly-through of a supernova, seen in the X-ray spectrum

(Source: youtube.com)




What’s the difference between leaving carbon progeny behind you and silicon progeny behind you? … [W]hat makes you feel that a planet teeming with sexually created successors would constitute a more valid extension of ‘we’-ness than a planet teeming with our intellectually created successors? [robots / cyborgs / conscious machines / strong AI computers]

The question comes down to how we human beings feel comfortable using and extrapolating the term pronoun “we”. Were “we” once languageless squirrel-sized mammals? Did “we” then become primates? Did “we” discover that “we” could use tools? Did “we” begin speaking some 50,000 years ago? Were “we” at that time an entirely agrarian society? Did “we” start living in cities a few thousand years ago? Did “we” discover geometry, algebra, and calculus? Did “we” try out communism for a few decades? Will “we” someday cure cancer? Will “we” someday fly to Mars? … Will “we” migrate into immortal software?

Doug Hofstadter, in Perspectives on Natural and Artificial Evolution

The whole essay (ok, most of it):

grâce à Virgil

 

The story of the primates reminds me of my favourite short story from Cosmicomics. Italo Calvino shrinks the generations of evolution into manageable bites, so that qfwfq, a lizard in this story, has a great-uncle n’ba n’ga who’s still a fish.

Well, you can read it yourself:




Is there really such a thing as a point? Well, not really….

  • Ask any of our undergraduates, why the real numbers? Can you say there’s something √π centimetres away from here?
    —Well, not really, it’s an approximation….
    —An approximation to what?
  • “We’re not really doing science. We don’t have any data, so we’re just indulging our own mathematical and philosophical prejudices. :)”
  • “If a pile of papers appeared on your desk and claimed to be the correct theory of quantum gravity, how would you know?”
  • “All of the standard formulations of quantum theory, whether it’s whatever you want — all of them more or less presuppose the use of standard real numbers. That’s one issue I find very problematic. … That seems to me very dubious.” 
  • Heidegger asked, What is a thing? And answered, on page ~60, A thing is the bearer of properties.
  • From Heidegger’s perspective, there is no ”way that things are”. (due to the Kochen-Specker theorem)

Slides here.




Some pitches sound louder than others. Displayed are equal-loudness curves. Depending how familiar you are with isoclines, they might mean the opposite of what they look like to you. Where the curve dips down, that means that instruments playing that pitch sound louder for their deciBel level. It&#8217;s crazy how non-monotonic these curves are. It&#8217;s like there is a general pattern that higher-pitched instruments sound louder per deciBel, but there are many pitch ranges where the pattern reverses. Strange, right? For reference, here are some of the pitches in that 12k-20k range where some of the curviness happens. Reminds me of the Lab colour scale &#8212; a nonlinear scale which is attuned to how we humans perceive colour, which differs from the linear scales (RGB, CMYK) along which colour &#8220;actually exists&#8221;. Acoustic science, you just blew my mind.

Some pitches sound louder than others.

Displayed are equal-loudness curves. Depending how familiar you are with isoclines, they might mean the opposite of what they look like to you. Where the curve dips down, that means that instruments playing that pitch sound louder for their deciBel level.

It’s crazy how non-monotonic these curves are. It’s like there is a general pattern that higher-pitched instruments sound louder per deciBel, but there are many pitch ranges where the pattern reverses. Strange, right?

For reference, here are some of the pitches in that 12k-20k range where some of the curviness happens.

Reminds me of the Lab colour scale — a nonlinear scale which is attuned to how we humans perceive colour, which differs from the linear scales (RGB, CMYK) along which colour “actually exists”.

Acoustic science, you just blew my mind.


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