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Mike Stay
Attends University of Auckland
Lives in Mountain View, CA
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There are dozens of approximate formulas for how the strong interactions work, good in different circumstances.  It's a huge messy subject.
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I have no idea how most of these transitions were done.
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wow.  The shopping mall and the dune bashing between 1:30 and 2 were just like our experience with Steve in Doha - except only 4 cars on the dune.
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What does a scientist mean when she talks about a theory?

Scientists and mathematicians often borrow words from common speech and give them new meanings, usually only loosely related to the original meaning.  In math, for example, we have groups, fields, rings, sheaves, stacks, and so on.  In physics, the color of a quark has nothing to do with visible light; we also talk about fields, but we mean something completely different than the mathematicians: the finite field ℤ₂ has absolutely nothing to do with the electromagnetic field, and a plot of treeless land is only a very weak metaphor for both of these meanings.

The same thing happens when we speak of a scientific theory.  The colloquial meaning of the word theory is a "hunch" or a "guess".  To a scientist, the word theory means something much more complicated.  

In 1960 the psychologist Peter Wason devised a simple game he called the "2-4-6 game" [1] to illustrate the process of scientific exploration and building theories, and also to try to understand how untrained minds think, .  

The game has two players; let's call them Alice and Bob.  Alice thinks of a rule describing triples of natural numbers, like "any three even natural numbers" or "any three strictly increasing natural numbers" or "any three consecutive natural numbers" and writes the rule down on a piece of paper, then tells Bob one example triple of numbers that passes her test.  In Wason's experiment, he used the rule "any three strictly increasing natural numbers" and Bob was told that the triple (2,4,6) was one example of a triple that passed the test.

Bob's job is to figure out what the rule is.  He can propose triples and Alice has to answer truthfully whether the triple fits the rule or not.  When Bob thinks he knows what the rule is, the game ends.  If he is correct, he wins; if he is incorrect, Alice wins.

Wason's results were staggering: only six of the twenty-nine adults got the rule on their first try!  A typical session went as follows:

B: (8,10,12)?  A: Yes.
B: (14,16,18)? A: Yes.
B: (4,6,8)? A: Yes.
B: (3,6,9)? A: Yes.
B: (5,10,15)? A: Yes.
B: I think it's any three numbers that go up by the same amount each time.

Having been forewarned, it's easy for us to see where Bob went wrong: he saw a pattern in the first example and then tested to see whether that pattern continued to hold.  Unfortunately, that perceived pattern was too specific.  How could Bob have discovered this?

The only way to test it is to look at a situation where Bob thinks the test should fail.  He never tried a triple like (1, 4, 5) where the numbers went up different amounts each time; if he had, he would have seen that his rule predicted a different answer.  In fact, given the transcript above, Alice's rule could have been "Any three numbers", because Bob never got a "no" answer!

When I played this with some friends a couple of weeks ago (I was Alice and everyone else was Bob), several interesting things happened.  First, a teenager named Andre noticed that he couldn't remember which triples had been guessed yet.  He wanted someone to write down their questions and my answers.  Tycho Brahe was a Danish astronomer who spent his life making very accurate measurements of the positions of the planets.  Telescopes hadn't been invented yet, but he had a large altimeter on a graduated, rotating base.  He rotated the base and measured the angular distance to the planets from nearby fixed stars every night for decades.  The brightest crater on the moon is named for him.  His student Johannes Kepler discovered that planets move in ellipses rather than circles, but he was only able to do so because Brahe had collected the data.

The next thing that happened in our game was that one of the players made exactly the same mistake as Bob above and got eliminated.

Next, Andre made a guess (10,9,8) that didn't fit the pattern.  When I said, "no", he was disappointed, as though he had failed.  I explained how 80% fail to do that and guess rules that are too specific: he was winning!

Finally, people's faces lit up when I pointed out that they were doing physics experiments: making measurements to try to learn a law of nature.

A theory is a set of principles and equations describing some measurable quantities that

1) explains all the observations that the previous theory did,
2) explains some observations that weren't explained by the previous theory,
3) makes predictions about what we should observe when we look in places or ways we haven't before, and
4) says what should not happen.

Note that a theory can restrict itself to ranges of observables: Newtonian physics works well in a "goldilocks" range: neither too big nor too small, neither too hot nor too cold, and not too fast.  When things get too small, we have to use quantum mechanics.  When things get too fast, we have to use special relativity.  When things get too massive, we have to use general relativity.  And when things are both very heavy and very small, we have no good theory; understanding quantum gravity is a very hard problem that no one has figured out satisfactorily yet.  String theory and loop quantum gravity are the major contenders, but neither one can make predictions yet.

The website "29+ Evidences for Macroevolution" [2] is an excellent website that explains how evolution does all four of the things above, and is therefore what a scientist means by a theory; for every principle of the theory, it gives existing confirmation, predictions that came true, and examples of observations that could falsify that principle.  For example, evolution predicts atavisms, features of ancestors that appear from time to time among groups that have, for the most part, lost those features.  Atavisms include humans with tails, extra toes on horses, whales with hindlimbs, and so on.  "No organism can have a vestigial structure that was not previously functional in one of its ancestors.  Thus, for each species, the standard phylogenetic tree makes a huge number of predictions about vestigial characters that are allowed and those that are impossible for any given species."

[1] Wason, Peter C. (1960), "On the failure to eliminate hypotheses in a conceptual task", Quarterly Journal of Experimental Psychology (Psychology Press) 12 (3): 129–140, doi:10.1080/17470216008416717, ISSN 1747-0226
[2] http://www.talkorigins.org/faqs/comdesc/
This article directly addresses the scientific evidences in favor of macroevolutionary theory and common descent. It is specifically intended for those who are scientifically minded but, for one reason or another, have come to believe that macroevolutionary theory explains little, makes few or no testable predictions, or is unfalsifiable.
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theory (Webster Dictionary 1828)
<Darwin's Dictionary>

THE'ORY, n. [L. theoria; Gr. to see or contemplate.]

1. Speculation; a doctrine or scheme of things, which terminates in speculation or contemplation, without a view to practice. It is here taken in an unfavorable sense, as implying something visionary.
2. An exposition of the general principles of any science; as the theory of music.
3. The science distinguished from the art; as the theory and practice of medicine.
4. The philosophical explanation of phenomena, either physical or moral; as Lavoisier's theory of combustion; Smith's theory of moral sentiments.
Theory is distinguished from hypothesis thus; a theory is founded on inferences drawn from principles which have been established on independent evidence; a hypothesis is a proposition assumed to account for certain phenomena, and has no other evidence of its truth, than that it affords a satisfactory explanation of those phenomena.


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Evolution at its finest: the spider-tailed viper has a tail with a bulb at the end that looks just like a spider's abdomen; the bulb is surrounded by spines that look just like a spider's legs.  The viper moves its tail in a perfect imitation of a large hunting spider: stop, crawl, stop again.  The rest of the viper is very well camouflaged.  The result is a perfect predator of insectivore birds. h/t +Yonatan Zunger 
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Add lowercase to your TRS-80 for only $59.00!

http://mashable.com/2015/02/06/radio-shack-catalog-1981/
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A TRS-80 (bought in 1980) was the first computer I owned. :)
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Just when you thought platypuses couldn't get any weirder:

Platypus have five male-specific chromosomes (Y chromosomes) and five chromosomes present in one copy in males and two copies in females (X chromosomes). These ten chromosomes form a multivalent chain at male meiosis, adopting an alternating pattern to segregate into XXXXX-bearing and YYYYY-bearing sperm. Which, if any, of these sex chromosomes bears one or more sex-determining genes remains unknown. The largest X chromosome, with homology to the human X chromosome, lies at one end of the chain, and a chromosome with homology to the bird Z chromosome lies near the other end. This suggests an evolutionary link between mammal and bird sex chromosome systems, which were previously thought to have evolved independently.

https://books.google.com/books?id=c9e9pqQCqrEC&pg=PA350
books.google.com - This new third edition updates a best-selling encyclopedia. It includes about 56% more words than the 1,392-page second edition of 2003. The number of illus...
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+John Baez Yes!  When it happens early enough, there are few enough cells that there's a high chance of a bilateral gynandromorph, but it's possible to have smaller parts.  The wiki page has pictures of a mosaic gynandromorph butterfly as well as a drawing of a female spider with one male pedipalp.

http://en.wikipedia.org/wiki/Gynandromorphism
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Algorithm for creating linkages that draw almost arbitrary curves:
http://www.koutschan.de/data/link/index.html
h/t +Mark Lentczner 
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+Mike Stay, i'm always looking for specialists to explain obscurious things to people who then like to explain these to nonspecialists...

+Boris Borcic :)
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This article clears up so much of the confusion I had about cosmology and the "Big Bang".  Back in the '60s when the Big Bang theory was first proposed, the "Big Bang" meant both
1. the hot, dense, smaller state of the universe that expanded and cooled, giving rise to the matter-dominated universe we now see, and
2. an infinitely dense singularity before which time had no meaning.

While #1 is indisputable, #2 is an idea on the ropes.  The chart below shows that universes dominated by radiation and matter both have a singularity at time 0; but over the past 50 years, we've discovered that the very early universe was dominated by vacuum energy, and as the chart below shows in yellow, such a universe tends to an asymptote as we go back in time, not a singularity.

The physics we're sure of only tells us what happened at the point where all three curves meet, around 10⁻³² seconds after the point where the singularity might be.  Before that, there are two different ideas about what happened.

In the traditional Big Bang model, from 10⁻³² back to 10⁻³⁶ seconds was the "electroweak epoch", a time when energy was high enough electromagnetism and the weak force unified; from 10⁻³⁶ back to 10⁻⁴³ seconds was the "grand unification" epoch, when the electroweak force and the strong force unified; and before that was the "Planck epoch" when the three other forces unified with gravity.

In the inflationary model, there was no initial singularity; the universe could be infinitely old.  The forces would still have been unified, but we'd have to go back a lot farther in time, and the Planck epoch would have been infinitely long instead of a mere 10⁻⁴³ seconds.  We can set the point from which we measure time anywhere, and it's reasonable to place it at the time where the singularity would have occurred in the absence of dark energy (or vacuum energy, or the cosmological constant---they're all synonyms) even though in that model, there was no singularity.  When people say "The inflationary epoch ended 10⁻³² seconds after the Big Bang," this is what they mean.

While there was definitely a time when the universe was much smaller and in a hot, dense state dominated by radiation, there are other observations that the singularity model doesn't explain but inflation does.  Inflation explains why there's the vast structure of stars, galaxies, clusters, and filaments throughout the universe, why space (not spacetime) is so nearly flat, why opposite sides of the universe are exactly the same temperature, the absence of weird stuff like magnetic monopoles and topological defects like cosmic strings, and predicted the particular kinds of fluctuations we should see in the cosmic microwave background before they were measured.
When scientists say “the Big Bang,” they mean two possible things. But only one of them is still correct.
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+straw walker "... as I remember"
Well then, you must not have been there. ;-)
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Tomorrow I turn 41, which is an interesting number.  +Robert Munafo writes (http://mrob.com/pub/math/numbers-6.html):

Euler discovered that the polynomial x² + x + 41 gives a prime number for all x from 0 to 39. There was much speculation about whether some polynomial or similar formula could give primes for all values of its variables, and that was eventually proven impossible (Goldbach, 1752).

There are other, similar polynomials with smaller constant terms, for example x² + x + 17. They are related to the same set of numbers that cause near-integer values of exp(π√n). The connection is more obvious if you use the quadratic formula: from x² + x + 41 we get
 (-1 ± √(1 - 4 × 41))/2, or (-1 ± √-163)/2.
Alternately the polynomial can be broken up into a squared monomial plus a constant:
 x² + x + 41 = (x + 1/2)² + 163/4.
Amazingly, this is connected to the Monster group, due to the Monstrous moonshine phenomena.
Notable Properties of Specific Numbers -- maths, interesting, number -- Explore a wide variety of topics from large numbers to sociology at mrob.com
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And next year you will have the answer to EVERYTHING.  
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A very big bug that eats raspberry & blackberry leaves.

http://en.wikipedia.org/wiki/Heteropteryx_dilatata
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Bat : bat :: vampire : umpire ?
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Yes, thank you!
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Partner, Biosimilarity, LLC
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Category theory, computer programming, theoretical physics
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Currently
Mountain View, CA
Previously
Lindon, UT - Redford, MI - Amherst, OH - Provo, UT - Puerto San Jose, Guatemala - Jocotenango, Guatemala - Villa Nueva, Guatemala - Villa Hermosa, Guatemala - Colorado Springs, CO - Epsom, New Zealand - Riverside, CA
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Introduction
Whenever I'm asked to describe myself, I immediately think of Gödel numbering and quines.
Education
  • University of Auckland
    Computer Science, 2007 - present
    PhD
  • University of Auckland
    Computer Science, 2004 - 2005
    MSc
  • Brigham Young University
    Physics, 1992 - 1997
    BSc
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Michael Stay