Overcoming Bias

Decoherence is Falsifiable and Testable

Continuation of:  Decoherence is Simple

The words "falsifiable" and "testable" are sometimes used interchangeably, which imprecision is the price of speaking in English.  There are two different probability-theoretic qualities I wish to discuss here, and I will refer to one as "falsifiable" and the other as "testable" because it seems like the best fit.

As for the math, it begins, as so many things do, with:

This is Bayes's Theorem.  I own at least two distinct items of clothing printed with this theorem, so it must be important.

Guilt By Association

I've long wondered: why do students pay such a premium to go to a school with impressive professors, even when those professors largely ignore them?  Yesterdays' Post gives a clue:

Social psychologist Michelle Hebl ... had volunteers evaluate a mock job applicant. Some volunteers saw the applicant sitting in a waiting room next to an overweight person, while others saw the applicant in the waiting room sitting next to a person of average weight. ... Hebl found that volunteers rated job applicants more negatively when they had been seen seated next to an overweight person than when they were seen seated next to an average weight person. The volunteers had no idea that they were showing not only a prejudice against fat people but also a bias against people who were merely in proximity to overweight people. ... Men and women seen in the company of beautiful partners are perceived as being more attractive than when they are seen in plainer company. ... Heterosexual men seen in the company of gay men had some of the stigma attached to homosexuality rub off on them.

Decoherence is Simple

(An epistle to the physicists.)

When I was but a little lad, my father, a Ph.D. physicist, warned me sternly against meddling in the affairs of physicists; he said that it was hopeless to try to comprehend physics without the formal math. Period.  No escape clauses.  But I had read in Feynman's popular books that if you really understood physics, you ought to be able to explain it to a nonphysicist.  I believed Feynman instead of my father, because Feynman had won the Nobel Prize and my father had not.

It was not until later - when I was reading the Feynman Lectures, in fact - that I realized that my father had given me the simple and honest truth.  No math = no physics.

By vocation I am a Bayesian, not a physicist.  Yet although I was raised not to meddle in the affairs of physicists, my hand has been forced by the occasional gross misuse of three terms:  Simple, falsifiable, and testable.

The foregoing introduction is so that you don't laugh, and say, "Of course I know what those words mean!"  There is math here.

Keeping Math Real

John von Neumann:

As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality" it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely I'art pour I'art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up. (from "The Mathematician")

This warning is rather similar to Gordon Tullock's.   HT to Jeff Helzner.

Spooky Action at a Distance: The No-Communication Theorem

Previously in series:  Bell's Theorem: No EPR "Reality"

When you have a pair of entangled particles, such as oppositely polarized photons, one particle seems to somehow "know" the result of distant measurements on the other particle.  If you measure photon A to be polarized at 0°, photon B somehow immediately knows that it should have the opposite polarization of 90°.

Einstein famously called this "spukhafte Fernwirkung" or "spooky action at a distance".  Einstein didn't know about decoherence, so it seemed spooky to him.

Though, to be fair, Einstein knew perfectly well that the universe couldn't really be "spooky".  It was a then-popular interpretation of QM that Einstein was calling "spooky", not the universe itself.

Walking On Grass, Others

Amelia Rawls in a Post OpEd:

During four years at Princeton University and nearly a year at Yale Law School, I have been surrounded by students who dazzle. ... But they are not always nice people. ... the kind of "nice" that involves showing compassion not merely because membership in community service groups demands it. The kind of "nice" that involves sharing notes with a student who is sick or lending a textbook to a friend who doesn't have one. The kind of selfless, genuine "nice" that makes this world a better place -- but won't get you accepted to college.

Of course, top universities accept hundreds of individuals who have demonstrated the highest levels of citizenship. These teenagers have volunteered in more food banks, sponsored more fundraisers and lobbied more officials than any previous generation. ... Sometimes some of these students will denounce world hunger but be unfriendly to the homeless. They will debate environmental policy but never offer to take out the trash. They will believe vehemently in many causes but roll their eyes when reminded to be humble, to be generous and to "do what is right."

Bell's Theorem: No EPR "Reality"

Previously in series:  Entangled Photons

(Note:  So that this post can be read by people who haven't followed the whole series, I shall temporarily adopt some more standard and less accurate terms; for example, talking about "many worlds" instead of "decoherent blobs of amplitude".)

The legendary Bayesian, E. T. Jaynes, began his life as a physicist.  In some of his writings, you can find Jaynes railing against the idea that, because we have not yet found any way to predict quantum outcomes, they must be "truly random" or "inherently random".

Sure, today you don't know how to predict quantum measurements.  But how do you know, asks Jaynes, that you won't find a way to predict the process tomorrow?  How can any mere experiments tell us that we'll never be able to predict something - that it is "inherently unknowable" or "truly random"?

As far I can tell, Jaynes never heard about decoherence aka Many-Worlds, which is a great pity.  If you belonged to a species with a brain like a flat sheet of paper that sometimes split down its thickness, you could reasonably conclude that you'd never be able to "predict" whether you'd "end up" in the left half or the right half.  Yet is this really ignorance?  It is a deterministic fact that different versions of you will experience different outcomes.

But even if you don't know about Many-Worlds, there's still an excellent reply for "Why do you think you'll never be able to predict what you'll see when you measure a quantum event?"  This reply is known as Bell's Theorem.

Beware Transfusions

New Scientist:

Blood transfusion became a mainstay of medicine during the two world wars, where it was used as a last resort to save soldiers who had suffered massive blood loss. But now, far from being restricted to catastrophic bleeding, transfusions are routinely used as an optional treatment, most commonly for patients in intensive care or undergoing major surgery. ... The rationale behind such blood transfusions seems incontrovertible. Red cells deliver vital oxygen to tissues, and seriously ill patients who are also anaemic fare less well, so a transfusion should help. Those assumptions went untested for the better part of a century.

Things started to change in 1999 with a randomised controlled trial on 838 critical care patients in Canada that used haemoglobin levels to determine when a blood transfusion was given. Normal levels of haemoglobin ... range from 120 to 170 grams per litre. A normal haematocrit - the proportion of red cells in the blood - ranges from 36 to 50 per cent.  Doctors decide whether to give a transfusion based on a number of factors, including haemoglobin levels and haematocrit, and the patient's overall robustness. Many guidelines exist, and practice varies from one hospital or doctor to another, but it is common for patients to receive transfusions when their haemoglobin dips to between 70 and 100 g/l or their haematocrit to 21 to 30 per cent.

But the Canadian study found significantly fewer patients died in hospital, 22 versus 28 per cent, if they received transfusions only when their haemoglobin fell below 70 g/l rather than when it fell below 100 g/l.

Entangled Photons

Previously in series:  Decoherence as Projection

Today we shall analyze the phenomenon of "entangled particles".  We're going to make heavy use of polarized photons here, so you'd better have read yesterday's post.

Beware Supplements

The Copenhagen team reviewed more than 815 clinical trials into the benefits of vitamins A, E, and C, alongside beta-carotene and selenium - all commonly-used supplements.  They selected 68 whose methods were more likely to produce an accurate picture of vitamin benefits ... [and] eliminated a further 21 trials which had a slightly higher possibility of producing a skewed result, ...  While the risk of death was unchanged among selenium and vitamin C users, a statistically significant increase in risk emerged for the other three supplements.   Beta-carotene produced an approximate 7% increased risk, vitamin E a 4% increase and vitamin A, a 16% increase.

More here.