What Can the Maths Tell Us?

Solvay Conference 1927*

Darwin, The Origin of Species

It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us.

Freeman Dyson, “How to Dispel Your Illusions

Another famous example of statistical prediction is the Dawes formula for the durability of marriage. The formula is “frequency of love-making minus frequency of quarrels.” Robyn Dawes was a psychologist who worked with Kahneman later. His formula does better than the average marriage counselor in predicting whether a marriage will last.

Steven Pinker, “A History of Violence

In the decade of Darfur and Iraq, and shortly after the century of Stalin, Hitler, and Mao, the claim that violence has been diminishing may seem somewhere between hallucinatory and obscene. Yet recent studies that seek to quantify the historical ebb and flow of violence point to exactly that conclusion.

Some of the evidence has been under our nose all along. Conventional history has long shown that, in many ways, we have been getting kinder and gentler. Cruelty as entertainment, human sacrifice to indulge superstition, slavery as a labor-saving device, conquest as the mission statement of government, genocide as a means of acquiring real estate, torture and mutilation as routine punishment, the death penalty for misdemeanors and differences of opinion, assassination as the mechanism of political succession, rape as the spoils of war, pogroms as outlets for frustration, homicide as the major form of conflict resolution—all were unexceptionable features of life for most of human history. But, today, they are rare to nonexistent in the West, far less common elsewhere than they used to be, concealed when they do occur, and widely condemned when they are brought to light.

“New Ways To Study Behavioral Economics Via Porn Industry

When he took his behavioral economics research out of the lab and into the world of Internet domainers and pornographers, UC Berkeley professor John Morgan found that business professionals in industries typically considered “shady” are better collaborators and more “trusting, trustworthy, and altruistic” than college students whom he tested in a lab setting.

“People are kinder, gentler, less selfish, and more giving than what the standard economic model predicts, and this has led researchers to think about how we should incorporate these preferences in our models,” says Morgan.

Running a Race Against Ourselves, Plucker and Rutkowski

The United States unquestionably has one of the very best and very worst performing school systems.

That’s not a typo. For example, the U.S. average on PISA in reading was 500, a rather mediocre showing that ranks us about 15th (similar to Iceland and several other European countries). But Asian-Americans scored a world-class 541 (second only to Shanghai, on par with South Korea and Finland), and Caucasians averaged an impressive 525 (on par with Singapore and Canada in the middle of the top 10). Not too shabby!

Hispanic Americans, however, scored a well-below-average 466 (similar to Lithuania and Turkey, ranked 40th and 41st, respectively), and African-Americans averaged 441 (similar to 45th-ranked Serbia and just ahead of 46th-place Bulgaria). Breaking out the scores by poverty level would tell a similar story: American “haves” are among the best-achieving students in the world, but the “have nots” perform at shockingly low levels.

Enriched with Information

So far, the new equations exist only as prototypes, like model airplanes that can’t fly but still help clarify how jumbo jets stay aloft. But researchers believe that these prototypes may one day lead to a tool that can measure consciousness, even when signs of it are ambiguous. Already, researchers are testing the math that would underpin such a tool in human brains as people lose awareness.

Tononi’s idea, though, extends beyond humans. By moving from nerve cells to the math that describes them, he has untethered the theory of consciousness from the physical brain. Like amorphous Silly Putty, the equations can be molded to fit any system. With the right calculations, scientists could test whether a tornado with its innumerable dust particles circling in unison, 2050’s iPhone or the trillions of megabytes of information zooming around the Internet could have some degree of consciousness.

Women in Love, chapter 26

`So beautiful, so pure!’ Birkin said. `It almost breaks my heart.’ They walked along between the heaps of rubbish. `My beloved country — it had something to express even when it made that chair.’

`And hasn’t it now?’ asked Ursula. She was always angry when he took this tone.

`No, it hasn’t. When I see that clear, beautiful chair, and I think of England, even Jane Austen’s England — it had living thoughts to unfold even then, and pure happiness in unfolding them. And now, we can only fish among the rubbish heaps for the remnants of their old expression. There is no production in us now, only sordid and foul mechanicalness.’

`It isn’t true,’ cried Ursula. `Why must you always praise the past, at the expense of the present? Really, I don’t think so much of Jane Austen’s England. It was materialistic enough, if you like –‘

`It could afford to be materialistic,’ said Birkin, `because it had the power to be something other — which we haven’t. We are materialistic because we haven’t the power to be anything else — try as we may, we can’t bring off anything but materialism: mechanism, the very soul of materialism.’

A Philosophical Inquiry into the Origin of our Ideas of the Sublime and Beautiful

Whatever is fitted in any sort to excite the ideas of pain, and danger, that is to say, whatever is in any sort terrible, or is conversant about terrible objects, or operates in a manner analogous to terror, is a source of the sublime; that is, it is productive of the strongest emotion which the mind is capable of feeling. I say the strongest emotion, because I am satisfied the ideas of pain are much more powerful than those which enter on the part of pleasure….All privation is great because they are all terrible: Vacuity, darkness, solitude, and silence. Low and intermittent sounds and shadows bring about feelings of the sublime. Above all, the actions of the mind are affected by the sublime.

 Uncertainty Relations

The simultaneous measurement of two conjugate variables (such as the momentum and position or the energy and time for a moving particle) entails a limitation on the precision (standard deviation) of each measurement. Namely: the more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa. In the most extreme case, absolute precision of one variable would entail absolute imprecision regarding the other.

*Solvay Conference Attendees:

Back: A. Piccard, E. Henriot, P. Ehrenfest, Ed. Herzen, Th. De Donder, E. Schrödinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin

Middle: P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr

Front: I. Langmuir, M. Planck, Mme. Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch. E. Guye, C.T.R. Wilson, O.W. Richardson

Photo Credit: Metsuke iLife’s photostream

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3 Comments

  1. SS February 27, 2012 at 12:44 pm

    I think your final passage about says it all! I find Pinker’s statement to be objectionable, as I’m sure anyone that is awake these days would.

    But, what do we gain by measuring anything? If someone can quantify my consciousness, what does that even mean? It seems to me that trying to make the world conceptually black and white (rather, black or white) is a self-fulfilling prophecy.

    I think I will take Dyson’s formula to hear, however.

    Reply
  2. SS February 27, 2012 at 12:44 pm

    * I meant to say that I will take Dyson’s formula to heart, though I hear it too…

    Reply
  3. dpopp February 28, 2012 at 11:12 am

    Goes to show, the maths may be correct, but the science may not.

    Reply

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