Category: Science

I had never thought of this:

In a sense, base 3 is the best of the integer bases because 3 is the integer closest to e…Suppose you are creating one of those dreaded telephone menu systems — press 1 to be inconvenienced, press 2 to be condescended to, and so forth.  If there are many choices, what is the best way to organize them?  Should you build a deep hierarchy with lots of little menus that each offer just a few options?  Or is it better to flatten teh structure into a few long menus?  In this situation a reasonable goal is to minimize the number of options that the wretched caller must listen to before finally reaching his or her destination.  The problem is analogous to that of representing an integer in positional notation: the number of items per menu corresponds to the radix r, and the number of menus is analogous to the width w.  The average number of choices to be endured is minimized when there are three items per menu.

I have no idea if it is correct.  It is from the often quite interesting Group Theory in the Bedroom, and Other Mathematical Diversions, by Brian Hayes.

This stimulating New Yorker essay (right now gated, but worth buying the issue for) focuses on where creative moments come from.  Excerpt:

Many stimulants, like caffeine, Adderall, and Ritalin, are taken to increase focus — one recent poll found that nearly twenty percent of scientists and researchers regularly took prescription drugs to "enhance concentration" — but, accordingly to Jung-Beeman and Kounios, drugs may actually make insights less likely, by sharpening the spotlight of attention and discouraging mental rambles.  Concentration, it seems, comes with the hidden cost of diminished creativity.  "There’s a good reason Google puts Ping-Pong tables in their headquarters," Kounios said.  "If you want to encourage insights, then you’ve got to also encourage people to relax."  Jung-Beeman’s latest paper investigates why people who are in a good mood are so much better at solving insight puzzles.  (On average, they solve nearly twenty percent more C.R.A. problems.)

Arnold Kling reports:

[Robin] Hanson says that the expected return from being cryonically frozen is positive. If it works, the benefits are high, and the probability of it working is greater than zero. Yet few people sign up for it. I think that we are afraid of looking weird if we sign up for it.

I wonder if people who already look weird, for whatever reason, sign up at disproportionate rates.  I suspect not and that only some very particular preexisting unusual traits predict an interest in cryonics.  Is the best predictor of signing up is interest in science fiction?  If so, does this mean that the non-signers are simply people who are not able to imagine the potential benefits?  Or does an interest in science fiction already label the person in some way where the marginal image cost of signing up is then especially low?  Both cryonics and science fiction of course have very high rates of male participation, some exceptions aside.  I predict that the reading of fantasy novels does not so well correlate with interest in cryonics, once you adjust for any prior interest in science fiction.

I’ve been reading Leonard Mlodinow’s The Drunkard’s Walk: How Randomness Rules our Lives.  The book covers the Monty Hall problem, Bayes’s Theorem, availability bias, the illusion of control and so forth.  If these are unfamiliar, look no further for an entertaining account.

On the other hand, I can’t say that I learned much I didn’t already know.  Nevertheless, I still enjoyed reading the book – it’s well written and filled with interesting nuggets (Did you know that the great mathematician Paul Erdos refused to believe that you should switch doors?).  If you teach probability theory or intro stats you will find lots of good examples to brighten up your lectures. 

One problem did intrigue me.  Suppose that a family has two children.  What is the probability that both are girls?  Ok, easy.  Probability of a girl is one half, probabilities are independent thus probability of two girls is 1/2*1/2=1/4.

Now what is the probability of having two girls if at least one of the children is a girl?  A little bit harder.  Temptation is to say that if one is a girl the probability of the other being a girl is 1/2 so the answer is 1/2.  That’s wrong because you are not told which of the two children is a girl and that makes a difference.  Better approach is to note that without any additional information there are four possibilities of equal likelihood for the sex of two children (B,B), (G,B), (B,G), (G,G).  If we know that at least one is a girl we can remove (B,B) so three equally likely possibilities, (G,B), (B,G), (G,G), remain and of these 1 has two girls so the answer is 1/3.

Ok, now here is the stumper.  What is the probability of a family having two girls if one of the children is a girl named Florida?

At first it seems impossible that knowing the name should make a difference.  Surely, the answer is 1/3 just as before?  After all, every child has a name.  But knowing the name does make a difference.  Here’s a hint, Florida is a rare name.

The main idea is that when you busy people’s minds with a routine task, they are less able to rationalize their own behavior and they are more likely to report the truth about what they are doing.  The most quotable excerpt assumes a bit of context

To find out, he and Dr. Valdesolo brought more people into the lab
and watched them selfishly assign themselves the easy task. Then, at
the start of the subsequent questioning, some of these people were
asked to memorize a list of numbers and retain it in their heads as
they answered questions about the experiment and their actions.

That
little bit of extra mental exertion was enough to eliminate hypocrisy.
These people judged their own actions [in assigning themselves the easy task] just as harshly as others did.
Their brains were apparently too busy to rationalize their selfishness,
so they fell back on their intuitive feelings about fairness.

If you wish, here is the whole piece.

Here are some thoughts:

So there would seem to be two models for achieving higher fertility:
the neosocialist Scandinavian system and the laissez-faire American
one. Aassve put it to me this way: “You might say that in order to
promote fertility, your society needs to be generous or flexible. The
U.S. isn’t very generous, but it is flexible. Italy is not generous in
terms of social services and it’s not flexible. There is also a social
stigma in countries like Italy, where it is seen as less socially
accepted for women with children to work. In the U.S., that is very
accepted.”

By this logic, the worst sort of system is one that
partly buys into the modern world – expanding educational and
employment opportunities for women – but keeps its traditional
mind-set. This would seem to define the demographic crisis that Italy,
Spain and Greece find themselves in – and, perhaps, Japan, South Korea,
Hong Kong, Taiwan and other parts of the world. Indeed, demographers
have been surprised to find rapid fertility changes in the third world,
as more and more women work and modern birth-control methods become
standard options. “The earlier distinct fertility regimes, ‘developed’
and ‘developing,’ are increasingly disappearing in global comparisons
of fertility levels,” according to Edward Jow-Ching Tu…the birthrate in 25 developing countries – including Cuba, Costa Rica,
Iran, Sri Lanka and China – now stands at or below the replacement
level.

Eating lunch in a working man’s restaurant in Hong Kong I hear mostly Cantonese but with occassional English words, "passion," for example.  Borrowed words or loanwords surely tell us something important about ideas or concepts that the first language lacks.  Most loanwords are for things (e.g. mouse for a computer device), it’s pretty easy to explain the adoption of such words.  But what about words for which the thing has always existed but not the word?  Chinese speakers tell me that there is a word for love but passion is more difficult to translate.

What are some of the major conceptual loanwords?  What do loanwords tell us about the Sapir-Whorf hypothesis? What loanwords does English need?  There appears to be a large literature in linguistics on the adoption and evolution of loanwords but less on the cultural significance of loanwords.  Comments?

Here is a fascinating article from The New Yorker, mostly about itching but not just.  Here is my favorite part:

A new scientific understanding of perception has emerged in the past few decades, and it has overturned classical, centuries-long beliefs about how our brains work–though it has apparently not penetrated the medical world yet. The old understanding of perception is what neuroscientists call “the naïve view,” and it is the view that most people, in or out of medicine, still have. We’re inclined to think that people normally perceive things in the world directly. We believe that the hardness of a rock, the coldness of an ice cube, the itchiness of a sweater are picked up by our nerve endings, transmitted through the spinal cord like a message through a wire, and decoded by the brain.

…Yet, as scientists set about analyzing the signals, they found them to be radically impoverished. Suppose someone is viewing a tree in a clearing. Given simply the transmissions along the optic nerve from the light entering the eye, one would not be able to reconstruct the three-dimensionality, or the distance, or the detail of the bark–attributes that we perceive instantly.

…The images in our mind are extraordinarily rich. We can tell if something is liquid or solid, heavy or light, dead or alive. But the information we work from is poor–a distorted, two-dimensional transmission with entire spots missing. So the mind fills in most of the picture. You can get a sense of this from brain-anatomy studies. If visual sensations were primarily received rather than constructed by the brain, you’d expect that most of the fibres going to the brain’s primary visual cortex would come from the retina. Instead, scientists have found that only twenty per cent do; eighty per cent come downward from regions of the brain governing functions like memory. Richard Gregory, a prominent British neuropsychologist, estimates that visual perception is more than ninety per cent memory and less than ten per cent sensory nerve signals.

And sorry, readers, for shouting in the header; sometimes I get carried away.  By the way, don’t let defenders of naive realism tell you that any attempt to contradict it is self-refuting.  Science proceeds in pieces, cross-tested in various ways, and the sum total of those pieces can revise our understanding away from naive realism without producing self-contradiction.

In reference to my Bloggingheads appearance, one loyal MR reader emails me:

you said don’t be certain, be 90-10 or 60-40 then [you] said 1-99 that humanity dies out when sun’s gone.

Yes, I believe the chance is very small that humanity survives the death of our sun or even gets close to that point.  I’ll give it p = .005.  But what’s the chance I think that is the correct p or even in the neighborhood of the correct p?  Maybe 60 percent.  Of course my p estimate could go either up or down and after I apply meta-rationality p = .005 is where I end up, for better or worse.  I expect that fragile estimate to undergo lots of revision as I age, read more, etc.  I just don’t know if it will go up or down, thereby satisfying one of Robin Hanson’s canons of rationality (or some approximation thereof).

Why am I skeptical?  The Fermi paradox, for one thing, plus I observe that humans aren’t very good at solving large-scale collective action problems.  Our environment may be more fragile than we had thought and that’s without even considering the impact of man.

Under one scenario, the shy become more extroverted and everyone enjoys their new bon mots and witty asides.  Gains from trade increase all around.  Under another scenario, shyness and extroversion are part of a larger positional game.  Some people take the anti-shyness drug, but the previous extroverts, facing new competition for sex and friends, become even more extroverted, thus feeling more strain.  Many of them start taking the drug to stay ahead.  The previously shy exhibit more "juice," so to speak, but without much net result in terms of an improved life since they are still coming in second, so to speak.  And those who don’t take the anti-shyness drug are even worse off than before, given the new and higher standard for extroversion.

Some of the remaining shy, however, might in fact feel relieved.  If the new standard of extroversion rises so high that they can’t possibly meet it, they might, to some extent, withdraw from social competition.  The truly shy might even form social clubs and band together in the interests of promoting shyness.  If they can signal that they do not take the drug, their shyness might become more socially acceptable than before.

Seth Roberts asks:

The photo shows the full faces of 22 men; 7 of them are touching
their mouths. I have noticed something similar at many faculty
meetings. I started to notice this after I read about its observation
in a study designed to measure something else.

I’ve known about this for many years but have never read an
explanation. Do we enjoy touching our mouths – or is the absence of
touch for a  long time unpleasant? If so, why?

Here is one poker player’s answer.

…the modelling, done by the world-renowned Hadley Centre at the Met
Office but using emissions calculated by the Stockholm Network,
highlighted three problems: ‘Current policy comes in too slowly, it
internationalises too slowly and it binds developing countries too
late.’

Privately, many climate scientists believe it will be impossible to
meet the 2C target, but they are reluctant to say so because they do
not want to discourage moves to cut emissions.

Here is more and that is from The Guardian not National Review.  I believe that some parts of the world will be in for a very rough ride.

By the way, while I was in Japan I read that a) about half the world’s people are consuming subsidized energy, not taxed energy, and b) Chinese energy-users are typically paying about half of the world price.  Recent energy price increases in India have induced riots.  Those are all signs of the magnitude of the problem.

Here and here.

Hat tip to Kottke.