Monthly Archives: September 2007

Occam’s Razor

Followup toBurdensome Details, How Much Evidence?

The more complex an explanation is, the more evidence you need just to find it in belief-space.  (In Traditional Rationality this is often phrased misleadingly, as "The more complex a proposition is, the more evidence is required to argue for it.")  How can we measure the complexity of an explanation? How can we determine how much evidence is required?

Occam’s Razor is often phrased as "The simplest explanation that fits the facts."  Robert Heinlein replied that the simplest explanation is "The lady down the street is a witch; she did it."

One observes that the length of an English sentence is not a good way to measure "complexity".  And "fitting" the facts by merely failing to prohibit them is insufficient.

Continue reading "Occam’s Razor" »

GD Star Rating
loading...

Even When Contrarians Win, They Lose

Imagine two people at a fork in the road of ideas, choosing between a standard and a contrarian view on some subject.  One takes a standard view, and gains a bit more favor with the "powers that be."  This helps him gain the right sort of contacts and opportunities to move up in the world.  Eventually he has somewhat more prestigious publications, affiliations, contacts, experience, and so on.   

At the fork in the road, the other person embraces a contrarian view.  This makes him a bit more suspect, and all else equal this costs him somewhat in terms of getting good contacts and opportunities.  Of course all else need not be equal.  He may still do well if he is very capable.  And his contrarian views may cost him little if he has few of them, if they are not important to his specialty, if he devotes little attention to them, or if he only acquires them late in his career.  (Also, if his contrarian view has long had a following, there may be contrarian "powers that be" to help him.) 

Imagine someone who ignores these low cost options, and starts early in his career to devote a lot of energy to a contrarian view, even without much support, thinking this will give him the best chance to still be around when the the world sees the light.  What if he wins this bet, and in fact the world does move toward his view, after a decade or three? 

Continue reading "Even When Contrarians Win, They Lose" »

GD Star Rating
loading...
Tagged as:

Einstein’s Arrogance

Prerequisite:  How Much Evidence Does It Take?

In 1919, Sir Arthur Eddington led expeditions to Brazil and to the island of Principe, aiming to observe solar eclipses and thereby test an experimental prediction of Einstein's novel theory of General Relativity.  A journalist asked Einstein what he would do if Eddington's observations failed to match his theory.  Einstein famously replied:  "Then I would feel sorry for the good Lord.  The theory is correct."

It seems like a rather foolhardy statement, defying the trope of Traditional Rationality that experiment above all is sovereign.  Einstein seems possessed of an arrogance so great that he would refuse to bend his neck and submit to Nature's answer, as scientists must do.  Who can know that the theory is correct, in advance of experimental test?

Of course, Einstein did turn out to be right.  I try to avoid criticizing people when they are right.  If they genuinely deserve criticism, I will not need to wait long for an occasion where they are wrong.

And Einstein may not have been quite so foolhardy as he sounded…

Continue reading "Einstein’s Arrogance" »

GD Star Rating
loading...

History is written by the dissenters

By way of Rod Dreher’s blog, a thought-provoking extract of Alan Ehrenhalt’s book: "The Lost City: The Forgotten Virtues of Community in America" After describing the indignities heaped upon black Americans, homosexuals and aspiring women in the 1950’s, it continues:

It is a powerful indictment, but it is also a selective one. While it is often said that history is written by the winners, the truth is that the cultural images that come down to us as history are written, in large part, by the dissenters — by those whose strong feelings against life in a particular generation motivate them to become the novelists, playwrights, and social critics of the next, drawing inspiration from the injustices and hypocrisies of the time in which they grew up. We have learned much of what we know about family life in America in the 1950s from women who chafed under its restrictions […] Much of the image of American Catholic life in those years comes from the work of former Catholics who considered the church they grew up in not only authoritarian but destructive of their free choices and creative instincts. […]

I am not arguing with the accuracy of any of those individual memories. But our collective indignation makes little room for the millions of people who took the rules seriously and tried to live up to them […]

Continue reading "History is written by the dissenters" »

GD Star Rating
loading...
Tagged as:

The Bright Side of Life

You young folks ever wonder why we geezers seem so cheery?  The September Psychological Science explains:

Studies of the negativity bias have demonstrated that negative information has a stronger influence than positive information in a wide range of cognitive domains. At odds with this literature is extensive work now documenting emotional and motivational shifts that result in a positivity effect in older adults. … The present study … suggest[s] that neural reactivity to negative images declines linearly with age, but responding to positive images is surprisingly age invariant across most of the adult life span.

Sure your body will degrade, and perhaps your mind too, but take heart: you won’t mind so much by then.  🙂

GD Star Rating
loading...
Tagged as:

How Much Evidence Does It Take?

Followup to:  What is Evidence?

Previously, I defined evidence as "an event entangled, by links of cause and effect, with whatever you want to know about", and entangled as "happening differently for different possible states of the target".  So how much entanglement – how much evidence – is required to support a belief?

Let’s start with a question simple enough to be mathematical: how hard would you have to entangle yourself with the lottery in order to win?  Suppose there are seventy balls, drawn without replacement, and six numbers to match for the win.  Then there are 131,115,985 possible winning combinations, hence a randomly selected ticket would have a 1/131,115,985 probability of winning (0.0000007%).  To win the lottery, you would need evidence selective enough to visibly favor one combination over 131,115,984 alternatives.

Continue reading "How Much Evidence Does It Take?" »

GD Star Rating
loading...

Treat Me Like a Statistic but Please Be Nice to Me

Most patients would be horrified if their doctor said that s/he planned to treat them like a statistic.  This might be due to a wish on the part of the patient to believe that there is something specific about them that makes them less sick than the best statistical evidence would suggest they are.  If this is the reason, then the doctor is in a real pickle; s/he must try to give the best possible advice to someone who fundamentally doesn’t want to hear it.  But the horror might just come from a fear that a doctor who regards them as a statistic denies their basic humanity, which is something that people don’t like even if it has no effect on their health.  Of course this need not be the case; it is perfectly possible for a doctor to base treatment recommendations almost entirely on statistical information and at the same time to have the utmost respect for the patient’s irreducible dignity and individuality.  It would help a lot if doctors were better at conveying this distinction, and making people feel like they are individually valued even when the medical advice comes straight from the cookie-cutter.  Furthermore, patients might not always be wrong in thinking that a doctor who wants to treat them like a statistic really does devalue their  humanity; doctors who are sophisticated enough to understand evidence-based medicine need to be on guard against the temptation to use it as an shield behind which to hide any contempt for their patients that they might happen to have.  The imperative that medical advice should be based on sound statistical evidence doesn’t make basic niceness any less important.  Heads should be hard, hearts should be soft.

GD Star Rating
loading...
Tagged as: ,

Small Business Overconfidence

The August Journal of Economic Psychology says that across 18 countries "subjective, and often biased, perceptions have a crucial impact on new business creation." For example, the strongest predictor of who starts a new business is "whether the person believes herself to have the sufficient skills, knowledge and ability to start a business."  But for those who do start a business, the higher such confidence, the lower their "approximate survival chances." Furthermore, "some countries exhibit relatively high rates of start-up activity because their inhabitants are more (over)confident than in other countries."

GD Star Rating
loading...
Tagged as: ,

The Lens That Sees Its Flaws

Continuation of:  What is Evidence?

Light leaves the Sun and strikes your shoelaces and bounces off; some photons enter the pupils of your eyes and strike your retina; the energy of the photons triggers neural impulses; the neural impulses are transmitted to the visual-processing areas of the brain; and there the optical information is processed and reconstructed into a 3D model that is recognized as an untied shoelace; and so you believe that your shoelaces are untied.

Here is the secret of deliberate rationality – this whole entanglement process is not magic, and you can understand it.  You can understand how you see your shoelaces.  You can think about which sort of thinking processes will create beliefs which mirror reality, and which thinking processes will not.

Mice can see, but they can’t understand seeing.  You can understand seeing, and because of that, you can do things which mice cannot do.  Take a moment to marvel at this, for it is indeed marvelous.

Continue reading "The Lens That Sees Its Flaws" »

GD Star Rating
loading...

Why so little model checking done in statistics?

One thing that bugs me is that there seems to be so little model checking done in statistics.  Data-based model checking is a powerful tool for overcoming bias, and it’s frustrating to see this tool used so rarely.  As I wrote in this referee report,

I’d like to see some graphs of the raw data, along with replicated datasets from the model. The paper admirably connects the underlying problem to the statistical model; however, the Bayesian approach requires a lot of modeling assumptions, and I’d be a lot more convinced if I could (a) see some of the data and (b) see that the fitted model would produce simulations that look somewhat like the actual data. Otherwise we’re taking it all on faith.

But, why, if this is such a good idea, do people not do it? 

Continue reading "Why so little model checking done in statistics?" »

GD Star Rating
loading...
Tagged as: