Friday, February 25, 2005

What Are the Chances It’ll Happen?

The following point is very obvious—but only when one thinks about it. The reason I bring it up is that I suspect, all too often, many people, especially when in haste, don’t think about it.

I was discussing something with someone and he said that a certain event we were discussing would likely occur. I pressed him and asked him how likely he thought it would be. He said he guessed it’d be about 80%.

When I asked him why, he said, event A is about 80%, which leads to B which is about 80%, which leads to C which is about 80%. So, he concluded, the likelihood of C occurring is about 80%.

Now this man is not a stupid man; he just wasn’t thinking. When I pointed out to him on that chain of probabilities, C is about slightly better than 50%, he immediately realized I was right.

I suspect that all too often, when people are estimating probabilities they merely average them out in their heads rather than multiply them; what I mean is, that if you asked many people about the probability of an event occurring when the prior events leading up to it all have a probability of around 80%, many people would unthinkingly answer about 80%. Yet, if there are five events in the 80% chain of events, the likelihood of the final event occurring is less than 1/3.

Just something to be mindful of.

Increasing Happiness

Thursday, February 24, 2005

New Yorker Article About Godel & Einstein

Tuesday, February 22, 2005

Injustice, in Secret

From the February 21, 2005, Washington Post:

"ATTORNEYS FOR the Justice Department appeared before a federal judge in Washington this month and asked him to dismiss a lawsuit over the detention of a U.S. citizen, basing their request not merely on secret evidence but also on secret legal arguments. The government contends that the legal theory by which it would defend its behavior should be immune from debate in court. This position is alien to the history and premise of Anglo-American jurisprudence, which assumes that opposing lawyers will challenge one another's arguments..."

Click the title above to read the entire article. (Registration may be required.)

Sunday, February 20, 2005

Evolving Law

Many people are opposed to the idea that the U.S. Consitution is a 'living document'. For example, some people argue that the 14th Amendment's Equal Protection clause doesn't mandate that same-sex couples be allowed to legally marry, since none of the people who were involved in enacting the 14th Amendment would have supposed that that would be the case, or indeed would have supported the legalization of same-sex marriage. I'm sympathetic to the idea that we should interpret laws in light of our best current understanding of the manifold purposes of law.

The Talmud, (the Jew's NEW Testament, in the sense that it amplifies and supersedes, in some sense, the Torah), evinces the argument that our understanding of law evolves and develops; read below.

http://www.jewishvirtuallibrary.org/jsource/Judaism/Halakha_&_aggadata_&_midrash.html

One particularly well-known bit of aggadata is found in the talmudic tractate Bava Mezia 59b. The aggadata follows a halakhic discussion in which the rabbis debated whether an oven that had become impure could be purified. While almost all the sages felt it couldn't be, Rabbi Eliezer, a lone voice but a great scholar, disagreed:

"On that day, Rabbi Eliezer put forward all the arguments in the world, but the Sages did not accept them.

"Finally, he said to them, 'If the halakha is according to me, let that carob­tree prove it.'

"He pointed to a nearby carob-tree, which then moved from its place a hundred cubits, and some say, four hundred cubits. They said to him 'One cannot bring a proof from the moving of a carob-tree.'

"Said Rabbi Eliezer, 'If the halakha is according to me, may that stream of water prove it.'

"The stream of water then turned and flowed in the opposite direction.

"They said to him, 'One cannot bring a proof from the behavior of a stream of water.'

"Said Rabbi Eliezer, 'If the halakha is according to me, may the walls of the House of Study prove it.'

"The walls of the House of Study began to bend inward. Rabbi Joshua then rose up and rebuked the walls of the House of Study, 'If the students of the Wise argue with one another in halakha," he said, "what right have you to interfere?'

"In honor of Rabbi Joshua, the walls ceased to bend inward; but in honor of Rabbi Eliezer, they did not straighten up, and they remain bent to this day.

"Then, said Rabbi Eliezer to the Sages, 'If the halakha is according to me, may a proof come from Heaven.'

"Then a heavenly voice went forth and said, 'What have you to do with Rabbi Eliezer? The halakha is according to him in every place.'

"Then Rabbi Joshua rose up on his feet, and said, 'It is not in the heavens' (Deuteronomy 30:12).

"What did he mean by quoting this? Said Rabbi Jeremiah, 'He meant that since the Torah has been given already on Mount Sinai, we do not pay attention to a heavenly voice, for You have written in Your Torah, 'Decide according to the majority' (Exodus 23:2).

"Rabbi Nathan met the prophet Elijah. He asked him, 'What was the Holy One, Blessed be He, doing in that hour?'

"Said Elijah, 'He was laughing and saying, "My children have defeated me, my children have defeated me.""'

The British-Jewish scholar and writer Hyam Maccoby has commented: "This extraordinary story strikes the keynote of the Talmud. God is a good father who wants His children to grow up and achieve independence. He has given them His Torah, but now wants them to develop it...."

Tuesday, February 15, 2005

Really Cool Visual Periodic Table of the Elements

Saturday, February 12, 2005

Quotable Quote

“If a man is offered a fact which goes against his instincts, he will scrutinize it closely, and unless the evidence is overwhelming, he will refuse to believe it. If, on the other hand, he is offered something which affords a reason for acting in accordance to his instincts, he will accept it even on the slightest evidence.” – Bertrand Russell, Roads to Freedom

Friday, February 11, 2005

Koranic Arguments Convince Terrorists to Renounce Terrorism

Tuesday, February 08, 2005

Reinventing Physics

A Nobel Laureate reflects...