An explanation of Pascal's Triangle can be found here. While you're at it you might also want to check out the Fibonacci sequence and its myriad occurrences in nature. It's fascinating.
Wednesday, August 3, 2011
The Beauty of Mathematics
Australian Geneticist Michael Denton talks about the strange beauty of mathematics and how that beauty militates against the hypothesis that mathematics is something that we invent. Denton argues instead that mathematical truth exists independently of us and that we discover rather than create it. This raises, of course, the intriguing question of how it came to be in the first place:
The Corrosive Effects of Liberalism
People sometimes think that the only differences between conservatives and liberals are political. They may differ on how to address our economic problems but which one chooses is pretty much a matter of taste. This is, however, not true. The differences extend far beyond how we should manage the nation's finances. Dennis Prager argues that liberalism is corrosive of a nation's moral character.
He gives ten ways in which liberalism corrodes our character both nationally and individually. This is not to say that individual liberals are not fine people, but rather that the policies they support have a pernicious effect that they doubtless don't intend.
Here's a summary of his argument:
He closes his piece by saying that if you want to feel good, liberalism is awesome. If you want to do good, it is largely awful.
He gives ten ways in which liberalism corrodes our character both nationally and individually. This is not to say that individual liberals are not fine people, but rather that the policies they support have a pernicious effect that they doubtless don't intend.
Here's a summary of his argument:
1. The bigger the government, the less the citizens do for one another. If the state will take care of me and my neighbors, why should I? This is why Western Europeans, people who have lived in welfare states far longer than Americans have, give less to charity and volunteer less time to others than do Americans of the same socioeconomic status.Prager opines that progressives don't try to refute these charges, rather they simply invoke emotionally charged terms like "social justice" and "compassion," and smear their opponents as "selfish" or "racist".
2. The welfare state, though often well intended, is nevertheless a Ponzi scheme. Conservatives have known this for generations. But now, any honest person must acknowledge it. The welfare state is predicated on collecting money from today's workers in order to pay for those who paid in before them.
3. Citizens of liberal welfare states become increasingly narcissistic. The great preoccupations of vast numbers of Brits, Frenchmen, Germans and other Western Europeans are how much vacation time they will have and how early they can retire and be supported by the state.
4. The liberal welfare state makes people disdain work.
5. Nothing more guarantees the erosion of character than getting something for nothing. In the liberal welfare state, one develops an entitlement mentality.
6. The bigger the government, the more the corruption. As the famous truism goes, "Power tends to corrupt, and absolute power corrupts absolutely."
7. The welfare state corrupts family life. Even many Democrats have acknowledged the destructive consequences of the welfare state on the underclass. It has rendered vast numbers of males unnecessary to females, who have looked to the state to support them and their children (and the more children, the more state support) rather than to husbands.
8. The welfare state inhibits the maturation of its young citizens into responsible adults....The loudest and most sustained applause I ever heard was that of college students responding to a speech by President Barack Obama informing them that they would now be covered by their parents' health insurance policies until age 26.
9. As a result of the left's sympathetic views of pacifism and because almost no welfare state can afford a strong military, European countries rely on America to fight the world's evils and even to defend them.
10. The leftist weltanschauung sees society's and the world's great battle as between rich and poor rather than between good and evil. Equality therefore trumps morality. This is what produces the morally confused liberal elites that can venerate a Cuban tyranny with its egalitarian society over a free and decent America that has greater inequality.
He closes his piece by saying that if you want to feel good, liberalism is awesome. If you want to do good, it is largely awful.
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