Number of words – 344 Imagine how surprised the first Neolithic farmer must have been when he hit a pebble with his stone hammer and instead of shattering, the pebble just bent. A nugget of native copper! Copper does sometimes occur pure, in small nuggets. By banging away at it our Neolithic hero could form … Read more
Number of words – 297 In more temperate regions in Africa, there are hunter-gatherer tribes today who manage well enough by spending only a couple of days a week in food gathering task. They may not have their own kinds of leisure time activities. So, if the Neolithic life style was that pleasant, why did … Read more
Number of words – 244 Occasionally, when an adult sheep has been killed by humans for food, a lamb remains that’s taken back to the camp for a pet. The lamb is fed and becomes somewhat tame. Others, over the generations receive the same treatment, and with the right genetic variations may lose some of … Read more
Number of words – 3,988 In this lecture, I would like to discuss whether time itself has a beginning, and whether it will have an end. All the evidence seems to indicate, that the universe has not existed forever, but that it had a beginning, about 15 billion years ago. This is probably the most … Read more
Number of words – 215 Science has proven that domesticated animals have significantly smaller brains than wild animals. Whether it’s a dog versus a wolf, or even farmed trout compared to wild trout, the brains of human-bred animals are just tinier. The statistics are dramatic: Domestic pigs have brains 35% smaller than wild boars, while … Read more
Though calculus represents a new sophistication in the understanding of sequences, that idea, like so many others, had already been familiar to the Greeks. In the fifth century b.c., in fact, the Greek philosopher Zeno employed a curious sequence to formulate a paradox that is still debated among college philosophy students today, especially after a … Read more
State governments tend to ignore arguments about the possible bad effects of lotteries. That’s because, for the most part, they know enough about mathematical expectation to arrange that for each ticket purchased, the expected winnings—the total prize money divided by the number of tickets sold—is less than the cost of the ticket. This generally leaves … Read more
A few years ago Canadian lottery officials learned the importance of careful counting the hard way when they decided to give back some unclaimed prize money that had accumulated. They purchased 500 automobiles as bonus prizes and programmed a computer to determine the winners by randomly selecting 500 numbers from their list of 2.4 million … Read more
In the two-daughter problem, an additional question is usually asked: What are the chances, given that one of the children is a girl, that both children will be girls? One might reason this way: since it is given that one of the children is a girl, there is only one child left to look at. … Read more
Unfortunately, it is hard to achieve quantitative dexterity when you’re juggling VIIIs and XIVs. In the end, though Roman law had a certain legal rationality and coherence, it fell short of mathematical validity. In Roman law, for example, two half proofs constituted a complete proof. That might sound reasonable to a mind unaccustomed to quantitative … Read more
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