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know what you're thinking: we're smarter than bacteria. No doubt about it, we're smarter than every other living creature that ever walked, crawled, or slithered on Earth. But how smart is that? We cook our food. We compose poetry and music. We do art and science. We're good at math. Even if you're bad at math, you're…
When an observation is made on any atomic system that has been prepared in a given way and is thus in a given state, the result will not in general be determinate, i.e. if the experiment is repeated several times under identical conditions several different results may be obtained. If the experiment is repeated a…
Just as you can't have one-third of a penny or two and a half quarters, Planck declared that when it comes to energy, no fractions are allowed. Now, our monetary denominations are determined by the United States Treasury. Seeking a more fundamental explanation, Planck suggested that the energy denomination of a…
Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the…
There is a strange disparity between the sciences of inert matter and those of life. Astronomy, mechanics, and physics are based on concepts which can be expressed, tersely and elegantly, in mathematical language. They have built up a universe as harmonious as the monuments of ancient Greece. They weave about it a…
All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and…
A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to…
What I remember most clearly was that when I put down a suggestion that seemed to me cogent and reasonable, Einstein did not in the least contest this, but he only said, 'Oh, how ugly.' As soon as an equation seemed to him to be ugly, he really rather lost interest in it and could not understand why somebody else was…
The name is symbolic. The first pale roots and shoots of a germinating seed look so tiny and fragile; it's hard to believe it can grow into a big tree. Yet there is so much life force in that seed that the roots can work their way through boulders to reach the water, and the shoot can work its way through cracks in a…
Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt…
Many well-meaning moms and dads think their child’s brain is interested in learning. That is not accurate. The brain is not interested in learning. The brain is interested in surviving. Every ability in our intellectual tool kit was engineered to escape extinction. Learning exists only to serve the requirements of…
Let me suggest a new axiom: juxtaposition is the spice of life. Humanity’s biggest talent, unique to us, is juxtaposing, finding and operating novel relationships between things or ideas... Recent ideas on neural activity suggest that the brain operates in a very associative way, with small neuron clusters containing…
...why does it matter what biases and emotional predispositions scientists bring to their studies, so long as they are scrupulously honest and other people with different proclivities check their results? Presumably no one would argue that the conservative view on the sum of fourteen and twenty-seven differs from the…
The contents of a Doomsday Chest will include stainless steel or titanium sheets, laser etched with an archive of the fundamentals of human knowledge. Each sheet would be carved, front and back, in the five most widely spoken languages of the 21st Century; Mandarin, Spanish, English, Arabic and Hindi. To aid in their…
My cousin, at that time, who was three years older, was in high school and was having considerable difficulty with his algebra and had a tutor come, and I was allowed to sin in a corder while (LAUGHS) the tutor would try to teach my cousin algebra, problems liek 2x plus something. I said to my cousin then, "What're…
There are many different types of reasoning, but not too many have been successfully automated beyond deductive linear reasoning and various statistical methods. What alternative methods has the Web facilitated? One obvious candidate is associative reasoning, where reasoning on the basis of associations - which can be…