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The famous Canadian physician William Osler once wrote, “In science the credit goes to the man who convinced the world, not to the man to whom the idea first occurs.” When we examine discoveries in science and mathematics, in hindsight we often find that if one scientist did not make a particular discovery, some other…
Benoit Mandelbrot asked his famous question “How long is the coast of Britain?” long before this symposium was written, but it perfectly captures the sort of puzzle people in this crowd love. The question seems simple. Just look it up in the encyclopedia. But as Mandelbrot observed, the length of the coast of Britain…
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful…
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution…
Now these numbers can be appreciated in many different ways. From the standpoint of calculation, they're as easy to understand as one plus one, which is two. Then one plus two is three, two plus three is five, three plus five is eight, and so on. Indeed, the person we call Fibonacci was actually named Leonardo of…
So why do we learn mathematics? Essentially, for three reasons: calculation, application, and last, and unfortunately least in terms of the time we give it, inspiration. Mathematics is the science of patterns, and we study it to learn how to think logically, critically and creatively, but too much of the mathematics…
The selfish gene theory is Darwin's theory, expressed in a way that Darwin did not choose but whose aptness, I should like to think, he would instantly have recognized and delighted in. It is in fact a logical outgrowth of orthodox neo-Darwinism, but expressed as a novel image. Rather than focus on the individual…
No word is more on people's lips than "Evolution"; and none is more frequently misused, and misunderstood. Social Evolution is often talked of as if it were a cosmic process forced on men wholly from the outside, regardless of their yea and nay; or again as if it were a beneficent dispensation "from on high" that…
Before there was an accurate seafaring clock, the sailor seeking his bearings had to be a trained mathematician. The accepted way to find longitude at sea was by precise observations of the moon, which required refined instruments and subtle calculations. An error as small as 5' in observing the moon meant an error of…
At least mathematicians try not to contradict one another. Not so philosophers! They are all "great"... and all in total disagreement! "Studying philosophy" really means gorging yourself on a stew of every idea imaginable. A Platonist thinks appearance is but a bad copy of reality... While an Aristotelian puts all his…
I request a last indulgence from the reader. The introductory material, thus far, has been written in the friendly and confiding first person singular voice. Starting in the next paragraph, I will inhabit the first person plural for the duration of the mathematical expositions. This should not be construed as a “royal…
Getting ready for the assumed inexorable Armageddon, each applied science and all of the great scientific specialization capabilities only toward weaponry, thus developing the ability to destroy themselves totally with no comprehensively organized oppositional thinking capability and initiative powerful enough to…
Kakeru Seki: A fact is somehow related to another fact. Unless you understand these relationships, you won't be a real reporter. Noriko Hikima: True journalism! Kakeru Seki: Well, you majored in the humanities. Noriko Hikima: Yes! That's true--I've studied literature since I was in high school. Kakeru Seki: You havea…
Studies 1 and 2. Our first two studies were naturalistic field studies, and examined whether upper-class individuals behave more unethically than lower-class individuals while driving. In study 1, we investigated whether upper-class drivers were more likely to cut off other vehicles at a busy four-way intersection…
Surveillance serves not just as a legal and historical record but as a record of rep: proof that you’ve done what you say you’ve done. You bark, and anyone on the mesh can search to see if you also bite. It’s the foundation of the reputation economy. It’s not just video, of course, but surveillance of all types…
Phrases like “things are looking up” and “look at the upside” once meant something like “consider the good in the situation,” but they went through an ironic shift in the solar system’s early spacecolonial culture, mutating in the microgravity of early tin-can stations to mean a variety of practically sarcastic…
Systems science is best seen as a science that consists of nested sub-sciences. It is presented most compactly using the notation of set theory. Let A represent a science of description. Let B represent a science of design. Let C represent a science of complexity. Let D represent a science of action (praxiology). Let…
Occasionally he made a comment similar to Archimedes' "Eureka!" about a discovery, as he did when he wrong T T T=N. This is part of number theory, the field that Gauss called the Queen of Mathematics. A triangular number T is a number that you can get by adding up a string of consecutive whole numbers beginning with…
Life began in water, and every single function of life takes place in an aqueous environment. A profound way of classification in chemistry is the relation and interaction between molecules, or groups within molecules, and water. Molecules (or parts of molecules) can attract water in which case they are called…
Information may be categorized into primary and secondary material. If information is new and has never been published before it research, new legislation and survey results, like government is termed primary. It includes original statistics. Primary information is always up-to-date, detailed, accurate and…