for Sunday reflection... just an old, classic joke:
“There are three kinds of people in the world: those who are good at mathematics and those who aren’t.”
...Links for math buffs and number-luvin' laymen
“There are three kinds of people in the world: those who are good at mathematics and those who aren’t.”
“You get surreal numbers by playing games. I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then, when I discovered surreal numbers, I realized that playing games IS mathematics.”
“Meanwhile, Nelson Goodman kept sharpening the knife of nominalism. In 1951 he published The Structure of Appearances. This book contains a logic of parts and wholes. Goodman denies that there are sets. Instead, there are fusions built up from smaller things. Unlike a set, a fusion has a position in space and time. You can touch a fusion. I’m a fusion. So are you. Goodman’s ‘calculus of individuals’ says that there are only finitely many atomic individuals and that any combination of atoms is an individual. Objects do not need to have all their parts connected, for instance, Alaska and Hawaii are parts of the United States of America. Goodman does not let human intuition dictate what counts as an object; he also thinks that there is the fusion of his ear and the moon. In a seminar Goodman taught at the University of Pennsylvania around 1965, John Robison pointed out that The Structure of Appearances implies an answer to ‘Is the number of individuals in the universe odd or even?’ Since there are only finitely many atoms and each individual is identical to a combination of atoms, there are exactly as many individuals as there are combinations of atoms. If there are n atoms, there are 2n - 1 combinations of individuals. No matter which number we choose for n, 2n - 1 is an odd number. Therefore, the number of individuals in the universe is odd! The exclamation point is not for the oddness per se. Aside from those who think the universe is infinite, people agree that the universe contains either an odd number of individuals or an even number of individuals. What they find absurd is that there could be a proof that the number of individuals is odd. ‘Is the number of individuals in the universe odd or even?’ illustrates the possibility of one good answer being too many. Our expectation is that this question is unanswerable. The lone good answer confounds beliefs about what arguments can accomplish.”Anyway, seems like an interesting thought exercise to play with.
“The minds of brilliant mathematicians are of perennial fascination. But in the onrushing era of synthetic neurobiology and genomic reconfiguration, the possibility that genius and mental illness are intertwined takes on monumental significance. If scientists are eventually able to alter living brains or edit human embryos with an eye to mitigating conditions such as autism and schizophrenia, do we risk excising brilliant outliers from the gene pool? Isaac Newton, John Nash, and Alexander Grothendieck are low-frequency, high-impact minds; they advanced civilization in the domain on which they trained their high beams. It is worth turning the high beams of scientific inquiry on those same unusual minds.”
“It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.”