10 FEB 2018 by ideonexus

 The Thermian Argument

So there's a bad habit people have gotten into. It's nothing new, but it's become more and more common. It goes like this: Critic: Hello. This is Folding Ideas. I recently watched the anime Women Getting Ripped Apart by Orcs and was, you know, disturbed by the seeming perverse glee the way the show takes the frequent and excessive dismemberment of its female cast members. In fact, the entire purpose of the show seems to be little more than showing women being brutally violated by orcs. Mino...
  1  notes
 
29 SEP 2017 by ideonexus

 Roman Arithmetic

...basic Roman arithmetic is largely rather simple, even for those of us spoiled by Arabic notation. Addition is no sweat, because complex Roman numbers already use what math pros call additive notation, with numerals set beside one another to create a larger number. VI is just V plus I, after all. To add large numbers, simply pile all the letters together, arrange them in descending order, and there’s your sum. CLXVI plus CLXVI? CCLLXXVVII, or CCCXXXII. And one of the advantages of the Rom...
Folksonomies: math mathematics education
Folksonomies: math mathematics education
  1  notes
02 SEP 2016 by ideonexus

 Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of us...
  1  notes
 
17 MAR 2016 by ideonexus

 All the Ways of Intuiting 1729

Stanislas Dehaene brings up the Ramanujan-G.H.Hardy anecdote concerning the number 1729. The idea of running through the cubes of all integers from 1 to 12 in order to arrive at Ramanujan's spontaneous recognition of 1729 as the smallest positive integer that can be written in two distinct ways as the sum of two integral cubes is inappropriate and obscures the workings of the naive mathematical mind. To be sure, a computer-mind could come up with that list at a wink. But what would induce it ...
  1  notes
 
14 MAR 2016 by ideonexus

 "Holistic" is a Word That Hides Our Ignorance

We're often told that certain wholes are more than the sum of their parts. We hear this expressed with reverent words like holistic and gestalt, whose academic tones suggest that they refer to clear and definite ideas. But I suspect the actual function of such terms is to anesthetize a sense of ignorance. We say gestalt when things combine to act in ways we can't explain, holistic when we're caught off guard by unexpected happenings and realize we understand less than we thought we did.
Folksonomies: ignorance words
Folksonomies: ignorance words
  1  notes
 
30 MAY 2015 by ideonexus

 Human Combinatoric Reasoning

Humans, of course, were not created in a state of Original Reason. We descended from apes, spent hundreds of millennia in small bands, and evolved our cognitive processes in the service of hunting, gathering, and socializing. Only gradually, with the appearance of literacy, cities, and long-distance travel and communication, could our ancestors cultivate the faculty of reason and apply it to a broader range of concerns, a process that is still ongoing. One would expect that as collective rati...
Folksonomies: reasoning combinatorics
Folksonomies: reasoning combinatorics
  1  notes
 
30 MAY 2015 by ideonexus

 Violence Must be Considered Proportionally When Compared ...

In absolute numbers, of course, civilized societies are matchless in the destruction they have wreaked. But should we look at absolute numbers, or at relative numbers, calculated as a proportion of the populations? The choice confronts us with the moral imponderable of whether it is worse for 50 percent of a population of one hundred to be killed or 1 percent of a population of one billion. In one frame of mind, one could say that a person who is tortured or killed suffers to the same degree ...
Folksonomies: violence quantification
Folksonomies: violence quantification
  1  notes
 
23 MAY 2015 by ideonexus

 Write With Style

Newspaper reporters and technical writers are trained to reveal almost nothing about themselves in their writings. This makes them freaks in the world of writers, since almost all of the other ink-stained wretches in that world reveal a lot about themselves to readers. We call these revelations, accidental and intentional, elements of style. These revelations tell us as readers what sort of person it is with whom we are spending time. Does the writer sound ignorant or informed, stupid or bri...
Folksonomies: writing style
Folksonomies: writing style
  1  notes
 
29 MAY 2014 by ideonexus

 The Kiss Precise

Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is half the square of their sum.
Folksonomies: poetry mathematics
Folksonomies: poetry mathematics
  1  notes

If four circles A, B, C, and D, of radii r1, r2, r3, and r4, are drawn so that they do not overlap but each touches the other three, and if we let b1 = 1/r1, etc., then

(b1 b2 b3 b4)^2 = 2(b1^2 b2^2 b3^2 b4^2).

24 DEC 2013 by ideonexus

 Gedankenexperiment

However, the subject need not be an esoteric one for a gedankenexperiment to be fruitful. My own favorite is Galileo’s proof that, contrary to Aristotle’s view, objects of different mass fall in a vacuum with the same acceleration. One might think that a real experiment needs to be conducted to test that hypothesis, but Galileo simply asked us to consider a large and a small stone tied together by a very light string. If Aristotle was right, the large stone should speed up the smaller one...
  1  notes

Gino Segre on the importance and validity of "thought-experiments," using Galileo's disproof of objects falling at different rates as an example.