06 JAN 2018 by ideonexus
Pattern-Seeking Through Play
Meredith's worldplay was shot through with yet another well-recognized ingigredienlent of creative thinking, the comparison and synthesis of two or more unlike things. As the mathematician and poet Jacob Bronowski famously expressed it, the discoveries of science and of art "are explorations—^more, are explosions, of a hidden likeness The same holds true for the insights generated in worldplay. Documents of play in Lewis, like many a child, combined the animal and the human in Lord Big. Una... 1 
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notes12 APR 2013 by ideonexus
All Models are Wrong, but some models are useful
As the statistician George E. P. Box wrote, “All models are wrong, but some models are useful.”90 What he meant by that is that all models are simplifications of the universe, as they must necessarily be. As another mathematician said, “The best model of a cat is a cat.”91 Everything else is leaving out some sort of detail. How pertinent that detail might be will depend on exactly what problem we’re trying to solve and on how precise an answer we require.
Nor are statistical models...
1 All models are simplifications of the universe, this includes language as a form of modeling.
21 JUN 2012 by ideonexus
Mathematicians Who Can Only Generalize or Specialize
A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. ... There is, I think, a moral for the teacher. A teacher of traditiona...Folksonomies: mathematics methodology
Folksonomies: mathematics methodology
1 notes
notesThey are like monkeys that can only climb either up or down a tree, nonviable.
24 APR 2012 by ideonexus
Mathematics Feels Real, but is Paradoxical
On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient. Folksonomies: mathematics philosophy
Folksonomies: mathematics philosophy
1 notes
notesReal to the mathematician, paradoxical to the philosopher.
23 MAR 2012 by ideonexus
Metaphor for the Mathematician
The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight. As a designer of garments for unknown beings, who delights in learning their shape as they go.
17 JAN 2012 by ideonexus
Science is Discovery, Not Creation
I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him. The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal. Folksonomies: discovery
Folksonomies: discovery
1 notes
notesThe scientist is simply following the path nature has provided, uncovering its mysteries along the way.
05 JAN 2012 by ideonexus
Roberto Bellarmino's Condemnaton of Galileo's Theory
It seems to me that your Reverence and Signor Galileo act prudently when you content yourselves with speaking hypothetically and not absolutely, as I have always understood that Copernicus spoke. To say that on the supposition of the Earth's movement and the Sun's quiescence all the celestial appearances are explained better than by the theory of eccentrics and epicycles is to speak with excellent good sense and to run no risk whatsoever. Such a manner of speaking is enough for a mathematicia... 1 notes
notesThe inquisitor responsible for Giordano Bruno's prosecution argues that Galileo's theory that the sun is the center of the Universe would refute scripture.
16 DEC 2011 by ideonexus
The Temperament of the Mathematician
It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, chusing [choosing] rather to acknowledge their ignorance, than affirm anything rashly. They...Folksonomies: mathematics
Folksonomies: mathematics
1 notes
notesAlways to acknowledge their ignorance and only indulge in those pursuits in which total certainty may be achieved.
