Cast of Thought

http://commons.wikimedia.org/wiki/File:Missing_blue_shade.svg

Suppose, therefore, a person to have enjoyed his sight for thirty years, and to have become perfectly acquainted with colours of all kinds, except one particular shade of blue, for instance, which it never has been his fortune to meet with. Let all the different shades of that colour, except that single one, be placed before him, descending gradually from the deepest to the lightest; it is plain, that he will perceive a blank, where that shade is wanting, and will be sensible, that there is a greater distance in that place between the contiguous colours than in any other. Now I ask, whether it be possible for him, from his own imagination, to supply this deficiency, and raise up to himself the idea of that particular shade, though it had never been conveyed to him by his senses?

— David Hume, An Enquiry Concerning Human Understanding, 1748

A Penny Saved

http://commons.wikimedia.org/wiki/File:Walther_Nernst.jpg

When German physicist Walther Nernst learned that his cowshed was warm because of the cows’ metabolic activity, he resolved to sell them and invest in carp.

A thinking man, he said, cultivates animals that are in thermodynamic equilibrium with their surroundings and does not waste his money in heating the universe.

“Plane Geometry”

‘Twas Euclid, and the theorem pi
Did plane and solid in the text,
All parallel were the radii,
And the ang-gulls convex’d.

“Beware the Wentworth-Smith, my son,
And the Loci that vacillate;
Beware the Axiom, and shun
The faithless Postulate.”

He took his Waterman in hand;
Long time the proper proof he sought;
Then rested he by the XYZ
And sat awhile in thought.

And as in inverse thought he sat
A brilliant proof, in lines of flame,
All neat and trim, it came to him,
Tangenting as it came.

“AB, CD,” reflected he–
The Waterman went snicker-snack–
He Q.E.D.-ed, and, proud indeed,
He trapezoided back.

“And hast thou proved the 29th?
Come to my arms, my radius boy!
O good for you! O one point two!”
He rhombused in his joy.

‘Twas Euclid, and the theorem pi
Did plane and solid in the text;
All parallel were the radii,
And the ang-gulls convex’d.

— Emma Rounds

À La Carte

Suppose there were an experience machine that would give you any experience you desired. Superduper neuropsychologists could stimulate your brain so that you would think and feel you were writing a great novel, or making a friend, or reading an interesting book. All the time you would be floating in a tank, with electrodes attached to your brain. Should you plug into this machine for life, preprogramming your life’s experiences? If you are worried about missing out on desirable experiences, we can suppose that business enterprises have researched thoroughly the lives of many others. You can pick and choose from their large library or smorgasbord of such experiences, selecting your life’s experiences for, say, the next two years. After two years have passed, you will have ten minutes or ten hours out of the tank, to select the experiences of your next two years. Of course, while in the tank you won’t know that you’re there; you’ll think it’s all actually happening. … Would you plug in?

— Robert Nozick, Anarchy, State, and Utopia, 1974

Round Trip

chandler perpetual motion

Eric Chandler offered this perpetual-motion scheme for Edward Barbeau’s “Fallacies, Flaws and Flimflam” column in the College Mathematical Journal. Points A and B are at the same height, and C is halfway between them. The ramp AC is a segment of a cycloid, a curve designed to produce the fastest descent under gravity.

A ball released at A rolls down the ramp AC to C covering a greater distance in a shorter time than it would have had it rolled down BC to C. The relation Velocity = Distance/Time thus implies that the ball arrives at C with greater velocity than it would have had it rolled down BC. This added velocity enables the ball to roll from C up to and past B to a point D a little farther along. It then returns to A along the inclined ramp DA to repeat the cycle endlessly.

Where is the error?

Math Notes

99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999989999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999 is prime.