Molyneux's problem

I shall here insert a problem of that very ingenious and studious promoter of real knowledge, the learned and worthy Mr. Molyneux, which he was pleased to send me in a letter some months since; and it is this:- "Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt one and the other, which is the cube, which the sphere. Suppose then the cube and sphere placed on...

 What People Can Achieve Grows Exponentially

The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube fo...

 The Circle of the Brain cannot be Squared

A Circle round divided in four partsHath been great Study 'mongst the men of Arts;Since Archimed's or Euclid's time, each BrainHath on a Line been stretched, yet all in Vain;And every Thought hath been a Figure set,Doubts Cyphers were, Hopes as Triangles met;There was Division and Subtraction made,And Lines drawn out, and Points exactly laid,But none hath yet by Demonstration foundThe way, by which to Square a Circle round:For while the Brain is round, no Square will be,While Thoughts divi...

 Number of Bits for a Set of Encyclopedias are Minuscule C...

I have estimaged how many letters there are in a the Enclyclopaedia, and I have assumed that each of my 24 million books is as big as an Encyclopaedia volume, and have calculated, then, how many bits of information there are (10^15). For each bit I allow 100 atoms. And it turns out that all of the information that man has carefully accumulated in all the books in the world can be written in this form in a cube of material one two-hundredths of an inch wide--which is the barest piece of dust t...