Fractional Quotes
We have tried occasionally to buy toads at bargain prices with results that have been chronicled in past reports. Clearly our kisses fell flat. We have done well with a couple of princes - but they were princes when purchased. At least our kisses didn't turn them into toads. And, finally, we have occasionally been quite successful in purchasing fractional interests in easily-identifiable princes at toad-like prices.
Warren Buffett
Protocols:
Number 10, paras. 6,7
A scheme of government should come ready made from one brain, because it will never be clinched firmly if it is allowed to split into fractional parts in the minds of many. It is allowable, therefore, for us to have cognizance of the scheme of action but not to discuss it lest we disturb its artfulness, and interdependence of its component parts, the practical force of the secret meaning of each clause. To discuss and make alteration in a labor of this kind by means of numerous votings is to impress upon it the stamp of all ratiocinations and misunderstandings which have failed to penetrate the depth and nexus of its plottings....
These schemes will not turn existing institutions upside down just yet, They will only effect changes in their economy and consequently in the whole combined movement of their progress, which will thus be directed along the paths laid down in our schemes.
Will Eisner
Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone. The question only remains how to do this.
Richard Dedekind
Find a fraction which, multiplied by itself, shall give 6, or... find the square root of 6. This can be shown to be an impossible problem; for it can be shown that no fraction whatsoever multiplied by itself, can give a whole number, unless it be itself a whole number disguised in a fractional form, such as 4⁄2 or 21⁄3. To this problem, then, there is but one answer, that it is self-contradictory. But if we propose the following problem,-to find a fraction which, multiplied by itself, shall give a product lying between 6 and 6 + a; we find that this problem admits of solution in every case. It therefore admits of solution however small a may be... as small as you please.
Augustus De Morgan
The possibility and significance of fractional angular momentum is discussed, and some simple physical realizations of it are mentioned. This leads naturally to consideration of the possibility of fractional quantum statistics, which is seen to be a possibility inherent in the kinematics of 2+1 dimensional quantum mechanics. Both sorts of fractionalization are intimately related to theories, and the classic considerations of Aharonov and Bohm on the significance of the vector potential in quantum mechanics. The meaning and importance of discrete gauge invariance in continuum theories is pointed out. Fractional statistics is shown to have a simple dynamical realization in the dynamics of charge-flux tube composites. Fractional statistics is shown to occur very naturally in the most geometrical quantum field theories in 2+1 dimensions, that is in the nonlinear sigma model and in quantum electrodynamics.
Frank Wilczek