A Quote by Aldous Huxley
Some of the greatest advances in mathematics have been due to the invention of symbols, which it afterwards became necessary to explain; from the minus sign proceeded the whole theory of negative quantities.
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[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.
The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
Even in relativity theory even though you can analyze space - time in terms of this four-dimensional geometrical structure one of the dimensions is different. And this shows up in the equations. It has a different sign - rather than plus it shows up as a negative minus. So even in relativity theory time is distinct from space in terms of the way in which these dimensions manifest themselves in the equations.
And happiness...Well, after all, desires torment us, don't they? And, clearly, happiness is when there are no more desires, not one...What a mistake, what ridiculous prejudice it's been to have marked happiness always with a plus sign. Absolute happiness should, of course, carry a minus sign — the divine minus.
The whole action of the laws tended to increase the number of consumers of food and to diminish the number of producers, was due the invention of the Malthusian theory of population.
Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.
As I considered the matter carefully it gradually came to light that all those matters only were referred to mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called 'universal mathematics'.
One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.
General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines. Mathematics attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge.
The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.
It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.
It would take a civilization far more advanced than ours, unbelievably advanced, to begin to manipulate negative energy to create gateways to the past. But if you could obtain large quantities of negative energy-and that's a big "IF" - then you could create a time machine that apparently obeys Einstein's equation and perhaps the laws of quantum theory.
Birth Control which has been criticized as negative and destructive, is really the greatest and most truly eugenic method, and its adoption as part of the program of Eugenics would immediately give a concrete and realistic power to that science. . . as the most constructive and necessary of the means to racial health.
The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.
Great abilities are not requisite for an Historian; for in historical composition, all the greatest powers of the human mind are quiescent. He has facts ready to his hand; so there is no exercise of invention. Imagination is not required in any degree; only about as much as is used in the lowest kinds of poetry. Some penetration, accuracy, and coloring, will fit a man for the task, if he can give the application which is necessary.
The theory of free speech, that truth is so much larger and stranger and more many-sided than we know of, that it is very much better at all costs to hear everyone's account of it, is a theory which has been justified on the whole by experiment, but which remains a very daring and even a very surprising theory. It is really one of the great discoveries of the modern time.
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