A Quote by Georg Cantor
I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
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I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
I can give an undertaking that we will respect the constructive opinion of the opposition. We will look into their views, and how they reflect the people's views.
All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
From a mathematical standpoint it is possible to have infinite space. In a mathematical sense space is manifoldness, or combinations of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, the 10-dimension system.
It used to be widely held that evil was incompatible with the existence of God: that no possible world contained both God and evil. So far as I am able tell, this thesis is no longer defended
For though, in nature, depth and height
Are equally held infinite:
In poetry, the height we know;
'Tis only infinite below.
Man has infinite power within himself, and he can realise it - he can realise himself as the one infinite Self. It can be done; but you do not believe it. You pray to God and keep your powder dry all the time.
The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.
I don't believe that math and nature respond to democracy. Just because very clever people have rejected the role of the infinite, their collective opinions, however weighty, won't persuade mother nature to alter her ways. Nature is never wrong.
However, I think the major opposition to ecology has deeper roots than mere economics; ecology threatens widely held values so fundamental that they must be called religious.
He was of an impressible nature, and lived a great deal in other people's opinions and feelings concerning himself.
Opinions are the cheapest commodities on earth. Everyone has a flock of opinions ready to be wished upon anyone who will accept them. If you are influenced by "opinions" when you reach DECISIONS, you will not succeed in any undertaking.
To do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.
The essence of the liberal outlook lies not in what opinions are held, but in how they are held; instead of being held dogmatically, they are held tentatively, and with a consciousness that new evidence may at any moment lead to their abandonment.
Truth is disputable; not taste: what exists in the nature of things is the standard of our judgement; what each man feels within himself is the standard of sentiment. Propositions in geometry may be proved, systems in physics may be controverted; but the harmony of verse, the tenderness of passion, the brilliancy of wit, must give immediate pleasure. No man reasons concerning another's beauty; but frequently concerning the justice or injustice of his actions.
I know this world is ruled by Infinite Intelligence. It required Infinite Intelligence to create it and it requires Infinite Intelligence to keep it on its course ... It is mathematical in its precision.
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