A Quote by Paul Dirac
Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.
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The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.
I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.
For a long time in my adolescence, comedy was the only tool I had for communication and dealing with the world and dealing with people - I didn't know any other lens in which to do it.
There's not a lot of room for un-ironic emotion in contemporary culture. I think that irony is an important tool in dealing with the world as we find it. It's a tool of protection, but it can also be a tool of incision to get to some truth. But along the way maybe we've lost some of what I think of as the power of straightforward emotion and earnestness and seriousness.
Logic is essentially a tool for getting at truth; it is the tool, for without it no reasoning is possible in any field of human enquiry whatsoever.
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created.
In abstract mathematics or abstract art, the purpose is to describe inner states of our mind, and to explore the limits of our own imagination and our capacity for creativity. While this has some applications in the world, I think it leads to a distance from the world. Going to Congo was for me an act of seeking proximity, of breaking that distance. With abstraction, which is brilliant and vain, you divorce yourself from any kind of proximity to other people.
I see philosophy as a fairly abstract activity, as concerned mainly with the analysis of criticism and concepts, and of course most usefully of scientific concepts.
Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
If you are dealing with life from a low-level sensibility, the Internet can be a tool for manifesting that. But if you're dealing with life from the highest sensibility, it can also be your tool for manifesting that. The simple reason is that it doesn't cost money.
To take a single step beyond the boundaries specially drawn around the powers of Congress is to take possession of a boundless field of power, no longer susceptible to definition.
The mind creates so many temptations - so alluring they are, so magnetic is their power - that unless you are in the power-field of someone whose magnetism is far more powerful than any other kind of temptation, it is impossible to reach. That is the meaning of disciplehood.
I consider the foundation of the Constitution as laid on this ground that 'all powers not delegated to the United States, by the Constitution, nor prohibited by it to the states, are reserved to the states or to the people.' To take a single step beyond the boundaries thus specially drawn around the powers of Congress, is to take possession of a boundless field of power not longer susceptible of any definition.
It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.
I say the law should be blind to race, gender and sexual orientation, just as it claims to be blind to wealth and power. There should be no specially protected groups of any kind, except for children, the severely disabled and the elderly, whose physical frailty demands society's care.
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