A Quote by David Berlinski
The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system.
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Music for a long time has been telling what the world is like. What music has to say now, in a manner that has both logic and emotion in it, is that the world has a structure persons could like; be stronger by.... [If] the world is the oneness of opposites - and music says it is - the world is given an everlastingly sensible basis; for what could be more sensible that to be calm and forceful at once, reposeful and intense at once?
The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.
None of us exist in a world that is the same world that any of the rest of us live in. The world that's important is the world behind each of our eyes, which is something that none of the rest of us can access.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
They said God was on high and he controlled the world and therefore we must pray against Satan. Well, if God controls the world, he controls Satan. For me, religion was full of misstatements and reaches of logic that I just couldn't agree with.
Every language having a structure, by the very nature of language, reflects in its own structure that of the world as assumed by those who evolved the language. In other words, we read unconsciously into the world the structure of the language we use.
Fairy tales, because they have a very clear structure, are easier to interfere with. Also they have this really weird logic: the kind of logic that you only really experience when you're not feeling very well, or as a child.
Fairy tales, because they have a very clear structure, are easier to interfere with. Also they have this really weird logic: the kind of logic that you only really experience when youre not feeling very well, or as a child.
If words are not things, or maps are not the actual territory, then, obviously, the only possible link between the objective world and the linguistic world is found in structure, and structure alone.
If human language, with its logic, is the way God has given us to understand the world, then the Torah must be understood in that same language and with that same logic.
We have to live with the rest of the world. And it's a mistake, in my view. Trade has generally developed in this country. We actually export 12 or 13 percent of our GDP. It was only 5 percent in 1970. But it benefits us. It benefits the rest of the world. It doesn't benefit the steelworker maybe in Ohio. And that's the problem that has to be addressed, because when you have something that's good for society, but terribly harmful for given individuals, we have got to make sure those individuals are taken care of.
The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician's "blank form of a universe" without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition. Just as Newton first conclusively showed that this is a world of masses, so Willard Gibbs first revealed it as a world of systems.
I think every film is somehow a political film. You show a perspective and a world that has logic, and that logic is inserted into a political environment, and it means something. Yes, why not?
Phonogram was explicitly about our world. It’s a fantasy which is happening around us all, unnoticed except for those who’ve fallen into its world. In a real way, it’s real. Conversely, W+D is much more overt. The appearance of the gods changes the world, and has changed the world going back. There’s the strong implication that certain figures in our world simply didn’t exist in The Wicked And The Divine‘s world, because they were replaced by a god.
The rules of logic are to mathematics what those of structure are to architecture.
Today, something is happening to the whole structure of human consciousness. A fresh kind of life is starting. Driven by the forces of love, the fragments of the world are seeking each other, so that the world may come into being.
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