Folks such as Newton, Copernicus, Pythagoras, and Einstein accomplished amazing things with little more than pen and paper. The few scientific and mathematical instruments they possessed would be little more than crude museum pieces by today's standards. This begs an interesting question: Would these people have accomplished a great deal more if they had access to today's computer technology, or what it have made any difference to them at all?
Having today's computer technology wouldn't have helped these people formulate their ideas in the slightest so, in that sense, the answer would be no.
However, once they have formulate their ideas, because of word processing and the internet, it would have made writing them down and then getting their ideas published and spread across the world a lot faster and easier.
Also, although I doubt computer simulations wouldn't have helped their line research in any significant way, for my line of research, computer simulations speed my research up by at least 4 fold, probably a lot more, and make my research considerably less tedious than what it would have otherwise be.
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@mchill
Computers wouldn't exist today without the discovery of their principles. So I don't think they would have been advantageous, as they are not advantageous today to the discovery of first principals.
@joe-shmo saidWell yes, would Turing have invented his eponymous machine had he had access to an implementation of one?
@mchill
Computers wouldn't exist today without the discovery of their principles. So I don't think they would have been advantageous, as they are not advantageous today to the discovery of first principals.
Computers are as much a hindrance to thought as a benefit. Instead of thinking a problem through one launches into a simulation. The expression about everything looking like a nail to a man with a hammer comes to mind. When AI really gets going we won't think at all, just respond to stimuli.
@wolfgang59 saidSure, but chaos theory is well outside the math realms of the early explorers. That was built on many generations of genius in math and physics. Besides, with a modern computer, suppose they go to the conversion app and Newton finds he needs to convert pounds into Newtons. That would be amusing, eh.
Computers have given mathematicians insight into Chaos Theory.
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@deepthought saidIts my understanding that computers or AI have generated some proofs, but do they do this by computation or by abstraction? How much more valuable is abstraction over computational proofs?
Well yes, would Turing have invented his eponymous machine had he had access to an implementation of one?
Computers are as much a hindrance to thought as a benefit. Instead of thinking a problem through one launches into a simulation. The expression about everything looking like a nail to a man with a hammer comes to mind. When AI really gets going we won't think at all, just respond to stimuli.
Another question that comes to mind is what percentage of (lets say) Newtons time was spent computing? Was he proving difficult limits computationally first? If so then a computer may have been massively advantageous in freeing up his time to "think". If he was predominantly working on the underlying concepts of Calculus then not so much.
I wonder for me personally how much less I would actually "know" without the aid of a computer to perform the tedious calculation steps of problem solving. I'm kind of lazy (and I don't think I'm alone on this) with respect to computation...it can wait until I'm at a computer. To the contrary, I believe the founders rather quite enjoyed the tedium, and I don't think the computational step shook there conviction in the least for verifying a result!
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@mchill saidThose men were innovative, intellectual giants. They were also swimming against a tide of superstition and moral opposition. I believe, with the tech-tools of today, they could move mountains. Especially Einstein.
Folks such as Newton, Copernicus, Pythagoras, and Einstein accomplished amazing things with little more than pen and paper. The few scientific and mathematical instruments they possessed would be little more than crude museum pieces by today's standards. This begs an interesting question: Would these people have accomplished a great deal more if they had access to today's computer technology, or what it have made any difference to them at all?
@joe-shmo saidAutomated theorem solving is a use for computers in symbolic logic. Newton-Rapheson is a method of approximating functions, and is the standard method for finding square roots and so forth on modern machines. Do calculators in schools prevent children from learning arithmetic? One's insight into how numbers work depends to some extent on being able to do basic calculations in one's head. So I think they're a mixed blessing.
Its my understanding that computers or AI have generated some proofs, but do they do this by computation or by abstraction? How much more valuable is abstraction over computational proofs?
Another question that comes to mind is what percentage of (lets say) Newtons time was spent computing? Was he proving difficult limits computationally first? If so then a computer ma ...[text shortened]... and I don't think the computational step shook there conviction in the least for verifying a result!
@joe-shmo
Any proof is done by manipulating a string of symbols using some rules. So there is no particular difficulty in getting a computer to generate proofs, it's just a matter of writing a program to do it. The real problem is working out what the rules ought to be. I doubt that a computer would discover the Axiom of Choice, for example.