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As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality" it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely I’art pour I’art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up. (from "The Mathematician")
This warning is rather similar to Gordon Tullock’s. HT to Jeff Helzner.
Keeping Math Real
I totally understand and support what von Neumann (and later V. I. Arnold) said. I am surprised that this is not screaming obvious to everyone here.
Mathematics today has no resemblance to the real world, and never will have again. I sometimes feel there is almost a cartel at work, a massive clan of academics, whose sole purpose is to justify their existence by developing theory after more esoteric theory, none of which actually matters. They need to do this because people need their PhDs, academics need to keep the hundreds of millions of dollars of grants flowing, and they need to keep publishing to go from being assistant processors to associate professors to professors to emeritus.
It’s their livelihood, fellas. Do you really expect them to rock the boat? What if the grants stop, or if the public start questioning the value of keeping up these behemoths that are pure maths departments?
Just like the credit crunch and the financial services industry today, the higher mathematics community just another industry that is not interested in governing itself. it couldn't care less.
Sometimes I think it’s even worse than that. I almost think mathematicians actually enjoy living in their fairy-tale land, in their make-believe world that they have created because they can’t handle the real world.
Here are some sample topics of recent papers taken from a randomly chosen journal:· "A Banach space without a basis which has the bounded approximation property"· "A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy"· "A class of idempotent measures on compact nilmanifolds"
If you think any of these have any resemblance with the world we live in (or people writing these have the slightest interest about the real world), you are living in the same cloud-cuckoo land.
Unknown, it's really simple. The force is different, the acceleration is the same. The mass which you are measuring the acceleration of cancels out.
If I put a nickel (little mass) into a cup (big mass) and then I take the nickel out (cancel out little mass during the acceleration) what's left? The cup.
If I put a quarter (medium mass) and then take the quarter out (medium mass again) what's left? The cup.
In both cases it is the cup which determines the acceleration not the coin.
You are correct though that the smaller acceleration of the Earth toward different masses is different. But that is not what Aristotle said. He said it depends on the mass of the object not the mass of the Earth. Aristotle is the grandfather of the big mass faster acceleration theory. This is exactly the theory that people still cling to because they make the same mistake he did.
The only way you could get out of it is to say you meant the Earth.