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Message-id: <9307022257.AA27610@gemini.cs.cornell.edu> To: qed@mcs.anl.gov Subject: Re: Motivation #1 In-Reply-To: <LYBRHED@delphi.com>'s message of "Fri, 02 Jul 93 02:13:20 EDT." <01H01TNJWG0I8ZFOWH@delphi.com> Date: Fri, 02 Jul 93 18:57:53 -0400 From: Wilfred Chen <chen@cs.cornell.edu> Sender: qed-owner Precedence: bulk

Lyle Burkhead wrote: Objection 10. The Manifesto begins by promising to solve a problem which either does not exist, or can't be solved. 1. The problem doesn't exist. ... 2. The problem exists but can't be solved. There is a sense in which there is a problem of "too much mathematics." There is an enormous amount of mathematics which is undeniably important, and which is inaccessible to me, because it would take a thousand years to read it. But this is an ineluctable fact. It's not a problem that could be solved. QED could not possibly change the situation. Nothing can change it. One man can't absorb all the mathematics produced by hundreds. If you take the collected works of Abel, Riemann, Poincare, Goedel, Thom, and two or three hundred other mathematicians whose work is at least sometimes on more or less the same level, and enter all that mathematics into a proof checker, it would still take many lifetimes to read it all. In fact it would take longer to read mathematics through a QED terminal than it would take to read it in printed form. (I envision a QED terminal as something resembling an ORION terminal.) If reading is the only thing we want to make use of QED. One of the advantage a teacher has over a book is that you can ask questions that either aren't answered explicitly in the book or you can't find it in the book easily. A successful QED system would be somewhere in the middle between a book and a teacher: being able to answer some questions that are obvious consequences of what's in the book. There really is no limit to how much we could want from such a knowledge representation system. Furthermore, even a very poor machine approximation to human intelligence is appealing, because it is very much easier to duplicate. 3. The "problem" can be mitigated, but not with QED. To the extent that there is a problem of "too much math," the only way to mitigate it is to increase one's reading speed. QED goes in the wrong direction. If the target is to increase my reading speed, you don't want to force me to resolve informal statements into all their nitty gritty logical and set theoretic details. That would be like forcing me to read program listings in assembly language. It would slow me down. To increase my reading speed, what you want to do is present mathematics on a computer screen in such a way that I can take in more of it at a glance, and see relationships quickly that I would otherwise have to discover with great labor. Better yet, you want to present mathematics on the screen in such a way that it trains my imagination, so that eventually I can learn to see vector fields the way Riemann saw them, without the aid of a computer, and maybe even learn to see everything from the center, as he did. Why limit to the screen? Surely there are limitations to the visual system. While we are at it (not exacly a QED topic) perhaps abstract mathematical objects can be presented by feeding it directly to some kind of brain implant, or, perhaps easier, some kind of direct stimulation of the retina with light beams. We'd probably have to be trained from an early age to handle these. Wilfred Chen