FOM: Re: Godel, f.o.m.

Steve Stevenson steve at
Wed Jan 26 13:45:22 EST 2000

 > > > Steve Stevenson wrote:
 > >I believe that his point is something different, especially given the
 > >"formal systems" tenor of Vladmir's comment. The machine is inherently
 > >different, period. Your criticism were used by Hoare and the rest of
 > >the formalist part of computer science.
 >     I wasn't aware anyone had responded to Fetzer.  As I recall, his remarks
 > begged for a response.  I'm glad to be in Hoare's company, except that I
 > hope you're not branding me a "formalist" in order to dismiss my points.  If
 > I'm wrong about Fetzer's points, what do you think they really were, and how
 > does "the 'formalist systems' tenor of Vlamir's comment" matter to the
 > points Fetzer made in his article?

I'll point you to an article by Jon Barwise. 

  author = 	 {Jon Barwise},
  title = 	 {Mathematical Proofs of Computer System Correctness},
  journal = 	 {Notices of the AMS},
  year = 	 {1989},
  OPTkey = 	 {},
  OPTvolume = 	 {36},
  OPTnumber = 	 {},
  OPTpages = 	 {844--851},
  OPTmonth = 	 {Sep},
  OPTnote = 	 {},
  OPTannote = 	 {}

 > >It would seem to me that 21st Century mathematics must include the
 > >computer as part of the tool kit. If this is not the case, then the
 > >principles of computing will lie elsewhere. If it is the case, then we
 > >must recognize the limits to what it does and does not do. For
 > >example, is it possible to put enough constraints on a computation to
 > >correct machine errors when they occur?
 >     What you're saying above is difficult for me to fully understand, though
 > I feel somewhat sympathetic with your remarks.  Just to clear the air, it
 > seemed to me when I read Fetzer's paper that it would be loved by some
 > people and hated by others.  The people who loved it were the--enormous
 > generalization coming--non-mathematical types who had dominated c.s. for
 > several years and could feel their power slipping away, as the new
 > generation of more mathematically sophisticated c.s people started asserting
 > themselves.   Whew!  The ones who hated it were the math people who for one
 > reason or another (often because they couldn't get good math jobs) landed in
 > the field of computer science and were using the authority of mathematics to
 > push the older generation of programmers, compiler writers, etc. into the
 > background.  Whew again!   I'm not taking a side here; I just wanted to
 > clear the air by saying that there  were passionate views behind this.
 > >Turing machines are really boring. And there was a time when people
 > >actually used mathematics for things ....
 >     Sorry, I don't get your point here.

No point. A gratuitous swipe at equating computing to
decidability/computability theory. See below.

 >  If it pertains to my allusion to
 > Turing, I meant only that the recursive unsolvability of the Halting Problem
 > makes it impossible for there to be a universal program checker.  I'd have
 > thought you'd be sympathetic with this.  As for Turing Machines being
 > boring, I don't think this is a disputable point, assuming you mean that
 > it's a struggle for a TM to do anything "interesting".   I don't want to get
 > preachy, and I know you know this anyway, but the value of a TM is not in
 > its actual use, but in its theoretical power.   I think I may be missing
 > your point, though, because in looking back at what you said, I re-read:
 > "there was a time when people
 > actually used mathematics for things ...." and am not sure what you're
 > getting at.  Is it that you think the mathematics behind TMs is not for
 > (doing) things.  If so, I agree.

Yes, that's all settled. But, I think a far more interesting question
for computing is not the universal-ganzenmacher algorithm and the
once-and-for-all (since we can't do it). I'd rather concentrate on
what I can do. I'll repeat something that I heard but can't properly
attribute but it was bW [before Wiles]: "No one cares about Fermat's
Last Theorem because nothing hinges on it. But we care about the proof
since that will tell us volumes."  I find myself taking on a position
that I cannot win in this forum. Mathematics is not always a
meaningless bunch of symbols being pushed around. For those people who
use mathematics to solve problems in their disciplines (like physics,
chemistry, and engineering), the question is "How reliable is your
mathematics?" Think about it the next time you fly, 'cause the plane
is being landed by computers, not humans.

Charlie, we're looking at this from different perspectives and so will
never quite come to grips with the whole thing. My view of mathematics
(and computer science) is this: is it part of the solution space or is
it part of the problem space? If it's part of the solution space, then
how reliable are the judgements I must draw from using it when it
comes down to building real <anything>?

  author = 	 {D. E. Stevenson},
  title = 	 {A Critical Look at Quality in Large-Scale Simulations}, 
  journal = 	 {IEEE Computing in Science and Engineering},
  year = 	 1999,
  volume =	 1,
  number =	 3,
  pages =	 {53--63},
  month =	 {May/June}


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