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Dave
science forum beginner
Joined: 03 Feb 2006
Posts: 27
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 Posted: Sat Jun 17, 2006 10:51 am Post subject:
DOES MATHS HAVE ALL ANSWERS?
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Hi everyone, I wonder if there is a discipline in maths to express knowledge, i mean, to express knowledge by mathematics expressions...is it possible?
Regards and thanks |
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Dan in NY
science forum beginner
Joined: 26 Mar 2005
Posts: 20
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| Posted: Fri Jun 23, 2006 10:28 am Post subject:
Re: DOES MATHS HAVE ALL ANSWERS?
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"Dave" <kohonen@hotmail.com> wrote in message
news:3743077.1150541544796.JavaMail.jakarta@nitrogen.mathforum.org...
| Quote: | Hi everyone, I wonder if there is a discipline in maths to express
knowledge, i mean, to express knowledge by mathematics expressions...is it
possible?
Regards and thanks
&&& |
Greetings Dave and other readers,
I will give a qualified but resounding opinion, "No, IMHO, mathematics
doesn't have all the answers." In mathematics we use definitions and axioms
to set up a system of thought. Using Mathematics, a person can do no more
than to make conjectures, then either demonstrate them, prove them true or
prove them false.
Before I retired, I was a programmer. I know that sometimes a computer
makes an error but much more often the computer does what the programmer
tells it to do -- whether it the results are intended or not. A similar
thing happens with mathematics. In order to apply mathematics to express
any knowledge, either one must make assumptions to make the knowledge fit
the mathematical system -- or -- create a mathematical system to fit the
knowledge. Usually this only gives an approximate result because the
assumptions don't fit the thought.
I will give one example. Consider equilateral triangles. In Geometry lots
of theorems are proved about them. However, if it is attempted to use these
triangles to apply it to knowledge, one soon realizes that assumptions are
needed. No one can actually create a "real' equilateral triangle. How can
one know whether all the sides are equal? No, to use the mathematics, one
needs to assume that they are equal -- or assume something else then prove
they are equal. One cannot even measure one side of a triangle exactly.
Years ago, I took a semester graduate course (that met three days a week) to
follow the proof that there are undecidable questions in any mathematical
system. The professor made a believer out of me. I surfed with Google and
got over 100,000 hits for 'Gödel undecidable'. One of them is
http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorem.
Enough of my babble. I tried to give a serious answer to the question in
the subject of this thread and I don't even know whether anyone cared to get
one.
--
Dan in NY
(for email, exchange y with g in
dKlinkenbery at hvc dot rr dot com) |
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Mark Lawton
science forum beginner
Joined: 22 Mar 2006
Posts: 11
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| Posted: Fri Jun 30, 2006 4:19 pm Post subject:
Re: DOES MATHS HAVE ALL ANSWERS?
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IMO, you could do a lot worse than starting your quest by looking at
set/list logic. Here's a relevant Wikipedia article:
http://en.wikipedia.org/wiki/Set
Dave wrote:
| Quote: | Hi everyone, I wonder if there is a discipline in maths to express knowledge, i mean, to express knowledge by mathematics expressions...is it possible?
Regards and thanks |
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mathsrwc
science forum beginner
Joined: 04 Oct 2006
Posts: 4
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| Posted: Mon Oct 16, 2006 4:13 am Post subject:
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Is there anything Wikipedia doesnt know?!
It is also so up to date - I remember when Steve irwin died they had it up there before most news services had broadcast it. |
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