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Re: algebraic numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg106316] Re: algebraic numbers
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Fri, 8 Jan 2010 04:15:22 -0500 (EST)
• References: <200912290620.BAA02732@smc.vnet.net> <hhpl0g$9l1$1@smc.vnet.net> <hi42kd$nai$1@smc.vnet.net>

I agree with Bob.

who says that "all computer reals are rationals" [The ones that are 
represented by fractions and exponents consisting of finite strings of 
bits.., not those that are symbols like Pi].

The fact that Penrose annoyed a lot of people with his attack on 
computer science does not mean he is right, or worthy of reading
(though I have read his first opus).

  I tried another Google search and got ..

  Results 1 - 10 of about 188,000 for "hannah montana" +philosophy. 
(0.24 seconds)



As for whether a computer program could conceptualize mathematics and 
"know" something, anyone could just say "no, computers can't".
Others might point to programs that prove new theorems as a 
demonstration that computers "know math". (There are conferences
on this topic, Mathematical Knowledge Management, and long-term research 
projects on theorem proving by computer). And a more cogent (but also
deeply flawed) discussion of what computers can/can't do has been 
presented by John Searle, who is not a physicist, but a philosopher by 
profession.

Others have said that computers will not replace mathematicians until 
computers learn to drink coffee.

RJF