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