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Re: Numerical accuracy/precision - this is a bug or a feature?

• To: mathgroup at smc.vnet.net
• Subject: [mg120304] Re: Numerical accuracy/precision - this is a bug or a feature?
• From: "slawek" <slawek at host.pl>
• Date: Mon, 18 Jul 2011 06:13:11 -0400 (EDT)
• References: <ius5op$2g7$1@smc.vnet.net> <ius7b6$30t$1@smc.vnet.net> <ivrmd0$82e$1@smc.vnet.net> <ivuc06$gqg$1@smc.vnet.net>

U¿ytkownik "Richard Fateman" <fateman at cs.berkeley.edu> napisa³ w wiadomo¶ci 
grup dyskusyjnych:ivuc06$gqg$1 at smc.vnet.net...
> Now it has been argued that any "science" that has "science" in its name
> is not a true science.  E.g. political science, social science,
> management science, and computer science.  So one could try, as some
> have, to call it "informatics". Or something else.  Maybe Wolframatics?

FYI, the term is the "informatyka" (informatics), which is a translation of 
the "computer science" into Polish.

I suggest also to read a short story "Trurl's machine" by S. Lem (see 
http://www.springerlink.com/content/t310542162241154/ , "How much is two 
plus two?")

In the science there is no rule that the error is "the last figure." If 
there is any tolerance or uncertainty, it must be explicitly marked. Any 
other presumption is wrong and therefore it is not allowed to leave the 
measured values ??without explicitly specified uncertainty. (See 
http://physics.nist.gov/cgi-bin/cuu/Value?tcomwl|search_for=atomnuc! for 
2010 CODATA, the Bohr radius is 0.529 177 210 92 x 10^-10 m with uncertainty 
0.000 000 000 17 x 10^10 m . This standard deviation is not "a last digit" 
or "a last pair" etc.)

Mathematica uses a different convention. By default, assumes that numbers 
such as 1.4 or 2.0 are inaccurate. It is even worse, because though a == b 
is True, then N [a] and N [b] are not the same. Hence we can prove that 1 == 
0, or if you prefer that 2 +2 == 7 .

It is a feature, but in my opinion it may leads to serious bugs.

slawek