Well, this opened a sore spot with me. It's always bothered me how
people get so involved with the method of solving a problem that they
forget about the quality of the input.
Yes, it's no problem to find alternate representations to binary which
avoid many of the problems such as decimals. In fact, earlier
commercially oriented computers were decimal, not binary, and completely
avoided having to count in pennies instead of dollars. Today's IBM
mainframes include decimal arithmetic instructions.
To me J's support of rational numbers is a major advancement. To
compute the exact inverse of a matrix is amazing to me. Mathematical
notation is still far ahead of computer science.
Miller, Raul D wrote:
Don Guinn wrote:
Computers use base two arithmetic because it is efficient and gives
practical solutions to real problems. The fact that it can't even
represent the number one-tenth exactly usually doesn't cause problems.
But I'm sure it does in the banking industry.
Be careful here.
It's possible to represent one-tenth exactly using base two arithmetic
just as it's possible to represent the square root of two exactly
using base two arithmetic.
For example, consider a three row numeric matrix and the tacit
expression
{. +/@:* 1&{ ^ {:
The result of applying that tacit expression to the three row
matrix will not be exact, but the matrix itself can be used
to exactly represent one tenth (,.1 10 _1), the square root
of 2 (,.1 2 0.5) and their sum (1,10 2,:_1 0.5)
Of course, this does not address obtaining the decimal
representation of these numbers to some arbitrary precision.
And there are plenty of other issues.
Of course, you're right about problems for the banking industry
(which can be solved simply. For example, represent
U.S. currency in cents rather than dollars.)
Computers manipulate symbols, and it's up to the user
to ensure that those symbols are being used in a manner
consistent with the user's thinking.
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