[LEAPSECS] BBC radio Crowd Science
zefram at fysh.org
Mon Feb 6 08:39:01 EST 2017
Warner Losh wrote:
>So either there's some weird math that lets one subtract two numbers
>that are different and get 0 as the answer, or the delta has to change
>at the start.
To the extent that they're different, the things being subtracted are
not numbers. The expression "TAI - UTC" is shorthand for something more
complicated than a numeric subtraction, which will nevertheless produce
a numeric result. The linear reduction of a timestamp that Clive and
I have separately described is sufficiently numerical to admit of a
straightforward subtraction, and the linear reductions of N:23:59:60 and
(N+1):00:00:00 are duly the same.
An analogy: suppose we do a bit of arithmetic in hexadecimal. We can
all agree that 0x5a0 - 0x5a0 = 0x0. Suppose that while keeping the
hexadecimal radix we additionally use the digit "g", with value sixteen.
Now we find that 0x5a0 - 0x59g = 0x0. The difference is zero, yet the
numbers appear different. What's going on? Well, the numbers per se
are the same: 0x5a0 = 0x59g is a single numerical value. The things
that are different are the digit sequences "5a0" and "59g", which under
the convention being used here are two different ways of expressing that
single number. The digit sequences are not themselves numbers.
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