On 03 Mar 2014, at 08:32, Kim Jones wrote:
On 2 Mar 2014, at 11:03 pm, Bruno Marchal <[email protected]> wrote:
On 02 Mar 2014, at 11:13, Kim Jones wrote:
Kim Jones B. Mus. GDTL
On 1 Mar 2014, at 7:43 pm, Bruno Marchal <[email protected]> wrote:
and I chose numbers as people are familiarized with them.
Bruno
How about music? Music is just a bunch of numbers.
Well, you can't say that. Especially to a literally minded stubborn
mathematician :)
I do agree that the relation between math and music are very deep
and profound though.
Yes. Tell me: are the following equivalent statements to a literally-
minded stubborn mathematician like you:
4 + 1 = 5
1 + 4 = 5
2 + 3 = 5
3 + 2 = 5
They are equivalent in many senses, and not equivalent in many other
senses.
They are equivalent semantically, but then with classical semantics,
all true statement are equivalent.
I mean that if you have the truth that 4+1 = 5 then 1+4=5. That is:
(4+1= 5 <-> 1+4=5) is true.
They are deductively equivalent in RA, PA, ZF, etc. because such
theories can prove the equivalence above.
They are not equivalent in any procedural sense. adding 1 to 4 is not
the same thing than adding 4 to 1. It happens that the result is the
same, but the procedure is not.
In fact "equivalent" means nothing, if you don't stipulate the
relation of equivalence applied.
because to a lateral-thinking, alternative-seeking musical thinker
like moi they are not.
OK. But I need your equivalence relation.
You only have to perform (ie clap or tap out) 4 + 1 followed by 1 +
4 to see ( ie hear -> ratiocinate) that they are not equivalent in
the musical sense.
OK, in the musical sense, assuming "+" introduce a time delay in the
claps, they are not.
Give me a shout if you cannot clap these sentences accurately.
Actually, your clap view of numbers make 1+x non equivalent with x+1
useful for the infinite ordinals.
1 + omega = omega
that is clap followed by clap clap clap clap ... is considered as
equivalent to clap clap clap ...
The "+" does not add delay, for the ordinal, unless there are an
infinity, and so:
omega + 1 is not = to omega,
clap, clap, clap, clap, ...., clap ≠ clap, clap, clap,
clap, ....,
That's a different rhythm indeed.
Bruno
K
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