If you are using a 2 point clock then 2+2=2, on a three point clock 2+2=1, in trinary 2+2=11, and in quaternary 2+2=10, and, of course, in quinary or higher (and on a four point clock) you get back to the mundane 2+2=4. But I always heard the basic statement of absurdity is 1+1=3 (unless you are a Cathar then 1+1=2).
What do you mean by a clock? I can't think of anything clock like that if it only had two-points would even have 2 defined on it. That is, 2 is undefined on a 2 point clock, so 2+2=2 is certainly undefined. As for the 3 point clock, you are absolutely correct, assuming by clock you really mean modular arithmatic.
What I'm talking about is any set for which an isomorphism to a subset of the integers can be defined. This is completely independent of which base you are in, that is, the valid equations that I had expressed above would be, in trinary: 2+2=0 2+2=1 2+2=11 and in quarternary: 2+2=0 2+2=1 2+2=10
Usually, I go with the traditional clock with no zero. Otherwise I think you may be beyond me, but I'll try. So you are doing a mapping from two sets of cardinality aleph-null arranged in integer order. If the operation is really arithmetic but the "=" indicates a specifically defined mapping (like it picks out the nth order) I could see it. Otherwise great sage I will need some help understanding. Afterall, I am taking my maths in the biology direction not the math direction.
Anyhow, you're not changing the "language", whatever you were attempting to say there, you're changing the proposition. 2+2=4 is not the same proposition as 2+2=1 (mod 3). Omitting the description of a thing does not make it magical.
Dear Lord, it's not often that I see something that makes my brain want to turn tail and run! Few people are up to meeting that challenge, but you, dear sir, have just succeeded. After forcing my brain out from under the bed and re-reading the above post and comments a couple times, I consider myself to have achieved a sufficient understanding of the salient points of the aforementioned...but I am not enough of a masochist to engage you in a conversation concerning said subject. ::walks off in astonished awe that someone posts stuff like this for fun...::
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What I'm talking about is any set for which an isomorphism to a subset of the integers can be defined. This is completely independent of which base you are in, that is, the valid equations that I had expressed above would be, in trinary:
2+2=0
2+2=1
2+2=11
and in quarternary:
2+2=0
2+2=1
2+2=10
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Hey, this reminds me of a comic I saw recently!
http://www.xkcd.com/c169.html
Anyhow, you're not changing the "language", whatever you were attempting to say there, you're changing the proposition. 2+2=4 is not the same proposition as 2+2=1 (mod 3). Omitting the description of a thing does not make it magical.
2+2=4, true
2+2=5, false
2+2=1 (mod 3), true
etc.
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;)
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