Undergrad Representations, Wittgenstein, and all the rest

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The discussion revolves around the philosophical implications of self-identity as explored by Wittgenstein, particularly in relation to mathematical concepts like equivalence and identity. Participants debate whether two representations of the same value, such as 1/2 and 2/4, should be considered identical or merely equivalent, highlighting the nuances of notation and context in mathematics. The conversation also touches on the relevance of group representations in physics, specifically regarding the general linear group and automorphism groups. Additionally, there are humorous asides about topology and the complexities of defining biological classifications. Overall, the thread illustrates the intersection of philosophy, mathematics, and physics while emphasizing the importance of clarity in discussions.
  • #31
The using of 'different than' alienates me ##-## one thing can be more different or less different from another thing than a third thing is, but one thing can't properly be said to be 'different than' another thing ##-## e.g. an elephant is more different from an amoeba than it is from a mouse, and an elephant is much bigger than either an amoeba or a mouse ##\dots##
 
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  • #32
A practical example: if a vending machine accepts US nickels, dimes, and quarters, whether I deposit 2 quarters or 5 dimes does not affect whether I get the candy bar ##-## if it's a 50-cent candy bar (as in the '70s) then I get the candy bar either way.

In the '80s in Chicago I knew a grocer who had formally studied engineering ##-## sometimes people would show up who wanted to spend their 'change jar' coin money ##-## he would tell them to sort it by which kind of coin, and then he would put the coins on the scale and accept them at value according to their weight ##-## he said that he knew that the per-coin weight varied a little but he didn't care if $35 worth of dimes was off by a dime or two one way or the other, he wasn't going to count them one-by-one, and he didn't want turn away a customer ##\dots##

A US nickel 'weighs' (under standard conditions) very close to 5 grams (5.000 g according to US Mint specs). I've used $2 worth of them to calibrate a scale.
 
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