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Re: [HM] Abstracted Ratio.
Posted:
Jul 26, 2006 6:22 AM
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Dear Julio, Ken, Bob et al.
My reaction when reading Bob's letter was very much the same as Ken's
Newton "abstracted" from "equal ratios" to "a single ratio"
sand I just want to add, that "playing with words" he is going from "a
unit" to "a unity".
I also find it interesting that as all applied mathematicians know the
arguments of a mathematical function have to be "numbers", not lengths or
weights or anything else - if "physical dimensions" are included then it
is no longer mathematics, but physics.
So, going back in history we do find that physicists and mathematicians
did have an intuitive feeling for the importance of numbers - long before
they had measured the continuum with numbers.
What I have in mind is that Euclid as a mathematician only allowed
proportions where both magnitudes were of the same kind - had he been a
physicist he could have divided weight by volume to define density ...
Best regards
Sten Kaijser
in Uppsala
***************************************************************
Sten Kaijser
Tel +46 (0)18 471 32 24
Fax +46 (0)18 471 32 01
e-mail: sten@math.uu.se
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