Comments on: Spending symmetry
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Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoSun, 21 Dec 2014 04:03:32 +0000hourly1http://wordpress.com/By: A mathematical formalisation of dimensional analysis « What’s new
http://terrytao.wordpress.com/books/spending-symmetry/#comment-211406
Sat, 29 Dec 2012 21:04:41 +0000http://terrytao.wordpress.com/?page_id=6307#comment-211406[…] We have already observed that to verify a dimensionally consistent statement between dimensionful quantities, it suffices to do so for a single choice of the dimension parameters ; one can view this as being analogous to the transfer principle in nonstandard analysis, relating dimensionful mathematics with dimensionless mathematics. Thus, for instance, if have the units of , , and respectively, then to verify the dimensionally consistent identity , it suffices to do so for a single choice of units . For instance, one can choose a set of units (such as Planck units) for which the speed of light becomes , in which case the dimensionally consistent identity simplifies to the dimensionally inconsistent identity . Note that once we sacrifice dimensional consistency, though, we cannot then transfer back to the dimensionful setting; the identity does not hold for all choices of units, only the special choice of units for which . So we see a tradeoff between the freedom to vary units, and the freedom to work with dimensionally inconsistent equations; one can spend one freedom for another, but one cannot have both at the same time. (This is closely related to the concept of spending symmetry, which I discuss for instance in this post (or in Section 2.1 of this book).) […]
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http://terrytao.wordpress.com/books/spending-symmetry/#comment-200750
Fri, 07 Dec 2012 08:43:25 +0000http://terrytao.wordpress.com/?page_id=6307#comment-200750Wish even more success for you, Professor.
I cannot wait to come to the deparment to study and hopefully become your student Someday.
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http://terrytao.wordpress.com/books/spending-symmetry/#comment-193914
Sun, 18 Nov 2012 18:16:37 +0000http://terrytao.wordpress.com/?page_id=6307#comment-193914[…] my 2011 blog posts (and also my Google buzzes and Google+ posts from that year), entitled “Spending symmetry“. The PDF of this draft is available here. This is again a rather assorted (and […]
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