I've sat in theoretical physics seminars where the Axiom of Choice was mentioned. I can't remember anything about what they were saying, it's too long ago. The stuff I did involved some results from graph theory so Zorn's lemma (not that I'd heard of it before) actually is relevant to what I was doing. In two dimensional lattice gravity the physics is extracted by considering all ways of gluing triangles together, the dual lattice for a given triangulation is obtained by putting a dot in the middle of each triangle and joining nearest neighbouring dots. This produces a phi cubed graph, in our jargon, a graph where each vertex has three links coming out of it. There was mention of spanning trees so knowing there's at least one spanning tree is important.
Originally posted by DeepThought The way the Planck time is obtained is a game of playing with numbers. One takes Newton's constant, Planck's constant, the speed of light and mixes them together so something with the units of time come out. This gives the scale at which one would expect Quantum Gravity effects to dominate. There are good reasons to believe that it is impossible to [i ...[text shortened]... me reasons to think it might be, as other things are quantized, but that question is still open.
As the matter of Planchk time has nothing to do with the original topic of the thread I am not going to comment anything more on this.
I am just surprised that people actually think it is possible to write out an infinite number of digits. Sometimes I hear that "the national dept is infinite", that "there are infinite number of sand grains on the beach" and such, meaning that it is very much, very very much. They just don't know the difference between something incredibly many and infinite many. But they haven't studied math much so I forgive them. And then I read it is actually possible to write down an infinite number of digits on a paper. That surprises me.
Most physicists I know indeed tend to have little interest in the formal foundations of mathematics. No knowledge of it is required for the vast majority of professional physicists. I would expect the average undergraduate in mathematics to have a better understanding of it than I do.
In my case that is true but it is not the only truth. I always did like pure mathematics and during my first year of college I almost decided to study mathematics instead of mathematics. I always read mathematics books that were intended for mathematics undergrads and sometimes even sometimes to mathematics graduate students and my colleagues always told me that I was more of a mathematician than a physicist.
Kazet explicitly said he expects the average undergrad student in mathematics to know more about maths than him. In my case this is not true. Maybe it is more true now that I'm very rusty, but it definitely wasn't true while I was an undergrad student in physics. In things like "theoretical" infinitesimal analysis, complex analysis, linear algebra i know for a fact that I knew a lot more than the average undergrad student in mathematics. And I'm talking about the run of the mill exercise solving but also about the fact that I was able to understand more, more deeply and more broadly then some mathematics good students that I knew back in the day.
In my post I said that we used results from graph theory. Trees on dual lattice were important structures and the existence of a spanning tree, which according to the Wikipedia page is a result from Zorn's lemma is of interest. Other people gave seminars where the Axiom of Choice was mentioned. That is all I was claiming, if you read anything more into it then it must have been because I expressed myself badly.
Originally posted by adam warlock In my case that is true but it is not the only truth. I always did like pure mathematics and during my first year of college I almost decided to study mathematics instead of mathematics. I always read mathematics books that were intended for mathematics undergrads and sometimes even sometimes to mathematics graduate students and my colleagues always tol ...[text shortened]... e, more deeply and more broadly then some mathematics good students that I knew back in the day.
Actually, I was talking about the "formal foundations" of mathematics, not mathematics in general. I would certainly expect to be more knowledgeable than the average undergrad in maths about, say, solving differential equations or numerical methods.
Originally posted by KazetNagorra Actually, I was talking about the "formal foundations" of mathematics, not mathematics in general. I would certainly expect to be more knowledgeable than the average undergrad in maths about, say, solving differential equations or numerical methods.
Yes, those math geeks are usually more interested in necessary and sufficient conditions and existence and uniqueness; while we the crazysexcool physicist are more interested in Taylor series and solving stuff. Even if we don't know if a such a solution exists and if it is unique.
But even in formal foundations of mathematics I gave a lot of math undergrads a run for their money.
True, But I was an undergrad in Physics and I was kicking their butts at their own turf. 😏😏😏
Also: I compared myself to the above average undergrads.
As I recall, no course specializing in set theory was required for students to earn
an undergraduate degree in mathematics at the universities that I attended.
In my university undergrads had a full semester of set theory.
Infinitely maddening
29 Nov '14 12:49
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