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age 22
visits member for 1 year, 8 months
seen Aug 30 at 12:27

Ascetic devoted to mathematics

MathJax basic tutorial and quick reference


Sep
24
awarded  Autobiographer
Aug
5
awarded  Notable Question
Jul
28
comment How was Newton able to guess that gravitational force is inversely proportional to distance squared?
So Newton chose an inverse square field because it fits Kepler's law, right ?
Jul
28
accepted How was Newton able to guess that gravitational force is inversely proportional to distance squared?
Jul
27
asked How was Newton able to guess that gravitational force is inversely proportional to distance squared?
Dec
19
comment Is physics rigorous in the mathematical sense?
@DavidH If physics ever becomes axiomatic, and we use the axiom to prove a certain statement P. It is not only a string of characters on paper. It is an assertion about the physical universe that can be checked using EXPERIMENTS, there is no analouge of this in mathematics. There is nothing to check against, just symbols on paper. However, I like mathematics not for manipulating symbols, but for its beauty (That is something that would take a lot to talk about). Sorry for the many comments
Dec
19
comment Is physics rigorous in the mathematical sense?
@DavidH I probably bothered you with a lot of comments, but I think what I will write now is worth reading. Even if physics becomes axiomatized, I still think it is different from mathematics in the following sense: You prove a theorem from a certain theory $T$, it does not matter if the universe satisfies theory $T$ or not, we are proving theorem s for worlds satisfying theroy $T$ only, it doesn't even matter if no such world exists. mathematics could be viewed as plain manipulation of symbols, physics is not just manipulation of symbols about.
Dec
19
comment Is physics rigorous in the mathematical sense?
Hi. I don't mind taking the gravity equation as an axiom. What I want to ask (perhaps different from what the OP would like to ask) is: Suppose we assume certain axioms to describe the universe and use them to derive a statement P. Is the derivation of P from the axioms rigorous ? This is like the question: Is physics axiomatic ?
Dec
19
comment Is physics rigorous in the mathematical sense?
@DavidH In group theory for example, I view the theorem that identities are unique as: The set of statements of group theory proves formally the statement: identities are unique.
Dec
19
comment Is physics rigorous in the mathematical sense?
@DavidH Secondly, I don't like to think of mathematics as if it asserts the theorems. I like to think of it as asserting the implication. For example, mathematics does not show us that the fundamental theorem of calculus is true, but rather that the of axioms of ZFC PROVE the fundamental theorem of calculus.
Dec
19
comment Is physics rigorous in the mathematical sense?
@DavidH Thus, the axioms were not just chosen to maximize theorem-proving power. I believe the axioms were chosen to describe our own intuition about sets. In my opinion, there are philosophical reasons why sets were chosen the way they are
Dec
19
comment Is physics rigorous in the mathematical sense?
@DavidH I disagree about "The common axiom sets found in formal mathematics were chosen to maximize theorem-proving power/efficiency, not because they are somehow "self-evident" truths". Firstly, if theorem power proving were given higher priority than being "self-evident truths" then the set of statements $\{\forall x [x\in x],\lnot\forall x[x\in x]\}$ could have been used as axioms for math instead of ZFC. It certainly has a higher theorem proving power since it can prove any statement as it is inconsistent.
Nov
8
comment Difference between torque and moment
and what's the difference between "turning" and "rotation" ?
Nov
8
awarded  Popular Question
Aug
20
comment Shear stress in directions other than the flow direction
Thanks for the books. As I intend to self-study mathematical physics.
Aug
20
revised Shear stress in directions other than the flow direction
added 152 characters in body
Aug
20
comment Shear stress in directions other than the flow direction
This is all good, but what is most cruical I want the inegral of shear that gives shear force. Was my guess correct
Aug
18
awarded  Promoter
Aug
17
comment Some complex-number manipulation when calculating coefficients
Isn't the solution to both simultaneous equations $a=b=0$ ? How can $a$ have a non-zero magnitude ?
Aug
16
revised Shear stress in directions other than the flow direction
edited body