The Belief Doctor wrote:Marabod wrote:
If good science is based on direct observation, then I am involved in a bad science, as direct observation in Physical Chemistry gives no scientific results.
Science and Mathematics are inseparable, and no science exists outside of mathematically described models. In order to prove the opposite, one must demonstrate some law from some fundamental or even applied science, which is used as formulated in words, not in the equations. The rules and some principles can be indeed formulated in words, such as Le Chatelier Principle, but they are not the laws as such, but only a generic representation of these laws, covering a variety of "similar" cases.
E=mc^2 is what is contained in the last lines of Einstein's own lectures on Special Relativity, it is a Law; the equation you are bringing in is containing a velocity evaluation v^2/c^2, and in case if v=c it makes no sense as e becomes equal to infinity... You may as well spend a time explaining for which cases such form may serve, as a formula without explanations of what it means possesses no sense, same as a word, written in an encoded alphabet.
Dear me,
What is it that causes people to misquote?
I said "observation of data" ... when is that not applicable?
Please name one mathematical theorem (just one) that is NOT based on some axiom (assumption). Once again, you are familiar with Godel (and Turing's Uncomputibility, Heisenberg's Uncertainty, and Chaitin's Randomness Theorems). E.g. Chaitin. "Some mathematical facts
are true for no reason, they're true by accident!" ( http://www.cs.umaine.edu/~chaitin/summer.html)
Science, did you say? All based on assumptions.
Again, what evidence do you have that supports your assumptions that deep reality is mathematical?
It's a rhetorical question. There is none, beyond further assumptions that there is, or would be evidence. That's the beauty of the infinite and genuine free-will (not sure what the philosophers bang on about, but free-will in the quantum space is FREE, big-time. Things happen for no logical reason at all. Pure, unadulterated 'magic'.)
As for e=mc^2. the equation that was given mc^2/sqrt (1-v^2/c^2) is correct (I've since checked). If v->c, then the energy becomes infinite. Correct. That is why normal physical things cannot get to, or exceed the speed of light. If v=0, then you get the standard e=mc^2. Correct. But this getting into the detail of mathematics is not of interest. Let's move on.
You confuse assumption and axiom, I would suggest you to check the dictionary! Axiom is not an assumption at all, it is
a statement which does not require any special proof due to it being OBVIOUS. The simple axiom would be "humans have two legs", and the factories making shoes are basing their production planning on this axiom. Yes, some people may present a special case of having 1 leg or having none at all, but this would be an exception from the rule, which the shoemakers do not take into account.
Assumption would be a mental construct, SUGGESTING that the things are exactly as the assuming person describes or envisions them.
Thus, an axiom is OBJECTIVE (exists independently from an observer) while an assumption is SUBJECTIVE (entirely depends of the observer).
Axioms are valid only in the framework of certain condition. For example, the axiom of parallelism by Euclides is ONLY applicable to the Euclidian spaces, and is not applicable to the spaces of Lobachevsky. Mathematics only uses the axioms when they are APPLICABLE - and it uses the assumptions ONLY as some temporary agreed on statements, needed for the purposes of proving some certain result, which themselves would be ONLY valid provided the assumption has been proven true.
Math DOES NOT use any assumptions at all as a base of some conclusion - if such assumption appears in the heading of some Mathematical theory, this assumption plays a role of a caveat emptor, a disclaimer, and specifies that the theory WOULD BE TRUE only if the initial assumption was a fact, was PROVEN as a fact (see wiki for a definition of a fact).
Just to explain the past - e=mc^2 is a Law of Special Relativity. This Law acts as valid in the Newtonian Inertial Reference Frame. In such frame the full energy of any (ANY!) material body can be calculated using this formula. If (IF!) the reference frame is not Newtonian, and a body MOVES in this reference frame with a speed v, somehow COMPARABLE to the speed of Light c, THEN its full energy would be calculated by the formula you brought in. We all (all?) know that General Relativity as a completed Theory does not exist. Moreover, we know that Science does not even target to establish it, instead the Science was since 1920s targeting the Unified Field Theory - as Relativity in a general form is (in common language) a mess. The formula, demonstrated by you has no practical implications at all, at least to date - and this is one of the reasons why the Large Hadrone Collider was built for several billion Euros, but it still does not work, alas.
Your question about some my "proofs" of some "assumptions" of Math validity about some "deep reality" makes no practical sense - as in all fairness, this validity in no way relies on your personal opinion - and if the computer, through which you are publishing these your bizarre doubts, is not a proof of this validity for you, then one can hardly present to you this proof at all. Just imagine yourself in a world, built on your own with no mathematical "assumptions" - you would be not able to even publish these your doubts, as all what you have in your world would be wax candle, a piece of parchment and a stylus from your favourite gender.