Is there a place for hermeneutics in math?

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That's just your interpretation.

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The problem is who decides what is wrong and not. Majority?

Maths is rigorous and definitive and has no scope for inaccuracies, its not open for interpretation, it provides none. The interpretation part comes on the solutions. Post mathematical operations.

Back to the same example, the GR equations has a solution, which talks of infinite mass and density confined to a point. (Don't ask me how you can confine anything with point). It is not necessary that this solution should make any real life sense, maths does not attach this with any phenomenon, its not at all aware. We have interpreted this as Black Hole. People like me feel that this solution can be discarded as useless. Subjective interpretation? Pseudo included.

 

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You're correct...until you're not.

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Math is rigorous and isn't open for interpretation. It's true that it's not "necessary" that this interpretation makes any real life sense and at it's extremes it may not and it doesn't fit well with Quantum Physics. However, GR is a falsifiable equation and so far all of the evidence has gone one way (in support of GR) so when you say "people like you feel feel that this solution can be discarded as useless" this is where you go off track.

It's your "feeling" but no evidence supports this feeling.

 

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Interpretation, etc? Here's one for the crowd:

The setting is a standard University two semester conjoined course in Calculus - Calc I&II: Limits, concepts, introduce the "derivative", try it out on a few standard functions and applications; then the "integral", Fundamental Theorem, applications thereof. A lot of students attending big Professorial lectures, divided up into Teaching Assistant sections of 15-20 that meet on days between lectures. The Prof is excellent, btw - clear and fair and well paced. The students are liberal arts, nursing and premedical, agronomy, etc - not engineering or the like, much less mathematicians in training. No difficult proofs set as problems.

About two months in, the TA handling one section notices a student's problem sets look funny. Upon inquiry the student is discovered to have taken up Newton's Principia as an auxiliary text, and to have encountered the fact that Newton did all this stuff with fancy Euclidean geometry in the first place. To get his "calculus" established, a simpler and faster and more powerful method, Newton showed it gave the same results as the familiar and thoroughly proved geometric methods - by getting those results with the geometric methods first.

So this kid has decided to complete this calculus course, as much as possible, using those geometric methods. And he succeeds: including the hard problems on the final exam - which he solves correctly (less than a third of the class did) without, as far as can be seen on the paper, employing a single theorem of calculus proper. But using the very techniques Newton used to establish the calculus, and the basic reasoning Newton employed in justifying the calculus, including methods the professor has used to derive important results in the lectures - for example, in proving that the limit as x -> 0 of sinx/x = 1.

The professor has given little guidance for grading, except that work must be shown and must justify the answer for credit. His work is shown, and justifies the answers.

The grader hammers his final exam, giving 0 points for the hard problems. And you're the TA in control of assigning the kid his grade (including fixing score errors, if any, on the final). Your call?

 

This is presumably an imaginary scenario. I question whether it would work for real, in the way the scenario suggests. If genuine, can you give references?

Given that the course is to train people in the use of certain techniques, and the student has failed to master them, I would award low marks. Getting the right answers by a laborious alternative method is not going to hep the student in practical applications, which presumably should be the object of taking the course.

 

This is what I call as convenience science. See you get division by zero in GR, you call it BH singularity but when you get division by zero in SR you say photon does not have rest frame! Moreover when you get division by zero in your ordinary algebra, you say it is undefined.

Then why do you want an alternative from me ? A wrong is wrong even in absense of an alternative.

 

The problem with subjects like math is the often memorization of formulas without understanding the mechanics and reasons behind it past simple arithmetic. So 'real' teaching as to how and why a formula or equation is valid, its function and what it can apply to in the real world isnt taught. So there is often no true understanding of math. This is why most schools are so poor.

 

I was the TA.

It makes an interesting "interpretation" example, no?

Gleaning another such example from that interlude in my life, I had a student make themselves an expert at applying one particular pair of theorems, easily proved, to almost all the application problems set in the exams:
1) That if an adjustable set of numbers adds to a fixed total, their maximum product is reached when they are all equal;
2) Complementarily, when their product is fixed their minimum sum is reached when they are all equal.

With enough ingenuity, a determined person can get through quite a bit of an elementary calculus class on those two ways of describing that single relationship.

I regarded that as of less worth, a lower quality approach, than the Principia obsession - despite its visually and ideographically more similar appearance, and "min/max" insight.

 

Sure it is. See this thread:

http://www.sciforums.com/threads/what-are-the-backwards-6s-in-the-schrödinger-equation.136750/

The OP in that thread was a request for the interpretation of a basic piece of mathematical symbolism, the meaning of the 'backwards 6's' that the thread-starter saw in Schroedinger's equation. Notice the nature of the responses.

Post #5 is a tsunami of mathematical symbolism that is seemingly intended to address the rather different issue of making Schroedinger's equation relevant to physics. It does so by interpreting the various mathematical terms in the equation in what may or may not be physical terms. Unless mathematical formulations receive a physical interpretation, they are irrelevant to physics. This seems to be interpretation in the formal semantics sense.

But that leaves the question in the OP still unaddressed. What do the backward 6's mean? That isn't a question about how the mathematical symbolism of the Schroedinger equation should be interpreted into the terms and concepts of physics. It's a question about the interpretation of the basic mathematical symbolism itself. In this case, what are partial derivatives and what motivates their use in physics?

In order for mathematics to be something more than a collection of meaningless hieroglyphs, its symbols and operators need to be understood as meaning something. The whole idea of logical implication needs to be understood or at least intuited as well. And each of those understandings will have a context, an origin in the history of mathematics that may have evolved over considerable time and may have involved some controversy as we see with the development of analysis and the definition of things like 'derivative', 'limit', people like Newton and Karl Weierstrass and the controversies surrounding 'infinitesimals'. They all have scholarly conversations surrounding them.

 

Math can be used to model the physics in video game engines. In game physics, we can have infinite lives, or fly as though we can generate anti-gravity. Just because math can model this does not mean it is real. Math is a tool, which can be used to model any assumption, we wish to begin with.

In a sense, the flexibility of tool making is basis for the hermeneutics in the bible. Different people will interpret the bible, starting with different foundation assumptions. The result is, the same quotes can appear to have different meanings. In math, we assume gravity is a force, or the curving of space-time. Both can be supported by math, with each sets of formula looking quite different.

Bible scholars will use the rules of logic. However, each might see the same quotes differently, based on how the logic follows from their foundation premises. Some premises are analogous to game engine premises. The same is true of math. In game engines, we get to assume super natural abilities in the characters. This is the foundation premise. After that the tool is cast, and game output will follow logic. In bible interpretation, some people will assume that law has been superseded, while others may assume law is still in affect. Based on that, different quotes will have different meaning, to maintain logical consistency with that premise.

Both math and logic have their own procedures. In the real world, we pick the tools we need to do the job, and then the tool behaves in its innate way. If we need to hammer nails or set screws; premises, we use a different math or logic tool. Once the task is set, that tool behaves the way it is designed.

Many seem to confuse the role of the tool; math or logic, as coming first. As an analogy, if we find a hammer in the garage, we are forced to only building wood structure with nails. That is not reality. The idea' premises, comes first, then we look for the tools we need, with hammer and level, doing what they we designed to do.

Math proof, by itself, does not make something right in terms of reality, if the premises are not supported; game engines. I don't bother doing math proof of theory, because I know you need to settle the premises first, so you know which tools are correct to use. Math can build game illusions, as easy as buildings.

 

No, I have not gone off track, by giving a physical meaning to x/0, GR guys have gone off track. Tell me where else, in verifiable domain, we have interpretation for x/0 ?

 

Well, while not perfect, the majority is far more likely to be right than the minority.

GR is a classical theory and was never meant to apply at the quantum/Planck level, so a mathematical singularity is inevitable.

Empty claims in regards to your usual claim re GR and 21st century cosmology in general being wrong, as recent experiments have verified.
On the second point, not putting any scientific alternative, leaves the door open for your "god of the gaps"

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By dismissing GR you are dismissing gravitational lensing, time dilation and other aspects that have been backing up by testing. You ideas don't have any of that.

 

(Thinking out loud) --- Something that would be of value as well, is changing how students are assessed in their math skills. Not all students process and learn in the same manner, and it's important that students are not only preparing for math tests, but also able to use their newfound problem solving skills in real life situations. In other words, math skills should be transferable to real world applications, and not just uniform exercises of sheer memorization that students plod through in order to pass standardized tests. This is where hermeneutics can play a vital role.

 

In this thread, I am just talking about interpretation of x/0. Why we are choosy?

 

1. Earth was flat?
2. The God exists?
3. The Mob is right?
4. All democratically elected politicians are great?

Despite your rider, You are totally out.

 

It's understood that GR breaks down at that point. Its predictive abilities are quite high and are why it's considered a theory (in scientific nomenclature). The "why" or "how" is frequently not known or fully understood (and therefore could be wrong) but its predictive powers are high and until something else (a more refined theory) comes along that has a better track record we stay with it.

Your argument seems to be that because everything isn't known the theory must be wrong and therefore is as useless as every other (wrong) idea. This is just silly (IMO).

 

Think we're veering off the path of how hermeneutics plays a role in mathematical activity. It's not the end result that is being interpreted (the end result will always be an objective, non-negotiable answer) Hermeneutics offers a different approach to how we can better understand math processes and problem solving, in order to get to that correct, non-negotiable answer. But, that's it. lol That is where the interpretation begins and ends, when it comes to math, anyway.

 

What do you mean GR breaks down? Have you though about this? GR contains rigorous maths, and maths is not defined when encountered with x/0.

No, my argument is not that everything is not known so something should be chucked out. My argument is that few of the interpretations of GR maths are bad and must be dropped.

1. Expansion of space.
2. Black Hole Singularity.
3. Worm Holes.
4. Time Travel

 

I don't think 3 and 4 need dropping. Aren't they already dropped? Regarding 1 and 2, I don't think there is any certainty regarding 2 and how do you explain red shifting or are you talking about inflation?