Discussion of math’s place in physics from a thread on cyclic cosmology

[Michael Mooney]

Moderation Note: The first two posts in this thread were split from 19324 where they were off topic.

 

Maddog,

This may come as a wake-up call for you on all those extra dimensions in string/M-theory.

From near the end of the "The Ontology and Cosmology of Non-Euclidean Geometry"

essay we are discussing in the spacetime thread:

The Ontology and Cosmology of Non-Euclidean Geometry

 

Just because the math works doesn't mean that we understand what is happening in nature. Every physical theory has a mathematical component and a conceptual component, but these two are often confused. Many speak as though the mathematical component confers understanding, this even after decades of the beautiful mathematics of quantum mechanics obviously conferring little understanding. The mathematics of Newton's theory of gravity were beautiful and successful for two centuries, but it conferred no understanding about what gravity was. Now we actually have two competing ways of understanding gravity, either through Einstein's geometrical method or through the interaction of virtual particles in quantum mechanics.

 

Nevertheless, there is often still a kind of deliberate know-nothing-ism that the mathematics is the explanation. It isn't. Instead, each theory contains a conceptual interpretation that assigns meaning to its mathematical expressions. In non-Euclidean geometry and its application by Einstein, the most important conceptual question is over the meaning of "curvature" and the ontological status of the dimensions of space, time, or whatever. The most important point is that the ontological status of the dimensions involved with the distinction between intrinsic and extrinsic curvature is a question entirely separate from the mathematics. It is also, to an extent, a question that is separate from science--since a scientific theory may work quite well without out needing to decide what all is going on ontologically. Some realization of this, unfortunately, leads people more easily to the conclusion that science is conventionalistic or a social construction than to the more difficult truth that much remains to be understood about reality and that philosophical questions and perspectives are not always useless or without meaning. Philosophy usually does a poor job of preparing the way for science, but it never hurts to ask questions. The worst thing that can ever happen for philosophy, and for science, is that people are so overawed by the conventional wisdom in areas where they feel inadequate (like math) that they are actually afraid to ask questions that may imply criticism, skepticism, or, heaven help them, ignorance.

 

It fits Modest's overblown estimate of 'the more math the better' (not a quote) as well.

 

Michael

[maddog]

Maddog,

This may come as a wake-up call for you on all those extra dimensions in string/M-theory.

From near the end of the "The Ontology and Cosmology of Non-Euclidean Geometry"

essay we are discussing in the spacetime thread:

The Ontology and Cosmology of Non-Euclidean Geometry

No I read that webpage already. However -- making a claim that [paraphrased] "mathematical theory" being "right" does not make it "correct". This does NOT in and of

itself Negate said mathematical theory. See mathematics is a tool, it goes as far as it goes

in the description or representation of what a theory is attempting to describe. Corroborating

evidence is always helpful. A theory can stand on its own (for a time) if it is

1. Self-Consistent.

2. Congruent with the ongoing knowledge with which it is attributable to.

3. Can be tested with some authority (even if eventually).

Your reference of the webpage did not Negate the value of mathematics. Yet you seem

to imply this. It is as though we "should" stop attempting to bother calculating anything.

Michael doesn't understand it so it is irrelevant.

It fits Modest's overblown estimate of 'the more math the better' (not a quote) as well.

I am a protaganist for "what works". :shrug: All the better.

If Mathematics works, I use it. If I ever [hasn't so far] found that Mathematics were

found to inadequate for the task, I would look for something else. Divinning rods, anyone ? :omg:

 

maddog

[modest]

Maddog,

This may come as a wake-up call for you on all those extra dimensions in string/M-theory.

From near the end of the "The Ontology and Cosmology of Non-Euclidean Geometry"

essay we are discussing in the spacetime thread:

The Ontology and Cosmology of Non-Euclidean Geometry

[cropped]The worst thing that can ever happen for philosophy, and for science, is that people are so overawed by the conventional wisdom in areas where they feel inadequate (like math) that they are actually afraid to ask questions that may imply criticism, skepticism, or, heaven help them, ignorance.

It fits Modest's overblown estimate of 'the more math the better' (not a quote) as well.

Michael, I have made no posts in this thread (the thread from which this one was split) and I have never expressed anything like what you attribute to me. I hope you understand that those two facts make your comment inappropriate. It is, in fact, me who gave you that quote regarding the idea that math doesn't prove ontology 6 months ago:

 

Don't count me out just yet from the latter group just because I haven't your math expertise.

I honestly am neither expert in math nor physics.

The worst thing that can ever happen for philosophy, and for science, is that people are so overawed by the conventional wisdom in areas where they feel inadequate (like math) that they are actually afraid to ask questions that may imply criticism, skepticism, or, heaven help them, ignorance."

 

-Dr. Kelly Ross

 

[...]

 

It's interesting, considering what you were saying about math, that this quote [i also quoted Faraday in the post regarding something different] can be found in "Great Physicists by William H. Cropper" which goes on to explain that Faraday's ideas on this topic were not well-received and gives reasons why:

Faraday’s theories were opposed because they were revolutionary, always sufficient reason to stir opposition, and also because Faraday did not speak the sophisticated mathematical language his fellow theorists expected to hear. Beyond rudimentary arithmetic, Faraday had no mathematics; his mathematical methods were about the same as those of Galileo. In Faraday’s time, that may actually have been an advantage for creativity. The field concept was the product of “a highly original mind, a mind which never got stuck on formulas,” wrote a great twentieth-century field theorist, Albert Einstein.

 

Many members will use math to critically analyze theories in the astronomy and cosmology forum. If, for some reason, you fail to see what is being implied by the math involved it would be best to simply ask and I'm sure the member would be willing to explain.

 

~modest

[Michael Mooney]

Modest,

I am sorry that I dragged you into this discussion.

My point was simply that "all that math" provided by maddog does not establish the existence of "all those extra dimensions" in string/M-theory. I think the quote spoke to that point very well.

Michael

[modest]

I agree. The math certainly does not establish something's existence or validate a theory... quite true :shrug:

 

~modest

[lawcat]

What is math? To me it is just a concise representation of ideas that replaces cumbersome language--almost like a computer code.

We observe something in nature, and then we put it in a logically sufficient symbol-form, so that it is universally understood. Then, we define another observation in the same manner. Then, we try to predict what will happen if first obesrvation effects second observation, and math lets us predict that on the paper in a universally understood language.

 

But, since math is logic, it is susceptible to fallacies.

 

If I combine supply and demand curve (2 dimensions), with entropy/temperature curve (2 dimensions), with a point position in eucledian space (x,y,z), then I can end up with 7 dimensions. Wonderful. But what does that do? What does mixing apples and oranges do?

[maddog]

Modest,

I am sorry that I dragged you into this discussion.

My point was simply that "all that math" provided by maddog does not establish the existence of "all those extra dimensions" in string/M-theory. I think the quote spoke to that point very well.

Odd. I gave you "all that math" in reference to your question about "string/M-theory".

String Theory (now M-Theory) is very "heavy" in math. True the "math" does not make

that (or any) theory "true". Only evidence can do that. Corroborating evidence.

With M-Theory this is currently lacking.

 

BTW, I don't think your "quote" spoke anything of the kind. Hardly mentioned it.

 

maddog

[Kriminal99]

I totally agree. I am often astounded by formal "mathematical proofs" that at the very least, completely leave the realm of mathematical certainty and enter into the dangerous terriitory of epistemology. In some cases, I would describe the proofs as violating fundamental principals of epistemology (something mathematicians are not always familiar with). It seems you can prove anything as long as the suspicious parts of the proof remain outside the realm of, and therefore outside the scrutiny of, strict mathematics.

 

If it was in fact the case that I simply did not understand something about the proof that would calm my suspicions, I would never know it because if I ever asked a professor said professor would have an emotional breakdown and result to debate fallacies and other immature behavior. At best, this tells me that most people in acadameia are more socially driven than truth driven.

[arkain101]

I agree that Math, and more specifically Mathematical Physics Equations must be coupled with real world explanations. Not only to provide evidence that the math is valid and applicable to reality, but to grasp the deeper conceptual understanding of the functions of nature, of which to build from to further theoretical methods, accuracy, and understanding.

 

Take for example kinetic energy. How well do we really understand it?

 

A Fact to consider: You can formulate an equation that calculates Kinetic Energy, prior to having the knowledge of any other existing equation. But what would you need to understand before you were able to accomplish that?

 

 

[math]Ke = \frac{1}{2}mv^2[/math]

 

Some time ago, I posed the question on these forums to explain in words and real world explanations why kinetic energy is expressed this way mathematically. It took nearly two pages of several members before that was accomplished. What began was 'explanations of the math' and derivations[?] of the equation to show its source. Very able people participating in that discussion were very limited in their ability to elaborate on it without math being conceived. This gives the expectation that understanding of physics even in the very basic was sliding into the mathematical only world.

 

During that discussion, I produced this equation to help elaborate mathematically what is happening ontologically.

 

[math]Ke = \frac{(m\times v)(m\times v)}{(m+m)}[/math]

 

This equation works to calculate the kinetic energy of a moving object. But why? What does two groups of mass have to do with ONE moving object?

 

So does:

 

[math]m \times a \times d = \frac{(m\times v)(m\times v)}{(2m)}[/math]

 

and:

 

[math]Ke = \frac{p^2}{(2m)}[/math] where [math]p[/math] is momentum.

 

 

Essentially we can show the mathematical relationships that exist within these equations, and prove that certain methods can provide the same results. However, the language that each equation is communicating and expressing is quite different amongst each equations. So we should ask, which one should we depend on to describe ontological conceptual evidence? Not to mention in other areas of physics.

 

 

 

Lets take a look at this one.

 

[math]Ke = \frac{(m\times v)(m\times v)}{(m+m)}[/math]

 

 

In words it appears to be expressing two reference frames. For example; if we treat m as the same value. We could say the following from this equation:

 

Kinetic energy is a construct that expresses the measurements found between the interaction of two frames of reference, of which contain mass. If for example, we have two objects in space, that each have the same mass, and the relative velocity between them is v, either object can be considered the one in motion(as expressed in the equation). In their interaction and in the totality of the situation we could say that each object does work. However, one object must do positive work and one object must do negative work. That is, we must choose which one is doing positive work. The energy exists as a concept, applicable to job choice.

 

We must acknowledge the fact that where work exists is in the job that is expected. If we consider the deceleration of an object a process of work, then we could call that the positive work while the partner of the relationship is considered negative; while if we consider the movement or acceleration of an object work, then we could call that positive work. A moving object has energy only if it is able to crash into another object which will infact produce the same force as the considered moving object. The totality of Energy can not be put into work unless there is a sufficient mass to allow to interact with.

 

Kinetic energy and energy in general can be considered as the observers focus of where (positive) work has been applied.

 

The conclusion we arrived to in that discussion mentioned earlier was that motion can only be non zero, and that a value exists somewhere between zero, and motion. Each step upwards from this minimum value, adds on top of the previous value, stacking the value on top of itself. Such the energy in motion can only be determined through a square of its velocity. That is, if you determine a specific speed of which to "refer" to, and you double your speed you acquire 4 times the energy, tripple your speed to acquire 9 times the energy; likewise, if you half your speed, you lose energy by a factor of 4.

 

If we don't have standardized units, such as; a Meter, and a Kilogram, then we can't produce any meaningful values. We could produce our own stanard units and provide our own meaningful results. The reason they are meaningful values is because the represent themselves. For example, when using units of meters and kilograms, and I calculate 500joules of energy in an object, that gives an impression on what it can do to a non zero kilogram object, at a non zero velocity. The idea of a standard unit is to create a non zero value, essentially, a value of 1, so that meaning can be applicable, and physics and relativity can birth forth.

 

Example of energy, using kilogram/meter standard units.

 

Mass = 10kg

Velocity = 10m/s

 

[math]Ke = \frac {p+p+p+p+p+p+p+p+p+p}{m+m} = \frac {10p}{2m}[/math]

 

 

 

 

 

However, one object must do positive work and one object must do negative work. That is, we must choose which one is doing positive work. The energy exists as a concept, applicable to job choice.

 

 

This causes me to ask a question. Should we consider negative work and/or energy real? For example: an object at rest can be considered negative energy. That is, if a moving object impacts that object at rest, the object at rest will decelerate the moving object. Essentially the relationship is such that they trade states.

 

If energy can be considered as the observers focus of where (positive) work has been applied. Then, the source of where that energy came from could suggest it as being a source or state of negative energy.

 

For example, if I see waves in a lake, I can consider in my relative observation that the water is a place where work has been applied. Let's say the source of that work was a large water balloon that was dropped into the lake and exploded on impact.

 

The water that was dropped became part of the medium, that the energy is traveling through. Such as, that, mass is and energy can be considered as sort of negative positive relationships.

 

What are your thoughts?

 

I ask this because math can't necessarily provide insight into these conceptual relationships, since math considers zeros as (nothing/infinite's, correct?).

[arkain101]

(does editing a post update the thread?)

 

 

Freeztar: Nope :)

 

 

 

I see...said the blind man...