On Theoretical Mathematical Models

[ajb]

If this thread does not quickly get away from discussing the details of your cosmological model then I am sure it will get closed.

[ponderer]

In theoretical physics a physical theory is synonymous with a mathematical model.

 

By model we mean a mathematical construction that can be used to describe (part of) the natural world.

 

There is also a mathematical meaning to the word model as in model theory. (Some how I think this is closer to your meaning.) In model theory one uses mathematical logic to study algebraic structure. Loosely, an algebraic structure that gives meaning to the sentences of a formal language is a model of the formal language.

 

In a sense the model here is a "realisation" of the formal language as an algebraic structure.

 

Well, I must be in uncharted territory. Whatever you want to call it, it is a fully functioning universe, most of which I can relate to the existing universe. I am sure the bits which I have not described contain the structure needed to compete the picture. You could apply a complete mathematical description to it if you wanted. My math skills such. I haven't had to use any serious math since I picked apart the Lorentz transformation in the late 90's, and I only needed algebra for that.

 

Should I not bother publishing something I think is of interest, because I have not completed a mathematical analysis, because I lack the skills?

 

If others agree that what I have produced is worthy of further study, they can work out the math.

 

I can't think of any one person who was expected to explain the whole universe to everyone in detail, without getting anything wrong. As I understand, even Einstein got help with the math.

 

Give me a break. This is my contribution. Take it for what it is worth. If it is worth nothing to you, then so be it. I just want it recorded. Maybe it will mean something to someone else, eventually. Maybe it will be the fools universe, like fools gold, a logical trap, a oddity of philosophy.

 

Who knows, I am not blowing any horns, and jumping up and down saying I'm right.

 

I am just happy to have a mental picture of the structure of space-time, even if it is not entirely correct. It's more than I had before.

 

I had no idea how to make any sense of it. I puzzled over it for years.

Edited February 5, 2010 by ponderer

[pywakit]

If this thread does not quickly get away from discussing the details of your cosmological model then I am sure it will get closed.

 

Then let's drop the not so veiled attacks on the model.

 

( Yeh. It's got problems. Deal with it.)

 

Ok?

 

It's fine with me!

 

I'm happy just to debate the current state of scientific methodology, and explore whether or not it needs an 'update' due to a new deeper awareness of the structure, and form of our universe.

 

Sound good?

 

And thanks Andrew. You are a voice of reason here.

---

Merged post follows:

Consecutive posts merged

Your model is no longer under debate here pywakit. That thread was closed.

Follow our rules, please.

 

 

If you want to continue lecturing about your model, I suggest you open a blog.

 

~moo

 

Then stop referring to it.

 

James

 

( When I write like this, I am speaking as a rational human being.)

Edited February 5, 2010 by pywakit
Consecutive posts merged.

[swansont]

Isn't it nice that the model has many many ways it could be falsified! So that leaves us with just 'completing the math' to determine it's true value.

 

I have a hard time reconciling the first sentence with the second. Without the math, you do not have the capability of making specific predictions, which cripples the ability to falsify it.

[ajb]

The OP was merely a series of observations on the state of mathematical theories, and their relationships to the actual, physical universe.

 

The relationship with a theory and the actual universe is very subtle. It is not usually appropriate to say if a theory is correct or not, but one can ask how well it relates to nature. We can ask if it describes nature very well or not very well.

 

So, a theory is by definition a mathematical construct. It is not to be thought of as actually being nature. So you have to be careful in quantifying well or not well, good or bad.

 

Given a theory one should be able to calculate observables. Say the path of a test particle, or the energy of a photon emitted from an atom etc. Now, if the calculated outcome(s) agree with the observation to some arbitrary, but specified degree of accuracy the theory is said to be good. If not it is bad.

 

There is also the issue of range of validity. So far all our theories are not going to describe all phenomena well for all possible ranges of parameters. Either the theory itself will mathematically break down, say infinities will appear or the calculated outcomes will not agree well with observation. Good examples of this are general relativity near the singularity of a black hole and classical Newtonian mechanics applied to a particle near the speed of light. No one will say that general relativity nor classical mechanics is wrong. The described situations are outside the theory's domain of validity.

 

There is also the issue of falsifiability. This is subtle. At some point our theory is considered to be so bad it cannot be reasonably used. This maybe due to some predicted phenomena not being observed or a large degree of difference between a calculated observable and a measured one.

 

In practice this can be buried in experimental errors or the theory can easily be modified to take this into account. At the moment the non-Gaussian part of the CMBR has not be resolved to the accuracy needed to falsify specific models of inflation. One day it will be. Another example is supersymmetry. It is possible that the supersymmetry scale is higher than we thought and so will not be detected at the LHC. So a null result will not exactly rule supersymmetry out as part of nature.

 

Ruling theories in or out is in general very subtle, but very bad models quickly get thrown out.

[pywakit]

I have a hard time reconciling the first sentence with the second. Without the math, you do not have the capability of making specific predictions, which cripples the ability to falsify it.

 

I can't make the mathematical predictions. But they do exist. Because the model closely follows the BBT.

 

Someone will look at this, and come up with a complete set to describe it.

 

But my model DOES make physical predictions. In the last year, all new and unexpected ( even shocking ) discoveries are inherently predicted by my model.

 

Good track record so far.

 

And there is a list of ways *sigh* to falsify it right now. So, no. Not 'crippled'.

[ajb]

Should I not bother publishing something I think is of interest, because I have not completed a mathematical analysis, because I lack the skills?

 

Under the banner of philosophy it maybe interesting. But, it may just be nonsense which bares no resemblance to what we call modern physics.

 

If others agree that what I have produced is worthy of further study, they can work out the math.

 

I don't think it really works that way. People are unlikely to work on something unless it shows real initial promise. That has to be in the form of a mathematical model as far as physics is concerned.

 

I can't think of any one person who was expected to explain the whole universe to everyone in detail, without getting anything wrong.

 

Scientists make mistakes. Mistakes do get published.

 

Science as a whole is a collaborative evolving thing. People only really understand small parts of the bigger picture.

 

As I understand, even Einstein got help with the math.

 

True, but Einstein was knowledgeable about contemporary physics of the time. He was not "mathematically illiterate" by any means.

 

Give me a break. This is my contribution. Take it for what it is worth. If it is worth nothing to you, then so be it. I just want it recorded. Maybe it will mean something to someone else, eventually. Maybe it will be the fools universe, like fools gold, a logical trap, a oddity of philosophy.

 

OK, I have no intention of "shooting you down".

 

But please notice that this is a science forum and any ideas posted here will be brutally evaluated. That is part of science and not a personal attack.

[pywakit]

The relationship with a theory and the actual universe is very subtle. It is not usually appropriate to say if a theory is correct or not, but one can ask how well it relates to nature. We can ask if it describes nature very well or not very well.

 

So, a theory is by definition a mathematical construct. It is not to be thought of as actually being nature. So you have to be careful in quantifying well or not well, good or bad.

 

Given a theory one should be able to calculate observables. Say the path of a test particle, or the energy of a photon emitted from an atom etc. Now, if the calculated outcome(s) agree with the observation to some arbitrary, but specified degree of accuracy the theory is said to be good. If not it is bad.

 

There is also the issue of range of validity. So far all our theories are not going to describe all phenomena well for all possible ranges of parameters. Either the theory itself will mathematically break down, say infinities will appear or the calculated outcomes will not agree well with observation. Good examples of this are general relativity near the singularity of a black hole and classical Newtonian mechanics applied to a particle near the speed of light. No one will say that general relativity nor classical mechanics is wrong. The described situations are outside the theory's domain of validity.

 

There is also the issue of falsifiability. This is subtle. At some point our theory is considered to be so bad it cannot be reasonably used. This maybe due to some predicted phenomena not being observed or a large degree of difference between a calculated observable and a measured one.

 

In practice this can be buried in experimental errors or the theory can easily be modified to take this into account. At the moment the non-Gaussian part of the CMBR has not be resolved to the accuracy needed to falsify specific models of inflation. One day it will be. Another example is supersymmetry. It is possible that the supersymmetry scale is higher than we thought and so will not be detected at the LHC. So a null result will not exactly rule supersymmetry out as part of nature.

 

Ruling theories in or out is in general very subtle, but very bad models quickly get thrown out.

 

All good points. Clearly my model does not fit in the 'very bad' category. So let's not throw it out just yet.

---

Merged post follows:

Consecutive posts merged

ajb writes :

 

Science as a whole is a collaborative evolving thing. People only really understand small parts of the bigger picture.

 

Collaboration .... Hey! This is where I come in!! I take all those small parts and put them together in a nice tidy package. It's great to have at least ONE talent, right?

 

[Sisyphus]

Another example of the significance of quantifiable (that is, mathematical) prediction is Aristotelean physics.

 

Aristotle described physical phenomena in qualititative terms. He said, for example, that earth seeks to go downward, explaining why the air is above the ground and not vice versa, and why rocks come back down when you toss them in the air. Sure, this agrees with observation. The air is over the ground. Rocks do fall. Because he never tried to predict the way in which rocks will fall (e.g. plot their course over time), this wasn't really falsifiable, and it wasn't a model. It wasn't until much later, when people like Galileo and Newton began making mathematical predictions, that there was actually something to test, to measure and confirm or deny. Newton's law of universal gravitation is a falsifiable model. "Rocks want to go down" is not a falsifiable model.

[ajb]

]

Collaboration .... Hey! This is where I come in!! I take all those small parts and put them together in a nice tidy package. It's great to have at least ONE talent, right?

 

 

Generally a scientist/mathematician only has a couple of good ideas and methods understood in their lifetime. The thing is to use these over and over again in as many contexts and specific situations as possible.

 

The overall idea is that you hand your modest contribution over to the rest of the community and humanity as a whole.

[pywakit]

Another example of the significance of quantifiable (that is, mathematical) prediction is Aristotelean physics.

 

Aristotle described physical phenomena in qualititative terms. He said, for example, that earth seeks to go downward, explaining why the air is above the ground and not vice versa, and why rocks come back down when you toss them in the air. Sure, this agrees with observation. The air is over the ground. Rocks do fall. Because he never tried to predict the way in which rocks will fall (e.g. plot their course over time), this wasn't really falsifiable, and it wasn't a model. It wasn't until much later, when people like Galileo and Newton began making mathematical predictions, that there was actually something to test, to measure and confirm or deny. Newton's law of universal gravitation is a falsifiable model. "Rocks want to go down" is not a falsifiable model.

 

Ok. There is proven math behind everything my model claims. Just because I don't have the ability to express it doesn't mean my model is reduced to 'rocks want to go down'. This is a false analogy. Sorry.

 

Centrifugal force, gravitational attraction over large distances, gravitational consolidation ... these are known, and mathematically sound principles.

 

There will be a complete mathematical expression for the model. Maybe it already exists. Let's give it time to surface.

 

There is nothing magical involved here. Just straight GR, etc. It's just a matter of some mathematician spending some time on it.

[insane_alien]

so there's maths but you don't know how to write it down(and therefore don't know how to use it either)

[Cap'n Refsmmat]

I thought we had agreed we weren't talking about your model any more.

 

Oh well. We certainly aren't going to be now.