I've noticed a lot of threads with arguments entirely based on people being unable to grasp mathematical concepts like infinity, or just rejecting it outright.
Now my question is how can we get this concept across to people?
Now my understanding is that math is a model that we can use to describe something. We establish rules and by working within these rules we come up with a model that is internally consistent. Within those rules the math always works.
Physics is the use of these models to describe reality, Relativity, String Theory, Quantum Mechanics etc... are all mathematical models that allow us to describe the world and make predictions within those models.
We can't say that relativity is wrong, it is consistent, the model works most of the time. That is not to say that it is a complete description, it is not wrong so much as it might not be giving us the complete picure, but it does work.
Now we need to be carefull when using these models, all the formulas and rules are defined within that model, so you can't take equations from say M theory and plug them in to Special Relativity and come up with a meaningfull answer. They are describing the same thing in different lanugages.
The other thing we need to be carefull with is that math is a description of a thing, not the thing itself. When you run into an infinity or some other crazy concept that you can't quite grasp remember that it might just be a feature of the model, you are working in. You can cancel out infinities and come up with a meaningfull and consistent answer, but they are sometimes necessary for the model to work.
Now I have noticed a lot of pet theories floating around, and there are a lot of ideas that I like and agree with. However you can't just pick and choose concepts from different models, thow in a few equations and call it a theory. The amount of math involved in building a model of the universe is mind boggling.
What I would like to suggest is that we make use of the work that has already been done and build on that. Find a model that allows you to describe your concepts, the math is there so you have the tools to model and test your concepts.
I am more of a philosopher than a physicist, I don't have the math to describe my ideas. I do understand a fair bit of what is out there though. Now I like the concept of the Aether, I can't justify creating a model to describe it at this point though. I can however explore the concept within the constraints of existing theories. So I look at it in terms of existing models. I look at what they could be describing, I look for similarities in what they describe.
Something like the aether for example is described in many of the different theories, it might be called a D-Brane or spin quantum foam, or even space-time. My point is this concept is already partially described in existing systems, so why not use these systems to explore these ideas before you dedicate yourself to decades of work creating a whole new model.
For example, take space-time. If you stop thinking of time as a phisical dimension that you can travel through, suddenly space time has substance. It becomes a thing that the mathematical abstraction time helps us describe. Now I haven't changed a thing in the model, I just looked at it differently. This new perspective might lead to insights that allow us to improve our understanding of reality.
Now by approaching the problem this way I can make valid arguments, the math is already consistent and so it is harder to dismiss me as a nutcase who thinks he knows more than the smartest people on earth. I'm not dismissing mathematical truth, I'm just looking at what the math describes from a different point of view.