Do mathematical proofs exist, of things that we are not sure exist?

[Rader]

I read the original question a little differently. What I'm seeing is: 'Are there some physical phenomena that have been derived/predicted mathematcally but have not (yet?) been found to exist?'

The answer is simply yes.

Many of the phenomena that theoretical physicists spend their time looking for have never been seen but are being searched for as a result of what the equations tell the physicists. I'm not real up on the current bleeding edge, but there are lots of examples of things that have been implied by equations and later found to exist: black holes for example.

Actually what i really wanted to know, is if mathematical proofs could exist for human experience. For physcial properties, it is quite self evident but then again where do you categorize black energy, even though you call pull numbers from gravitational forces?
I would imagine that the latest information obtained by the COBE in 2003, on the amount of black energy 73%, black material 23% and atoms 4% was predicted by mathematics of GR, well before satellite detection. Or was it?

 

[selfAdjoint]

Actually what i really wanted to know, is if mathematical proofs could exist for human experience. For physcial properties, it is quite self evident but then again where do you categorize black energy, even though you call pull numbers from gravitational forces?
I would imagine that the latest information obtained by the COBE in 2003, on the amount of black energy 73%, black material 23% and atoms 4% was predicted by mathematics of GR, well before satellite detection. Or was it?

No it wasn't. This is a perfect example of why mathematics, all by itself, doesn't predict details of experience. If you want to solve a differential equation, and Einstein's equations are an example, you can't do it without some extra information. This information can come as Initial Conditions or as Boundary Conditions. It is the values of the positions and momenta (or more generally the space and time cooordinates and their derivatives) for some point in time (initial condition) or some bounding hypersurface (boundary condition). This knowledge is not something math can generate by itself; it has to be delivered by experience, such as the WMAP observations.

 

[Rader]

No it wasn't. This is a perfect example of why mathematics, all by itself, doesn't predict details of experience. If you want to solve a differential equation, and Einstein's equations are an example, you can't do it without some extra information. This information can come as Initial Conditions or as Boundary Conditions. It is the values of the positions and momenta (or more generally the space and time cooordinates and their derivatives) for some point in time (initial condition) or some bounding hypersurface (boundary condition). This knowledge is not something math can generate by itself; it has to be delivered by experience, such as the WMAP observations.

Then you answer my question satisfactorily saying, that experience must proceed the mathematical proofs, with that in mine, why the sky is blue under certain conditions has math proofs, to describe it.

 

[matt grime]

Then you answer my question satisfactorily saying, that experience must proceed the mathematical proofs, with that in mine, why the sky is blue under certain conditions has math proofs, to describe it.

It has physical reasons to describe it that may be modeled, or treated, mathematically. That doesn't make it a mathematical proof.

 

[selfAdjoint]

To explain why the sky is blue you need physical information - such as the percentage of O² molecules in the atmosphere, the energy levels of their electron shells and so on, plus the math needed to work out the photon scattering from that data. So you have a cooperation between physical data and math description. I don't see that either one is "prior" because you couldn't do the explanation without both.

 

[sol2]

Just thought I would throw this in here. Quantum gravity and Quantum geometry.

This is a interesting world (?) and it is mathematically consistent?

In terms of math of experience, I would refer to http://superstringtheory.com/forum/metaboard/messages18/345.html Hope you enjoy the links

...to infinity and beyond:)

 

[gravenewworld]

In the late 19th and early 20th century mathematicians tried to come up with set of axioms which would allow ALL of mathematics to be derived, even proofs which yet did not exist could be formulated from these axioms. Kurt Godel however proved through logic that it is impossible to formalize such a mathematical system. He proved that for any system with its axioms there exists a statement that is not provable or disprovable with the axioms given. In order to prove this statement more axioms would have to be added. This only creates another system of axioms in which another statement exists that can neither be proven or disproven etc. For example even with the axioms of Euclid, there exists a statement in analytical geometry that can not be proven or disproven with those axioms, although mathematicians haven't found it yet. Einstein regarded Godel's paper as one of the most important peices of work ever contributed to humanity. Godel's incompleteness theorem has far reaching consequences for not only mathematics,but for philosophy and science as well.

 

[MaxNumbers]

And, in agreement with gravenworld above, I suggest looking into "Godel Numbers," a system that translates statements into mathematics. There's a fantastic and relatively comprehensible book, Godel's Proof, that walks you through the Godel's process of constructing a proof, from a mathematician/logician's point of view.

 

[Rader]

Thanks for the hint on Godel

It appears to foredoom hope of mathematical certitude through use of the obvious methods. Perhaps doomed also, as a result, is the ideal of science - to devise a set of axioms from which all phenomena of the external world can be deduced.

Given any consistent set of arithmetical axioms, there are true mathematical statements that cannot be derived from the set... Even if the axioms of arithmetic are augmented by an indefinite number of other true ones, there will always be further mathematical truths that are not formally derivable from the augmented set.

Rational thought can never penetrate to the final ultimate truth

http://www.miskatonic.org/godel.html