The limits of mathematics

Axiom of Choice potentially defines the "causal" limits of which mathematics can be defined. If physics acts differently than what can be causally defined, then perhaps a method of modeling physics that does not use mathematics will need to be created to further relate to physics.

Within any closed causal system there are a finite number of states before sequencing of states repeats; even for our universe. Evolving states that progress toward the Big Bang of an alternate dimensional system. Eventually progressing toward a repeat of our dimensional Big Bang, but not before incredible numbers of alternate dimensional spaces pop into and out of relativistic existence.

Using an extension of Axiom of Choice, proposed is a method to model relativity to define the causal limits of physics; non-relativistic quantum causality.

"Axiom of Choice extended to include Relativity"

http://vixra.org/pdf/1402.0041v1.pdf

So if mathematics has a causal limit, and a potential limit for a physical model to extend mathematics to alternate dimensional spaces, then what relationships are there beyond mathematics to describe things other than causal? Where causal is a subset of a super-set. What characteristics might the super-set be composed? Evolving analog relationships?

Correction:

quote: Evolving analog relationships?

revision 1: Non-repeating evolving analog relationships?

I would hold Kantian position and limit mathematics to pure intuition of space and time. Also if you hold German Idealist position on intellectual intuition, that the intellect (logic) and sensibility (intuition) is not separate you can unite intuitionism with logicism. In both ways maths is limited to space and time. All phenomena appear in space and time therefore maths is limited to phenomena and lies at the basis of them.

https://www.academia.edu/7347240/Our_Cognitive_Framework_as_Quantum_Computer_Leibnizs_Theory_of_Monads_under_Kants_Epistemology_and_Hegelian_Dialectic

''6.22 The logic of the world, which is shown in tautologies by the propositions of logic, is shown inequations by mathematics."

http://www.academia.edu/8991727/Phenomenal_World_as_an_Output_of_Cognitive_Quantum_Grid_Theory_of_Everything_using_Leibniz_Kant_and_German_Idealism

Mathematics applies not directly to phenomena but to the invariant ideal structure of space and time in which phenomena appear.

Hi Pentcho. Thanks for drawing attention to the light speed experiment. I am posting here because I have a question that may be more relevant here and also hoping to bait you to read my essay if it is accepted. In your latest post you talked of adding two and two and I ask...

When we write 2 3 = 5,

is it a very high probability that when we add 2 and 3 we get 5 or is it a certainty?

Thanks,

Akinbo

Tim Rappl:

I made your message disappear by reporting it as inappropriate. I did that because of the vulgar rubbish that you included. I can't speak for web archive but, my messages in topic/617 appear to be complete. There is one on Feb 13th and a later group of 69 that ran from Feb 17, 2010 to April 12, 2010. Nothing in them is related in anyway to the rubbish that was included as part of your message. Please be more careful in the future. If you find that any messages of mine posted here at FQXi.org do disappear, I would appreciate your notifying me. That does not appear to have happened this time.

James Putnam

Tim Rapp;,

Please direct your complaint about disappearing messages to the forum administrator.

James Putnam

@Ian Durnham,

Your 2010 question about "those places in which mathematics describes something that is very clearly not physically possible" is very interesting. Maybe I can contribute some clarity.

Max Tegmark's "Ultimate Ensemble theory of everything" states: "all structures that exist mathematically exist also physically"...

Suppose our universe is a mathematical set. That means we are composed elements within this all-inclusive set. Some of us even describe the properties and alterations of other composed elements around with the help of mathematical tools (physics). Moreover, we have developed and checked these tools with the help of the surroundings to simplify reality.

"Do these mathematical tools represent ultimate reality?" Not the "practice" of the tools, because they cannot describe the mechanism of the mathematical set, they represent the relations between composed elements inside the mathematical set.

Modern mathematical theories are optimizations to describe relations. We have not yet developed the mathematical tool to describe the all-inclusive set. However, we have mathematical components so the search for the right description of the universe is the search for a consistent mathematical framework.

Dear member Ian Durham,

You promised to comment on my first two essays. Hopefully you dealt with all others too. I reiterate just my comment made here to MI of Feb 23, 2010:

There seems to be a lot of arbitrarily founded guesswork in mathematics and even more in its applications on physics. Belonging opinions include:

- Rotate or blow up a point (Confusing the point with a phasor of a tiny sphere)

- Nonsensical singular treatment of a real number, e.g. |sign(0)| = 0.

- Denial of restriction for physical quantities to finite positive real values

- Spacetime is thought to extend from minus infinity to plus infinity, amen.

Meanwhile I understood that G. Cantor just mistook Leibniz/Bernoulli's pragmatism for a logically correct basis of rigor.

++++

Towards a new mathematics for science

I've recently drafted a paper with the title "Towards a new mathematics for science" which argues, with a subsidiary paper, that there are weaknesses in today's mathematics as it is applied in science, and that those shortcomings may be overcome in a new mathematics for science (more below).

The two papers may be downloaded via these links:

* Towards a new mathematics for science (PDF, bit.ly/2o1pr8p). This is the main paper.

* On the "mysterious" effectiveness of mathematics in science (PDF, bit.ly/2otrHD0). This is the subsidiary paper.

Ideas in the paper relate to Chapter 12 in Carlo Rovelli's excellent book Reality Is Not What It Seems, especially "Many scientists suspect today that the concept of 'information' may turn out to be a key for new advances in physics."

Here's a bit more about what's in the two papers:

To cut short a lot of evidence and argument:

* Much of human learning, perception and thinking may be understood as compression of information.

* Science may be seen to be, at root, a search for compression of information about the world.

* Mathematics may be seen to be a set of techniques for compression of information, and their application.

* The SP theory of intelligence (and its realisation in the SP computer model) has compression of information at its core.

The proposed new mathematics for science would be an amalgamation of mathematics of today with the SP system. There would be two main benefits:

* It would expand the scope of mathematics with new ways of representing and processing knowledge.

* It would introduce a new discipline into mathematics: quantitative evaluation of calculations in terms of information compression. This may help to guard against unfalsifiable theories and spurious applications of mathematics.

* In several sections, I've discussed possible implications of the new thinking in, for example: the goal of unifying quantum mechanics with general relativity; new interpretations of concepts in quantum mechanics including superposition, nonlocality, and entanglement; a new interpretation of some of the two-slits experiments; and potential advantages of the proposed new mathematics for science in the realm of statistics.

A theme in these proposals is that: 1) Science is the product of the human intellect so it should not be surprising that features of human learning, perception and thinking should have an influence on scientific theories. 2) In much of science those kinds of influence may be ignored. But 3) in physics, and quantum mechanics in particular, it seems that aspects of human cognition can be important.

Comments or suggestions will be very welcome.

Gerry Wolff

Hi Gerry, I had a quick read through " Towards a new mathematics for science. It seems well written, clearly set out and argued and you share some interesting ideas. I found spaghetti programming interesting as it is not something I have previously thought about but I see how it could be very problematic. While compression of information and DONSVIC may be helpful in uncovering some new insights, the incompatibility of Einstein's relativity and comprehension of seeming 'spookiness' are outside of its grasp, in my opinion. I think you have been too accepting of non-locality, closing the door on other possibilities. AI may provide new insights because it learns and operates differently to the human mind and can handle very large data sets; making it very good at looking 'inside the box' at a problem. That however is not necessarily where the answers reside. The issue of the incompatibility of QM and Einstein's relativity stems from an un-noticed category error and I suspect that quantum 'spookiness' has seemed unavoidable because particles in superposition have been considered to passively accept their fate rather than actively interacting with their environment, participating in the evolution of their final state and experiment outcome. So while I think your proposition may be useful and is interesting in its own right, I also think it will not provide the answers that you hope, as they are outside of the collected data alone.

Hello Everyone,

I have discussed the limits of mathematics on my previous essay "Our Numerical Universe". I have shown that how mathematical limits are hindering our progress in mathematics and physical science.

Here is the link to the essay: Our Numerical Universe by Ajay Pokharel

Hope you will like it.

Regards

Ajay Pokharel