Archives for posts with tag: maths

⚫ and ⚫⚫ makes ⚫⚫⚫ (physical quantity)

1 + 2 = 3 (human number)

each of the ‘equations’ describes the same relationship; each is based on the same principles

each expresses inviolable laws which govern the combination of identical entities into groups

natural numbers are physical constants

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Part of the reason that the formal, natural connections between mathematics and physics are rejected as significant by most physicists is because the the two fields are so firmly intertwined at the most basic levels that the epistemological becomes confused with the ontological.

In fact, it is not that mathematics underlies physics and it isn’t that they look the same because mathematics is only our tool to examine physics with. It’s that the same fundamental principles – laws which are both natural AND mathematical – underlie them both. But we shouldn’t be surprised at this.

Human concepts of number and maths developed from experience and observation of the real world: geometry can be developed from both theory AND by measuring the physical world; counting systems are based on measuring and comparing the physical properties of different groups of the same or equivalent physical objects.

It’s not so much that either maths or physics underlie the other, it’s more that they develop from the same first principles, and are parts of the same thing. There’s only a single ‘sum total of existence’: you can define the mathematical concept 1, physically. And the first law of thermodynamics can be expressed as 1a+2a=3a.

Issues of efficiency act as constraints on how mathematical complexities develop naturally from first principles into a physical spacetime. These constraints are the difference which leads to a separation of human abstract mathematics from physical mathematicality.

mathematics is developed from number theory

number theory is developed from a rigorous counting system

a rigorous counting system is based on physical property of quantity

the physical property of quantity is a result of natural laws of physics

 

 

Quantum Mechanical Derivation of the Wallis Formula for

Further evidence that the connections between mathematics and physics are non-trivial.

the quantity of things we call 1

put with the quantity of things we call 2

will always make the quantity of things we call 3

physical quantities are not the result of human number systems

human number systems are the result of our perception of physical quantity

Peter Woit, University of Columbia, ‘Towards a Grand Unified Theory of Mathematics and Physics’.

A paper which outlines some of the already established connections between number theory and physics, acknowledges that there are as yet no satisfactory explanations for these connections, and concludes it is an area which deserves much more attention.

What seems to be the central reason preventing mathematicians and physicists from acknowledging the significance of the connections between their respective fields is a fundamental, but understandable, misunderstanding about the nature of number systems. Numbers are considered to be abstract inventions of pure human imagination, and mathematical formulations are seen therefore as being based in nothing more than abstraction. As a consequence, the idea that number theory and physics are formally connected is rejected – even as the evidence for formal connections between the two fields is being examined and analysed as profound mystery.

This is a crucial mistake.

Number systems are at their most basic level, founded on the concretely physical property of quantity. Numerical relationships are quantitative relationships, and quantitative relationships are at the heart of physics.

Quoting the same page as the last post, watch how it sums up the resistance in the scientific community, against maths and physics being formally linked. This resistance leads to complete cognitive dissonance, where evidence for formal connections is explicitly referenced followed immediately by the denial that any formal connections are possible.

“…the surprising thing is that often some newly discovered abstract formulation in mathematics turns out, years later, to describe physical phenomena which we hadn’t known about previously…”

“…physics cannot be derived from mathematics alone…”

The first statement undermines the second statement.

the law of conservation of energy is precisely described in mathematics

1a+1a=2a

where ‘a’ is anything

http://phys.org/news/2014-12-mathematicians-umbral-moonshine-conjecture.html

another intersection of number theory and physics