Archives for posts with tag: theory of everything


this is maths and theoretical physics

more evidence of the significance of the connections between math and physics

more evidence that mathematical principles are natural laws

nothing can be created or destroyed, which makes 1a+1a=2a an entirely natural law



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.

A playfully serious theory of everything isn’t really an attempt to offer answers to the detailed question of how number theory and maths are connected to physics. Exploring the various ways physical entities emerge from, and are governed by, the operation of laws of quantity – that is, laws which are absolutely and naturally mathematical – is not what this theory is about.

What a playfully serious theory of everything seeks to explain is WHY those connections exist.

  1. is quantity a physical property? (do physical objects naturally exist in various quantities?)

  2. are quantitative relationships absolute? (that is, for any class of physical object, if you put a quantity that we call 2 with a quantity we call 3, will it always result in a quantity we call 5 ..?)

  3. what’s the connection between number systems and quantity? (how come number systems match up precisely with quantity and quantitative relationships?)

1. Yes.

2. Yes.

3. Number systems are fundamentally based on principles of quantity, which a)explains why they’re so useful for measuring and describing the physical universe and b)explains the “strange”, deeper connections between number theory and physics such as those documented here:

From a lecture by Paul Adrien Maurice Dirac titled ‘The Relation Between Mathematics and Physics’, on presentation of the JAMES SCOTT prize, February 6, 1939

Published originally in: Proceedings of the Royal Society (Edinburgh) Vol. 59, 1938-39, Part II pp. 122-129

Reposted at

“I would like to put forward a suggestion as to how such a scheme might be realized. If we express the present epoch … in terms of a unit of time defined by the atomic constants, we get a number of the order 1039, which characterizes the present in an absolute sense. Might it not be that all present events correspond to properties of this large number, and, more generally, that the whole history of the universe corresponds to properties of the whole sequence of natural numbers? At first sight it would seem that the universe is far too complex for such a correspondence to be possible. But I think this objection cannot be maintained, since a number of the order 1039 is excessively complicated, just because it is so enormous. We have a brief way of writing it down, but this should not blind us to the fact that it must have excessivly complicated properties.

There is thus a possibility that the ancient dream of philosophers to connect all Nature with the properties of whole numbers will some day be realized. To do so physics will have to develop a long way to establish the details of how the correspondence is to be made. One hint for this development seems pretty obvious, namely, the study of whole numbers in modern mathematics is inextricably bound up with the theory of functions of a complex variable, which theory we have already seen has a good chance of forming the basis of the physics of the future. The working out of this idea would lead to a connection between atomic theory and cosmology.”

if human numbers are merely names for physical quantities, and numerical relationships merely describe the physical relationships between quantities… this would explain how human mathematics is so precisely useful for describing the physical universe