Yoga Anatomy
Leslie Kaminoff
Human Kinetics
ISBN-13:978-0-7360-6278-7
Saturday 29 September 2007
Sunday 16 September 2007
The Mathematical Universe
Inspired by: "Reality by Numbers", Max Tegmark, New Scientist, 15 Sept 2007, p38.
The holy grail of theoretical physics is a theory of everything - a complete description of the universe. Max Tegmark argues that our Universe is not just described by mathematics - it is mathematics.
The foundation of his argument is the pre-supposition that there exists a universe independent of human experience. For such a description to be self-consistent it must also be well formed for non-human entities (ranging across all scales from sub-atomic particles, to animals, to universes).
Physical theories comprise two components: mathematical equations defining relationships, and descriptions of how those equations relate to our observations, intuitions and concepts. The physicist in me wants to rationalise the abstract mathematics with human conceptual meaning, but in principle the evolution of the universe could be calculated from the equations without the need for human conceptual interpretation.
Is it possible to find an objective description of the universe that does not rely on human concepts? If so such a description would be completely abstract with no meaning. The only properties of the entities described would be those defined in the relationships between them.
And mathematics is precisely this: sets of abstract entities with relationships between them. Mathematics is the formal study of structures that can be defined in a purely abstract way. Max Tegmark pre-supposes that humans don't invent mathematical structures, we discover them, and invent only the notation for describing them.
Here is the crux of Tegmark's argument: if you believe in an objective universe, independent of the human mind, then to be consistent you must also believe in the mathematical universe hypothesis: that the objective universe is a mathematical structure.
The theory of everything then must be purely abstract, objective and mathematical. Physics has reached the point in its development where across all scales, from particles to universes, all objective measurements ever made are consistent with a few pages of equations that involve 32 unexplained numerical constants.
Amusingly inconsistent with his thesis, Tegmark takes a sidestep to ask: What does this mean? Despite the searing rigour of his argument he cannot resist the human temptation to ask: Why?
First he distinguishes the dissociated observer studying the structure from outside, like a bird hovering overhead, from the associated observer living in the structure, like a frog living in the pond. The associated frog feels the passing of time in the pond moment by moment. The dissociated bird above observes the entire evolution of the universe unfolding below like a movie .
Then he asks: How do we relate the two perspectives? The abstract mathematical structure of the movie exists outside the snapshot of the individual frame. How can an observer be purely mathematical? The complex structure of the observer stores and processes information in a way that gives rise to the sensation of self-awareness.
How do we test the mathematical universe hypothesis? It predicts that further mathematical regularities remain to be discovered in nature, and it predicts the existence of parallel universes.
The holy grail of theoretical physics is a theory of everything - a complete description of the universe. Max Tegmark argues that our Universe is not just described by mathematics - it is mathematics.
The foundation of his argument is the pre-supposition that there exists a universe independent of human experience. For such a description to be self-consistent it must also be well formed for non-human entities (ranging across all scales from sub-atomic particles, to animals, to universes).
Physical theories comprise two components: mathematical equations defining relationships, and descriptions of how those equations relate to our observations, intuitions and concepts. The physicist in me wants to rationalise the abstract mathematics with human conceptual meaning, but in principle the evolution of the universe could be calculated from the equations without the need for human conceptual interpretation.
Is it possible to find an objective description of the universe that does not rely on human concepts? If so such a description would be completely abstract with no meaning. The only properties of the entities described would be those defined in the relationships between them.
And mathematics is precisely this: sets of abstract entities with relationships between them. Mathematics is the formal study of structures that can be defined in a purely abstract way. Max Tegmark pre-supposes that humans don't invent mathematical structures, we discover them, and invent only the notation for describing them.
Here is the crux of Tegmark's argument: if you believe in an objective universe, independent of the human mind, then to be consistent you must also believe in the mathematical universe hypothesis: that the objective universe is a mathematical structure.
The theory of everything then must be purely abstract, objective and mathematical. Physics has reached the point in its development where across all scales, from particles to universes, all objective measurements ever made are consistent with a few pages of equations that involve 32 unexplained numerical constants.
Amusingly inconsistent with his thesis, Tegmark takes a sidestep to ask: What does this mean? Despite the searing rigour of his argument he cannot resist the human temptation to ask: Why?
First he distinguishes the dissociated observer studying the structure from outside, like a bird hovering overhead, from the associated observer living in the structure, like a frog living in the pond. The associated frog feels the passing of time in the pond moment by moment. The dissociated bird above observes the entire evolution of the universe unfolding below like a movie .
Then he asks: How do we relate the two perspectives? The abstract mathematical structure of the movie exists outside the snapshot of the individual frame. How can an observer be purely mathematical? The complex structure of the observer stores and processes information in a way that gives rise to the sensation of self-awareness.
How do we test the mathematical universe hypothesis? It predicts that further mathematical regularities remain to be discovered in nature, and it predicts the existence of parallel universes.
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