Log24

Saturday, April 28, 2012

Sprechen Sie Deutsch?

Filed under: General,Geometry — m759 @ 10:48 AM

A Log24 post, "Bridal Birthday," one year ago today linked to
"The Discrete and the Continuous," a brief essay by David Deutsch.

From that essay—

"The idea of quantization—
the discreteness of physical quantities
turned out to be immensely fruitful."

Deutsch's "idea of quantization" also appears in
the April 12 Log24 post Mythopoetic

"Is Space Digital?

— Cover storyScientific American 
     magazine, February 2012

"The idea that space may be digital
  is a fringe idea of a fringe idea
  of a speculative subfield of a subfield."

— Physicist Sabine Hossenfelder 
     at her weblog on Feb. 5, 2012

"A quantization of space/time
 is a holy grail for many theorists…."

— Peter Woit in a comment 
      at his weblog on April 12, 2012

It seems some clarification is in order.

Hossenfelder's "The idea that space may be digital"
and Woit's "a quantization of space/time" may not
refer to the same thing.

Scientific American  on the concept of digital space—

"Space may not be smooth and continuous.
Instead it may be digital, composed of tiny bits."

Wikipedia on the concept of quantization—

Causal setsloop quantum gravitystring theory,
and 
black hole thermodynamics all predict
quantized spacetime….

For a purely mathematical  approach to the
continuous-vs.-discrete issue, see
Finite Geometry and Physical Space.

The physics there is somewhat tongue-in-cheek,
but the geometry is serious.The issue there is not
continuous-vs.-discrete physics , but rather
Euclidean-vs.-Galois geometry .

Both sorts of geometry are of course valid.
Euclidean geometry has long been applied to 
physics; Galois geometry has not. The cited
webpage describes the interplay of both  sorts
of geometry— Euclidean and Galois, continuous
and discrete— within physical space— if not
within the space of physics.

Thursday, April 12, 2012

Mythopoetic*

Filed under: General,Geometry — m759 @ 9:29 PM

"Is Space Digital?

Cover storyScientific American  magazine, February 2012

"The idea that space may be digital
  is a fringe idea of a fringe idea
  of a speculative subfield of a subfield."

— Physicist Sabine Hossenfelder
     at her weblog on Feb. 5, 2012

"A quantization of space/time
 is a holy grail for many theorists…."

— Peter Woit in a comment at his physics weblog today

See also 

* See yesterday's Steiner's Systems.

Friday, February 17, 2012

Pregeometry and Finite Geometry

Filed under: General,Geometry — Tags: — m759 @ 7:35 PM

Today's previous post, on the Feb. 2012 Scientific American
article "Is Space Digital?", suggested a review of a notion
that the theoretical physicist John Archibald Wheeler called
pregeometry .

From a paper on that topic—

"… the idea that geometry should constitute
'the magic building material of the universe'
had to collapse on behalf of what Wheeler
has called pregeometry  (see Misner et al. 1973,
pp. 1203-1212; Wheeler 1980), a somewhat
indefinite term which expresses “a combination
of hope and need, of philosophy and physics
and mathematics and logic” (Misner et al. 1973,
p. 1203)."

— Jacques Demaret, Michael Heller, and
Dominique Lambert, "Local and Global Properties
of the World," preprint of paper published in
Foundations of Science  2 (1): 137-176

Misner, C. W., Thorne, K. S. and Wheeler, J. A.
1973, Gravitation , W.H. Freeman and Company:
San Francisco.

Wheeler, J.A. 1980, "Pregeometry: Motivations
and Prospects," in: Quantum Theory and Gravitation ,
ed. A.R. Marlow, Academic Press: New York, pp. 1-11.

Some related material from pure mathematics—

http://www.log24.com/log/pix12/120217-Pregeometry_And_Geometry.jpg

Click image for further details.

Physics vs. Geometry

Filed under: General,Geometry — m759 @ 12:25 PM

Physics

The February 2012 issue of Scientific American 
has a cover article titled "Is Space Digital?".

http://www.log24.com/log/pix12/120217-IsSpaceDigital.jpg

The article discusses whether physical space
"is made of chunks. Blocks. Bits."

Maybe it is, maybe it isn't.

Geometry

The word "space" in pure mathematics
(as opposed to physics) applies to
a great variety of structures.

Some are continuous, some are not.

For some purely mathematical structures
that are not  continuous, (i.e., are made of
"chunks, blocks, bits") see finitegeometry.org/sc
in particular, the pages on Finite Geometry and Physical Space
and on Noncontinuous Groups.

The geometry of these structures may or may not eventually
be relevant to the "21st-century physics" discussed
in the February Scientific American.

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