Posts tagged with the universe

3D map of the large-scale distribution of dark matter, reconstructed from measurements of weak gravitational lensing with the Hubble Space Telescope.
via davidaedwards

3D map of the large-scale distribution of dark matter, reconstructed from measurements of weak gravitational lensing with the Hubble Space Telescope.

via davidaedwards


Playing around with polaroid screens at Google.

If you shine light through

  • a light polariser A
  • another light polariser B that’s perpendicular to A (i.e., A ⊥B or A×B=0)
  • i.e., AB represents “shine the light through A then through B which ⊥A
  • then no light comes through (it’s black.)

If you shine light through

  • a polaroid A
  • another polaroid B ⊥ A
  • a third polaroid C that’s halfway between A and B (either halfway)

then no light comes through (it’s black.)

So far, formulaically, we have:

  • AB=0
  • BA=0
  • whence it follows
  • ABC=(AB)C=(0)C=0
  • CBA=C(0)=0
  • BAC=0
  • CBA=0

But! This is surprising to watch and surprising to see the formula.

  • If you shine through A then C then B, it’s kind of light!
  • ACB≠0
  • furthermore
  • BCA≠0

Woo-hoo, Noncommutativity!

Earlier in the talk Ron Garret does a two-slit experient with two mechanical-pencil leads and a laser pointer. Wave-particle duality with an at-home science kit.


It wasn’t Einstein, but the mathematician Hermann Weyl who first addressed the [distinction] [between gravitational and non-gravitational fields] in 1918 in the course of reconstructing Einstein’s theory on the preferred … basis of a “pure infinitesimal geometry”….

Holding that direct…comparisons of length or duration could be made at near-by points of spacetime, but not … “at a distance”, Weyl discovered additional terms in his expanded geometry that he … formally identified with the potentials of the electromagnetic field. From these, the electromagnetic field strengths can be immediately derived.
Maxwell's equations in differential form (reduces 20 to 4)Choosing an action integral to obtain both [sorts of] Maxwell equations as well as Einstein’s gravitational theory, Weyl could express electromagnetism as well as gravitation solely within the confines of a spacetime geometry. As no other interactions were definitely known to occur, Weyl proudly declared that the concepts of geometry and physics were the same.
Gauss' law for rmagnetism
Hence, everything in the physical world was a manifestation of spacetime geometry. (The) distinction between geometry and physics is an error, physics extends not at all beyond geometry: the world is a (3+1) dimensional metrical manifold, and all physical phenomena transpiring in it are only modes of expression of the metric field, …. (M)atter itself is dissolved in “metric” and is not something substantial that in addition exists “in” metric space. (1919, 115–16)


Ryckman, Thomas A., "Early Philosophical Interpretations of General Relativity", The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), Edward N. Zalta (ed.), forthcoming URL = <>.

via University of David

What is the world made of?There are twelve basic building blocks.

Six of these are quarks—- they go by the interesting names of up, down, charm, strange, bottom and top. (A proton, for instance, is made of two up quarks and one down quark.) The other six are leptons—- these include the electron and its two heavier siblings, the muon and the tauon, as well as three neutrinos.

There are four fundamental forces in the universe: gravity, electromagnetism, and the weak and strong nuclear forces. Each of these is produced by fundamental particles that act as carriers of the force…: …photon…graviton…eight…gluons…three…W+, … W- , … Z.

The behavior of all of these particles and forces is described with impeccable precision by the Standard Model, with one notable exception: gravity.

The central message that Bohr and von Neumann taught us about the Standard Quantum Logic is that it can be viewed as a manifold of interlocking perspectives that cannot be embedded into a single perspective. Hence, the perspectives cannot be viewed as perspectives on one real world.

So, even considering one world as a methodological principle breaks down in the quantum micro-domain.

Question. Why do we live in a 3-dimensional universe?

Tentative Answer. Maybe because 3 dimensions is the most interesting number of dimensions? Maybe 3-D is the boundary between “too constrained” and “too free”.

The above link is to some mathematicians discussing other interesting dimensions besides 3 — because they already know 3-D is uniquely suited to complexity.

In other words, lots of “facts” are only facts in ℝᵈ when d=3. So by the anthropic principle…we live in 3-D.

Here’s one fact that’s unique to just the fourth dimension.

Exotic ℝ⁴: There are infinitely many non-diffeomorphic smooth structures on the topological space ℝᵈ if and only if d=4.

Otherwise there is only one diffeomorphism class.

^ pictures of diffeomorphisms

(A diffeomorphism preserves the relationships between neighbouring points.)