Powers of 10

This is an image my brother Doug and I made. A blanket is at the far left; then grass, streets, city, shoreline, clouds, the earth, orbits of the moon, Earth, Mars, Jupiter, Saturn, Neptune, nearby stars, the Milky Way, and distant galaxies. (Click for a much bigger view.)

Can you guess how we made it?

Regular tilings of three-dimensional spaces

If you start at the north pole and make an equilateral triangle 6000 miles on a side, the bottom will lie on the equator, each of the angles will be 90 degrees, and only four of them will fit around the pole.

In a similar way, large enough tetrahedra would tile the surface of a hypersphere. This paper identifies the eleven regular tilings of three-dimensional spaces and whether they’re spherical, Euclidean, or hyperbolic tilings, and then looks at the geometry of spacetime to see how it might be tiled.

The “cubic” tilings (where eight polyhedra meet around a vertex like cubes do in Euclidean space) are amenable to taking cross-sections; this tiling of hyperbolic space with dodecahedra

has a cross section with a tiling of the hyperbolic plane with pentagons:

The Word of God

From desert cliff and mountaintop we trace the wide design,
Strike-slip fault and overthrust and syn and anticline…
We gaze upon creation where erosion makes it known,
And count the countless aeons in the banding of the stone.
Odd, long-vanished creatures and their tracks & shells are found;
Where truth has left its sketches on the slate below the ground.
The patient stone can speak, if we but listen when it talks.
Humans wrote the Bible; God wrote the rocks.

There are those who name the stars, who watch the sky by night,
Seeking out the darkest place, to better see the light.
Long ago, when torture broke the remnant of his will,
Galileo recanted, but the Earth is moving still.
High above the mountaintops, where only distance bars,
The truth has left its footprints in the dust between the stars.
We may watch and study or may shudder and deny,
Humans wrote the Bible; God wrote the sky.

By stem and root and branch we trace, by feather, fang and fur,
How the living things that are descend from things that were.
The moss, the kelp, the zebrafish, the very mice and flies,
These tiny, humble, wordless things–how shall they tell us lies?
We are kin to beasts; no other answer can we bring.
The truth has left its fingerprints on every living thing.
Remember, should you have to choose between them in the strife,
Humans wrote the Bible; God wrote life.

And we who listen to the stars, or walk the dusty grade,
Or break the very atoms down to see how they are made,
Or study cells, or living things, seek truth with open hand.
The profoundest act of worship is to try to understand.
Deep in flower and in flesh, in star and soil and seed,
The truth has left its living word for anyone to read.
So turn and look where best you think the story is unfurled.
Humans wrote the Bible; God wrote the world.

-Catherine Faber, The Word of God

Entropic gravity

Erik Verlinde has been in the news recently for revisiting Ted Jacobson’s suggestion that gravity is an entropic force rather than a fundamental one. The core of the argument is as follows:

Say we have two boxes, one inside the other:

+---------------+
|               |
| +----------+  |
| |          |  |
| |          |  |
| |          |  |
| +----------+  |
+---------------+

Say the inner box has room for ten bits on its surface and the outer one room for twenty. Each box can use as many “1”s as there are particles inside it:

+---------------+
|      X        |
| +----------+  |
| |          |  |
| |  X       |  |
| |          |  |
| +----------+  |
+---------------+

In this case, the inner box has only one particle inside, so there are 10 choose 1 = 10 ways to choose a labeling of the inner box; the outer box has two particles inside, so there are 20 choose 2 = 190 ways. Thus there are 1900 ways to label the system in all.

If both particles are in the inner box, though, the number of ways increases:

+---------------+
|               |
| +----------+  |
| |          |  |
| |  X  X    |  |
| |          |  |
| +----------+  |
+---------------+

The inner box now has 10 choose 2 ways = 45, while the outer box still has 190. So using the standard assumption that all labelings are equally likely, it’s 4.5 times as likely to find both particles in the inner box, and we get an entropic force drawing them together.

The best explanation of Verlinde’s paper I’ve seen is Sabine Hossenfelder’s Comments on and Comments on Comments on Verlinde’s paper “On the Origin of Gravity and the Laws of Newton”.

Passive polarization clock

Here’s a design for a passive polarization clock.

The sky is polarized in concentric circles around the sun. The polarization of the southern sky moves through around 180 degrees during daylight hours. It is polarized vertically in the morning, horizontally at noon, and vertically again in the evening.

Align slices of polarized film such that they are parallel to the contours. Any given ray from the center of the sundial outward always hits the contours at the same angle; the angle changes by 360 degrees as the ray passes through 180 degrees. In other words, the clock goes from 6am to 6pm as the sun moves through the sky.

Powers of 10 toward the black hole in the center of the galaxy

http://www.cs.indiana.edu/%7Ehanson/Movies/blackhole.mov

Also see Hanson’s other visualizations here:
http://www.cs.indiana.edu/~hanson/
and this 3-d projection of the 5-d Calabi-Yau manifold:
http://www.bathsheba.com/crystal/calabiyau/

Killer Asteroids

Large asteroid impacts may be WAY more common than we think.

Pictures of the moon and sun

A picture of the sun, taken with nutrinos, partly at night, RIGHT THROUGH THE EARTH.
http://cosmicvariance.com/2006/10/13/sun-shots/

A picture of muons from the glow of the night sky, with the moon casting a shadow.
http://en.wikipedia.org/wiki/Image:Moons_shodow_in_muons.gif