Tolstoy on God

Toward the end of War and Peace, Tolstoy gives his protagonist, Pierre, who has been through terrible hardships as a prisoner of the French during the War of 1812, the following thoughts on God:

He could not see an aim, for he now had faith -- not faith in any kind of rule, or words, or ideas, but faith in an ever-loving, ever-manifest God.  Formerly he had sought Him in aims he set himself.  That search for an aim had been simply a search for God, and suddenly in his captivity he had learnt, not by words or reasoning but by direct feelings what his nurse had told him long ago: that God is here and everywhere.  In his captivity he had learn that in Karataev [an uneducated but naturally pure man] God was greater, more infinite and unfathomable than in the Architect of the Universe the Freemasons acknowledged.  He felt like man who, after straining his eyes to see into the far distance, finds what he sought at his very feet.  All his life he had looked over the heads of the men around him, when he should have merely looked in front of him without straining his eyes. 

... That dreadful question, What for? which had formerly destroyed all his mental edifices, no longer existed for him.  To that question, What for? a simple answer was now always ready in his soul: 'Because there is a God, that God without who will not one hair falls from a man's head.'

Book 4, Part IV, Chapter 12

Ether Is Back

I sounds to me as if the discovery of the Higgs boson means that ether is back.  A hundred years ago, scientists believed that there was something that permeated the universe and served as a medium of transmission.  They thought that light waves, for example, propagated through the ether.  The famous Michelson-Morley experiment determining the speed of light, disproved that hypothesis.  It found that the speed of light did not change with the movement of its source, unlike the propagation of sound waves through air, for example. 

So there is not ether, but there appears to be a Higgs field.  I'm not sure, but it appears that only Higgs bosons interact with the Higgs field.  Thus, a photon, which has no mass, has no Higgs boson, and thus is not affected by, and does not interact with the Higgs field.  Particles with mass, like protons and neutrons and the various sub-particles that have mass, such as quarks, would contain Higgs bosons and thus would interact with the Higgs field. 

Presumable, everything with mass is attracted to every other thing with mass through gravity.  Thus gravity would somehow seem to be connected to the Higgs field.  Intuitively, it would seem that the interaction of gravity is instantaneous, unlike light.  Thus, it might be that all of these interactions between masses through the Higgs field date back to the Big Bang and have been carried within that field as the universe expanded.  Thus the Higgs field would carry information about every Higgs boson in the universe. 

That idea may contradict some aspect of quantum theory, which says that you can't know everything about everything.  I'm also not sure what it says about "dark matter," which would appear to contain Higgs bosons, since it has mass, although we can't see it.  We can only detect its effects. 

Temper

I was very unphilosophic recently, and I'm just noting why.  Our next door neighbor has been having lots of work done on his house lately, and the construction workers have been parking in our driveway.  In an effort to be neighborly, we didn't object, although it would seem to make more sense to park on the street.  Yesterday I was backing out of our garage, and all I could see in my rear view mirror was the truck parked at the bottom of our driveway.  As I tried to get around it, I turned too sharply and ran into the trees lining the driveway.  One of the workmen was standing ten feet away talking on his cell phone.  I was furious, although turning too sharply was my mistake.  He could have said, "Is my truck blocking you?  Let me move it."  But he didn't.  He did yell to warn me as I hit the tree, but it was too late.

I was so mad that I cussed him out, which is somewhat unlike me.  So much for being neighborly.

Plato's Cave of Shadows

After writing the previous post, something called my attention to Plato's allegory of the cave of shadows.  It make me think how similar his example of shadows was to the two-dimensional world visualized in the Scientific American article, although he was interested in a completely different issue. The Scientific American article was concerned with the external, physical world, while Plato was concerned with the internal, mental world.  For Plato, the two-dimensional world of shadows represented the unenlightened world in which most men live.  As they improve themselves they exit the cave of shadows and see the bright, three-dimensional world, but then, I think, Plato argues that after seeing the bright world, leaders have to re-enter the cave of shadows to lead those poor souls with the knowledge they have gained from the outside world.  If they stay in the light, they are no benefit to their fellow men.

Although their points are different, it's interesting that thinkers thousands of years apart resorted to the same type of thought experiment, although in one case (Plato's) what is learned in the three-dimensional world benefits the two-dimensional, while in the other (the Scientific American's) what is learned in the two-dimensional world helps explain the three-dimensional.  One is concerned with the physical world, while the other is concerned with the metaphysical.

Two Dimensional Gravity

The April Scientific American has an article on two-dimensional gravity, "Quantum Gravity in Flatland."  It shows how you can simulate gravity to some extent in two dimensions by changing the topology of the two dimensions. 

For me, the main interest is in seeing how an n-1 environment can help us understand an environment with n dimensions.  We think that we live in an environment of three spacial dimensions, plus time.  What if we live in an environment of more dimensions, which we cannot sense.  We have five senses: sight, touch, hearing, smell, and taste.  Most of what we know about our universe comes from just two of those, sight and touch.  Microscopes, telescopes, machines and tools help us extend these senses to very large and very small things, but we are still basically depending on sight and touch.  What if the things we sense are only part of the universe; they might be just part of, or effects of, things which we cannot sense directly. 

That is what is interesting to me about two-dimensional simulations of a three dimensional world.  Suppose you lived in a two dimensional world where you could only see the flat shadows of three-dimensional objects.  As the sun rose and set, shadows would go from being infinitely long to small, and back to being infinitely long again.  What could you figure out about the object; would you think it changed size or shape, when only the light source was moving? 

Or what if there is some other dimension, like time, that is not a physical dimension.  Could we even conceive of what it is?  Basically what makes a dimension is our ability to measure it.  We measure time with clock.  Einstein found that the measurable dimensions are not absolute, but vary relative to each other.  Could it be that we are looking at the moving "shadows" and that there is something out there that is constant? 

String Theory

The reports of neutrinos moving faster than the speed of light and the entanglement of electrons lead to the possibility of additional dimensions. Extra dimensions could also help explain the possibility of dark matter and dark energy, which seem to be necessary to explain the makeup of the universe, although there is no physical evidence of them.  One response to this possibility is string theory. 

To see the possibility of additional dimensions, think about trying to figure out our three dimensional universe by looking at two dimensional shadows.  By looking only at the shadows, it would be very difficult to figure out exactly what the three dimensional shadows casting the shadows looked like.  A sphere, for example would cast a circular shadow, but so would a cylinder, if it was held the right way.  An egg could cast a circular shadow or an oblong shadow, and so on. 

For string theory, consider drawing a line on a sheet of paper.  If you look at the edge of the paper, you would only see a dot, where the line started, but if you could look down on the paper, you might see an infinitely long line, if the paper was infinitely long.  Or, you could draw a line that started at one point on the edge of the paper, then then went in crazy curves all over the paper, before coming back to the edge.  If you looked only at the edge, you would see only two points, one where the line started and one where it ended.  You would think these were separate points, but in fact they would be part of the same line.  This concept could explain the idea of entanglement, which says that if you know the state of one electron in a pair, you instantly know the state of the other.  In the line case, you would think you are looking at two separate points, but in fact you are looking at two ends of the same line.  Therefore, if one point was blue, for example, you would know that the other point would also be blue, because they are part of the same line.  But from looking only at the two points on the edge of the paper, it would be impossible to know what the line did between those two points, whether it went in a relatively smooth curve from one to the other, or went for miles and miles in all sorts of crazy curlicues between the two points. 

NYT Likes Carmelo Anthony

The New York Times ran a complementary article about Denver's Carmelo Anthony today. He is apparently one of the stars in a documentary of one of the first professional black basketball teams.