Monday 9 February 2009

Too soon to state objectives, lets just set down a few relevant discussions/arguments. Always start with the obvious (though it was not always so . . )

Why did it take us until the middle ages to begin to realise that the earth was spherical? Everyone believed the earth to be flat, and then wrestled with the problems that creates, of what happens at the edges - won't the sea run off? And what is beneath this plate-shaped earth. And why is the horizon apparently a fixed distance, dependent on only the height ASL of the observer? Just looking at a peeled orange has all the clues of a sphere with poles, and lines of longitude. Was the moon also a flat disc, which just happened to present its surface normal to the earth?

People were trapped in their local view of the world, and so oranges could be spherical but planets must be flat. And then the great navigators proved the earth's true shape by sailing around it in one direction and ending up where they started. The earth's surface has finite area, and it has no boundaries. Like an orange, you (or an ant) can travel around it without ever stopping, but its area is only 4PiR^2/3. For someone with a two-dimensional view, where there is only forward/reverse and left/right, the gentle downwards curvature of the globe does not exist and to return to where you started without falling off the edge is a total mystery. Slot in the third dimension, the same one that up and down exist in, and all fits into place.

How many people think the universe is infinite? In any case it is unimaginably large, so why not? Cosmologists (using the term broadly) know it is not, in fact its total mass has been estimated, I have seen a figure of 10^40kg give or take some orders of magnitude. They see evidence of the Big Bang and can measure the age and the speed of expansion.

I worked out as a teenager that the universe must be finite. The method was simply that if it were infinite, there must be another earth exactly like ours, but for that to happen there must be a near-infinite number just like it except for one molecule etc etc, even thinking about an infinte universe is scary. Fortunately we have a model from our two-dimensional world - as the surface of a sphere is finite but unbounded, so the volume and mass of the universe is finite but unbounded. In this case whichever direction you set off in (forward/back, left/right or up/down), and think you are travelling in a straight line, you will end up where you started.

So where is the hidden dimension, the forgotten up/down of the flat earther? Let's say that is time (I haven't a better idea), something we are familiar with in our local view, but find it hard to imagine on a cosmic scale. And something which links cosmic distances and the speed of light.

I once failed an interviewing course, and one reason was a dumb question I gave a bright test interviewee - what would you reply to a precocious nephew who asked you why we are attracted to the ground. (I did not ask him to explain gravity, just how he would reply to a cute question.) I think his answer was to ask his dad - or someone who understood big things. But he copped out. What do you say - shut up and eat your porridge? But if we can't be expected to understand the size of the universe, why should we question why gravity exists. There are far more pressing mysteries, like whether UFOs are real.

But there is a model for gravity that lay people should be able to understand, that involves slipping off the tricky dimension and going back to just three. Take a rubber toy balloon, stick some pieces of lead shot around its surface, what happens? (Don't forget, gravity doesn't exist yet, we can do without the sticky stuff). Nothing happens. But start to blow up the balloon, and the pieces of lead shot will resist the movement, and make indents in the surface of the balloon. And if two of the pieces of lead shot are close together, their indentations will tend to be lower in the region between them, and they will roll (or gravitate?) towards one another. We have a model of masses being attracted to each other when being accelerated in an elastic medium.

Put back the magic dimension, the one that takes us from a 2-D surface to a 3-D volume, and we have the elastic medium of space with masses in it. If the space is static the masses don't bend it and there is no gravity. But if the elastic space is expanding, the masses resist by making indents in the space. Two masses nearby each other 'share' an indent, and roll down its 'sides' towards each other - hence gravity. Astronomers make measurements of stars by observing how light from distant stars is bent around planets as they 'line up' to our view. Space is elastic, and it bends as it pushes masses along in its expansion.

So what? If you didn't know before, then you've learned something fundamental. And if you did, well let's move to the next step. Yes, all of us.

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