Tuesday, April 01, 2003

Large Numbers pt. 2

Paul Dirac was probably the most brilliant physicist who is not commonly known among non-scientists. Most physicists regard him as among the top 10 most brilliant physicists of all time among such others as Einstein, Newton and Feynman.

Among his achievements, Dirac was the first to achieve a unification of Einstein's special relativity with Schrodinger's wave mechanics. The invented Dirac algebra is a thing of sublime beauty and a testament to Dirac's heroic intuition. One result was the prediction of the existence of negative states of matter - what we now call anti-matter. Dirac's equations revealed these things years before such particles were eventually discovered in particle accelerators.

Later in his life, Dirac sought out order among the seemingly disconnected variables and constants which sprout up in physics. His Large Numbers Hypothesis proposed that large numbers are all connected in some way, that they are not independent artifacts of nature.

An example will make this clearer. The ratio between the strength of electromagnetic forces and the gravitational force is on the order of 10^42. That is, the electromagnetic attraction between an electron and a proton is about that many times stronger than any gravitational attraction, at least according to theory.

Now 10^42 is a large number. As it happens, the ratio between the time of a typical event in an atom and that of the age of the universe is on the order of ... 10^42.

The human mind grasps at patterns and this seems like an enticing one. If we assume that the two are related and not a mere coincidence then we can make some immediate conclusions. One is that, since the universe is expanding, then it follows that the gravitational force in the universe is becoming weaker and weaker.

This is revolutionary. Dirac was one of the first major figures to seriously propose that some of the major constants in nature are actually a slow function of time - that the rules of the universe are themselves changing or evolving in some way. And that they are in many ways interlinked, all part of a vast, mysterious clockwork, only apparent to us by their immense scale.

With what we know today, Dirac's hypothesis does not seem likely, but it has not been entirely ruled out.
posted by banubula 6:33 PM

Monday, March 31, 2003

Large Numbers pt.1

As a kid, I loved to play with large numbers on paper and in my head. I remember watching Cosmos or maybe some other show where they mentioned googols and googolplexes and I was unimpressed.

The first obvious extension i played with was building functions on functions. This was an extension of how the operation of multiplication worked on top of addition. It goes something like this:

1 x+x=x+1+1+.. (x times)=x*2
2 x*x=x+x+x... (x times)=x^2
3 x^x=x*x*x... (x times)=x@2
4 x@x=x^x^x... (x times)=x&2
5 x%x=x@x@x....(x times)=x#2

and so on...

Now, we define x(y) as the operation of order y performed on x. So, x(4)=x&2 for example. you can see that 100(100) is unimaginably large.

Its not easy to create large numbers like this, at least not in a way that is properly defined. For further reading, anything you could wish to know is explained on this page.
posted by banubula 1:36 AM

This is a first attempt to create a place where I can write about science, technology, networks, mathematics and about xul solar.
posted by banubula 12:11 AM

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