From here to infinity... logarithmically

Contributed by
Jan 11, 2010
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Logarithms are cool. Sure, some of you may have flashbacks to middle school and may collapse on the floor twitching upon their mere mention, but seriously, logs are the language of the Universe. Our senses (eyesight and hearing) are sensitive logarithmically, and a lot of ways the world behaves make a lot more sense when you plot them using logs.

For those of you scratching your heads, a simple way to think of logs is to think factors of ten. Instead of counting like we normally do -- 1, 2, 3, 4 and so on -- in log space you count by factors of 10: 1, 10, 100, 1000, and so on. There are lots of advantages to this, one being that you can make graphs that show things that are very small and very big on the same plot. Using regular numbers, it would be hard to make a graph showing the size of a human (2 meters tall) and a skyscraper (200 meters tall) on the same plot, but using logarithms, they are only two ticks apart in size. Easy peasy.

And if you take this idea to the extreme, what do you get? Why, you could get a plot of the whole freaking Universe, from the surface of the Earth out to the fires of the Big Bang itself!

But who would do such a thing? Astronomers at Princeton, that's who.


[Click to exponentiate.]

That picture is just a small piece of a much larger graphic showing, well, everything. At the bottom is the Earth and at the top is the most distant thing we can see: the cosmic microwave background, the cooling fireball from the Big Bang. Included are planets, asteroids, stars, galaxies, and pretty much everything you can think of, all plotted out for your perusal. The vertical axis represents distance, and the horizontal is cleverly done in Right Ascension, sorta like longitude (East/West) on the sky. That way they get the whole sky -- the whole Universe -- on one graph.

I know xkcd did something like this, but I'd love to see this done up as a vastly scrollable webpage with actual images instead of dots, and the objects actually described (rollovers, popups, links, whatever). If done correctly, that would cause a wave of nerdgasms across the web, and not-so-incidentally be an awesome learning tool. Any takers?

Tip o' the order of magnitude to Stuart at @astronomyblog.