Monday, January 28, 2008

Dinner table discussions with home school kids...

OK so we are talking at the table about math (I still have to grade Rene's paper from today) and Nathan uses the term Jillian, as in there are a jillian stars. Then I think it was Rene who brought up the googleplex which as you may know is a 1 followed by 100 zeros. Then my wife was wondering if there was anything in the universe we could apply googleplex to and I told her I didn't think so, at least not in the visible universe (meaning everything we could potentially see with the world's best telescope.)

This of course brought me to my computer after dinner to do some research and fairly basic exponential math.

Here is what I came up for a universe comprised entirely of salt (that just happened to be the first figure I came accross that I could use to start some computations) and based on Internet info which of course is not always precise. With numbers this big, I felt I could get away with a bit of imprecision. I also rounded up in many cases for easier math... it is just to see how close to a gooleplex we come anyway.

10 to the 18th power of atoms = 1 grain of salt (half sodium and half chlorine)

5000 grains of salt in 1 gram

453 grams in a lb

(22 to the 24th power) 22,000,000,000,000,000,000,000,000 atoms in a lb of salt

(12 to the 24th power) 12,000,000,000,000,000,000,000,000 lbs = earth

26 (49) atoms in the earth (times 300,000 for sun's mass)

78 (54) atoms in the sun (rounded up to account for entire solar system =>

10 (55) atoms in solar system (times 400 billion stars in galaxy => rounded up to 1 trillion to be conservative)

10 (64) atoms in the entire Milkyway galaxy

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Now at this point we have 35 more zeros to account for before reaching a googleplex of atoms in the universe... therefore we would need to see
100,000,000,000,000,000,000,000,000,000,000,000 galaxies which is far beyond our technology at this point. Now the Bible says that regarding the increase of God's government there shall be no end... so prophetically we can expect a truly infinite universe, but as for what we can see right now even with the Hubble deep field observations we come far FAR short of being able to utilize the term googleplex in any practical way. You could even start going the other way and subdividing the atom but even if you found 1,000,000,000 unique particles in a single atom that only lowers the necessary exponents from 35 to 26.

OK I've done more thinking than is absolutely healthy right after dinner. I think I am going to go practice on the new guitar I just borrowed from a friend of mine.

2 comments:

The Unabashed Blogger said...

Have you shown all this to your children? I bet they were not nearly as impressed as I am. I mean, AFTER DINNER? Wow. I usually veg. Way to use the brain.

The Irascible Neufonzola said...

See, smart (read: lazy) scientists came up with a nice symbol so we wouldn't have to deal with all these unfathomable large numbers:



Basically, some egghead was sitting down trying to write all the zeros to a googleplex or whatnot and then he realized that Mystery Science Theater 3000 was about to come on TV so he he said forget this and made up a symbol for infinity, defined as follows:

Infinity - n., The exact quantity at which humans no longer care to accurately measure or convey the quantity.

Gross misinformation aside, very cool analysis. It seems hard to fathom that there is not even that many atoms in the observable universe.