Quick Arithmetic

A lot of the fascinating numbers in our world can be found by simple calculations.

Let's start with something simple. There are 60 seconds in one minute and 60 minutes in an hour. That means there are 3600 (60x60) seconds in one hour. There are 24 days in an hour, 365.25 (roughly) days in a year, 10 years in a decade, 10 decades in a century, 10 centuries in a millennium. Therefore:

3600*24*365.25 = 31557600 seconds in a year.
" "*10 = 315576000 seconds in a decade

3155760000 seconds in a century.
31,557,600,000 seconds in a millennium.

What can we conclude from this? A second is a lot longer than we give it credit for. The CDC says that the average life expectancy in the U.S. is 77.8 years. This is 2,455,181,280 seconds.

77.8*3600*24*365.25 = 2455181280

Now 2.5 billion may sound like a lot and it certainly is. But we are used to dealing with numbers much larger than this. One number we all have to deal with is 100 trillion, the rough estimate of the amount of bacteria in the human intestine. If that is too hard to conceive, there are more examples. The U.S. debt is at about $11 trillion (11,000,000,000,000). This means the U.S. owes 174.28 times more dollars than the amount of seconds that have taken since the birth of Christ supposedly happened up till Y2K was supposed to happen.

11*10^12 / (31557600000 * 2) = 174.28----

But that's not the only way to look at this. The measure of two millennia, despite being longer than most life expectancies of all species, is a very insignificant portion of the whole if the whole is the longest length of time that can ever be conceived: the age of the universe. The age of the universe is approximately 4.3*10^17 seconds (430 quadrillion seconds). This is almost 40,000 times more than the U.S. national debt.

4.3*10^17 / 11*10^12 = 39090.909----

And yet the story gets even better. The lower bound estimate for the amount of stars is 70 sextillion (7*10^22, or 7 followed by 22 zeroes). If the universe is 4.3*10^17 seconds old, then this tells us a truly remarkable statistic. The average rate of star formation in our universe up until now is 162790.70 stars per second.

7*10^22 stars / 4.3*10^17 seconds = 162790.697---- stars/second

Still, we are dealing with numbers with colloquial names. Thousand, hundrend thousand, billion, trillion, sextillion. Let's see how we can obtain numbers astronomically [ :-) ] larger than these with simple calculations. The vast majority of stars are at least 70% hydrogen. There are 6.022*10^23 (602 sextillion) atoms of hydrogen in 1 gram of hydrogen. There are 1000 grams in 1 kilogram. The mass of the sun just so happens to be fairly close to the average mass of a star. The mass of the sun is 1.99*10^30 (almost 2 nonillion) kilograms. So here we go.

(7*10^22 stars)*(1.99*10^30 kilograms per star)*(1000 grams per kilogram)*(6.022*10^23 hydrogen atoms per gram)*70% =

A ridiculous 5.87----*10^79 atoms of hydrogen in the universe, at least. More than a trillion times a trillion times a trillion times a trillion times a trillion times a trillion.

Now that's all well and good, but there are two problems. I said that these numbers can be found by simple calculations. This is true for all of the numbers I calculated, but not for all the numbers I used. Every calculation I did, aside from the first, had a number in it that no human would be capable of measuring by himself. The amount of bacteria in a human intestine, the age of the universe in seconds, Avogardro's number. These were all determined through very complex means and integral parts of the fascination in the outcome of each calculation.

The other problem is that despite the fact that these numbers may not be very simple to calculate, they might also not be that fascinating. I tried to fit in a little bit of everything in my calculations: society (U.S. debt), biology (life expectancy, bacteria), chemistry (hydrogen atom, avogadro's number), physics (age of the universe, mass of stars). But it is impossible to encompass every aspect. Mathematics has numbers that are either too difficult to conceive (Graham's number) or calculate (particle in a box) or both (Moser's number). And then we have the arts, strongly correlated with human emotion and behavior, in which calculations do not even exist. Sure, we can observe some number having to do with the amount of neuron signaling that goes on in the brain or calculate the weight of paint used in a masterpiece, but doing so would not be a good representation of what we're trying to represent. If there are numbers in these fields, it will be a long time until we find them. And when we do, perhaps our definition of fascinating will exclude the entirety of this article.

So I suppose the conclusion is that we are actually incapable of finding fascinating numbers through simple calculations, if at all. Then again, there could be some fascinating numbers that do not even need to be calculated. They could be staring right at us in our round, circular or ellipitical, faces.

Happy Pi Day

Circumference(circle) / Diamter (circle) = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651 and so on till eternity.




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