“Gigantic multiplied by colossal multiplied by staggeringly huge…”

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I have been watching a brilliant show produced by the BBC called “Wonders of Life”, a 5-part series about the origins and functionality of life, narrated by Dr. Brian Cox, whose mouth my wife takes issue with.  As you can imagine, the program starts with a description, using the current scientific wisdom, of the beginning of life on Earth and, indeed, anywhere.  I have no intention (at this point, anyway), to descend into a discussion on the origin of life.  To quote Neal Stephenson’s Cryptonomicon, “let’s set the existence-of-God issue aside for a later volume, and just stipulate that in some way, self-replicating organisms came into existence on this planet and immediately began trying to get rid of each other, either by spamming their environments with rough copies of themselves, or by more direct means which hardly need be belabored.”  But, there is a point that is made in debates about the origin of life that I would like to address, as it is frequently on my mind.

A common argument against life “just happening” seems to be that the complexity that exists today simply could not have randomly occurred, presumably over the given timescale. It’s like digging up a naturally occurring pocket watch or monkeys with typewriters creating a Shakespeare sonnet.  As I see it, a core issue here is the human mind’s lack of ability to comprehend large amounts of anything: time, money, number of things, etc.  As a scientist, I have to deal with quantities that are completely beyond everyday experience all the time…so ridiculous, in fact, that we had to invent scientific notation to express the numbers because words just fail.  Archimedes, the Greek badass that brought us things like the screw and the lever, pondered huge numbers in his work title The Sand Reckoner, where he conjectured that the grains of sand on the beaches of Sicily were infinite.  The Hitchhikers Guide to the Galaxy has this to say about infinity: “Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real ‘wow, that’s big’, time. Infinity is just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we’re trying to get across here.”  Are they really infinite?  Well, no…but the number is so ridiculously huge that they are uncountable.  We have words and concepts, but we can’t really connect them to reality without really digging in and calculating something or generating a sequence of “things” to put it in perspective.

Take, for example, the chemical quantity known as the mole.  All matter is made up of atoms, but the number of atoms in “stuff” is incomprehensibly large.  The mole was created to scale that huge number down to something manageable.  One mole of “things” is equal to 6.02e23 items.  The “e23” just tells you how many times you multiply by 10.  So, 6.02e23 is equivalent to  602,000,000,000,000,000,000,000 things.  That’s a stupid amount of things.  How stupid?  Here’s an exercise to help put it in perspective.

I went into my wife’s office an snagged a random romance novel…“Slightly Sinful” by New York Times best-selling author Mary Balogh.  Not my thing, but anything for science!  Busting out my ruler, which I have since placed in a more accessible location since the last time I measured something, I find that the average area covered by a single letter on any given page is about 2 mm².  The page itself has dimensions 10.5 cm wide by 17.5 cm high, which gives an area of 183.75 cm².  If the page was completely packed with letters, each page would contain 6589 letters; more realistically, given indentation, spacing, margins, and empty space, 1500 letters per page is a reasonable estimate.  Now, the book has 355 pages, which means there are approximately 532,500 letters in this book.  So far so good…

This book is 2.5 cm thick.  Given that a mole is stupid huge, we need a large distance to work with…like the distance from the Earth to the Moon!  This distance, from surface to surface, is 376,292 km.  Thus, if you were to stack up copies of “Slightly Sinful” from the surface of the Earth to the surface of the Moon, you would have 15,100,000,000 books in the stack, that’s 15.1 billion books.  Side note: if you bought these books for the list price of $6.78, the national debt ($16.7 trillion) would buy you 163 of these Earth-Moon stacks…New York Times best-selling author indeed.

Each stack of books gives us 8.04e15 letters.  Now, create that stack 74, 875,622 times (!!!), and you will have one mole of letters.  If you were to count the books, not the letters, just the books, at a rate of 1 per second, it would take roughly 36 billions years, almost three times the age of the universe.  If you were to stack them up in a single stack, that stack would extend 28 trillion miles.  Voyager 1, of which there has been much hoopla as of late, wouldn’t even be halfway up stack by now.

Damn…

When you look on the Periodic Table, you see stuff like this:

Fe

In the top-right of the square is the atomic mass of iron, 55.847.  This is the number of grams of iron you need to collect to have one mole of iron atoms.  Now, this…

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…is a cool nail that I inherited from my dad’s garage a few months ago.  It has a mass of just over 40g.  So, there are as many atoms of iron in this nail as there are letters in 54 million stacks of “Slightly Sinful” that reach from here to the Moon.

Again I say, damn…

To carry on the ridiculousness, consider that the Earth’s core is about 0.5% the total mass of the Earth itself and is comprised almost entirely of iron.  The mass of the Earth is about 6e24 kg, therefore the core is a lump of iron with a mass of about 3e22 kg.  Divide that by the mass of my bitchin’ nail, an you get 7.5e23.  So, there is about 1 mole of nails in the Earth’s core.  Which means there is a mole of mole’s worth of iron atoms!!!

Continuing on, ask yourself where does all of the iron come from?  Supernovae!!  It is formed in the cores of superheavy stars and then blown out into the Universe, where it accretes due to gravity and eventually forms planets like ours.  There is a debate, but the average amount of iron ejected into space in a supernova is projected to be near 0.2 solar masses, that is 20% the mass of the Sun.  The mass of the Sun is a whopping 2e30 kg!!  That’s 4e29 kg of iron per supernova…13 million moles of nails!!

Current estimates place the number of stars in the observable Universe at about 1e24…there’s 10 moles of stars!!!  Only about 3% of stars will be massive enough to die in a supernova.  Consider that the Universe is estimated to be about 13.7 billions years old and stars that are massive enough to supernova have a lifespan, say, of around a billion years (a high estimate).  So, it is estimated that there have been at least 2 generations of stars in the universe before the current crop, given the amount of time it takes to accrete enough mass to make a star in the first place.  So, 3% of the current number of stars is about 3e21 stars.  If each generation had the same number of stars supernova, then 6e21 stars have blown up, each injecting 4e29 kg of iron into the Universe.  That is 2.4e51 kg of iron…that is almost 1 million moles of moles of nails!!!!!!

Raiders-of-the-lost-ark-melting-face

This exercise got really, really stupid a long time ago.  The point is that people have such difficulty understanding ridiculously large numbers that it is hard to trust yourself when you start working with them.  When you start writing down numbers that have 51 zeroes on the end, you are obviously well beyond common experience.  When science starts talking about things that involve such large quantities, it is really difficult for people who aren’t comfortable with them to understand.  It’s hard to imagine the amount of water in the ocean (1,386,000,000 cubic km), the distance to the nearest star (39,900,000,000,000 km), the number of neurons in the human brain (100,000,000,000 cells), or the amount of carbon dioxide humans put into the atmosphere each year (26,000,000,000 kg).  And yet, we have conversations about these types of things all the time.

Back to my original inspiration, when one talks about the origin of life as having randomly occurred because one cosmic ray hit one molecule in the ocean just right so that it formed the amino acid need to self-replicate, that seems completely impossible.  But, consider the fact that you had an entire ocean’s worth of chemicals “steeping” for a billion years being bombarded by cosmic rays in an era well before there was any kind of atmospheric shielding to protect the surface.  One mole of reactions could have easily have occurred…maybe, nigh probably, more.

My ultimate point here is not about the origin of life.  What I want to convey is the simple fact that our everyday notions of number an probability just don’t cut it when we talk about things on geologic timescales and in quantities that defy language.  Am I an expert on such existential things as how life began?  No.  But, I am comfortable with ridiculous quantities that one encounters when discusses it.

The question, then, is this: did “God” have to create life on Earth?  Maybe he just put the pot in the oven and let the soufflé rise on it’s own…

5 thoughts on ““Gigantic multiplied by colossal multiplied by staggeringly huge…””

  1. First, yes the guy from the show drives me bonkers with his freaking silicon injected looking Mick Jagger lips. Ew! They’re so bizarre… Like he let the vacuum suck on his face too long. Secondly, hey, that’s a great book! Why you stealing my ronchy romance books for your post? Any of yours would have sufficed. :). Third, awesome post baby! Gotta live Niel Stephenson.

    1. Hey now…I didn’t knock your book LOL. In fact, if you noticed, I linked to it’s Amazon page. Just think of all of the tens of dollars I’m going to make the author with this article! I’m glad you liked it!

  2. Great read. I have often pondered such large things and honestly my brain keeps trying to put a beginning and an end on infinity and space. I keep telling it there is not an end, but it keeps arguing. Stupid brain.
    I find it interesting that people have issues understanding large numbers and infinite concepts, but they have no issue thinking they will go to “heaven” and live forever.

    1. Thank you. Yeah, the infinite is an even further stretch for most people. Indeed, that’s probably the one thing that separates the men from the boys, as it were, when learning calculus. If you can’t get down with the concept of carrying something out infinitely many times, then calculus destroys you.

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