Wednesday, December 16, 2015

Forever. You Keep Using That Word

"Someday soon, we'll have techniques that will allow us to live forever."

"We need to set up safeguards so this sort of thing never happens again."

You see stuff like this all the time. Well make some change that will last forever, or we'll prevent some bad thing from happening forever. I'm a geologist. Don't use words like "forever" to me. They do not mean what you think they mean.

Even in historic times, the spans involved can be stunning. Thomas Jefferson and John Adams both died on July 4, 1826, the 50th anniversary of the signing of the Declaration of Independence. That event is closer in time to us than it is to the Pilgrims landing at Plymouth Rock. The Golden Age of Islam can roughly be dated between 632 AD, when Mohammed died, and 1258 when the Mongols sacked Baghdad. That's 626 years. If we date our scientific epoch from the time of Copernicus (died 1543), 626 years takes us to 2169 AD. Cleopatra (died 30 BC) is closer in time to us than to the building of the Pyramids. We are closer in time to the Battle of Hastings (1066 AD) or the Crusades than Jesus was. 

When we talk about geologic time, things get even more extreme. Compress a single year into a second and count backward. Your own life is barely a minute. Count backwards at the rate of one year for every second. Fifteen seconds takes you back to 2000 AD. If you're retiring soon, a minute takes you back to the time you were born and ten seconds more takes you back to World War 2. Three and a half minutes takes you back to the Declaration of Independence and roughly half an hour (33 minutes) takes you back to the time of Christ. It takes over an hour to get back to the building of the Pyramids and three hours to get back to the end of the Ice Age. 

A million years? That will take you 11-1/2 days, counting at one second equals a year. To the time of the dinosaurs will take you over two years of counting. Our numbering system is so efficient it conceals the true sizes of things from us. 10,000 years to the end of the Ice Ages and the last mammoths (1), and 65,000,000 years to the time of the dinosaurs, don't look terribly different in size. One number looks only a few times bigger than the other. The reality is the last dinosaurs are 6500 times older than the last mammoths. And the age of the dinosaurs wasn't just an instant - it lasted about 150 million years. Everyone's favorite dinosaur bad boy, T-Rex, lived toward the very end of the Cretaceous Period about 65 million years ago. Anyone who has seen the original Fantasia by Walt Disney has seen the famous duel between a T-Rex and a Stegosaurus, the herbivore with the bony plates on its back. Stegosaurus lived in the previous period, the Jurassic, around 150 million years ago. That means that not only could they not have fought as in the movie, but T-Rex is actually closer in time to us than to Stegosaurus. As Tim Urban put it on, a T-Rex had a better chance of seeing a Justin Bieber concert than a live Stegosaurus.

The first abundant fossils appear about 540 million years ago. That will take you over 17 years to count off at the rate of one year per second. A billion years - and there are many places with rocks that old, like the Adirondacks - will take you 31 years. Two billion years, the age of many of the rocks in northern Canada will take over 63 years to count off. That means if you start counting when a baby is born, you'll hit two billion about the time he retires. Most people will never live long enough to count off three billion years (the age of some rocks in southern Minnesota) - 95 years.

And nobody will live long enough to count off the 4.6 billion year age of the earth - almost 146 years. That means if you started counting when the Golden Spike was driven on the Transcontinental Railroad in 1869, you would just now be counting off the age of the earth.

On a geologic time scale, even rare events become commonplace. In a million years, there will be about 7000 magnitude 8 earthquakes on the San Andreas Fault, and the Mississippi river will change course maybe a couple of thousand times. No, our flood control structures will not last long enough to delay it significantly. Any given spot on the U.S. Atlantic coast will see thousands of hurricanes. No human structure made with steel will last that long and even the Pyramids will probably collapse, since they're steeper than the angle of repose.

Let's assume we eliminate all disease. That still leaves accidents, and some will destroy you no matter what miracles our medicine can perform. The death rate from unintentional injury in the U.S. is about 41 per 100,000, or roughly one chance in 2500 of dying in a year. Your chances of living 1000 years at that rate are about 2/3. You have about a 44 percent chance of making it 2000 years and about 1.6% of making it to 10,000 years. You probably won't make it to the next Ice Age. Your odds of making it to 20,000 years are 0.03%. A million years? A lousy million years, not even close to the time of the dinosaurs? Decimal point, followed by 176 zeroes, followed by a one, per cent (2).

And we aren't anywhere close to forever. We haven't even scratched the surface of how big numbers can get. The universe is about 13.6 billion years old, but the tiniest speck of dust you can see has more atoms in it than that. Atoms have relative weights, called atomic weight. Hydrogen is 1, carbon is 12, oxygen is 16. That many grams of each (1 hydrogen, 12 carbon, etc) contains 6.02 x 1023 atoms. That's 6 followed by 23 zeroes. Counting those atoms, one per second, will take you about 140,000 times the age of the Universe. 

You have about 30 trillion cells in your body and the DNA in each cell is about a meter long. Strands of DNA are only a dozen or so atoms wide, and very tightly crinkled. That means if you could take all the DNA out of your body, well, you would die. But it would total 30 trillion meters or 30 billion kilometers in length, enough to wrap around the orbit of Pluto. Which is so awesome it would be a real shame you wouldn't be there to contemplate it. You probably have around 2 x 1027 atoms in your body. The total number of atoms in the earth is around 1.3 x 1050 atoms. Scientific notation is even more compact and efficient than ordinary numbers and is even better at concealing the true sizes of things. The difference between the number of atoms in your body and the number in the earth isn't the difference between 27 and 50, it's about 1 followed by 23 zeros

The sun is 300,000 times as massive as the earth, but the earth is largely made of iron and silicon. The sun is made up mostly of light hydrogen and helium, and it takes a lot more of those atoms to equal the same mass. The sun has about 1057 atoms. The difference between 50 and 57 doesn't seem great but it translates to the sun having ten million times as many atoms. In the whole universe, the number of elementary particles - protons, neutrons and electrons, is estimated to be about 1080

According to some theories, the Universe is running down and will eventually expand to a cold inert place where everything is at the same low energy. This "heat death" is estimated to be about 10100 years in the future. That's about the largest number used in science for actually counting discrete objects. How long is that? Take the age of the universe, spend that amount of time contemplating every single individual subatomic particle in the universe. Then do it ten billion times10100 years isn't just a bit longer than the age of the universe, it's incomprehensibly longer. I can write the numbers and do the math. I can't actually picture it.

It's clear that when people say "live forever," they don't mean insane quantities like 10100 years, or even a million years. A million years would allow you to spend a thousand years as a doctor, as a politician, as a teacher, as a soldier, as a farmer... Then you could spend a thousand years living in each country on Earth and still have time left over. No, "forever" likely means "until I get tired of it." It means going out on your schedule and nobody else's.

And we've just stumbled onto a fascinating theological point. Whatever happens after we die, it cannot involve linear time as we experience it. What would you do with a million years' worth of memories? "Oh, but I believe in the Bible." Funny thing, check this out:

“What no eye has seen,
    what no ear has heard,
and what no human mind has conceived”—
    the things God has prepared for those who love him— (1 Cor. 2:9)

When it says "no human mind has conceived," do you suppose it actually means "no human mind has conceived," as in, nobody can possibly imagine it?

As long as I have the pulpit, a lot of religious believers seem to picture that they're five or six feet tall, and God is maybe eight or nine feet. But consider this: "As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts." (Isaiah 55:9). So the reality is, there's the floor, with bacteria and mold and stuff the dog tracked in, and there's us, a fraction of an inch above that, and there's God, beyond the roof, beyond the Solar System, beyond the galaxy, beyond the remotest quasar. To paraphrase Douglas Adams, "Infinity is big. You just won't believe how vastly, hugely, mind-bogglingly big it is."

Surely 10100 is the biggest number anyone would ever actually use, right? Not even close. There are numbers so big they're even hard to write. What's the biggest number you can write with three 9's? 999, right? What about 999 ? That equals 9.1 x 1017. But we can do way better. 999  = 2.5 x 1094. But what if we take nine to the ninth power (387,420,489) and raise the third nine to that? Exponents do screwy things to documents, especially if they're stacked, so we can use the alternate notation 99  = 9^9, and the biggest number we can write with three nines is 9^9^9 = 9^387,420,489 = millions of digits. The rule is you start with the outermost exponent and work down. 2^2^2^2 = 2^2^4 = 2^16 = 65,536.

Numbers get really huge when you start calculating the number of different ways things can happen. For example, the number of different sequences you can deal a deck of cards is 52 for the first card, times 51 for the next and so on down to one for the last card. That's 52x51x50x49....x1, and that sort of thing crops up often enough to have a name and a symbol. It's written 52! and called 52 factorial. (It suggests that people who claim to have seen a perfect bridge deal where everyone gets all cards of one suit are - putting it delicately - mistaken. At the very least they failed to shuffle and deal properly.) Going back to three nines, care to contemplate how big (9^9^9)! is? Let alone ((9^9^9)!)! or ((9!^9!^9!)!)! ?

How many possible chess games are there? Information scientist Claude Shannon estimated a possible paltry 10120, chicken feed compared to some of the numbers we've just discussed. Of course, you could ignore the rules about stalemate and simply repeat the same sequence of moves forever, but that's trivial. But to study the quantum mechanics of materials, you have to calculate the possible number of energy states of the material, which means some number for each atom times all the others. For example, how many atoms in a room are moving slower than 10% of the average velocity? There could be 10^30 atoms or molecules of air in a large room, so the number of possible energy states of those atoms is something like 10 raised to the power of the number of atoms. That is 10^10^30. In quantum mechanics, it is possible for a camel to pass through the eye of a needle; the odds are so mind-bogglingly tiny that "impossible" barely does it justice.

These are about the biggest numbers I know of in physics. In abstract math, you can obviously write arbitrarily large numbers like 9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.... But in "serious" math, where someone is actually trying to solve a real problem, they can still be stupendous. 

Tim Urban  has a great discussion of large numbers on the site "Wait But Why" ( Consider the first few levels of making big numbers:
9 = 1+1+1+1+1+1+1+1+1
10 x 9 = 10+10+10+10+10+10+10+10+10
10^9 = 10*10*10*10*10*10*10*10*10
10^^9 = 10^10^10^10^10^10^10^10^10
10^^^9 = 10(10^^9 terms)
Graham's Number, at one time the largest number ever used in a serious mathematical proof, defined a number g1 = 3^^^^3, then g2 = had g1 up arrows, then carried that process out to 64 levels

As Urban put it: "Imagine living a Graham’s number amount of years.  ... it’s a reminder that I don’t actually want to live forever—I do want to die at some point, because remaining conscious for eternity is even scarier."

So don't use the word "forever" around anyone who deals with large time spans or numbers. You have no conception what it means.


1. There were some holdout mammoths that survived on Wrangel Island off the coast of Siberia until 4000 years ago. They lived until the time the Pyramids were being built. Fascinating and poignant, but not really relevant here.
2. The way to calculate odds like these is to calculate the odds of something not happening. If you have 41 in 100,000 odds of dying in an accident each year, you have 99,959/100,000 or 0.99959 odds of surviving. Your chances of surviving 1000 years are 0.999591000  = 0.6636, and so on.