What is 21e8
You're so 21e8? That's so 21eLate
I’ve heard a lot of references to 21e8 lately. Here’s a nonfiction explainer I wished had existed before I started.
But first, imagine you are hanging out with an aspiring magician who correctly predicted four cards drawn from a shuffled deck.
That should only happen 1 time in 6.5 million. You might not conclude your friend has magic powers, but they might have a trick you’d like to learn about.
Suppose instead this trick was performed over video, but this time:
They only got three of the four cards right, which is almost correct!
They may have picked their guesses after seeing the results.
They tried hundreds of thousands of times before showing you their prediction.
In this scenario, nothing magical happened. There isn’t even a trick. Something normal happened, and your friend is passing it off as magic.
I submit that 21e8 is more like the latter scenario than the former.
In June 2018, a bitcoin block was mined which made some people very excited. The block in question has the following hash output:
00000000000000000021e800c1e8df51b22c1588e5a624bea17e9faa34b2dc4a
The hash starts with eighteen zeroes. Is this an unlikely result? Well, yes, but also no.
The Bitcoin algorithm defines the hash’s difficulty by specifying the number of leading zeroes. It is unlikely to randomly generate a hash with a large number of leading zeroes, but it wouldn’t be an official hash without this feature. Note that the blocks immediately before and immediately after also had 18 leading zeroes.
Some Bitcoin enthusiasts describe the next four characters as God deciding to be a tech-bro. 21e8 is scientific notation for 2.1 billion, equal to the number of bitcoins which will ever be created. If someone was performing the magic trick of encoding the number of bitcoins in a hash result, they did a great job!
Except, they were only almost correct. There won’t be 2.1 billion bitcoins, there will be 21 million aka 21e6. 21e8 is close to 21e6. It’s almost correct!
Some enthusiasts claim that 21e8 references E8, a mathematical — something — that I’ll let Wikipedia explain.
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8.
We all perfectly understood that sentence, so I see no need to dwell on it further. Isn’t it odd that the Bitcoin hash happened to reference an obscure mathematical system?
Since similar pages exist for E6, E7, and F4 - all of which are potential hash outcomes. Imagine an archer shooting an arrow into a forest and claiming victory if it hits any tree.
Apparently, a 2007 paper used the E8 algebraic group to develop “An Exceptionally Simple Theory of Everything.” I have no expertise in this subject matter, and I assess any particular “paper claiming to be a theory of everything” like any other “paper claiming to be a theory of everything.”
“But RandomSprint,” you object. “Isn’t it still unlikely we would generate a hash that references 100 times the number of bitcoins?”
“Sure,” I respond. “Let’s crunch the numbers.”
Bitcoin hashes are written in Hexadecimal, a base sixteen system with the digits “0” - “9” and “a” - “f”. The probability of generating any specific four-digit string is one over 65,000 (one over 61,000 when you exclude leading zeroes).
On June 18, 2018, if someone had predicted that one of tomorrow’s blocks would lead with 21e8, that would have been impressive. However, this almost correct coincidence was noted after the fact. And, given that this was block number 528,249, it’s not too surprising a 1/61,000 event occurred.
We would have expected this to occur about eight times before this hash was generated. In fact, look at the following eight blocks: 26284, 83434, 187323, 259695, 304822, 349158, 437039, 475118. I’m making spooky noises while you verify they all start with 21e8. You can either believe I’m an all-powerful miracle worker, or you can believe that I selected them because of how they happened to start. Consider Pascal’s Wager.
I should pause here to say a company named after the 21e8 meme is starting THINGS. I have no expertise in this subject matter, and I assess any tech startup like any other tech startup. I am not writing about that. There’s nothing wrong with naming your company after a meme, just like there’s nothing with naming your company after Greek mythology.
Instead, imagine us sitting on a beach where sand meets water as the Earth rotates around its axis, orbits around the sun, and screams through the unending void of space. In our chaotic universe, we cannot predict if, when, or where any one water molecule may crash into the shore. Still, we can strongly predict that many water molecules will behave in a predictable pattern.
Each wave that breaks upon the sand is an impossibly unlikely miracle — never to be replicated, beautiful to behold, yet truly, fundamentally unremarkable.
Take a sip from your pina colada and take comfort in the sand between your toes and the inevitability of large numbers eventually playing out.