Earlier this week I mentioned that “this coming Saturday is a doubly special date (especially this year).” One of the things that makes it special is that it is pi day — 3/14 (at least for those who put the month before the day). What makes it extra-special this year is that it’s 3/14/15— a pi day that comes around only once per century. (Super-duper extra-special pi day, which happens only once in a given calendar, happened way back on 3/14/1529.)
I’ve written before about the magical pi, and I’m not going to get into it, as such, today. I’m more of a tau-ist, anyway; pi is only half as interesting. (Unfortunately, extra-special tau day isn’t until 6/28/31, and the super-duper extra-special day isn’t until 6/28/3185!)
What I do want to talk about is a fascinating property of pi.
If you’ve read Carl Sagan’s science fiction book, Contact, you may recall the part about a message hidden deep within the digits of pi.
When Ellie Arroway and the team of travelers meet the “Vegans” they learn that there are messages hidden in pi and e and other transcendental numbers.
The Vegans don’t tell them what the messages are, just that they exist.
At the very end of the novel, a computer program Ellie set to calculating digits of pi discovers the first, very simple, message.
Here is a quote from the end of that final chapter:
“Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.
“The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle — another circle, drawn kilometers downstream of the decimal point. There would be richer messages further in. It doesn’t matter what you look like, or what you’re made of, of where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It’s inside everything. You don’t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe.
“The circle had closed.
“She found what she had been searching for.”
It’s a striking, lovely, lyrical, mystical idea. That hidden deep inside fundamental, simple, universal objects, such as the ratio of a circle’s outside and its diameter, is a message.
A message that says, “This all has meaning.”
A message that could only be put there in the making of the universe.
It turns out that this is probably true.
The (perhaps disappointing) thing is that — outside of any mathematical mysticism about the real, let alone transcendental, numbers themselves (and there is plenty of fodder for such ruminations) — this is both expected and normal.
In fact, “normal” is exactly the right word.
If the digits of pi — which we know go on forever without repeating — have the mathematical property of being normal (and we think they do), then that raster pattern of a circle does exist somewhere within it.
But that’s just the beginning.
So does every GIF, JPEG, and PNG, ever created. So does every image file that could be created. So do the entire works of Shakespeare in every language on Earth. So does every book ever written or which could be written. So does any sequence of numbers you can name.
An infinite normal string contains every possible finite string somewhere within it. It may take longer than the age of the universe to find it, but it’s there.
Let me repeat this: If the infinite series of digits comprising pi are mathematically normal — and we think they are — then every possible finite sequence exists somewhere within it.
That means every image file, every audio file, every text file, every PDF file, every file of any type or encoding. They all exist somewhere in pi.
This may boggle the mind (but so do many other true things). It may be hard to believe that a highly structured sequence could exist in a “random” series of digits, but as with many things, human intuition tricks us here.
I’ve heard of an experiment that used college kids flipping a coin thousands of times and recording their results. The kids did this on their own time, and were not observed.
As you might expect, some cheated thinking they could just write down a series of “random” tails-heads results.
They were all caught.
The problem was that humans don’t credit a sequence such as “tails, tails, tails, tails, tails, tails, tails, tails” as random. It certainly doesn’t seem to fit in with our impression of randomness.
But if you flip a coin often enough — and these students were asked to do thousands of flips — you will get sequences of eight tails in a row.
That’s just a trivial example of apparent structure in a really quite short random sequence. With an infinite random sequence, much larger sequences of structure emerge.
Here’s the kicker: We think almost all real numbers (the irrational ones, not just the transcendental ones) have the property of being mathematically normal. And given that the real numbers are uncountably infinite, nearly all numbers are real.
Therefore, almost all numbers contain every secret ever told, every universal truth, every lie, every book, every text, every image, every sound, every video, every spreadsheet, every building plan, every finite thing that can be described with numbers.
And that is something to think about on pi day!
You may be wondering, if 3/14/15 is extra-special pi day, why did I say this coming Saturday was “doubly special” (and not just extra special). The answer to that involves a birthdate that — delightfully — happens to coincide with pi day.
The part about “(especially this year)” also applies to this, but you’re going to have to wait for tomorrow for the details!
Suffice to say that I’m about to take you on a special journey!
Until then, tomorrow and every day, get real and be irrational!
March 13th, 2015 at 7:55 am
Happy Pi Day tomorrow!
March 13th, 2015 at 11:16 am
Thank you, and likewise! (Although I still prefer tau day, which is twice as geeky, but when I can have twice the (pizza) pi.)
March 13th, 2015 at 11:18 am
I am not that much of a maths geek but Ok! why not, have a good tau!
March 13th, 2015 at 11:35 am
June 28! An excuse to order two pizzas!
March 13th, 2015 at 11:36 am
March 13th, 2015 at 7:56 am
Pi pie, anyone?
March 13th, 2015 at 11:16 am
In all honesty, I don’t like pie. Unless it’s pizza pie. (I just can’t abide cooked fruit.)
March 13th, 2015 at 11:17 am
Mince pies? Apple pie? You’re missing out!! All that pastry… nyum
March 13th, 2015 at 11:34 am
Well, honestly, I’m not really a fan of light and flaky pastries, either. I’m more a bread and rolls kinda guy — gluten with some gravitas! Cooked fruit of any kind just isn’t on my menu. Meat and various kinds of pot pies… those are a whole different story. Those I like!
March 13th, 2015 at 8:13 am
Just the idea of a circle brings to mind a completeness and a forever-ness. Interesting post Smitty! ❤
March 13th, 2015 at 11:28 am
That’s a good observation, Lady Di! The circumference is both infinite and complete and contained (unlike, say, an infinite line, which just goes off into the distance forever). And circles are everywhere we look: the moon and sun are themselves circles (or discs, rather, but same thing); drop a pebble in still water and you make lots of circles; cut a tree and see the circles (rings) hidden inside; tie a rock to a string and swing it in circles around your head.
Thus, the simple circle has long been an important and meaningful symbol for us. (Don’t forget the ultimate circle: Yin and Yang!) The idea that little old pi is this really interesting number intimately associated with circles is really kinda cool! 😀
March 13th, 2015 at 9:57 am
Excellent post! I just read about pi day in my Penzey’s spice catalogue (which featured pie recipes, of course) and I noticed early on that the math professor from my college had contributed.
Well Happy Doubly Special Pi day to you!
I may have to make a Pi cake to celebrate. (Not Pi Pie, because pie is not actually “easy as pie” unless you buy a crust, and that’s sacrilege.)
March 13th, 2015 at 11:31 am
I’m totally down with pi cake! I’m not a fan of pie (I just don’t like cooked fruit, especially when a bunch of sugar has been added.) Or better yet, pizza pie!
I remember how my mom always used to make pie crusts from scratch. Rolling them out really thin and then fitting them into the pie pan, cutting away the extra parts (which got folded into the top crust… or me, since I’ve always loved raw dough), and doing that crimping thing to make the edges scalloped. It’s almost a pity I never ate a single slice of the finished product.
March 13th, 2015 at 12:04 pm
You never ate your mom’s pie? That is a pity! Not everyone gets homemade pie. Oh well. People criticize me for not eating kimchi when I have access to the real stuff.
I’m not a fan of most American desserts because they’re often too sweet. French is the way to go for me. I like just a touch of sweet and lots of butter. 🙂
I’m not a huge pie fan myself, but I do like a good apple pie. I use the Julia Child’s pie crust recipe the Silver Palate sour cream apple pie filling whenever I make one. The apples are not supposed to be mushy, but slightly tart and slightly crisp. That’s hard to do. Finding the right apples can make a big difference. I wonder if you’d like something like that.
Honestly, I’ve only had a perfect apple pie once at a friend’s house. She did the Julia Child’s crust and I don’t know what she did with the filling. Her crust was far better than mine, even though we used the same recipe. Perhaps technique? I still remember eating that pie…I was totally stuffed and I didn’t want dessert, but I didn’t want to offend either. Then I tasted it and OMG! Everyone stopped talking. The only sounds were exclamations of gratitude and moans of pleasure.
Pizza pie is a great idea! I might have to do that if I can muster up the energy. I like to make grilled pizza. When you get those soaring temperatures, you can get an excellent crust.
I’m a crust person, in case you hadn’t noticed.
March 13th, 2015 at 12:32 pm
Ah! You once said something like, “don’t get me started on bread” and I wondered if that meant you hated it or loved it. I’m totally a bread man and always have been (I’ve written a couple of posts about my search for a decent bread). Olive Garden bread sticks, or those rolls at Red Lobster,… that’s my kinda heaven!
But I’ve never met a cooked fruit dish I’ve liked. The idea of cooking apples… is just so wrong. (I do love fresh apples, although they often give me a mild tummy ache for some reason.) And I love berries, and cooking them — and then adding sugar — is also a sin against fresh fruit.
So, no, I was a horrible son in that regard. Never ate my mom’s apple pie. Or apple cobbler. Her apple butter, on the other hand, was tasty on toast. (Toast is one of the most wonderful things you can do to bread! My standard breakfast is two slices of really good bread toasted! With I Can’t Believe It’s Not Butter. Raw honey optional.)
Regular pizza is often called “pie” — as in: “When the moon hits your eye, like a big pizza pie, that’s amore” But an actual pizza pie would be delish! (Isn’t that basically what a calzone is?)
Grilled pizza! Sounds good to me! Maybe throw on some swordfish while we’re at it!
March 13th, 2015 at 6:12 pm
Have you heard of Borges’s [Library of Babel](http://en.wikipedia.org/wiki/The_Library_of_Babel)? It’s another explanation of the whole “infinite, sufficiently random sequence contains every possible text” concept. One thing it emphasizes, which I think is fun to bring up in reference to pi as well, is that not only is every book/picture/movie in pi, but also every book/picture/movie *but slightly wrong*. Every truth is out there…but also every falsehood, and a whole lot of gibberish in between. Infinity is fun.
March 13th, 2015 at 6:28 pm
Yes, I have heard of it and read that Wiki article. (It’s possible I heard it from you a while back. I definitely heard about it from a blogger who mentioned it in a comment.) I thought of working it into the post, but decided it would take too long to explain.
I do like how wrong books are in the library, too. A Rudy Rucker book (Mind Tools) very long ago turned me on to the idea that any text can be considered a (huge) natural number, so Borges’ Library was like meeting an old friend in a very cool form. Of course, it goes the other way: all numbers can be considered as texts — most of them gibberish, but also single misprinted words and all sorts of subtle differences (every book backwards, for instance).
I wrote a post (a couple, actually) about his “L27” encoding system. I even made a Python program that generated “Hello, my name is” badges with names converted to L27 (or L80, which includes case and punctuation).
Totally agree! Infinity is fun and fascinating. I have a standing reservation at the Hilbert Hotel… There’s always room! 😀
March 14th, 2015 at 2:19 pm
Reblogged this on Happily Curious and commented:
It’s Pi Day
March 14th, 2015 at 2:37 pm
Spread the Wyrd! 😀
March 14th, 2015 at 2:51 pm
I just noticed this post was Freshly Pressed today, so it’ll be Open House around here for a while…
Welcome guests! Feel free to look around. (Just don’t go through the blue door!)
March 14th, 2015 at 4:54 pm
Congrats. for being Freshly Pressed…I noticed you are a regular reader of Di’s blog.
March 14th, 2015 at 5:57 pm
Thank you! Yeah, Lady Di and I go way back to when I started in 2011. She was one of the first bloggers I followed!
March 14th, 2015 at 8:53 pm
Groovy post mate, very enjoyable info
March 14th, 2015 at 10:23 pm
Thanks, I’m glad you liked it!
March 14th, 2015 at 9:10 pm
I love how meaningful this is: the idea that every possible sequence is contained within pi, within infinity. So powerful.
March 14th, 2015 at 10:24 pm
And not just pi, but an infinity of other numbers, too!
March 14th, 2015 at 10:21 pm
Reblogged this on EXPRESSION… the essence of life and commented:
March 14th, 2015 at 10:24 pm
Thanks. And the Wyrd spreads! 🙂
March 14th, 2015 at 11:23 pm
Reblogged this on Pendidikan: Benteng Terakhir Peradaban Manusia and commented:
Pi mistery started on Pyramid era which become more contained within the new era of mathematics……
March 14th, 2015 at 11:56 pm
That’s what happens when you start playing with circles!
March 15th, 2015 at 2:47 am
March 15th, 2015 at 3:12 am
March 15th, 2015 at 5:12 am
that’s to good for all pi day special
March 15th, 2015 at 9:49 am
March 15th, 2015 at 5:17 am
Reblogged this on inspirepro and commented:
March 15th, 2015 at 9:50 am
The Wyrd gets around! 🙂
March 15th, 2015 at 7:14 am
This made me smile this morning. A fun read.
March 15th, 2015 at 9:51 am
Thank you; I’m glad enjoyed it!
March 15th, 2015 at 8:39 am
Incredibly, it is interesting what you write 🙂 good luck!
March 15th, 2015 at 9:58 am
March 15th, 2015 at 9:48 am
Reblogged this on rababoojee and commented:
March 15th, 2015 at 9:48 am
March 15th, 2015 at 9:52 am
March 15th, 2015 at 10:58 am
Reblogged this on Engineer Marine Skipper.
March 15th, 2015 at 12:35 pm
Wow, yet another Wyrd-spreader! 😀
March 15th, 2015 at 11:58 am
Yesterday was the best! My favorite day, besides from christmas, the mix of math and food is perfect!
March 15th, 2015 at 12:36 pm
Everyone loves some kind of π! Did you get or give any presents?
March 15th, 2015 at 5:29 pm
Yes! In fact I posted about a competition I had! You can check it out if you want! 🙂
March 15th, 2015 at 10:11 pm
Ha! So I see! Looks like you guys all had a lot of fun. Learned about π and had some tasty treats, too!
March 15th, 2015 at 1:02 pm
3.14159265358979233832626233838327 is all I know from memory. Yes, I’m only in middle school.
March 15th, 2015 at 1:31 pm
Well, unless you need to precisely calculate the circumference of the galaxy, that’s plenty of digits for most use!
March 15th, 2015 at 11:09 pm
Reblogged this on AQUAHIKARI.
March 15th, 2015 at 11:34 pm
Welcome to the π party!
March 16th, 2015 at 6:30 am
Reblogged this on hindibol.
March 16th, 2015 at 10:54 am
That makes eight…
March 16th, 2015 at 7:12 am
Reblogged this on HADWEB.
March 16th, 2015 at 10:54 am
March 16th, 2015 at 9:22 am
Reblogged this on Myrealjourney and commented:
This is a reblogging post from Logos con carne. Thank you
March 16th, 2015 at 10:55 am
…and ten! (You’re welcome.) ((Also, thank you! 🙂 ))
March 16th, 2015 at 10:19 am
March 16th, 2015 at 10:57 am
Ah, great! That balances the guy above who said: “No” XD
March 16th, 2015 at 10:59 am
March 16th, 2015 at 11:19 am
Balance is all! Yin-Yang in everything.
March 16th, 2015 at 10:20 am
Shared your words here https://www.pinterest.com/AdamR0berts/blog-posts/ Merci
March 16th, 2015 at 10:58 am
My wyrds are really getting around! Does this mean I’ve been pinned? 😎
March 16th, 2015 at 10:59 am
March 16th, 2015 at 11:20 am
March 16th, 2015 at 11:25 am
March 16th, 2015 at 11:37 am
Aw… careful… you’ll turn my head!
March 16th, 2015 at 11:58 am
Great post! A really fun read
March 16th, 2015 at 12:05 pm
Thank you! I’m glad you enjoyed it.
March 16th, 2015 at 12:05 pm
This day becomes even more special at 9:26:53 a.m. or p.m., when the sequence 3/4/15 9:26:53 make the first 9 digits of Pi.
March 16th, 2015 at 12:06 pm