Pi is Meaningless

Ladies and Gentlemen. Introducing…a completely random series of numbers:

 3.11037 55242 10264 30215 14230 63050 56006 70163 21122 01116 02105 14763 07200 20273 72461 66116 33104 50512 02074 61615

Those are the first 100 digits of Pi in base 8.

“Base 8?” you screech. “Why base 8”.

Why not? We humans use base 10 because (scientists conjecture) we have ten fingers, and our ancestors used them to learn how to count. Having five digits at the end of each appendage is common in most animals we are familiar with.

But if the octopus had become the dominant species on Earth, and developed complex language, math and the internet (underwater), it is quite likely that it would have come up with a base 8 number system.

Therefore, octopuses would celebrate Pi Day by reciting its digits in base 8.

Or not.

Maybe they would think Pi is boring.

Like me.

No I’m not an octopus. And no, that’s not me. But it’s cute, don’t you think?

The point is:

I don’t understand why people pride themselves on being able to recite the digits of Pi (in any base). It is a waste of valuable gray matter that could be used for something useful.

According to Michael Hartl, “some people memorize dozens, hundreds, even thousands of digits of this mystical number. What kind of sad sack memorizes even 40 digits of π ?”

It has been found that the digits of Pi are indistinguishable from a random sequence of digits, no matter how high you count. If you select any sequence of digits in Pi (like, say, the first 100 digits starting at the billionth digit), you will find no particular bias or pattern. In fact, the likelihood of any digit (or sequence of digits) occurring is statistically flat: evenly-distributed. It’s as random as it gets (although there is no PROOF yet of the “normality” of Pi).

This is why I suggested in a previous blog post that the music in this video:

…is meaningless. This guy Blake (who is a fine musician) could have just as easily used the digits from a random number generator.

By the way – I now see that there was a legal battle regarding copyright infringement in a case of using Pi as the basis for a melody.

Two unfortunate first-world preoccupations rolled into one.

Instead of fetishizing the digits of Pi (or any irrational number), why not explore the teachable aspects of Pi such as this:

…or this:

 

 

 

…or this:

According to Wolfram,

What’s interesting is how chaos is formed – whether in an abstract number system or in a natural system. The digits of Pi should be understood as the result of a dynamical process that emerges when we try to find relationships between circularity and linearity. The verb is more meaningful than the noun.

-Jeffrey

Advertisement

Pi is Random. Stop Trying to Turn it into Music.

I have seen and heard several attempts at turning the digits of Pi into music.

The highly-flourished music in this YouTube video is well-crafted. But I agree with the way one comment sums it up…

“So basically we’ve learned that any random sequence of numbers will sound reasonably pleasant if interpreted as notes in a major scale…”.

Yes. It is oh so convenient that the digits 1 through 8 can be mapped to the ever-so agreeable, politically-correct notes of the diatonic scale.

Don’t confuse this talented musician’s performance with anything remotely meaningful about the digits of Pi. Because……

Pi is INDISTINGUISHABLE from a sequence of random numbers. Extensive statistical analyses of the first six billion digits have been done to try to find tendencies, frequencies, repetitions, ANYTHING that constitutes a feature or a pattern.

Nothing.

Perhaps there is something in this apparently-random sequence that will someday reveal the existence of an alien intelligence. Yea, right.

Here is Vi Hart’s reaction to some of this musical Pi insanity…

At least Jim Zamerski has the sense to consider that Pi can be expressed in other bases than 10, for making music. But again, regarding the use of Pi as the raw input into this musical treatment, how much musical content is there?

NONE.

Personally, I would love to hear the results of a search algorithm that finds segments of Pi that come close to mimicking a famous melody. I have no doubt that “Happy Birthday To You” … using the digit 0 to represent a rest, and the digits 1 through 8 to represent the notes G₃ through G₄ in the C-major scale … can be found somewhere in Pi.

Just for fun, I figured out what those digits would be. Here they are:

112010403000112010504000118060403020776040504

Sure, it might require wading through billions of digits using a special-purpose pattern-finding algorithm to get statistically close to this exact sequence. But at least the musician would have done some work. And it would be just as original.

What about “Pi Art”?

It’s beautiful.

But meaningless. The digits of Pi are statistically no different than a random sequence of digits. Why not use the golden mean, or e, or the square root of 2? The digits in these irrational numbers are just as meaningless as Pi.

I submit that the best way to get creative over Pi is to think about its real meaning: Pi is the ratio of a circle’s circumference to its diameter. This ratio shows up in some interesting, and sometimes unexpected, situations – like Buffon’s needle:

I will close with a simple, elegant expression of Pi. It may not be beautiful, but it says it all.