Happy Pi Day

[Candy_Kane54]

In celebration of PI day, I'd like to give you one of my favorite quotes from the TV series "Person of Interest" when Harold Finch is acting as a substitute teacher to get closer to an irrelevant number and is discussing what PI is:

Let me show you. Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it's all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world's infinite possibilities rest within this one simple circle. Now what you do with that information; what it's good for, well that would be up to you.

 

[lovecraft68]

I thought this was Private Investigators! Sleazy bastards don't deserve a day, but they do make great characters.

 

[EmilyMiller]

In celebration of PI day, I'd like to give you one of my favorite quotes from the TV series "Person of Interest" when Harold Finch is acting as a substitute teacher to get closer to an irrelevant number and is discussing what PI is:

Sadly a few things:

1. Every single non-zero Real Number possesses a decimal expansion that goes on forever
2. Every single Irrational Real Number possesses a decimal expansion that goes on forever without settling down to repeating a finite string of digits
3. Every Normal Real Number (actually Normal is overkill, there is a weaker requirement but it’s kinda complicated) will contain any given finite string of digits in its decimal expansion not just once but an infinite number of times
4. Most (in a technical sense*) Real Numbers are Normal, but it’s notoriously hard to prove that any given one is - this is one Normal Number: 0.1234568910111213141516…
5. While most mathematicians would be astonished if π was shown to not be Normal, no one has proved that it is, so the assertion made in POI is unproven

Happy ‘π approximation day’

—

* The Reals are uncountable, the Normals are uncountable, the Rationals are countable. Hence ‘most’ Real numbers are Normal, in kinda the same way that ‘most’ Real numbers are Irrational. Comparing infinite cardinalities is not straightforward, and it’s easy to be sloppy with language.

Wish Lit supported LaTeX

 

[TomTeacher19]

Sadly a few things:

1. Every single non-zero Real Number possesses a decimal expansion that goes on forever
2. Every single Irrational Real Number possesses a decimal expansion that goes on forever without settling down to repeating a finite string of digits
3. Every Normal Real Number (actually Normal is overkill, there is a weaker requirement but it’s kinda complicated) will contain any given finite string of digits in its decimal expansion not just once but an infinite number of times
4. Most (in a technical sense) Real Numbers are Normal, but it’s notoriously hard to prove that any given one is - this is one Normal Number: 0.1234568910111213141516…
5. While most mathematicians would be astonished if π was shown to not be Normal, no one has proved that it is, so the assertion made in POI is unproven

Happy ‘π approximation day’

That is one of the sexiest posts I've ever read on Lit.

Thank you

 

[EmilyMiller]

That is one of the sexiest posts I've ever read on Lit.

Thank you

I love math, sadly it didn’t reciprocate my feelings

 

[TomTeacher19]

I love math, sadly if didn’t reciprocate my feelings

Math is fun and amazing and sexy and terrific, but sometimes it is just a tease.

We should definitely hang out and I'll write all the digits of pi on your body.

 

[BeechLeaf]

* At this point Attenborough starts narrating, quietly. *

 

[EmilyMiller]

We should definitely hang out

and I'll write all the digits of pi on your body.

Rain

 

[EmilyMiller]

* At this point Attenborough starts narrating, quietly. *

Young or middle aged Attenborough can narrate me any time . I think I’d shatter his bones nowadays. Life on Earth was a major factor in me focusing on Biology at college / grad school. That and sucking at more complex (no pun intended) math .

 

[MrPixel]

Possibly repeats, but worthwhile repeats:

 

[MrPixel]

I love math, sadly if didn’t reciprocate my feelings

Oh, let me count the ways...

 

[Baztrachian]

Now I need a slice of 𝝅

 

[Actingup]

It's just like Americans to celebrate Pi day on 14th of March instead of the 3rd day of the 14th month like normal people.

 

[EmilyMiller]

It's just like Americans to celebrate Pi day on 14th of March instead of the 3rd day of the 14th month like normal people.

Nice use of ‘normal,’ and our date system is truly bizarre. Makes Imperial measures seem logical . I like the Japanese format, YYYY-MM-DD, which I use as the prefix for all my work documents and they then order properly.

 

[Candy_Kane54]

Sadly a few things:

1. Every single non-zero Real Number possesses a decimal expansion that goes on forever
2. Every single Irrational Real Number possesses a decimal expansion that goes on forever without settling down to repeating a finite string of digits
3. Every Normal Real Number (actually Normal is overkill, there is a weaker requirement but it’s kinda complicated) will contain any given finite string of digits in its decimal expansion not just once but an infinite number of times
4. Most (in a technical sense) Real Numbers are Normal, but it’s notoriously hard to prove that any given one is - this is one Normal Number: 0.1234568910111213141516…
5. While most mathematicians would be astonished if π was shown to not be Normal, no one has proved that it is, so the assertion made in POI is unproven

Happy ‘π approximation day’

—

Wish Lit supported LaTeX

Since π is irrational, and the universe is finite, the point he was trying to make is that the entire universe can be found somewhere in the digits of π. The circumference of the universe can be accurately measured to within the width of a hydrogen atom using only the first forty digits of π.

 

[Djmac1031]

I love math, sadly it didn’t reciprocate my feelings

Math and I have an understanding. And a restraining order.

 

[Actingup]

Nice use of ‘normal,’ and our date system is truly bizarre. Makes Imperial measures seem logical . I like the Japanese format, YYYY-MM-DD, which I use as the prefix for all my work documents and they then order properly.

I agree - it makes total sense for filing systems and it's just as logical as DD-MM-YYYY

 

[EmilyMiller]

Since π is irrational, and the universe is finite, the point he was trying to make is that the entire universe can be found somewhere in the digits of π.

That’s not a deduction we can robustly make based on what we know about π at present. What he claims is NOT a feature of merely Irrational numbers, we need additional properties.

That’s the point I was making. It is most likely true, but it’s not proven. And an uncountable infinity of other Real numbers have this property. This aspect of π - if it is ever proved - is wholly unremarkable.

However the assertion is true of: 0.123456789101112131415161718192021…

The circumference of the universe can be accurately measured to within the width of a hydrogen atom using only the first forty digits of π.

Agreed

 

[KittyOfSteele]

Wish Lit supported LaTeX

You might want to check out Fetish and BDSM for that type of support.

Happy π day, math nerds!

 

[EmilyMiller]

You might want to check out Fetish and BDSM for that type of support.

Happy π day, math nerds!

I know

But it’s pronounced ‘lay-teck’

 

[EmilyMiller]

Since π is irrational, and the universe is finite, the point he was trying to make is that the entire universe can be found somewhere in the digits of π. The circumference of the universe can be accurately measured to within the width of a hydrogen atom using only the first forty digits of π.

This number is irrational by observation:

0.1010010001000010000010000010…

But it never includes the string 11.

 

[EmilyMiller]

If anyone cares, the definition of a Real number being Normal is quasi-probabilistic.

Consider the digits the decimal representation of a Real number being spat out one at a time.

If the frequency of any single digit is 1/10

And the frequency of any pair of digits is 1/100

And the frequency of any triple of digits is 1/1000

And the frequency of any set of n digits is 10^-n

And the same holds in binary and hexadecimal and any other base

Then the number is Normal.

 

[EmilyMiller]

Just did a brief Google - whether or not π is Normal remains an open question as of today.

 

[crookedletter]

I thought we'd be talking about, like, the fruity stuff versus the savory ones.

 

[EmilyMiller]

I thought we'd be talking about, like, the fruity stuff versus the savory ones.

I think math education is a great way to celebrate π approximation day