Does Pi Contain the Universe?

I just ran across a very poetic meme about the number pi .

Pi is an infinite, non-repeating decimal — meaning that every possible number combination exists somewhere in pi. Converted into ASCII text [computer representation], somewhere in that infinite string of digits is the name of every person you will ever love; the date, time and manner of your death; and the answers to all the great questions of the universe. Converted into a bitmap [computer image], somewhere in that infinite string of digits is a pixel-perfect representation of the first thing you saw on this earth; the last thing you will see before your life leaves you; and all the moments, momentous and mundane, that will occur between these two points.

All the information that has ever existed or will ever exist, the DNA of every being in the universe.

EVERYTHING: all contained in the ratio of a circumference and a diameter.

Googling around for more about this, I saw someone point out that if the universe is finite, then pi must somewhere contain a representation of the entire universe.

I find this beautiful and very appealing. Judging by all the “Wow!” comments on the Internet, a lot of other people are equally fascinated.

The only problem is, it ain’t necessarily so. The non-sequitur is in the very first sentence: “Pi is an infinite, non-repeating decimal — meaning that every possible number combination exists somewhere in pi.” I studied a lot of math in college, and I admit that the error slipped by me. Before I knew it, I was carried away by the poetry and joined in the chorus of “Wow!”

The error (obvious now!) is that just because a number never repeats itself into all infinity, it does not follow that every possible number combination occurs. For example, maybe there are no sevens after the trillionth digit, but the other nine digits continue without repeating. If you’re looking for a sequence that contains a seven, and you don’t find it in the first trillion digits, you will never find it.

Sadly, the frisson I felt while reading transcendent thoughts about everyone’s favorite transcendental number was … unwarranted. Even a methodological naturalist like me must be careful to practice shaphat.

After further Googling, I learned that it could be true that pi contains all finite sequences. In fact, mathematicians suspect that it is true, even though it has not been proven one way or the other.

Now … how tempted am I to believe without proof, just because it’s beautiful?

I’ll leave that question with you as an exercise in shaphat. Can you refrain from judging what’s in my head when you have no proof? 🙂

17 responses to “Does Pi Contain the Universe?

  1. A fun fact; the value of π is mentioned in 1 Kings 7:23. This if often overlooked for two reasons: 1) the Bible is viewed primarily as a religious book 2) it can’t been seen in the translation. Yes, the translation is correct; it’s the Hebrew letters which hold the value that go unnoticed. Hebrew uses letters (more properly pictures) also as numbers. The Hebrew word for ‘and a line’ there in the King James is ‘v’quvah’ (וקוה). The first vav (ו) denoting the conjunction ‘and’ is not part of the word which leaves us with ‘quvah’ (קוה). The ‘hey’ (ה) is out of place because the Hebrew word for ‘a line’ is correctly spelled ‘quv’ (קו). (Hope I’m not losing you here.)

    So why the difference? Let’s add up the values. Quf’s (ק) value is 100, vav’s (ו) value is 6, and hey’s (ה) value is 5. Adding them together ‘quvah’ (קוה) equals 111 and ‘quv’ (קו) equals 106. If we divide the difference 111/106 we get 1.0471698… If we multiply that by 30 which is the circumference and divide that by 10 which is the diameter we get 3.141509… (30/10 = 3; 3 x (111/106)) which varies from actual π by only 0.00026% (0.0000026). This was recorded around approximately 900 BCE.

    • That is a fun fact, but I’m skeptical. If they knew the value of pi to such precision, why does the passage say the circumference is 30, and not 31.41509? Or at least 31, if they didn’t have decimals.

      But maybe you’re saying that God inspired the writer with a hidden value of pi that even the writer did not know. Possible, I suppose.

      I imagine you’re familiar with Bible Codes, but if not, check out this site: . I’m sure you’d enjoy it.

      • Yes, I am although I haven’t looked into it much. I’ll look at the site a little, thanks.

        As far as I’ve been able to find, ancient Hebrew didn’t have a decimal place so such a concept would have to be expressed another way. Often times this is done in a Hebrew word via letters. He could have attached any letter to ‘quv’ (קו) but the letter he did attach was the ‘hey’ (ה). When this is done, something is being communicated beyond the definition of the word. This is done elsewhere in the Bible as well but the purpose isn’t to hide anything but to reveal something. Hebrew is mathematically based, the extent of which I don’t yet understand; I’m still working on learning and understanding the language.

        Kings is a historical book. Judaism refers to it simply as ‘writings’ and not ‘prophetic’ or ‘instructional’. While it is possible that the writer could have been inspired to record a value of π it is more likely he recorded it the way he did on purpose. I’m not saying either way because honestly nobody knows; I’m only noting it is there. Whether it was an intentional or not is besides the point. How ancient Israel performed math, accomplished architecture, and such details are mostly lost. What we do have is a record of the things that were build, their measurements, their materials, their color, etc.

    • It occurred to me that pi could be the “Book of Life” mentioned in the Bible Since it is theorized to contain a record of every human’s life.

  2. If you studied a loth of maths at the college, then you surely studied about chances and random events. If you say that “there is not a Seven after the trillionth digit, for 1 million digits”, well, there is an infinitesimal chance, but it might happen. Same happens if you flip a coin and try to get only heads for a million times. Infinitesimal chance, but it might happen.
    However, if you states “No seven, EVER”, that chance is 0:

    Chance of not getting a seven in one try: 9/10
    Chance of not getting a seven in two tries: (9/10) ^ 2
    Chance of not getting a seven in infinite tries: (9/10) ^ infinite = 0.

    Same in the case of the coin,

    I know that the concept of “infinite” is difficult to catch, but the consequence of that can not be negated: every possible combination of digits in somewhere in Pi.
    So sorry, but everything that existed, exists or will exist, your ADN, the mine, T-Rex’s one, creatures that do not exist yet one, aliens one…
    ALL is contained in the ratio of a circumference, ANY circumference, huge as a star or small as coin, and its diameter.

    Pi could be considered God’s Code Repository.

  3. I believe the point is just because pi is an infinite non-repeating decimal does not automatically mean every digit has to be repeated infinitely. For example maybe it settles into every possible combination of only 9 digits infinitely after the first 100 googol digits. If that is possible – and I don’t see why it couldn’t be – then the appealing notion that all information is contained in pi is potentially erroneous. Or in other words there is an erroneous assumption that infinitely non-repeating must require the inclusion of all integers infinitely. Why would that have to be, isn’t it just as likely some integers would eventually be excluded from the party?

  4. Yes, because pi is an infinite non-repeating decimal *does* automatically mean every digit has to be repeated infinitely.

    As I told before, if you draw number at random for a finite place, lets say, 100 googol digits, and try to not draw a 7, for example, chance is infinitesimal, but it might happens.

    But it you draw numbers at random for an infinite place, the chance of not getting a 7 is 0. Sorry but it can not happen. I understand that the concept of “infinite” is hard to catch, but in my previous post you have the maths.

    And no, you can not flip a coin infinite times and pretend draw heads all the times. It can happen for a while, but not forever. Chance drops to 0.

    • Liouville’s number is an infinite non-repeating decimal yet manages to not have any 7s or any number besides 0 and 1.

  5. I would be very careful to rely on base-10 to draw conclusions about patterns in pi. Consider that in base-4, the value is represented as a string of digits from 0-3. In binary, only two digits are available to represent the value. In fact, there is nothing about pi that even requires it to be a decimal, since technically pi is a ratio. And, furthermore, the Universe knows nothing about numbers.

    Perhaps in our quest to uncover the mystery of pi, we are overlooking its true beauty: the circle, seemingly the most basic and commonplace geometric figure in the Universe, is inherently irrational and can never be represented in simple mathematical terms. If pi truly holds the key to everything, then perhaps that merely establishes that we can never know “everything”.

    I think that pi is better likened to a cosmic riddle to play on the minds of those who seek infinite knowledge to prove them as fools. Since nobody calculate the value of pi, that establishes that nobody can know everything about the Universe — except, of course, the Creator (whomever or whatever you believe that to be).

  6. So even if a certain number like 9 eventually stopped occurring and then 8,7,6,5,4,3,2… You know in the end AT LEAST two digits must remain. Otherwise if it ended in just 0000000 or 333333 it would be rational which it is not.

    There seems to not be any known Natural normal numbers that weren’t simply constructed to be normal (although non normal numbers have provably 0 lebesgue measure) . The poetic exception might be Chaitins constant which is in some sense very natural, DOES contain all information, is proven normal, but is unknowable!!! ( uncomputable see incompleteness theorem and undecidability)

  7. I believe physicists and mathematicians using technology could find proof of what some called the theory of everything and find the eleven dimensions, as well as the strings that some theorize exist in everything.

  8. Pingback: An Ode to Pi

  9. I don’t think pi is infinite….it can be calculated to the plank length but it’s value after that is uncertain…

  10. nothing is absolutely true
    everything is relatively true
    all things are permitted
    anything is possible.

  11. daivd scott
    If you said “nothing is absolutely true” you are saying that very statement of yours may not be true. It opens up the possibility of “Absolute”.
    If you said “everything is relatively true”, you are saying that very statement of yours is just relatively true, it opens up the possibility of “absolute true”.
    If you said “all things are permitted”, you are saying that very statement of yours is permitted, you are permitted to be “no permitted”.
    If you said “anything is possible.”, you are saying that it’s possible to be “impossible”.

    See the pattern? 😛

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