Pi Day thoughts

I just realized that Pi Day is almost over, and thought I should post a little something on the subject. However (and I hope π (pi) does not take offense), a good bit of what I will post is a bit anti-π. For instance…

  • I’ve finally given in to the idea that π is not the legitimate holder of the title of “circle constant,” and that the title should go to τ (or tau, the name suggested by the value’s proponents for 2π). For those (few) interested in the reasoning, check out tauday.com. I admit that what happens to everyone’s favorite equation (explained here) does not please me (and the attempt to sooth that reaction by author of the Tau Manifesto doesn’t succeed much), but the evidence is hard to ignore.
  • I wish that my favorite constant got more attention: e. However, I recognize that e‘s value, 2.718281828459045235360…, doesn’t lend itself to being made into a day easily, since 2/7 only carries two significant digits. Some, however, have taken to using the Day/Month format and celebrating e Day on January 27 (27/1). Perhaps, rather, there could be a build up to the e-minute at 6:28PM on February 7. I don’t know. e just doesn’t get the respect it deserves. Poor little guy. Though perhaps September 18 might be a good date to celebrate e.  Anyone know why?
  • As a day to muse on things mathematical, I’ll point out that it’s interesting to me that two of the posts on this blog that have the longest tail of search engine hits (meaning they continue to get hits regularly long after they were written) are the one I wrote on why a negative times a negative is a positive and the one about why 0.999999… equals 1. So hopefully I have contributed to someone’s understanding somewhere about something.
    🙂

Enjoy the remainder of Pi Day! (Unless you’re a protester holding out for Tau Day, of course, in which case we’ll see you in June.)

29 thoughts on “Pi Day thoughts

  1. Texasborn

    Continuing the musings on things mathematical: I have often wondered what the largest negative integer and the largest positive integer would be. I posed that wonderment on Facebook sometime back, but I only got nebulous suppositions in reply. I also asked if even God could not answer the questions as well, since we humans–if we had the spiritual ability to live forever–could always subtract one more integer and add one more integer to the negative and positive categories, respectively. Can there really be a numerical limit to integers–in either direction?

    Like you, I have also seen the funny video–alas, no longer on YouTube!–of the young lady’s revealing the largest(?) prime number, which won the discoverer a cool $100,000.00! But does that REALLY mean that when ones are added to that special number, then certain other smaller numbers can ALWAYS divide evenly into integers higher than said special number? Perhaps God could step in and say: “Sorry, Mr./Mrs./Ms. $100,000.00 winner, I can give you a higher prime number!”

    Or conversely, would this line of reasoning lead to the famous question of what the limits of God could possibly be: “Is there a rock that God could make so heavy, that even He would not be able to lift?”

  2. John Wheeler (Johanan Rakkav)

    Mr. Smith: I put up something for Pi Day on your Facebook page. It’s my favorite of the genre, so far. Enjoy. 😀

    MY favorite number is phi (1.618033989…) and one reason it is has to do with the fact that it is the most irrational of all irrational numbers (the demonstration is in a book I have on that number). In that sense it leaves pi, e, and all other irrational numbers and constants in the dust. And I think that when the dust settles in the Great Beyond, we will learn that it’s a LOT more fundamental than that overhyped pretender to the throne, “e”. 😛 pbbt 😉

    Next year, if I remember, I’ll celebrate an International Phi Day, January 6. Sure beats celebrating Epiphany. 😀

  3. John Wheeler (Johanan Rakkav)

    Though perhaps September 18 might be a good date to celebrate e. Anyone know why?

    Because (2+7 = 9) and then 18 follows? 😀

  4. Some of my math posts as well have proven to be very popular for reasons I don’t entirely understand–such as my connection between James’ reference to “no variation and shadow of turning” to the truths of calculus. At any rate, I hope you had a good Pi day. Sadly, I did not get to eat any pie yesterday myself.

  5. I vote for pi, because it sounds like “pie.” Pies are round. I like pie.

    The military dates things according to day-month-year (as in 14 MAR 2012). You could hold the “e” day on the 2nd of July, and start the festivities precisely at 1828 hrs (6:28 PM). That would give you at least six digits – 2.71828.

  6. Augh! I’ve been away from my computer a lot last night and today and I see a LOT of comments have built up! My apologies! Here’s some quick responses:

    Texasborn: Quick answers: No, there is no biggest positive or negative integer. More importantly, there is no biggest prime number, either; they do, indeed, go on forever. Euclid published a famous proof of this that goes as follows…
    Assume a finite amount of n primes, say, p1, p2, p3, …, pn. Then form the product of those primes, p1p2p3pn, and add 1. That number is not divisible by any of the n primes and must, therefore, be prime itself, contradicting the earlier assumption of a finite list of primes. Hence, there must be an infinite number of primes.

    John Wheeler: φ. Yeah, whatever. 🙂 I can’t believe that it is the “most irrational of irrational numbers” without knowing what is meant by comparative irrationality. Not that I am not a fan of φ, and I’ve appreciated its relationship to the Fibonacci Sequence and the facts that φ² = φ + 1 and 1/φ = φ – 1. But, really, compared to e or π? Meh.

    (Also, interesting, but no — September 18 still remains a mystery, it seems! The choice is not a mathematical one, necessarily.)

    nathanielbright: I’ll have to check out that post! Methinks certain mathematical matters inspire a curiosity — or, in some cases, a befuddlement — that drives people to the Internet in the hope of enlightenment.

    steve: My wife liked your reasoning for supporting pi. She thought it was pretty solid. 🙂

    Teresa: The video at that website did not work for me, but I was able to find it through other means. (Here it is on YouTube: http://youtu.be/YOQb_mtkEEE) I’ve heard other “Pi into Music” performances before, but that was the best one so far. Very nice!

  7. Texasborn

    Thank you, sir, for the very provable fact that the number posted on Vi Hart’s video was incorrect, just as I thought! Now, will the Mr./Mrs./Ms. $100,000.00 winner please stand up and return (what little) funds remain in his/her checking, savings, CDs, stock holdings, municipal bonds, gold, silver, etc., etc., etc. accounts to the award holder, because of having received monies under false pretenses? (Nahh, I didn’t think so.)

    Since you state that there is no largest negative or positive integer, do you mean that God knows what both of them are? (After all, He created mathematics, which I believe is the foundation of the creation of the universe. So, you are in “pretty good company”, mathematically speaking!) (:-D)

    Do you think God can create a stone so weighty that even He could not lift?

  8. Texasborn: I don’t imagine that Vi Hart would post an inaccurate number, so what was likely posted was the largest known prime. The larger the numbers get, the harder it is to determine whether they are prime or not. Currently, the largest known prime number is 243,112,609 – 1. But we know with certainty that there are primes larger than that, we just don’t know any specific one. (It would not be unlike knowing that there are people in Sweden but not knowing any of their names.) You might try viewing Ms. Hart’s video again; it likely makes the same distinction I am here.

    As for God knowing the largest integer, no He does not for there is no such thing in existence (nor can there be). Just like God does not know the average height of a leprechaun, the average heartrate of a unicorn, or the largest flibbertyhickey in a set of smacketybonks.

    For similar reasons, God cannot make a rock so big He cannot lift it because no such rock can exist. It isn’t a limitation on God, it is a limitation on possible rocks. Similarly, God cannot create a married bachelor, since, by definition, bachelors are unmarried. (I discuss this in more detail in my post “Can God make a rock so big He can’t lift it?” if you are interested.)

  9. John Wheeler (Johanan Rakkav)

    Mr. Smith: Since I can’t spell out the reasons here mathematically, and if I can photocopy the pages without breaking the book’s spine, I’ll send you the reasoning and you can make up your mind on the claim for yourself (and hopefully, deal with it here).

    Go eat your pi. With sprinkles of natural (organic?) e on top, if that’s to your taste. 😉

  10. Texasborn

    Thank you, Mr. Smith, for refreshing my memory of what Ms. Hart said about the prime number. I reviewed the video and she DID say “highest KNOWN prime number.”

    As you might have suspected, I was playing the Devil’s Advocate concerning the question about God not being able to lift a rock He created. Some who visit your blog site, not having yet viewed your referenced blog page about the subject, might be inclined to speculate that God could possess that inablity. (Especially the naysayers who occasionally visit your blog site from time to time, contesting your statements.) Wow! Thirty-four comments on that blog page! Is that a record for the most comments on any of your blog posts? (Or do you not keep such a trivial statistic?)

    Those who speculate about God’s limitations remind me of the Greek philosophers who would daily discuss erudite subjects such as speculating whether or not they were living in reality, or was their current moment only just a dream. (Acts 17:18-21 comes to my mind here.) I find it interesting that the etymological derivation of the word “erudite” comes from the Latin “eriditus”, which descended in meaning in the15th century to “rude, ignorant.” How appropriate would it be applied to the Grecian philosophers! They were truly ignorant (in their human “knowledge”) of the truth of really important matters, especially of a spritual nature!

  11. Texasborn

    Several years ago, I was reading a computer nerdy/geeky web page thread. The repliers were posting things at the bottom of their posts from time to time by completing the statement of “You know you are a geek if/when…” One person completed it with “…if you have memorized pi to the 27th decimal.” (I copied about 50 of the funnily completed statements! Yes, folks, there is such a word as “funnily.”)

  12. Teresa

    One of the girls at my son’s school, in honor of pi day, recited the number to its 500th decimal place…..

  13. John Wheeler (Johanan Rakkav)

    Mr. Smith and TexasBorn: You can get shirts from ThinkGeek and probably elsewhere with pi and phi printed in the form of the symbols themselves, with the symbols comprised of the numbers to some huge number of places. Way over 500 in both cases, I believe. I used to own both, but they shrunk and, quite likely, I grew. 😛

    Not even I am crazy enough to memorize phi beyond 1.618033989… If I want precision, I just say (1 + the square root of 5)/2. On my iPod Touch I get a maximum set of significant digits thus: 1.618033988749895.

  14. Texasborn

    Teresa, did she win the fruit “pie” of her choice for accomplishing that magnificent feat?

    I read about a year ago that someone had calculated the value of pi to something of over a million decimals! (Not sure of the exact number of decimals, due to loss of memory as time passes.) But I think he used a computer instead of manual computation; he might not have been able to live long enough to do it manually.

  15. John Wheeler (Johanan Rakkav)

    Mr. Smith: Stand by, I found the reference I was looking for. If you already have the book The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number by Mario Livio (take that, enthusiasts of any other number whatever! 😛 – save 7, God seems to like that one a lot 😀 ), you can find what I refer to, on pp. 82-85 and there is more related to that matter in the chapter that deals with fractals.

    PDF, I hope, created and sent soon, just in case. 🙂

  16. Texasborn: Pi has been calculated to about 10 trillion digits (further, I think). If she did one million digits, then I can virtually guarantee you a computer was used. 🙂

    John Wheeler: I have a Livio book or two, but not that one. I saw the pages on Google books, though, and all I can say is that there is a reason he uses “scare quotes” around “most irrational” as slow convergence is hardly a decent reason for the description. Given the fundamental simplicity of its continued fraction expression, I’d be more tempted to say that it is the “least irrational.” It’s not even transcendental! 🙂 But, perhaps irrationality (on the part of numbers, at least) is in the eye of the beholder.

  17. John Wheeler (Johanan Rakkav)

    From Wikipedia, article “Pi”: ” Reports on the latest, most-precise calculation of π are common news items;[5][6][7] the record as of October 2011 stands at 10 trillion decimal digits.[8]”

    Now that’s a lot of “slices of pi”. 😉

    And within moments, Mr. Smith, what I referred to above will be in your hot little electronic hands. Note the last two pages especially. Not news to you perhaps, but at least I can clarify what I’m talking about.

  18. Teresa

    No pie prize for Sarah. Just an amazing little girl to be able to memorize like that. My son said she slowed down and hesitated once or twice once she reached the 400th digit, but then finished up.

  19. John Wheeler (Johanan Rakkav)

    Mr. Smith: Thanks for your e-mail and your reply above, which I didn’t see. Looking up “transcendental number” on good old Wikipedia alone practically blew a fuse in my poor ENFP head. When I get into that rarefied sort of mathematical air, I am definitely out of my depth (how’s that for a mixed metaphor?).

    You certainly have a point in response. Phi isn’t transcendental and really I prefer the description in the poem included in the text: the continued fraction that can express phi is the simplest of its kind. That sort of elegance appeals to me. It may take another kind of mental wiring to appreciate whatever appeal e might have. Frankly, I still can’t grasp that appeal, although maybe it’s because I don’t understand the concept of that particular constant in the first place. 🙂

  20. Texasborn

    Mr. Smith, here is a cartoon related to pi: The cartoon box shows a long sign put just inside the storefront window of a bakery that displayed “Now on sale for only $5.00: 8″ Cherry 3.141592653589793238462643383!!”

    Now if you memorize that pi figure containing 27 figures past the decimal point, then you will be a true geek! (:-D) See my comment posted above at 12:42 AM on today’s date.)

  21. John Wheeler (Johanan Rakkav)

    You’re welcome. I find the reasoning about “tau” specious. Sure, 2pi is all over the place. Sure, using the quantity tau makes some things a lot easier to see and work with (I like especially what you can do in marking positions on a circle with it). Tau is still… well, you know the mathematical term for such a combination, but it’s still an integer multiplied by an irrational number. To me that qualifies pi and not tau as a fundamental constant.

    At best this is yet another example of two out of the six blind men and the elephant (“For each was partly in the right / And all of them were wrong!”). At worst, we have one man who sees the elephant (the pi proponents, who can then be introduced to the equally fascinating qualities of 2pi or tau) and the blind man who thinks his perspective and only his perspective is “right” and any other is “wrong”. 😛

  22. Too many Preparation Day things yet to do to comment much, but I will say jst a bit…

    Actually, you can’t say that tau is an integer multiplied by an irrational number as a defect, as every irrational number can be so construed, even pi. If the “natural” circle constant is actually tau, then that would make pi half of an irrational number (or one-half times an irrational number). [Any rational number times an irrational number is an irrational number, itself.] Pi only has precedence because it represents the ration of measurements man first noticed: the circumference and the diameter. That the circumference and the radius were not first put into ratio is an accident of history, not matter of mathematical priority.

  23. I’d sprinkle the pi(e) with infinite sequences. That way you’d never run out. Unless I were standing in the room, of course.

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