Pi is Overrated



This morning, the wildly popular Facebook blog, I Fucking Love Science, posted the above image.  The blog, probably one of the most popular on Facebook, is getting a lot of attention recently due to the (somehow shocking?) revelation that it is run by a young woman.  It’s a wonderful blog that uses little-known scientific facts to blow people’s minds on a daily basis.  And though usually I enjoy their posts, I woke up to this one, and felt a little disappointed.  The image explains the nature of the irrational number Pi, and goes on to describe its magical wonder at having an infinite, non-repeating series of integers.  Though most of the information she gives is theoretically true, it really has more to do with the nature of infinity than the magic of the number pi, which really isn’t all that special.

To see why, let’s think about what pi actually is.  Pi is simply a number.  It’s the ratio of any circle’s circumference to its diameter.  And while it is somewhat fascinating that every circle ever has this same ratio, it is more a result of the definition of a circle, than a miraculous coincidence.  As discussed in my post, The Limits of Languagescience and mathematics are simply the languages we use to understand the universe.  If we forget to think about them that way, then when these coincidences and patterns crop up, we assume they are miracles of the universe and attribute special meaning to them, when they are simply anomalies in our language system.  Take pi for example.  There is a constant number that exists that defines the ratio of any circle’s circumference to its diameter, but because that number doesn’t fit nicely into our number system, we have to make up a symbol for it.  If we try to define that number using our numerical language, it yields the irrational number that the Facebook blog considers so magical, when it is really just a problem of translation. And, yes, it is true that in an infinite, non-repeating, random series of integers, theoretically every combination of integers will exist, but this is more a result of the series being infinite, than anything that has to do with pi specifically.

Another reason that pi is not special (sorry bud) is that there are literally an infinite amount of irrational numbers.  In fact, as Georg Cantor proved, and as can easily be seen, there are actually more irrational numbers than rational ones.  Once again, this goes back to how we define our numbers.  Numbers exist on a scale, much like wavelengths of light.  This scale can be, for lack of a better term, ‘zoomed in’ on to the nth degree (meaning infinitely).  So between any two integers, 3 and 4 for example, there are an infinite amount of numbers that we cannot fully represent using the number system that we’ve created, and each one of them translates into an infinite, non-repeating decimal that has the same characteristics of pi.

So yes, infinity as a concept is really something special, but it is simply that: a concept.  Though we can represent it and theorize about it and try to define its characteristics, it merely exists in our own minds.

11 thoughts on “Pi is Overrated

  1. I’m not a math whiz, but I sort of agree with you. Explaining everything with Pi smacks of forcing a miracle. I love your statement there are “more irrational numbers than rational ones.” That makes sense at a profound level. There are times when all numbers seem irrational to me. But that usually happens early in the morning before sufficient intake of caffeine.

  2. I agree that there is nothing miraculous about the number, and that facebook is just expressionistic.

    But, of course there are going to be more irrational numbers than rational numbers, right? They are simply everything else … like the dark matter of the universe.

    I’m not sure — Are you trying to say that there are limits to numbers like there are with the language of words?

    If we all spoke to each other in numbers, there would never be a single misunderstanding.

    • Finally! A real discussion on this blog! I feel like a real blogger! *knock on wood*

      But yes, I think that our numerical language is as arbitrary as our written language. Though it yields vastly more knowledge and understanding of the universe, it is still limited by our own definition of it. Quantities themselves are a concept we invented in order to communicate with each other. Three bushels of wheat for five goats, and so on. Numbers don’t represent a physical object in the universe, simply a way to define a collection of them.

      As for the hypothetical… I’ll have to think about that. If we were to only speak in numbers, which would be vastly counter-intuitive for us, the changes to our understanding would be so vast it’s sort of hard to imagine…. but a fun thought experiment! Perhaps the topic of one of your conversations with your immortal nobody….

      • hmmmm… maybe not our consciousness, but the rest of our brain. Our consciousness might not even exist in the material world… If we could somehow transfer our consciousness into a computer, though, we’d be cookin! Then we’d be able to store and access information flawlessly. The only question then would be, would we still process that information subjectively? hmmm…..

  3. You raise an interesting question. Could we redefine the number scale in such a way that π would not the mathematical equivalent of a non-repeating decimal. Like TR I too am not a math whiz, but I have had plenty of coffee and I don’t think so.

    The reason is that π is just a name for a particular ratio or proportion, but I do agree with you that there is nothing magical about any of these naturally existing ratios. The stability of recognizable patterns does, however, permit engineering or applied physics to develop. There may be some ‘magic’ in that. Welcome to blogging.

    • If we did, I don’t think the new number system would be anywhere near as useful as our current one is, I was just trying to demonstrate why Pi becomes a repeating decimal.

      Mathematics obviously does help unlock the mysteries of the universe, but I think mathematical mysticism is just as misguided as any other mysticism. Numerology can be pretty interesting though, so I don’t want to discourage it, just want to point out that sometimes the reasons for these ‘coincidences’ are inherent to the mathematical process, not some mysterious master plan of the universe.

  4. Your omnist views greatly appeal to me. And even more so your interest in mathematics. That being said, perhaps we have some coincidences happening worthy of some correspondence or more, sir.

    To wit, this is feedback I recently received from someone on a Philosophy of Math forum about a Beth El mathematics I am developing in support of the work of a Ph.D. candidate in Israel, whose advisor is going to give a posterboard presentation about our efforts next week at the Science of Consciousness event in Tuscan, Arizona (http://memo.ahsc.arizona.edu/index.cfm/memos/view/24161/0d5fc7fc2b2c06e4) Chalmers will be there!!! -)…

    “So you’re exploring a mathematical space and a psychological one. It’s a sort of maths version of being presented with the duck-rabbit picture. There will be those who can only see the duck and who get upset when told by you – who can see both – that there’s an alternative. Yes?”

    I would love to send you some diagrams and get your thoughts about the unconventional, but logical work we are doing to extend the attitude of omnism to the efforts of mathematicians, e.g., seeing what the possible consequences might be of 0 being distinct from 1/inf?

    Warmest regards and greatly looking forward to hearing back from you!


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