Again, I am surprised by my new found ignorance of pi... .But, what is time anyways, I didn't know then, but know it now- making the subject regardless. So, early this morning, I was 'off to the races' to explore this new term, this new bit of information about an odd, interesting and as I perceived it unnatural number.
Unnatural, you might ask? Well, it's only strange that a number might not end because.. a number is a measurement of something. Quite obviously, a number cannot be a representation, if it is incomplete. This number is so very, very long that in decimal form- it's been measured to millions of digits of decimal numbers after the number 3. A common approximation is 3.14159...but, it never ends (at least to the extent it is currently understood.)
Let me explain. pi is the ratio of the circles radius to the circumference. It doesn't matter the size of the circle, it is always the same. O.k.,,, makes sense. I can comfortably shake that about my globe. But, at some point, doesn't a number hit 3.2? So, the number should, rationally, end! Imagine, if you will, ten lines between the number three and the number four. Imagine again that there are also ten smaller lines between each of those ten lines (and so on...) If 3.1 is one line and 3.2 is another- pi must lie on some line somewhere in between. Where it lies, must be rigid.. no?
Circles.. hmmm. So, is round a predominant state in the universe? Or, some fundamental law or universal basis for math? From planets and stars to cells and to atoms?
So, here I manage to stray my attention (happens often.) I turned right at round and ran into atoms; happened as I wrote the word atom, remembering simultaneously that we cannot see atoms- I questioned. How can I state that atoms are round if I do not understand how we know that atoms exist. hmmm again.
Just as a minimal diversion; I must explain what I found. I thank Dr. Bill Robertson for this wonderful conceptual explanation that I have recreated (revision) below;
Imagine you are in a room. You are sitting in a chair and you open your eyes to complete darkness. You try to move and are unable to do so because, rope is tied around your waste and securing you to that chair. You feel around in the dark, leaning your arms and hands as far to the surrounding floor areas as possible. You find something. A pile of rocks.. you think, hmmm. I am tied to a chair in the dark with a pile of rocks within reach. Hmmm.
You hear nothing, but think that waiting is likely a detrimental survival plan choice. You have seen Saw and Saw two... So, you pick up a rock and decide that you want to know what the room is like. You decide that the noise is irrelevant as someone left you there and knows where you are and someone also left you a pile of rocks. So, you chuck a rock to judge the distance between where you are and where whatever the rock hits- is. It's not far. You repeat this experiment until you learn that the room is small and judging by the dimensions and different impact noises, you gestimate that you are in a rectangle shaped bathroom. You now have a good estimate of both the size and the shape of the room.
This is exactly how atoms are measured.. albeit, from the outside. I'll leave it at that as I started to wander on to STM or scanning tunneling microscopy- a method of the above test that results in images. These images are in appearance, not circles.
Alas. nonetheless, pi is invariably interesting for the reason I initially state. If numbers are representations of a measurement of something. What the hell is pi a measurement of?
KAS
A non-hard-science mind, who loves explaining, writing, teaching, and most of all, understanding.
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I've Thought...
03.09 ~ I am but human, in my thoughts and desires- in my inconsistencies. It makes my opposing decisions no less real, no less quantitative... confusion is but the eye of truth, beckoning reason. ~ 03.12 ~ Time. It's existence is action progression, regression, reflection and projection. What in time is solidified and carried to another time is my choice. In one choice you lose all others; as an atom appreciates when the observer decides. It's a blue ocean of intrigue and a wave of contentment- that I am lost in, whilst, carried by. ~ 03.23 ~ That we are all part of one pulsing energy of life.. ~ 3.28 ~ There is no greater power, than the power of words. In speech we pass each other in halls, ride in elevators and embark in the great adventure that are words - with all of their beauty and intrigue. There are no wrong words spoken, only wrong interpretations and implications. Honest words are organic, true and expressions of what we are; existing autonomously and innocently, regardless of what others may think of them. 3.30 ~ That, the more I learn, the more I realize how little I know. It certainly doesn't help being in the company of those who have succeeded in accumulating far more knowledge than I. Is the differentiation between intelligence and knowledge simply the accumulation verses the ability to learn/understand? Or, are the two interchangeable. I feel as though time is passing faster than my ability to accumulate... do other people share this conundrum, I wonder... 4.02 ~ That, "It is what it is" isn't exactly accurate. "It is what I make it" is more so... 4.08 ~ That, "it's not time that matters... it's that mattering is what makes time." 4.12 ~ I watch and wonder... think and ponder... about it. Should I find that I have analyzed to much, to little; or that the quandary was all for not, I'll not know till the applicable time has passed.I hereby instill time as my guide, innocently and fully without disposition and without angst. (4.17) ~ Though random, we should not ignore paths crossed. Just as, we should not entirely exclude emotion from our conclusions. (4.26) ~ That I dispise my lack of control over my own intentions and wonder why I am so weak in this regard. (4.27) ~ That I have opened doors, I wished to open, while simultaniously putting other doors at risk of closing. It's not with resistance I contemplate, it's with anxiety. (4.28) That, I should take a break. Time to simply be, for a bit. (5.01) Its hunger drives decent of rational, a battle of wit and need. Like rain pouring down, wisped by winds, settled by gravity, I’m drawn to it ~ KAS
Well, it's only strange that a number might not end because.. a number is a measurement of something. Quite obviously, a number cannot be a representation, if it is incomplete.
ReplyDeleteBut π does measure something - the circumference of a circle of radius 1/2 (in whatever units you want).
Such things are called "irrational" numbers - not because they are contrary to reason, but because they aren't ratios of two integers.
Don't be alarmed with numbers that "don't end". The length of the diagonal of a square of side 1 (any units) is √2 - and that "doesn't end" either.
This really bothered the Pythagoreans about 2500 years ago, too. But it turns out to be a problem with how we represent numbers, not with the numbers themselves.
Charles, thank you for your comment. I researched Pythagoreans after your mentioning along with other known irrationals - like e and the square root of 2. I still can't grasp the lack of a final figure, but appreciate the idea that it is a numerical limitation more than a limitation of reality. Presuming that numbers are a creation of humanity in order to measure. I was leaning towards the idea that a lack of definitive calculation could be something of a representation of something other than a measurement; like energy or a universal constant. Math eludes me at this stage in my learning though and is something I am just recently growing in affiliation to.
ReplyDeleteI'm having a hard time agreeing even that the problem is with our representation of numbers. Even if we represent numbers in binary, or Roman numerals, or I suspect any other way you could think of, pi would still be endless.
ReplyDeleteWhat, afterall, is wrong with how we have invented numbers in the first place that pi should turn out this way?
Shon, Thank you for your comment. I agree with you in your questioning; it makes no sense to me that a number might not end. As I stated when I said "Well it's only strange that a number might not end because... a number is a measurement of something..." It's a thought provoking conundrum indeed.
ReplyDeleteAs I do not know, I am open to any route to understanding such as Charles mentioning of numerical limitations... But, I still feel that the number either ends at some figure, or is not definitive and therefor cannot be pinned down to a measurement.
KAS