Leftover Pi
Inaccuracy of measurement is important in concept and practice. It greases the skids of social discourse; it conveys a sense of cheerful tolerance; it contributes to the give and take of pleasant conversations.
By this point of view we have a liking for the man who, when asked what time it is, says “about 3:30.”
He has taken a run at accuracy without being a slave to it. He does not brood over the matter. He is aware of the passage of time without being preoccupied by it.
He is to be preferred to the fellow who says in response to the same question, ‘daytime.’
But he is much to be preferred to this other gentleman who says 3:33:14.
This former tells us something we already knew or could figure out for ourselves.
The latter asks too much of us and of our own intermittent attention to the passage of time, and puts us at a disadvantage in the conversation. We can never relax in his company. We predict that we will have trouble keeping pace. We must always be on our guard to try to live up to his sense of accuracy.
We won’t miss this chance here though to pay homage to a sense of accuracy.
You do not want your Mars Explorers, hydrogen bombs, hazardous waste incinerators, or photon accelerator centrifuges – if accelerate them is what we do with photons – being designed and built by folks who, when asked how far this one way or the other way to nudge the photon accelerator in order to guard against a complete photon meltdown event and the destruction of the planet, answer “oh, a smidge this way. Maybe a smidge and half.”
When asking a fellow worker the diameter of the hole to be drilled through the titanium outer layer of the Personal Space Propulsion Unit carrying us into outer space in order that the plutonium rods fueling that flight can be threaded perfectly through that newly bored hole, it is not pleasing to us for this other fellow to reply by making a small circle with his thumb and index finger and say “‘bout so.”
No, these are instances where even the casual observer would wish to see some numbers cited that stretch out for a few dozen decimal points. We would like to think that at the least someone would pull out one of those measuring tapes that spools out of its case and snaps back into it with a rush when done with, while making pencil marks on the foundation of the accelerator or Propulsion Unit to get it just right.
A round of applause for these fine people.
We come a bit closer to the point when we note that there are an entire slew of measurement type words that have no accuracy to them, that hardly have any sense to them, but that we have no trouble at all knowing the meaning of.
To take a point, what exactly is a slew? It was flung around with abandon in the paragraph above with the confidence that most readers knew that it meant, say, ‘more than five but less than a hundred.’ Which in fact is just about what I did mean. But how did you and I come to this agreement between us, this ‘somewhere between five and a hundred’ business?
There is a time and a place for accuracy and inaccuracy, and it is a good thing to know which time and place you’re residing in at the moment. There are great batches of life – there we go again – where you can get into real trouble being the one when you ought to be the other.
When the young fiancée asks her beau how much he loves her, this is not the time – not the time, I say – to…well, let us spell it out in dialogue as they do in plays.
Young Fiancée: Tell me how much you love me, Billy.
Bill: How much I love you? (Musing.)That’s an interesting question.
Young Fiancée: Yes, how much do you love me?
Bill: What’s my unit of measure?
Young Fiancée: (taken aback) Unit of measure?
Bill: Yes, would you prefer I decimalize the answer or provide it in cu ft. /lbs, or meters, or a measure of velocity? All are valid.
Young Fiancée: (warningly) You ask some might funny questions for a fellow who has just been asked to measure his love for his betrothed which by rights I would think would be nearly immeasurable.
Bill: (nodding his head with assurance, the young sap) Oh, everything can be measured. Let us see here. We shall use a scale of ten, yes, this being a measure well understood by even the quantitatively challenged among us (he smiles indulgently at this, thinking he has made a joke that she will enjoy. The young sap.)
Young Fiancée: (coldly now, warmth has been left far behind.) Yes, yes, I can’t wait to hear this, William, this very important measurement that your betrothed has just asked you for.
Bill: (musing and doing some figuring in his head.) Well, then, I would say on a scale of 10 that I love you about 8.2. Well, wait, that’s not quite right, there’s a bit of variance from day to day. Say a range from 8.1 to 8.25.
Young Fiancée: (saying nothing at all in an icy cold manner and continuing to say it for some stretch of time.)
You don’t have to be Einstein to know that Bill is going to be lucky to get out of this conversation alive.
We look for some middle ground in our everyday dealings. If we were to ask the next five people that we meet what the value of Pi is, that number which, if you take it and multiply it by the diameter of a circle you get a general feel for the circumference of that same circle, I imagine we would get just about these five answers:
1. I’ll have to think about that one.
2. 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778
3. What’s pi?
4. Isn’t it three point something?
5. What’s pi.
The answer that gets us closer to where we really want to go is #4. ‘Three point something’ places us in the ballpark which is sometimes as close as you’re going to get. It just about meets the needs of the occasion.
Same with the fellow at the side of the road that we ask how far it might be to the Sledge County Root Vegetable Festival. We are content if he answers:
1. A mile or two that way.
2. Yonder.
3. Wish I knew but I don’t.
These aren’t accurate in the least, there’s a big difference in answer #1 between one mile and two, but they convey a sense of helpfulness, a sense that such a thing as the Root Vegetable Festival exists, which is a step in the right direction, and evidence that the gentleman speaks to strangers at all. These are things we can build on.
It gives us less ease if he answers:
1.35 miles, 43 yards, two feet, three inches.
This by contrast paints a portrait of a personality who has for some reason been waiting years for you to drive by, who thinks altogether too much on distances and lengths, and whom you are from here on out inclined not to trust at all.
And he’s the guy with the right answer! That’s the thing about it.
So have a care how you answer these questions if you are asked. People are listening to your response, and if asked exactly how carefully they are listening, I would be tempted to give you a number but advise that you might want to adjust it a smidge this way or a smoosh that way. That ought to help you understand.
