You know how you know stuff without remembering where you learned it? Happens all the time, that is, drawing on stored information without thinking about its source or accuracy, right? All of us have garnered information from study, observation, inculcation, and experience. Among the bits of information that made their way into my brain is one about π, particularly a curious fact about the accuracy it lends to drawing a circle: With just 39 decimal places of π, I remember from an unknown source, one could calculate a circle the size of the known universe to the accuracy of a single hydrogen atom’s radius. * I just can’t tell you where I got that brain-bit; it could have come from any one of a number of sources.**
Now, you might say, “So? What am I going to do knowing the size of such a big circle? If I mention the fact at Starbucks, will the barista give me a discount on a cup of coffee?”
Actually, figuring that large of a circle with such accuracy isn’t the end point here. Instead, think of the measurements you make in your daily life, measurements like the distance from kitchen to bedroom, the size of a carryon suitcase, the volume of your glass compared to the amount of smoothie you made in the blender, or the measurement of other humans, that is, not their shape or size, but the measurement of their character and behavior. How accurate are your measurements? How accurate are your conclusions?
In his Mathematics: The Loss of Certainty, Morris Kline write about Georg Cantor’s “law of conservation of ignorance. “A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held” (103). *** Where does this connect to the effectiveness of π?
It’s almost impossible to escape the barrage of accusations loosely thrown about by political enemies today. Radio news-talk shows, TV talk shows, social media’s cascade of comments, and newspaper editorials reveal our penchant to accept uncritically any accusation made against the politics and character of anyone the powers of the day deign as despicable. The product is widely accepted false conclusions based on inaccuracies. I don’t have to tell you, if you are discerning enough to seek π-like 39-decimal-place accuracy in not only your beliefs but also in the beliefs of others, what those falsehoods are.
With so many false conclusions out there in the world of cyberspace, print, and broadcast media, it’s difficult even for a discerning person to find the Certain. In truth, we have abandoned Doubt in favor of Comfort. We draw approximate circles, maybe even enclosed harmonic oscillators whose variations from a true circle we ignore. We accept imperfections when we generalize, and generalizing is precisely the way we help spread false conclusions.
We simply ignore how out-of-round our circles of acceptable truth truly are.
As you listen to or read statements from various sides of political arguments, for example, wouldn’t a good rule of thumb be to check out the decimal places of accuracy? Now consider this. As accurate as that universe-sized circle would be as measured against the thickness of a hydrogen atom, it is still not a perfect circle. And even running the decimal places of π beyond 39 places cannot get you to a perfect circle. Try it. You can set your computer to run π from now till the Sun becomes a red giant, and you still won’t have a perfect circle.
So, we go on with our imprecise generalizations and false conclusions because we believe they serve us well enough. Accuracy and truth are difficult to come by because we are always in the business of converting one kind of view into another, that is, in understanding the terms of another in our own terms. For about 4,000 years, people tried to find an accurate and handy fraction for π. In those four millennia and until the rise of computers, the number seems to have bounced between 3 1/7 and 3 1/8. Try Archimedes’ 22/7. Yes, you know the 3.14 you learned in school, and maybe you kept 3.1415 or 3.1416 in your head. You probably don’t remember your first exposure to π, and you probably don’t have the inclination to spend years running π to a million decimal places. So, three and one seventh or three and one eighth, which are numbers that the ancient Babylonians and Egyptians used would suffice for your needs. After all, if the mathematicians can’t get the fraction down without arguing about their accuracy, then why should you bother? If they can’t translate decimals to a universally agreed upon fraction, how are you supposed to translate the language of your intellectual opposition into your own language?
Many voices out there proclaim without checking the accuracy of their accusations because they assume they have obtained an accuracy very much on the order of those 39 decimal places. Every generation has its false conclusions based on inaccuracies. And sometimes—maybe often—what is argued so vehemently in one generation becomes the acceptable “fact” in the following generation either because that following generation subjects a controversy to unemotional examination or simply accepts the inculcation as a way of the world or a cultural truth. **** An ensuing generation often doesn’t know the source of its beliefs, and it only rarely takes the time and makes the effort to find a more accurate measurement of the past and the beliefs that the past left as a heritage. It’s easier to accept than to discover, as we all know. *****
The past is lost quickly, so, as Georg Cantor argued and Morris Kline worded as I repeat here for emphasis: “A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held.”****** A comforting conclusion, however false, is accurate enough for most of us most of the time.
*A distance measured in picometers. We’re talkin’ trillionths of a meter here in a universe that has stretched its diameter nearly 100 billion light years. Even if my foggy memory of the 39 decimal places is incorrect on a circle the size of the entire inflated universe, it’s probably very close to what it would be without cosmic inflation in a universe 13.7 or 13.8 billion years old.
**One book comes to mind, but I’m guessing: Petr Beckmann’s A History of π (Pi). However, there are other possible sources of the fact. So, anyway, that number would be: 3.141592653589793238462643383279502884197 (I think)
***New York. Fall River Press, 1980.
****An idea expressed by Max Planck: Something controversial doesn’t become acceptable in “its time.” Those involved in the controversy simply die off, passing on the idea to the next generation that can examine without emotional involvement. I can think of Alfred Wegener, for example. His idea of moving continents wasn’t accepted until after he died.
*****I’m thinking of the parallels between the creation stories of the Babylonian Enuma Elish and first of the two creation stories in Genesis. Of course, there are differences, such as the Babylonian water goddess Tiamat and the Hebrew “Formless Void” from which all came into being. The Hebrew text seems to draw on the older Babylonian model of a Hexaemeron, so my unprovable guess is that the writer(s) of Genesis did not know from where they derived the idea for a six-day creation; but they did draw a difference. The Babylonians did not conceive of a time before time, a Nothing that preceded Everything. Their cosmos was created out of Tiamat, a pre-existing entity.
******Here I’m thinking of the “Russian collusion” pushed relentlessly over the past two years or more and even after the Mueller Report and its mostly anti-Trump lawyers found no evidence of collusion. Once a false conclusion takes hold, it clings to the mind like a polyplacophoran on a tidal pool rock.
Now, you might say, “So? What am I going to do knowing the size of such a big circle? If I mention the fact at Starbucks, will the barista give me a discount on a cup of coffee?”
Actually, figuring that large of a circle with such accuracy isn’t the end point here. Instead, think of the measurements you make in your daily life, measurements like the distance from kitchen to bedroom, the size of a carryon suitcase, the volume of your glass compared to the amount of smoothie you made in the blender, or the measurement of other humans, that is, not their shape or size, but the measurement of their character and behavior. How accurate are your measurements? How accurate are your conclusions?
In his Mathematics: The Loss of Certainty, Morris Kline write about Georg Cantor’s “law of conservation of ignorance. “A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held” (103). *** Where does this connect to the effectiveness of π?
It’s almost impossible to escape the barrage of accusations loosely thrown about by political enemies today. Radio news-talk shows, TV talk shows, social media’s cascade of comments, and newspaper editorials reveal our penchant to accept uncritically any accusation made against the politics and character of anyone the powers of the day deign as despicable. The product is widely accepted false conclusions based on inaccuracies. I don’t have to tell you, if you are discerning enough to seek π-like 39-decimal-place accuracy in not only your beliefs but also in the beliefs of others, what those falsehoods are.
With so many false conclusions out there in the world of cyberspace, print, and broadcast media, it’s difficult even for a discerning person to find the Certain. In truth, we have abandoned Doubt in favor of Comfort. We draw approximate circles, maybe even enclosed harmonic oscillators whose variations from a true circle we ignore. We accept imperfections when we generalize, and generalizing is precisely the way we help spread false conclusions.
We simply ignore how out-of-round our circles of acceptable truth truly are.
As you listen to or read statements from various sides of political arguments, for example, wouldn’t a good rule of thumb be to check out the decimal places of accuracy? Now consider this. As accurate as that universe-sized circle would be as measured against the thickness of a hydrogen atom, it is still not a perfect circle. And even running the decimal places of π beyond 39 places cannot get you to a perfect circle. Try it. You can set your computer to run π from now till the Sun becomes a red giant, and you still won’t have a perfect circle.
So, we go on with our imprecise generalizations and false conclusions because we believe they serve us well enough. Accuracy and truth are difficult to come by because we are always in the business of converting one kind of view into another, that is, in understanding the terms of another in our own terms. For about 4,000 years, people tried to find an accurate and handy fraction for π. In those four millennia and until the rise of computers, the number seems to have bounced between 3 1/7 and 3 1/8. Try Archimedes’ 22/7. Yes, you know the 3.14 you learned in school, and maybe you kept 3.1415 or 3.1416 in your head. You probably don’t remember your first exposure to π, and you probably don’t have the inclination to spend years running π to a million decimal places. So, three and one seventh or three and one eighth, which are numbers that the ancient Babylonians and Egyptians used would suffice for your needs. After all, if the mathematicians can’t get the fraction down without arguing about their accuracy, then why should you bother? If they can’t translate decimals to a universally agreed upon fraction, how are you supposed to translate the language of your intellectual opposition into your own language?
Many voices out there proclaim without checking the accuracy of their accusations because they assume they have obtained an accuracy very much on the order of those 39 decimal places. Every generation has its false conclusions based on inaccuracies. And sometimes—maybe often—what is argued so vehemently in one generation becomes the acceptable “fact” in the following generation either because that following generation subjects a controversy to unemotional examination or simply accepts the inculcation as a way of the world or a cultural truth. **** An ensuing generation often doesn’t know the source of its beliefs, and it only rarely takes the time and makes the effort to find a more accurate measurement of the past and the beliefs that the past left as a heritage. It’s easier to accept than to discover, as we all know. *****
The past is lost quickly, so, as Georg Cantor argued and Morris Kline worded as I repeat here for emphasis: “A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held.”****** A comforting conclusion, however false, is accurate enough for most of us most of the time.
*A distance measured in picometers. We’re talkin’ trillionths of a meter here in a universe that has stretched its diameter nearly 100 billion light years. Even if my foggy memory of the 39 decimal places is incorrect on a circle the size of the entire inflated universe, it’s probably very close to what it would be without cosmic inflation in a universe 13.7 or 13.8 billion years old.
**One book comes to mind, but I’m guessing: Petr Beckmann’s A History of π (Pi). However, there are other possible sources of the fact. So, anyway, that number would be: 3.141592653589793238462643383279502884197 (I think)
***New York. Fall River Press, 1980.
****An idea expressed by Max Planck: Something controversial doesn’t become acceptable in “its time.” Those involved in the controversy simply die off, passing on the idea to the next generation that can examine without emotional involvement. I can think of Alfred Wegener, for example. His idea of moving continents wasn’t accepted until after he died.
*****I’m thinking of the parallels between the creation stories of the Babylonian Enuma Elish and first of the two creation stories in Genesis. Of course, there are differences, such as the Babylonian water goddess Tiamat and the Hebrew “Formless Void” from which all came into being. The Hebrew text seems to draw on the older Babylonian model of a Hexaemeron, so my unprovable guess is that the writer(s) of Genesis did not know from where they derived the idea for a six-day creation; but they did draw a difference. The Babylonians did not conceive of a time before time, a Nothing that preceded Everything. Their cosmos was created out of Tiamat, a pre-existing entity.
******Here I’m thinking of the “Russian collusion” pushed relentlessly over the past two years or more and even after the Mueller Report and its mostly anti-Trump lawyers found no evidence of collusion. Once a false conclusion takes hold, it clings to the mind like a polyplacophoran on a tidal pool rock.
RSS Feed