I: Can you draw a perfect geometric figure?
You: Depends on what you mean by perfect. I know I can draw one in my mind.
I: And that’s the key: In the mind. I would hazard that no physical drawing mechanism and no actual drawer could produce a perfect geometric figure because geometry assumes lines have no thickness. And any angle you might draw has only a degree of approximation since physical lines drawn by a person or even by a machine would vary in thickness, no matter how fine the pen point or sharp the pencil. But we’re used to such approximations of what we hold mentally as perfect. In that regard, we’re Platonists, accepting a “reality” for ideal geometric figures.”
You: Okay, if not geometric figures, how about mathematical precision and perfection?
I: For example, Planck’s length?
You: Yes.
I: It’s really small, supposedly so small there’s nothing smaller than 1.616255(18)×10−35 m. But in my limited understanding, I believe that measure depends on the length of a meter. Sixty some years ago a meter was 1,650,763.73 wavelengths of orange-red light, in a vacuum, produced by burning the element krypton (Kr-86). In 1984, the Geneva Conference on Weights and Measures defined the meter as the distance light travels in a vacuum in 1/299,792,458 seconds with time measured by a cesium-133 atomic clock. Seems pretty accurate, right?
You: Good enough for me.
I: I agree. Good enough, but it makes my point here and one I have made elsewhere. What’s the level of resolution, what’s the pixel count of refinement we accept as an ultimate guide? Does your TV give you what your eyes give you during your walk through a flower garden? My TV screen seems to give a very clear image, but it’s five years old. When I installed it, I was astounded by its clarity and color intensity that surpassed the 2005 model I watched for 15 years. Walking past a TV store, I saw a more recent model that surpassed the clarity of my newer TV. The difference reminded me of my recent cataract surgery after which everything I saw was brighter and edges more defined, and all the colors more intense. I see a world more accurately than I saw it for years. Put me in front of an eye chart and ask me to read the smallest letters, and I’ll say, “Printed in USA.”
But I'm overstating my point.
You: Which is?
I: It’s that point underlain by my statement on perfect geometric figures, the length of a meter, and a TV screen’s resolution: Much in our lives is approximation. Much is a matter of interpretation, application, and appropriateness. I’ll stick with math for one more example: Why do we have decimal points? Accuracy, correct? But look at the Planck length. What if I were to stop at 1.6.
“I’d say, “Not good enough.”
I: And I would agree. For mathematical, that is, quantitive, accuracy, we want lots of places to the right of the decimal point. And short of running those places to infinity, we settle on a limit like hundredths, or hundred millionths, or trillionths, and so on. We say, “Accurate enough” according to our purposes and goals and go on with our lives in the security that we have an understanding. People in a lab need more accuracy than people in a kitchen. People in a lab can’t use a measurement like “a pinch of salt” because it lacks precision.”
You: Sure.
I: The language of math provides accuracy through decimal points and fractions. In contrast, language doesn’t because words have various meanings, often dependent on their delivery and context. I remember a college English professor defining poetry as ‘efficient language.’ Yet, if you read literary critics’ interpretation of the words ‘Here buckle’ in one of the recognized great poems, ‘The Windhover’ by Gerard Manley Hopkins, you’ll see various interpretations. So, how accurate is poetry? How precise? Pretty much every scientist would say the Planck length is the ultimate measurement, the ultimate level of accuracy, especially if coupled with the Planck time—really short, the time it takes for a photon to travel the Planck length. So, we interpret language, but we usually exclude interpretation from our most precise measurement systems as long as their quantities are useful, such as using International Units, milligrams, and micrograms for dosages of substances like vitamins and pain killers.
You: This all adds to…?
I: The need for accurate interpretation. Take sign language as an example. Elon Musk’s raising his arm to acknowledge a political crowd was for Democrats a chance to accuse him of being a Nazi. Hakim Jeffries did the same gesture, but the same group saw no parallel to the Nazi salute. And that’s where we are with words. No matter what you mean, today someone will interpret it differently or twist your meaning for ideological or political reasons, too often to fuel hate for whatever you support and by extension, for you.
You: I know that. That’s why I’m careful not to say something offensive.
I: But there’s no agreed upon measure of what is offensive.
You: I see…
I: And then there’s the interpretation of implications. Obviously, the Iranian leaders did not interpret or infer well with regard to Trump’s statement that they should negotiate. Somehow they didn’t accept that in regard to threats against Americans and the ramifications of those threats, the President says what he means. They didn’t get either the implied message or the direct one that they would not get an atomic bomb. Now, some of those leaders are still misinterpreting the President, as they say they will close the Strait of Hormuz.
You: I saw that. Dumb. How will they sell their own oil to the Chinese?
I: Thus the importance of accurate language. There is, however a lesson in precision they could have learned in a single night.
You: What’s that.
I: The US can put 14 30,000-lb bombs in a very precise zone, not as small as the Planck length, but definitely as small as an air vent for an underground nuclear facility. So, whereas what one says should be as accurate as one can make it, what one hears should be interpreted as accurately as possible.
You: Depends on what you mean by perfect. I know I can draw one in my mind.
I: And that’s the key: In the mind. I would hazard that no physical drawing mechanism and no actual drawer could produce a perfect geometric figure because geometry assumes lines have no thickness. And any angle you might draw has only a degree of approximation since physical lines drawn by a person or even by a machine would vary in thickness, no matter how fine the pen point or sharp the pencil. But we’re used to such approximations of what we hold mentally as perfect. In that regard, we’re Platonists, accepting a “reality” for ideal geometric figures.”
You: Okay, if not geometric figures, how about mathematical precision and perfection?
I: For example, Planck’s length?
You: Yes.
I: It’s really small, supposedly so small there’s nothing smaller than 1.616255(18)×10−35 m. But in my limited understanding, I believe that measure depends on the length of a meter. Sixty some years ago a meter was 1,650,763.73 wavelengths of orange-red light, in a vacuum, produced by burning the element krypton (Kr-86). In 1984, the Geneva Conference on Weights and Measures defined the meter as the distance light travels in a vacuum in 1/299,792,458 seconds with time measured by a cesium-133 atomic clock. Seems pretty accurate, right?
You: Good enough for me.
I: I agree. Good enough, but it makes my point here and one I have made elsewhere. What’s the level of resolution, what’s the pixel count of refinement we accept as an ultimate guide? Does your TV give you what your eyes give you during your walk through a flower garden? My TV screen seems to give a very clear image, but it’s five years old. When I installed it, I was astounded by its clarity and color intensity that surpassed the 2005 model I watched for 15 years. Walking past a TV store, I saw a more recent model that surpassed the clarity of my newer TV. The difference reminded me of my recent cataract surgery after which everything I saw was brighter and edges more defined, and all the colors more intense. I see a world more accurately than I saw it for years. Put me in front of an eye chart and ask me to read the smallest letters, and I’ll say, “Printed in USA.”
But I'm overstating my point.
You: Which is?
I: It’s that point underlain by my statement on perfect geometric figures, the length of a meter, and a TV screen’s resolution: Much in our lives is approximation. Much is a matter of interpretation, application, and appropriateness. I’ll stick with math for one more example: Why do we have decimal points? Accuracy, correct? But look at the Planck length. What if I were to stop at 1.6.
“I’d say, “Not good enough.”
I: And I would agree. For mathematical, that is, quantitive, accuracy, we want lots of places to the right of the decimal point. And short of running those places to infinity, we settle on a limit like hundredths, or hundred millionths, or trillionths, and so on. We say, “Accurate enough” according to our purposes and goals and go on with our lives in the security that we have an understanding. People in a lab need more accuracy than people in a kitchen. People in a lab can’t use a measurement like “a pinch of salt” because it lacks precision.”
You: Sure.
I: The language of math provides accuracy through decimal points and fractions. In contrast, language doesn’t because words have various meanings, often dependent on their delivery and context. I remember a college English professor defining poetry as ‘efficient language.’ Yet, if you read literary critics’ interpretation of the words ‘Here buckle’ in one of the recognized great poems, ‘The Windhover’ by Gerard Manley Hopkins, you’ll see various interpretations. So, how accurate is poetry? How precise? Pretty much every scientist would say the Planck length is the ultimate measurement, the ultimate level of accuracy, especially if coupled with the Planck time—really short, the time it takes for a photon to travel the Planck length. So, we interpret language, but we usually exclude interpretation from our most precise measurement systems as long as their quantities are useful, such as using International Units, milligrams, and micrograms for dosages of substances like vitamins and pain killers.
You: This all adds to…?
I: The need for accurate interpretation. Take sign language as an example. Elon Musk’s raising his arm to acknowledge a political crowd was for Democrats a chance to accuse him of being a Nazi. Hakim Jeffries did the same gesture, but the same group saw no parallel to the Nazi salute. And that’s where we are with words. No matter what you mean, today someone will interpret it differently or twist your meaning for ideological or political reasons, too often to fuel hate for whatever you support and by extension, for you.
You: I know that. That’s why I’m careful not to say something offensive.
I: But there’s no agreed upon measure of what is offensive.
You: I see…
I: And then there’s the interpretation of implications. Obviously, the Iranian leaders did not interpret or infer well with regard to Trump’s statement that they should negotiate. Somehow they didn’t accept that in regard to threats against Americans and the ramifications of those threats, the President says what he means. They didn’t get either the implied message or the direct one that they would not get an atomic bomb. Now, some of those leaders are still misinterpreting the President, as they say they will close the Strait of Hormuz.
You: I saw that. Dumb. How will they sell their own oil to the Chinese?
I: Thus the importance of accurate language. There is, however a lesson in precision they could have learned in a single night.
You: What’s that.
I: The US can put 14 30,000-lb bombs in a very precise zone, not as small as the Planck length, but definitely as small as an air vent for an underground nuclear facility. So, whereas what one says should be as accurate as one can make it, what one hears should be interpreted as accurately as possible.
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