Saturday, August 14, 2010
Tuesday, August 10, 2010
Past Mistakes
Every one of us can look back and recall times when we made choices that were not all that good—times when a choice led to subsequent problems and pain, or just wasted valuable time. (We each enjoy a preciously small amount of time in this existence, so why waste any of it?) The wisdom of hindsight tells us that we could have done better. So how do we deal progressively with these regrettable actions that we once took? It doesn’t help to dwell upon them because they caused us pain, or wasted our precious time, or led us down dead ends that got in the way of happiness.
It also doesn’t help if I bemoan my past poor choices or wallow in self-pity. It’s easy to become consumed with feeling sorry for myself or blaming others for what happened, or even disapprove of myself.
There is another reaction that I’ve sometimes had people suggest—a way that can help one to get past self-pity or blame. That is, to say, “Well, I didn’t do all that well, but I did the best I could at the time.” There may be truth in that sentiment, but it can also become a justification for what was simply a bad choice or a lackadaisical performance. Such a response can just help us fall into the same bad choice again, because it justifies coming up short. If I take this route, maybe I’m not wallowing in self-pity or blaming others, but I also haven’t learned much from the mistake; in fact, I may rationalize the situation so much that I don’t even see it as a mistake.
If I’m candid about my previous poor choices, however, I can admit to times when I simply didn’t do my best, or when I just made a dumb choice. If I go into it a little deeper, I can recall times, for example, when I made bad choices because my priorities at the time were poorly arranged. Can I be honest with myself and admit to those screw-ups, without either dwelling on them or dismissing them?
I got a nice suggestion recently from a passage in a book by Joyce Sequichie Hifler, A Cherokee Feast of Days. She writes about how we may look back and regret the time we wasted, “…wishing we knew then what we know now. But we did not know and life is not lived by hindsight. We did what we knew to do—sometimes with great ignorance.” And it’s not too late at all, she adds: “Many have started over and have had more happiness and contentment in a short time than is in all of what is known as the wasted years.”
I like the idea of simply accepting the mistakes and letting them go, rather than hanging onto them and thus continuing to waste time and continuing to stave off happiness. As Hifler says, we can begin again, despite our past mistakes. Each day is fresh. The challenge is to get past excuses and regrets, admit to messing up, and find self-forgiveness and self-acceptance. Tomorrow’s true happiness begins with today’s wiser choices; and they are best made when we’re unencumbered by dwelling on the past. It’s a key way that we learn and grow.
It also doesn’t help if I bemoan my past poor choices or wallow in self-pity. It’s easy to become consumed with feeling sorry for myself or blaming others for what happened, or even disapprove of myself.
There is another reaction that I’ve sometimes had people suggest—a way that can help one to get past self-pity or blame. That is, to say, “Well, I didn’t do all that well, but I did the best I could at the time.” There may be truth in that sentiment, but it can also become a justification for what was simply a bad choice or a lackadaisical performance. Such a response can just help us fall into the same bad choice again, because it justifies coming up short. If I take this route, maybe I’m not wallowing in self-pity or blaming others, but I also haven’t learned much from the mistake; in fact, I may rationalize the situation so much that I don’t even see it as a mistake.
If I’m candid about my previous poor choices, however, I can admit to times when I simply didn’t do my best, or when I just made a dumb choice. If I go into it a little deeper, I can recall times, for example, when I made bad choices because my priorities at the time were poorly arranged. Can I be honest with myself and admit to those screw-ups, without either dwelling on them or dismissing them?
I got a nice suggestion recently from a passage in a book by Joyce Sequichie Hifler, A Cherokee Feast of Days. She writes about how we may look back and regret the time we wasted, “…wishing we knew then what we know now. But we did not know and life is not lived by hindsight. We did what we knew to do—sometimes with great ignorance.” And it’s not too late at all, she adds: “Many have started over and have had more happiness and contentment in a short time than is in all of what is known as the wasted years.”
I like the idea of simply accepting the mistakes and letting them go, rather than hanging onto them and thus continuing to waste time and continuing to stave off happiness. As Hifler says, we can begin again, despite our past mistakes. Each day is fresh. The challenge is to get past excuses and regrets, admit to messing up, and find self-forgiveness and self-acceptance. Tomorrow’s true happiness begins with today’s wiser choices; and they are best made when we’re unencumbered by dwelling on the past. It’s a key way that we learn and grow.
Sunday, August 8, 2010
Tuesday, August 3, 2010
Is Beauty Truth?—Part 2
I believe that the previous posting describes Stewart’s restrictive use of the word beauty. And how about his use of truth? The meaning of truth is where philosophers can really wax endlessly. But let’s narrow the field (according to Stewart) by considering truth to mean physical reality. The main aim of the physicist is to discover nature’s story, to seek nature’s truth. While the mathematician plays with abstract (not necessarily real) concepts, a physicist plays with nature’s rules and behavior—looking to discover the reality of how the world works. Nature holds the truth and the physicist is attempting to uncover her secrets.
When beauty and truth are described this way, I think I see the crux of Stewart’s argument, because as it turns out, the mathematician’s beauty has often been the same as nature’s truth. Time and again physicists, struggling to grasp a given physical reality, have come upon a rule or law (not their law, but nature’s) that previously was neatly expressed by a mathematician who was completely unconcerned with the physical world. The mathematician may have thought the rule was her theoretical and beautiful insight, but nature was already operating that way. Beauty becomes truth.
Another way to view this situation is to note that nature consistently prefers elegance. Time and again physicists have discovered that Mother Nature takes the simple path. When physicists are bumbling about and, say, are positing two different theories of how things might work, they’ve often gotten closer to reality by choosing the simpler one. I’ve written before of how Kepler’s three elegant laws of planetary motion (expressed by three simple—and beautiful—mathematical equations) came to be seen as having far more truth than Ptolemy’s contorted and confusing model of how the planets were supposed to move.
Ian Stewart’s main point is that symmetry can demonstrate to us the equivalence of mathematical beauty and physical truth. I won’t try to describe his definition of symmetry—it’s a little too esoteric for me to try and tackle here. In a general way, however, when something possesses symmetry, we find it has a pleasing quality—for it helps our mind to more easily and fluently grasp it. Symmetry literally helps to smooth our mental processing. Symmetrical things, it turns out, not only appear to us as true, but it’s also pretty much the way that nature works: being both symmetrical and true.
So nature—by definition “The Truth”—is at root beautiful. A giant of pure mathematics and physics, Paul Dirac, once put it, “A physical law must possess mathematical beauty.” Ian Stewart wraps up his book Why Beauty is Truth with, “In physics, beauty does not automatically ensure truth, but it helps. In mathematics, beauty must be true—because anything false is ugly.”
Over the last 2-3 decades I’ve been privileged to become increasingly absorbed in local nature, as I’ve watched the flora and fauna surrounding me. In the process I have come to consider nature as something to be revered. The local creatures and plants have been teaching me their truths as they have been showing me their beauty. The more I learn, the more I can comprehend that the story of nature, at root, is elegant. The totality of it, however, is beyond mere human comprehension. I am in awe of it; I’m overwhelmed by its beauty. Is that not something divine?
When beauty and truth are described this way, I think I see the crux of Stewart’s argument, because as it turns out, the mathematician’s beauty has often been the same as nature’s truth. Time and again physicists, struggling to grasp a given physical reality, have come upon a rule or law (not their law, but nature’s) that previously was neatly expressed by a mathematician who was completely unconcerned with the physical world. The mathematician may have thought the rule was her theoretical and beautiful insight, but nature was already operating that way. Beauty becomes truth.
Another way to view this situation is to note that nature consistently prefers elegance. Time and again physicists have discovered that Mother Nature takes the simple path. When physicists are bumbling about and, say, are positing two different theories of how things might work, they’ve often gotten closer to reality by choosing the simpler one. I’ve written before of how Kepler’s three elegant laws of planetary motion (expressed by three simple—and beautiful—mathematical equations) came to be seen as having far more truth than Ptolemy’s contorted and confusing model of how the planets were supposed to move.
Ian Stewart’s main point is that symmetry can demonstrate to us the equivalence of mathematical beauty and physical truth. I won’t try to describe his definition of symmetry—it’s a little too esoteric for me to try and tackle here. In a general way, however, when something possesses symmetry, we find it has a pleasing quality—for it helps our mind to more easily and fluently grasp it. Symmetry literally helps to smooth our mental processing. Symmetrical things, it turns out, not only appear to us as true, but it’s also pretty much the way that nature works: being both symmetrical and true.
So nature—by definition “The Truth”—is at root beautiful. A giant of pure mathematics and physics, Paul Dirac, once put it, “A physical law must possess mathematical beauty.” Ian Stewart wraps up his book Why Beauty is Truth with, “In physics, beauty does not automatically ensure truth, but it helps. In mathematics, beauty must be true—because anything false is ugly.”
Over the last 2-3 decades I’ve been privileged to become increasingly absorbed in local nature, as I’ve watched the flora and fauna surrounding me. In the process I have come to consider nature as something to be revered. The local creatures and plants have been teaching me their truths as they have been showing me their beauty. The more I learn, the more I can comprehend that the story of nature, at root, is elegant. The totality of it, however, is beyond mere human comprehension. I am in awe of it; I’m overwhelmed by its beauty. Is that not something divine?
Sunday, August 1, 2010
Friday, July 30, 2010
Is Beauty Truth?—Part 1
For a couple of centuries scientists, mathematicians, and philosophers have argued about the validity of the last two lines of John Keats Ode on a Grecian Urn: “Beauty is truth, truth beauty—that is all/ Ye know on earth, and all ye need to know.” Keats seems to be equating truth and beauty in these lines, and there are many who agree with him. However, there is an equally adamant group of folks who take issue with Keats and find all sorts of reasons why beauty and truth are not the same, or at least that one does not necessarily imply the other.
As often happens when parties disagree, they frequently are using different definitions, and there are few words that have more contradictory interpretations than beauty and truth. Beauty certainly is a relative term—one person’s beauty is another’s ugly. Truth, although it infers an absolute state, can at best be only partially fathomed by us humans. Truth, if we pursue it unwaveringly, may slowly reveal itself, but we can never fully own it. So the arguments persist. If people can’t even agree on whether something is true or not, or whether it’s beautiful or not, how do they ever expect to settle the dispute of whether or not they are equivalent?
I recently read a book by the eminent British mathematician and prolific writer Ian Stewart, that unequivocally takes a stand on the issue. Stewart titled his book Why Beauty is Truth. It’s really “a history of symmetry” (that’s the subtitle of his book), but along the way he builds a pretty strong case for why “beauty must be true,” but he does so in a rather narrow definition of each term.
One of my frustrations in reading the book (besides having my brain become numb by all the pure mathematics he goes into) is that Stewart never clearly defines what he means by either beauty or truth. He seems to assume that anyone brash enough to tackle his book will already know what truth and beauty are, as he uses them. He’s kind of like the musician who delves into a detailed lecture on timbre and counterpoint rhythms, assured that everyone is familiar with those words.
The book was still rewarding for me to tough out, though. Afterwards I kept pondering what beauty and truth are, as Stewart uses them. Here’s what I came up with, thanks one more time to wonderful Internet resources. (I really appreciate Wikipedia!)
Stewart—being a mathematician—is primarily concerned with mathematical beauty. Pure mathematicians love to refer to a mathematical concept or proof as beautiful, and when they do they usually mean that it is elegant, in the sense of being (1) clean, with a minimum of details, (2) succinct, and/or (3) original and unexpected (as in a discovery of some fundamental mathematical relationship). In other words, it must be simple, straightforward, unique, and balanced.
When a mathematician plays with theoretical concepts in algebra, geometry, and number theory, and eventually comes upon a pure, simple insight, he literally gets a feeling of aesthetic pleasure and considers it beautiful. The Babylonian and Greek mathematicians fell in love with the beauty they found (particularly Pythagoras’s geometrical discoveries).
Next time, truth…
As often happens when parties disagree, they frequently are using different definitions, and there are few words that have more contradictory interpretations than beauty and truth. Beauty certainly is a relative term—one person’s beauty is another’s ugly. Truth, although it infers an absolute state, can at best be only partially fathomed by us humans. Truth, if we pursue it unwaveringly, may slowly reveal itself, but we can never fully own it. So the arguments persist. If people can’t even agree on whether something is true or not, or whether it’s beautiful or not, how do they ever expect to settle the dispute of whether or not they are equivalent?
I recently read a book by the eminent British mathematician and prolific writer Ian Stewart, that unequivocally takes a stand on the issue. Stewart titled his book Why Beauty is Truth. It’s really “a history of symmetry” (that’s the subtitle of his book), but along the way he builds a pretty strong case for why “beauty must be true,” but he does so in a rather narrow definition of each term.
One of my frustrations in reading the book (besides having my brain become numb by all the pure mathematics he goes into) is that Stewart never clearly defines what he means by either beauty or truth. He seems to assume that anyone brash enough to tackle his book will already know what truth and beauty are, as he uses them. He’s kind of like the musician who delves into a detailed lecture on timbre and counterpoint rhythms, assured that everyone is familiar with those words.
The book was still rewarding for me to tough out, though. Afterwards I kept pondering what beauty and truth are, as Stewart uses them. Here’s what I came up with, thanks one more time to wonderful Internet resources. (I really appreciate Wikipedia!)
Stewart—being a mathematician—is primarily concerned with mathematical beauty. Pure mathematicians love to refer to a mathematical concept or proof as beautiful, and when they do they usually mean that it is elegant, in the sense of being (1) clean, with a minimum of details, (2) succinct, and/or (3) original and unexpected (as in a discovery of some fundamental mathematical relationship). In other words, it must be simple, straightforward, unique, and balanced.
When a mathematician plays with theoretical concepts in algebra, geometry, and number theory, and eventually comes upon a pure, simple insight, he literally gets a feeling of aesthetic pleasure and considers it beautiful. The Babylonian and Greek mathematicians fell in love with the beauty they found (particularly Pythagoras’s geometrical discoveries).
Next time, truth…
Sunday, July 25, 2010
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