Roland Omnès, author of Quantum Philosophy, begins his book with a dialogue with pre-Socratic philosophers, writing, “Physics has found its primitive objects: space-time and the elementary particles of matter, but at the price of accepting that its principles and its foundations should be irrepresentable to the eyes of the mind” (xix in Prelude).* Whether or not one can actually see is not an impediment to the impediment we all have with regard to “seeing” the “primitive objects” that make up our universe. The figurative “eyes of the mind” are all blind to such objects.
That’s what the physicists of the late nineteenth and early twentieth centuries did to us: They gave us an “irrepresentable” world, a world we can describe only in relationships, only in mathematical terms. The well-informed among us, the mathematicians, have the rest of us at a disadvantage. Familiar with “irrepresentable” entities, they use their special languages to describe and predict, and only with the help of some models, graphs, and computer displays do we come close to “representing.” For centuries, we have relied on the tangible and experienced as the roots of understanding and representation. Now, at the very best we rely only on probabilities, where, for example, an electron can be found or how a photon makes itself known to our actual eyes. And we don’t, as Richard Feynman says in his book on quantum electrodynamics, know “why” the world of the elementary “things” like photons works the way it does.
If I ask you to describe an atom, chances are you will draw a little “Solar System” of nucleus and electrons. Yet, we do know that such a model is a gross oversimplification. But a little Solar System is easy to represent in the mind’s eyes. We so depend on representation, but the world the mathematicians and physicists have given us just isn’t representable. And on top our knowing that the fundamental makeup of the world is a matter of probabilities, we have to deal with our difficulties in thinking and language because of people like Kurt Gödel, who taught us that axioms cannot be proved by their own logic. That hurts. We like to think axiomatically. We just love our fundamental assumptions. They provide us with what is representable.
There’s been somewhat of a mind’s-eye crisis for more than a century, enough of one for Morris Kline to title his 1980 book, Mathematics: The Loss of Certainty.** Most of us are either ignorant of the uncertainty or merely vaguely familiar with it—having either paid attention to the science teacher in the classroom or gone off into a dreamland of our own probabilities. As long as the practical, representable world works for us, we’re happy. The idea of a world based on irrepresentable probabilities of the quantum doesn’t enter into our daily dealings.
But we do deal with uncertainties in events and human behaviors. And, of course, there are the uncertainties that become very representable in our representable daily world, such as the famous onstage tiger attack during the Sigfried and Roy performance in Las Vegas. Controlling large predators is chancy, and no one can really explain “why” the tiger attacked its longtime trainer (though I would argue a simple explanation: It’s a tiger). And, of course, there are those fender-benders and more serious car accidents. Electrons rapidly traveling about nuclei don’t collide, but slow-moving cars in parking lots do.
Dealing with uncertainty can make people anxious, particularly those who want the mind’s eyes to see not only all that lies in the present, but also all that lies in their personal futures. Just as the fundamental makeup of the world is invisible, so also are many of the probabilities we face. And just like the physicists’ inability to tell us simultaneously the place and movement of photons and electrons beyond the probabilities of both, so we are whirling through a world in which our own probabilities are largely guesswork. That’s the way of our world.
Thus, I come back to my oft-repeated aphorism: What you anticipate is rarely a problem. Unfortunately, you can’t “see” all the probabilities of your life. And even in hindsight, to use the metaphor of Robert Frost, you don’t know the consequences of the “road not taken.” But there’s also a fortunate side to this. Yes, fortunately, you live in a world of immense probabilities. Every day—every second—is an adventure. Anticipate what you can, and deal the best you can with the rest.
You live in a large amusement park called the Cosmos. And you spend most of your time in its fun house, where you encounter mirrors that give both true and distorted reflections that can fool the mind’s eyes, and where you meet surprises at every turn. Would you spend money and time to enter a “fun house” with no surprises?
Face it. Deep down there’s something in you that doesn’t want to see ahead and to know all the probabilities. Such a cosmos would be boring. Even riding the same rollercoaster can become tiresome once the thrills become known and the ending is predictable—you do, for example, get on the coaster at a point to which it consistently returns. The amusement park of the Cosmos gives you no repeat thrill and no guarantee of a safe return.
So, in a world of “uncertainty” and “probability” that is also a world in which fundamental axioms fail to explain themselves, you are on a wild ride of an adventure whose outcome is just a guess. Enjoy.
*Omnès, Roland. Quantum Philosophy, Princeton, 1999.
**Kline, Morris. Mathematics: The Loss of Certainty. New York. Fall River Press, 2011 edition.
That’s what the physicists of the late nineteenth and early twentieth centuries did to us: They gave us an “irrepresentable” world, a world we can describe only in relationships, only in mathematical terms. The well-informed among us, the mathematicians, have the rest of us at a disadvantage. Familiar with “irrepresentable” entities, they use their special languages to describe and predict, and only with the help of some models, graphs, and computer displays do we come close to “representing.” For centuries, we have relied on the tangible and experienced as the roots of understanding and representation. Now, at the very best we rely only on probabilities, where, for example, an electron can be found or how a photon makes itself known to our actual eyes. And we don’t, as Richard Feynman says in his book on quantum electrodynamics, know “why” the world of the elementary “things” like photons works the way it does.
If I ask you to describe an atom, chances are you will draw a little “Solar System” of nucleus and electrons. Yet, we do know that such a model is a gross oversimplification. But a little Solar System is easy to represent in the mind’s eyes. We so depend on representation, but the world the mathematicians and physicists have given us just isn’t representable. And on top our knowing that the fundamental makeup of the world is a matter of probabilities, we have to deal with our difficulties in thinking and language because of people like Kurt Gödel, who taught us that axioms cannot be proved by their own logic. That hurts. We like to think axiomatically. We just love our fundamental assumptions. They provide us with what is representable.
There’s been somewhat of a mind’s-eye crisis for more than a century, enough of one for Morris Kline to title his 1980 book, Mathematics: The Loss of Certainty.** Most of us are either ignorant of the uncertainty or merely vaguely familiar with it—having either paid attention to the science teacher in the classroom or gone off into a dreamland of our own probabilities. As long as the practical, representable world works for us, we’re happy. The idea of a world based on irrepresentable probabilities of the quantum doesn’t enter into our daily dealings.
But we do deal with uncertainties in events and human behaviors. And, of course, there are the uncertainties that become very representable in our representable daily world, such as the famous onstage tiger attack during the Sigfried and Roy performance in Las Vegas. Controlling large predators is chancy, and no one can really explain “why” the tiger attacked its longtime trainer (though I would argue a simple explanation: It’s a tiger). And, of course, there are those fender-benders and more serious car accidents. Electrons rapidly traveling about nuclei don’t collide, but slow-moving cars in parking lots do.
Dealing with uncertainty can make people anxious, particularly those who want the mind’s eyes to see not only all that lies in the present, but also all that lies in their personal futures. Just as the fundamental makeup of the world is invisible, so also are many of the probabilities we face. And just like the physicists’ inability to tell us simultaneously the place and movement of photons and electrons beyond the probabilities of both, so we are whirling through a world in which our own probabilities are largely guesswork. That’s the way of our world.
Thus, I come back to my oft-repeated aphorism: What you anticipate is rarely a problem. Unfortunately, you can’t “see” all the probabilities of your life. And even in hindsight, to use the metaphor of Robert Frost, you don’t know the consequences of the “road not taken.” But there’s also a fortunate side to this. Yes, fortunately, you live in a world of immense probabilities. Every day—every second—is an adventure. Anticipate what you can, and deal the best you can with the rest.
You live in a large amusement park called the Cosmos. And you spend most of your time in its fun house, where you encounter mirrors that give both true and distorted reflections that can fool the mind’s eyes, and where you meet surprises at every turn. Would you spend money and time to enter a “fun house” with no surprises?
Face it. Deep down there’s something in you that doesn’t want to see ahead and to know all the probabilities. Such a cosmos would be boring. Even riding the same rollercoaster can become tiresome once the thrills become known and the ending is predictable—you do, for example, get on the coaster at a point to which it consistently returns. The amusement park of the Cosmos gives you no repeat thrill and no guarantee of a safe return.
So, in a world of “uncertainty” and “probability” that is also a world in which fundamental axioms fail to explain themselves, you are on a wild ride of an adventure whose outcome is just a guess. Enjoy.
*Omnès, Roland. Quantum Philosophy, Princeton, 1999.
**Kline, Morris. Mathematics: The Loss of Certainty. New York. Fall River Press, 2011 edition.
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