Do we economize our assumptions to explain the physical world and social relationships?
In his popularization of physics, Clarence E. Bennett writes that “explanations are only relative to [ a person’s] background.” He made that statement in the context of Bohr’s model of the atom, the familiar one we see in textbooks that makes atoms look like little Solar Systems. “Although today this picture has been more or less replaced by abstract mathematical representation in the mind of the theoretical physicist, many of the Bohr features are still useful….” Bennett then says that this raises the “question of how a picture can be accepted if it is not correct…In other words, there can be any number of ways of explaining anything…It is not a question of which is the correct one; it is rather a question of which is the better one for the purpose, i.e., which explains the most with the fewest assumptions….”*
Do you agree? Surely, you have either provided or received such explanations. Think explaining the death of a pet or a favorite uncle to a toddler. Practically all of us gear our explanations to the background of the person, and that’s why textbooks have labels, such as “Introductory,” “Intermediate,” and “Advanced.”
As I have said elsewhere, all of us think axiomatically. We live mostly by “self-evident” truths; assumptions underlie everything. Certainly, you, for example, aren’t spending your current energy on anxiety that your screen will go blank. You assume no power outage even though you know such events occur, and you assume your chair and the floor beneath it will hold you. All of us have our own version of Occam’s Razor: Operate on as few assumptions as we can in the moment, and keep explanations simple. Many have extolled the virtue of simplicity in explanations, including Newton, Einstein, and da Vinci. Is there a similar virtue in the fewest possible assumptions, in the fewest axioms?
We just can’t get around our assumptions very easily because they’ve been incorporated into our education. And I don’t mean education as in what you learned in school though I can’t discount it. I’m thinking life lessons, those experiences that have added up to a world that doesn’t contradict itself, that, for example, fire is both hot and dangerous. Performances by fire-eaters tend to make audiences believe that there’s somehow a “cold fire” because the entertainer suffers no burns. Magicians, too, play on assumptions about a non-contradictory world. We assume what we witness is a trick because we can’t reconcile our assumptions with a disappearing elephant or a gravity-defying person.
To identify some minerals in the field, mineralogists use an unglazed ceramic plate that serves as a kind of “chalkboard.” Certain minerals leave a “streak” with a characteristic color much the way a piece of white chalk leaves a white line or green chalk leaves a green line on a piece of slate. You do the same with an ordinary pencil whose “lead” is actually a mix of graphite and clay. The graphite disintegrates on the paper, leaving a gray-black streak. You assume by experience that the color of an object will be the same as its streak. But brass-yellow pyrite (fool’s gold) leaves a greenish-black streak on the unglazed ceramic. That’s counterintuitive and amazes most people on first witnessing it. Something gold in color leaves a dark streak? Imagine going to a chalkboard with a piece of white chalk only to find that the line you draw is red. Recognize that our assumptions lead to representations. Maybe that’s why we favor those Solar-System models of atoms in textbooks even though we have long determined their scientific limitations. Of course, as Gödel noted, even our formal, mathematical representations, though non-visualizable, also rely on assumptions.
Almost any explanation that fits our axioms also fits our emotional, if not also our mental, needs.
So, we accept representations that confirm our assumptions in our personal and professional relationships. That is particularly the case in our explaining the attitudes and behavior of those who differ from us. Did you ever listen to a political discussion between two people with differing viewpoints? (That’s almost unavoidable when you channel-surf) The speakers present you with two images or two representations that stem from a limited number of assumptions, often just two assumptions: One that underlies a favored perspective and another that underlies an un-favored one. On occasion, you hear someone argue from multiple assumptions, but that usually turns into a cacophony.
Think Euclid. Apparently, he thought just five axioms and five “common notions” made a sufficient basis for understanding shapes and relationships. Remember high school geometry? You spent an entire year on those five axioms and how they underlie geometric representations of shapes in our world. It wasn’t just a high school math course that made us Euclidean thinkers; we started our training as babies reaching for fire.
Every political discussion seems to follow the same process of representation that makes sense in the context of one or two assumptions, first about one’s own perspective and second about any alternative perspective. And just as we accept the faulty Bohr “Solar System” model of atoms, so we accept or reject representations of attitudes and behaviors because they fit our assumptions about a world that can’t in our eyes contradict what we base on those assumptions. Fire-eaters just have to be eating “cold fire.” Fool’s gold must have a dark color just underlying the brassy color on the surface: How else can it defy the representations we have? And electrons just make sense if they carry a charge and somehow orbit a nucleus like little planets.
And those with whom we find ourselves in contention certainly fall into the geometry that underlies our lives. They have to because, as Euclid told us, just a few axioms are necessary. They have to because, as Occam, Einstein, da Vinci, and others have told us, the simplest explanation is the best. As Clarence E. Bennett writes, “In other words, there can be any number of ways of explaining anything…It is not a question of which is the correct one; it is rather a question of which is the better one for the purpose, i.e., which explains the most with the fewest assumptions.”
*Bennett, Clarence E. Physics without Mathematics. Barnes & Noble, Inc. New York, 1970. P. 25.
In his popularization of physics, Clarence E. Bennett writes that “explanations are only relative to [ a person’s] background.” He made that statement in the context of Bohr’s model of the atom, the familiar one we see in textbooks that makes atoms look like little Solar Systems. “Although today this picture has been more or less replaced by abstract mathematical representation in the mind of the theoretical physicist, many of the Bohr features are still useful….” Bennett then says that this raises the “question of how a picture can be accepted if it is not correct…In other words, there can be any number of ways of explaining anything…It is not a question of which is the correct one; it is rather a question of which is the better one for the purpose, i.e., which explains the most with the fewest assumptions….”*
Do you agree? Surely, you have either provided or received such explanations. Think explaining the death of a pet or a favorite uncle to a toddler. Practically all of us gear our explanations to the background of the person, and that’s why textbooks have labels, such as “Introductory,” “Intermediate,” and “Advanced.”
As I have said elsewhere, all of us think axiomatically. We live mostly by “self-evident” truths; assumptions underlie everything. Certainly, you, for example, aren’t spending your current energy on anxiety that your screen will go blank. You assume no power outage even though you know such events occur, and you assume your chair and the floor beneath it will hold you. All of us have our own version of Occam’s Razor: Operate on as few assumptions as we can in the moment, and keep explanations simple. Many have extolled the virtue of simplicity in explanations, including Newton, Einstein, and da Vinci. Is there a similar virtue in the fewest possible assumptions, in the fewest axioms?
We just can’t get around our assumptions very easily because they’ve been incorporated into our education. And I don’t mean education as in what you learned in school though I can’t discount it. I’m thinking life lessons, those experiences that have added up to a world that doesn’t contradict itself, that, for example, fire is both hot and dangerous. Performances by fire-eaters tend to make audiences believe that there’s somehow a “cold fire” because the entertainer suffers no burns. Magicians, too, play on assumptions about a non-contradictory world. We assume what we witness is a trick because we can’t reconcile our assumptions with a disappearing elephant or a gravity-defying person.
To identify some minerals in the field, mineralogists use an unglazed ceramic plate that serves as a kind of “chalkboard.” Certain minerals leave a “streak” with a characteristic color much the way a piece of white chalk leaves a white line or green chalk leaves a green line on a piece of slate. You do the same with an ordinary pencil whose “lead” is actually a mix of graphite and clay. The graphite disintegrates on the paper, leaving a gray-black streak. You assume by experience that the color of an object will be the same as its streak. But brass-yellow pyrite (fool’s gold) leaves a greenish-black streak on the unglazed ceramic. That’s counterintuitive and amazes most people on first witnessing it. Something gold in color leaves a dark streak? Imagine going to a chalkboard with a piece of white chalk only to find that the line you draw is red. Recognize that our assumptions lead to representations. Maybe that’s why we favor those Solar-System models of atoms in textbooks even though we have long determined their scientific limitations. Of course, as Gödel noted, even our formal, mathematical representations, though non-visualizable, also rely on assumptions.
Almost any explanation that fits our axioms also fits our emotional, if not also our mental, needs.
So, we accept representations that confirm our assumptions in our personal and professional relationships. That is particularly the case in our explaining the attitudes and behavior of those who differ from us. Did you ever listen to a political discussion between two people with differing viewpoints? (That’s almost unavoidable when you channel-surf) The speakers present you with two images or two representations that stem from a limited number of assumptions, often just two assumptions: One that underlies a favored perspective and another that underlies an un-favored one. On occasion, you hear someone argue from multiple assumptions, but that usually turns into a cacophony.
Think Euclid. Apparently, he thought just five axioms and five “common notions” made a sufficient basis for understanding shapes and relationships. Remember high school geometry? You spent an entire year on those five axioms and how they underlie geometric representations of shapes in our world. It wasn’t just a high school math course that made us Euclidean thinkers; we started our training as babies reaching for fire.
Every political discussion seems to follow the same process of representation that makes sense in the context of one or two assumptions, first about one’s own perspective and second about any alternative perspective. And just as we accept the faulty Bohr “Solar System” model of atoms, so we accept or reject representations of attitudes and behaviors because they fit our assumptions about a world that can’t in our eyes contradict what we base on those assumptions. Fire-eaters just have to be eating “cold fire.” Fool’s gold must have a dark color just underlying the brassy color on the surface: How else can it defy the representations we have? And electrons just make sense if they carry a charge and somehow orbit a nucleus like little planets.
And those with whom we find ourselves in contention certainly fall into the geometry that underlies our lives. They have to because, as Euclid told us, just a few axioms are necessary. They have to because, as Occam, Einstein, da Vinci, and others have told us, the simplest explanation is the best. As Clarence E. Bennett writes, “In other words, there can be any number of ways of explaining anything…It is not a question of which is the correct one; it is rather a question of which is the better one for the purpose, i.e., which explains the most with the fewest assumptions.”
*Bennett, Clarence E. Physics without Mathematics. Barnes & Noble, Inc. New York, 1970. P. 25.
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