I might well be. Given the value of empiricism-type virtues, anyone want to go test it (by creating an operationalized notion of what it is to understand the heuristics, and then finding randomly choosing several people independently from e.g. your local grocery store and testing it on them), and let us know the results?
Jasen Murray and Marcello and I tried this the other day concerning what portion of native English speaking American adults know what a “sphere” is (“a ball” or “orange-shaped” count; “a circle” doesn’t), and found that of the five we sampled, three knew and two didn’t.
I once taught middle- and high-school teachers who wanted to get certified to teach math. I was a TA for a class in geometry (basically 8th or 9th grade Euclidean geometry.) I had an incredibly hard time explaining to them that “draw a circle with center point A” means that A goes in the middle of the circle, instead of on the boundary. As I recall, it took more than a week of daily problem sessions before they got that.
Of course, I may have been a bad teacher. But I was trying.
I find that very surprising; I thought of using “circle” to refer to just the boundary and not the interior as being primarily a mathematical usage… though I suppose not to the same extent as it is with “sphere”.
Marcello and I and (damnit, I can’t remember who) tried this the other day >concerning what portion of native English speaking American adults know what a >”sphere” is (“a ball” or “orange-shaped” count; “a circle” doesn’t), and found that of >the five we sampled, three knew and two didn’t.
Did you do this test by asking them to define the word “sphere” verbally? Because I can easily imagine a less-articulate person saying “circle” when they really do understand the difference between a plane figure and a sphere. It might be better to ask them to select which of a given set of objects is a sphere, or even to name something that is shaped like a sphere, although in the latter case they might use the rote knowledge that the earth is a sphere, which could create bias in the opposite direction.
My estimate would be far on the other side: I think at least 95% of the population could understand and agree with those heuristics. I pay less attention to what people say they understand, and look at what they do, and am usually impressed by how intelligent people are—in ways academic tests would not typically fully measure.
.. I think only 5% could compose these heuristics, if asked to. And only half of 1% could know to compose them, without being told to…
Regarding your study, I’m not sure what you could deduce other than that ‘sphere’ is not in common usage, at least not as the geometric object. (For example, any 4 year old child can distinguish a sphere from other shapes, and then ‘sphere’ is just a label.)
Perhaps ‘sphere of influence’ is heard slightly more frequently than sphere as a geometric object. I would expect that the former connotation, if superseding the geometric one, would result in a little confusion and waving of hands, since it is so abstract.
Did the ones who failed to give correct answers say something like “a species of worm found in south America,” or did they refrain altogether from answering—possibly from fear of a trick question, or that they might be asked to explain the Banach-Tarski theorem about sphere doubling via the axiom of choice if they worded their answer in a way vulnerable to that?
Did you hold clipboards or wear lab coats while doing the questioning?
We tried to be friendly and unintimidating and, if asked, we explained with a bit of embarrassment that it had to do with a bet. Many just assumed we needed to know what a “sphere” was, though. We might have said we weren’t looking for a fancy answer, I’m not sure. (Ideal, if you want to repeat this experiment, would be to get a child to do the asking and to say it’s for their homework or something.) I don’t clearly remember what wrong answers we got; it’s possible that someone said “Does it mean circle-shaped?” but couldn’t give follow-up detail and someone else, who looked rather blank, said something like “Um. ‘Sphere?’ Do you know what that is, Frank?” and then asked the man she was with, who answered correctly.
Like SarahC, I used to tutor folks who were en route to becoming high school math teachers, and who had to pass a math exam to be allowed to teach. Many of them genuinely didn’t know what a sphere was, in the sense that often their eyes would light up if I told them that “sphere” meant “ball-shaped” (and, if I didn’t, they would memorize the formula for the volume of a sphere but would often not know they could apply it to estimate the volume of a ball). This was one of those pieces that I initially didn’t realize I needed to teach. Other such pieces included e.g. the fact that a “square centimeter” is a 1-cm by 1-cm square, that “area” is about how many such squares it takes to cover a given shape, that one can find the area of a compound shape by adding or subtracting the area of the components, and that there is a difference in meaning between “If A, then B” and “If B, then A”.
It is important to note that real Bayesians wear robes, not lab coats. And they carry with them archival quality notebooks and archival quality pens. Lab coats are just silly.
...in the weeks and months that followed, San Franciscans became accustomed to being accosted and asked a brief series of questions by a friendly young person carrying an archival quality notebook and wearing a clown suit.
I might well be. Given the value of empiricism-type virtues, anyone want to go test it (by creating an operationalized notion of what it is to understand the heuristics, and then finding randomly choosing several people independently from e.g. your local grocery store and testing it on them), and let us know the results?
Jasen Murray and Marcello and I tried this the other day concerning what portion of native English speaking American adults know what a “sphere” is (“a ball” or “orange-shaped” count; “a circle” doesn’t), and found that of the five we sampled, three knew and two didn’t.
I once taught middle- and high-school teachers who wanted to get certified to teach math. I was a TA for a class in geometry (basically 8th or 9th grade Euclidean geometry.) I had an incredibly hard time explaining to them that “draw a circle with center point A” means that A goes in the middle of the circle, instead of on the boundary. As I recall, it took more than a week of daily problem sessions before they got that.
Of course, I may have been a bad teacher. But I was trying.
I find that very surprising; I thought of using “circle” to refer to just the boundary and not the interior as being primarily a mathematical usage… though I suppose not to the same extent as it is with “sphere”.
Did you do this test by asking them to define the word “sphere” verbally? Because I can easily imagine a less-articulate person saying “circle” when they really do understand the difference between a plane figure and a sphere. It might be better to ask them to select which of a given set of objects is a sphere, or even to name something that is shaped like a sphere, although in the latter case they might use the rote knowledge that the earth is a sphere, which could create bias in the opposite direction.
My estimate would be far on the other side: I think at least 95% of the population could understand and agree with those heuristics. I pay less attention to what people say they understand, and look at what they do, and am usually impressed by how intelligent people are—in ways academic tests would not typically fully measure.
.. I think only 5% could compose these heuristics, if asked to. And only half of 1% could know to compose them, without being told to…
Regarding your study, I’m not sure what you could deduce other than that ‘sphere’ is not in common usage, at least not as the geometric object. (For example, any 4 year old child can distinguish a sphere from other shapes, and then ‘sphere’ is just a label.)
Perhaps ‘sphere of influence’ is heard slightly more frequently than sphere as a geometric object. I would expect that the former connotation, if superseding the geometric one, would result in a little confusion and waving of hands, since it is so abstract.
What about “a 3D circle”?
We counted that as correct.
Did the ones who failed to give correct answers say something like “a species of worm found in south America,” or did they refrain altogether from answering—possibly from fear of a trick question, or that they might be asked to explain the Banach-Tarski theorem about sphere doubling via the axiom of choice if they worded their answer in a way vulnerable to that?
Did you hold clipboards or wear lab coats while doing the questioning?
We tried to be friendly and unintimidating and, if asked, we explained with a bit of embarrassment that it had to do with a bet. Many just assumed we needed to know what a “sphere” was, though. We might have said we weren’t looking for a fancy answer, I’m not sure. (Ideal, if you want to repeat this experiment, would be to get a child to do the asking and to say it’s for their homework or something.) I don’t clearly remember what wrong answers we got; it’s possible that someone said “Does it mean circle-shaped?” but couldn’t give follow-up detail and someone else, who looked rather blank, said something like “Um. ‘Sphere?’ Do you know what that is, Frank?” and then asked the man she was with, who answered correctly.
Like SarahC, I used to tutor folks who were en route to becoming high school math teachers, and who had to pass a math exam to be allowed to teach. Many of them genuinely didn’t know what a sphere was, in the sense that often their eyes would light up if I told them that “sphere” meant “ball-shaped” (and, if I didn’t, they would memorize the formula for the volume of a sphere but would often not know they could apply it to estimate the volume of a ball). This was one of those pieces that I initially didn’t realize I needed to teach. Other such pieces included e.g. the fact that a “square centimeter” is a 1-cm by 1-cm square, that “area” is about how many such squares it takes to cover a given shape, that one can find the area of a compound shape by adding or subtracting the area of the components, and that there is a difference in meaning between “If A, then B” and “If B, then A”.
It is important to note that real Bayesians wear robes, not lab coats. And they carry with them archival quality notebooks and archival quality pens. Lab coats are just silly.
...in the weeks and months that followed, San Franciscans became accustomed to being accosted and asked a brief series of questions by a friendly young person carrying an archival quality notebook and wearing a clown suit.
… I think San Franciscans are already accustomed to that. It’s just that kind of place.
My memory suggests either Jasen or Louie.
Thanks, Kaj.