When Egan said any subject could be taught to any child at any stage of development, how young do you think he meant?
My oldest son is not quite two, and he loves to walk past our local elementary school and see their painting of the solar system along the wall. I'm happy to name all the planets for him, but I'm not sure how much that actually teaches him.
For now, my main strategy is to focus on things he sees in the real world. For example, he recently realized that he has a shadow. So I'll point out that his shadow points in different directions or gets longer or shorter at different times of day.
Noticing things about the world and asking why seems to me like the beginning of science, even if he's still too young to understand the explanation.
Oh, good to press that quote to its limit! Here's my spitball of an answer, in a few different chunks:
1. Though Egan quoted it approvingly (quite a few times, if memory serves) that line first came from psychologist Jerome Bruner. I think the context in which Egan quotes it was when he's talking about the Progressivist/Traditionalist curriculum war, where the question was "how young should schoolchildren learn about things like ancient history?"
2. So if I'm right, that quote isn't about kids who've yet to master language. (In Egan's paradigm, that'd be kids who have some "Somatic" understanding, but who are just dipping their toes into "Mythic".)
3. But how WOULD one teach the planets to a not-quite-two-year-old (if, for some reason, that was a thing someone really wanted to do)? I'm not sure — and am excited to be thinking about this! (Partly that's because I have an 8-month-old; partly that's because a number of other people with preschoolers have begun to ask.) Egan himself didn't much write about this age of kids, but some of his co-laborers have opened preschools.
4. You wrote: "Noticing things about the world and asking why seems to me like the beginning of science, even if he's still too young to understand the explanation." Absolutely — and Egan would emphasize that science also burbles out of reverie. (I talk about this a bit in the "Elementary Science" section of the book review; if you search it for "tree", you'll go right there.) So extended time out in the natural world is a must.
5. Hmm. That last bit seems incredibly important. I should probably emphasize that. Thanks for the productive question!
" A lot of this sounds very avant-garde, but I worry that it would really confuse kids, especially young ones.
You know who else was confused? Aristotle. Ptolemy. Copernicus. Galileo. Even Newton.²³ When it comes to the big picture of the Universe, if you’re not confused, you’re not paying attention."
The other big benefit to comfort with confusion is that it shows children that confusion is a natural part of the learning process, and not a signpost that says "STOP, wait for the teacher."
When confusion is part of the storytelling of science, and we're honest a lot of our theories *conflict* with day to day experience and require something beyond what you passively observe, we're representing the call to adventure of science well.
Yes, I love this! There’s something wonderful in what you’re saying about how this sort of teaching can allow kids to (get ready for a terrible metaphor) wallow in confusion without feeling the acrid burn of the mud…. I might leverage that for the next post, actually. Thanks!
Also, please tell us you think we should used Turns/Tao instead of PI. It seems like a person who feels strongly that the image of a solar system should be pictured so gravity should act downwards (genius btw) would appreciate that maybe in math class we shouldn’t be so obsessed with half circles :)
Wow! You’re cracking my brain open here — our whole system of trigonometry is EXPLICITLY a model of a flat Earth (no really, it’s incredible, and once you see it everything makes sense — a radius is just a sun ray. I learned this from the inimitable mathematician James Tanton, who is an essential piece of humanizing the math curriculum: https://youtu.be/Lr9Epp5eKUQ?si=sTIzclCIPaz9Q6zc).
But now I’m stymied: when we understand that a math conventions is based on a very wrong image, should that encourage us to change the convention? Up until now, I’ve been using it to get students to laugh as all the terminology (radius, sine, cosine…) clicks into place.
There’s definitely a post somewhere in here; thanks!
Interestingly I wrote an article here in Substack along similar lines of challenging my assumptions of what a species is. (Maybe why the algorithm led me here). I did already ask in your other post about the problems book, so I'll just repeat. I would love your insights about teaching High School Biology to an online class. Meanwhile I shall be exploring all of the resources you shared already.
Ha! As someone who teaches biology online, I know that if I start talking now, I'll never shut up! I enjoyed your post on species — if you'd like a handful of thoughts about how it might be Eganized, reach out to me on scienceisWEIRD.com, and I'd be honored to send you a quick email. (And if you'd be willing for me to expand on those thoughts, work with you to Eganize that post, and then turn that experience into something we could post here, let me know.)
An academic named Alec Ryrie gave a lecture (it's on YouTube) about atheism during the medieval period, and mentioned modern flat-earthers by way of comparison. After reading this, thought you might appreciate it:
***
The great French literary historian Lucien Febvre, whose argument that unbelief was impossible in earlier in pre-modern times, is now routinely dismissed by historians of the subject. But Febvre's point is more subtle than he's usually given credit for. He was well aware that pre-modern Europeans frequently attacked religion, sometimes in pretty scabrous terms, and also that they readily accused one another of unbelief. His point was that...these attacks and accusations had no intellectual substance, and as such, he concluded with magnificently Gallic disdain:
"Unbelief of this kind did not matter, historically speaking...It hardly deserves to be discussed any more than the sneers of the drunkard in the tavern who guffaws when he's told the earth is moving, under and with him, at such speed that it cannot even be felt."
...Let's hear the drunkard out. How do we here today know that Febvre's drunkard is wrong and that the earth is in fact moving? Not many of us have the astronomical skill to determine the question for ourselves. We believe it because we're universally told it's true by learned authority, because it's an important part of a wider web of knowledge that we have about the world around us, and because we've seen some very persuasive pictures explaining it. And yet, like Febvre's drunkard, we sometimes struggle to hold on to the fact. We still say that the sun rises, even though we know does no such thing. We treat the ground beneath our feet as if it were stationary. It feels stationary; for most practical purposes it might as well be.
To wonder nowadays whether the earth really is moving, you do not need to be a drunkard or a fool. what you need to be is independent minded and self-confident. You also need to be suspicious, ready to believe that you are being lied to, and it also helps if you are not very well educated. If you're woven too tightly into our civilization's web of knowledge, then you're not going to be able to kick against it.
If you want to see this at work, I recommend spending some time—not too much time—visiting the websites of modern flat-earther organizations, which in their stubborn refusal to be hoodwinked by the intellectual consensus of their age are the closest thing that our own world has to medieval atheists...
Whether you're a modern flat-earther or a medieval atheist, your lack of deep engagement with the dominant intellectual systems of your age makes your doubts possible, but also blunts their force. You might have some slogans and some hunches, but you won't be able to refute astronomers who come at you with their orbits and laws of motion, or theologians wielding essences and ontologies. All you can reply with is the mulish wisdom of the skeptic who is told to admire the stitching on the emperor's clothes: "I just don't see it."
You wrote: "If you want to see this at work, I recommend spending some time—not too much time—visiting the websites of modern flat-earther organizations, which in their stubborn refusal to be hoodwinked by the intellectual consensus of their age are the closest thing that our own world has to medieval atheists..."
Funnily enough, I have a chat planned with a leading flat-Earther this week! If it goes as well as I hope, I may write about it here...
This was a great read! The engineer in me is screaming that a 200 lbs astronaut does not weigh the same, because pounds (lbs) is a measurement of weight (i.e. directional force caused by gravity), not mass, which represents the collection of stuff that makes up a body (and, heaven help me, I have no idea where "slug" derived as the English system's unit for mass).
Is this not helpful because gravity and mass are too abstract? or is it important to understand why the further planets are "falling" slower (regardless of size/mass)?
I could be wrong, but I think the whole point is that an astronaut in space is still experiencing most of the gravitational pull towards the Earth. It’s just that he’s moving too fast horizontally to feel it.
Depending on the distance the astronaut is to the earth, then yeah, you could be right, but distance has an exponential impact on the force of gravity, so the force of it really deteriorates over distance... and I think it is the lack of air resistance that makes the astronaut not feel the movement... we don't really start to feel gravity until we are at multiple Gs and our body starts squashing in weird ways under the pressure.
It's interesting... we experience gravity pulling us down to earth, but the gravitational force is technically always operating between every object with mass. While the earth pulls on me, I pull back. My keyboard and my fingers are experiencing fluctuating amounts of gravitation pull towards each other as the distance changes as I type. (It kinda gets crazy, but this is why gravity is considered a weak force, because it's hardly noticeable compared to the nuclear and electromagnetic forces that maintain the integrity of every object and molecule.)
You're right that the astronaut doesn't weigh the same -- as Brandon pointed out, the astronaut will weigh about 180 pounds in low Earth orbit. For certain definitions of "weigh," of course. From an outside point of view, the astronaut is accelerating as if 180 pounds of force is being applied, but from the astronaut's point of view, it feels as if there's no force at all. The reason why you don't feel the force of gravity is a little complicated and has to do with Einstein's equivalence principle and the fact that gravity arises from curved spacetime (see this video for a more in-depth explanation: https://www.youtube.com/watch?v=NblR01hHK6U).
When you "feel" weight or gravity, what you're actually sensing is the force that's holding you in place against gravity trying to accelerate you toward the center of the Earth. Gravity pulls me against the ground, the ground pushes back because my electrons are repelling the ground's electrons, and that's the force I actually sense. In terms of free body diagrams, what you're feeling isn't gravity, but the normal force that opposes gravity.
As long as you're accelerating freely toward the center of the Earth with nothing opposing you, you will feel weightless regardless of how much force gravity is exerting on you. This is why roller coasters and zero-g flights cause weightlessness. The roller coaster or plane is accelerating with you, so you don't push on it and it doesn't push on you. Gravity hasn't changed; you've just taken away the normal force.
The sideways motion of an astronaut isn't important to feeling weightless. If you took an astronaut up to 400 km and just dropped them, they would feel as weightless as an astronaut in orbit. Which isn't to say that sideways motion is unimportant! It allows the astronaut to miss the Earth as they fall and so they can keep falling indefinitely. If you don't have sideways motion, you smack into the Earth pretty quickly and you stop feeling weightless (among other things).
Air resistance can provide the normal force (I believe this is what happens when a skydiver reaches terminal velocity) but you can still feel pretty weightless in Earth's atmosphere as long as you're not going fast enough for drag to create much force. I think the reason we have such a close mental association between vacuum and weightlessness is that you can't have an extended period of weightlessness near a massive body unless you're going fast enough to continually miss that body as you fall toward it. Maintaining that speed while flying through an atmosphere would take a lot of energy and might generate a noticeable force on its own.
Gravity does decrease with distance squared, but remember that you're measuring that distance from the center of the mass of the objects. The Earth has a radius of about 6400 km, and low Earth orbit is only about 400 km above the surface. Going from 6400 km to 6800 km decreases the force of gravity by only 10%. Which is where the 180 pound number comes from. And of course, the mass remains the same regardless of where you are.
Hi, I loved this post and your book review and I want to learn more. I teach jiu jitsu, mostly to 4-7 year olds, sometimes to adults. Would you recommend I start with The Educated Mind or Unsaddling Pedagogy or some other resource?
I'm taking jujitsu (I mean, I know everyone is, but I am too), and MAN have I spent some time thinking about this!
There isn't a great Egan book on that. If anything, I'd say flip through "An Imaginative Approach to Teaching". But you've gotten me thinking of what I could write on here... maybe I'll do a post unpacking the pull I feel toward the practice (as terrible at it as I am), and kicking around some ideas for how I think Egan could help people learn it more quickly.
I already use stories to teach the kids. I'm going to spend some time thinking about how to make the stories more mythical, and find places to add jokes.
Here's a fun supplemental note about Newton and the apple: there's an alternate version of the story. In this version, the apple doesn't fall on his head, but rather he sees the wind blow it off the tree and it falls in a (~)parabolic arc. This leads him to wonder what would happen if the wind was blowing faster. If it blew fast enough, the apple might never fall to the ground. And thus, he understood orbits.
I don't remember where (during my very long physics education) that I picked up this story, and I have no particular proof that it's any less apocryphal than the popular version. But it's certainly more inspiring!
When Egan said any subject could be taught to any child at any stage of development, how young do you think he meant?
My oldest son is not quite two, and he loves to walk past our local elementary school and see their painting of the solar system along the wall. I'm happy to name all the planets for him, but I'm not sure how much that actually teaches him.
For now, my main strategy is to focus on things he sees in the real world. For example, he recently realized that he has a shadow. So I'll point out that his shadow points in different directions or gets longer or shorter at different times of day.
Noticing things about the world and asking why seems to me like the beginning of science, even if he's still too young to understand the explanation.
Oh, good to press that quote to its limit! Here's my spitball of an answer, in a few different chunks:
1. Though Egan quoted it approvingly (quite a few times, if memory serves) that line first came from psychologist Jerome Bruner. I think the context in which Egan quotes it was when he's talking about the Progressivist/Traditionalist curriculum war, where the question was "how young should schoolchildren learn about things like ancient history?"
2. So if I'm right, that quote isn't about kids who've yet to master language. (In Egan's paradigm, that'd be kids who have some "Somatic" understanding, but who are just dipping their toes into "Mythic".)
3. But how WOULD one teach the planets to a not-quite-two-year-old (if, for some reason, that was a thing someone really wanted to do)? I'm not sure — and am excited to be thinking about this! (Partly that's because I have an 8-month-old; partly that's because a number of other people with preschoolers have begun to ask.) Egan himself didn't much write about this age of kids, but some of his co-laborers have opened preschools.
4. You wrote: "Noticing things about the world and asking why seems to me like the beginning of science, even if he's still too young to understand the explanation." Absolutely — and Egan would emphasize that science also burbles out of reverie. (I talk about this a bit in the "Elementary Science" section of the book review; if you search it for "tree", you'll go right there.) So extended time out in the natural world is a must.
5. Hmm. That last bit seems incredibly important. I should probably emphasize that. Thanks for the productive question!
" A lot of this sounds very avant-garde, but I worry that it would really confuse kids, especially young ones.
You know who else was confused? Aristotle. Ptolemy. Copernicus. Galileo. Even Newton.²³ When it comes to the big picture of the Universe, if you’re not confused, you’re not paying attention."
The other big benefit to comfort with confusion is that it shows children that confusion is a natural part of the learning process, and not a signpost that says "STOP, wait for the teacher."
When confusion is part of the storytelling of science, and we're honest a lot of our theories *conflict* with day to day experience and require something beyond what you passively observe, we're representing the call to adventure of science well.
Yes, I love this! There’s something wonderful in what you’re saying about how this sort of teaching can allow kids to (get ready for a terrible metaphor) wallow in confusion without feeling the acrid burn of the mud…. I might leverage that for the next post, actually. Thanks!
I loved this. Thank you 🙏
Also, please tell us you think we should used Turns/Tao instead of PI. It seems like a person who feels strongly that the image of a solar system should be pictured so gravity should act downwards (genius btw) would appreciate that maybe in math class we shouldn’t be so obsessed with half circles :)
Wow! You’re cracking my brain open here — our whole system of trigonometry is EXPLICITLY a model of a flat Earth (no really, it’s incredible, and once you see it everything makes sense — a radius is just a sun ray. I learned this from the inimitable mathematician James Tanton, who is an essential piece of humanizing the math curriculum: https://youtu.be/Lr9Epp5eKUQ?si=sTIzclCIPaz9Q6zc).
But now I’m stymied: when we understand that a math conventions is based on a very wrong image, should that encourage us to change the convention? Up until now, I’ve been using it to get students to laugh as all the terminology (radius, sine, cosine…) clicks into place.
There’s definitely a post somewhere in here; thanks!
I teach Biology and I am mind blown!
Interestingly I wrote an article here in Substack along similar lines of challenging my assumptions of what a species is. (Maybe why the algorithm led me here). I did already ask in your other post about the problems book, so I'll just repeat. I would love your insights about teaching High School Biology to an online class. Meanwhile I shall be exploring all of the resources you shared already.
Thank you a million times!
Ha! As someone who teaches biology online, I know that if I start talking now, I'll never shut up! I enjoyed your post on species — if you'd like a handful of thoughts about how it might be Eganized, reach out to me on scienceisWEIRD.com, and I'd be honored to send you a quick email. (And if you'd be willing for me to expand on those thoughts, work with you to Eganize that post, and then turn that experience into something we could post here, let me know.)
Oh definitely! Reaching out shortly.
And oh yes, us Biology teachers love to talk!
An academic named Alec Ryrie gave a lecture (it's on YouTube) about atheism during the medieval period, and mentioned modern flat-earthers by way of comparison. After reading this, thought you might appreciate it:
***
The great French literary historian Lucien Febvre, whose argument that unbelief was impossible in earlier in pre-modern times, is now routinely dismissed by historians of the subject. But Febvre's point is more subtle than he's usually given credit for. He was well aware that pre-modern Europeans frequently attacked religion, sometimes in pretty scabrous terms, and also that they readily accused one another of unbelief. His point was that...these attacks and accusations had no intellectual substance, and as such, he concluded with magnificently Gallic disdain:
"Unbelief of this kind did not matter, historically speaking...It hardly deserves to be discussed any more than the sneers of the drunkard in the tavern who guffaws when he's told the earth is moving, under and with him, at such speed that it cannot even be felt."
...Let's hear the drunkard out. How do we here today know that Febvre's drunkard is wrong and that the earth is in fact moving? Not many of us have the astronomical skill to determine the question for ourselves. We believe it because we're universally told it's true by learned authority, because it's an important part of a wider web of knowledge that we have about the world around us, and because we've seen some very persuasive pictures explaining it. And yet, like Febvre's drunkard, we sometimes struggle to hold on to the fact. We still say that the sun rises, even though we know does no such thing. We treat the ground beneath our feet as if it were stationary. It feels stationary; for most practical purposes it might as well be.
To wonder nowadays whether the earth really is moving, you do not need to be a drunkard or a fool. what you need to be is independent minded and self-confident. You also need to be suspicious, ready to believe that you are being lied to, and it also helps if you are not very well educated. If you're woven too tightly into our civilization's web of knowledge, then you're not going to be able to kick against it.
If you want to see this at work, I recommend spending some time—not too much time—visiting the websites of modern flat-earther organizations, which in their stubborn refusal to be hoodwinked by the intellectual consensus of their age are the closest thing that our own world has to medieval atheists...
Whether you're a modern flat-earther or a medieval atheist, your lack of deep engagement with the dominant intellectual systems of your age makes your doubts possible, but also blunts their force. You might have some slogans and some hunches, but you won't be able to refute astronomers who come at you with their orbits and laws of motion, or theologians wielding essences and ontologies. All you can reply with is the mulish wisdom of the skeptic who is told to admire the stitching on the emperor's clothes: "I just don't see it."
You wrote: "If you want to see this at work, I recommend spending some time—not too much time—visiting the websites of modern flat-earther organizations, which in their stubborn refusal to be hoodwinked by the intellectual consensus of their age are the closest thing that our own world has to medieval atheists..."
Funnily enough, I have a chat planned with a leading flat-Earther this week! If it goes as well as I hope, I may write about it here...
This was a great read! The engineer in me is screaming that a 200 lbs astronaut does not weigh the same, because pounds (lbs) is a measurement of weight (i.e. directional force caused by gravity), not mass, which represents the collection of stuff that makes up a body (and, heaven help me, I have no idea where "slug" derived as the English system's unit for mass).
Is this not helpful because gravity and mass are too abstract? or is it important to understand why the further planets are "falling" slower (regardless of size/mass)?
I could be wrong, but I think the whole point is that an astronaut in space is still experiencing most of the gravitational pull towards the Earth. It’s just that he’s moving too fast horizontally to feel it.
Depending on the distance the astronaut is to the earth, then yeah, you could be right, but distance has an exponential impact on the force of gravity, so the force of it really deteriorates over distance... and I think it is the lack of air resistance that makes the astronaut not feel the movement... we don't really start to feel gravity until we are at multiple Gs and our body starts squashing in weird ways under the pressure.
It's interesting... we experience gravity pulling us down to earth, but the gravitational force is technically always operating between every object with mass. While the earth pulls on me, I pull back. My keyboard and my fingers are experiencing fluctuating amounts of gravitation pull towards each other as the distance changes as I type. (It kinda gets crazy, but this is why gravity is considered a weak force, because it's hardly noticeable compared to the nuclear and electromagnetic forces that maintain the integrity of every object and molecule.)
You're right that the astronaut doesn't weigh the same -- as Brandon pointed out, the astronaut will weigh about 180 pounds in low Earth orbit. For certain definitions of "weigh," of course. From an outside point of view, the astronaut is accelerating as if 180 pounds of force is being applied, but from the astronaut's point of view, it feels as if there's no force at all. The reason why you don't feel the force of gravity is a little complicated and has to do with Einstein's equivalence principle and the fact that gravity arises from curved spacetime (see this video for a more in-depth explanation: https://www.youtube.com/watch?v=NblR01hHK6U).
When you "feel" weight or gravity, what you're actually sensing is the force that's holding you in place against gravity trying to accelerate you toward the center of the Earth. Gravity pulls me against the ground, the ground pushes back because my electrons are repelling the ground's electrons, and that's the force I actually sense. In terms of free body diagrams, what you're feeling isn't gravity, but the normal force that opposes gravity.
As long as you're accelerating freely toward the center of the Earth with nothing opposing you, you will feel weightless regardless of how much force gravity is exerting on you. This is why roller coasters and zero-g flights cause weightlessness. The roller coaster or plane is accelerating with you, so you don't push on it and it doesn't push on you. Gravity hasn't changed; you've just taken away the normal force.
The sideways motion of an astronaut isn't important to feeling weightless. If you took an astronaut up to 400 km and just dropped them, they would feel as weightless as an astronaut in orbit. Which isn't to say that sideways motion is unimportant! It allows the astronaut to miss the Earth as they fall and so they can keep falling indefinitely. If you don't have sideways motion, you smack into the Earth pretty quickly and you stop feeling weightless (among other things).
Air resistance can provide the normal force (I believe this is what happens when a skydiver reaches terminal velocity) but you can still feel pretty weightless in Earth's atmosphere as long as you're not going fast enough for drag to create much force. I think the reason we have such a close mental association between vacuum and weightlessness is that you can't have an extended period of weightlessness near a massive body unless you're going fast enough to continually miss that body as you fall toward it. Maintaining that speed while flying through an atmosphere would take a lot of energy and might generate a noticeable force on its own.
Gravity does decrease with distance squared, but remember that you're measuring that distance from the center of the mass of the objects. The Earth has a radius of about 6400 km, and low Earth orbit is only about 400 km above the surface. Going from 6400 km to 6800 km decreases the force of gravity by only 10%. Which is where the 180 pound number comes from. And of course, the mass remains the same regardless of where you are.
Hi, I loved this post and your book review and I want to learn more. I teach jiu jitsu, mostly to 4-7 year olds, sometimes to adults. Would you recommend I start with The Educated Mind or Unsaddling Pedagogy or some other resource?
I'm taking jujitsu (I mean, I know everyone is, but I am too), and MAN have I spent some time thinking about this!
There isn't a great Egan book on that. If anything, I'd say flip through "An Imaginative Approach to Teaching". But you've gotten me thinking of what I could write on here... maybe I'll do a post unpacking the pull I feel toward the practice (as terrible at it as I am), and kicking around some ideas for how I think Egan could help people learn it more quickly.
I already use stories to teach the kids. I'm going to spend some time thinking about how to make the stories more mythical, and find places to add jokes.
Here's a fun supplemental note about Newton and the apple: there's an alternate version of the story. In this version, the apple doesn't fall on his head, but rather he sees the wind blow it off the tree and it falls in a (~)parabolic arc. This leads him to wonder what would happen if the wind was blowing faster. If it blew fast enough, the apple might never fall to the ground. And thus, he understood orbits.
I don't remember where (during my very long physics education) that I picked up this story, and I have no particular proof that it's any less apocryphal than the popular version. But it's certainly more inspiring!
How do you do that alt-text footnote thing? I dig that.