If you start changing the definitions of your metrics, you should expect different results. Like, if I start changing the definition of who the richest person in the world is by measuring total...
Exemplary
As it turns out, by some phenomenon of carelessness, ambiguity, or groupthink, science popularizers have disseminated information based on a flawed assumption about the average distance between planets. Using a mathematical method that we devised, we determine that when averaged over time, Earth’s nearest neighbor is in fact Mercury.
If you start changing the definitions of your metrics, you should expect different results. Like, if I start changing the definition of who the richest person in the world is by measuring total square footage of land they own, or total liquid assets, instead of the total of all of their assets, I assume the richest person by those different metrics are not the same (or at least the relative ordering of all persons is not the same).
While the math is neat, I don’t think the explanation of the motivation for which metric is better was sufficient. I understand the two metrics presented are different, but explaining why one metric is better than another (or why they are merely different but equal) is basically the most important thing a scientist needs to do when speaking to a lay audience. I guess, from my lay perspective, I don’t really care, probabilistically, which planet is closest to which other. So, if you tell me that Mercury is the closest planet to all other planets according to this metric, I’ll accept it, but I don’t really see how that is useful (other than as a piece of trivia—same as the naive metric of considering the difference in radii of orbits).
What is the flaw in the popular, naive method? That it doesn’t agree with this newly proposed metric? That is not a flaw! That is just a difference. You need to make a better case for why your metric is superior other than it’s different, newer, and requires integration.
I think you're overthinking it. I read that as a tongue in cheek poke at common knowledge. I don't think they're actually proposing that we teach that the order of plants have changed; it's more...
I think you're overthinking it. I read that as a tongue in cheek poke at common knowledge.
I don't think they're actually proposing that we teach that the order of plants have changed; it's more an interesting discovery of how close we are, on average, to another planet.
I know you’re not trying to attack me, but I really take offense at this. I didn’t overthink this. I merely thought about it critically. I expect the content on here to be thoughtful, and to stand...
I think you're overthinking it.
I know you’re not trying to attack me, but I really take offense at this. I didn’t overthink this. I merely thought about it critically. I expect the content on here to be thoughtful, and to stand up to critical thought from readers. I can get mindless fluff most places on the web—I come here with higher expectations.
This is intended as merely an item of mathematical interest, not as a sweeping revision of planetary education. I would argue that this is pretty close to an example of pure mathematics, not...
This is intended as merely an item of mathematical interest, not as a sweeping revision of planetary education. I would argue that this is pretty close to an example of pure mathematics, not applied physics, and I would also argue that pure mathematics is not "mindless fluff". I don't want to put words in your mouth, so I'll simply ask: are you saying that Mathematics that isn't applied is "mindless fluff"? To me, it's the most mindful fluff around.
It’s presented in the domain of astrophysics, though, not pure math. I have no qualms with presenting math. My issue was with the article taking the position that they were correcting some...
It’s presented in the domain of astrophysics, though, not pure math. I have no qualms with presenting math. My issue was with the article taking the position that they were correcting some long-standing problem. If they just framed it as, “here’s a novel way of computing the distances between planets”, that would be fine. Instead they editorialize it in a way that took a strong position which is not backed up at all (maybe there is a way to back it up, but they didn’t present it). That’s my issue. The math, and the explanation, I agree, is neat. The presentation is problematic.
Your demand for an argument in support of a clear "superior" methodology for understanding the distance between planets in our solar system eclipses what I feel is the more important impression of...
That is just a difference.
Your demand for an argument in support of a clear "superior" methodology for understanding the distance between planets in our solar system eclipses what I feel is the more important impression of this finding: that we should strive to understand simple concepts like "how far apart the planets are" in as many different ways as we can.
What this article presents is an alternative way of thinking about the distance between our planets. What's the flaw in the popular naive method, you ask? The fact that it is presented as the final, definitive answer to a question which in fact is deceptively simple.
Your argument is like demanding someone make a case for why knives should be used for spreading butter, as opposed to cutting potatoes. They are different use cases. We are talking about understanding the concept of distance between planets from two separate vantage points.
So I have two questions for you.
What is problematic about the way the article presents this alternate understanding of distance between planets?
What makes the popular method superior to this one?
Imo, from a rocketry position, the metric from the article is... misleading, bordering on inferior. The cost of travel usually comes from the dV (velocity change) expended for the required orbital...
What makes the popular method superior to this one?
Imo, from a rocketry position, the metric from the article is... misleading, bordering on inferior. The cost of travel usually comes from the dV (velocity change) expended for the required orbital maneuvers. Venus is cheaper there than mercury, though there is nonlinearities all over the place, which makes generalized statements hard. On top of that, in interplanetary travel, you'd of course wait for a decent window of opportunity, thus averaging over all constellations is misleading again; the optimal path counts. (The average path to rome, assuming there exists at least one circle, is infinitely long. Yeah, better to use that min operator.) Now, if one insists on using straight-line distance, at least give it a square-root discount. Why? If we assume that at some point, we'll have engines that can burn extremely long -which is a reasonable precondition to throwing out the "just wait for a launch window" and optimal-energy arguments- then the optimal path is to accellerate towards the target half of the way and use the rest of the way to slow down. Your covered distance grows as the square of the invested time. Hence, square root the distance before averaging. I have to admit: that does bring mercury closer, relatively.
Of course, for other domains (amateur astronomy anyone?) other concerns might apply. The above holds only as it relates to current-day rocketry and orbital mechanics.
I already laid out my problem with the way the article lays it out: the author takes a strong, editorial position and then never backs it up. I never claimed it was superior so I don’t there’s any...
What is problematic about the way the article presents this alternate understanding of distance between planets?
I already laid out my problem with the way the article lays it out: the author takes a strong, editorial position and then never backs it up.
What makes the popular method superior to this one?
I never claimed it was superior so I don’t there’s any onus on me to defend that position.
I thought this was a delightful non-obvious result of some (not-really applicable to anything) applied mathematics. Earth's closest planetary neighbour based on the average distance away is...
I thought this was a delightful non-obvious result of some (not-really applicable to anything) applied mathematics.
Earth's closest planetary neighbour based on the average distance away is actually Mercury, and in fact Mercury is the closest neighbour, by average distance, to every other planet.
If you start changing the definitions of your metrics, you should expect different results. Like, if I start changing the definition of who the richest person in the world is by measuring total square footage of land they own, or total liquid assets, instead of the total of all of their assets, I assume the richest person by those different metrics are not the same (or at least the relative ordering of all persons is not the same).
While the math is neat, I don’t think the explanation of the motivation for which metric is better was sufficient. I understand the two metrics presented are different, but explaining why one metric is better than another (or why they are merely different but equal) is basically the most important thing a scientist needs to do when speaking to a lay audience. I guess, from my lay perspective, I don’t really care, probabilistically, which planet is closest to which other. So, if you tell me that Mercury is the closest planet to all other planets according to this metric, I’ll accept it, but I don’t really see how that is useful (other than as a piece of trivia—same as the naive metric of considering the difference in radii of orbits).
What is the flaw in the popular, naive method? That it doesn’t agree with this newly proposed metric? That is not a flaw! That is just a difference. You need to make a better case for why your metric is superior other than it’s different, newer, and requires integration.
I think you're overthinking it. I read that as a tongue in cheek poke at common knowledge.
I don't think they're actually proposing that we teach that the order of plants have changed; it's more an interesting discovery of how close we are, on average, to another planet.
I know you’re not trying to attack me, but I really take offense at this. I didn’t overthink this. I merely thought about it critically. I expect the content on here to be thoughtful, and to stand up to critical thought from readers. I can get mindless fluff most places on the web—I come here with higher expectations.
This is intended as merely an item of mathematical interest, not as a sweeping revision of planetary education. I would argue that this is pretty close to an example of pure mathematics, not applied physics, and I would also argue that pure mathematics is not "mindless fluff". I don't want to put words in your mouth, so I'll simply ask: are you saying that Mathematics that isn't applied is "mindless fluff"? To me, it's the most mindful fluff around.
It’s presented in the domain of astrophysics, though, not pure math. I have no qualms with presenting math. My issue was with the article taking the position that they were correcting some long-standing problem. If they just framed it as, “here’s a novel way of computing the distances between planets”, that would be fine. Instead they editorialize it in a way that took a strong position which is not backed up at all (maybe there is a way to back it up, but they didn’t present it). That’s my issue. The math, and the explanation, I agree, is neat. The presentation is problematic.
Your demand for an argument in support of a clear "superior" methodology for understanding the distance between planets in our solar system eclipses what I feel is the more important impression of this finding: that we should strive to understand simple concepts like "how far apart the planets are" in as many different ways as we can.
What this article presents is an alternative way of thinking about the distance between our planets. What's the flaw in the popular naive method, you ask? The fact that it is presented as the final, definitive answer to a question which in fact is deceptively simple.
Your argument is like demanding someone make a case for why knives should be used for spreading butter, as opposed to cutting potatoes. They are different use cases. We are talking about understanding the concept of distance between planets from two separate vantage points.
So I have two questions for you.
What is problematic about the way the article presents this alternate understanding of distance between planets?
What makes the popular method superior to this one?
Thank you for your comment.
Imo, from a rocketry position, the metric from the article is... misleading, bordering on inferior. The cost of travel usually comes from the dV (velocity change) expended for the required orbital maneuvers. Venus is cheaper there than mercury, though there is nonlinearities all over the place, which makes generalized statements hard. On top of that, in interplanetary travel, you'd of course wait for a decent window of opportunity, thus averaging over all constellations is misleading again; the optimal path counts. (The average path to rome, assuming there exists at least one circle, is infinitely long. Yeah, better to use that min operator.) Now, if one insists on using straight-line distance, at least give it a square-root discount. Why? If we assume that at some point, we'll have engines that can burn extremely long -which is a reasonable precondition to throwing out the "just wait for a launch window" and optimal-energy arguments- then the optimal path is to accellerate towards the target half of the way and use the rest of the way to slow down. Your covered distance grows as the square of the invested time. Hence, square root the distance before averaging. I have to admit: that does bring mercury closer, relatively.
Of course, for other domains (amateur astronomy anyone?) other concerns might apply. The above holds only as it relates to current-day rocketry and orbital mechanics.
I already laid out my problem with the way the article lays it out: the author takes a strong, editorial position and then never backs it up.
I never claimed it was superior so I don’t there’s any onus on me to defend that position.
Ok then, perhaps I misunderstood what you were saying slightly. I reread your comment and I think I agree with what you're saying for the most part.
No worries! No harm in asking for clarification.
I thought this was a delightful non-obvious result of some (not-really applicable to anything) applied mathematics.
Earth's closest planetary neighbour based on the average distance away is actually Mercury, and in fact Mercury is the closest neighbour, by average distance, to every other planet.
That's something that I had never considered before, and it tripped me out haha