The centre of gravitational mass will be the same point as the centre of mass.
So? Just because they coincide doesn't make them the same concept. That's like calling the kilogram a unit of weight.
the ham sandwich theorem deals with volume rather than with mass
Why? That's dumb. I want to slap whoever decided that, too. If you want to approximate ham and bread as uniform-density solids, fine... I'd rather leave density in the equation. I damn well know that if the ham has a big chunk of fat on one side I still don't want one half of the sandwich being mostly fat.
We've grown rather off-topic from the original point.
My original point was that "cutting through the center of mass" isn't any more "obviously wrong" than "splitting in two parts of equal volume" when you're trying to define the ambiguous phrase "cutting in half". Both of them are "obviously wrong" if you're talking about the most obvious way to split Mt. Everest into top and bottom halves.
Furthermore, there's absolutely no reason to define the problem as "divide x into two parts of equal volume" when you can just as easily define the problem as "divide x into two parts of equal mass", particularly since you can convert the latter into the former just by assuming constant density.
Yes, to such a degree that it is the difference between impossible and possible.
What you're saying amounts to "but it's too hard".
And if you're bisecting by mood, you can just hang it up, until you get rid of that variable. You can always generalize an overly simple model and sure, you generally can simplify a complex model, but you can't always derive a complex model to simplify.
Yes... because it's extremely hard to define a theoretical model to describe how you bisect something by mass. So hard, in fact, that scientists should just pretend mass doesn't exist and approximate everything as a uniform-density solid of a particular volume and shape.
Agreed. There is already a perfectly good way of tracking valuable slips of paper.
Recently I had in my hand a slip of paper worth over $600. I presented it to a guy, he held it under a blinking light for a moment, and something went "ding" and a light turned green. Then he let me on the plane.
If we needed to track every last hundred dollar bill, we could already be doing it. There are perfectly good ways already. The reason we're not is because it would require expensive new equipment being rolled out nationwide and finding some way to get people's money to pass through it so it can be tracked, and although the technology to put electronics on banknotes may be fascinating I don't see that it changes any of those things.
The thing about bisections into equal volumes, is that it happens to be particularly parsimonious. That is, it requires very little information to define the concept and design an algorithm which yields the desired bisection.
What you're saying amounts to "but it's easier this way".
By the same argument it makes the most sense to bisect Mt. Everest into top and bottom halves of equal height, because I can do that with a single picture and a ruler (very little information), whereas bisecting it into halves of equal volume would require, at the least, two pictures from different angles to give me a rough idea of its 3-dimensional shape.
It makes the most sense to take into consideration as many different properties as possible, because you can always just assign them constant values later and they'll fall out of the equation. If you define bisection in terms of bisecting something by mass, you can always simply assume that the density is near-uniform... lo and behold, now you're bisecting by volume.
There's no "right" or "wrong" place to cut it. There is only a "correct" place to cut it if you want to bisect it by volume, which most people don't want to do, and therefore it's quite wrong to do that in most situations.
There's a million different ways to cut it, and all of them are "right" answers to different questions. So what's the right question?
Suppose you're trying to divide an apple and an orange between two children, giving them equal portions. The boy says apples and oranges are both fruit, so it would be fair to give one of them the apple and the other the orange since they'll have equal amounts of fruit. The girl contradicts that and says that apples and oranges are not really the same and she likes both kinds, so in order to really be fair they should each get half an apple and half an orange. Then the boy retorts that he doesn't like oranges and she likes both kinds, and it wouldn't be fair for her to have two kinds of fruit that she likes while he only gets one kind that he likes and one that he doesn't... so to really be fair she should have to eat the orange and let him eat the apple. And then the girl suggests that to be fair they should be allowed to take turns on alternating days to decide how to divide their fruit!
Even in such a very simple situation there's more than one way that you could divide things to be "equal", and the only "obvious" answer is that there is no "obvious" answer. Also, I'd hate being a parent.
I'm not sure which makes me want to slap you more... the fact that you needlessly restricted the attribute of matter to its "center of gravity" instead of its "center of mass", or the fact that you then relaxed back to the general word "mass" in referring to the property which you'd just indicated was specifically its gravitational mass.
And... for those of us who are neither scientists nor athletes (which should be pretty much all of us)... it's a bit like saying "Ford's truck model they built that one year".
Of course you can bisect anything by volume. But is it obvious that you ought to? Most people, I suspect, would logically bisect Mt. Everest into "top" and "bottom" halves by altitude, not by volume. I was countering Anonymous Coward's claim that the "obvious" way to bisect something is by volume.
If we approximated Mt. Everest as a perfect sphere of constant density, it wouldn't matter how you bisected it, because no matter which method you selected (height, cross-sectional area, volume, or mass) they would all give exactly identical results. But real-world objects usually aren't perfect spheres, and often don't have a reasonably-constant density.
If the subjective states of "better" and "worse" are defined in such a way that "nothing" is, in fact, preferred over "eternal happiness", then yes, a ham sandwich is "better" than eternal happiness.
For instance, if the problem is referring to someone you hate, you'd prefer them to have a ham sandwich instead. Especially if they can't eat pork.
You could wave away some of that by saying the meat is all one "piece" for purposed of discussion, but that might only appease the physicists and engineers.
No, the physicists have already approximated the pieces as point masses and they are all trying to figure out why you want to cut them in half.
Actually it's a theorem that was postulated by a pig named Ben who ruminated for a while and realised that in 4-space pigs would be kosher because there would be a specific 3-dimensional hyperplane which would split their 4 feet precisely in halves.
That "blocks all new websites shortly after they are created" kinda implies they have a list of all known websites.
They do. Once an employee visits the site, they know about it. They have logs.
Apparently their firewall rule allows visits to unknown websites on the first visit. Then, presumably after the first visit or a predefined length of time after it, the site is blacklisted. So that LOLcat link you got in your e-mail works once, cause apparently their IT department doesn't want to seem like a complete bunch of killjoys, but you won't be spending hours there, because you're at work. And if a site gets blacklisted that you actually need for work purposes, well, they're sure they'll hear about it pretty soon and they can move it from the blacklist to the whitelist.
Slashdot Mirror
Yes, I'm well aware that the 2nd assertion doesn't grammatically mean what it's logically asserted to mean.
The centre of gravitational mass will be the same point as the centre of mass.
So? Just because they coincide doesn't make them the same concept. That's like calling the kilogram a unit of weight.
the ham sandwich theorem deals with volume rather than with mass
Why? That's dumb. I want to slap whoever decided that, too. If you want to approximate ham and bread as uniform-density solids, fine... I'd rather leave density in the equation. I damn well know that if the ham has a big chunk of fat on one side I still don't want one half of the sandwich being mostly fat.
What you call the Ham Sandwich Theorem is true, trivial, and most definitely _not_ the Ham Sandwich Theorem.
So? He added another dimension (density) and called it the ham sandwich theorem.
If you cut a body by a plane through its center of gravity you _do not_ necessarily have equal volumes on either side of the plane.
He didn't say you have equal volumes. He said you have equal masses.
We've grown rather off-topic from the original point.
My original point was that "cutting through the center of mass" isn't any more "obviously wrong" than "splitting in two parts of equal volume" when you're trying to define the ambiguous phrase "cutting in half". Both of them are "obviously wrong" if you're talking about the most obvious way to split Mt. Everest into top and bottom halves.
Furthermore, there's absolutely no reason to define the problem as "divide x into two parts of equal volume" when you can just as easily define the problem as "divide x into two parts of equal mass", particularly since you can convert the latter into the former just by assuming constant density.
Yes, to such a degree that it is the difference between impossible and possible.
What you're saying amounts to "but it's too hard".
And if you're bisecting by mood, you can just hang it up, until you get rid of that variable. You can always generalize an overly simple model and sure, you generally can simplify a complex model, but you can't always derive a complex model to simplify.
Yes... because it's extremely hard to define a theoretical model to describe how you bisect something by mass. So hard, in fact, that scientists should just pretend mass doesn't exist and approximate everything as a uniform-density solid of a particular volume and shape.
Agreed. There is already a perfectly good way of tracking valuable slips of paper.
Recently I had in my hand a slip of paper worth over $600. I presented it to a guy, he held it under a blinking light for a moment, and something went "ding" and a light turned green. Then he let me on the plane.
If we needed to track every last hundred dollar bill, we could already be doing it. There are perfectly good ways already. The reason we're not is because it would require expensive new equipment being rolled out nationwide and finding some way to get people's money to pass through it so it can be tracked, and although the technology to put electronics on banknotes may be fascinating I don't see that it changes any of those things.
The thing about bisections into equal volumes, is that it happens to be particularly parsimonious. That is, it requires very little information to define the concept and design an algorithm which yields the desired bisection.
What you're saying amounts to "but it's easier this way".
By the same argument it makes the most sense to bisect Mt. Everest into top and bottom halves of equal height, because I can do that with a single picture and a ruler (very little information), whereas bisecting it into halves of equal volume would require, at the least, two pictures from different angles to give me a rough idea of its 3-dimensional shape.
It makes the most sense to take into consideration as many different properties as possible, because you can always just assign them constant values later and they'll fall out of the equation. If you define bisection in terms of bisecting something by mass, you can always simply assume that the density is near-uniform... lo and behold, now you're bisecting by volume.
Actually, no it wouldn't be.
There's no "right" or "wrong" place to cut it. There is only a "correct" place to cut it if you want to bisect it by volume, which most people don't want to do, and therefore it's quite wrong to do that in most situations.
There's a million different ways to cut it, and all of them are "right" answers to different questions. So what's the right question?
Suppose you're trying to divide an apple and an orange between two children, giving them equal portions. The boy says apples and oranges are both fruit, so it would be fair to give one of them the apple and the other the orange since they'll have equal amounts of fruit. The girl contradicts that and says that apples and oranges are not really the same and she likes both kinds, so in order to really be fair they should each get half an apple and half an orange. Then the boy retorts that he doesn't like oranges and she likes both kinds, and it wouldn't be fair for her to have two kinds of fruit that she likes while he only gets one kind that he likes and one that he doesn't... so to really be fair she should have to eat the orange and let him eat the apple. And then the girl suggests that to be fair they should be allowed to take turns on alternating days to decide how to divide their fruit!
Even in such a very simple situation there's more than one way that you could divide things to be "equal", and the only "obvious" answer is that there is no "obvious" answer. Also, I'd hate being a parent.
What's more, they've applied the known fact that any 3 points define a plane in 3-space and if you could "cut" a point in half with a plane, obviously its two halves on the two sides of the plane would have equal masses, so it's quite bleedingly obvious that any plane that cuts all 3 points also bisects the 3 objects they represent.
center of gravity ... mass
I'm not sure which makes me want to slap you more... the fact that you needlessly restricted the attribute of matter to its "center of gravity" instead of its "center of mass", or the fact that you then relaxed back to the general word "mass" in referring to the property which you'd just indicated was specifically its gravitational mass.
/pedant
Why would you want to divide a sandwich by volume? To check you'd have to dunk it in water and then it'd be all soggy. Gross.
You divide it into halves by weight, and then you check it with a grocer's scale, dummy.
And... for those of us who are neither scientists nor athletes (which should be pretty much all of us)... it's a bit like saying "Ford's truck model they built that one year".
Of course you can bisect anything by volume. But is it obvious that you ought to? Most people, I suspect, would logically bisect Mt. Everest into "top" and "bottom" halves by altitude, not by volume. I was countering Anonymous Coward's claim that the "obvious" way to bisect something is by volume.
If we approximated Mt. Everest as a perfect sphere of constant density, it wouldn't matter how you bisected it, because no matter which method you selected (height, cross-sectional area, volume, or mass) they would all give exactly identical results. But real-world objects usually aren't perfect spheres, and often don't have a reasonably-constant density.
Cutting in half means splitting in two parts of equal volume.
So the "top half" of Mt. Everest is obviously of equal volume to the "bottom half"?
Yeah... of the two applicable requirements for kosher (cloven hooves and ruminating), pigs actually do have cloven hooves.
It was kinda backward but I don't know how to make it into a proper joke the correct way. :/
If the subjective states of "better" and "worse" are defined in such a way that "nothing" is, in fact, preferred over "eternal happiness", then yes, a ham sandwich is "better" than eternal happiness.
For instance, if the problem is referring to someone you hate, you'd prefer them to have a ham sandwich instead. Especially if they can't eat pork.
Magic.
(Go to Google, type "french military victories" including quotes, and click I'm Feeling Lucky.)
You could wave away some of that by saying the meat is all one "piece" for purposed of discussion, but that might only appease the physicists and engineers.
No, the physicists have already approximated the pieces as point masses and they are all trying to figure out why you want to cut them in half.
Actually it's a theorem that was postulated by a pig named Ben who ruminated for a while and realised that in 4-space pigs would be kosher because there would be a specific 3-dimensional hyperplane which would split their 4 feet precisely in halves.
You dunce, you posted the wrong link. That's not the google search, it's the page at the first search result.
Here's the correct link.
People are human, and some people react humanely when subjected to imagery consisting of people actually suffering.
There, fixed that.
That "blocks all new websites shortly after they are created" kinda implies they have a list of all known websites.
They do. Once an employee visits the site, they know about it. They have logs.
Apparently their firewall rule allows visits to unknown websites on the first visit. Then, presumably after the first visit or a predefined length of time after it, the site is blacklisted. So that LOLcat link you got in your e-mail works once, cause apparently their IT department doesn't want to seem like a complete bunch of killjoys, but you won't be spending hours there, because you're at work. And if a site gets blacklisted that you actually need for work purposes, well, they're sure they'll hear about it pretty soon and they can move it from the blacklist to the whitelist.
If it's your union, then it is part of your work.
If you're an official union liaison, maybe.
Well... that's why I read them.