Silly ways to weigh an elephant
How would you weigh an elephant without using scales?
This is, I have learned a bit later than everyone else, legendarily a Google Interview Question. A hoary old-school one, I think, but I’m not well informed about Google’s interview practices, so who knows. Maybe it's IBM or something.
However, it struck me as a really interesting question, so I thought I’d have a go.
My first response is to attack the question and want to know more.
What are you meaning by scales? You might not-unreasonably call any method for determining weight “scales”, which would make the question impossible by definition. But for the sake of fun we’ll assume that’s not an issue, and it simply means you can’t use the sorts of scales that you put an elephant on and get a near-immediate readout in kg or cwt or firkins or whatever. I instantly think of a weighbridge: that’d be ideal in terms of range (it's calibrated to the right sort of weight for an elephant) and practicality (you can easily imagine how it could be done), and is my guess for the right answer to “How would you weigh an elephant?” without the qualification. I'd guess zoo vets have a mini-weighbridge/scales for just this purpose, but that’s very obviously what the question is not allowing is to do.
My next thought is to imagine some sort of ersatz scale or balance that might work at elephant size. A very large, long, strong plank on a fulcrum, for instance. Or just plopping it in water and seeing how much water is displaced. By Archimedes' Principle that will be equal to the mass, assuming elephants float, which I'm pretty sure they do. I think they also really like water, so this procedure might be fun for the elephant, if not for any bystanders who prefer being dry. Or, on the same principle, you could get the elephant to walk on to a cargo ship (it'd need to be a very small one rather than one of those megacontainer jobs) and see how far down it sinks on the waterline - the ship’s master will probably have solid info on waterline vs load. Hell, I bet you could get a pretty good estimate just from how deep its footprints are in slightly soft ground, either by some complex physical model or more practically by simply comparing it to the depressions made by calibrated elephant-a-like masses. An elephant is a pretty large mass in some senses, and mass has gravity, so presumably if one had a sensitive-enough piece of equipment one could weigh it by measuring the gravitational force felt by another large, known mass. An elephant is much bigger than the masses Cavendish used to measure G - but perhaps less steady. Ooh, these days we have some pretty accurate hi-res maps of the Earth's gravitational field, so we just need the elephant to stand somewhere we already have an ultra-hi-res gravitational map, then map the area again, subtract one from the other, and get the mass of the elephant.
These are probably the sorts of ideas the question is aimed at, and I'm not sure I've hit an obvious Right One, but my mind isn’t happy just running through more of those possibilities. There’s something practical I’m missing.
I start thinking about the practicalities of getting an elephant to stand where you want it to, and immediately think that you want a mahout or other specially-trained elephant keeper for that, because it’s pretty specialist work that I know nothing about, and by the ghods I don’t want a pissed-off elephant anywhere near me, or even one that is placid and well-meaning but not totally comprehending of my ill-informed efforts at telling it where to move.
Which makes me think: if we’re assuming an elephant keeper in to existence for convenience, can’t we just ask them how much their elephant weighs? They would probably know, at least in rough terms. Rather like offering the building’s caretaker the shiny new barometer if they’ll tell you how tall the building is. But this is obviously not addressing the project of the question, although it probably would be my first thought if I actually wanted to know the weight of a real elephant.
Why do we need to weigh an elephant? How accurately do we need to do it? Can’t we just go with a typical average figure? I don’t know without looking, and different (sub-)species are different, but it’ll be in the several-tonnes range, probably not much more than ten. So without knowing much about the elephant, and assuming it's not a baby, it'll be somewhere between 2 and 10 tonnes; let's say 5 tonnes as a within-an-order-of-magnitude guess. Would that do? [Later edit on looking it up: Not bad, actually.]
What is it that’s stopping us from using scales? That’s what’s been bothering me about the question!
I didn’t like those inventive ways of weighing elephants because they seemed like they were inventing a set of scales that doesn’t get called a set of scales, and thus wriggling out of a constraint by semantics rather than dealing with the problem. For instance, you could get the elephant to stand on an inflatable cushion (a large, strong one) and measure the pressure of the air inside, then calibrate the pressure reading against known masses on the cushion, but really that’s just an elaborate and inconvenient set of scales. What is the actual constraint here?
Why would you want to weigh an elephant in the first place? Most cases I can think of where you might need an accurate weight have scales easily to hand as part of the workflow (e.g. transport). One other obvious answer is: to give it an appropriate dose of drugs. Drug dosages are generally worked out in terms of dose per kg bodyweight, so you need to know the patient’s weight to calculate the dose.
Hey! Maybe the elephant is too ill to move to the scales! Which would rule out almost all of the ‘clever’ methods for weighing I was thinking of. Now we have a proper question that makes sense. How do you weigh a sickly elephant that is too ill to be moved to the scales?
For those purposes, you might be able to get close enough by eyeing up the elephant in relative size terms, then looking up on Wikipedia or EoL for the typical weight range for large/small male/female elephants of this (sub)species, and interpolating a bit.
That'd be Ok for some medicines, but certainly not all: there are some serious drugs that have a fairly narrow therapeutic window. So if you need to be a bit more accurate, you could take a few measurements and see how big or small your elephant is compared to others/average. I know there are rough rules-of-thumb for estimating the weight of a horse given its height (in hands! another lovely unit), so there are probably similar ones for elephants. Or you could take quite a lot of measurements and work out its volume. A really simple model is a big cylinder for the body, four smaller cylinders for the legs, and a sphere for the head. Then guess that its average density is a little less than water (as I said earlier, I’m pretty sure they float, because they can swim nicely, and possibly float a bit higher in the water than humans) to work out the mass.
Ooh, these days you don’t do that sort of model-making with a tape measure and crude cylinders. This is a tech job interview question! We can build a detailed 3D model of the elephant very easily: either with a sensor like a Kinect, or with one of those nifty systems that derive 3D models from a series of photographs. That will give us a really accurate figure for the volume, way more accurate than our guess at its density.
How could we get an accurate density figure? The easy answer is to look it up, although it might be rather variable by age and size. Assuming we can’t look up a figure that someone else has measured, this is a really tough question without scales and with an immobile elephant. Gravimetry - as mentioned above - is probably the answer, and come to think of it that would work nicely for an elephant that can’t move, so long as we had good data about the underlying gravitational field, or could confidently interpolate it from measurements surrounding the elephant.
Except when I think about how gravimeters work, I suddenly remember that they are essentially nothing more than a really, really accurate set of scales. Which leads back to my first question - "What are you meaning by scales?" - so I’ll stop there.
I really don't know what the "right" answer to the question is. I suspect that if I answered along these lines in an actual interview, some employers might want to hire me on the spot, but more of them might glance at their watch, shuffle uncomfortably, look down at their papers, and tell me that they would let me know.
This entry crossposted to http://doug.dreamwidth.org/314274.html, where there are
comment(s) not shown here.
This is, I have learned a bit later than everyone else, legendarily a Google Interview Question. A hoary old-school one, I think, but I’m not well informed about Google’s interview practices, so who knows. Maybe it's IBM or something.
However, it struck me as a really interesting question, so I thought I’d have a go.
My first response is to attack the question and want to know more.
What are you meaning by scales? You might not-unreasonably call any method for determining weight “scales”, which would make the question impossible by definition. But for the sake of fun we’ll assume that’s not an issue, and it simply means you can’t use the sorts of scales that you put an elephant on and get a near-immediate readout in kg or cwt or firkins or whatever. I instantly think of a weighbridge: that’d be ideal in terms of range (it's calibrated to the right sort of weight for an elephant) and practicality (you can easily imagine how it could be done), and is my guess for the right answer to “How would you weigh an elephant?” without the qualification. I'd guess zoo vets have a mini-weighbridge/scales for just this purpose, but that’s very obviously what the question is not allowing is to do.
My next thought is to imagine some sort of ersatz scale or balance that might work at elephant size. A very large, long, strong plank on a fulcrum, for instance. Or just plopping it in water and seeing how much water is displaced. By Archimedes' Principle that will be equal to the mass, assuming elephants float, which I'm pretty sure they do. I think they also really like water, so this procedure might be fun for the elephant, if not for any bystanders who prefer being dry. Or, on the same principle, you could get the elephant to walk on to a cargo ship (it'd need to be a very small one rather than one of those megacontainer jobs) and see how far down it sinks on the waterline - the ship’s master will probably have solid info on waterline vs load. Hell, I bet you could get a pretty good estimate just from how deep its footprints are in slightly soft ground, either by some complex physical model or more practically by simply comparing it to the depressions made by calibrated elephant-a-like masses. An elephant is a pretty large mass in some senses, and mass has gravity, so presumably if one had a sensitive-enough piece of equipment one could weigh it by measuring the gravitational force felt by another large, known mass. An elephant is much bigger than the masses Cavendish used to measure G - but perhaps less steady. Ooh, these days we have some pretty accurate hi-res maps of the Earth's gravitational field, so we just need the elephant to stand somewhere we already have an ultra-hi-res gravitational map, then map the area again, subtract one from the other, and get the mass of the elephant.
These are probably the sorts of ideas the question is aimed at, and I'm not sure I've hit an obvious Right One, but my mind isn’t happy just running through more of those possibilities. There’s something practical I’m missing.
I start thinking about the practicalities of getting an elephant to stand where you want it to, and immediately think that you want a mahout or other specially-trained elephant keeper for that, because it’s pretty specialist work that I know nothing about, and by the ghods I don’t want a pissed-off elephant anywhere near me, or even one that is placid and well-meaning but not totally comprehending of my ill-informed efforts at telling it where to move.
Which makes me think: if we’re assuming an elephant keeper in to existence for convenience, can’t we just ask them how much their elephant weighs? They would probably know, at least in rough terms. Rather like offering the building’s caretaker the shiny new barometer if they’ll tell you how tall the building is. But this is obviously not addressing the project of the question, although it probably would be my first thought if I actually wanted to know the weight of a real elephant.
Why do we need to weigh an elephant? How accurately do we need to do it? Can’t we just go with a typical average figure? I don’t know without looking, and different (sub-)species are different, but it’ll be in the several-tonnes range, probably not much more than ten. So without knowing much about the elephant, and assuming it's not a baby, it'll be somewhere between 2 and 10 tonnes; let's say 5 tonnes as a within-an-order-of-magnitude guess. Would that do? [Later edit on looking it up: Not bad, actually.]
What is it that’s stopping us from using scales? That’s what’s been bothering me about the question!
I didn’t like those inventive ways of weighing elephants because they seemed like they were inventing a set of scales that doesn’t get called a set of scales, and thus wriggling out of a constraint by semantics rather than dealing with the problem. For instance, you could get the elephant to stand on an inflatable cushion (a large, strong one) and measure the pressure of the air inside, then calibrate the pressure reading against known masses on the cushion, but really that’s just an elaborate and inconvenient set of scales. What is the actual constraint here?
Why would you want to weigh an elephant in the first place? Most cases I can think of where you might need an accurate weight have scales easily to hand as part of the workflow (e.g. transport). One other obvious answer is: to give it an appropriate dose of drugs. Drug dosages are generally worked out in terms of dose per kg bodyweight, so you need to know the patient’s weight to calculate the dose.
Hey! Maybe the elephant is too ill to move to the scales! Which would rule out almost all of the ‘clever’ methods for weighing I was thinking of. Now we have a proper question that makes sense. How do you weigh a sickly elephant that is too ill to be moved to the scales?
For those purposes, you might be able to get close enough by eyeing up the elephant in relative size terms, then looking up on Wikipedia or EoL for the typical weight range for large/small male/female elephants of this (sub)species, and interpolating a bit.
That'd be Ok for some medicines, but certainly not all: there are some serious drugs that have a fairly narrow therapeutic window. So if you need to be a bit more accurate, you could take a few measurements and see how big or small your elephant is compared to others/average. I know there are rough rules-of-thumb for estimating the weight of a horse given its height (in hands! another lovely unit), so there are probably similar ones for elephants. Or you could take quite a lot of measurements and work out its volume. A really simple model is a big cylinder for the body, four smaller cylinders for the legs, and a sphere for the head. Then guess that its average density is a little less than water (as I said earlier, I’m pretty sure they float, because they can swim nicely, and possibly float a bit higher in the water than humans) to work out the mass.
Ooh, these days you don’t do that sort of model-making with a tape measure and crude cylinders. This is a tech job interview question! We can build a detailed 3D model of the elephant very easily: either with a sensor like a Kinect, or with one of those nifty systems that derive 3D models from a series of photographs. That will give us a really accurate figure for the volume, way more accurate than our guess at its density.
How could we get an accurate density figure? The easy answer is to look it up, although it might be rather variable by age and size. Assuming we can’t look up a figure that someone else has measured, this is a really tough question without scales and with an immobile elephant. Gravimetry - as mentioned above - is probably the answer, and come to think of it that would work nicely for an elephant that can’t move, so long as we had good data about the underlying gravitational field, or could confidently interpolate it from measurements surrounding the elephant.
Except when I think about how gravimeters work, I suddenly remember that they are essentially nothing more than a really, really accurate set of scales. Which leads back to my first question - "What are you meaning by scales?" - so I’ll stop there.
I really don't know what the "right" answer to the question is. I suspect that if I answered along these lines in an actual interview, some employers might want to hire me on the spot, but more of them might glance at their watch, shuffle uncomfortably, look down at their papers, and tell me that they would let me know.
This entry crossposted to http://doug.dreamwidth.org/314274.html, where there are
comment(s) not shown here.