Pardon, there was a dead link to a New Scientist article in which they used the water displacement method to come up with a weight of 4.25 kilos.
Do y’all remember that mad magazine cartoon about how to get rid of ten pounds of ugly fat?
Anyone willing to point out why my method won’t work?
Shalmanese all your method will do is show the displacement of your head. This will only allow the calculation of the weight of your head if you know the precise density of your head, which you don’t.
Further investigation seems to indicate that the various sources stating that the braoin is 60% fat are mirepresenting a statistic.
Myelin, the material of which neural tissue is composed, is apparently around 60% structural fat, but of course not all of the brain is made of myelin.
Now, if my head were veal, which I know it is not, if my head were veal, how much would it be worth?
(Determination of human brain weight in vivo by skull measurements - Brunholzl C, Widmer AC, Buser MW, Muller HR.; Neurologische Universitatsklinik, Kantonsspital Basel, Schweiz.)
Still can’t find either:
- average weight of human skull (have seen unreferenced claim of 2.2lbs)
- proportion of total weight of head represented by the skull
Don’t know what’s so difficult about this one, just weigh the torso, legs and arms, then weigh the entire body, remove the combined weights of the torso, legs, and arms and hey presto! You are left with the weight of your head.
I believe Shalmanese is proposing to measure both the volume of the head and the loss of measured weight caused by submerging it in water. It seems that this would allow the specific gravity and thus the weight to be determined.
OK then but that can only be done if you can measure the loss of bouyancy precisely. Which you can’t because the head is attached to the neck, which is going to make your measurements imprecise. If this problem didn’t exist, this whole question would be very simple.
And then, you make it wear a hat.
ADMIT IT!
You do!
How about…
You put a person in a big test tube. You attach just enough weights to his feet that the body floats just below the chin. Then add weight in small increments until the head submerges. The weight added is the difference between the weight of the head and the weight of an equivalent volume of water. Measure how much the water rises, and you have the volume of water displaced by the head submerging. Subtract the added weight from the weight of the displaced water, and you have the weight of the head.
(This assumes that the head floats)
Computed tomography can quantitatively measure tissue density, with every voxel in the image has an associated Hounsfield number.
So:
Take one (1) head, preferably attached to one (1) body.
Place head into bore of one (1) high-resolution CT scanner.
Scan head entirely, use voxel Hounsfield numbers to figure out all tissue densities.
Use water bucket procedure to determine head displacement.
Use tissue densities and displacement to determine mass.
Re-read what I posted. You hold a person upside down over a bucket of water and attach a newton meter to their feet. You can measure the the weight precisely and the neck muscles wont interfere.
Imagine a rigid dummy with a head made of a hollow fibreglass sphere. Imagine a rigid dummy with a head made of lead. Each head is precisely the same volume. Now do your upside down dunking trick. In each case, the head will displace precisely the same amount of water, and the reading on the newton meter will decrease by precisely the same amount. Yet the head weights are going to be totally different.
To measure the difference in bouyancy, you would need the head to be free to float/sink and find its own level but this is not going to be precisely possible when it is attached to a neck.
If you suspend a person upside down from a newton scale with just their head underwater, the forces on the system are (besides the reaction force from the scale):
- the force of gravity on the person (downwards)
- the buoyant force from the water (upwards)
The problem is that the buoyant force does not equal the weight of the head, it equals the weight of the displaced fluid, i.e. the volume of the head times the specific weight of water. You can use this setup to calculate the volume of someone’s head, but unfortunately not its weight.
I think bonzer has it correct:
That is, of course, provided that measurements of the gravitational field are excluded (also suggested by bonzer, in his gravitational lensing comment). I think that the proper approach to rigor here is to first demonstrate that the moment of inertia tensor contains all of the information which can be mechanically determined about an object’s mass distribution, and then to note that there are an infinite number of possible mass distributions for any given moment of inertia tensor, with different “head masses” associated with them.
Note, however, that this assumes a rigid object, which a human body is not. Eyer8’s suggestion of measuring moment of inertia with head and neck in various configurations should in principle give fairly good results, given some simplifying assumptions about the biomechanics of how the head moves. We do still need those simplifying assumptions, though: One could in principle, for instance, have most of the mass of the head concentrated in a small lump rigidly attached to the torso, with a hollow shell of a head of negligible mass moving around it. In this case, moving the head would not change the moment of inertia of the body, indistinguishable from the case where the entire head is of negligible mass.
And of course, if we’re going to settle for pretty good approximations given the human body, then the uniform-density method and the cadaver method are both much simpler than any measurement of moment of inertia.
That’s the joke I came in here to make 
Awwww, and I thought it had gone completely unnoticed. You just made my night!