Tumbling toast, Murphy's Law and the Fundamental Constants
European Journal of Physics 16 172-176 1995
There's a widespread suspicion among the public that toast sliding off a plate or table has a natural tendency to land butter side down, thus providing prima facie evidence for Murphy's Law: "If something can go wrong, it will". Most scientists, in contrast, dismiss such belief as ludicrous. Indeed, an investigation by the BBC-TV science programme Q.E.D. in 1993 claimed to have proved definitively that the whole notion was nothing but an urban myth. However, as I show in the paper, the experiments carried out by the programme were dynamically inappropriate (in that they consisted of people simply tossing buttered bread into the air - hardly common practice around the breakfast table). When the problem of toast sliding off a plate or table is examined more carefully - with the toast modelled as a thin, rigid, rough lamina - it turns out that the public perception is quite correct. Toast does indeed have a natural tendency to land butter side down, essentially because the gravitation torque induced as the toast topples over the edge of the plate/table is insufficient to bring the toast butter-side up again by the time it hits the floor. Note that this has nothing to do with some aerodynamic effect caused by one side being buttered - it is just gravity, plus a bit of friction.However, I go on to show that the tumbling toast phenomenon has far deeper roots than one might expect. If tables were a lot higher - around 3 metres high - the problem of toast landing butter-side down would go away, as the toast would have enough time to complete a full rotation. So why are tables the height they are ? Simple: to be convenient for humans. So why are humans the height they are ? Using a simple chemical bonding model of the human frame, I show that there is a limit to the safe height for bipedal, essentially cylindrical creatures like humans. The limit is around 3 metres - above that height, a simple fall results in gravity accelerating the skull to such a high kinetic energy that the chemical bonds in the skull are ruptured, causing severe fracturing. This limit, in turn, sets a maximum height on tables suitable for creatures with human articulation of about 1.5 metres - which is still not high enough to prevent toast landing butter-side down. It thus seems that human-like organisms are doomed to experience this manifestation of Murphy's Law.
But then comes the real cosmic twist in the tale. The formula giving the maximum height of humans turns out to contain three so-called "fundamental constants of the universe". The first - the electromagnetic fine-structure constant - determines the strength of the chemical bonds in the skull, while the second - the gravitational fine-structure constant - determines the strength of gravity. Finally, the so-called Bohr radius dictates the size of atoms making up the body. The precise values of these three fundamental constants were built into the very design of the universe just moments after the Big Bang. In other words, toast falling off the breakfast table lands butter-side down because the universe is made that way.
Having made this depressing discovery about the nature of our universe, I felt duty-bound to come up with some ways around it. After all, we should not be fatalistic about such things. There are any number of daft ways (eating from 3 metre high tables, eating tiny squares of toast, putting the butter on the underside, tying the toast to a cat, which of course knows how to get right-side up during a fall, etc. etc). The physicist's approach is to minimise the amount of time the toast is exposed to the turning effect of gravity. This means doing the opposite of what you might expect. If your toast is sliding off the table, you should give it a swipe with your hand, to increase its horizontal speed off the table. If you're lucky, it may stay butter side up. If toast is sliding off a plate, you should move the plate rapidly downward and backward, breaking contact with the toast, which then descends butter-side up.
I've since expanded my investigations of Murphy's Law to encompass the question of why there are so many odd socks in our drawers. 1996 Robert A.J. Matthews All Rights Reserved.
