Toast Proves There's A God
By Lewis Dartnell
CoMPLEX, University College London, UK.
Introduction
We’ve all experienced it. It’s Monday morning, you've slept through your alarm and are now in a hopeless rush to get in on time. The toast comes out of the toaster, you give it a quick sweep of butter, or in these more health-conscious times, margarine, and pick it up to take over to your newspaper on the kitchen table. And then it happens.
Whether it simply slips out of your fingers or it burns slightly and you subconsciously release it, the toast begins to drop towards the filthy floor. You watch in dismay as the toast falls, neatly performing a half-turn and landing flat on the floor, butter-side down in the grime. You don't even know why you tentatively hoped for the toast to land otherwise - the Universe seems out to get you as far as free-falling toast is concerned. Well, in fact it is.
The butter-side down eventuality is the necessary outcome due to a specific combination of parameters concerned with the dimensions of humans and ultimately the fundamental structure of the universe. This argument-by-design, therefore, not only conclusively demonstrates the existence of the Creator, but that he is a cantankerous old blighter who organised the Universe in this way to continually torment us with dirty toast.
Methods A mathematical model of the toast situation can be constructed in order to demonstrate the butter-side down condition as the invariant outcome. To simplify the situation, the cuboid of toast is modelled as a rigid rod with uniform density and length 2a. Thus rotation in only one plane, a change in pitch, is considered; roll and yaw during the descent are ignored.
At the initial condition, the moment of release, the toast is horizontal and supported only at one extreme by the breakfaster’s finger. The weight of the toast has become an unbalanced force and so creates a turning moment and thus rotation about the pivot (finger). This turning force is equal to the component of the weight perpendicular to the toast's surface. Figure 1 below shows the situation when the toast has pitched down through an angle of θ.
As long as the toast remains in contact with the pivot the rate of rotation increases. When the toast has pitched down to a certain dip-angle static friction between bread and finger is overcome and the toast slips off the pivot. The toast now enters freefall towards the floor, rotating at a steady rate about its centre of mass. The total drop height is given as h. The analysis is made simpler by two assumptions; that the size of the toast is insignificant compared to the drop height, and that the pitch angle at the point of slippage is a negligible proportion of a complete turn, i.e.:
a << h and θ << 360°
a << h and θ << 360°