First, we begin with what we are given. At any given bus stop, x, we know that a bus, y, will eventually appear. We will now use Heisenberg's Uncertainty Principle -- which states that for a given particle, p, the closer our approximate of its location, l, gets to its actual location l1; its velocity moves toward undefined. The inverse is also true, as is the corollary involving its momentum and mass.

So, we can then substitute the bus y for the particle p and state that any accurate evaluation of the bus's velocity will undoubtably return an inaccurate evaluation of the bus's position. Now, as we extrapolate these evaluations across any time interval, delta t, we can constrain the location estimate, l, to an upper bound of delta t times the constant c (speed of light) plus or minus the initial location, which is the constant BB (Bus Barn).

Now, we can constrain the location again with knowledge that the velocity can never drop below 0 (stopped -- a negative number would reflect time travel backwards, a feat which the MBTA has been working on but is still unable to solve). Thus, for the lower bound, we make two approximations of the location with the same margin of uncertainty. As velocity in this case is 0, the locations are identical and by using a Lagrangian transformation on the difference between approximations, we can reduce our inaccuracy by at least a factor of two.

However, because we know from the given that the bus will eventually appear, its velocity cannot be 0 if we choose a sufficiently large delta t. Thus we now have the contridiction which allows for The Smoker's Bus-Summoning Axiom, which states that upon lighting a cigarette, the odds that the mass transit device will arrive before the cigarette is complete increases by no less than factor of two.

Thus if we let the rider, r, be a smoker, and light a cigarette during the time interval, delta t, the probability of bus arrival can be mapped as a waveform, with the lower bound a non-dampening sinusoidal function of the fourth power and the upper bound a linear function. If we solve for the intersecting points, we can know that the bus will arrive at a given actual location l1 (that is to say the absolute value of l minus l1 will move to zero as delta t moves to zero) at delta t equal to m/(n * pi) for all n in the set of natural numbers (where m is equal to the mass of the bus in moles and then delta t equal to seconds).

As the bus's mass can accurately be evaluated upon entering the bus and counting the number of people, this evaluation can be empirically checked after the fact and thus substantiated by experience rather than just by logic.

We solve for destination with a similar argument, only we constrain velocity rather than location. QED.

Thus, we have successfully proven that :
1) riding a bus sucks.
2) smoking is good for you.
3) math is best used to prove things we already know.