How Are Probability Amplitude Arrows Drawn as Spirals in Feynman's Lectures?

[AlchemistK]

I just saw a few of Feynman's lectures on QED: Reflection and transmission, and he describes the concept of probability amplitude arrows, and their representation as vectors, from what I interpreted, the length of the arrow is proportional to the probability of an event, and its angle is dependent on the time.
In the part where he describes the first law of reflection, the arrows form two spirals. (This is perhaps not the best way to describe it, but the important thing is that it forms a spiral)
Now to form these spirals, the length of each successive arrow should be less than the previous one, but since we do not know the probability of these events (which is what we have to find) and hence the lengths, how can he draw them as spirals?

(link : http://youtu.be/-QUj2ZRUa7c )

 

[dlgoff]

Quantum mechanics introduces an important change on the way probabilities are computed. It has been found that the quantities which we have to use to represent the probabilities are not the usual real numbers we use for probabilities in our everyday world, but complex numbers which are called probability amplitudes. Feynman avoids exposing the reader to the mathematics of complex numbers by using a simple but accurate representation of them as arrows on a piece of paper or screen.

http://en.wikipedia.org/wiki/Quantum_electrodynamics#Probability_amplitudes

 

[AlchemistK]

Yes I did refer the Wikipedia page before coming here, but other than its use like complex numbers, I could not find the answer to my question, which is based on the video. How do we know the length of those arrows?

 

[dlgoff]

Here's An Introduction to QED & QCD. See 3.4 Interactions in Perturbation Theory.