Perhaps you could write a formal proof of the bijection, on a side note, just so one can see how it would look like. I think we must not fear losing readership by being a bit technical, especially since you did a great job giving an informal explanation.
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I think I'll make the bijection proof another post and then link to it from this article. I think that way it is least intrusive to anyone who is not interested, but there for the people who want to see it.
No promises, but I'll try to get it done by tomorrow.
thanks!
Hey there, the formal proof is now up. You can find it here.