How Long Until It Gets There
Last timeWhy the Chain Forgets Where It Started
Condition on the first hop and the average number of hops to reach a situation becomes one small linear system. The average gap between visits then turns out to be one over the resting share.
The last two lessons answered where a chain ends up and how long before it has
forgotten where it started. Neither answers the question most people arrive
with, which is how long until something in particular happens.
How many mornings before this machine needs a part. How many clicks before this
reader reaches the checkout. How many steps before this process hits the level
that triggers an alarm. These are arrival questions, and they have their own
method, which is short.
Take one hop, then ask the same question again
Suppose you want the average number of hops from here to some destination.
Take one hop. You have used one hop and you are now somewhere else, and from
there the question is the same question, because the chain does not remember how
it arrived.
So the average from here is one, plus the average from wherever the hop lands,
weighted by the chance of landing there.
Doing it on the machine chain
Take the machine of the first lesson and ask how many mornings until it is
waiting for a part, starting from running.
The lesson stops here
5 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents