The way I visualize how the particle は works is that it opens a giant circle
underneath the word it is attached to wherein you can discuss things related
to it.

Sort of like this: ![This](https://i.stack.imgur.com/emGo7.png)

When I use ば I sort of visualize it in the same way... like I am attaching a
giant circle to a hypothetical situation as exemplified by the 仮定形{かていけい} form
and then talking about possibilities within it.

So I want to know... are they related in any way?
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question
particles etymology
Is ば derived historically from は?
Yes, they are. The conditional ば is just a voiced version of the particle は.
[See page 273, on the
bottom.](http://archive.org/stream/historicalgramma00sansuoft#page/160/mode/2up)
See also p.329.

The second seems to be a more recent coining, but it illustrates the
principle:

> 願【ねが】わくは
>
> 願わくば

[Both are possible, and mean the
same.](http://keigo.livedoor.biz/lite/archives/946281.html)

By the way, 仮定形【かていけい】 is the modern term reflecting its current usage (only
with ば). Its historical name is 已然形【いぜんけい】 ("Perfect", as in finished),
reflecting how it signified completion. You could say 「我【われ】、忘【わす】るれや」(have I
forgotten?) or 「言【い】えど」(=言う けれど). See p.142 of the book linked above.
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answer