I like to visualise things to try and understand them as an idea not a
rehearsed rule. I like to think of hazu in terms of it being a notch in a bow
for the arrow as I hear the meaning stemmed from there. I won't get into that
too much but...

Is there any way to understand べき in a similar manner? I hear it is related to
"CAN" because it uses the same kanji "可き". How should I understand its nuance?
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grammar etymology
What is the etymology of べき? How should I visualize it?
> Is there any way to understand べき in a similar manner?

I am afraid not.

べき is the 連体形 form of inflectable suffix べし in Classical Japanese, and in
Classical Japanese, 連体形 form was used as an abstract noun by itself in
general. According to
[Daijisen](http://dic.yahoo.co.jp/dsearch?dtype=0&dname=0na&index=16563700),
the widely accepted origin of べし is adverb
[うべし](http://kobun.weblio.jp/content/%E3%81%86%E3%81%B9%E3%81%97) in Classical
Japanese, which meant something similar to “indeed.” I do not know the origin
of うべし.

But I doubt that this knowledge (plus the knowledge about the origin of うべし)
helps you understand the meaning and usage of べき in the modern Japanese. While
I respect your experience that etymology helped you understand the meaning and
usage of _some_ words, I think that you were lucky in those cases.

> how should I understand its [べき’s] nuance?

I do not know. Maybe you can check the examples of べき and べし in a textbook or
a dictionary?

Just in case, do not try to remember the meanings listed in a dictionary. We
use words in English (e.g. “should”) without remembering its ten or so
meanings listed in a dictionary. You should do the same thing with words in
Japanese.
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answer
The best way to understand べし is to look at how it was used in classical
Japanese, because some of that usage extends into modern Japanese. Then,
separately look at how it is used commonly in modern Japanese.

Etymologically, べし probably came from the adjective うべし as Tsuyoshi Ito said,
just shortened for use as an auxiliary adjective, and additional
meanings/usages were added to it over time.

べし attaches to the 終止形{しゅうしけい} or 連体形{れんたいけい}(ラ変). In modern Japanese, the
distinction between 終止形 and 連体形 has deteriorated, but in classical Japanese,
for instance, this would mean 食{た}ぶべし rather than 食{た}ぶるべし, すべし instead of
するべし, あるべし instead of ありべし. - As a given rule there is always an "u" sound
before the べし.

The classical conjugation for べし is like all classical ク形容詞{けいようし},
(べから・べく、べかり・べし・べき、べかる・べけれ、べかれ）.

However in modern Japanese べき basically transformed into a restricted な
adjective. Or, if you don't want to call it that, a 終止形 form べき(だ)、and 連体形
form for use with particles べき(なの), that are like the corresponding な
conjugations were added to the list of possible べき forms in modern Japanese.
Other strange and restricted な adjectives that used to be 形容詞 include 同{おな}じ
(mix of original and な-adj-ish form) and 大{おほ}し→大{おお}きな (連体形 only).

These conjugations mix together in modern Japanese, using the classical for
phrases like ～べからず, ～べからざる, すべき - and modern for するべき, ～べきだ.

Anyway, the best way to understand is studying on your own. 頑張ってください。

Knowing the etymology is very helpful to understanding sometimes, but you have
to remember that it isn't always everything.

You could think of しかし in terms of of しかじ (classical form), which is just a
conjugation of the verb 如{し}く, which is the basis for a whole slew of other
things, and give yourself a headache, or you could just pay attention to how
and where it is used regularly in sentences.
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