How did 涉 semantically shift to mean 'to experience, be involved'? What semantic notions underlie definition 1 below with 2 and 3? Do the Chinese customarily &quot;experience&quot; ford streams? I can't imagine how &quot;ford streams&quot; would attract tourists.
I can't even guess how 1 relates to 3.
涉 - Wiktionary

Ideogrammic compound (會意): 水 (“water”) + 步 (“walk”) – to wade across.
Its oracle bone script and bronze inscription were composed of a 水 and two 止 (“foot”), depicting two feet on both sides of the water. Two forms, however, were given in Shuowen, with the first one consisting of a 步 sandwiched between two 水, and the second a 水 to the left of a 步, the predecessor of the current form.
Definitions

ford stream; wade across
to experience
to be involved
Great question. The original meaning of "涉" is that stepping into and wading across the stream by my feet. (The phrases "涉水"、"涉江" are specific examples of the original meaning.)  

In my opinion, "涉", to some extent, can be regarded as "step into".(Not very exact) 

And if I stepped into something dangerous yesterday, it also means that I experienced something dangerous yesterday. (The phrase "涉猎" is the specific example of the second meaning. )

And if something "stepped into" me, it also means that I was involved in something. ("涉及"、 "涉外". To some extent, you can understand "涉" as "about". )

Examples：

1、我一路跋山涉水。
explanation: I've been trekking all the way. (跋山涉水: trekking. And "涉" means that I wade across the rivers.)

2、涉险事故。
explanation：Misadventure. (The accident("事故" means something bad) about("涉") dangerousness(险))

3、他涉猎广泛。
explanation：He has a wide range of interests. (He step into("涉") and hunt("猎") a lot of things.)