Okay - I’ll admit that might have been a click-baity caption (at least in this here neighborhood) just to draw you into the most trivial of potentially weird things to ponder, but here it is…
As I was doing something productive (working on Geometry stuff for school), I found myself pondering this question:
If lines are randomly plunked down on a plane, are they guaranteed to form a triangle?
The trivial answer to it is: no. If any of the three lines are parallel, then no triangle is formed. Or likewise they could all converge on one point, like spokes.
But what is the probability of these non-triangular occurrences happening? Well - for perfect lines, the probability of anything being perfectly parallel, much less all coinciding at a point of concurrence is precisely zero! So statistically speaking, you have a 100% chance (certainty, actually) of getting a triangle. And yet logically speaking, the non-triangular scenario singularities do exist - (and in fact there are an infinite number of them too - it’s just an infinitely smaller infinity). So it can’t be considered as ‘proven’ that a triangle must occur - since those are there to function as counter-examples. And yet, there it is: 100% certainty in all its glory, thumbing its nose defiantly at anybody who asks for proof!
So … we’ve talked about different levels of ‘wrongness’ - so many creative ways to be wrong. But here on the flip side, do we actually have different levels of valid certainty? Certainty with proof, but yet also valid certainty even without it! And no - this has nothing to do with apologetics, though I recognize how the religious mind can’t resist taking it there. Do so if you must. I’m just thinking about something interesting here - as a great way of avoiding productivity here at the moment.
