If we start together, and walk a mile one degree off from each other, one of us is lost.
-me
The point of this post…there are three points in fact (which is a triangular shaped pun):
Walking thru our life, if our job, from the Biblical perspective, is to follow Christ…what if we were only ONE degree off?
How far apart would we be, in terms of physical distance, if Christ and myself walked one mile, but I was one degree off?
How long would it take to walk one mile?
What if we walked 100 miles?
Let’s do some math and find out. Turns out that just “one degree off” is subtle…except for how fatal it is.
First, some basics:
How fast does a typical human walk?
The internet says “3mph”. Fine, I’ll use that.
The starting conditions:
Let’s pretend you and I set out for a long walk outside. We start shoulder to shoulder, literally touching each other. We both walk exact same speed, both go exact same distance…
What type of math will we use?
An isosceles and right triangles of course.
This allows me to calculate the ‘as the crow files’ distance to you after our walk…because one of us is going to get lost… That’s a literary technique called “foreshadowing”.
A picture:
Alpha: 1 deg
V: Walking speed
d1: Distance walked
t: Time spent walking
d2: How far apart we are…the important part
Let’s assume:
V = 3mph
d1 = 1mi = 5280ft
t —> d1 = Vt —> t = d1/V —> (1mi)/(3mph) —> 1mi will take 1/3 of an hour, so t = 20min
How far apart are we?
Let’s split this isosceles into two right triangles, makes the math a bit easier:
You can do the math yourself here if you wanna:
https://www.omnicalculator.com/math/right-triangle-side-angle
But, for reference, here is the formula:
d2/2 = (d1)(sin(radians(alpha/2*deg))) —> (5280ft)(sin(radians(0.5deg))) = 46ft
…but that is only half the original isosceles triangle…so have to double that, so d2 = 92ft
If you and I start walking a mile shoulder-to-shoulder, one degree off:
We will end up 100ft apart.
This is a linear relationship, “for every 1 mile walked, we’re ~100ft apart”.
10 miles, we’d be ~1000ft apart.
10 miles of walking only takes (10)(20min) = ~3hrs 20min, we’d still be able to see each other, but there’s no way we can hear each other.
Go 100mi, which would take 33.3hrs (only a day and a half!), and now we’re 1.75 mile apart.
You’re lost.
If I’m one degree off from Christ my whole life, I’m lost. Also known as dead.