95% right is good enough
How sure do you need to be before you make a decision?
Are you the type of person who has to know the absolute right answer to your problems before doing anything?
If so, you may be wasting your time.
Why?
Because reality seems to allow for a bit of “slack.”
For example, I took a physics course recently and was amazed by 3 facts:
1) The solutions we calculated for many problems were not 100% correct because of the various assumptions we made.
2) We didn’t need to be 100% right to use what we learned to make predictions that worked in the lab.
3) Many of the wonderful things the power of applied knowledge has brought to our lives (cars, the Internet, preserved food, clean water, electricity, men on the moon), come from scientific knowledge that is not 100% complete or “right.”
For example, it is very common in entry-level physics to ignore air resistance when doing projectile motion problems even though air resistance against say, a bullet fired across is a distance, is a significant factor in real life.
Technically, the answers you get when doing textbook problems are not 100% correct.
But so what?
The basic equations of kinematics for objects with a constant acceleration work for most situations in real life and you can use them to predict things, plan, build, invent, and create.
The knowledge is not perfect or total but it’s better than not knowing anything about how motion works: 95% right is better than 100% wrong.
Or take your height for example.
Seems simple enough.
You use a meter stick and measure how tall you are and that’s that.
But even that is not a complete answer.
Why?
Special relativity.
The length contraction equation of special relativity is:
L’ is the observable length, L is the standard length in an inertial (non-accelerating) frame of reference, v is your velocity, and c is the speed of light (299 792 458 m/s).
According to Einstein, the faster you go the more length contracts. If you were traveling at the speed of light length would cease to exist (just as time slows down as you go faster and would stop if you traveled at the speed of light).
Our normal frame of reference is the Earth.
The Earth rotates about its axis at various speeds depending on where you are (approximately 465 meters per second at the equator) and you, if you stand still, rotate along with it at the same speed.
As such, with respect to the Earth you are normally in an inertial frame of reference.
If you stood still and measured your height to be 5’11’’or 1.8034 meters you could be fairly certain to observe the same height again the next day and the day after that assuming you stayed in the same place, used the same measuring tool, and didn’t grow or shrink.
But if you got in the space shuttle and went into Earth orbit your observed height would change.
The v in the equation above would be about 7860 meters per second (17,580 miles per hour)[2] with respect to the Earth.
Your height would now be 1.803399999 meters.
Again, even in a simple operation like measuring your own height you will never have an answer that is 100% complete or “right:” in this case, your result will depend on your frame of reference.
Luckily for us, we don’t need to be 100% right to use science and technology and get answers that make a difference in our lives and allow us to accomplish things (like build cars that can seat people at least 5’11’’ tall).
Of course, this begs the question: what does 100% complete/right/accurate really mean, if anything?
But that’s for another day.
For now, cover 95% of your bases and stop trying to find the 100% answer: it doesn’t exist and even if it did, odds are you don’t need it to do whatever it is you are trying to do.
[1] http://en.wikipedia.org/wiki/Length_contraction
[2] http://hypertextbook.com/facts/2001/InnaSokolyanskaya1.shtml; this is one number you can use. There are others as well depending on which orbit the shuttle is actually in.
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