Looking back on that last post (You know, the one about science, in case you forgot), I couldn’t help but think that there was something missing. I imparted to you the idea of what science is, but it’s not really enough. It’s not the real point I wanted to make. There is something vital missing to us as a society today, and it’s not the overarching concept of “SCIENCE!” While science is very important, there’s a more basic piece that needs to be grasped by everyone--the piece that holds science together.
What we need is critical thinking. Yes, I’m serious. That term that gets thrown around in English class. Except when I say it, I don’t mean “find some subtext that the author never actually intended and then write a 12-page essay about it”. When I say critical thinking, I mean thinking, critically--taking your ideas, your assumptions, and questioning them; not taking information for granted; backing up argument with fact; the ability to evaluate the worth of the information you are given.
I’m pretty sure I can’t impart the importance and usefulness of critical thinking in a blog post. Critical thinking is a skill that needs to be practiced and built up, like any other skill. I think what I’m hoping to relay is just that critical thinking is a critical component in modern thought, and that without it we’re an easily misled mob of savages.
Why is critical thinking important? Well, if you don’t stop and ponder the information you’re given, it cements itself in your mind. Whether the information is correct or incorrect, it becomes the truth to the person who doesn’t examine it. And when you are not confronted about your viewpoints, you will not understand how someone else could have opposing views.
I am of the opinion that most stupid people aren’t just born stupid, they’re taught to be stupid; they are not taught how to evaluate information. They are raised being fed facts with no regard for how those facts are garnered.
You might have heard a while ago that people eat on average about 8 spiders a year in their sleep. In fact, I’d wager 12 yen you’ve heard it so often it’s essentially a fact for you. Well, it’s wrong. Someone made it up. That is a false bit of information that we all just assumed was true, for no other reason than because someone told it to us. But this time, don’t just take my word for it, there’s references:
This also has far-reaching implications when it comes to politics, but that’s a long rant that I’ll have to save for later. And what a rant I’m sure it’ll be.
You’ll recall the cornerstone of my definition of “science” (Yes, you need to read that post first! Haha!) was that it relies on data and evidence to form conclusions. Critical thinking is the piece that lets you go from data and experiments to making a theory and conclusions.
Of course, science isn’t the only profession relying on critical thinking (just the most important, amiright?). Programmers must use critical thinking skills to debug or troubleshoot. Philosophers must take logic classes to learn to form cogent arguments. In fact, before scientists were called scientists, they were called natural philosophers. And, you know, other professions that I can’t really think of offhand.
I bring up professions because critical thinking shouldn’t simply be a skill, it should be part of our lifestyles. We should be able to evaluate all information we take in for its merit.
Alright, all this talk of critical thinking is completely asinine if we don’t actually connect it to something real. Here’s a critical thinking problem, one you can solve with your skill set. I guarantee you have the mathematical knowledge to solve it.
Three men are staying at a hotel one evening. This apparently a few decades ago and the hotel only costs $30 for the night. So in the spirit of fairness, each of the men pays $10 to the bellboy. The bellboy gets the money to the desk and the desk manager says “We’ve got a sale tonight, the room’s only $25, go give their change”. So the bellboy heads back, and, realizing that the $5 refund does not divide into 3 people (no fractions), decides to give $1 back to each man and keep the remaining $2 for tip.
So in the end, each man paid $9, for a total of $27, plus the $2 the bellboy kept is $29, so where is the last dollar of the original $30?
Think about that for a few minutes, then I’ll try and walk you through it.
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Have you figured it out?
It’s been a while since I first heard this problem, but I think this was my line of thought.
-Total money involved: $30
-Cost of room: $25
-Total refund $5
-Tip: $2
-Remaining Refund: $3
-Money Spent 1: $30 = $25 + $2 +$3
-Final cost per capita: $9
-Money Spent 2: $9 x 3 = 27 ; $27 +$2 = $29
My “Money Spent” lines are not consistent. That must be where the problem is.
Let’s back up. Where is the money now? The men have $1 each of the original $30, the hotel has $25, and the bellboy has $2.
They spent $25 on their hotel room, then $2 for the bellboy, so that’s $27. Then $2 to the bellboy for $29… wait a second. I already added the tip in to get $27. That original $30 was $25 + $2 +$3, or $27 spent + $3 refund.
So wait, what?
It was a ruse! I like the Bellboy problem because it so easily demonstrates all the bases for critical thinking. First, the whole problem is based on you getting fast-talked--you are lied to directly with $27+$2, and you lose track of the real meaning of the numbers. Second, there’s no need for some zany creative solution; the solution is there for you to find, once you’ve sorted the facts. You rely purely on logical deductions. And third, the math is simple. You don’t need any advanced knowledge of calculus to grasp this problem.
And now I’d like to end with a similar riddle for you to parse out. You’re on your own for this one, but after that last one, this should be a piece of cake.
13 people come to a hotel that only has 12 vacancies. Once again, the bellboy thinks he has the perfect solution to this problem. He takes the thirteenth guest and has him wait with the first guest in room 1. With 2 people waiting in room 1, the bellboy puts the third guest into room 2, fourth into room 3, on down until the twelfth guest into room 11. Finally, he goes back to the beginning, grabs the thirteenth guest out of room 1 and puts him in room 12, and now everyone has a room to themself. Why doesn’t this plan work?
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