Even in the movie 3 Idiots, at the end of the movie, the man with the pen points out that there's a reason for the complexity: bits of graphite flying around in zero gravity near instrument panels and people's eyes, etc.
Simplicity is great, but sometimes complexity is warranted. More importantly, assuming other smart people (many other smart people) are wrong without deep thought is not a good idea.
Not only graphite, but assuming a proper non-mechanical pencil, you'd end up with wood shavings in addition to the graphite bits flying about — which you could solve by adding a vacuum to the pencil sharpener, to capture the debris.
The second example is funny but it is a classic example of misdirection. It is made out to be about mathematics but has got nothing to with it. How exactly is that about overthinking something?
The third example is a ingenious solution by the author himself, a solution that is the product of thinking hard about coming up with a simple solution - hardly a case of whatever the opposite of overthinking is. If anything it is the opposite - just slice it up into 12 bites and take a small piece each of the last bit. If it's a mathematical question a mathematical approach seems more than reasonable.
All these examples seem to me to be weak examples of overthinking.
Here is a much better example of overthinking in my opinion, The Centipede's Dilemma:
The part about the string made me smile a bit, because I guess there aren't too many climbers on Quora. As any salty old trad climber knows, it only takes a couple of wraps around an object before the rope (or string in this case) becomes fixed to the object.
So unless you're lucky, the process would actually look like: take string, make space between thumb and index finger, wrap some number of ... oh, darn, it didn't come out even at all ... rats, can't move my fingers ... OK, start over, let's make the fingers a little farther apart ... wait, rats, didn't get 11 even wraps that time either ...
(I experimented with this before posting my comment, just in case.)
Or you could, y'know, take the string, measure the circumference, divide by 11. Or, you could throw away the string, take the diameter of pizza -- which is written in black marker on a tin or cardboard round and displayed on the wall at every pizza joint I've ever been to, I think -- and multiply by 3 and divide by 11 and space your cuts about that far apart.
There's a lot of good stuff out there on the benefits of "thinking like a child" -- learning to clear your mind of the preconceptions and opinions and expectations that we tend to develop as we get older. I don't think this post was a step in that direction, though.
I think the string thing is inaccurate enough (try it!) that you might as well just eye-ball it. If accuracy mattered, I would make a paper circle of about the size of the pizza, divide into twelve (sixteen would work too) slices, remove one (or five), and adjust the spaces between them until they looked about equal. Then slice between the paper pieces. If I were in a pizza shop, I'd probably just use actual pizza slices.
It is made out to be about mathematics but has got nothing to with it.
Well, as I understood it Andrew Wiles' proof of Fermat's last theorem ultimately also came down to counting doughnut holes in things which you wouldn't normally regard as doughnuts, so there is some mathematics there. But yes, you would "normally" expect the mathematician to cut the pizza into five slices (which look like four, he explains, because one of them is a point), and rearrange them smoothly across the plane without collisions into two whole pizzas identical to the first, which he can do with the Axiom of Choice (see the "Banach Tarski Paradox" for the 3D case).
"Repeating this process ten times," says the mathematician, "you have the trivial partition of the original pizza into eleven identical pizzas."
Andrew Wiles' proof of Fermat's last theorem ultimately also came down to counting doughnut holes in things which you wouldn't normally regard as doughnuts
Ok, only did a few minutes research but intuitively it doesn't make sense to me that ballpoint pens a) work in space but b) don't work upside down. There wouldn't be an upside down in space because of 0 gravity.
The film scene is one of the things that motivated me to write this. So I used it for some humor. Whether it is true is besides the point. Though an urban myth, it made me think about the subject.
Overthinking leads to over-enginnering, because humans aren't great at knowing what to do with all the free time we'd have if we did our job in 10% of the time :) Perhaps overthinking is required to keep us busy. Even though we all claim our time is money, in reality most get paid by the hour and not by the amount of work that has been accomplished. Plus complexity gives more weight to what we do, allowing us to claim that there's no shortcut to where we're going. That degree, that level of experience, are all job requirements that protect us.
Experienced entrepreneurs often fall for this trap. Too much prior knowledge of a particular industry leads them to quickly find faults in most ideas, and the just-do-it attitude that leads to simple approaches that stun everyone slowly fades.
Prior knowledge. Yes. Exactly what I was telling. I gave the numbers question to some of my friends and they all seem to be crippled by their prior knowledge.
I was thinking about the iPad too. I wonder what astronauts are using now. Surely not the space pen.
yep I couldn't solve that in the first 5 mins and gave up :)
strange how our pattern recognition gets worse with age ... I wonder if prior knowledge actually messes with the pattern recognition functions in the brain somehow ...
Did you give it to any kids yourself, rather than relying on the article's claim that kids are usually able to solve it? If you're going to try to repeat the experiment, you must repeat all of it before claiming it repeatable.
The solution is very clever. However, it is incomplete. In addition to the equally divided markings around the circumference, you also need to know the midpoint of the circle. Without the midpoint, the cuts may still yield unequal slices. Fortunately, using the author's same technique, you can easily produce the midpoint by making marks at the opposite ends of a single loop. Those two additional markings provide a guide for you to make cuts into the midpoint of the pizza.
Based on my extensive pizza eating experience, the average pizza slice is no wider than the distance between my thumb and forefinger, so start by wrapping the string around thumb & forefinger 11 times, leaving a bit dangling at the end. Then gradually expand the distance between the two fingers until the loose bit is eliminated.
I suspect you don't even have to mark the string with a pen (meaning the author possibly overthought the solution). You can just use the gap between your fingers. The chances are that the additional length added by the circumference of your fingers probably compensates for the curvature of the pizza circumference, depending on the size of the pizza and the size of your fingers. If you're doing this regularly you'll quickly learn the appropriate degree of compensation.
I solved the second one in a couple minutes in my head with value substitutions. Unless you were to do with with a pen and paper, it'd be pretty difficult to pick up on the closed loops.
Generating the following list took less than 30 secs when I looked it over, so obviously the example of it taking a long time to solve is a bit contrived. What threw me off a bit at first was that the number 4 was not used at all. I spent a little time trying to figure out why that was excluded before moving on.
Similar way here, given 0000, 1111, 2222, 3333, 5555, 6666, 7777, 9999, we know the value of each number except for 4 and 8, disregard 4 (not in any value), sub those values in to any slot with an 8, and you get the answer.
If the alternative to overthinking would be staring at this looking for a pattern until you realize it is the number of loops, then that is not something I am interested in :)
I came to the same conclusion alas with some different thought process behind it - all prime numbers are actually 0, the 0 we increase to 1. Then what's left dividable by 3 a 1, and what's left dividable by 2 a 2...
I guess that might be some sort of overcomplicating it, but I was quite happy until I scrolled to the bottom
I too solved it in 1-2 minutes just by looking at the patterns and deducing from the combinations, especially the ones with four of a kind. The loops never occurred to me until I read the "real" solution.
IMO the "fuck_you" of the currently most popular comment is what most people who are skimming HN during their morning coffee are bound to think, but most programmers and anyone used to deducing patterns would probably be able to figure the puzzle out in a relatively short amount of time. Not an hour. Sheesh!
I'm in the "higher education" category, yet that puzzle only took me about 2-3min of looking at it... I got briefly red-herringed by digit sums / digital roots looking promising, so spent most of the time thinking about those, but, once I'd found counter-examples, it didn't take long to crack.
That said, the "pre-school children" bit was a big hint as to how to approach it.
The use of '=' instead of, say, '→' made the math pedant in me twitch, though ;)
If you give an engineering problem to an engineer in a corporate environment, he will try to do what he's been told to be a good job: good precision and low cost, complexity not being a problem as far as the solution is achieved. If he's given 1 hour, then using 59 minutes is just as valid as using 5. And rightly so.
As for the numeric problem, same thing. You are not giving a measure of "goodness" and you are not providing rules. I'd go ahead and fill in 2581 = fuck_you , where fuck_you is a constant defined as 3.15. That's a point-wise defined polynomial there. Voila, solved in 3 seconds. Just as valid as making up something as arbitrary as counting loops in a given numeric representation. Also, I'd bet the house I don't own that if I give that in a paper to a kid with no instructions he wouldn't come up with that "solution" - ever.
In the (urban legend) problem about the pen and pencil in zero-gravity, there is context. The objective is to take notes. It's a real world problem with a fixed solution, so yeah, just using a pencil would be a much better solution than engineering a special ballpen. An engineer can and should be expected to solve that. Engineers are expected to solve real world problems and consider real world situations and realistic expectations.
When I'm presented bullshit like that IRL I get pissed off, but I can generally take the challenge of pointing out how and why is it bullshit.
Being presented it in HN, it's a good chance to educate more people on why this is NOT thinking out of the box or being clever, and why these are NOT proper tests unless adequate context is provided.
The problem is, if your definition of engineering is solving problems where all the context is fully provided, then 99% of what is interesting on HN isn't engineering. It's apparently bullshit.
Changing the rules and picking a different context are perfectly valid ways of solving a problem.
Squinting hard at real-life patterns and trying to find the rule that generates them is most of the value in business and programming. Ever run an a/b test or looked at analytics and tried to understand why things were changing? The truth is generally as different from what you expect as a number problem whose solution is the shapes of the numerals.
In real life you usually know at least 1 or 2 of these:
- what the problem is
- what you want to achieve
- what the constraints are
- what works (a means to know when you have found a solution)
Without that, you have an undefined riddle and you can try to do something original or clever and see how that goes. Obviously the less you know the less convoluted things will even occur to you.
If you give a bunch of numbers to mathy people they will very likely try some math. They will expect it to be math. That's not loss of creativity, that's reasonable expectations.
In real life, if I'm given a pizza and told to divide it in 11 equal slices I'm pretty sure I can achieve reasonable precision without any measurements. 1/11 is just slightly more than 1/(4*3) which is easy enough to figure out. At most I'd make a few tentative marks before going ahead and cutting it. When you give a problem like this in an interview, you can assume you're expected to prove your relevant skills to the job. In a software company that would be math, algorithms, etc. not just problem solving. If your objective is to get upvoted, then maybe you should try something clever and accessible.
I think it's totally relevant, I have worked with guys that have fancy PHD's from MIT that always over complicated the crap out of simple things. It's like when you buy something expensive or make an investment, you feel the need to defend and justify it to others.
It's the same thing here, you get a fancy degree and everything you do has to be complex to justify getting that degree otherwise what separates you from a guy with an average degree. It's probably more an ego thing, but I see this all the time.
I agree, but when that's the case then it's right to call it.
Actually, it's one of my greatest pet peeves. How so many things are so massively over-engineered. I could go on forever about that and there is not a single day I don't spend a while realising this about something.
I don't understand why you presume it's a need to defend and justify it to others. Getting a PhD from MIT isn't exactly a walk in the park, I imagine the person got it BECAUSE of a pleasure to tackle complicated problems in the first place.
If I really enjoy dealing with complexity and you give me something really simple to do, well I'm gonna go ahead and have some fun with it. It's not a matter of justifying, it's just that simple stuff is boring to somebody who enjoys complexity.
To clarify, I'm not saying over-engineering is a good thing. I'm saying there's a mismatch between the complexity of the problem and the desires/personality of the person having to solve it. Give the simple problem to people who valor elegance, minimalism, simplicity, and keep the MIT PhD for rocket surgery and stuff.
"it's just that simple stuff is boring to somebody who enjoys complexity."
This doesn't work very well with business. Sometimes, you just need the simple solution.
It's also the reason why many startups never get off the ground. I'm guilty of it myself, but I have learned over the years to not over-engineer something until it's really needed.
This is what happens when you hire someone that's overqualified for a job, I guess. :) People in that situation need to find work that will satisfy their thirst for complexity. They are making trouble for themselves and others, otherwise.
>> Conjuring complex mathematical equations may make you look smart but to become truly creative you need to be able to liberate your mind from the the shell of knowledge, education and adultification you have accumulated. Only then can you think like a child again.
This claims that creativity and education are diametral opposites. This essentially replicates the myth of the natural artist who can only achieve true creativity within nature and by forgetting culture. The basis for both assumptions is a fundamental divide between culture and nature, whereas culture is seen as hindering the creativity and freedom of the homo naturalis.
While I'm sure you can always find some cases where this distinction might hold true, there are plenty of others that reveal the false dichotomy at work here.
There is a difference between a solution perceived as complicated or simple, but there is no objective measurement for a difference in creativity. The combination and application of maths (in the example with the pizza cutter) is as much a creative use of ideas as is the "manual" method with the string.
Uhm I guess it's about common sense and not being an engineer all the time!!
If someone would call a pizza place in reality saying they wanted 11 equal pieces, they would have answered that at most they could have the pizza cut in some slices! :D HA!
I figured out the number one in about 30 seconds. The biggest clue is that it claims preschoolers get it easily. That means all mathematical operations, except addition and less likely subtraction, is out of the question. A quick glance showed that adding or subtracting in any simple way would not yield a result - a more complicated way would not be done by a preschooler. So that meant it probably was some sort of spacial or visual problem. Seeing 6666=4 and 0000=4 got me thinking about the shapes of the numbers, and from there I quickly determined the answer was the number of closed loops.
Ugh, the government did not finance the space pen. It was a private company that attached their product to space exploration. It was the space age after all. They are nice pens, they even write under water. I am also blown away that the author saw this first in that movie and didn't hear it absolutely everywhere first (usually crediting Russian cosmonauts as the smarter ones).
Nobody really needs to divide a pizza into eleven pieces with such precision. It's presented as a "real" situation, but it's a classic type of mathematical problem, the constraints of which are entirely made up for fun. When he dismisses the geometrical solution as "overthinking" and a sign of a lack of creativity, he not only misses the point, he's mocking what other people do for fun. Nice.
Also, as someone else already pointed out, he didn't specify how to find the middle point of the pizza, so his answer isn't a complete practical solution anyway.
I believe that one reason why things can get overcomplicated is because often this has proven to be profitable. Why did it cost millions of dollars to create a pen in space when a pencil would do? Obviously, someone benefited greatly financially from the government contracts that were given to them for the purpose of creating a pen that would work in space- even when it wasn't truly necessary. Many believe the old saying that "money makes the world go round." Could this be the reason why else we have legally allowed for financial instruments such as derivatives which are so complex that the majority of the public does not even understand them? Is it profitable for someone to have something such as this be so complicated that the general public will fail to see their inherent danger? While overthink is dangerous for productivity, someone has also figured out that it is profitable- at least for them.
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[ 2.7 ms ] story [ 172 ms ] threadBut is it our problem to over think everything. School, university, bureaucracy, everything we encounter in life pushes us into that direction.
Probably to stop us from getting killed. Something evolutionary...
Simplicity is great, but sometimes complexity is warranted. More importantly, assuming other smart people (many other smart people) are wrong without deep thought is not a good idea.
The second example is funny but it is a classic example of misdirection. It is made out to be about mathematics but has got nothing to with it. How exactly is that about overthinking something?
The third example is a ingenious solution by the author himself, a solution that is the product of thinking hard about coming up with a simple solution - hardly a case of whatever the opposite of overthinking is. If anything it is the opposite - just slice it up into 12 bites and take a small piece each of the last bit. If it's a mathematical question a mathematical approach seems more than reasonable.
All these examples seem to me to be weak examples of overthinking.
Here is a much better example of overthinking in my opinion, The Centipede's Dilemma:
A centipede was happy – quite!
Until a toad in fun
Said, "Pray, which leg moves after which?"
This raised her doubts to such a pitch,
She fell exhausted in the ditch
Not knowing how to run.
From https://en.wikipedia.org/wiki/Centipedes_dilemma
So unless you're lucky, the process would actually look like: take string, make space between thumb and index finger, wrap some number of ... oh, darn, it didn't come out even at all ... rats, can't move my fingers ... OK, start over, let's make the fingers a little farther apart ... wait, rats, didn't get 11 even wraps that time either ...
(I experimented with this before posting my comment, just in case.)
Or you could, y'know, take the string, measure the circumference, divide by 11. Or, you could throw away the string, take the diameter of pizza -- which is written in black marker on a tin or cardboard round and displayed on the wall at every pizza joint I've ever been to, I think -- and multiply by 3 and divide by 11 and space your cuts about that far apart.
There's a lot of good stuff out there on the benefits of "thinking like a child" -- learning to clear your mind of the preconceptions and opinions and expectations that we tend to develop as we get older. I don't think this post was a step in that direction, though.
Well, as I understood it Andrew Wiles' proof of Fermat's last theorem ultimately also came down to counting doughnut holes in things which you wouldn't normally regard as doughnuts, so there is some mathematics there. But yes, you would "normally" expect the mathematician to cut the pizza into five slices (which look like four, he explains, because one of them is a point), and rearrange them smoothly across the plane without collisions into two whole pizzas identical to the first, which he can do with the Axiom of Choice (see the "Banach Tarski Paradox" for the 3D case).
"Repeating this process ten times," says the mathematician, "you have the trivial partition of the original pizza into eleven identical pizzas."
No...
Unless the author means upside down on earth?
Overthinking leads to over-enginnering, because humans aren't great at knowing what to do with all the free time we'd have if we did our job in 10% of the time :) Perhaps overthinking is required to keep us busy. Even though we all claim our time is money, in reality most get paid by the hour and not by the amount of work that has been accomplished. Plus complexity gives more weight to what we do, allowing us to claim that there's no shortcut to where we're going. That degree, that level of experience, are all job requirements that protect us.
Experienced entrepreneurs often fall for this trap. Too much prior knowledge of a particular industry leads them to quickly find faults in most ideas, and the just-do-it attitude that leads to simple approaches that stun everyone slowly fades.
I was thinking about the iPad too. I wonder what astronauts are using now. Surely not the space pen.
strange how our pattern recognition gets worse with age ... I wonder if prior knowledge actually messes with the pattern recognition functions in the brain somehow ...
Here's a classic article about that game, dating back to 1977, describing Bill Gates trying to figure it out: http://www.borrett.id.au/computing/petals-bg.htm
I suspect you don't even have to mark the string with a pen (meaning the author possibly overthought the solution). You can just use the gap between your fingers. The chances are that the additional length added by the circumference of your fingers probably compensates for the curvature of the pizza circumference, depending on the size of the pizza and the size of your fingers. If you're doing this regularly you'll quickly learn the appropriate degree of compensation.
Quite unimpressive solution, imo. It's not about 'over thinking' any more, it's about giving up precision to find a low-tech solution.
Generating the following list took less than 30 secs when I looked it over, so obviously the example of it taking a long time to solve is a bit contrived. What threw me off a bit at first was that the number 4 was not used at all. I spent a little time trying to figure out why that was excluded before moving on.
0 = 1 1 = 0 2 = 0 3 = 0 5 = 0 6 = 1 7 = 0 8 = 2 9 = 1
If the alternative to overthinking would be staring at this looking for a pattern until you realize it is the number of loops, then that is not something I am interested in :)
I guess that might be some sort of overcomplicating it, but I was quite happy until I scrolled to the bottom
IMO the "fuck_you" of the currently most popular comment is what most people who are skimming HN during their morning coffee are bound to think, but most programmers and anyone used to deducing patterns would probably be able to figure the puzzle out in a relatively short amount of time. Not an hour. Sheesh!
That said, the "pre-school children" bit was a big hint as to how to approach it.
The use of '=' instead of, say, '→' made the math pedant in me twitch, though ;)
If you give an engineering problem to an engineer in a corporate environment, he will try to do what he's been told to be a good job: good precision and low cost, complexity not being a problem as far as the solution is achieved. If he's given 1 hour, then using 59 minutes is just as valid as using 5. And rightly so.
As for the numeric problem, same thing. You are not giving a measure of "goodness" and you are not providing rules. I'd go ahead and fill in 2581 = fuck_you , where fuck_you is a constant defined as 3.15. That's a point-wise defined polynomial there. Voila, solved in 3 seconds. Just as valid as making up something as arbitrary as counting loops in a given numeric representation. Also, I'd bet the house I don't own that if I give that in a paper to a kid with no instructions he wouldn't come up with that "solution" - ever.
In the (urban legend) problem about the pen and pencil in zero-gravity, there is context. The objective is to take notes. It's a real world problem with a fixed solution, so yeah, just using a pencil would be a much better solution than engineering a special ballpen. An engineer can and should be expected to solve that. Engineers are expected to solve real world problems and consider real world situations and realistic expectations.
When I'm presented bullshit like that IRL I get pissed off, but I can generally take the challenge of pointing out how and why is it bullshit.
Being presented it in HN, it's a good chance to educate more people on why this is NOT thinking out of the box or being clever, and why these are NOT proper tests unless adequate context is provided.
Changing the rules and picking a different context are perfectly valid ways of solving a problem.
Squinting hard at real-life patterns and trying to find the rule that generates them is most of the value in business and programming. Ever run an a/b test or looked at analytics and tried to understand why things were changing? The truth is generally as different from what you expect as a number problem whose solution is the shapes of the numerals.
- what the problem is
- what you want to achieve
- what the constraints are
- what works (a means to know when you have found a solution)
Without that, you have an undefined riddle and you can try to do something original or clever and see how that goes. Obviously the less you know the less convoluted things will even occur to you.
If you give a bunch of numbers to mathy people they will very likely try some math. They will expect it to be math. That's not loss of creativity, that's reasonable expectations.
In real life, if I'm given a pizza and told to divide it in 11 equal slices I'm pretty sure I can achieve reasonable precision without any measurements. 1/11 is just slightly more than 1/(4*3) which is easy enough to figure out. At most I'd make a few tentative marks before going ahead and cutting it. When you give a problem like this in an interview, you can assume you're expected to prove your relevant skills to the job. In a software company that would be math, algorithms, etc. not just problem solving. If your objective is to get upvoted, then maybe you should try something clever and accessible.
It's the same thing here, you get a fancy degree and everything you do has to be complex to justify getting that degree otherwise what separates you from a guy with an average degree. It's probably more an ego thing, but I see this all the time.
Actually, it's one of my greatest pet peeves. How so many things are so massively over-engineered. I could go on forever about that and there is not a single day I don't spend a while realising this about something.
If I really enjoy dealing with complexity and you give me something really simple to do, well I'm gonna go ahead and have some fun with it. It's not a matter of justifying, it's just that simple stuff is boring to somebody who enjoys complexity.
This doesn't work very well with business. Sometimes, you just need the simple solution.
It's also the reason why many startups never get off the ground. I'm guilty of it myself, but I have learned over the years to not over-engineer something until it's really needed.
This claims that creativity and education are diametral opposites. This essentially replicates the myth of the natural artist who can only achieve true creativity within nature and by forgetting culture. The basis for both assumptions is a fundamental divide between culture and nature, whereas culture is seen as hindering the creativity and freedom of the homo naturalis.
While I'm sure you can always find some cases where this distinction might hold true, there are plenty of others that reveal the false dichotomy at work here.
There is a difference between a solution perceived as complicated or simple, but there is no objective measurement for a difference in creativity. The combination and application of maths (in the example with the pizza cutter) is as much a creative use of ideas as is the "manual" method with the string.
They don't even consider humility a virtue.
Study King Author and the sword in the stone.
They don't see that God runs the universe with laws such as "pride before a fall" and "humility before honors."
If someone would call a pizza place in reality saying they wanted 11 equal pieces, they would have answered that at most they could have the pizza cut in some slices! :D HA!
Also, as someone else already pointed out, he didn't specify how to find the middle point of the pizza, so his answer isn't a complete practical solution anyway.