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.
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."
Unless the author means upside down on earth?
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.
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.
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.
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.
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.
The most talkedabout scene in the whole film involves a vaginal delivery using a vacuum blower as a suction device, and a AA battery as an inverter as the OB barks out instructions on a webcam. As a former electrical engineer I refuse to even entertain the possibility of such a stunt. Yet everybody in the media - the newspapers/TV/talkshows went gaga over this scene, suposedly a parable for "necessity is the mother(pun intended) of invention".
There's 2 scenes where the conductivity of brine is demonstrated when a person urinating on a live wire gets electrocuted, again played for laughs.
There's a scene where a student in his final year is unable to graduate because his thesis involves getting a toy helicopter to fly. He's unable to figure out the propulsion mechanics, so in disgust he throws the helicopter into the trash. The hero, our natural genius sophomore, picks up this helicopter, spends the time rigging up wires in the EE lab & finally gets it to fly. He puts a camera on the copter & as it coasts high in the air, it captures the video of the senior who has committed suicide by hanging in his dorm! Now is that crass or what ? Commiting suicide for failing to figure out some stupid propulsion mechanics! I remember thinking at the time that if this same film had been made in English, the critics & audience in the US would have torn it to shreds for such pandering & crass footage. But India being what it is, this very scene was lauded for its authenticity!
Even setting aside all that, the wrapping a string around your palm 11 times is simply trading off precision for some trial & error , not sme clever solution. For the preschool numbers thing, he's making up the rules as he goes along.
Frankly, the article should be titled "Not thinking".
I'm not suggesting this movie was something that raised awareness about an unknown issue, but it did succeed in bringing it to the forefront for quite a while, as Aamir's movies have been known to do. If you've seen other Bollywood movies, you know that 3 Idiots is a godsend when compared to the literally thousands of song filled intellectually vacuous love stories that we've been inundated with.
Furthermore, that suicide wasn't for the helicopter. It was after the dean called his (sick?) father, and told him that his son was not graduating that year. I do not remember the specific circumstances (I have terrible memory and watched this movie a few months ago), but claiming that the suicide was due to an engineering failure is ignoring many aspects of the student's life.
As for the string solution--I don't really see why you need precision in cutting a pizza in 11 slices for a random customer. It's an interesting solution, one I hadn't thought of, and I'd say one that many others hadn't thought of. The point was to deal with what a cook would have in his hands, not a mathematically sound approach. While the latter might be clean, it would be physically impossible to implement with a pizza cutter that might not be sharp enough, or a pizza where the cheese and sauce still oozed over the crust* (in which case you never could get equal slices).
* You can tell I haven't had lunch yet.
0. By a twisted quirk of fate( ie. being an Indian by birth), I happen to be addicted to Bollywood movies. I average 4 per month & have been doing so for atleast 2 decades now.
1. The guy is supposed to make a quadcopter fly in order to graduate. He is unable to. The Dean says he'll flunk if he doesn't make it fly. The guy looks at the wall in his dorm which says "loser" ( or was it "rebel" )in giant letters. The hero makes the copter fly. There's a tiny camera on the copter. The camera transmits aerial footage to a wintel laptop. As the copter soars, the laptop shows the guy hanging from a ceiling fan in his dorm .....impressively manipulative, yeah ? I think we call that camp out here. It was so in-your-face, manufactured outrage...
2. In reality, that quadcopter was built by Ashish Bhatt, a smart EE engineer out of IIT Bombay. He sells those at his startup IdeaForge (http://www.ideaforge.co.in/web/products )
3. Suicides on Indian campuses is a legitimate issue. Back when I was a student, there were 2 suicides in my campus, both because the student in question flunked some engineering/math course. The number of student suicides is disproportionately large ( http://www.google.com/search?q=suicide+IIT ). There were quite a few seminars on suicide prevention after that film.
4. Strictly speaking, it was a movie by-the-numbers...lets insert a suicide here, lets talk about pencils in outer space there, kind of thing. otoh the audience/critics were completely awed by it & made it the biggest film ever out of Bollywood.
I wasn't trying to say this movie has amazing merit; just that it served its purpose in an industry and to an audience where it isn't very easy to do so.
> Commiting suicide for failing to figure out some stupid propulsion mechanics! I remember thinking at the time that if this same film had been made in English, the critics & audience in the US would have torn it to shreds for such pandering & crass footage. But India being what it is, this very scene was lauded for its authenticity!
But that's kind of unsound to assume that the suicide must have been due to the specific event (not getting a helicopter to fly), rather than the bigger picture in this person's life.
Surely failing to graduate in an environment that places everything on having a paper diploma, including one's own image/self-worth, is more to the point of the suicide.
I can't speak for the parent poster but my criticism of the film is not with the themes, but with the trite way in which they are portrayed. I can't imagine an audience not understanding that this is what the filmmakers intended them to take away from the scene, but I can imagine them being put off by how they went about it.
Remember that we're talking about the same movie industry where a man can slap another man and have him fly some 20 feet, after which he gets up and starts dancing with a lover. Relatively speaking, 3 Idiots was sane.
There is some background of truth in the article, that most people lose the will to be creative (not the ability) over time. But it's over-generalizations galore.
You would be absolutely amazed at what that does to your problem solving ability. You actually stop over-thinking. You don't go to your advanced number-theory knowledge you may or may not have and you look for a simple solution.
Sorry, but everyone that read the article and then solved the problem is tainted.
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
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!
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
Any post-sophomoric software engineer will lament an over-designed system they helped create, lauded for its superior design, only to have it become unwieldy and unmanageable under its own monstrous complexity, and then refactored to a far simpler and more intuitive solution. It's no coincidence KISS is taught in every Engineering 101 class across the country.
I found the article to be light and refreshing, reminding me that as an engineer, often I am my own worst enemy...
Or the very least, the enemy of that tragic racquetball launcher I built in Freshman engineering that _literally_ crumpled under its own weight on demo day. Lol.
Our brain is just a amazing pattern matching machine. As soon as it is presented with a problem it starts to find patterns/relations in the problem along with going through the knowledge base it has acquired till now and trying different permutations and combinations to find the solution. In the number question, as soon as you read it, the brain will try to find patterns "using" the mathematical knowledge it has and it will keep on doing so until it gets frustrated an says WTF there is no relation here but it may happen that few days later you subconscious do find a pattern here based on "shapes" and not "numbers" but that is very very unlikely because as soon as we see numbers we think in numbers and not their shapes. If this problem was presented using shapes, anybody could have solved it in seconds.
But 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...
Here's a classic article about that game, dating back to 1977, describing Bill Gates trying to figure it out:
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 ;)
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.
Looking for 8+8+0+9 being 6 : found 2+2+1+1 : 6
Looking for 7+1+1+1 being 0 : found 0+0+0+0 : 0
Looking for 2+1+7+2 being 0 : found 0+0+0+0 : 0
Looking for 6+6+6+6 being 4 : found 1+1+1+1 : 4
Looking for 1+1+1+1 being 0 : found 0+0+0+0 : 0
Looking for 3+2+1+3 being 0 : found 0+0+0+0 : 0
Looking for 7+6+6+2 being 2 : found 0+1+1+0 : 2
Looking for 9+3+1+3 being 1 : found 1+0+0+0 : 1
Looking for 0+0+0+0 being 4 : found 1+1+1+1 : 4
Looking for 2+2+2+2 being 0 : found 0+0+0+0 : 0
Looking for 3+3+3+3 being 0 : found 0+0+0+0 : 0
Looking for 5+5+5+5 being 0 : found 0+0+0+0 : 0
Looking for 8+1+9+3 being 3 : found 2+0+1+0 : 3
Looking for 8+0+9+6 being 5 : found 2+1+1+1 : 5
Looking for 1+0+1+2 being 1 : found 0+1+0+0 : 1
Looking for 7+7+7+7 being 0 : found 0+0+0+0 : 0
Looking for 9+9+9+9 being 4 : found 1+1+1+1 : 4
Looking for 7+7+5+6 being 1 : found 0+0+0+1 : 1
Looking for 6+8+5+5 being 3 : found 1+2+0+0 : 3
Looking for 9+8+8+1 being 5 : found 1+2+2+0 : 5
Looking for 5+5+3+1 being 0 : found 0+0+0+0 : 0
Looking for 2+5+8+1 being 2 : found 0+0+2+0 : 2
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.
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 ...
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!