8 ms·

Overthinking

151 points by aen 15y ago

aen 15y ago
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.
myspy 15y ago
Well, my pizza solution would have been to find a measuring tape and divide the circumference by eleven with your phone calculator ;) 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...
- Tichy 15y ago
  I totally want to work on an augmented reality cake divider now. Point phone at cake to get a divider overlay.
  - mbq 15y ago
    Such app is already shown in the Quora thread: http://www.quora.com/What-is-the-easiest-way-to-cut-a-pizza-into-11-equal-slices http://www.quora.com/What-is-the-easiest-way-to-cut-a-pizza-...
lani 15y ago
they stopped using the pencil in space because the graphite got everywhere !!
thelastnode 15y ago
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.
- bandy 15y ago
  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.
oskarth 15y ago
The space pen affair is a well known urban myth, see for example http://io9.com/5838635/the-million-dollar-space-pen-hoax http://io9.com/5838635/the-million-dollar-space-pen-hoax 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 https://en.wikipedia.org/wiki/Centipedes_dilemma
- thaumaturgy 15y ago
  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.
akrymski 15y ago
Who cares about pens and pencils, use an ipad :) 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.
- aen 15y ago
  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.
  - akrymski 15y ago
    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 ...
  - vertex-four 15y ago
    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.
bazzargh 15y ago
The numbers puzzle was easy to spot if you've ever played Petals around the Rose. 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 http://www.borrett.id.au/computing/petals-bg.htm
buddydvd 15y ago
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.
roel_v 15y ago
I'm probably an idiot, but how do you divide the string in 11 equal pieces without measuring the length and dividing by 11?
- lusr 15y ago
  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.
  - roel_v 15y ago
    Oh but then it's just trial and error, unless like you say there is low enough friction to open your fingers and loosen all loops at the same time. Quite unimpressive solution, imo. It's not about 'over thinking' any more, it's about giving up precision to find a low-tech solution.
xarien 15y ago
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. 0 = 1 1 = 0 2 = 0 3 = 0 5 = 0 6 = 1 7 = 0 8 = 2 9 = 1
- nik_0_0 15y ago
  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 :)
- rpsw 15y ago
  That is how I did it. I actually don't understand what is meant by looking for shapes or closed loops.
  - WiseWeasel 15y ago
    Notice how an 8 has two loops (circles), and a 0, 6 and 9 have one each? The other numbers don't have closed loops, except sometimes 4.
- mastef 15y ago
  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
- scelerat 15y ago
  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!
EvilTerran 15y ago
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 ;)
CrLf 15y ago
Ball-point pens actually work in space. The ink does now flow because of gravity, it flows because of ink viscosity.
- nosse 15y ago
  You mean capillary action? http://en.wikipedia.org/wiki/Capillary_action http://en.wikipedia.org/wiki/Capillary_action I think this is somehow linked to viscosity, but I don't seem to find how.
muyuu 15y ago
It's not overthinking, it's called context. 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.
- aen 15y ago
  I'm sorry that my article offended you.
  - muyuu 15y ago
    It didn't. 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.
    - asolove 15y ago
      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.
rmk2 15y ago
>> 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.
losethos 15y ago
Indians are noxiously arrogant. 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."
hiromichan 15y ago
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!
Porter_423 15y ago
three idiots ha,Every time I watch it seems to be the same new.awesome movie
lifeformed 15y ago
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.
- Melyan 15y ago
  I bet it was more like 2 minutes. It only took me 64 minutes.
neckpunch 15y ago
What's up with the scrolling on this site? I was too irritated with the scrolling (in Firefox) to read the post.
napierzaza 15y ago
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).
dkarl 15y ago
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.
- irishcoffee 15y ago
  Stretch a string over the middle of the pizza. Stretch another string over the middle of the pizza perpendicular to the first.
instakill 15y ago
I hate that story. The reason pencils weren't used was because broken bits of graphite can cause havoc if it floats into electronic crevices.
toddnessa 15y ago
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.
nitid_name 15y ago
[Sigh] Pencils aren't used because some graphite would rub off into the air and muck up the filter.
mastef 15y ago
If you think kids are good at simplifying, just go on Draw Anything and try to figure out some of their drawings.
lhorie 15y ago
Am I the only who would cut the pizza in 12 pieces, then eat one?
- georgemcbay 15y ago
  I'm an American, I'd just eat the whole damn pizza.
dxbydt 15y ago
I hate to say this, but the article is complete bullcrap. Have you even seen the movie he references ? The protagonist is supposed to be this "naturally talented genius" who detests the bookish Indian academic education system, so throughout the film he takes potshots at the stuff he's taught in school, ultimately choosing to drop out without a degree until the Dean formally requests him to take the finals, upon which he gets the highest grade in the university. Its a completely one-sided portrayal, and while it is valid in the sense that Indian education system is wholly bunk, it is unfair to draw any deep profound lessons out of a shallow screenplay played for laughts. The pencil thing as has been pointed out by the commentators below is an urban legend. 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".
- powertower 15y ago
  I've never seen the movie. > 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.
swah 15y ago
http://www.therussiansusedapencil.com http://www.therussiansusedapencil.com
ankurdhama 15y ago
The numbers based question was hilarious!!, specially to know that pre-school children can solve it in 5 mins. Try to show this question to a pre-school child and let us know what happens. 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.
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petchang 15y ago
What a well written article! Must have taken a lot of thought to write this well :)
mastef 15y ago
>php abc.php 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 :D
- revolutions 15y ago
  Excuse my ignorance, but how does this work?
- deleted 15y ago
  [deleted]
eldude 15y ago
I'm surprised by how defensive the comments are here. They seem out of place, especially on "Hacker" News, an entity whose name by definition emphasizes thinking outside of the box. Frankly the post seems spot on regarding providing multiple examples (1 hypothetical and humorous, 1 general, and 1 specific) of how "engineering" minds' over thinking causes them to be outperformed by "simpler" minds and more obvious solutions. Even his string example could be kept obvious and simple by saying, "Measure the circumference, divide by 11, mark on string at regular intervals, cut to lines," and I'm fairly confident it would still be the best answer. 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.
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sdenheyer 15y ago
I have two children, a pre-schooler and a kindergardener, and I very much doubt either of them could solve that puzzle.

151 points by aen 15y ago

aen 15y ago

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.

myspy 15y ago

Well, my pizza solution would have been to find a measuring tape and divide the circumference by eleven with your phone calculator ;) 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...

Tichy 15y ago
I totally want to work on an augmented reality cake divider now. Point phone at cake to get a divider overlay.
- mbq 15y ago
  Such app is already shown in the Quora thread: http://www.quora.com/What-is-the-easiest-way-to-cut-a-pizza-into-11-equal-slices http://www.quora.com/What-is-the-easiest-way-to-cut-a-pizza-...

lani 15y ago

they stopped using the pencil in space because the graphite got everywhere !!

thelastnode 15y ago

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.

bandy 15y ago
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.

oskarth 15y ago

The space pen affair is a well known urban myth, see for example http://io9.com/5838635/the-million-dollar-space-pen-hoax http://io9.com/5838635/the-million-dollar-space-pen-hoax 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 https://en.wikipedia.org/wiki/Centipedes_dilemma

thaumaturgy 15y ago
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.

akrymski 15y ago

Who cares about pens and pencils, use an ipad :) 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.

aen 15y ago
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.
- akrymski 15y ago
  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 ...
- vertex-four 15y ago
  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.

bazzargh 15y ago

The numbers puzzle was easy to spot if you've ever played Petals around the Rose. 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 http://www.borrett.id.au/computing/petals-bg.htm

buddydvd 15y ago

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.

roel_v 15y ago

I'm probably an idiot, but how do you divide the string in 11 equal pieces without measuring the length and dividing by 11?

lusr 15y ago
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.
- roel_v 15y ago
  Oh but then it's just trial and error, unless like you say there is low enough friction to open your fingers and loosen all loops at the same time. Quite unimpressive solution, imo. It's not about 'over thinking' any more, it's about giving up precision to find a low-tech solution.

xarien 15y ago

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. 0 = 1 1 = 0 2 = 0 3 = 0 5 = 0 6 = 1 7 = 0 8 = 2 9 = 1

nik_0_0 15y ago
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 :)
rpsw 15y ago
That is how I did it. I actually don't understand what is meant by looking for shapes or closed loops.
- WiseWeasel 15y ago
  Notice how an 8 has two loops (circles), and a 0, 6 and 9 have one each? The other numbers don't have closed loops, except sometimes 4.
mastef 15y ago
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
scelerat 15y ago
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!

EvilTerran 15y ago

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 ;)

CrLf 15y ago

Ball-point pens actually work in space. The ink does now flow because of gravity, it flows because of ink viscosity.

nosse 15y ago
You mean capillary action? http://en.wikipedia.org/wiki/Capillary_action http://en.wikipedia.org/wiki/Capillary_action I think this is somehow linked to viscosity, but I don't seem to find how.

muyuu 15y ago

It's not overthinking, it's called context. 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.

aen 15y ago
I'm sorry that my article offended you.
- muyuu 15y ago
  It didn't. 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.
  - asolove 15y ago
    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.

rmk2 15y ago

>> 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.

losethos 15y ago

Indians are noxiously arrogant. 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."

hiromichan 15y ago

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!

Porter_423 15y ago

three idiots ha,Every time I watch it seems to be the same new.awesome movie

lifeformed 15y ago

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.

Melyan 15y ago
I bet it was more like 2 minutes. It only took me 64 minutes.

neckpunch 15y ago

What's up with the scrolling on this site? I was too irritated with the scrolling (in Firefox) to read the post.

napierzaza 15y ago

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).

dkarl 15y ago

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.

irishcoffee 15y ago
Stretch a string over the middle of the pizza. Stretch another string over the middle of the pizza perpendicular to the first.

instakill 15y ago

I hate that story. The reason pencils weren't used was because broken bits of graphite can cause havoc if it floats into electronic crevices.

toddnessa 15y ago

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.

nitid_name 15y ago

[Sigh] Pencils aren't used because some graphite would rub off into the air and muck up the filter.

mastef 15y ago

If you think kids are good at simplifying, just go on Draw Anything and try to figure out some of their drawings.

lhorie 15y ago

Am I the only who would cut the pizza in 12 pieces, then eat one?

georgemcbay 15y ago
I'm an American, I'd just eat the whole damn pizza.

dxbydt 15y ago

I hate to say this, but the article is complete bullcrap. Have you even seen the movie he references ? The protagonist is supposed to be this "naturally talented genius" who detests the bookish Indian academic education system, so throughout the film he takes potshots at the stuff he's taught in school, ultimately choosing to drop out without a degree until the Dean formally requests him to take the finals, upon which he gets the highest grade in the university. Its a completely one-sided portrayal, and while it is valid in the sense that Indian education system is wholly bunk, it is unfair to draw any deep profound lessons out of a shallow screenplay played for laughts. The pencil thing as has been pointed out by the commentators below is an urban legend. 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".

powertower 15y ago
I've never seen the movie. > 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.

swah 15y ago

http://www.therussiansusedapencil.com http://www.therussiansusedapencil.com

ankurdhama 15y ago

The numbers based question was hilarious!!, specially to know that pre-school children can solve it in 5 mins. Try to show this question to a pre-school child and let us know what happens. 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.

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petchang 15y ago

What a well written article! Must have taken a lot of thought to write this well :)

mastef 15y ago

>php abc.php 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 :D

revolutions 15y ago
Excuse my ignorance, but how does this work?
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eldude 15y ago

I'm surprised by how defensive the comments are here. They seem out of place, especially on "Hacker" News, an entity whose name by definition emphasizes thinking outside of the box. Frankly the post seems spot on regarding providing multiple examples (1 hypothetical and humorous, 1 general, and 1 specific) of how "engineering" minds' over thinking causes them to be outperformed by "simpler" minds and more obvious solutions. Even his string example could be kept obvious and simple by saying, "Measure the circumference, divide by 11, mark on string at regular intervals, cut to lines," and I'm fairly confident it would still be the best answer. 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.

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sdenheyer 15y ago

I have two children, a pre-schooler and a kindergardener, and I very much doubt either of them could solve that puzzle.