I was able to get the first five exactly with a bit of luck and think with a bit of thinking it should be possible to always land near 1% or 2%. But is there a good way to cut the cup, bird or map one without calculating it? I got lucky and got the cup exactly but I don't think I could get close without just beeing lucky on the bird and map onea.
The cup is symmetrical and so is the donut shading, so the trick is to flip it on its head: instead of cutting the cup with the donut, cut the donut with the cup by ensuring either the top or bottom half of the donut overlays the cup. With that line of thinking I get a perfect split every time.
I believe you, I don’t know. Show me different areas for both and maybe instinct will suggest something different. As it is, and because this was a game, I went for what seemed like a logic-y puzzle-y solution.
But they don't have the same area. The donut seems to be at least 1.5x larger than the cup (check out the screenshots posted by latexr in another comment. The area covered by the donut is half that of the cup but it's clearly less than half that of the donut, it looks more like a third or even a quarter of the donut)
Can you explain more? (I might be stupid and don't see some obvious proof of why your approach is correct), but intuitively it doesn't seem that the fact that the cup is symmetrical is enough. Say if the handle of the cup was really really big, while still preserving symmetry, then its outstanding area would be huge compared to what the doughnut could cover.
Note how the middle of the donut aligns with the bottom or top of the cup.
> don't see some obvious proof of why your approach is correct
I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.
Thanks for the reply and for the screenshots.
before writing my initial reply, I went back and tried to get a 50/50 split based on your comment and came up with the same solution. But I didn't understand why it worked.
I now believe it's either pure luck, or there's something about the sizes that result in a 50/50 split.
I think it's easy to see that if the central hole of the doughnut were either smaller or larger, or if the handle of the cup was smaller or larger, these splits would not work.
> I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.
Sure, that's fair, it's just that your original explanation for how the solution is to swap the problem from splitting the cup to splitting the doughnut was so intriguing and puzzling that got me curious.
With the cup, I moved the doughnut up from below, and just eyeballed when the area above the midline of the cup equalled the area in the hole. Turns out I can do this fairly accurately.
100%! Not sure what this measures, but I've spent decades trying to gauge whether a design is one pixel off, or if some minor change has affected the layout of something. Maybe that was all preparation for slicing America in two using an Australia-shaped knife.
"Maybe that was all preparation for slicing America in two using an Australia-shaped knife" one of those sentences I feel like no one has ever said before (/r/brandnewsentence material)
now if only the America vs Australia cut was on spherical (or ellipsoidal I guess) geometry rather than projecting both countries to a plane prior to slicing
I got 97% on the first part and was impressed with myself, but you're experience with design work is certainly the professional difference. That's impressive!
You are Homer Simpson and I claim my £5, Mr Cthulu_.
Err what are your pronouns, O tentacled horror of an old one (with a trailing ledge).
I got 98% The two I cocked up I spent too long trying to align edges and geometry but actually it seems us humans do have a pretty decent hard wired equal area estimator built in. The last one - AUS/US - should be really hard but I suspect that the results are pretty good.
I'd love to see the results for this. There is almost certainly a decent paper in it.
97% (5 perfect). I don't know either. My guess is that most people are pretty good at judging what the half of something looks like. I feel like if the movement (on my phone anyway) wasn't as jerky/sticky I would have gotten one more perfect. I definitely had one that was very inaccurate (55/45) though.
Lol, I got the America/Australia one perfect too! That surprised me!
They seem to be fudging it a bit. In the first example with the circle, anything better than 45%-55% (as measured in my graphics editor) is reported as a perfect 50-50 split.
This is a great read. While I'm not 100% sure the method (looking time) is the best, I love how the results are consistent across many experiments. Ofc, the key take away is that it doesn't really matter because personal experiences take over the inherent human "hard wiring".
Oh man, that reminds me of the Parable in the bible[1] where everyone gets a full day's wage for as little as one hours work; the workers were fine getting a full day's wage for a full day's work up until those working just one hour got the same at which point they were furious.
Quite simple if you think of Darwinian evolution - those who get more (and their offspring) outcompete you and your offspring for a limited resource so a resource struggle ensues.
The dynamics of envy leads to individuals segregating, revolting, starving and dying. Is not for nothing that all religions have it as a sin. And I am looking at it with darwinian eyes.
That idea would imply that homo sapiens (and perhaps other species) instinctually compute possible future dangers of making enemies out of what would be perceived as taking an unfair share. This can trigger a very rich discussion in so many directions. Thanks again for the insight.
It's a simple precommitment that avoids huge classes of ways to exploit you. Probably similar to instinctively refusing to pay blackmail even when it's notionally in your interest.
A lot of it probably has to do with competition with siblings too. I know personally that was always a thing with us. We aggressively monitored each others' getting of stuff. I still laugh about it sometimes. So silly but I'm glad people learn this way while the stakes are lower
It would be interesting to see how the ability correlates with social behaviour. Having one or more siblings and the need to share pie, cake, or vlaai probably creates a modest selective pressure.
Is there any proof that doing this regularly helps with anything? Not necessarily making one 'smarter', but at least keeping dementia at bay for older folks? All I could find is that playing board games seems to help with cognitive decline, but this could also be the social part of it.
This was probably the best thing in the latest b3ta newsletter (one of those bizarre Barley-esque hangovers from the British internet circa 2004)
https://b3ta.com/newsletter/issue880/
I think it would be a bad captcha—it is impressive how good some people are at this, in the sense that it is surprising that people can just eyeball areas very precisely, but a computer could really easily count the pixels.
They are probably counting pixels but you could for example use destination-out compositing operation on canvas and resize to 1x1 pixel and read brightness of single pixel.
I had to check. It's Next.js /React and the images are all CSS using Chakra. Just looking at the payload, it's sending the byte sizes which tells me they are counting bytes and checking for the difference. Pretty clever.
Only tangentially related: There was a great talk about Brilliant's custom diagramming language at last year's StrangeLoop conference: https://www.youtube.com/watch?v=gT9Xu-ctNqI
Many people are saying they did very well, but if I were trying to sell a service I'd tell people that same thing. "Sure, you did a lot of these perfectly, want to do more games that will feel satisfying" seems like a great onboarding strategy.
152 comments
[ 4.7 ms ] story [ 184 ms ] threadI got 91% overall with 3 perfect splits.
97%, 5 perfect.
A leaderboard would be pretty cool. I had tried this a few times and it's the last two that get me. Curious to see how good people are at those.
(I got the bird perfectly, to my surprise. Australia/US I bodged completely.)
https://i.imgur.com/ESLd1WV.png
No insights to share on the other ones, though.
https://i.imgur.com/yE43nun.png
https://i.imgur.com/NTfbt5U.png
Note how the middle of the donut aligns with the bottom or top of the cup.
> don't see some obvious proof of why your approach is correct
I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.
I think it's easy to see that if the central hole of the doughnut were either smaller or larger, or if the handle of the cup was smaller or larger, these splits would not work.
> I’m not a mathematician; maybe I got lucky with my approach. Crucially this is a brain teaser so it plays by the rules of a game. I formulated an hypothesis by starting from the assumption that they give you a satisfactory fighting chance.
Sure, that's fair, it's just that your original explanation for how the solution is to swap the problem from splitting the cup to splitting the doughnut was so intriguing and puzzling that got me curious.
:)
I did best when I worked intuitively and fast.
Err what are your pronouns, O tentacled horror of an old one (with a trailing ledge).
I got 98% The two I cocked up I spent too long trying to align edges and geometry but actually it seems us humans do have a pretty decent hard wired equal area estimator built in. The last one - AUS/US - should be really hard but I suspect that the results are pretty good.
I'd love to see the results for this. There is almost certainly a decent paper in it.
Lol, I got the America/Australia one perfect too! That surprised me!
https://parentingscience.com/babies-expect-fairness/
Though they are sensitive to more than the size; they also want the slices with the nice colors and toppings :)
https://www.youtube.com/watch?v=meiU6TxysCg
1: https://en.wikipedia.org/wiki/Parable_of_the_Workers_in_the_...
You really made me think there.
Thanks for sharing that one.
That idea would imply that homo sapiens (and perhaps other species) instinctually compute possible future dangers of making enemies out of what would be perceived as taking an unfair share. This can trigger a very rich discussion in so many directions. Thanks again for the insight.
I was introduced to this subject through this concise book: https://www.cambridge.org/core/books/evolution-of-the-social...
https://boardgamegeek.com/boardgame/244995/illusion
I win
Constructive solid geometry, and then some sort of computer graphics algorithm for area?
Or is it an SVG, and they're doing some sort of complex integral? (<--probably not)
[0] https://en.wikipedia.org/wiki/File:Mug_and_Torus_morph.gif
This might not have been tested on desktop Firefox.
However, I figured it out; interaction with Dark Reader extension.
Really neat way to advertise Brilliant. Reminds me of Google Doodles or something.