[HN Gopher] A solution to The Onion problem of J. Kenji Lopez-Al...
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       A solution to The Onion problem of J. Kenji Lopez-Alt (2021)
        
       Author : fanf2
       Score  : 247 points
       Date   : 2024-11-26 11:38 UTC (11 hours ago)
        
 (HTM) web link (medium.com)
 (TXT) w3m dump (medium.com)
        
       | jfengel wrote:
       | Not "The Onion". The original capitalization is "the Onion
       | Problem", i.e. the problem of dicing onions into even pieces.
        
         | kunwon1 wrote:
         | I was confused, especially considering this [1] is still very
         | recent
         | 
         | [1] https://theonion.com/kenji-lopez-alt-returns-from-beef-
         | dimen...
        
           | dole wrote:
           | I also thought I had my finger on the pulse of some The
           | Onion/Lopez-Alt beef, like TMZ on the Food Network.
           | 
           | ontopic edit: I _am_ interested in an optimal onion cutting
           | technique, while I 'm happy with mine, the upside-down banana
           | teaches that there's always a few ways to approach and learn
           | something.
        
           | jghn wrote:
           | This is exactly what I thought of when I saw the headline!
        
       | ackbar03 wrote:
       | You want even cuts you throw it into a blender
        
         | greenpresident wrote:
         | That's the engineering solution.
         | 
         | You could also hire two interns to do it layer by layer, call
         | it the consultant's solution.
        
           | octocop wrote:
           | Then it seems you need consultants to get a guide Michelin
           | star
        
             | selimthegrim wrote:
             | That sounds like a cost plus defense contract if there ever
             | was one
        
           | 1propionyl wrote:
           | If you want an extremely fine and even brunoise that's
           | exactly what you do.
        
           | Maken wrote:
           | The consultant solution would be to buy precut onions, so
           | cutting perfect slices becomes someone else's problem.
        
         | karaterobot wrote:
         | Besides a dice that's as even as possible, the other
         | requirement this solution attempts to satisfy is using the
         | minimum number of cuts. A blender doesn't satisfy that, as it's
         | making hundreds of cuts.
         | 
         | Then, when you present your solution to the client, you find
         | out there was a third, unspoken requirement: that it should
         | involve as little cleanup as possible, which the blender also
         | doesn't satisfy. The user researcher was on vacation, and you
         | didn't find out about this before beginning design. Damn!
         | 
         | The blender solution turns out to be overoptimized on a single
         | requirement at the expense of the others.
        
           | Hikikomori wrote:
           | They're optimizing for time as knife cuts = time. A food
           | processor will do it faster if you're more than one onion or
           | so, assuming you can get the size you want.
        
             | karaterobot wrote:
             | Ahh, so in addition to having trouble getting consistently-
             | sized pieces the size of a dice or chop, the other reason
             | knives are preferred is that a food processor damages the
             | onion, releasing more water compared to a knife. The result
             | doesn't caramelize as well. This is why higher-end
             | restaurants cut onions by hand, even when operating at
             | scale.
        
               | Hikikomori wrote:
               | You don't have to turn it into mush with a food
               | processor, not all veggies are caramelized. High end
               | restaurants usually optimize for speed but not over
               | quality. Not sure why were talking that when this
               | technique is for home chefs.
        
         | ImPostingOnHN wrote:
         | A blender will make the bottom layer into paste before the top
         | is touched. If you want to toss the paste into a skillet and
         | caramelize it, that'll make a good sauce.
         | 
         | Food processor might be better, but still won't be even.
         | 
         | Source: I cook onions a lot, and am lazy. This article is
         | great!
        
           | Hikikomori wrote:
           | Always bust out the food processor when making soffritto or
           | similar very small dice. Can do onions quickly and even with
           | the method but carrots and others take quite some time.
        
         | ska wrote:
         | That's really not true, unless you are really mincing it or
         | making a paste .
        
         | laweijfmvo wrote:
         | two words: Slap Chop.
        
         | somerandomqaguy wrote:
         | Blender's not really well suited for dicing dry foods, they
         | typically need some sort of liquid to bring the solids down to
         | the blades.
         | 
         | Food processor might be more what you're thinking about but
         | it's more so for dice or mince. You won't ever really get an
         | even chop out of a processor.
        
         | aiinnyc wrote:
         | I don't think this gets you the texture you're looking, or even
         | cuts. My eyes are tearing up right now thinking about scooping
         | this out of the blender.
        
       | yunwal wrote:
       | > First, we model the onion as half of a disc of radius one, with
       | its center at the origin and existing entirely in the first two
       | quadrants in a rectangular (Cartesian) coordinate system.
       | 
       | Can someone explain to me why a half sphere (the shape of half an
       | onion) can be modeled as a half-disk in this problem? Why would
       | we expect the solutions to be the same? If you think about the
       | outermost cross-sections at the ends of the onion (closest to the
       | heel and tip of the knife), as you get closer and closer to the
       | ends, you approach cutting these cross-sections more vertically.
       | I'd expect that you'd have to make the center cross-section a bit
       | shallower to "make up" for the fact that the outsides are being
       | cut vertically. Idk, either way I think declaring this the true
       | "Onion constant" is probably wrong.
        
         | Cerium wrote:
         | I share simular concern, but also think of an onion more as a
         | bulging cylinder due to center weighted thickness variation in
         | layers. Each layer extends from root to stalk.
        
         | dole wrote:
         | Even though onions aren't perfectly symmetrical, they still
         | optimally grow or radiate out from one axis/line through the
         | middle. Stick a toothpick through a sphere as this line, and
         | slice the sphere through perpendicular to the axis, you'll get
         | circles from a sphere, or half-disks from a half onion if you
         | keep slicing perpendicular.
         | 
         | I'm lazy and cut my onions perpendicularly through halves, and
         | don't try a radial cut for uniformity.
        
           | yunwal wrote:
           | > Even though onions aren't perfectly symmetrical
           | 
           | The question I have is not about modeling an imperfect object
           | as a perfect abstraction, it's about modeling a 3D object as
           | a 2d object, and assuming that the optimization still holds.
           | I think it's pretty plainly clear that it doesn't. Think
           | about some cross-section of the onion that's closer to you
           | and smaller than the center cross-section. Let's say it's of
           | radius 0.25 instead of 1. The slices you take of it will be
           | much more vertical than the center slice. This changes
           | things. My intuition tells me it means the optimal solution
           | is shallower than the solution found here, since you'd want
           | the "average" cross-section to follow this constant.
        
             | StrangeDoctor wrote:
             | Haven't had enough coffee to think about this rigorously.
             | 
             | My intuition says that as long as you could get to the
             | desired 3D shape from revolving the 2D shape around an
             | axis, essentially integrating the area into a volume, the
             | results will be valid or equivalent.
             | 
             | I don't think that's the entire story, there are probably
             | other ways to simplify 3D shapes. And yes, onions will have
             | non constant variations (or ones that don't cancel out to
             | 0) along the sweep which is what actually invalidates the
             | real world application.
        
               | jameshart wrote:
               | If you model the (half) onion as a stack of these slices,
               | it's clear that the radius of each slice varies over the
               | height of the onion; so the points below the onion found
               | by this method towards which you need cut will form a
               | curve, not a straight line. That is hard to accomplish
               | with a straight knife that makes planar cuts.
        
             | dylan604 wrote:
             | Isn't that where calculus and intergrals come into to play?
             | As the radius approaches infinity type of stuff?
        
             | sgc wrote:
             | The author dealt with this outside the article, and posted
             | a link to his slides in this HN post. The relevant slides
             | begin at [1].
             | 
             | At the end of the day a straight cut is limiting. The next
             | step would be to design the perfect onion dicing knife.
             | 
             | [1] https://drspoulsen.github.io/Onion_Marp/index.html#44
        
             | stonemetal12 wrote:
             | I believe you are supposed to calculate R*0.55... once for
             | the max onion radius and use the same cut on the smaller
             | disks. That way the smaller disk is cut identically to the
             | inner part of the larger disk.
        
               | yunwal wrote:
               | The same cut (in terms of angle) on smaller disks would
               | be impossible with a real knife. You'd have to bend the
               | knife in order to achieve it.
        
           | PittleyDunkin wrote:
           | Only some types, of course. Shallots are not spherical,
           | though they are radial, but the centerline is often curved.
        
         | dhosek wrote:
         | For a moment, I thought that "the onion problem" related to
         | some challenging issue of topology or group theory, before my
         | brain finally sorted through its connections to identify Kenji
         | Lopez-Alt as a chef and not a mathematician.
        
           | glompers wrote:
           | J. Kenji Lopez-Alt _was_ actually mentioned (featured?) in
           | alt-weekly The Onion this month. The problem, though, was
           | that it was in an un-funny piece about the beef dimension,
           | and it is not worth footnoting here. I guess they should have
           | researched this 2021 article and spun off of it instead. But
           | maybe a Quanta Magazine and infowars joint venture could
           | enter the beef dimension. An onion with too many alt-layers.
        
             | bigstrat2003 wrote:
             | I thought it was funny. Probably the first funny thing I've
             | seen from the Onion in years, actually.
        
           | giraffe_lady wrote:
           | He's not a chef either he's a food writer and recipe tester.
           | I don't mean this as disrespect at all just they are very
           | different professions, using different skills and producing
           | different outputs.
        
             | grgbrn wrote:
             | Before he was a food writer he worked in a number of fairly
             | high-end restaurants in Boston (which he talks about
             | occasionally on his Youtube channel), and then he opened
             | his own restaurant in 2017ish. Not sure how that's "not a
             | chef"
        
               | giraffe_lady wrote:
               | I simply didn't realize he had ever run a restaurant.
        
         | Maken wrote:
         | He's also ignoring that the layers of the onion become
         | significantly thinner the farther away from the center they
         | are. So this analysis is way off even for a perfectly
         | symmetrical onion.
        
         | gus_massa wrote:
         | The solution is later in the article.
         | 
         | > _The insight that leads to a solution comes from the
         | Jacobian._
         | 
         | It's not a unform half disk. It has more weight away from the Y
         | axis.
         | 
         | You can imagine it's painted with watercolors and you want to
         | collect the same ammount of ink.
         | 
         | In an uniform disk you have                   xx        xxxx
         | xxxx       xxxxxx       xxxxxx       xxxxxx
         | 
         | But in the weighted disk of the article the top and bottom are
         | darker and the center lighter                   ..        x..x
         | x..x        x..x       Xx..xX       Xx..xX       Xx..xX
         | 
         | but there are no strips like in my ASCII art, the shade changes
         | slowly.
        
       | OJFord wrote:
       | Is the _problem_ explained in text anywhere? (TFA delegates to a
       | video and afaict only discusses another video-suggested solution
       | and a novel solution in text, I don 't understand what we're
       | solving.)
        
         | ruds wrote:
         | You would like to slice (half) an onion in a way that minimizes
         | the variance in volume of the pieces. The problem is then
         | simplified to slicing half an onion in a way that minimizes the
         | variance in cross-sectional area of the pieces at the widest
         | part of the onion.
        
         | ska wrote:
         | The problem is how to get roughly equal sized pieces from
         | cutting an onion. If you cut towards the center the inner
         | pieces are much smaller than the outer.
        
         | sampo wrote:
         | > Is the problem explained in text anywhere?
         | 
         | Not very well. There are some snippets:
         | 
         |  _" to keep the pieces as similar as possible"_
         | 
         |  _" The Jacobian r dr dth gives a measure of how big the
         | infinitely small pieces are relative to each other"_
         | 
         |  _" The variance is a good measure of the uniformity of the
         | pieces."_
        
         | ipsento606 wrote:
         | > Is the problem explained in text anywhere
         | 
         | the problem is that you want to cut up an onion in such a way
         | as to minimize variation in the size and shape of the cut-up
         | pieces
         | 
         | usually, so that the pieces will cook evenly
        
           | dylan604 wrote:
           | meh, the food processor usually handles that for me pretty
           | damn well
        
             | marssaxman wrote:
             | You are clearly not the target audience.
        
             | sleepybrett wrote:
             | yes, atomization is certainly one strategy, though often
             | people enjoy onions that are not a slurry.
        
               | dylan604 wrote:
               | i think you are confusing a food processor and a blender.
               | a food processor has other attachments/blades that do not
               | result in a puree.
        
             | bigstrat2003 wrote:
             | You're not wrong, but I think that the author's goal was
             | not "how do I cut an onion evenly" but rather "how would
             | someone do this if they had only a knife". He was solving a
             | puzzle, not trying to suggest cooking technique.
        
         | dfxm12 wrote:
         | The problem is "I have an onion that is spherical with even
         | layers. How do I cut it into pieces with equal volume?"
         | 
         | It's more of a geometry thought experiment than a practical
         | epicurean "problem".
        
       | CarVac wrote:
       | I'm surprised Kenji still does the horizontal cut at all. With
       | the angled vertical cuts I find the horizontal cut entirely
       | unnecessary. (Also a few years back I gave myself a nice flap
       | avulsion doing the horizontal cut in an onion...)
        
         | ImPostingOnHN wrote:
         | Invest in cut-resistant gloves. The few dollars will pay for
         | themselves in non-lost time, plus you can use them on a
         | mandolin.
         | 
         | NB: maybe stick a hotdog in one of the fingers to test it
         | first.
        
           | CarVac wrote:
           | I have them now, but's simpler to just avoid that one
           | dangerous and unnecessary cut that proceeds towards my body
           | instead. They taught that in Scouting, never cut towards
           | yourself.
        
             | Kototama wrote:
             | You need to cut in the direction of your body in some cases
             | (for example when carving wood).
             | 
             | Two things to prevent injuries: a) never put any force if
             | the material resists b) do it slowly.
        
               | bloopernova wrote:
               | And either learn to sharpen your knives yourself, or take
               | them to a sharpening service. Dull knives require more
               | force, and slip/catch more, so are more dangerous.
        
               | therealdrag0 wrote:
               | Oft repeated, but I don't think I've ever seen this
               | actually studied in practice. And personally I suspect
               | it's more a clever meme by knife sellers.
        
               | dylan604 wrote:
               | > for example when carving wood
               | 
               | I've watched a lot of shows about the tools used for
               | building log cabins in the pioneer days. I don't even
               | know the names of them, but the tool for taking the bark
               | off the tree by pulling the knife to you as you sit on
               | the log is crazy. Also, the one where you straddle the
               | log and swing the blade towards you between your legs is
               | right up there too. Yet, I can't think of any way of
               | making them better without using power tools.
        
               | jcoby wrote:
               | Drawshave or drawknife and adz.
               | 
               | The drawknife is the safer of the two by far. It's fairly
               | hard to cut yourself when your whole body is moving the
               | same direction. Similar to using a paring knife in your
               | palm facing your thumb.
               | 
               | The adz however you just have to have good aim or pay the
               | consequences!
        
               | JamesSwift wrote:
               | Haha, jinx : )
        
               | JamesSwift wrote:
               | Draw knife. As long as you are leaning instead of pulling
               | its relatively safe. Same as its safe to pare by
               | contracting your hand muscles instead of pushing a knife
               | toward yourself.
        
               | SAI_Peregrinus wrote:
               | Draw knives are even safer than paring knives: the
               | handles are placed such that they're closer to you than
               | the blade, it's extremely difficult to get your chest far
               | enough forward that it could contact the blade without a
               | very large chest.
        
           | resource_waste wrote:
           | Another thing to get out, another thing to clean, another
           | thing to put away.
           | 
           | All because we want to chew less. (I suppose nice texture
           | too)
        
             | ImPostingOnHN wrote:
             | Just always keep them on and never wash them. Bonus:
             | immunity to papercuts forever.
        
           | bloopernova wrote:
           | My standard housewarming gift is cut gloves and a pack of
           | nitrile gloves to put over them. The nitrile gloves are so
           | you don't have to wash the cut gloves so often.
        
         | tptacek wrote:
         | The weirder thing for me is that he makes the horizontal cut
         | after the vertical cuts --- in fact, most cooks I've seen
         | dicing onions do that --- and it seems completely backwards.
         | It's safe and easy to make the horizontal cut on an intact
         | onion half, but much harder after it's been cut up vertically.
        
           | momoschili wrote:
           | making the single horizontal cut first makes every vertical
           | cut after more difficult to perform without harming the
           | structure of the onion.
           | 
           | technique and a sharp knife enable the horizontal cut second
           | to be vastly superior to doing it first.
        
             | tptacek wrote:
             | I'm not sure I understand. My knives are razor sharp (I
             | keep a Shapton 1000 and 4000 on my counter along with a
             | strop, my daily driver is a carbon steel I have to wipe
             | down every time I cut a vegetable). They sail through the
             | onion, but the sliced-up onion still splays out to both
             | sides when I make the horizontal cut, and if you watch
             | cooks doing it, it happens there too. What harm am I doing
             | to the structure of the onion by doing it in the "wrong
             | order"? They're the same cuts. The difference seems to be
             | that in my order, the onion stays more stationary.
             | 
             | Don't get me wrong, I'm sure there's a reason everyone is
             | doing it this way, because it's kind of clearly more
             | annoying than the way I'm doing it?
             | 
             | (I'm just nerding out on this).
        
               | CarVac wrote:
               | I still don't get why you need the horizontal cut at all.
               | The diagram at the bottom of the blog post shows how
               | unnecessary it is when you do the vertical cuts at a
               | narrow range of angles like that (which I have been doing
               | for a while now).
        
               | foretop_yardarm wrote:
               | I'm sure I've seen a clip of some tv chef saying it is
               | unnecessary. Maybe Jacques Pepin but not sure.
        
         | momoschili wrote:
         | angling the horizontal cut down is a good way to handle this.
         | The horizontal cut is mostly only necessary for the lower sides
         | of the onion anyways.
        
       | ortusdux wrote:
       | On the other hand, fellow food youtuber Adam Ragusea swears by
       | the importance of heterogeneity. Optimizing for uniformity might
       | not be the best strategy!
       | 
       | https://www.youtube.com/watch?v=5cWRCldqrxM
        
         | jfactorial wrote:
         | Well the logic presented in that video certainly cannot be
         | argued against.
        
         | andrewmcwatters wrote:
         | I remember reading about the consistency of cuts from
         | classically trained chefs. I think Adam Ragusea has a lot of
         | niche, quirky practices that don't align with actual
         | profession. He's more of a culinary advocate in the same way
         | that Bill Nye is a science advocate. They're not professional
         | chefs or scientists.
        
         | stickfigure wrote:
         | I literally came in here just to make this comment. Like
         | Ragusea, I prefer every bite to be slightly novel and
         | different.
         | 
         | One of my favorite hacks for Ceasar Salad: Take a bag of
         | packaged croutons, put it flat on the table, and crush it with
         | the bottom of a pan. Repeatedly. Until you get a mix of various
         | sized crouton chunks, gravel, and dust. Apply to salad.
         | 
         | I ate a Ceasar this way in some fancy restaurant and I've been
         | making it that way ever since.
        
           | ndileas wrote:
           | You brought your own croutons and pan to a fancy restaurant??
           | Bold.
        
             | mywittyname wrote:
             | If it was a fancy restaurant, he probably asked the waiter
             | for pan-smashed croutons.
             | 
             | At normal restaurants, you can use the two-plate method to
             | approximate the effect of pan-smashing croutons.
        
               | ndileas wrote:
               | Gar son, jay nay pal a crooton pan? Smoosh?
        
         | alliao wrote:
         | it's definitely one of the more subtle tool to use when
         | cooking, mixing heterogeneity and homogeneous!
        
         | momoschili wrote:
         | really isn't a right and wrong way to do it. Erring too far
         | toward either extreme makes your food probably a bit boring
         | versus poorly executed.
         | 
         | That being said, most of Ragusea's takes haven't aged all that
         | well, some by his own admission.
        
         | catapart wrote:
         | Adam was solving a different problem statement. Kenji's point
         | was to have one simple rule that anyone could remember and
         | follow to make the best cuts without having to worry about
         | precision. This rule gets you close enough to the homogeneity
         | that is expected in most recipes (for things like onions)
         | without having to fuss over particular cuts. Having watched
         | Ragusea for a while, I'm betting he would be perfectly on board
         | with that solution to that problem.
        
       | dessimus wrote:
       | >To get the most even cuts of an onion by making radial cuts, one
       | should aim towards a point 55.73066% the radius of the onion
       | below the center. This is close, but different from, the 61.803%
       | claimed in the Youtube video at the top.
       | 
       | Wife walks into kitchen with 3447 cut onions in piles: "What are
       | you doing?!" This guy: "I just cannot get these onions cut to a
       | point 55.73066% below the origin! The best I have achieved is
       | only 2 significant digits of accuracy." Wife, mumbling: "Maybe
       | that's why Kenji said: 60%..."
        
         | wcfrobert wrote:
         | Mathematicians are wired differently than engineers. To us
         | engineers, e is approximately pi is approximately 3.
        
           | momoschili wrote:
           | think you got it the wrong way bud
        
       | drspoulsen wrote:
       | Hi everyone, the author of the blog here. I'm glad to see the
       | interest here on this piece!
       | 
       | I have slides that detail the problem setup and the mathematics,
       | as well as a consideration of three-dimensional onions, here:
       | https://drspoulsen.github.io/Onion_Marp/index.html
       | 
       | I have submitted a formal write-up of the details of the problem
       | and the solution to a recreational mathematics journal.
       | 
       | I'm also happy to answer any questions about this!
        
         | timClicks wrote:
         | I love how deeply nerd-sniped you have been by this topic. It's
         | wonderful to be able to observe your delight in solving this.
         | Thank you for sharing.
        
         | andrewmcwatters wrote:
         | I feel like mathematics and many other rigorous field-friends
         | have tons of great questions like this that are ripe for fun
         | research. Thanks for publishing this and contributing to that
         | world of curiosity!
        
         | dawnofdusk wrote:
         | Would be really interesting if you could reverse engineer the
         | model which yields 1/phi as the correct answer. Evidently for
         | some non-uniform measure on the onion you could do it. What
         | about for considering the onion as a half-ball? (Although if
         | you're cooking it really is primarily the thickness that
         | matters.)
        
         | dgacmu wrote:
         | This is tremendously fun, thank you!
         | 
         | Your solution seems to assume that all cuts need to be directed
         | towards a single point, but doesn't it seem likely that an even
         | more optimal solution increases h (depth of cut target) as the
         | cuts move outward? Or did I miss a reason that's not the case?
        
         | therealfiona wrote:
         | The thing I love about Hacker News is that someone can post an
         | article like this, then the author of the paper shows up to
         | answer any questions. Keep being awesome.
        
       | balls187 wrote:
       | Off topic, but the incorrect capitalization of the article
       | misleads one to believe this is related to "The Onion" rather
       | than "an onion."
        
         | mehlmao wrote:
         | I saw the headline and assumed it was going to be about the
         | Beef Dimension: https://theonion.com/kenji-lopez-alt-returns-
         | from-beef-dimen...
        
       | me_again wrote:
       | Marco Pierre-White recommends _grating_ onions, which ingeniously
       | avoids the entire issue.
       | 
       | Grating the Gordian knot, if you will.
        
         | tdeck wrote:
         | At that point why not just grind them in a food processor?
        
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