[HN Gopher] A solution to The Onion problem of J. Kenji Lopez-Al...
___________________________________________________________________
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?
___________________________________________________________________
(page generated 2024-11-26 23:00 UTC)