Mathematicians are wired differently than engineers. To us engineers, e is approximately pi is approximately 3.

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...

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

    ..
   x..x
   x..x
   x..x
  Xx..xX
  Xx..xX
  Xx..xX

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.

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.

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.

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.

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.

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!

Well the logic presented in that video certainly cannot be argued against.

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.

> 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

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.

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".

> 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 dθ 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."

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.

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.

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.

That’s the engineering solution.

You could also hire two interns to do it layer by layer, call it the consultant‘s solution.

That’s really not true, unless you are really mincing it or making a paste .

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!

two words: Slap Chop.

I was confused, especially considering this [1] is still very recent

[1] https://theonion.com/kenji-lopez-alt-returns-from-beef-dimen...