A Formal Mathematical Investigation on the Validity of Kellogg's Glaze Claims | Hacker News Reader

A Formal Mathematical Investigation on the Validity of Kellogg's Glaze Claims

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71 pointsZeroCool2u20 comments

For the benefit of any other European readers who wonder what on earth this product is, it is a sugary breakfast cereal not on sale in the European Union. A brief search [1] states that it contains 86 g of carbohydrates (of which 30 g sugar), 4 g fat, and 5 g protein per hundred grams, along with 13 mg of iron. Its ingredients are:

> INGREDIENTS: Whole Grain Yellow Corn Flour, Sugar, Degerminated Yellow Corn Flour, Modified Food Starch, Contains 2% or Less of Hydrogenated Vegetable Oil (Coconut, Soybean and/or Cottonseed), Natural and Artificial Flavor, Brown Sugar Syrup, Salt, Enriched Flour (Wheat Flour, Niacin, Reduced Iron, Vitamin B₁ [Thiamin Mononitrate], Vitamin B2 [Riboflavin], Folic Acid), Red 40, Yellow 5, Blue 1, Yellow 6, BHT for Freshness, Vitamins and Minerals: Iron, Niacinamide, Zinc Oxide, Vitamin B1 (Thiamin Hydrochloride), Calcium Pantothenate, Vitamin B6 (Pyridoxine Hydrochloride), Folic Acid.

Entirely relatedly, butylated hydroxytoluene (BHT) exposure above 0-0.3 mg/kg bw/day is potentially deleterious based on effects in the reproduction segments and (precancerous) hepatic enzyme induction seen in two separate 2-generation studies in rats.[2] Quoting a rather dry academic paper:

> The Panel noted that exposure of adults to BHT from its use as food additive is unlikely to exceed the newly derived ADI [acceptable daily intake] of 0.25 mg/kg bw/day at the mean and for the high consumers (95th percentile). Exposure of children to BHT from its use as food additive is also unlikely to exceed this ADI at the mean, but is exceeded for some European countries (Finland, The Netherlands) at the 95th percentile. If exposure to BHT from its use as food contact material is also taken into account the new ADI would be exceeded by children at the mean and at the 95th percentile [everywhere].

Given that iron is listed after BHT (and therefore presumably is present at a lower concentration), I'll stick to toast & oats for breakfast, thanks...

[1] https://www.nutritionix.com/i/kelloggs/cereal-glazed-origina... [2] https://efsa.onlinelibrary.wiley.com/doi/pdf/10.2903/j.efsa....

Literal poison. No wonder obesity is so bad and getting worse. How anyone could eat this garbage boggles me. That people give this to kids ought to be criminal.

All this manual calculation rather than just invoking the isoperimetric inequality? I mean, manual calculation isn't bad, if you want to do it also as an additional demonstration, but I think the isoperimetric inequality is worth a mention here!

The calculation is somewhat bogus since comparing a sphere and a torus with the same radius isn't really valid.

The author should either compare the surface areas of spheres and toroi with the same volume, or vice versa.

The author does indeed do that via their definition of the volume equivalent sphere radius r_s.

The isoperimetric inequality is correct but too short. You need a longer proof with more equations and integrals to convince people.

It’s so sad that he just got a formulaic templated response. No one at Kellogg’s read, appreciated, or understood his humour.

Thank you for your comment. We appreciate you taking the time to share your thoughts.

Is "Hoping to restore your faith in us" really part of their form letter? It fits right in with the melodrama of the complaint, but I guess it's plausible that's what they always say.

I’m going out on a limb to guess that his commendable efforts at writing (and keeping a digital copy of) a hilarious satirical mathematical takedown were aimed squarely at going viral after the fact, exactly as has been done, rather than reaching the eyeballs of a petty corporate bureaucrat with a drawer full of coupons.

That being said, hopefully he brightened someone’s day over there, because surely the Complaints Department for a shitty breakfast brand consists of a thankless saga of reading illiterate screeds full of abuse and trivial outrage. Who needs Facebook?

> illiterate screeds

You pa'int a darn picture

A sphere minimizes surface area. If you want to deliver more glaze for a given volume of cereal, literally any other shape would be superior.

the claim is that it's the perfect shape for delivering glaze. assuming the interior of a torus does not contact the tongue, i submit that a torus wastes glaze, and the spherical shape is indeed perfect for delivery.

That holds if we assume a frictionless digestive tract that performs no action on the cereal. Since the cereal will be crushed in the mouth, and all parts mushed together, it's reasonable to assume that the inner radius of the torus will touch the tongue, and what's more, the original claim was never about touch the tongue, but delivering more glaze in the same volume.

i think even if you shatter thr torus the hyperboloidal curvature of the inner surface is suboptimal

Once you assume crunching, the glaze metric should probably be measured as volume rather than surface area, because it is a solid frosting with thickness. Assuming the unit sphere, a basic torus like R=2r with equal volume, and any glaze thickness (<=r), the sphere does provide more glaze volume.

Well well well.

The donut vs donut hole debate is a trap, though, that even the most brilliant breakfast-savvy mathematician fall into.

Truth is, the original flat flakes had infinitely more glaze than either the donut hole or the donut, mathematically speaking.

But because Kelloggs compared the donut hole to the donut, people are easily tricked into settling for the most optimal of these two shapes, while completely ignoring that either shape is a massive step backward for any cereal lover out there.

This is blatant case of enshittification, Kellogg's. It's not Grrrrrrrrrrrrrrreat.

I am reminded of the claim put forward by the Quaker Oats Company, in the 1980s, that Captain Horatio Magellan Crunch had developed (and was distributing, in exchange for box tops or something similar) a timepiece that could keep time 'here on Earth and in outer space.'

Is it really a formal mathematical investigation if it wasn't typeset in LaTeX? Hmm.

Spheres optimize for minimum sogginess. Kellogg could change the marketing angle without changing anything else to be correct.

Maybe. I haven’t done the math.

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