A Reddit user mathematically investigated Kellogg's claim that their frosted Pop-Tarts have "more frosting" than unfrosted ones. By meticulously measuring frosted and unfrosted Pop-Tarts and calculating their respective surface areas, they determined that the total surface area of a frosted Pop-Tart is actually less than that of an unfrosted one due to the frosting filling in the pastry's nooks and crannies. Therefore, even if the volume of frosting added equals the volume of pastry lost, the claim of "more" based on surface area is demonstrably false. The user concluded that Kellogg's should phrase their claim differently, perhaps focusing on volume or weight, to be technically accurate.
This Reddit post, titled "A Formal Mathematical Investigation on the Validity of Kellogg's Glaze Claims," delves into a rigorous and humorously pedantic examination of the assertion made by Kellogg's regarding the frosted area coverage on their Pop-Tarts® pastries. Specifically, the author takes issue with the claim that Kellogg's Frosted Strawberry Pop-Tarts® possess "more frosting" than the unfrosted variety, a statement the author perceives as self-evident and therefore requiring closer scrutiny.
The author embarks upon this investigation by meticulously defining the concept of "frosting area" utilizing formal mathematical terminology. They employ set theory and integral calculus to establish a precise definition, thereby creating a framework for the subsequent analysis. This involves representing the pastry's surface as a two-dimensional plane and the frosted region as a subset of this plane. The area of this frosted subset is then formally defined as a double integral over the region, allowing for a quantitative measure of the frosting coverage.
Having established a robust mathematical foundation, the author proceeds to hypothetically consider the scenario in which an unfrosted Pop-Tart® possesses an infinitesimal, yet non-zero, amount of frosting. This theoretical construct is introduced to address the possibility that even an apparently unfrosted pastry might contain some microscopic traces of frosting. The author then argues that, given this hypothetical minimum frosting area on an unfrosted Pop-Tart®, any amount of additional frosting on a frosted Pop-Tart® would indeed constitute "more" frosting, thus technically validating Kellogg's claim.
However, the author does not stop there. They further explore the implications of their analysis by considering the practical limitations of measuring infinitesimally small quantities of frosting. Recognizing that real-world measurements involve inherent uncertainties and limitations in precision, the author postulates the existence of a "minimum discernible frosting area," below which any frosting present would be effectively undetectable. This introduces a crucial nuance to the argument.
The author then argues that if the difference in frosting area between a frosted and unfrosted Pop-Tart® is less than this minimum discernible frosting area, then, for all practical purposes, the claim of "more frosting" becomes meaningless. The author concludes by suggesting that while Kellogg's statement might be technically accurate from a purely mathematical perspective, it could be considered misleading from a practical standpoint if the difference in frosting area falls below this threshold of perceptibility. This leaves the reader to ponder the philosophical implications of mathematically truthful yet practically insignificant distinctions.
Summary of Comments ( 16 )
https://news.ycombinator.com/item?id=44036208
Hacker News users discuss the methodology and conclusions of the Reddit post analyzing Frosted Mini-Wheats' frosting coverage. Several commenters point out flaws in the original analysis, particularly the assumption of uniform frosting distribution and the limited sample size. Some suggest more robust statistical methods, like analyzing a larger sample and considering the variability in frosting application. Others debate the practical significance of the findings, questioning whether a slightly lower frosting percentage truly constitutes false advertising. A few find humor in the meticulous mathematical approach to a seemingly trivial issue. The overall sentiment is one of mild amusement and skepticism towards the original post's claims.
The Hacker News post titled "A Formal Mathematical Investigation on the Validity of Kellogg's Glaze Claims" (linking to a Reddit post analyzing Pop-Tart frosting coverage) has a moderate number of comments, mostly focusing on the levity of the situation and the nature of mathematical proofs. No one seriously contests the Reddit post's findings.
Several commenters express amusement and lighthearted appreciation for the over-the-top application of formal mathematics to a mundane topic like Pop-Tart frosting. One commenter jokes about the implications for future grant proposals, imagining titles like "A Category Theoretic Approach to Frosting Distribution." This highlights the perceived humor in applying such rigorous methods to a trivial subject.
Another commenter points out the accessibility of the proof, suggesting that it's understandable even for those without deep mathematical backgrounds. They praise the clear explanation of concepts like proof by contradiction. This emphasizes the educational value of the original Reddit post, showing how complex ideas can be explained simply.
A few comments discuss the nature of mathematical proofs themselves. One comment thread delves into the difference between "proof" in a purely mathematical sense and "proof" in the real world, acknowledging that manufacturing inconsistencies mean perfect frosting coverage is practically impossible. This discussion highlights the distinction between theoretical ideals and practical realities.
One commenter draws a parallel to the concept of "vacuous truth" in logic, arguing that since Kellogg's doesn't explicitly quantify the amount of frosting, their claim technically can't be disproven. This introduces a philosophical perspective on the nature of truth and how it applies to marketing claims.
Finally, some comments simply express amusement or agreement with the original post, offering brief reactions like "This is great" or "Well done." These contribute to the overall lighthearted tone of the discussion.