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The cake equation - December 20, 2011
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Spiked Math Comic - The cake equation


Mmmm cake... (I don't think this equation quite works, perhaps someone can fix it for me?)

Also check out this neat application by Peter Backus (PDF File).

I probably won't post another comic until next week some time :-). In the mean time, Happy Holidays to all the math lovers out there!



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14 Comments

Perfect! Just in time for my birthday - of course I'd probably have to take the location into account, since I won't be able to travel around the globe today and won't be able to have them shipped here at such short notice... :-)

The cake equation is look very ideal.

A cake comics and no pie joke?

Happy holidays to all!

"Pi are square. Cake are round"?

Somebody should sing this to the tune of 'Frank Drake's Equation, Oh' by Dr. SETI. (Which I've just found out is actually to the tune of 'Green Grow the Rushes, Oh', but I don't know that one.)
http://www.setileague.org/songbook/equation.htm http://www.setileague.org/songbook/songs/equation.mp3

I approached this as an order-magnitude estimation. I assumed that ~10^4 chefs graduate annually from chef schools on Earth, of which 10% specialize in dessert preparation. I postulate that the ability to graduate from chef school with a dessert specialization implies the ability bake cake, suggesting a value of 1 for n_e. Given the slow rate at which my life experience suggests new forms of cake propagate, I hold further that the value of f_l does not exceed 0.1. However, since all considered individuals are chef school graduates, it seems likely that the value of f_i is close to 1; that is, if an individual develops a new recipe, they will attempt to bake it. Being chef school graduates, I expect that f_c has a value of not less than 0.9, so f_c was taken as 1 for estimation purposes. Noting that L must be taken as a fraction of year to balance with R* (chefs/year), a value of 10^-2 was used; a cake does not generally remain fresh over a period of longer than several days as indicated by a number of empirical studies (Ramsey et al 2009).

Note that this assumes further that the new devised recipe does not modify the nature of the cake in such a way that it remains fresh over a longer-than-normal period. Thus, this cake equation is only a special case, examining tasty cakes that are modified in ways effecting only tastes and aesthetic elements, rather than duration of freshness. Future research may attempt to generalize this cake equation to new cake recipes in which L becomes a function of f_l to take this defect into account.

Using the figures selected in the initial paragraph, a value of ~1 is calculated for N, suggesting that the average Earth inhabitant can consume at most a number of new tasty cakes on the order of 1-10 over the course of the average year. This is in close agreement with personal observation and with studies analyzing rates of global tasty cake consumption (Emeril et al 2010).

As a potential modification to this idealized cake equation, we propose the addition of a D factor to take into account the ability of an individual to reach a chef capable of preparing a new tasty cake. More formally, D could be defined as the n-th root of the percentage of the population within a 30-mile radius of considered individual capable of preparing the new tasty cake in question, with the appropriate value of n to be determined by future empirical research. This modification has the advantage of driving N to zero for individuals living in societies where cakes are not prepared, or for those who are otherwise unable to obtain cake due to geographic considerations. It does have the disadvantage of making N a locally-defined variable, requiring information about an individual rather than society as a whole, but the pragmatic value of a given N-value is boosted dramatically.

The girlfriend theory surprised me. I probably should stop dating it is worthless anyway. Thanks for the paper it backed my up......
not.

Wouldn't the equation make N = cake minutes, the availability of fresh delicious cakes?

Ah... You're trying to work from the number of chefs but you used the rate of arrival of chefs. To get the number of currently baking chefs on the planet you need Little's Theorem from queueing theory here.
The number of chefs on the planet Nc is given by
Nc = R* D
where R* is your rate of graduation of chefs and D is the average duration for which someone is a working chef.

So your equation is missing a factor of D.

(I have assumed certain limits exist -- it is necessary for Little's theorem to hold to assume, for example, that the number of chefs and mean duration of cheffing is finite.)

Ooops sorry -- replying too fast... you also need a factor for the mean rate at which cake-baking chefs bake cakes.

The cake equation is a lie

I am sorry that I have to mention this, but the sentence "I ... time :-)." is incorrect. A smiley can not be a part of a sentence because it is not a word or a valid punctuation mark. It is just a tool to express your emotions with regards to a remark/sentence. :)

Who says being a graduated chef is a requirement to bake a tasty cake? (Or, is baking a tasty cake sufficient to become a chef?)

Not long ago i came accross your website and also have been reading along. I thought I would leave my initial comment. Nice blog. I will keep visiting this web site very frequently. Many thanks

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