Chocolate Chip Cookies & Financial Markets
Forrest Gump famously said, “Life is like a box of chocolates.”
Rocky Humbert counters, “Life is like a rack of homemade chocolate-chip cookies.”
To celebrate the first snowfall of the season, Rocky baked three racks of chocolate-chip cookies using the Nestle Toll House Recipe. A trained scientist, Rocky weighed the ingredients precisely; he used an ice-cream scoop to size each cookie; he timed each tray’s bake time to the nano-second. The oven and rack temperatures were kept constant and carefully monitored.
Nonetheless, the cookies had a mean size of 6.93 cm with a standard deviation of 0.93 cm. The smallest cookie diameter was 5.5cm and the largest cookie diameter was 8.5cm.
This is a statistically improbable dispersion — and it jibes with Rocky’s view of the apparent randomness of markets.
[Disclosure: Rocky’s only explanation for the size dispersion is the cookie dough temperature as it entered the oven. Rocky’s daughter offered a mathematical explanation that uses fractals. Any reader who offers a better hypothesis will win a unique prize of dubious monetary value. The Blackberry model (as shown above) did not go in the oven.]
One Honest Man 
“Rocky’s daughter offered a mathematical explanation that uses fractals,” stated earlier in his disclosure is simply wrong. Fractals, geometric patterns that are repeated at every scale, form from repeatedly changing coefficient values. This would be saying that the only variations in the cookies would be size (diameter). This would not be taking into account: the number of chocolate chips per cookie, the depth of the cookie, any cookie imperfections, and most importantly the cookie’s taste. *Daughter suggests that a possible explanation for varying cookie diameters might be:
Cookies with more chocolate chips grew in depth as opposed to length. In the oven, the chips compiled to form large bumps for the dough to grow around. The dough cooked in this way, continually packing on to the chocolate ‘lumps’, leading to cookies with small diameters, but large depths.
*Daughter inherited third-person speaking habits from her father.
As a person who has owned a couple of bakeries(silent partner), with chocolate chip cookies are heavily dependent on the amount of salt and baking powder added. They must be exact, and that will control spreading. Next time, use a pastry bag(which I will gladly give you), and bag the cookies out. You will be more consistent and the product will peak better……just a thought in my drug induced haze.
Jeff
Jeff: The recipe called for baking soda not baking powder. So Rocky stuck a six-pack of Coke in the oven. Maybe that’s the explanation.
I will give you a better recipe than that toll house recipe. Jeff
Did the cookies come out of a convection oven? I’m told (haven’t actually been able to test) that inside an oven there are warmer and cooler spots and the fan in the convection oven makes for a more even temperature throughout the entire oven. Mix consistency is my only other guess. If I did the analysis, with each set of measurements, there would be one less cookie to measure. 🙂
Just another example of the effects of climate change. 🙂
Seriously though, looking at the recipe, you get a 2:1 ratio of chocolate chips to chopped nuts by volume. Unless from the batch, you can guarantee the exact ratio of chocolate to nuts to batter, you will get different results. The chocolate likely expands as it melts in the oven, the nuts not likely as much. This would explain some of the variance.
Also, Rocky missed an important control. Weighing each cookie before it was baked. How do final dimensions correlate to weight? Or perhaps you could normalize the varying dimensions of the already baked cookies by weighting them to, well, weight …
Finally, if you wish analyse the IMPACT of the variances in weight between the cookies, you might want to calculate the energy each produces.
Calories would be OK, and waht I would expect from a typical cook-book, but E=mc**2 is more fun, mainly because you can list the result in kilo-tons of TNT equivalent. For example, which of your cookies would be best-suited to taking out Toledo, vs say Paris?
Finally, you may want to consider Fed-exing your cookies to CERN (not all of them of course – I’m sure the bulk of them will go very nicely with a glass of milk), to determine, if the nut-shift between one cookie vs the next tells us something about the Big Bang.
Cheers,
George
Ld: Yes, it was a convection oven.
George: It’s obvious that there are already too many nuts in the Rocky Humbert household. Hence nuts were excluded from this batch of cookies. Your point about weighing may have merit — it echoes the sentiment expressed by Rocky’s daughter and LD’s comment about mix consistency and variable density (chips, etc.) If Rocky goes into the cookie business, he will be sure have a warning on the outside of the box: “These cookies are sold by volume and not by weight. The bag was full when packed, and although settling may have occurred during the shipping process, the more likely explanation for an apparently half-empty bag is that someone ate your cookies in the name of pseudo-scientific inquiry into the relationship between cookie-baking and market behavior.”
Gentlemen: Thank you for your insights. George: You are not eligible for another unique prize of dubious monetary value until there’s a new Secretary of the Treasury…
Fakename has so many comments she hardly knows where to begin. First, she recommends a book: http://www.amazon.com/Science-Cooking-Peter-Barham/dp/3540674667. All your questions will be answered.
Second, Fakename would be very scared to live in a house with scary-smart Infamous Daughter, or frankly, anyone else who understands fractals.
Third, Fakename thinks it is unfair that George has been rendered ineligible, because, can he help it if he is more right than anyone else? (This could generate a whole new discussion: is there such a thing as right, more right, and most right?) But let’s face it: who else would have come up with that Toledo v. Paris explanation?
Finally, Fakename would like you to explain the word “apparent” 🙂
Fakename: Apparent is someone with an annoyingly smart teenage daughter.
Thanks for the support fakename2, but I already have a unique prize of dubious monetary value, and to acquire another would make my life even more dubious than it is now. I believe Rocky is genuinely taking my interests to heart in this matter. 🙂
I think this a thermo problem. Assuming same mass and volume for each uncooked cookie:
If the cookie dough was perfectly homogeneous, and the heating was perfectly uniform, the dispersion in final diameters should be quite small – and dependent on extension of initial random movements a la chaos. Since the dispersion was large, you must have had non-uniformity in the heating and/or initial dough.
Inhomogeneity in the dough, either as result of chips or imperfect mixing, would retard heat-transfer. Some areas would cook/liquify faster than others, resulting in more slumping, or becoming rigid and carbonized.
Economic key-words: Inhomogeneity, chips, slumping, random, chaos, retard
Kim: Rocky is honored to welcome you to his blog; he enjoys your posts over at DailySpec. Thank you for your comment.
If Dr. Bacon, ( http://scienceblogs.com/pontiff/
the blog’s resident theoretical physicist) concurs, Kim will be declared the official winner of the Unique Prize of Dubious Monetary Value. Kim, please send an email with your address to Rocky @ Rockyhumbert.com (non-clickable) and your UPODMV will be shipped via First Class Mail.
Lastly, Rocky politely objects to Kim’s use of the key-word “retard.” It’s not politically correct. The proper term should be “speed-challenged.”
Thanks Rocky. Have enjoyed your posts as well.
I will be honored if Dr. Bacon concurs.
I have a prize from that site as well: a cane (for walking out to buy when there’s blood in the streets). Perhaps dust it off eventually.
Well, George, I tried. In the event that Fakename ever wins a UPODMV (using her questionable mathematical skills, she calculates her chances at “slim” to “none”), she has already decided what to do with it. She will donate it to the federal government in order to increase the existing pile of dubious money. Or maybe she will donate it to Goldman Sachs. Better yet, maybe she will just send it directly to China.
Fakename: George and Rocky are laughing out loud right now. It’s an inside joke understood only by members of the select group known as “UPODMV Winners .”
Ahhh. Using her questionable skills of perception, Fakename believes she has decoded the underlying premise of the game, and now upgrades her chances from “slim” to “Fakename will never win”. And, “inside joke”. Does that have anything to do with baseball?
Please send the half-bag of cookies destined for the pseudo-scientific inquiry to me …
Fakename will take the other third.
Fakename — Fakesister can take half, and you can take the third. Just don’t take the Fifth.
http://idioms.thefreedictionary.com/I+take+the+Fifth
That is to say, fakename is groaning.
Cookie physics? This sounds like a question for Seattle’s local cookie monster Nathan Myhrvold (http://starchefs.com/chefs/chris-young-nathan-myhrvold-intellectual-ventures-bellevue/html/index.shtml … this cookie monster may or may not be the patent world anti-christ, depending on who you talk to, but he is certainly someone who knows a load about the physics and chemistry of cooking. I saw a presentation by Myhrvold recently on his new book about the science of cooking and it looks fascinating…plus who doesn’t want to cook with liquid nitrogen?)
But to the question at hand. As a physicist, my first question would be: what phase of matter is cookie dough? Solid, liquid, gas, glass, etc? Okay we can rule out gas! Certainly cookie dough is not crystallized, and so I think it is what people call an amorphous solid or a glass. As such it probably wants to form a more structured setup: i.e. the combination of hydrated proteins in the floor wants to crystallize but it can’t because at room temperature it can’t move around and form the necessary structure. As you heat up the cookie dough the dough will begin to flow. Clearly there is a battle here between gravity (making it spread out) and the viscosity of the dough. So the only way I can think that the cookie can stop flowing is that the viscosity changes. Certainly this is not because we are heating it up and it is staying a glass: viscosity increases with temperature. But it may be that the dough goes through a glass transition as a function of temperature: usually at these transitions the free molecular volume increases. If this model is anywhere near correct, then the cookie will expand constantly as a function of time until it hits the glass transition, and then it will stop expanding. This is a testable hypothesis that I think I shall observe next time we bake cookies. I want diameter versus time and temperature graphs, damnit.
So why the variation in diameters? Well I’m guessing that Kim is right that non-uniform heating could be a factor: if they reach the glass transition temperature at different times they will be difference sizes. Inhomogeneity could also change that transition temperature across the cookie, but my guess it that such inhomogeneity’s larger effect would be on how it changes the actual flow of the cookie.
Of course there is an even more evocative hypothesis. Glasses are substances that want to find a lower energy configuration, but are stuck in one of numerous local minimum which are separated from the global minimum by too high an energy barrier and too much entropy (too many states near the equilibrium to go to.) As such they are excellent examples of out of equilibrium behavior: the equilibrium would be, for example, to crystalize. Further what state they are in is a large function of their history. Thus it could be that since each chunk of your cookie dough had its own history of mixing, even though you uniformly distributed the ingredients, the dough has been put into different states of closeness to the equilibrium state. Then it could be that there is a variation between cookie of the glass transition temperature between these differently prepared states. This is completely counter to what equilibrium ideas would tell you. Of course this would require the differences to be apparent over a traditional cookie size. Yeah, well, like I said a crazy hypothesis (but maybe some trader can take this metaphor and run with it somewhere interesting..yeah right)
Anyway Rocky, damn you for trapping me in a local minimum of thinking about cookie growth when I should be calculating some correlation functions (whether the later is in any form more optimal than the former is, however, doubtful.)
Dave – Thank you for your most excellent analysis!!! A lot of “food for thought…” Rocky will need to spend some time “digesting” your ideas…. but his “gut” reaction is to always blame the Mpemba Effect. http://en.wikipedia.org/wiki/Mpemba_effect
All of this over a cookie. As long as the proper amount of salt and soda(or power) are applied and the oven has a consistent temperature, the cookies should turn out OK. Also, any sugar and butter and other wet ingredients must be creamed for a couple of minutes before adding in the rest of the dry ingredients, and don’t overmix as that causes gluten in the flour to form. Home ovens suffer from when you open the door at 375, the temp drops at least 125 degrees, and takes a couple of minutes to get back to proper temp. Commercial bakery ovens, by design, do not lose heat and the product turns out much more uniform. When I owned a couple of bakeries(silent partner) they used to put a sugar cookie on each pan and when that was done, the other cookies would be done. Cookies should be taken out of the oven a little early, as they will bake another minute or two.
Jeff: The ill-shaped cookie is a metaphor for life … As Sir Francis Bacon said, “Certainly virtue is like freshly baked cookies, most fragrant when they are incensed, or crushed; for prosperity doth best discover vice, but adversity doth best discover virtue.”
Fakename loved the Mpemba effect article, especially these two quotes:
“Even if the Mpemba effect is real–if hot water can sometimes freeze more quickly than cold–it is not clear whether the explanation would be trivial or illuminating.”
Then Aristotle’s definition of “antiperistasis”: the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality. While the writer states this is an erroneous property, Fakename believes there is evidence of this in real life. For example, Joe Lieberman appears to be a genius, because he is surrounded by…Congress.
Fakename was also tickled pink by the question, “Define frozen”, and by the list of references, which begins with “How To Fossilise Your Hamster”.
Dr. Bacon should get the dough; for adding inhomogeneity of change in viscosity.
The cookie flows as it heats per (change viscosity)/(change temperature)
So final expanded size variation could result from areas with different viscosity change per degree heating, different thermal conductivity, or some combination of both.
Think of a cookie which has perfectly uniform viscosity change on heating. If heat transfer is non-uniform (some areas heat faster than others), viscosity change will be non-uniform and the cookie will warp. (we call these warped cookies)
Now think of a cookie with perfectly uniform heat transfer, but non-uniform (change viscosity)/(change temp). This too will wind up in the warped cookie jar.
The market parallel would be trained engineers designing cookies which have viscosity change uncorrelated with heat transfer, counter-acting the tendency on heating to toss cookies.
On the drive home from work I described this crummy problem to Mucky Muck Wife, who is an incredible chef (score me), and while she liked the term “glass transition”, she thought I wasn’t thinking hard enough about the butter. In particular while both Kim and I focused in on the inhomogeneity, the real question, of course, is what causes the inhomogeneity? (Apparently I am married to a reductionist.) Mucky Muck Wife noted, anecdotally, that when she makes chocolate chip cookies from the New York Times recipe (http://www.nytimes.com/2008/07/09/dining/091crex.html), which requires refrigerating the dough for a day before cooking, the cookies were more uniform. Now as a trained scientist, my gut reaction is to ignore anecdotal evidence. But countering this, as a trained scientist at a public university, this is the NYTIMES we are talking about, and so we must conclude that this anecdotal evidence, having been obtained via the Gray Lady, should be considered as fact (This is written into my contract at the university, I think.)
If we take it as true that refrigerating the dough produces more uniform cookies, then, Mucky Muck Wife reasoned, this seems to indicate that the inhomogeneity is somehow temperature sensitive. Her most likely villain was the butter: perhaps different cookies have different amounts of melted butter in them when you don’t cool them down first. This would give with Jeff’s observation about creaming the wet ingredients. When you cool the cookies you are effectively solidifying the butter and making its state uniform across all the cookies.
Now personally I think Mucky Muck Wife is milking her anecdotal evidence for the effect of butter inhomogeneity on cookie shape far beyond the margarines of rigorous scientific inquiry. On the other hand, now that Mucky Muck wife has taken Bacon as her last name, perhaps she is channeling a new version of the scientific method a la Sir Francis Bacon. And when it comes to cooling butter, it should be noted that Sir Francis was not only one of the founders of the scientific method but, as my father used to tell us, he also invented the refrigerator ( http://en.wikipedia.org/wiki/Francis_Bacon#Death ).
This calls for a transition from the state of theoretical to empirical:
To test effects of refrigeration; split the dough, refrigerate half, bake and measure dispersion in diameters for cooled and uncooled.
To test effects of inhomogeneity, test batches with and without chips (they are most likely source of non-uniformity).
Look for significant difference in variance.
This has been been an interesting and delightful dialogue — thanks to everyone who contributed. After consulting with the powers-that-be, the winner of the Unique Prize of Dubious Monetary Value is… (drum roll please), Mucky Muck Wife. The UPODMV will be shipped to Mucky Muck c/o Dr Bacon at 460 CSE…
Mindful that Rocky’s favorite platitude is: “There’s no point in beating a dead horse, but there ain’t no harm in it neither….” Rocky just discovered a research paper entitled, “Effect of fat-type on cookie dough and cookie quality” from the Journal of Food Engineering. (Yes, there ARE food engineers!) This paper confirms Mucky Muck Wife’s reasoning that the source of inhomogeneity is almost certainly the butter temperature. If one replaced butter with oil, there would be more spreading, but it would be uniform…
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T8J-4JFHDRD-6&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1127734353&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=59620fc4910e8d423af7ccebf1d4a741
Here’s the abstract:
“Effect of four different fat types on the rheology of the cookie dough and subsequently their effect on the quality of cookies were studied. The dough containing sunflower oil had the least initial farinograph consistency while that containing the bakery fat (‘marvo’) had the most consistency. Observation of the response of the above two cookies doughs to farinograph mixing showed that the one containing the oil showed more resistance to mixing while the other containing the bakery fat decreased in its consistency denoting the softer nature of the later. The cookies containing the oil had relatively higher spread value than the others. While the cookies containing the non-emulsified hydrogenated fat (‘dalda’) had the least spread. Studies also showed that the cookies containing the oil started to spread earlier and continued to spread for a longer time. Cookies containing oil had relatively harder texture and probably so because of the poor entrapment of air during creaming. However, the quality of these cookies was significantly improved by including 0.5% sodium steroyl lactylate in the formulation.
Good thing that Rocky bought a used Farinograph on Ebay! He keeps it in the same room as the X-22 Computer. http://en.wikipedia.org/wiki/Farinograph
Fakename is feeling very sorry for the horse at this point, but can’t help but ask: has Rocky also purchased a supply of 0.5% sodium steroyl lactylate? It may help with those troublesome glitches in the X-22.
Damn you Rocky. Mucky muck wife just did an “I’m smarter than you” dance in my face, which is true, but still…
Dave, your Unique Prize of Dubious Monetary Value shipped this morning. If you are lucky, Mucky Muck Wife will choose NOT to display it prominently in your home.
Rocky, the Unique Prize of Dubious Monetary Value has arrived and Mucky Muck wife thanks you very much. Amusingly she has a collection of similar prizes which she displays in her office and yours will be prominently displayed among this collections of trophies to her intellectual prowess.