All that and nobody figured out that the cookie isn't 63% things that are not chocolate chips. The Chips are milk instead of semi-sweet and so they are 37% Chocolate.
Years ago I embarked upon a quest to maximize the amount of chips I could put into a cookie and still have it meet a rough operational definition of cookie: It had to look like a cookie and I had to be able to pick it up and eat without getting chocolate on my fingers.
In other words, a blob of chocolate wouldn't qualify, but a blob of chocolate with pastry handles might.
But that seemed like a lot of work and not very Occam-y.
I found that by playing with the butter-flour-chip ratio, I could get a very thin very crisp cookie, almost more of a wafer, that I could grasp by the edges and lift to my mouth with clean fingers; there was enough chocolate that the shock of biting in didn't travel through the cookie and cause it to break, but enough dough to prevent anything beyond reasonable crumbs from falling away.
I cannot remember the recipe and don't know if I ever wrote it down, but I'm pretty sure the order by quantity was chips, butter, flour, and maybe an egg or two.
This is incredibly confusing: 37% of what? By mass or by volume?
The answer about even distribution pre-supposes physical dispersion characteristics, but does not mention which measure of proportion is relevant (it would seem volume); nor any means of reliable testing. As another commenter has aluded, the "100% chocolate%" concept (even for the chocolate) is also at best inaccurate. So, this looks to be more of a coincidental alignemnet of numbers, and a game of causation/correlation. To wit: A cookie with 37% by volume of 72% chocolate is in no way the same cookie as one with 37% by mass of 40% milk chocolate. Either by taste, consistency, or chemistry. So, i would think any proper answer for this question would need to be robust the these particulars.
I read the hypothesis as relating the appearance of the cookie. That is the proportionate ratio of visible chocolate to dough on the surface of the cookie as it relates to the maximizing the visual appeal of the cookie on product packaging.
So we are talking about "perceived" cookie quality based on visible surface area of chocolate.
Now in this case, what I think is happening here is that we are observing a simple case of the golden ratio. Humans, consistently and subconsciously see distributions of ~38% to be harmonious (sometimes crudely approximated as the rule of thirds).
Therefore it stands to reason that this "golden mean" ratio of visible chocolate creates the most visibly appealing image.
With the cooperation of a chocolate chip packaging manufacturer or online retailer we could test this. Simply conduct some extensive A/B testing of chip packaging that varies only by ratio of visible chocolate. And see if the golden mean comes out best.
However, I suspect this testing has already been done.
As for the best tasting ratios of all ingredients (including chocolate) in a chocolate chip cookie, fortunately, significant research in this area has recently been published. You may have seen this link from the food lab: http://sweets.seriouseats.com/2013/12/the-food-lab-the-best-...
It starts with the curious observation that 2014, spoken aloud as "twenty fourteen", becomes "teen 420" in reverse. Perhaps just a coincidence. But then it further notes that April 20, or 4/20, is the date of Easter in 2014. Two coincidences! Now the numerologist starts getting suspicious...
This feels like pure numerology to me, with the entire argument being based on some vague numeric coincidence. I have no experience in food manufacturing, but I'm willing to bet there are much easier ways to mix dough at any desired proportion than the one described here.
Here's another, potentially simpler explanation: I am no pastry chef, but it seems these recipes often use a 2:1 mix of different types of chocolate (e.g. dark and milk) [1]. Now if the recipe contains 1/4 of one type and half of this of another type, that's 25% + 12.5% = 37.5%, which is about as close to 37% than 1/e. Ta-da!
And this is just one explanation I just made up on the spot; I'm sure one can find many others by playing around with the numbers. I don't know for sure what the real answer is or if there even is one (it could just be that marketing thought 37% sounded more elaborate than a round number like 40% while also costing less to produce and tasting the same), but one shouldn't forget to apply Occam's razor here.
Clifford Stoll has a great chocolate chip cookie recipe in his book "cuckoos egg" - about his experience tracking crackers through international networks. (With cameo appearance from RTM and the worm).
I'd put it here but the experience of cutting / pasting on iPhone is painful. (Hints and tips gratefully received).
"Two eggs, 1 cup brown sugar, 1/2 cup regular sugar, 2 sticks softened butter. Fold in 2 1/4 cups flour, 1/2 teaspoon salt, 1 teaspoon baking soda, and a couple tablespoons of vanilla. For an extra chocolate jag, toss in 3 tablespoons of cocoa. Oh, don't forget 2 cups of chocolate chips. Bake 'em at 375 degrees for 10 minutes."
This is very similar to the Toll House cookie recipe, but with even more vanilla which I think is an excellent idea. And that extra cocoa powder looks good too!
Edit: For metric measures, 250 ml white sugar, 250 ml soft butter, 530 ml flour, 2.5 ml salt, 5 ml baking soda, 30 ml vanilla, (optional 45 ml cocoa), 250 ml chocolate chips.
I wonder if someone could do this in by-weight measures? Flour is too compressible to measure accurately by volume.
I doubt it has anything to do with 1/e. Someone in marketing probably liked the number 37% and manufacturing said, "yeah, that won't cost us much extra". Nothing to do with infinite sums or the distribution of chocolate chips in dough. Just marketing.
For the same reason, why is Ivory 99.44% pure? Because 99.44% sounded catchier than 99%.
25 comments
[ 2.2 ms ] story [ 61.0 ms ] threadJust like these are not 28% not Chocolate bar. http://www.amazon.com/gp/product/B004BR1C46?tag=itemsid-20
But I did sell 3 Chocolate bars with that link so it might work out better than I thought.
I'll promise in a week to do a follow up with stats from the link and Post it on HN "How I made 84 cents on a single Hacker News Post And So Can You"
In other words, a blob of chocolate wouldn't qualify, but a blob of chocolate with pastry handles might.
But that seemed like a lot of work and not very Occam-y.
I found that by playing with the butter-flour-chip ratio, I could get a very thin very crisp cookie, almost more of a wafer, that I could grasp by the edges and lift to my mouth with clean fingers; there was enough chocolate that the shock of biting in didn't travel through the cookie and cause it to break, but enough dough to prevent anything beyond reasonable crumbs from falling away.
I cannot remember the recipe and don't know if I ever wrote it down, but I'm pretty sure the order by quantity was chips, butter, flour, and maybe an egg or two.
62%? Yeah, well past that, if memory serves.
The answer about even distribution pre-supposes physical dispersion characteristics, but does not mention which measure of proportion is relevant (it would seem volume); nor any means of reliable testing. As another commenter has aluded, the "100% chocolate%" concept (even for the chocolate) is also at best inaccurate. So, this looks to be more of a coincidental alignemnet of numbers, and a game of causation/correlation. To wit: A cookie with 37% by volume of 72% chocolate is in no way the same cookie as one with 37% by mass of 40% milk chocolate. Either by taste, consistency, or chemistry. So, i would think any proper answer for this question would need to be robust the these particulars.
So we are talking about "perceived" cookie quality based on visible surface area of chocolate.
Now in this case, what I think is happening here is that we are observing a simple case of the golden ratio. Humans, consistently and subconsciously see distributions of ~38% to be harmonious (sometimes crudely approximated as the rule of thirds).
Therefore it stands to reason that this "golden mean" ratio of visible chocolate creates the most visibly appealing image.
With the cooperation of a chocolate chip packaging manufacturer or online retailer we could test this. Simply conduct some extensive A/B testing of chip packaging that varies only by ratio of visible chocolate. And see if the golden mean comes out best.
However, I suspect this testing has already been done.
As for the best tasting ratios of all ingredients (including chocolate) in a chocolate chip cookie, fortunately, significant research in this area has recently been published. You may have seen this link from the food lab: http://sweets.seriouseats.com/2013/12/the-food-lab-the-best-...
"Max... You will find that thing everywhere... As soon as you discard scientific rigor, you're no longer a mathematician, you're a numerologist."
http://www.youtube.com/watch?v=d1IzNKIHhp0
It starts with the curious observation that 2014, spoken aloud as "twenty fourteen", becomes "teen 420" in reverse. Perhaps just a coincidence. But then it further notes that April 20, or 4/20, is the date of Easter in 2014. Two coincidences! Now the numerologist starts getting suspicious...
Here's another, potentially simpler explanation: I am no pastry chef, but it seems these recipes often use a 2:1 mix of different types of chocolate (e.g. dark and milk) [1]. Now if the recipe contains 1/4 of one type and half of this of another type, that's 25% + 12.5% = 37.5%, which is about as close to 37% than 1/e. Ta-da!
And this is just one explanation I just made up on the spot; I'm sure one can find many others by playing around with the numbers. I don't know for sure what the real answer is or if there even is one (it could just be that marketing thought 37% sounded more elaborate than a round number like 40% while also costing less to produce and tasting the same), but one shouldn't forget to apply Occam's razor here.
[1] a quick Google search gives me this: http://www.talkfood.com/forum/showthread.php/3230-37-Chocola...
I'd put it here but the experience of cutting / pasting on iPhone is painful. (Hints and tips gratefully received).
This is very similar to the Toll House cookie recipe, but with even more vanilla which I think is an excellent idea. And that extra cocoa powder looks good too!
Edit: For metric measures, 250 ml white sugar, 250 ml soft butter, 530 ml flour, 2.5 ml salt, 5 ml baking soda, 30 ml vanilla, (optional 45 ml cocoa), 250 ml chocolate chips.
I wonder if someone could do this in by-weight measures? Flour is too compressible to measure accurately by volume.
For the same reason, why is Ivory 99.44% pure? Because 99.44% sounded catchier than 99%.