Pizza Math

September 2nd, 2014 by Potato

A reader requested this a long time ago, sorry for taking so long Ben!

The age-old question: is the medium the better deal, or the large? The medium may be cheaper per slice, but each slice on the large is bigger…

The math to figure this out is not hugely complicated, but it’s just a bit more than you might be able to do in your head or with a smartphone while you’re hungry and staring at a menu board. What we’re interested in is the area of pizza that you get per dollar. The area of a circle is simply pi * r2. Pizzas are sized by their diameter (double the radius). However, there are no points for crust (“pizza bones”), so we’ll subtract 1″ from each diameter (for a typical 0.5″ of crust on each side of the line through the circle) when computing the area factor. Because we’re really just interested in the relative value we don’t necessarily need to do the division by two or multiplication by pi — the pizza value will scale with the square of the adjusted diameter — unless we’re comparing to a square pizza. While some pizza places use their own wacky sizes, or have irregular hand-shaped crusts, most places have settled on standard sizes. I’ve listed the rounder area factors and actual edible areas below:

Small (nominally 10″): Usable diameter of 9″, area factor is 81 (edible area of 63.6 sq. in.).
Medium (nominally 12″): area factor is 121 ( 95 sq. in.).
Large (nominally 14″): area factor is 169 (132 sq. in.).
Extra Large (nominally 18″): area factor is 289 (227 sq. in.).
(note that Pizza Pizza and some other stores have 16″ extra larges)

Square pizzas: most often encountered with party sized pizzas. In this case to make a true comparison you would need the circular pizzas area in square inches. For a 15×21″ (nominal) party pizza, there are 280 sq. in. of edible pizza. Converting into “area factor” above, that would be 356.

To put this into practice then requires a division step with the price. You can divide the price by the area factor to get a price per unit area — then lower is better. However, because pizzas are often priced near $10 or $20, the inverse may be more convenient to work with — pizza units per dollar — in which case the higher the number the better value. For example, if a large is on for $10, the pizza per dollar is 169/$10 = 16.9. If the medium is $8, that’s 121/8 = 15.1; if the party size is $20 that would come to 356/20 = 17.8. In that case the bigger you go, the better your value.

For your convenience, I made a reference card for your wallet. (Be sure to select “actual size” when printing)

I’ll note that dollar per unit pizza should be the preferred unit/method if you want to look at how the value difference scales across pie sizes rather than just which is larger — analogous to the L/100 km measurement system vs MPG issues.

Lab-Grown Meat

August 23rd, 2013 by Potato

Meat is an interesting and contentious meal choice. I’m personally a vegetarian, but a lacto-ovo one. I don’t have any particularly strong moral objections to using animals for human purposes: though I personally would prefer not to get involved in the process, I don’t throw a fit every time a friend has a BBQ (and my daughter is an omnivore until she decides otherwise). Yet I think people eat vastly too much meat. So many animals raised just for food, it’s so wasteful. Grazing animals can better make use of marginal farm/pastureland/scrub, but many acres of prime farmland is also given over to raising animals or growing feed for them. A laying hen can produce hundreds or thousands of eggs in its lifetime, but you consume way more chicken than that ratio of eggs:meat would suggest should be in your diet (generally you don’t eat the old egg-layers, you grow chickens just for meat and a separate group for eggs that you then feed to your dog).

For cows, it takes 5-100 times as much inputs like land, water, fossil fuels, and grains to make a pound of beef as it does to make a pound of vegetarian feed (in some reports these figures are adjusted for the protein content, so a report that says that it takes 10 pounds of vegetable protein to make 1 pound of beef protein may mean that ~100 pounds of feed went into the pound of meat). The rough rule of thumb I have heard is that we can feed about 10 times as many people on a vegetarian diet as a heavily meat-based one given the same input constraints. Whatever the exact number is, it’s a lot: there’s a fair bit of waste putting a cow between you and your food. I like to cut out the middle man.

The announcement that lab grown meat has been made (and eaten) made the news recently, spurring a lot of speculation about what the future will bring. I think it will be interesting, particularly for those simultaneously interested in animal cruelty and eating hamburgers, but I don’t think this is ushering a new paradigm of how we feed ourselves, and it’s not an immediately apparent investment opportunity.

The big question in my mind is what will the inputs be under the lab-grown scenario? Is there a business case there?

Land: One of the big advantages of lab-grown meat is that you don’t need to waste all that space letting the animal move around. You can pack the meat in close and even stack the building up with multiple stories, putting a lot of production into a small footprint. However, land is not expensive. It perhaps is not right, but anyone can just go and buy up farmland — prime farmland — and plop a condo on it, and most of the cost will still come from the construction process. So saving land is great, but we simply don’t value it enough right now to have this become a factor. Indeed, the need for infrastructure will likely make this way of producing a hamburger much more costly than just letting herds of cattle roam across the foothills of Alberta, and the capital investment required will likely keep many from making the plunge out of curiosity.

Water: I honestly don’t know where all the water is used in cattle farming, the reports suggest ridiculous amounts of it in use. Are the cows being bathed nightly? Anyway, water use will likely decline, but unless these meat factories get built in the boonies the water expense will likely remain unchanged as expensive, treated city water gets used.

Feed: Here is my big question. By not growing a full cow (just the meaty parts), and by just growing it long enough to harvest (rather than burning up resources in ongoing metabolism as the cow wanders around the fields day after day for months and years on end), there should be a big gain in the ratio of feed inputs to meat outputs. But it’s still not going to be very close to 1:1 — there are still inefficiencies in growing muscle tissue. There might be a decent efficiency between the growth medium energy and the meat-like substance protein content, but the question is whether that gain helps us any when you consider the full chain. With a full cow you just shovel a bucketful of corn/hay/wheat/oats into a trough and let the cow do its job. With a lab-grown collection of cells you will have to predigest the grain inputs through some kind of process to produce a sterile nutrient solution. What losses and inefficiencies will be associated with that value chain?

I doubt that having a disembodied bovine stem cell grow a muscle cell in a vat is going to come anywhere near the efficiency of eating some corn and growing a muscle cell yourself. Perhaps the ratio will come down, from say 100:1 to 10:1, but given the other costs I don’t think that makes a business case. I suspect that, at the end of the day, there will be next to no advantage here: 100 pounds of unprocessed grains may be cheaper and less resource intensive than distilling 10 pounds of grains down to soluble carbohydrates and an osmotically balanced protein slurry.

Other inputs: What antibiotics and growth hormones will be needed to keep these cells alive and stimulate them into growing? There won’t be as many fossil fuels needed to drive trucks and manure-spreaders, but what about the electricity needs of the incubators and buildings? What of the plastics and glassware?

Manpower: How educated will the meat rustlers of the future have to be? How many cowboy technicians will we need per pound of beef, versus farmhands per pound the old way, and what wages and benefits will they demand?

I simply have trouble seeing this as the future of food.

Food is cheap. Fundamentally it is the most basic and essential need of every person — even the poorest — and we go through a lot of it. I don’t see how lab-grown meat will come close to the price of traditional meat. Even with scaling up and industrializing the process in a factory, will this be competitive? There might be a niche market for PETA members to get their guilt-free burger fix, no matter the price, but will it truly become an industry?

In some dystopian future where process efficiency trumps capital requirements, maybe. But if we’re in a world that’s down to counting every last grain of wheat, why not just eat the plant matter ourselves?

Now, lab-grown organs are not so different from lab-grown meat (indeed, just a specialized form of lab-grown meat). But people will be willing to pay vastly more per pound of life-saving kidney than they would for mediocre appetite-satisfying hamburger. So while I don’t think lab-grown meat will be a food source to count on soon, lab-grown organs might be here sooner (despite the added complexity). Indeed, if lab-grown meat is to become a viable business, it will likely depend on innovations and technologies developed for organ regeneration.

Little Known Facts About Calories Part 2

July 22nd, 2013 by Potato

Continued from yesterday…

Calories are loyal. If someone buys a meal, the calories in the food belong to them. If you try to steal a bite, the calories will run away from that bite and stay with the group, remaining loyal and whole to the person who bought the food. Yes, free food is also calorie-free.

Calories can’t swim, at least not in water (gravy and syrup are a whole other matter). This is why drinking lots of water is a hot diet tip. However, it makes us question the wisdom of not eating while swimming: calories would never follow you into the pool.

Pile the calories up and leave them. One good way to avoid calories is to scare them away into one pile on your plate, for instance by making soft yet menacing banging noises with your fork. Then, leave a few bites behind. The calories will have piled into those last few bites. Babies know this instinctively, and will smash, shake, and scream at their food during mealtimes… and then never, ever eat the last bite of anything.

“Light” means that some of the calories have been removed from the food. The remaining calories are thus lonely and feeling vulnerable. This makes them more likely to want to make friends with your hips. To compensate for this you should build up the self-esteem of any “light” foods before eating them by praising and encouraging the calories. Make light conversation, complement them, maybe even sing a soft, cheerful song. Once the “calorie reduced” food has been built back up, the other methods will work again.

Air of course has no calories, and to a very close approximation Rice Krispies are 100% air, so they’re calorie-free. With a small extension of the principle, anything largely made up of puffed rice is also calorie-free. For example, Whatchamacallit bars. A similar principle is at work with popcorn and whipped cream.

Did you know that calories get sleepy? Calories get very set in their ways, and don’t adjust well to changes in their sleeping schedule. This is why it’s important to get a good breakfast early in the morning: not only is it a good start to your day, but it’s also so you can sneak up on the calories when they’re too tired and sleepy to make you fat. Of course, you have to find the right calories for that.

Some calories go to bed early, while others are all-night party animals. This is why drinking Coke and eating nachos and chocolate at night will always make you fat, because those are night-time foods. But, those same foods make excellent breakfast selections. Breakfast-for-dinner, or Brenner is always a good idea for the same reason. Plus, who doesn’t love waffles at midnight?!

Little Known Facts About Calories Part 1

July 20th, 2013 by Potato

Calories are little things that live in food. They’re tasty and give your body energy. Things without any calories aren’t really food at all. In small amounts, calories are great things. Trouble arises when large groups of calories get together though. They start getting mischievous ideas, and once inside your body avoid getting burned, instead turning into fat — which is not what we want. There are a great many resources out there to help you diet, to find ways to count the calories in things, and limit how many you allow to get together at once in your body. But why give them that kind of power over you? Did you know that calories are just as afraid of you as you are of them? This handy guide will show you the many unknown facts about calories so that you can keep them in line and eat whatever you want — without getting fat.

First, threaten your food. It’s never polite to threaten other people, but calories aren’t people. Severe threats or growling noises can scare away calories, and other people at the diner. Just be sure to leave them a safe place to run to, or they’ll be back with a vengeance! (True for both groups).

This beady-eyed nasty thing is a calorie. It is more than a unit of heat energy: it is a malevolent agent that lives in your food and on your hips. It does not love you, it will never die... but it can know fear. Threaten it! Control it! Bend it to your will!

Calories are afraid of heights. If you put your food in a high place, such as on top of the fridge, the calories will get scared and jump out. This is best facilitated by giving them a ramp or ladder to climb down from. Calories are small, with hundreds of them fitting into a single cookie, so even a piece of thread looks like a grand staircase to them. They’ll have no trouble making their way down if they’re scared enough of being up high. Even if they have to jump. They hate heights that much, and do not have logical responses to stressful situations.

A corollary to this is that food in low places may collect the fleeing calories from the food in high places. This is why even when you’re following your diet and only eating the lettuce in the crisper drawer of your fridge, you always seems to gain weight anyway. The calories from your butter have snuck down there! Lettuce, by the way, is secretly evil. Under controlled lab conditions, it presents itself as largely free of calories, hardly associating with them at all. But out in the wild real world, lettuce readily aligns itself with calories, harbouring them and building them up within its nested leaves as some kind of highly fortified barracks, turning those mindless loitering calories into a highly trained force to be handled with extreme caution and delicacy.

Calories have weak grips. If you shake your food before you eat it, you can loosen up the calories and even shake some out entirely! They can’t hold on to the delicious food with their weak grips, and will fly away. A good way to facilitate this is to break your food in half: the calories will just come pouring out! Combine this tip with the previous one, and shake your food above your head — just watch out for crumbs and sloshing.

Calories go on vacation. They don’t want to work at making you fat any more than you want to work on TPS reports when on vacation. Take them out for a nice trip by the river, and lay out a picnic under a shady tree. Who can think of work in situations like that?

To be continued tomorrow…

Almost three years ago I created a video called Little Known Facts About Calories. I had planned to make a whole series of such videos, but the first two had such a cold reception and so few views that I gave up — making those flash videos is a fucktonne of work, and after three years it still hasn’t even hit 100 views (though to be fair the subsequent installments would have been easier after I had climbed partway up the Flash learning curve and had created the base shapes for the calories and other elements). So here, with minimal editing and embellishing, are the notes that would have formed the basis for the planned ten-episode run (would have been about 6 minutes of animation all-together).

On the Magic of Peanut Butter

September 30th, 2012 by Potato

Peanut butter is a truly magical substance. Like many people I have at one time or another tried to make it myself by blenderizing peanuts (and once tried to smoosh honey roasted peanuts in a failed attempt to create the world’s most delicious spread) and it is just not the same. This is reflected in the fact that there is peanut-butter-flavoured ice cream, but not peanut-flavoured ice cream: somehow the process of turning peanuts into peanut butter creates an all-new taste that is just that much better.

Yes, there’s sugar in there, but it’s not just that it’s sweeter. It goes with everything, a kind of universal compatibility that doesn’t just come from a little bit of sweetening. There’s the classic peanut butter and chocolate pairing, but as good as that is it doesn’t really demonstrate peanut butter’s intrinsic cooperative nature, since chocolate-covered peanuts are also good. Consider instead apples, jam, bacon (or so I am told), bananas, crackers, rice krispies, soy beans, and that mass of cellulose fibre that spans the border between food and building material: celery. Nothing made of mere matter could be so universally compatible, so delicious, and yet still contain nutrients.

I asked the question recently of some friends: what doesn’t go with peanut butter? And really all we came up with was laundry (indeed, I got some peanut butter on my shirt while eating apples writing this, and that’s going to need to be pre-treated).

In my head, the Kraft factory consists of large cauldrons of bubbling peanut mush, overseen by teams of witches who imbue it with that magical essence, channelling the vital incantations that transmute a mere collection of ground peanuts into something that is not of this realm. A magical substance composed more of the essence cooperation and taste than it is of sugar, protein, and fat.

I will leave you with one last combination that I thought was common-sense, but my sister (who learned it from me) says blew the mind of some of her friends: peanut butter and pop tarts. Just get yourself a frosted (or plain, though that defeats the point) pop-tart — I’m partial to raspberry but strawberry is every bit as good — toast as usual, and cover with peanut butter before eating. Breakfast is served!