When does variable A equal variable B and variable B equal variable C but variable A does not equal variable C? In cooking. And other conversions that make use of the same units to measure weights as well as volumes. The problem comes in because cooking equipment is set up for liquid volumes but ingredients are packaged by weights. So if you get an eight-ounce package of bread crumbs not all those bread crumbs are going to fit in one cup even though a cup is eight ounces. Not unless you could somehow make those crumbs into a liquid of the same density as water- because that is the real problem. Eight ounces of water and eight ounces of crumbs weigh the same but the density is different so you end up with a whole lot of difficult questions for your math teacher that he will not be happy answering.
This conversion problem has come up many times without my thinking about it. I've made a lot of fudge in my life and over the course of dozens of batches I've found out that making fudge on a day with low enough barometric pressure results in taffy instead and that forgetting the teaspoon of salt ruins the whole thing and that substituting mint for vanilla requires caution because the mint has a higher alcohol content and thus causes a much more intense but still brief amount of boiling when you pour it in. But the recipe I originally used called for a cup and a half of chocolate chips. I asked my mother whether it was important if I actually measured or if I should just put in the whole twelve-ounce package. I couldn't say exactly how that conversation went except the result was that I used the whole package, more because it seemed silly to have half a handful of chips left over than any other reason, I suspect. The fudge came out wonderfully and has come out wonderfully every time I've made it without screwing it up in some other way. However, that same recipe calls for two cups of mini marshmallows and I didn't ask if I should put in sixteen ounces of that instead of packing the marshmallows into the cup twice and ending up with considerably less than sixteen ounces of weight- if I had I wouldn't have ended up with fudge at all.
I was making vegetarian meatballs yesterday (and I say "meatballs" because it's easier and causes less explaining than breadcrumseggsnutschesseballs) and the recipe called for two cups of bread crumbs. When buying the crumbs the night before I had to know how much to get, the net weight on the box said eight ounces so I concluded that I should get two boxes. I babbled this to my roommate as I was cooking. Saying that I had gotten two because I needed two cups and each cup is eight ounces so if I had sixteen ounces of bread crumbs I should be all set. Then I rattled off the obvious algebraic equation. A = B, B = C, so A = C. Or at least it should. In this case I fortuitously decided to measure the crumbs out rather than dumping in both boxes because sixteen ounces of weight would have been far too much volume for meatballs. And it turned out that A didn't really equal C. I decided I had a lot of questions about that.
Except really it's not so much a problem of math as of recipes. There are no standards in recipes and the writers also make a lot of assumptions about the readers. And that's why people who have never really cooked find it so difficult to do. Because recipes are written in an illogical language. A recipe calls for eggs but doesn't say from what kind of animal or what size. A recipe can tell you to beat the eggs. But if you aren't aware that whisking eggs is referred to as "beating" you aren't going to know what instrument, if any, you needed for beating. Not to mention all the inconsistencies in measurements and the set ups for A does not equal C failures.
I'd like to create a logical, standardized recipe system that does not require conversion. After I make this up I suppose I'll have to translate recipes into this new "language", and then convince people to actually use it in the future and then... I wonder if it wouldn't just be easier to make fun of the whole thing instead?
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Wednesday, April 13, 2011
Thursday, January 13, 2011
Excuse Me But Your Beliefs Are Mathematically Ridiculous
Excuse Me But Your Beliefs Are Mathematically Ridiculous
-or-
Comfort for People Who Think Science is Bad
I'm not writing this with the intention of upsetting anyone. As a general rule I'm painfully polite and avoid confrontation when possible. I don't like to argue because it tends to be futile. These are more the kinds of things I might say to certain people if I were the kind of person who confronted people. Just my personal beliefs. I'll leave out the age of the world and the actual date of Christ's birth and even the exactness of the calendar year as most people have heard all those. Instead I'll focus on some a little less common.
Waiting in Line: I started with this one intentionally. If there are multiple lines someplace and you choose one but then find yourself thinking that the other line is moving faster- you're right. You're right even if you switch lines. Statistically speaking the other line will always be shorter and faster moving. You're actually right about this. Feel vindicated- you're not paranoid. Unfortunately there's nothing you can do about it.
Winning the Lottery: Despite the fact that the lottery is sometimes won by people the odds that it will be won by you are slated millions to one against. You'd be better off saving the money you usually spend on lottery tickets instead of wasting it (unless, of course your only purpose for buying them is for the purchase of false hope and in that case you go ahead.)
Vaccination/Autism: Correlation is not causation. Anyone who has ever taken any kind of statistical analysis course knows very well that the correlation of two things occurring does not mean that one causes the other. All of the people who think that we shouldn't vaccinate children (vaccination being the single most effect wide-spread public health measure ever implemented in terms of lives saved) because there is anecdotal "evidence" that they cause autism are sadly deluded. Children usually start displaying signs of autism spectrum disorder before the age of three. Children with autism spectrum disorder may seem to be more or less normal children until then. Vaccinations for various diseases are given to children before they start school as required by law (and if they go to a daycare before then they are generally required to have them before entering though it depends on the child care provider). It's generally agreed that after a certain period it's better to get your children vaccinated sooner rather than later. Studies, slates of studies, some of them even double-blind if that's something that concerns you, have shown again and again that the incidence of autism among children is, if anything, possibly a little lower in children who have been vaccinated versus those who were not. If as much money was spent on trying to determine an actual cause of autism as opposed to pursuing this fictitious link maybe we would know the real causes behind it.
Another thing that people say about Autism is that there are so many more cases now and the numbers keep increasing. That is true. Absolutely true. But the numbers aren't higher because of environmental or medical reasons. The numbers are higher, firstly, because the population is a lot larger than it used to be and secondly (and more importantly) because the term "autism" is used very broadly and encompasses a huge number of disorders.
Fair Dice: I decided I had to include this one as a jab at the four years I spent on the high school math team. Teachers tend to teach students about probability and statistics through coin-flips, dice rolls, and decks of cards as these are things that both give board games an element of chance as well as being widely-known. Thereafter every time you play a game and someone rolls too many box cars you say that it's unfair. It is. It is unfair. It's statistically improbable. But the fact that it's statistically improbable makes perfect sense. That wasn't where you were wrong. You were wrong in your assumption that the dice were fair. It's rare to find a die that is never mind the fact that all those neat little problems in your books always forget to account for everything else in the world of physics.
Voting: Both the idea that your individual vote matters immensely and the idea that it does not matter at all whether you vote or not are incorrect. The first is not true because votes in large-scale, important elections never come down to a single vote cast by a single individual. The latter is untrue not because it does come down to a single vote but because if everyone like you failed to vote then the lack of the segment that thinks like you will affect the end result of the vote. So vote or not- it doesn't matter as long as you know that your justifications are wrong.
Gambling: Much like the lottery the odds are harshly in the favor of the house. The only difference is that people win from gambling often enough to make you optimistic enough to waste a lot of money.
Men & Dinosaurs: Dinosaurs went extinct tens of millions of years before anything even remotely like modern man ever existed.
Organic Farming: The idea that strictly organic farming can save the world is absurd. Unless, when you say 'the world' you are talking only about the planet itself, and not the people on it. There just isn't enough arable land feed everyone that does exist or will exist through organic farming alone. So unless you would like to kill off a great deal of the population so that you can make your vision a reality it's just not going to work.
"Protection": The idea that condoms are always effective is wrong. Especially when they are put on improperly, defective, come off, or break. 15-25 out of one hundred women become pregnant after sex using a condom. When used faithfully hormone-based methods are much more effective for preventing pregnancy and, of course, sterilization, IUDs and Implants are most effective at preventing pregnancy. Don't throw away your condoms just yet, though. Because one in five Americans have an STD and eighty percent of those who do have no idea that they do. That means that if you've had sex with more than four different people you're virtually guaranteed to have had sex with someone with an STD. So unless you are your partner are faithful and have been recently tested for an STD you're still going to want to use protection.
Airplane Safety: The idea that airplanes are not safe is incorrect. Flying in an airplane is just as safe mile-per-mile as driving in a car. The only reason you might think otherwise is because the media is obsessed with planes but car crashes happen so frequently that they get far less news coverage.
Bestsellers: Bestselling books are not necessarily books that have sold the most copies. The most popular list of bestsellers (put out by the New York Times) is calculated using both sales reported from retail sales as well as how many books are being printed and 'other factors' which are kept as a trade secret. So the more books a publisher has printed the more likely a book is to become a bestseller. And once a book has become a bestseller the popularity is self-propagating. Books on the bestseller lists are often discounted by retailers, making them more attractive to buyers.
Endings: The sad belief that an author knows when to stop. I could go on but I may have gone long enough and then some already. Anyway. The end whether it's appropriate or not.
-or-
Comfort for People Who Think Science is Bad
I'm not writing this with the intention of upsetting anyone. As a general rule I'm painfully polite and avoid confrontation when possible. I don't like to argue because it tends to be futile. These are more the kinds of things I might say to certain people if I were the kind of person who confronted people. Just my personal beliefs. I'll leave out the age of the world and the actual date of Christ's birth and even the exactness of the calendar year as most people have heard all those. Instead I'll focus on some a little less common.
Waiting in Line: I started with this one intentionally. If there are multiple lines someplace and you choose one but then find yourself thinking that the other line is moving faster- you're right. You're right even if you switch lines. Statistically speaking the other line will always be shorter and faster moving. You're actually right about this. Feel vindicated- you're not paranoid. Unfortunately there's nothing you can do about it.
Winning the Lottery: Despite the fact that the lottery is sometimes won by people the odds that it will be won by you are slated millions to one against. You'd be better off saving the money you usually spend on lottery tickets instead of wasting it (unless, of course your only purpose for buying them is for the purchase of false hope and in that case you go ahead.)
Vaccination/Autism: Correlation is not causation. Anyone who has ever taken any kind of statistical analysis course knows very well that the correlation of two things occurring does not mean that one causes the other. All of the people who think that we shouldn't vaccinate children (vaccination being the single most effect wide-spread public health measure ever implemented in terms of lives saved) because there is anecdotal "evidence" that they cause autism are sadly deluded. Children usually start displaying signs of autism spectrum disorder before the age of three. Children with autism spectrum disorder may seem to be more or less normal children until then. Vaccinations for various diseases are given to children before they start school as required by law (and if they go to a daycare before then they are generally required to have them before entering though it depends on the child care provider). It's generally agreed that after a certain period it's better to get your children vaccinated sooner rather than later. Studies, slates of studies, some of them even double-blind if that's something that concerns you, have shown again and again that the incidence of autism among children is, if anything, possibly a little lower in children who have been vaccinated versus those who were not. If as much money was spent on trying to determine an actual cause of autism as opposed to pursuing this fictitious link maybe we would know the real causes behind it.
Another thing that people say about Autism is that there are so many more cases now and the numbers keep increasing. That is true. Absolutely true. But the numbers aren't higher because of environmental or medical reasons. The numbers are higher, firstly, because the population is a lot larger than it used to be and secondly (and more importantly) because the term "autism" is used very broadly and encompasses a huge number of disorders.
Fair Dice: I decided I had to include this one as a jab at the four years I spent on the high school math team. Teachers tend to teach students about probability and statistics through coin-flips, dice rolls, and decks of cards as these are things that both give board games an element of chance as well as being widely-known. Thereafter every time you play a game and someone rolls too many box cars you say that it's unfair. It is. It is unfair. It's statistically improbable. But the fact that it's statistically improbable makes perfect sense. That wasn't where you were wrong. You were wrong in your assumption that the dice were fair. It's rare to find a die that is never mind the fact that all those neat little problems in your books always forget to account for everything else in the world of physics.
Voting: Both the idea that your individual vote matters immensely and the idea that it does not matter at all whether you vote or not are incorrect. The first is not true because votes in large-scale, important elections never come down to a single vote cast by a single individual. The latter is untrue not because it does come down to a single vote but because if everyone like you failed to vote then the lack of the segment that thinks like you will affect the end result of the vote. So vote or not- it doesn't matter as long as you know that your justifications are wrong.
Gambling: Much like the lottery the odds are harshly in the favor of the house. The only difference is that people win from gambling often enough to make you optimistic enough to waste a lot of money.
Men & Dinosaurs: Dinosaurs went extinct tens of millions of years before anything even remotely like modern man ever existed.
Organic Farming: The idea that strictly organic farming can save the world is absurd. Unless, when you say 'the world' you are talking only about the planet itself, and not the people on it. There just isn't enough arable land feed everyone that does exist or will exist through organic farming alone. So unless you would like to kill off a great deal of the population so that you can make your vision a reality it's just not going to work.
"Protection": The idea that condoms are always effective is wrong. Especially when they are put on improperly, defective, come off, or break. 15-25 out of one hundred women become pregnant after sex using a condom. When used faithfully hormone-based methods are much more effective for preventing pregnancy and, of course, sterilization, IUDs and Implants are most effective at preventing pregnancy. Don't throw away your condoms just yet, though. Because one in five Americans have an STD and eighty percent of those who do have no idea that they do. That means that if you've had sex with more than four different people you're virtually guaranteed to have had sex with someone with an STD. So unless you are your partner are faithful and have been recently tested for an STD you're still going to want to use protection.
Airplane Safety: The idea that airplanes are not safe is incorrect. Flying in an airplane is just as safe mile-per-mile as driving in a car. The only reason you might think otherwise is because the media is obsessed with planes but car crashes happen so frequently that they get far less news coverage.
Bestsellers: Bestselling books are not necessarily books that have sold the most copies. The most popular list of bestsellers (put out by the New York Times) is calculated using both sales reported from retail sales as well as how many books are being printed and 'other factors' which are kept as a trade secret. So the more books a publisher has printed the more likely a book is to become a bestseller. And once a book has become a bestseller the popularity is self-propagating. Books on the bestseller lists are often discounted by retailers, making them more attractive to buyers.
Endings: The sad belief that an author knows when to stop. I could go on but I may have gone long enough and then some already. Anyway. The end whether it's appropriate or not.
Subscribe to:
Posts (Atom)