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Lecture 1 | Modern Physics: Special Relativity (Stanford)
modern algebra?
what are the prerequites and how do you know you are ready?
Prerequisite is Set theory ,functions and highschool algebra
How to Rationalize Your Cooking: Using Laws of Proportion in the Kitchen
The word "rational" has all kinds of connotations - good and bad - in today's culture. Be rational, we say to people who seem unable to see reason. Or, conversely, we tell people all too skilled at using fake logic to justify their own bad ideas: You're just rationalizing.
The word - and its varying valuations - attests to the deep uncertainty we feel toward the rational mind; we worry that it cuts us off from emotion and bias, from much of what it means to be human, even as we celebrate its capacity to raise us above the animals. What many people don't know is that the very word rational is rooted in ancient mathematics, coming to us via the word ratio - a key concept beloved of ancient architects and philosophers alike. And it can help you in the kitchen, too.
First, some background. Ratio is simply a number denoting the proportion of one quantity to another. If I have five apples and six oranges, the ratio of apples to oranges is 5:6. (Sometimes ratios are also expressed as fractions: 5/6.)
The concept is one of the oldest in math; we're not sure who first discovered its usefulness, but the Harappan civilization of modern-day North India, early pioneers in mathematics, were already using ratios to as part of their surprisingly elaborate brick technology. But the concept of ratio has an especially interesting history because of its importance to the Greeks.
The Greeks were obsessed with the Golden Ratio - a special kind of numerical relationship in which the sum of two numbers to the larger of the two numbers has the same ratio as the larger number to the smaller. Usually credited to Pythagoras, the discovery of the Golden Ratio allowed for the design of the ancient Greek Parthenon (fifth century BCE), and the 12th-century mathematician Fibonacci discovered that many patterns in nature also embodied it (shells, for example).
So ratio is both simple and fundamental. It relates to the ability to keep everything in a proper balance. The fact that the Parthenon is constructed according to the Golden Ratio, for example, helps to account for the clean, timeless, geometrical appeal of that building.
Knowing the ratio of commodity to waste product in a company's manufacturing cycle helps us to determine whether that company is working efficiently. And ratio is an important part of keeping track of what happens to different quantities in a mathematical operation as they are all in turn equally acted upon - for example, in multiplication.
But ratio can also help you in the kitchen. Any cook - and any eater - knows that the balance among ingredients in a recipe has an all-important role to play in the taste of your kitchen creations. A simple measuring mistake can mean the difference between a golden, fluffy cake and one with the toxic taste of backing powder. Salt, flour, seasonings: any of these can make a recipe, or, if you add a pinch too much or too little, break it.
So we might say that most recipes can be expressed as ratios - relationships between the quantity of one ingredient and the quantity of another. If salt overpowers the taste of sugar, then you need to remember how many teaspoons of salt can safely coexist with how many teaspoons of sugar.
This becomes important when you need to make more, or less, of something than what the written recipe promises. Let's say you have a recipe for a dozen pancakes, but you're having your child's youth soccer team over for breakfast - obviously, you're going to need, say, three dozen. The recipe you have, for one dozen, indicates that you need 1 cup of mix, half a cup of milk, and one egg. The knowledge of ratio tells you that you need to multiply every ingredient on the list (by three) so that the proportional relationship among ingredients isn't destroyed. Otherwise, you'll end up with eggy pancakes, or sugary pancakes, or pancakes so brittle with wheat that they fall apart.
Multiplying by three, you get 3 cups of mix, a cup and a half of milk, and three eggs - and 36 pancakes, none of them ruined by a lack of proportion between one ingredient and the other.
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