CH 26: When you Need Randomness in Life
When someone says, “That was random” we generally think of it as an event without any seeming connection to anything. The idea of unpredictability, the lack of a pattern, a process that is not deterministic, these are all traits of the term random. When we think of random numbers we tend to think of numbers that are impossible to predict from whence they came. There are many situations that model this behavior, like those lottery machines that create a fan, and then the lottery balls are randomly pulled out. This works quite well for not being able to determine what numbers will be chosen.
In the digital domain however, that randomness is a bit harder to emulate. In fact, it is so difficult that there is a term called a pseudo- random number, which refers to a number that appears to be random but is in fact not. In cryptography, which is all about how to protect information, it is dangerous to use pseudo-random numbers to protect your data. Since there is a deterministic process to arriving at a pseudo- random number, generally an algorithm, that process can be uncovered and therefore the information stolen. There are, however, random generators, like the Open Source Lavarnd that work by measuring noise and random.org offers free random numbers.
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CH 27: e = mc2 Redux
No big surprise, physics is tough, real tough. However, a physics equation might be the most well known equation to the world, with the possible exception of the Pythagorean Theorem. This is Einstein's e = mc2. Its direct translation is that energy, measured in joules, is equal to the mass, measured in kilograms, multiplied by the speed of light squared. Since the speed of light is 186,282 miles per second then we know that even a very small amount of mass will contain a very large amount of energy. One of the first profound results of this formula is that any mass (whether it is an ant or a skyscraper) and energy are just different forms of the same things. This means that energy can be converted into mass and mass can change into energy. When you plug in some values, it is surprising to learn that the amount of energy in something like 30 measly grams of hydrogen is equivalent to thousands of gallons of gasoline. When extra mass suddenly converts as energy, it is called nuclear fission. This is more commonly known as the atomic bomb, which was tangible evidence of the truth and power of e =mc2.
Part of the reason why this is one of the most famous equations of all time is in its simplicity. In mathematics, we are always trying to consolidate as much truth into as compact a form as possible. Mathematicians like to use the adjective “elegant” to describe this quality of being very simple and simultaneously very concise. For Einstein to be able to see that energy and mass are two sides of the same coin and to then use math to express this fact, and then do it in such a simple form is an intellectual marvel and the likely reason why you have heard of it before.
Energy : Mass :: Yin : Yang