![]() From an ecological point of view, it is best if the terrain is species-differentiated. The higher the entropy of your password, the harder it is to crack.Įcologists use entropy as a diversity measure. It takes into account the number of characters in your password and the pool of unique characters you can choose from (e.g., 26 lowercase characters, 36 alphanumeric characters). It's a measurement of how random a password is. You may also come across the phrase ' password entropy'. In information theory, the entropy symbol is usually the capital Greek letter for ' eta' - H. It's said to have been chosen by Clausius in honor of Sadi Carnot (the father of thermodynamics). In physics and chemistry, the entropy symbol is a capital S. Before, it was known as "equivalence-value". It comes from the Greek "en-" (inside) and "trope" (transformation). The term "entropy" was first introduced by Rudolf Clausius in 1865. Know you know how to calculate Shannon entropy on your own! Keep reading to find out some facts about entropy! They argue that the name "uncertainty" would have been much more helpful since "Shannon entropy is simply and avowedly the 'measure of the uncertainty inherient in a pre-assigned probability scheme. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. You should call it entropy, for two reasons. Interestingly, Caianiello and Aizerman say the name entropy is thanks to von Neumann who said You can read more about this in Shannon's seminal paper A Theory of Mathematical Communication. ![]() H(x, y)=H(x)+H(y) only when x and y are independent events. The joint entropy of two events is less than or equal the sum of the individual entropies.Entropy H is maximized when the p_i values are equal.(Uncertainty vanishes only when we are certain about the outcomes.) Entropy H is 0 if and only if exactly one event has probability 1 and the rest have probability 0.Shannon observes that H has many other interesting properties: He named this measure of uncertainty entropy, because the form of H bears striking similarity to that of Gibbs Entropy in statistical thermodynamics. However, the independence property tells us that this relationship should hold: If the second flip is heads, x=1, if tails x=2. If the flip was tails, flip the coin again. Supposed we generate a random variable x by the following process: Flip a fair coin. Second, If each event is equally likely ( p_i=1/n), H should increase as a function of n: the more events there are, the more uncertain we are.įinally, entropy should be recursive with respect to independent events. A small change in a single probability should result in a similarly small change in the entropy (uncertainty). He thought that "it is reasonable" that H should have three properties:įirst, H should be a continuous function of each p_i. ![]() , p_n) describing the uncertainty of an arbitrary set of discrete events (i.e. In general, Shannon wanted to devise a function H(p_1, p_2. We might want to say the uncertainty in this case is 1. However, if the coin is fair and p=0.5, we maximize our uncertainty: it's a complete tossup whether the coin is heads or tails. Since there is no uncertainty, we might want to say the uncertainty is 0. Claude Shannon asked the questionĬan we find a measure of how much "choice" is involved in the selection of the event or of how uncertain we are of the outcome?įor example, supposed we have coin that lands on heads with probability p and tails with probability 1-p. Supposed we have a discrete set of possible events 1,\ldots, n that occur with probabilities (p_1, p_2. ![]()
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