The Future of Everything: The Science of Prediction
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Protein: A protein is a molecule consisting of a string of amino acids folded into a particular shape. Proteins make up the structure of cells and carry out most of an organism’s functions.
Random walk: If a drunk stumbles around, taking steps of fixed length in random directions, then the path he traces out is a random walk. The random walk theory is used in physics to describe the random motion of small particles, in finance to describe the random fluctuations of an asset’s value, and by the police to test drunk drivers. See also stochastic process.
RATIONAL NUMBERS: These are numbers that can be expressed as a fraction, such as ID="365"> . All other numbers (i.e., most of them) are called irrational.
Reductionism: This is the belief, championed by Descartes, that the behaviour of systems can be understood by reducing them to their simplest parts. An example is the selfish gene theory. See also holism.
RMS (ROOT MEAN SQUARE): For a set of N numbers {x, x, ID="368"> , x}, the RMS 12Nis given by the square root of the sum of squares: x2+ x122+ ID="369"> + xN2 . The RMS has many applications. For the case N = 2, it can be viewed in terms of a diagonal distance, from the theorem of Pythagoras. If the different numbers represent errors in N separate variables, the RMS is often used as a measure of the total error.
RNA (RIBONUCLEIC ACID): Created by transcription of DNA, RNA plays a key role in the cell, especially as an intermediary between genes and proteins.
SCEPTIC: One who questions and critically examines whatever passes for knowledge, and acknowledges doubt and uncertainty. A global-warming sceptic should therefore be someone who believes that we cannot predict climate change, rather than (its current usage) someone who believes it will not happen.
SELFISH GENE THEORY: This is the reductionist theory, first proposed by Richard Dawkin (1976), that evolution is the net product of independent, individual genes trying to maximize their reproductive success. The theory is therefore a kind of efficient market theory for the genome (see EMH). Supporters of the theory emphasize that it does not imply that genes are endowed with their own motives—only that they can be viewed as acting as if they are.
SENSITIVITY TO INITIAL CONDITION: A mathematical model has this property if small changes to the initial value of the variables (i.e., the initial condition) result in very different forecasts. See also butterfly effect.
SENSITIVITY TO PARAMETERIZATION: A mathematical model has this property if small changes to the parameterizations used (for example, the value of certain parameters) result in very different forecasts. Climate change predictions are generally insensitive to small changes in initial condition but sensitive to parameterization.
SHADOW ORBIT: This refers to a trajectory of a dynamical system that stays within a specified distance—the shadow radius—of a sequence of observations. A model’s accuracy over a certain time period can be assessed by searching for a trajectory, starting from a perturbed initial condition, which shadows within as small a shadow radius as possible (while allowing for uncertainty in the observations). The smaller the shadow radius, the better the model is at matching the data. The expected radius can be compared with estimates from the model drift. Together, they provide two independent methods to assess model error.
STANDARD DEVIATION: This is a measure of the width of a normal distribution. It’s also used as a measure of volatility of some fluctuating quantity, where the implicit assumption is that the deviations from the mean follow a normal distribution. The square of the standard deviation is known as the variance.
STOCHASTIC: A process is stochastic if it is random. If two players bet repeatedly on the flip of a coin, then the score will represent a stochastic process, with some similarity to the fluctuations of a financial asset.
TRAJECTORY: A trajectory is the solution to a dynamical system, starting from a particular initial condition, which traces out the values of the variables as a function of time. It’s sometimes also called an orbit (as in shadow orbit).
UNCOMPUTABLE: This term is used here to refer to a physical, biological, or other real-world system that cannot be accurately modelled using equations. Some features of uncomputable systems may be compared with the emergent properties of complex mathematical systems. An example is the formation or dissipation of clouds, for which no accurate equations exist.
VALIDATION: An argument is considered valid if it is free from any obvious logical flaws. By analogy, a mathematical model is valid if there isn’t anything obviously wrong with it. The word is confusingly used in areas such as climate science; people say, for example, that a model has been “validated” because its results are consistent with a set of observations. This “validity” is then used to imply that the model is an accurate representation of the underlying system. However, the model equations can always be tuned to fit observed data, and no matter what tests are applied, there is no guarantee that a model will continue to work in the future, or that it even bears any close resemblance to the function of the system (Oreskes et al. 1994). Note that even highly imperfect models can still be useful for gaining insights and proposing testable hypotheses.
VARIABLE: A variable is any number in an equation that is allowed to change. In the example of the falling stone in Chapter 2, time, position, and velocity are all variables. See also parameter.
VOLATILITY: In economics, volatility refers to the size of fluctuations in an asset’s value around its mean. It’s often used as a proxy for risk. Volatility can be measured by the standard deviation, though this assumes that the deviations follow a normal distribution.
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