**Average**: also called mean - the average of a set of values is the sum of the values divided by the number of values in the set. So the average of {1, 3, 5} is (1+3+5)/3=3.**Continuous**: something that is uninterrupted. A continuous medium doesn't come in little pieces, but fills space completely everywhere.**Correlation**: the degree to which a collection of random measurements change together. For example, many stock traders speculated that the stock market was correlated to the color on former Fed. Chairman Alan Greenspan's tie; they thought that the stock market prices would tend to go up if he wore one color tie, or down if he wore another. Both the tie he would pick and the direction of the stock market were random events, but knowing one would, according to this theory, give a strong indication of what the other would likely be.**Correlation Length**: How far away correlations reach. In the liquid-gas transition example, this corresponds to how big an island of non-uniform density can grow. Another example might be which sports team a community supports - say people like to support local teams. Then people living in the same area are likely to support the same team (their team preference is correlated). But there is a limit to "local"-ness. A team might not feel local for a community if that community is, say, 400 km away from the stadium. This radius of local-ness plays the role of a correlation length - in our model, communities are likely to support the same team if they are within around 400 km of each other.**Critical Exponent**: a parameter which describes how fast a quantity gets really big (diverges) as its temperature approaches the critical temperature.**Critical Opalescence**: a phenomenon associated with continuous (second order) phase transitions where large fluctuations in density develop over many size scales; these irregularities scatter light, so that a normally transparent fluid appears cloudy or milky at its critical point.**Critical Point**: For water: Mix of temperature and pressure at which difference between liquid and gas disappears (374 degrees deg;C, 218 atm). In general: when the natural length scale of correlations becomes infinite**Density**: mass (stuff, e.g. kilograms) per unit volume (e.g. cubic meters).- Discrete: occurring in individual, separate units or elements. Integers are discrete numbers (-1,0,1,2,3...). The stars appear as discrete balls of light.
**Distribution**: by distribution, we mean the way the probability (likelihood) of encountering a certain outcome is spread among all of the outcomes. For example, flipping a coin is a random experiment, and is characterized by a uniform probability distribution over the possible outcomes (head or tails) because the probability (likelihood) of encountering either outcome is the same (50%). Two different coins have the same probability distribution; every coin flip has the same probability distribution. This doesn't mean that every outcome is the same; it only means that the likelihood of one outcome or the other is the same.**Fractality**: (see self similarity)**Medium**(plural:**media**): a region of space that may be characterized in a certain single, distinct way; usually, the context is that some*information is transferred through the medium*.**Order parameter**: thermodynamic function that is different in each phase and hence can be used to distinguish between them. "Order" refers to how the elements are arranged in a particular phase, and "parameter" is a (hopefully measurable!) quantity or variable.**Phase**: Think of a phase as a “flavor” of something. Water, for example, comes in several “flavors” – ice, liquid, and gas (steam). All three are made from the same thing (H2O), but they’re definitely different from one another in that they have different*properties*(for example, ice is hard, but you can walk through steam – different mechanical properties).**Phase Diagram**: a graphical tool which shows which phases are stable for any combination of temperature, pressure, and volume (more generally, for a set of thermodynamic variables). In this website, we used a phase diagram for water, and examined isotherms (constant temperature lines) in the pressure-volume plane.**Phase Transition**: a change between two or more phases in a material. Ice melting into water, rain condensing from vapor in the sky, gas in a fluorescent tube becoming and ionized plasma - these are all phase transitions. Some phase transitions are characterized by having both phases present and distinguishable in the same environment at the same time, and the phase transformation proceeds until enough energy has been exchanged (the latent heat) such that the pockets or islands of one phase eventually grow to include all of the available substance. This is a**first-order phase transition**, and characterizes the situation for melting or freezing ice and boiling or condensing water. Another situation is the**second order**or**continuous**transition, for which there is not a mixed-phase regime (and no latent heat); rather, the substance*smoothly*and uniformly transitions from one phase, say a supercritical phase, into a different phase (or phases), say liquid and gas.**Recursion**: the process or scheme of applying the same*algorithm*(set of instructions) over and over again. Recursion holds a prominent position in the computer programmer's toolkit, as well as that of the mathematician. It is kind of like a fractal approach to solving problems.**Reflection**: the bouncing of light off of an interface between two media.**Refraction**: the bending of light at an interface between two media.**Scale**: The scale refers to the size of something. Bacteria, ants, and humans live at different scales - different length scales, mass scales, and so on; a town of 10 000 and a city of 10 000 000 have different scales, too.**Scale Invariance**: See**statistical self similarity**.**Scattering**: when light is scattered, its path is interrupted, and it is redirected in many different directions - it "bounces" off of something. We see objects because light scatters off of them and into our eyes. The sky is blue because the atmosphere scatters blue end of the visible spectrum more strongly than it does the red end, as predicted by Rayleigh scattering theory.**Statistical Self Similarity**: (also, statistical fractality, statistical scale invariance) in our context, something with statistical self similarity has the property that as you change the scale you are looking at, micrometers or millimeters or meters or kilometers, statistical quantities stay the same. Imagine you're at a giant trash heap from a helicopter - from far away, the trash looks like a bunch of pieces of junk and specs of dirt, maybe with a certain distribution of sizes or colors. Now, you land your helicopter right in the trash heap! Up close, it looks kind of like it did far away - like a bunch of pieces of junk and specs of dirt. If the trash heap has statistical self similarity, then you should see about the same distribution of really big, medium big, small, and tiny pieces of trash that you did from the helicopter. Or maybe the same percentage of red-, green-, blue-, yellow-, mauve-, and cyan-colored junk. The point is that the trash heap doesn't look exactly the same up close or far away, but there's something about the statistics of its building blocks that is the same at different size scales.**Supercritical Phase**: the phase above the critical point. In the liquid-gas transition, the difference between the liquid and gas phases disappears in the supercritical ("above" critical) regime.**Ubiquitous**: appearing everywhere; omnipresent.**Uniform**: the same everywhere.**Universality**: applicability to all situations within a certain class. The critical exponents are the same for all members of a certain*universality class*, defined by generic parameters like dimension (2D, 3D) and number of components (i.e. density, a scalar quantity with one component, or a spin which might point in any spatial direction (say three components)). Aside from being amazing in its own right, universality is a useful property in that we are able to pick the simplest out of all the situations in the universality class and still get as much information as if we had picked any other situation.