**Theorem**
A statement in a formal system that has proof.

**Theorization**
A process by which scientists attempt to understand nature; it is the
complement to experimentation. Theorization is the process of
building mathematical models for how things work. Scientists
always desire theories that are simpler than the data they explain.
See also Occam's Razor and simulation.

**Three Body Problem**
The problem of determining the future positions and velocities of
three gravitational bodies. The problem was proved unsolvable in the
general case by Henri Poincaré, which forshadowed the importance of
chaos. Although no analytical solutions are possible in the
worst case, a numerical solution is sometimes sufficient for
many tasks.

**Threshold**
A quantity added to (or subtracted from) the weighted sum of inputs
into a neuron, which forms the neuron's net input.
Intuitively, the net input (or bias) is proportional to the amount
that the incoming neural activations must exceed in order for a
neuron to fire.

**Time Complexity**
A function that describes the amount of time required for a
program to run on a computer to perform a particular task. The
function is parameterized by the length of the program's input. See
also space complexity.

**Time-Reversible**
A property of dynamical systems that can be run unambiguously
both forward and backward in time. The Hénon map, Lorenz
system, and vant cellular automata are all time-reversible,
while the logistic map, the Mackey-Glass system, and most
other cellular automata are not. Time-reversible systems are
described by functions that are invertible.

**Time Series**
A sequence of values generated from a dynamical system over time.
Chaotic systems can be analyzed by examining the time series
generated by a single portion of the system. See also
embedding.

**Tit-for-Tat**
An effective strategy for playing the Iterated Prisoner's
Dilemma. Tit-for-Tat starts by cooperating, and then does whatever
its opponent did in the previous round of play.

**Top-Down**
A method of examining things that first looks at higher-level
phenomena and then tries to explain lower-level patterns in terms of
the higher-level observations. This is the exact opposite of
bottom-up. See also holism and reductionism.

**Transpose**
An operation that flips a matrix about the main diagonal.

**Turing Machine**
A model of computation that uses an underlying finite-state
automaton but also has an infinite tape to use as memory. Turing
machines are capable of universal computation.

**Turtle Graphics**
A simple language for drawing graphics in which a ``turtle'' is used
to make strokes on a plotting device. Typical commands include ``move
forward,'' ``draw forward,'' and ``turn left.''