Computers use math, data and computer instructions to create representations of real-world events. They also can predict what’s happening — or what could happen — in complex situations, from climate systems to the spread of rumors throughout a town. And computers can spit out their results without people having to wait years or to take big risks.

The scientists who build computer models start with important features of whatever events they hope to represent. Those features may be the weight of a football that someone will kick. Or it might be the degree of cloud cover typical of a region's seasonal climate. Features that can change — or vary — are known as *variables*.

Next, the computer modelers identify rules that control those features and their relationships. The researchers express those rules with math.

“The math built into these models is rather simple — mostly addition, subtraction, multiplication and some logarithms,” notes Jon Lizaso. He works at the Technical University of Madrid in Spain. (Logarithms express numbers as powers of other numbers to help simplify calculations when working with very big numbers.) Even so, there’s still too much work for one person to do. “We are talking about probably thousands of equations,” he explains. (*Equations* are mathematical expressions that use numbers to relate two things that are equal, such as 2 + 4 = 6. But they usually look more complicated, such as [x + 3y] z = 21x - t)

Solving even 2,000 equations might take a whole day at the rate of one equation every 45 seconds. And a single mistake might throw your answer way off.

More difficult math might bump up the time needed to solve each equation to an average of 10 minutes. At that rate, solving 1,000 equations could take nearly three weeks, if you took off some time to eat and sleep. And again, one mistake might throw everything off.

In contrast, common laptop computers can perform billions of operations per second. And in just one second, the Titan supercomputer at Oak Ridge National Laboratory in Tennessee can do more than 20,000 trillion calculations. (How much is 20,000 trillion? That many seconds would come to about 634 million years!)

A computer model also needs algorithms and data. *Algorithms* are sets of instructions. They tell the computer how to make decisions and when to do calculations. Data are facts and statistics about something.

With such calculations, a computer model can make predictions about a specific situation. For instance, it might show, or simulate, the result of a particular football player’s kick.

Computer models also can deal with dynamic situations and changing variables. For example, how likely is it to rain on Friday? A weather model would run its calculations over and over, changing each factor one by one and then in various combinations. After that, it would compare the findings from all the runs.

After adjusting for how likely each factor was, it would issue its prediction. The model would also rerun its calculations as Friday got closer.

To measure a model’s reliability, scientists might have a computer run its calculations thousands or even millions of times. Researchers also could compare a model’s predictions with answers they already know. If the predictions closely match those answers, that’s a good sign. If not, researchers must do more work to find out what they missed. It could be they didn’t include enough variables, or relied too much on the wrong ones.

Computer modeling isn’t a one-shot deal. Scientists are always learning more from experiments and events in the real world. Researchers use that knowledge to improve computer models. The better computer models are, the more useful they can become.

## Power Words

**algorithm** A group of rules or procedures for solving a problem in a series of steps. Algorithms are used in mathematics and in computer programs for figuring out solutions.

**climate** The weather conditions prevailing in an area in general or over a long period.

**computer **An electronic device that processes information based on rules stored in the device.

**computer model** A program that runs on a computer that creates a model, or simulation, of a real-world feature, phenomenon or event.

**computer program** A set of instructions that a computer uses to perform some analysis or computation. The writing of these instructions is known as **computer programming.**

**data **Facts and statistics collected together for analysis but not necessarily organized in a way that give them meaning. For digital information (the type stored by computers), those data typically are numbers stored in a binary code, portrayed as strings of zeros and ones.

**equation **In mathematics, the statement that two quantities are equal. In geometry, equations are often used to determine the shape of a curve or surface.

**logarithm **The power (or exponent) to which one base number must be *raised — *multiplied by itself *— *to produce another number. For instance, in the base 10 system, 10 must be multiplied by 10 to produce 100. So the logarithm of 100, in a base 10 system, is 2. In base 10, the logarithm of 1,000 would be 3, the *log* of 10,000 would be 4, and so on.

**simulate **(in computing) To try and imitate the conditions, functions or appearance of something. Computer programs that do this are referred to as **simulations**.

**variable** (in mathematics) A letter used in a mathematical expression that may take on more than one different value. (in experiments) A factor that can be changed, especially one allowed to change in a scientific experiment. For instance, when measuring how much insecticide it might take to kill a fly, researchers might change the dose or the age at which the insect is exposed. Both the dose and age would be variables in this experiment.

**virtual** Being almost like something. An object or concept that is virtually real would be almost true or real — but not quite. The term often is used to refer to something that has been modeled — by or accomplished by — a computer using numbers, not by using real-world parts. So a virtual motor would be one that could be seen on a computer screen and tested by computer programming (but it wouldn’t be a three-dimensional device made from metal).

## NGSS:

- HS-ETS1-4

## Further Reading

K. Kowalski. “Models: How computers make predictions.” *Science News for Students*. October 9, 2014.

S. Perkins. “Reviving dinosaurs.” *Science News for Students*. March 4, 2014.

D. Mackenzie. “Cool Jobs: Data detectives.”*Science News for Students.* Dec. 17, 2013.

S. Ornes. “The data flood.” *Science News for Students.* Dec. 13, 2013.

D. Mackenzie. “Cool Jobs: Math as Entertainment.” *Science News for Students.* Dec. 19, 2012.