Forces and Motion

Equality and identity are not assignment

Teaching Guidance for 14-16 Supporting Physics Teaching

Empirical discoveries, computing, and defining

The equals sign appears in many relationships, but also in computer programs. In these two contexts the meanings are different, but the symbol is the same.

When we use it for doing calculations there is a danger that we conflate the two meanings, tending to undermine both.

There are three separate use cases:

  • Assignment – used in computations.
  • Equality – used in empirical assertions.
  • Identity – used in definitions.

Taking care with symbols, one might use different symbols for different meanings. The difficulty is in computation, both when using pencil and paper, and when using software.

In many cases in physics, an = is often making an assertion about the world. It's a claim that what appears on its left hand side is identical in value (so physical quantity – number plus unit) to what appears on its right hand side. You test the validity of this assertion of the relationship between the two sets of values by empirical test. The use of the = sign is the final step in explaining how you think the world works.

In some other cases, the = sign plays a part in creating a framework that allows you to describe the world. In this case you're defining new entities in terms of existing ones. These are not empirical statements, and so could not be wrong (they're stipulative definitions).

Here is a simple example:durationspeed = distance

There is no experiment you could do to show that this is wrong.

(Some choose to write these kinds of relationships as:distanceduration  ≡  speed. We've not chosen that representation here, because it's not widespread.)

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