### Linear #Metaphor #maths #mathematics #nerds #geek

This is the first in a series of posts on mathematical metaphors. Don’t let the topic scare you. We all use these metaphors, most of us use them every day.

This is a graph of a linear function. It is the most common metaphor, and undoubtedly the most often wrong.

The linear graph says nothing is going to change. This is a graph of a car going at a constant speed…forever. The is total income from the job that never changes. The is the total happiness of a relationship that never changes.

People use this metaphor when their candidate wins an election and they expect everything to go their way from now forward. Alternately when something does not go their way, they foresee constant calamity going forward. This is the metaphor of click bait: “You won’t believe what happened, and is going to continue to happen forever more.”

Reality has never delivered on this model of consistency, yet people continue to hold to this idea.

Stay tuned. There are better metaphors.

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This entry was posted in Mathematicians, Metaphor.

January 7, 2017 at 9:12 pm

I’m not quite sure where you intend to go with this, but it is striking to me (and not in a good way) that you appear to be using the term “linear function” as if it just meant that the graph of the function traces a straight line, instead of the standard definition that the dependence of the function on its parameters/coefficients is linear. Thus, any polynomial, no matter how sinuous, is a linear function, because it is linear in its coefficients. Nonlinearity, in the canonical mathematical sense, is complicated largely because of nonlinear dependence on the function’s parameters.

I understand that this is a distinction of importance only to mathematicians, and thus it might seem unnecessarily complicated if one is trying to illustrate a point about English usage. But it is an essential distinction for mathematical accuracy, so glossing over it when linking between mathematics, metaphor and English usage seems ultimately destined to lead to fuzzy, indeed potentially misleading, exposition.

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January 9, 2017 at 3:00 pm

I am not sure I follow your comment. Starting from the basics:

A linear function is a function f which satisfies

f(x+y)=f(x)+f(y) and f(alpha*x)=alpha*f(x)

for all x and y in the domain, and all scalars alpha.

These properties of linear functions are the foundation of linear algebra.

I’m not sure how you come to the conclusion that higher-order polynomials are linear. They are not. “Linear in its coefficients” is something else.

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