*Hint: it’s not 50 degrees Fahrenheit.*

100 ℉ = 311 K, half of which is 105.5 K = **−180℉**

Yup — **half of 100℉ is −180℉.**

The difference between the Kelvin scale ℝ⁺ and the Fahrenheit scale is like the difference between a linear scale and an **affine** scale.

You were taught in 6th grade that `y = mx + b`

is a “linear” equation, but it’s technically affine. The `+b`

makes a huge difference when the mapping is iterated (like a Mandelbrot fractal) or even when it’s not, like in the temperature example above.

(The difference between affine and linear is more important in higher dimensions where `y = Mx`

means `M`

is a matrix and `y`

& `x`

vectors.)

Abstract algebraists conceive of affine algebra and manifolds like projective geometry — “relaxing the assumption” of the existence of an origin.

(Technically Fahrenheit does have a bottom just like Celsius does. But I think estadounidenses *conceive* of Fahrenheit being “just out there” while they conceive of Celsius being anchored by its Kelvin sea-floor. This conceptual difference is what makes **Fahrenheit : Celsius :: affine : linear**.)

It’s completely surprising and rad that mere linear equations can describe so many relevant, real things (examples in another post). Affine equations — that barely noticeable `+b`

— do even more, without reaching into nonlinear chaos or anything trendy sounding like that.

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Tags: affine, affine transformation, Daniel Gabriel Fahrenheit, degrees, Fahrenheit, gender binary, Kelvin, linear transformation, math, mathematics, maths, temperature, William Thomson 1st Baron Kelvin

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