In many showers there are two taps: `Hot` and `Cold.` You use them to control both the pressure and the temperature of the water, but you do so indirectly: the pressure is controlled by the sum of the (position of the) two taps, while the temperature is controlled by their difference. Thus, the basis you are given:

```Hot = (1,0)
Cold = (0,1)```

Isn’t the basis you want:

```Pressure = (1,1)
Temperature = (1,−1)```

($\dpi{200} \bg_white \large \begin{bmatrix}+1 & +1 \\ +1 & -1 \end{bmatrix}$ would be the basis isomorphism)

` `

other bases:

(Source: qr.ae)

76 notes

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16. trismegistousse said: old style. a comparision with “mixers” ?
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20. eelfriend said: The shower in my apartment has temperature and pressure knobs. It really is a better basis.