Proline reads in the thousands and hue under two, so each assay needs its own ruler

Why can't thirteen wine assays share one axis? Each row is one Italian wine with thirteen chemical measurements. The numbers are honest but incommensurable: proline is reported in milligrams per liter and runs to 1,680, while hue is a ratio that never reaches two. Put them on one scale and twelve assays flatten into a line along the floor.

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Each axis gets its own ruler

A parallel plot scales every axis to its own field, so a wine's line shows where it sits among the 178 on each assay. The maximum recorded proline value was 1680.0 mg/L. The maximum recorded hue value was 1.710. On a shared axis the hue column would be a dot at zero; here it spreads the full height and separates cultivar 3 at the bottom.

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The rulers differ a thousandfold

The summary puts the scales side by side as numbers. Summing proline over the wines gives 780 times the sum of hue. Magnesium runs in the tens and hundreds, alcohol between 11 and 15, and the phenol assays mostly between zero and five.

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Proline alone picks out cultivar 1

The largest-scaled field also carries the clearest signal for one cultivar. Mean proline in Cultivar 1 was 1,116 mg/L. Mean proline in Cultivar 2 was 520 mg/L. The line at 760 mg/L sits above almost every cultivar 2 and 3 wine: 96.6% of cultivar 1 wines are at or above 760 mg/L, against 8.4% of the others.

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Takeaway

The thirteen assays describe the same wines on rulers a thousandfold apart, so any view that shares an axis shows only proline. Scale each axis to its own field and the small-valued assays, hue and flavanoids, separate the cultivars as well as the large one does.

Limits

The publisher gives units for few of the assays; proline and magnesium are taken as milligrams per liter and hue as a ratio. Parallel axes are independent, so the slope between two axes measures nothing physical. No classifier is fitted.