Sugar stages, and why temperature is concentration
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What the thermometer is really telling you
A sugar syrup boils hotter as it concentrates, so the temperature is a direct read of how much water is left. The stage names are the traditional way of expressing that, and the final water content is what decides whether the cooled product is soft, chewy, hard or glassy.
Which is why a few degrees changes the product
The difference between a caramel you can chew and one that breaks a tooth is a small temperature difference at the end of the cook. That is not a recipe being fussy; it is the concentration moving quickly as the last water leaves, the same acceleration the syrups property describes.
Altitude shifts every number
Water boils lower at altitude, so every stage temperature shifts down with it. A recipe written at sea level will overcook at elevation if the numbers are followed literally. Calibrate by boiling water on the day and adjust the targets by the difference.
The cold water test still works
Dropping a little syrup into cold water and judging the ball it forms is the traditional method and it is a real measurement, not folklore. It is slower and less precise than a thermometer and it is the check that tells you a thermometer has gone wrong.
It keeps cooking after you take it off
A heavy pan holds heat and the syrup continues to concentrate for a while after the heat stops. Pulling slightly before the target, and knowing how far your own pan carries over, is the difference between hitting the number and passing it.
Record the number, not the stage
A batch sheet that says hard ball describes a range you can land anywhere in. One that records the actual temperature, with the thermometer and the date it was calibrated, is a specification somebody else can follow.