The Temperature That Remembers Which Way It Came

The pressurestat on the Gaggia Achille has a small brass screw on top. Turn it clockwise, you raise the boiler pressure — and therefore the brewing temperature. Turn it counter-clockwise, you lower it. Simple enough.

But there’s a second adjustment inside, usually factory-set and rarely touched: the differential. This is the gap between the pressure at which the heating element turns off and the pressure at which it turns back on. Set it too narrow and the element chatters — on-off-on-off, dozens of times per minute, burning out relays and stressing the boiler. Set it too wide and the temperature swings wildly between shots.

This gap has a name: hysteresis. The system’s output depends not just on the current input, but on which direction the input is moving. A thermostat with 3°C of hysteresis might turn off at 95°C but won’t turn back on until the temperature drops to 92°C. The history of the system — rising or falling — determines when transitions occur.

The concept formalised in control theory during the 1970s, though mechanical implementations are much older. Every bimetallic thermostat has hysteresis built into its geometry. Digital controllers have to implement it explicitly.

package main

import "fmt"

type Boiler struct {
	heating         bool
	onBelow, offAbove float64
}

func (b *Boiler) Update(temp float64) bool {
	if temp < b.onBelow {
		b.heating = true
	} else if temp > b.offAbove {
		b.heating = false
	}
	return b.heating
}

func main() {
	boiler := Boiler{onBelow: 92, offAbove: 95}
	for _, t := range []float64{90, 93, 96, 94, 91, 93} {
		fmt.Printf("%.0f°C → heating: %v\n", t, boiler.Update(t))
	}
}

local function pressurestat(on_below, off_above)
    local heating = false
    return function(temp)
        if temp < on_below then heating = true
        elseif temp > off_above then heating = false
        end
        return heating
    end
end

local update = pressurestat(92, 95)
for _, t in ipairs({90, 93, 96, 94, 91, 93}) do
    print(string.format("%.0f°C → heating: %s", t, tostring(update(t))))
end

Both produce:

90°C → heating: true
93°C → heating: true
96°C → heating: false
94°C → heating: false
91°C → heating: true
93°C → heating: true

Notice 94°C stays off even though it’s below the shutoff point. The boiler had already crossed 95°C and won’t resume until it falls below 92°C — wait, no, the 91°C sample does that, so heating resumes.

The state carries forward. The present alone isn’t enough information.

The Gaggia’s pressurestat differential was factory-set at 0.2 bar — about 3°C worth of temperature swing. Forty years of mineral buildup had narrowed it. The element was cycling every eight seconds when I first powered it on. An hour with citric acid and a careful quarter-turn of that inner screw, and the boiler now holds steady for minutes at a time, relay clicking only when it should.

PID controllers mostly replaced this approach in modern machines, continuously modulating power rather than bang-bang switching. But the concept persists anywhere you need a system to commit to a state rather than oscillate at the boundary.