Halving quantities is arithmetic, but a halved dish frequently comes out wrong. The reason is that several things in the recipe do not scale with the ingredient list.
Surface area does not halve
Putting half the volume of a gravy into the same pan spreads it thinner, exposing proportionally more surface to the air. Evaporation runs faster relative to the amount of liquid present.
A sauce that was meant to reduce over twenty minutes now reduces in eight, before the aromatics and spices have had time to soften and merge. It thickens correctly but tastes raw.
Moving to a smaller pan restores the ratio, which is why halved recipes work far better with a change of cookware than with a change of timing alone.
Tempering does not tolerate scaling down
Whole spices need to be submerged in hot fat to release their oils. Half the fat in the same pan can be too shallow to cover them, so they scorch on the base instead of infusing.
The fat also heats faster in a smaller quantity and overshoots, which shortens an already narrow window. Halved tempering usually needs a smaller pan and a lower flame rather than half the attention.
Some quantities are already at their minimum
Asafoetida, ajwain and other assertive ingredients are used in fractions of a teaspoon to begin with. Halving them means measuring quantities that cannot be measured accurately with ordinary spoons.
In practice cooks leave these unchanged, which technically doubles their proportion. The dish usually tolerates that better than it tolerates an unmeasurable pinch.
Aromatics behave nonlinearly
Onions browning in a pan lose water first and then color. Half the quantity loses its water sooner and browns much faster, so the same visual endpoint arrives with less time spent developing flavor underneath.
Garlic and ginger pastes burn readily in the small amount of fat a halved recipe provides. Their timing relative to the onions often has to be adjusted rather than copied.
What scales cleanly and what does not
Salt, sugar and acid scale linearly and can be halved without thought, though final adjustment by taste is still the correct method. Liquids for cooking rice or lentils also scale reliably.
Cooking times, pan sizes, flame levels and any ingredient used in a pinch do not. Treating a halved recipe as a new recipe that needs its cues watched, rather than as the same recipe in smaller numbers, avoids most of the failures.