Indian recipes are specific about how vegetables are cut, and the instruction changes with the dish rather than staying constant. The cut is a cooking variable, not a presentation choice.
Size sets the cooking rate
Heat enters a vegetable from the outside and travels inward, so the distance from surface to center determines how long the middle takes to cook. Halving the size roughly quarters that time.
A dish cooked quickly over high heat therefore needs small pieces, or the outside burns before the inside softens. A slow-cooked preparation can use large pieces because there is time for heat to reach the center.
This is why the same vegetable appears finely diced in one preparation and in thick wedges in another, and why swapping the cut breaks the timing of the recipe.
Surface area sets water loss and browning
Small pieces expose more surface relative to their volume, so they lose water faster and brown more readily. A dry sabzi depends on that, since browning is where much of its flavor comes from.
Large pieces retain water and steam themselves from the inside, staying soft rather than developing color. For a gravy dish where the vegetable should stay juicy, that is the desired behavior.
Structure decides whether a piece survives
Vegetables held together by cell walls and pectin, such as potato and carrot, keep their shape until those structures break down. Cutting across or along the fibers changes how quickly that happens.
Eggplant and okra have weaker internal structures and collapse readily, which is why they are often cut large or cooked whole when the dish needs them to hold together.
Some cuts exist to manage a specific problem
Okra is cut and cooked dry rather than wet because contact with water releases mucilage. The cut, the pan and the absence of liquid are all addressing the same property.
Bitter gourd is sliced thin and salted so that the cut surfaces can release liquid, drawing out some bitterness before cooking begins. The thinness is what makes the treatment effective.
Uniformity matters more than precision
Pieces of different sizes in the same pan finish at different times, which is the most common cause of a dish having both undercooked and disintegrated vegetables in it.
Exact geometry is less important than consistency, which is why home cooks working fast with a curved knife or a floor-mounted blade still produce even results. The eye is matching pieces to each other, not to a standard.