A long line of implications
May 09, 2017
Humans have trouble comprehending a long line of implications
Doing "a" leads to consequence "b" (mathematically, written as a => b) is clear enough. But a long sequence of a=> b => c ... is that really clear or intuitive enough?
Sometimes it is not true if there is some unstated assumption in the single implication but that assumption gets broken or magnified when you have a long string of assumption. Here is an example. Imagine you keep a stone next to another stone. Then you can say one stone is left of another. You can place another stone left of the left-most stone. In fact you can keep going like that. But lets say, if this sequence is continued all around the earth, then the last one is not to the left but right of first one. A long sequence of implications is broken! There was an unstated assumption in the first implication that all stones are kept in a flat 2D plane. There was no need to state this assumption when there were only a few stones. But it becomes critically important if there are a large number of stones.
Humans also have problem thinking of a long line of implications. Climate change is an indirect result of everyday activities of all humans over last several centuries but it started becoming clear only in the last few decades. Similarly, petty corruption and societal development are inversely related but it is not obvious.
Sometimes it is not true if there is some unstated assumption in the single implication but that assumption gets broken or magnified when you have a long string of assumption. Here is an example. Imagine you keep a stone next to another stone. Then you can say one stone is left of another. You can place another stone left of the left-most stone. In fact you can keep going like that. But lets say, if this sequence is continued all around the earth, then the last one is not to the left but right of first one. A long sequence of implications is broken! There was an unstated assumption in the first implication that all stones are kept in a flat 2D plane. There was no need to state this assumption when there were only a few stones. But it becomes critically important if there are a large number of stones.
Humans also have problem thinking of a long line of implications. Climate change is an indirect result of everyday activities of all humans over last several centuries but it started becoming clear only in the last few decades. Similarly, petty corruption and societal development are inversely related but it is not obvious.