How Does CyclePad Detect Contradictions?
An important aspect of carrying out any form of mathematical analysis is to check whether or not your results are physically meaningful. CyclePad helps in this respect by detecting when the assumptions you have made correspond to a physically impossible situation. CyclePad detects such situations by using an approximation of the kinds of intuitive knowledge that human engineers use to catch such mistakes. For example, CyclePad knows that
- To make compression occur you must perform work.
- An expansion process generates work.
- If you put stuff through a heater then it cannot come out cooler than it came in.
- If you put stuff through a cooler then it cannot come out hotter than it came in.
When these or other simple physical intuitions are violated, CyclePad switches to contradiction mode. In this mode, the report window shows you the particular intuitions that were violated and the list of assumptions which caused the contradiction.
This style of computation is called constraint propagation. It is a very simple yet powerful way to calculate answers given numerical assumptions. Because it uses constraint propagation, CyclePad does more work than it has to, strictly speaking. When analyzing designs by hand, one generally thinks carefully about the solution process, in order to do the minimal work necessary to deduce the information we need for our goals. The advantage of CyclePad's method is that it is relentless in checking all the consequences of your assumptions, not just the ones you might have thought about checking. This means that CyclePad is reasonably good at finding out when the numbers you have proposed are physically not possible.
See also:
What Causes Contradictions?
How Do I Get Out of Contradiction Mode?
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