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By treadair
This idea would require a simple computer program that displayed a screen asking 3 questions -

1. What equation/formula are you interested in?

2. What constant do you want replaced?

3. How many degrees of separation do you want?

After you answer the questions the program would search a database that had been pre-loaded with as many standard equations / formulae as possible (engineering books are full of them) looking for ones that said the chosen constant equaled something else. The first equation it found would then be used as a replacement value in the formula you chose. This is the first degree of separation. Next, each constant in the replacement value would be substituted with equivalent equations found for them. The second degree of separation. The process would continue until you got the number of degrees of separation you asked for and then the result would be displayed. Some new and surprising connections will be sure to come up because the program will be acting like a divergent thinker (someone who can take two ideas from seemingly unconnected disciplines to form a new idea).

The following two rules would have to be enforced in order to make this program work -

1. Each constant must always mean the same thing: m=mass, c=speed of light, etc.

2. No replacement formula could have a constant that was used in a previous formula (to prevent recursive logic).
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By Steve
Now I don't understand enough about maths/physics to know if this would be truely useful, but I do like the divergent approach. If more than one replacement function is available, would the computer's choice be just random?
By treadair
The computer's choice would be based on its sequential reading of the database of formulas that was loaded. The default setting would be to pick the first valid replacement it found.

That could be changed though just by adding one more question to the prompt screen asking the user if they wanted to replace the default selection with a different number. If they keyed a 5 into that field then it would always pick the 5th replacement formula it found.

Or we could add a Y/N "random" flag that would make the program pick a random valid replacement in the sequence of possibilities when it was changed to a Y.

Or we could add a Y/N "common" flag that would make the program pick a replacement whose constants were found most often in the database when it was changed to a Y (increasing the odds that whoever was reading the results would be familiar with the values found in them).
By jstr
What a wonderful idea. I wonder if it could be combined with the genetic algorthims that badly try to solve mathmatical problems...

By Texan Impeacher
While in practice this sounds like a good idea, it would quickly approach a limit of computation. This problem is a (more complicated) variation of finding a word ladder between two words. Essentially the computer is trying to find the shortest path between equations of a constant on one side, and its equivalent value.

The problem comes in when the number of equations in the database grows to be large. It soon approaches a value that exceeds the amount of memory or processing power available to computers today.

Additionally, the computer would only simulate a divergent thinker. That is, you could give a person with a knowledge of algebra (or calculus, should the equations require it) a pencil and have them perform the same calculations the computer would, and arrive at the same result. The computer can only execute an algorithm if it is a defined series of steps. To be a divergent thinker, one must use undefined steps to come up with an entirely new way of doing things.

Just one more thing that keeps us humans in power and the computers out of power ;-D
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