Inverse Symbolic Calculator 2.0

05Feb08

For all you numerologists out there trying to explain the hierarchy of Yukawa couplings, you might enjoy playing with the Inverse Symbolic Calculator 2.0 (via Reddit some time ago).

The Inverse Symbolic Calculator (ISC) uses a combination of lookup tables and integer relation algorithms in order to associate with a user-defined, truncated decimal expansion (represented as a floating point expression) a closed form representation for the real number.

In other words, you give the decimal and the ISC gives you an expression (involving things like e and pi) that evaluates to that number to the same precision.

The real geeks out there will test out the ISC with a real problem, what is the inverse symbolic expression for 42?

The Answer to Life, the Universe, and Everything.

That’s the honest-to-Witten verbatim output of the program. I think it passes the test with flying colors.



3 Responses to “Inverse Symbolic Calculator 2.0”

  1. 1 andy.s

    That’s really impressive. I put in the value for the solution of cos(x) = x and it reproduced the expression (well pretty close).

    I wonder – if you put in the masses of all particles, would it reproduce the Standard Model for you?

  2. 2 robert

    Is there a challenge here, to trip the inverse symbolic calculator up? The response to 42 was indeed impressive. Sadly, it failed to recognise

    3.141592653589793238462643383279726619348

    as

    Log[262537412640768744]/Sqrt[163]

    and came up with Pi (which to the same number of decimal places is

    3.141592653589793238462643383279502884197)

    instead.

  3. 3 robert

    I know that this is really sad. Perhaps the ISC doesn’t know about logs (see previous example) Putting in .3010 elicits exp(-6/5) (0.3012). So where was log[2]/log[10]? (3010 was also the telephone number of Marianne Faithful’s next door neighbour when she was a girl – could the internet, or any computer, tell you that?) And, even worse, 0.707 could only be approximated to by 5/(4 Sqrt[Pi]) (circa 0.677) rather than the sine of Pi/4. i.e. 1/Sqrt[2]. No need for modular equations and theta functions to kick its ass, then – trig 101 is all it takes. 42 still does the business, though.



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