RE: [math-fun] beautiful equations and E.T.
Simon asks: << What would be the best way to write them down in a universal language because for ET the equation exp(Pi*i)+1=0 means nothing at all if we can't explain what is Pi, e, 1, 0 and the equal sign, isn't?
Cool question! It may be self-evident that multiple vertical strokes signify 1,2,3,...: |, ||, |||, . . . A few simple equations like | + | = || and || + ||| = ||||| should reveal the meanings of + and =. A circle with one diameter drawn in, labeled | could reveal pi by showing a sequence of increasingly unrolled circles, culminating in a straight line, all the while keeping its length constant. This straight line can be labeled with the symbol pi. (The meaning of labeling could be explained by showing two diameters end to end labeled ||, three labeled |||, etc.) If E.T. knows anything about exp, then by this point they will recognize the series definition for exp(z) (for simplicity, call it e(z)) without further explanation: e(z) = | + z/(|) + zz/(|| |) + zzz/(||| || |) + ... Now writing | + -| = -| + | = should explain the minus sign, and finally i i = -| should yield the (ambiguous) meaning of i. Finally, e(pi i) + | = ought to be clear to any being who's familiar with it, irrespective of their symbology for it (assuming they use symbols!). --Dan
"Lincos: a language for cosmic intercourse", by the Dutch mathematician Hans Freudenthal, prescribes a sequence of radio signals that would establish for another civilization a common language for mathematics, physics, and interpersonal relations. The book was written in the 1930s, but libraries have it.
=John McCarthy ...prescribes a sequence of radio signals...
What would be a good initial attention-getter? What they call "attract mode" in arcade games? The primes are often suggested, but where to stop and repeat is a puzzler. I think it should be a distinctive finite sequence. How about cycling (the negatives of) the Heegner numbers? ||: 1, 2, 3, 7, 11, 19, 43, 67, 163 :||? Precariously tilting the math/fun ratio: Of course if the ETs are Militant Pythagoreans it might only provoke them to dispatch berserkers to quash our secret blabbing. My son and I while away gate holds proposing wrong-headed interpretations of the supposedly "universal" pictorial airplane emergency cards ("Caution! Beware this flying arrow!"). Similarly:
=Daniel Asimov A few simple equations like | + | = || and || + ||| = ||||| should reveal the meanings of + and =.
optimistically assumes Murphy's Law isn't universal! More likely, "If anything can be misinterpreted, it will be." For example those graphics are equally true equations if we interpret "+" as equal-to and "=" as subtraction (with opposite our conventional handedness). Or, worse, "+" as multiplication and "=" as unequal-to... Perhaps the ETs find it grossly offensive to baldly state facts, preferring a delicate silhouette chiaroscuroed by non-facts? Thus trying their elder-race politeness to find interpretations for which all our equations are UNtrue? But actually the ETs have already gone home, based on early telescopic reconnaissance. Why, just yesterday I was admiring the huge ad (something about two services for the price of one) on the side of an SBC (telco) truck which said (in a meter-high font, easily visible from orbit) 1 + 1 = 1 Doubtless, the berserkers are coming to quash our insidious intergalactic mathematical disinformation campaign... --Tixe Ylno
For awhile, I've had a strong desire to see nice pictures of famous graphs. One large graph I was glad to make nice was the Foster graph. http://mathworld.wolfram.com/FosterGraph.html The graph I *really* wanted was the Hoffman-Singleton. http://mathworld.wolfram.com/Hoffman-SingletonGraph.html Recently, Gordon Royle found a 7-coloring of the graph. After some tweaking, his solution led me to a beautiful realization: http://www.mathpuzzle.com/Hoffman.gif I knew there was a beautiful way to depict it. I'm glad I can finally see it. --Ed Pegg Jr
Freudenthal starts with several examples of additions, e.g. xxxyxxzxxxxx, followed by xxyxxzxxxx, etc. Then he switches from unary to octal or decimal notation and then puts in variables.
participants (4)
-
Daniel Asimov -
ed pegg -
John McCarthy -
Marc LeBrun