- #1

Gerenuk

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I was trying to think how to introduce complex numbers in a more natural way. I find defining [itex]\mathrm{i}=\sqrt{-1}[/itex] just to not get stuck in maths and then be surprised by the power of complex numbers unsatisfactory. There are probably other ways, but they are abstract, too? Here is some visual way, so that even simple-minded aliens would get this (at least it would be visual if I could draw pictures here; its possible to draw all this reasoning here very graphical).

Suggestions, corrections and comments welcome!

Aliens have trees [itex]\Psi[/itex]. Many of them mean [itex]\Psi\Psi\Psi\Psi[/itex]. To shorten notation the aliens introduce natural number algebra multiplication of object to write [itex]4\Psi[/itex]. They notice that sometimes parts are important so the introduce positive rational numbers. An by considering algorithms they define rational number outcomes of equations.

But the alien notice that not all trees are equal, but

The

[tex]\{t+1\}=\{t\}[/tex]

[tex]\{a\}\,\{b\}=\{a+b\}[/tex]

Of course the age can be combined with the multiplication operator.

Now for some reasons I don't know the aliens assume that the

[tex]A\{a\}+B\{b\}=C\{c\}[/tex]

The difficult task is to determine the result of the addition.

----- to be continued in next post (physicsforum has problems) ---------

Suggestions, corrections and comments welcome!

Aliens have trees [itex]\Psi[/itex]. Many of them mean [itex]\Psi\Psi\Psi\Psi[/itex]. To shorten notation the aliens introduce natural number algebra multiplication of object to write [itex]4\Psi[/itex]. They notice that sometimes parts are important so the introduce positive rational numbers. An by considering algorithms they define rational number outcomes of equations.

But the alien notice that not all trees are equal, but

*have some age*and cycle through state every year. So with the use of the positive number system they introduce the aging operator written as [itex]\{t\}\Psi[/itex], which means age by time [itex]t[/itex].The

*age is periodic*and additive[tex]\{t+1\}=\{t\}[/tex]

[tex]\{a\}\,\{b\}=\{a+b\}[/tex]

Of course the age can be combined with the multiplication operator.

Now for some reasons I don't know the aliens assume that the

*sum of trees with different age is equal to a single age*again[tex]A\{a\}+B\{b\}=C\{c\}[/tex]

The difficult task is to determine the result of the addition.

----- to be continued in next post (physicsforum has problems) ---------

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