## Complex 3D Time

Can complex number theory be applied to time? Would a “complex time” component would effectively turn a time line into a time plane (or time volume?) possibly allowing for multitasking?

Here’s my wall clock. Again. I ‘introduced’ it and its angle on warped space time in this post back in October 2013. That’s not really that long ago, but the clock’s given up the ghost now and moved on to places and times beyond the ken of humankind.

I admit it – I’m playing with your perspective here! Naturally the wall clock’s off the wall, but it’s also been in the hands of my young daughter (after the time of death! 😉 )

Do you ever have time on your hands? My daughter did – and this is how my clock looks from another angle after she’d finished with it.

Her child’s play got me thinking about the ‘normal’ movement of hands around a clock. What if they could move not only clockwise on the plane of the clock face, but also in the third dimension?

It sounds like it might be complex…

## Complex time

Time moves linearly – usually forwards – hence we have a time line. We also have number lines (also linear) which range from lower integer values, through real numbers to the next highest integer, and so on. Or in reverse if we count backwards.

But perpendicular movement is possible on the number line – “complex numbers” (multiples of the square root of minus 1, often denoted by i or j) explain a deviation away from the time line along the “imaginary axis”.

So can complex number theory allow for a similar methodology to be applied to time? Can there be a “complex time” component which effectively turns a time line into a time plane? Or a time volume?

Admittedly, this might look a little like a sundial with pturned hands casting time shadows across the clock face area.

I remember watching a lunar eclipse and someone nearby mentioned that this was the largest shadow that there was. Being keen on astronomy (and a nerd with no social skills) I was compelled to mention that actually the shadow on the moon was just a 2D image of the 3D shadow of the Earth which projected into space and struck the moon.

Perhaps as sundials signaled the advent of clocks and telling the time, they may also signal the beginning of an understanding multi-dimensional time.

Now, I’m not a mathematician but is this idea of complex time something which can be worked out further?

Practically speaking I’m guessing the realisation of complex time into the real everyday world would be something similar to multitasking (something my wife’s good at).

Worth a try, surely? Is 3D time so complex? Or is it just child’s play? 😉

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