## 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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## A unique signature of time

In the same way as Plato’s prisoners or Hawkins’ goldfish, are each of us seeing shadows of time, or a distorted view of it? How is it that each of us judge the duration of a second differently, just as each of us reproduce a uniquely shaped “0” when we hand write?

My teachers at school were always harping on about my poor level of handwriting as it clearly fell outside the margins of what was considered to be acceptable (to them).

It’s a fair point – we all try to write a “0”, for example, but each of us draws it differently – our handwriting is unique, despite each of us trying to replicate an identical shape. And if we are ‘too unique’, we call it “bad handwriting”.

Sure, there are some general patterns (bubbly, scrawly, etc.) but the point is that we all have our own personally unique interpretation of a common number or letter. Perhaps the same can be said too of art – that each of us would draw or paint a different picture even if we are given an identical object to reproduce.

Is it the same with personal time?

Not that we judge time differently. If a group of friends decide to meet outside a bar at 8 pm, it’s likely that there’ll be a spread of times of arrival, probably centered on 8 pm but perhaps with a spread of some +/- 10 minutes.

But whose version of the time is correct?

In Plato’s Allegory of the Cave he postulates the idea of prisoners who are only able to see projections of shadows on a wall in front of them – they have no idea of the ‘real’ objects making the shadows, the light behind them, or the source of any sounds that the puppeteers may make and which echo off the cave walls. For them, the echoes and the shadows are the real world.

Stephen Hawkins reproduced this idea with a fish who looks out of a goldfish bowl and sees a distorted view of things outside the bowl as the light travels through the glass. On a similar footing, that distorted view is the real world as it really is…for the fish.

In the same way as the prisoners and the goldfish, are each of us seeing shadows of time, or a distorted view of it? How is it that each of us judge the duration of a second differently, just as each of us reproduce a uniquely shaped “0” when we handwrite? Surely a 0 is a 0? There’s even a mathematical formula for a circle! Surely time is time?

Perhaps we’ll never know. Plato’s prisoners, once taken to the surface and shown how things really stand, were unable to accept the truth. And we all know that a fish out of water can’t survive. Could we?

In days old it was said that the camera never lies, but in modern times with digital photography, sophisticated editing software, or even basic filters, the final photo can often look very different from the image which first appeared in the view finder.

Some clocks and watches can [be made to] ‘lie’ too – a readjustment of a setting, or through mechanical fault. Except for a sundial. It’s much harder to tamper with the position of the sun…but isn’t it ironic that a sundial points the time…with a shadow? 😉

Paul

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