From: chris.m.thomasson.1@gmail.com   
      
   On 1/6/2026 11:47 PM, Thomas Heger wrote:   
   > Am Dienstag000006, 06.01.2026 um 00:47 schrieb Thomas 'PointedEars' Lahn:   
   >> Chris M. Thomasson wrote:   
   >>> On 1/5/2026 3:09 PM, Chris M. Thomasson wrote:   
   >>>> Say to explain a 3d point in time we need (x, y, z, t), t for time.   
   >>>>   
   >>>> For a 4d point we need (x, y, z, w, t), t for time.   
   >>>>   
   >>>> t is in every dimension?   
   >>>>   
   >>>> For a 2d (x, y, t)   
   >>>>   
   >>>> For a 1d (x, t)   
   >>>   
   >>> Why not keep time in the dimension, [...]   
   >>   
   >> Again, this wording does not make sense.  Time, here represented by the   
   >> coordinate t, *is* a dimension then *implicitly*.   
   >>   
   >   
   > The word 'dimension' has different meanings, hence it is necessary to   
   > write, which meaning was meant.   
   >   
   > If we refer to space, the 'usual' space has three dimensions of the type   
   > 'length', which are orthogonal towards each other.   
   >   
   > This wouldn't allow an additional orthogonal dimension of space for time.   
   >   
   > So, we need a different meaning for 'dimension' and a different 'space'.   
   >   
   > If we add t to the 'x,y,z-space' we end up in what is called spacetime.   
   >   
   > But I would suggest a different approach and use complex numbers and   
   > assume, that time is imaginary and the dimensions of space real.   
   >   
   > An even better approach would be to use a construct called   
   > 'biquaternions' and assume, that the 'real space' has actually such   
   > features, as if it was a quaternion-field, where points have the   
   > features of bi-quaternions.   
   >   
   > This would allow three imaginary axes of time and three real axes of   
   > space, plus two additional 'dimensions' for scalars and pseudo-scalars.   
      
   When I would add a t to a vector, say (x, y, z, t), yes its confusing. I   
   would only use the (x, y, z) parts for the vector math, ect. The t was a   
   point in time for that (x, y, z) vector. So, say:   
      
   (-.5, .1, -.16, 0)   
      
   The t aspect is at say, a stop watch started from zero. It ticks. Now,   
   the same point can be:   
      
   (-.5, .1, -.16, 0.0000001)   
      
   well, the granularity of the t aside for a moment. However, we now have   
   the same point in a different time.   
      
   As time ticks by we have a shit load of vectors at the same point, but   
   with different non-zero t components. We can sort them based on t after   
   some iterations... ect. Its fun to do, ponder on. So a single point that   
   stays the same can have different t's. However, it does not mean that t   
   is a 4d space. No, its a 3d space with t. For a 4d space (x, y, z, w,   
   t), on and on. But it is confusing.   
      
   Actually, I don't know where to plot a 4d point with a non-zero w   
   component. One time I said just plot the 3d components (x, y, z), and   
   use w as a color spectrum that is unique. So, I can say here is a 4d   
   point and its a certain color. This tells me that the point is off axis   
   from the pure 3d world, aka non-zero w.   
      
      
   > I have written a kind of book about this idea some years ago, which can   
   > be found here:   
   >   
   > https://docs.google.com/presentation/   
   > d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing   
      
   Hummm... Need to read that when I get some more time. Thanks!   
      
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