The Problem with i

[Jameela]

Of all the brilliant insights that make up the developments of RS2, there is however one issue which for me is a problem – the use of complex numbers! I fully accept and agree with the Yin and Yang principle used in connection with linear and polar aspects of motion, but imaginary numbers in mathematics are just not the same…

The concept √ (–1) is a fix to get a mathematically consistent way of using two axis to define a quantity on an Argand diagram. It does nothing more than that; we could just as easily use 'blue numbers' and 'red numbers', or 'east-west' numbers and 'north-south' numbers! The mathematical significance of complex numbers on an Argand diagram is that we can define a position on two axis by either Cartesian coordinates, or Polar coordinates – and therefore do mathematical manipulations which have practical applications. For example: in AC electric induction motors there is usually a phase angle between the Voltage and the Current drawn, say for example 45 degrees. The use of an Argand diagram therefore is an excellent mathematical modeling tool for this effect, as both AC Voltage and AC Current can be written as Vectors. Apologies for going through this in such a basic way, but please bear with me as I want to explain the difference.

In relation to RS theory, we are talking quite different quantities: It is between what we experience normally in life, and the "inside-out-subtle-inverse"! Consider for example: Shirts 'right-way-out' and Shirts 'inside-out' …If we have 5 shirts right-way-out and 5 shirts inside-out, can we have a phase angle between them at 45 degrees? – Humorous Nonsense! …So why do we try to use the same with RS2 when likewise attempting to put two completely different concepts on the same graph axis?

There is a mathematical connection between normal right-way-out and the inside-out-subtle-inverse; it is Projective Geometry, (but gosh it does hurt my brain!)

It can also be pointed out; that while an Argand diagram has an Origin or Datum, in our 'right-side-out' / 'inside-out' dichotomy, there is none! So it is therefore impossible to have any sort of common diagram that is more than figurative! The closest we can get to an Origin or Datum is the concept of a "Line", as in projective geometry the sequence: 'Point-Line-Plane' compared with the reciprocal sequence: 'Plane-Line-Point', has the common middle position of 'Line' – though they are not usually the same "Lines".

So if "i" stands for "inside-out-subtle-inverse", then I'm with you,

But if "i" stands for "imaginary number", then I'm afraid I don't buy it!

To avoid confusion; would it not be better to use a completely different symbol, and then enter its definition in a Glossary?

The concepts 'Subtle' and 'Imaginary' do have somewhat similar meanings, and the mistake is therefore understandable, but in our context with RS2, they are actually quite different!

In Peace, Jameela

[bperet]

The concept √ (–1) is a fix to get a mathematically consistent way of using two axis to define a quantity on an Argand diagram.

I do not use the mathematical interpretation of i in RS2, I use the geometric interpretation as a "rotational operator."

I use i exactly the same as your AC motor example, which can be either a rotational speed (frequency) in the natural reference system, or a phase angle in the coordinate reference system. (The natural reference system, being magnitude only, does not have the geometric concept of phase.)

The √ (–1) is the result of the projection of rotational motion on a linear system--could not have a wave without it. But it is not the basis of the concept. i² refers to two 90° CCW turns about the origin, so anything that was sitting on the +real axis is not stuck out over on the -real axis.

To avoid confusion; would it not be better to use a completely different symbol, and then enter its definition in a Glossary?

I use j in my notes, because of my EE background, since i means current. But when dealing with atomic systems, three rotational operators are needed, so it is probably best to stick with the conventional i, j, k system. If you prefer, I can refer to i as a rotational operator rather than an "imaginary number," as that would be more generally descriptive of the function.

Daniel's paper on Extradimensional entities (EDs) has shed a lot of light on this rotational function, which I was just about to write up as a separate topic. Quick summary... it is not time that is being represented by the rotational operator, but equivalent space.

[Jameela]

Space and Counterspace, or Yin and Yang - Do Not have a common Origin or Datum - they are intrinsically different to Vectors! ...Rather they taper-in and taper-out as they overlap - but no common Origin or Datum.

In Peace, Jameela

[dbundy]

Jameela,

It's interesting to note that, while the number 'i' enables the use of scalar algebra in a higher dimension, it loses one of its important properties: the distributive property. No datum at all, actually, since no point in the rotation is any greater or lesser than any other point, except by fiat.

Employing the same method to move up one more dimension, adding two more imaginary numbers, robs the scalar algebra of yet another property, the property of commutativity, making the order of multiplication non-reversible.

Finally, adding four more imaginary numbers takes the algebra to the third dimension, but at the cost of losing its third and final associative property, making the grouping of terms non-reversible.

Believe it or not, this has a tremendous relevance to the development of RS theory.

Here is a wonderful presentation by John Baez on it: http://www.youtube.com/watch?v=Tw8w4YPp4zM

You will notice the confusion that results from reference to mathematical dimensions and geometric dimensions, as John fails to distinguish them, but you will be able to handle it no doubt.

[Jameela]

Sorry but I am not convinced! ...I watched the YouTube of John Baez talking about the number 8 as you suggested, and it certainly is very clever advanced mathematics, and I can see the connections to RS theory, but...

The clever math is a model, nothing more. The mathematics can be correct in itself, it can be symmetrical and beautiful, but that doesn't make it conceptually correct for any given application we are attempting to model.

Putting the Cart before the Horse?

Firstly, we need look to what is going on in 'Nature', which anyone who looks holistically can realize is more than just Physics. Secondly we try to model our findings with mathematics, then see what feedback that can give us to our understanding of 'Nature'. ...It must be this way; Not the other way around.

I guess my problem with i does mean my departure from the evolved RS2 theory, even though I do accept so many other RS2 corrections or extensions of Dewey Larson's ideas. ...I guess another consequence of this realization is that Time is not so much polar or planar, rather it is "volumetric" - or in other words a 3D bundle!

The Yin analogy of Time (in the material sector) is it's a 3D "bundle", whereas Space dimensions are "individual" dimensions (Yang analogy).

Did not Dewey Larson plead that ideas must first be conceptually correct? ...So how can any mathematical proof of RS be authoritative?

Sorry to upset the apple cart, as it were, but the horse has got to go in the front! ...there is a problem with using i

In Peace, Jameela

[Horace]

Read Doug's post again. He is not a proponent of "i" either. In fact he is an avid oponent of it. So much so, that he has written a series of articles about the evil "i". I bet he would happily provide you with links to these articles, if you asked him.

I don't understand why you had replied to him "Sorry but I'm not convinced" if you have objections to "i" just like he does.

[dbundy]

Hi Jameela,

You wrote:

The clever math is a model, nothing more. The mathematics can be correct in itself, it can be symmetrical and beautiful, but that doesn't make it conceptually correct for any given application we are attempting to model.

I agree. You can read my view of it here.

[Ardavarz]

Would it be correct to represent what Larson calls "progression of the natural reference system" with diagonal line in the complex plane?

Thus since the projections of this motion along the both axes are equal, considering one of them as imaginary will have the effect of making the interval between any two points lying upon such diagonal line zero which will correspond to the lack of change of the "absolute location" resulting from such motion. Then the "displacement from unity" could be seen simply as angle, but measured from the diagonal line, not form the axes.

I also imagine that the relation between the natural reference system and the stationary ones is logarithmic and this will transform that line in a spiral, but I haven't figured it out yet.

It seems very simple if seen this way, but is this image correct?

[Horace]

Would it be correct to represent what Larson calls "progression of the natural reference system" with diagonal line in the complex plane?

That depends if the "progression of the natural reference system" is 1-dimensional or 3-dimensional. See this link. If the progression is assumed to be 1D then it begs the question "is the progression a sequence of positions along a line" ?

If "yes" then this is not thinking in terms of "speed only" but in terms of succession of positions in some kind of container.

It will be very hard to draw anything before the concepts of RS2 start yielding points and positions

[bperet]

Would it be correct to represent what Larson calls "progression of the natural reference system" with diagonal line in the complex plane?

That is how I started working with it in my "lineland." But with my recent updates to the rotational operator, "i", being equivalent space, the axes are (space, equivalent-space), not (space, time). That is why rotation proceeds as a dimensional change, not a linear one. The temporal aspect of motion drives the equivalent space rotation, but is not directly represented on the chart.

You also need to consider that motion is actually a ratio, and a ratio is the slope of the line, not the coordinates. So (1,1) gives a unit slope when referenced from (0,0), but it is in actuality more of (Δ1, Δ1).

I also imagine that the relation between the natural reference system and the stationary ones is logarithmic and this will transform that line in a spiral, but I haven't figured it out yet.

Yes, it is the natural log, which occurs because the type of measurement changes. Outside the unit boundary, motion is linear and translational, so it proceeds 1, 2, 3, 4, ... what is called step measure where the final value is the total. But inside the unit boundary, motion is in the sequence 1/1, 1/2, 1/3, 1/4... growth measure, where the net is the sum, not the last value, so you integrate 1/t dt = ln(t) for the relationship.

Larson discusses this in Basic Properties of Matter, regarding inter-atomic distances.