Consciousness, Information and Measurements

[msasa79]

if i may , perhaps @msasa79 "as going in opposite time directions" is more apropriate as " going away in different time/space directions" maybe ?

Yeah, it could probably be viewed that way too. Or maybe better said, coming closer to each other from different or opposite directions.

In many cases, the authorities have adopted and openly propagated the so called Feynman's approach, in which it's said that he instructed others, pondering about these things in an attempt to better understand them, to just "shut up and calculate". FWIW.

 

[Ricardo]

( " Time/space doesn't flow through a worldline of a universe for light but does jump from one complete universe state worldline to another. Gravity would be the continuum between universe states so would kind of be the road time travels on. " so this would account for both the fractal nature , the "split " between densities ( and lateral dimensions ) , as well as both the so called ever present now , and the diference in time scales according to different densities ? hm , just wondering out loud I'll shut up now XD, this way too mathy for me eh bold parts added and changed )

 

[John G]

So my perspective on this is via human body ( since lack of formal Ph. ed.) is easier to grasp (?) , as both reflect , so the pentagon , via , the hexagon , (within the circle ) would be the interaction/through that moves all the states ? this seems to reflect as well the 5 and 6 numbers , via ofc the previous 3 centers ?

The pentagon/hexagon clues aka the 5/6 additions for gravity could certainly relate to more connections between states in a short cuts through the interior of the circle/ball kind of way.

 

[John G]

Yeah, it could probably be viewed that way too. Or maybe better said, coming closer to each other from different or opposite directions.

In many cases, the authorities have adopted and openly propagated the so called Feynman's approach, in which it's said that he instructed others, pondering about these things in an attempt to better understand them, to just "shut up and calculate". FWIW.

The Feynman approach probably figures into Ark's anti-universe too where if you go past infinity in our universe you might end up going backwards (anti-matter-like) in the anti-universe or something like that.

 

[John G]

( " Time/space doesn't flow through a worldline of a universe for light but does jump from one complete universe state worldline to another. Gravity would be the continuum between universe states so would kind of be the road time travels on. " so this would account for both the fractal nature , the "split " between densities ( and lateral dimensions ) , as well as both the so called ever present now , and the diference in time scales according to different densities ? hm , just wondering out loud I'll shut up now XD, this way too mathy for me eh bold parts added and changed )

Universe states could certainly be the expanded present the Cs have mentioned. This gravity connection would be a continuum thing not on the brane universe state though there would be one link on the brane too just not a bunch of different parallel universe-like ones that the continuum offers.

 

[Ricardo]

re most math/physics talk "here" i'm at most playing with crayons ( if not eating them ) , but wanted to make 2x further comments .

---
Session 28 May 2013:

A: If there is truth within that will manifest naturally like the pieces of a puzzle snapping into place.
---

This and the similar previous comment ,IMO , seems to relate as how Human Female/Male are .... literally complimentary (ideally), and further the same applies to the fractured Human group. The other is to say that even at the micro-micro level , there's a similar structure in the elemental atom that "resembles"(?) the dna structure ( as per Occult chemistry by C.W. Leadbeater)

 

[msasa79]

After some stretching in spiraling fashion and a bit of rest to have our muscles in proper tone, and applying almost extremely simplified classical logic to apparent Ark's indifference as meaning that he either doesn't care or tacitly approves, we are going to borrow a part of that chunk of the framework from his blog.

Jumping right in medias res, it was shown there that the Clifford algebra Cl(V), where V is our ordinary flat Euclidean 3-dimensional space, can be represented by the algebra of biquaternions. If we know what a quaternion is, q=q₀+q, where q₀ is scalar and q is vector, then we get a biquaternion by turning the coefficients from real numbers into complex numbers. Meaning that from a quaternion
q = a₀e₀ + a₁e₁ + a₂e₂ + a₃e₃,
where a_μ are the real numbers and e_μ are basis unit vectors with e₀ being the unit vector in the scalar real direction perpendicular to the basis e_i of the ordinary 3-dimensional space, we get a biquaternion
q = (a₀+ib₀)e₀ + (a₁+ib₁)e₁ + (a₂+ib₂)e₂ + (a₃+ib₃)e₃.
Written to explicitly denote real and imaginary parts, a biquaternion would look like
q = q₀^Re + iq₀^Im + q^Re + iq^Im,
where q^Re and q^Im would be perpendicular to each other.
In principle, a biquaternion would be an 8-dimensional object, real and imaginary direction for each of our 4 dimensions in the sense of a scalar one plus three for 3-dimensional space.

The complex numbers can also be written in so called Euler notation in polar coordinates as (a+ib)=re^iφ, where r is distance from the center of the polar plane, r²=a²+b², and φ is angle of a sort of a rotation measured from positive real axis, tgφ=b/a. Written using sine and cosine we get (a+ib)=r(cosφ+isinφ).

Applying this to biquaternions, we see that they are in fact made of 4 real-imaginary planes, so we can perhaps simplify things a bit by using usual mathematical notation for a plane, where it is represented by the normal, i.e. the unit vector pointing in perpendicular direction to that plane. So, for a complex scalar plane, we got a direction which might tentatively be called the depth of the information field. As the scalar dimension, and so also complex scalar plane, is perpendicular to our ordinary 3-dimensional space, the depth of the information field would then be pointing in the directions of our everyday world. Or more specifically, since we know that it is not of this world, the perception might be that it would point in so called direction of our consciousness or of knowledge and/of being as local individual segment of the cosmic information field. In general and simplified view, this normal would point in the direction perpendicular to what we might perceive as a surface of consciousness, representing its depth in which direction we might go when we for instance go deeper in meditation or zone-out, as the C's have suggested.

Another interesting implication of the above might be that this direction perpendicular to the scalar plane or perhaps the surface of information field, might in fact represent fourth spatial dimension that was previously referred to as inner or inside dimension in contrast to three dimensions usually perceived as outside world we encounter in our everyday lives. Which brings us back to 3-dimensional Euclidean space kind of left with its 3 complex planes, that perhaps can all together be joined and represented by a 3-dimensional direction perpendicular to our q^Re and q^Im. If we associate q^Re and q^Im to electromagnetic field as q^Re+iq^Im ~ E+iB, then that perpendicular direction is basically represented by Umov-Poynting vector E×B, which in layman terms is the direction of the ray of light as an EM wave.

With that we come to yet another interesting probable implication of this biquaternion discussion. In addition to being perpendicular to each other, q^Re and q^Im as representatives of the complex vector part of our biquaternion, would also be perpendicular to the scalar dimension or the complex scalar plane. In that sense, if association in previous passage holds water, light or light rays would in fact point to sort of collinear directions to the cosmic information field or its complex scalar surface.

Well, perhaps that would do for this post folks, to leave enough room for your thoughts and comments before going to other things that could possibly arise from what has been just presented here.

 

[axj]

apparent Ark's indifference as meaning that he either doesn't care or tacitly approves

You can tag @ark directly and ask him. Maybe he didn't see this thread.

 

[msasa79]

Got more than the whole page of introduction part written on paper, which more or less usually, in this thread at least, exceeded the main body of the post sometimes even greatly, but the excitement got the better of me so skipping all that and going directly to the main part this time.

Another thing that we can borrow in verbatim from Ark's blog is the formula for biquaternion product, which says that biquaternions p=p₀+p and q=q₀+q when multiplied give the result:
pq = p₀q₀ + pq + p₀q + q₀p + ip×q.

Using this formula together with the expression for the norm squared of a complex number
||z||² = zz* = (a+ib)(a-ib) = r(cosφ+isinφ) r(cosφ-isinφ) = re^iφ re^-iφ = r² = a²+b²,
where z* is a complex conjugate of a complex number z, for a biquaternion we get:
qq* = (r₀e^iφ₀ + q^Re + iq^Im) (r₀e^-iφ₀ + q^Re - iq^Im) =
= r₀² + r₀e^-iφ₀ (q^Re + iq^Im) + r₀e[sup-iφ₀[/sup] (q^Re - iq^Im) + (q^Re + iq^Im) (q^Re - iq^Im) + i(q^Re + iq^Im) × (q^Re - iq^Im) =
= r₀² + (q^Re)² + (q^Im)² + r₀ q^Re (e^-iφ₀ + e^iφ₀) + ir₀ q^Im (e^-iφ₀ - e^-iφ₀) + i(iq^Im×q^Re - iq^Re×q^Im) =
= (skipping explicitly writing the simplifying of exponential function and vector cross product in this step) =

qq* = r₀² + (q^Re)² + (q^Im)² + 2r₀ q^Re cosφ₀ + 2r₀ q^Im sinφ₀ + 2 q^Re×q^Im.

A striking thing looking back at us from this result is that it contains only real components, no imaginary parts anymore. The three vector components are all perpendicular to each other, and by definition to scalar part also, implying that we got our three perpendicular dimensions of Euclidean space. Together with the scalar part, which is sum of three squares and usually referred to as the norm squared of a biquaternion which implies it's a non-negative valued, we apparently got in total our 4 spatial dimensions, briefly discussed in previous post.

Another interesting and funny implication is that exchanging places of the factors in the product, in addition to changing the sign of the cross product, also changes the sign of the second vector component, implying de facto that what happens by exchanging places is that the q^Im switches to point in the opposite direction. If we relate q^Im to magnetic component of EM field, this might indicate why we sort of observe in nature that magnetic fields, like solar and possibly geomagnetic, periodically change their orientations. If we relate also q^Re to the electric field, like we tentatively did in previous post, the scalar part of our product basically plays the role of energy, at least for the EM vector part, as the sum of squares of electrostatic and magnetostatic fields' magnitudes. The three vector directions or dimensions are then explicitly spanned by the directions of electric and magnetic fields in EM wave and its direction of propagation as represented by the Umov-Poynting vector S~E×B.

In QM, the product of the wave function with its conjugate represents probability density, or something to that extent. Maybe we could use that as an analogy to relate our product to density, density of light or EM energy perhaps?

Before going further, I am asking for a cross-check of the result and of the tentative interpretation presented in this post.
Following the suggestion given above, pinging @ark again here in case first time slipped his attention.

 

[msasa79]

Another interesting and funny implication is that exchanging places of the factors in the product, in addition to changing the sign of the cross product, also changes the sign of the second vector component, implying de facto that what happens by exchanging places is that the qIm switches to point in the opposite direction. If we relate qIm to magnetic component of EM field, this might indicate why we sort of observe in nature that magnetic fields, like solar and possibly geomagnetic, periodically change their orientations.

In fact, the second vector term, 2r₀ q^Im sinφ₀, does not switch signs when we exchange place in the product, i.e. for q*q. That might be interpreted though that when q^Im changes its orientation, the angle φ₀ also sort of changes its orientation, becoming -φ₀, i.e. going in the opposite direction or simply that r₀ starts rotating in counter orientation it previously was rotating. Potentially speaking that the real time can go in both directions perhaps, indicating what the C's suggested "that not only is the future open, but also the present and the past" (26-december-1998)?
Well, better to wait for Ark or somebody to do some cross-checking before going around jumping and exclaiming "Eureka!".

 

[msasa79]

When excited, it's not so rare that we jump ahead of ourselves, basically like I did with previous post. And as also demonstrated with previous posts, we more often than not make small and big errors and mistakes when emotions get the better of us. So when things settled down a bit, a cross-check was done in a slightly different way which brought up new insights to the light of the day.

Nice thing about the result obtained previously is that we didn't specify a particular 3-dimensional space basis at the beginning so the end expression revealed sort of naturally the 3 orthogonal directions that can serve as the natural basis of our ordinary everyday space,

• qq* = r₀² + q² + 2r₀ q^Re cosφ₀ + 2r₀ q^Im sinφ₀ + 2 q^Re×q^Im,

where q² = (q^Re)² + (q^Im)² is the norm squared of the complex vector part of biquaternion.

Leaving aside for the time being the other product q*q, we can check what would the product qq* look like if we choose a specific orthonormal basis (e₀, e₁, e₂, e₃), apply the multiplication rules for the basis vectors as presented on Ark's blog in the context of the Cl(V), while using the polar notation for each of the 4 complex planes of our 4 dimensions.
In that case, the arbitrary biquaternion q=q₀+q for which we calculate the product qq* would look like,

• q = (a₀+ib₀)e₀ + (a₁+ib₁)e₁ + (a₂+ib₂)e₂ + (a₃+ib₃)e₃ = r₀e^iφ₀ e₀ + r₁e^iφ₁ e₁ + r₂e^iφ₂ e₂ + r₃e^iφ₃ e₃

where we explicitly see its 8-dimensional nature represented by sort of 8 coordinates, 4 distances (r₀, r₁, r₂, r₃) from the origins of complex planes for each dimension and 4 angles (φ₀, φ₁, φ₂, φ₃) between real and imaginary axes in each of those planes. As noted in previous posts, the exponential polar notation represents (a+ib)=re^iφ=r(cosφ+isinφ), and the complex conjugate needed for our product is simply (a-ib)=r(cosφ-isinφ)=re^-iφ, which then for the product qq* gives,

• qq* = (r₀e^iφ₀ e₀ + r₁e^iφ₁ e₁ + r₂e^iφ₂ e₂ + r₃e^iφ₃ e₃) (r₀e^-iφ₀ e₀ + r₁e^-iφ₁ e₁ + r₂e^-iφ₂ e₂ + r₃e^-iφ₃ e₃).

After straightforward multiplication and grouping the terms by the basis vectors, while using e₀=1 and multiplication rules, we get,

• qq* = r₀² + (r₁² + r₂² + r₃²) + r₀ {r₁ e₁ [e^{i(φ₀ - φ₁)} + e^{i(φ₁ - φ₀)}] + r₂ e₂ [e^{i(φ₀ - φ₂)} + e^{i(φ₂ - φ₀)}] + r₃ e₃ [e^{i(φ₀ - φ₃)} + e^{i(φ₃ - φ₀)}]} + i {e₁ r₂ r₃ [e^{i(φ₂ - φ₃)} - e^{i(φ₃ - φ₂)}] + e₂ r₁ r₃ [-e^{i(φ₁ - φ₃)} + e^{i(φ₃ - φ₁)}] + e₃ r₁ r₂ [e^{i(φ₁ - φ₂)} - e^{i(φ₂ - φ₁)}]}.

Applying the formulas for sine and cosine as expressed in exponential notation, we finally obtain the result for the product qq* in a particular orthonormal basis (e₀, e₁, e₂, e₃),

• qq* = r₀² + R² + 2r₀ [r₁ cos(φ₀-φ₁) e₁ + r₂ cos(φ₀-φ₂) e₂ + r₃ cos(φ₀-φ₃) e₃] + 2 {e₁ r₂ r₃ sin(φ₃-φ₂) - e₂ r₁ r₃ sin(φ₃-φ₁) + e₃ r₁ r₂ sin(φ₂-φ₁)},

where R² = (r₁² + r₂² + r₃²) = q² stands for norm squared of the complex vector part of a general biquaternion q=q₀+q.
We are now in position to compare this result for qq* with the one obtained in previous post and shown here under the first bullet point.

Following what light tells us in order to bring these two expressions in accordance and applying the freedom to choose where to place and how to arrange our chosen coordinate system, we see that alignment by EM wave leads to,

• axis e₁ in the direction of q^Re, that is φ₁=0, i.e. q^Re = r₁ e₁;
• axis e₂ in the direction of q^Im, that is φ₂=π/2, i.e. q^Im = r₂ e₂;
• placing the origin of 3-dimensional spatial part at r₃=0, that is in the plane spanned by q^Re and q^Im, i.e. q^Re×q^Im = r₁ r₂ e₃.

Arrangement by these chosen principles will give a general biquaternion in the form q = (q₀^Re + iq₀^Im + q^Re + iq^Im) = (r₀e^iφ₀ + r₁ e₁ + ir₂ e₂), which for the general product qq* then gives,

• qq* = (r₀e^iφ₀e₀ + r₁e₁ + ir₂e₂) (r₀e^-iφ₀e₀ + r₁e₁ - ir₂e₂) = r₀² + r₁² + r₂² + 2 r₀ r₁ cosφ₀ e₁ + 2 r₀ r₂ sinφ₀ e₂ + 2 r₁ r₂ e₃.

Interesting thing that arises from this choice of alignment or arrangement is that the angle φ₃ becomes sort of so called free parameter in the whole story. Using again light as a guiding principle, this free parameter might perhaps be expressed as φ₃=ωt, where ω would be frequency of light as an EM wave, in our realm represented through the photon as a quantum of EM energy with relation E=ℏω, where ℏ=h/2π is so called reduced Planck's constant.

But, let's not jump ahead again and let things settle a bit before proceeding with possible interpretations of our result here.

 

[John G]

Supposedly the 4-dim Feynman Checkerboard can be put in a form to emphasize biquaternions but I can't overly follow details a lot. You get EM gauge symmetry and Maxwell's equations full symmetry out of the Checkerboard and this is as close as I get to something like what you are doing. You do get a hypersphere out of the full symmetry which is as close as I get to your polar coordinate scheme but detail checking is not something I can do.

 

[msasa79]

Interesting thing that arises from this choice of alignment or arrangement is that the angle φ₃ becomes sort of so called free parameter in the whole story. Using again light as a guiding principle, this free parameter might perhaps be expressed as φ₃=ωt, where ω would be frequency of light as an EM wave, in our realm represented through the photon as a quantum of EM energy with relation E=ℏω, where ℏ=h/2π is so called reduced Planck's constant.

Although the φ₃ free parameter might be related to Planck's constant, i.e. ℏ, it's probably not related to time as briefly contemplated is the quoted passage, but more likely to elusive spin or helicity or "enigmatic" chirality.

Leaving everybody to choose their own ways to arrange the axes and directions of their reference systems, let's turn our attention to complex scalar part of the biquaternion as perhaps it's time to breathe some life into our almost static picture and, instead of circling the bowl with hot just cooked soft chicken meat like my ex's cat, tackle with the real time in more appropriate manner.

In the general form of biquaternion q = r₀e^iφ₀ + q^Re + iq^Im, we explicitly wrote its complex scalar part in the polar notation, (a₀ + ib₀) = r₀(cosφ₀+isinφ₀) = r₀e^iφ₀. This allows us, by following the C's suggestion that "information recorded equals time", to introduce time into our picture in sort of natural way. Time in this context can be put in relation to the speed of rotation in complex scalar plane, that is the speed with which angle φ₀ changes, which can be represented in mathematical terms as Δφ₀ ~ elapsed time or Δt, for which we could use symbol Δt₀ or maybe τ as the "proper time" or "own time" as it is sometimes called in relativity for instance. Factor of proportionality is usually referred to as angular frequency or velocity, or in some contexts speed of rotation, ω₀ = Δφ₀/Δt₀, but these contexts as a general rule consider time to be independent variable, a dimension of its own, outside of possible influences from the let's say consciousness units, which is not the case here as our time as recording of information, presumably by consciousness, is variable and selective.

So, instead of using frequency ω₀, which we still might come back to in the context of frequency of light or knowledge, we might define time in the same units as Δφ₀ or perhaps simply say that one unit of time corresponds to one complete round in the complex scalar plane, that is Δτ = Δφ₀/(2π), so we have a dimensionless value that won't mess up the mathematical apparatus when using and applying it. So, for complex scalar part of biquaternion we now have, (a₀ + ib₀) = r₀e^2πiτ = r₀(cos(2π τ)+isin(2π τ)), that is we got let's say imaginary part of our time in the story.

To have also the real part of the time explicitly visible on the stage, we might express the so called distance from the center of the complex scalar plane, r₀, also as a function of angle φ₀, that is (2πτ). In principle, here again we come to the choice, as the functional form r₀(φ₀)=r₀(2πτ) is a matter of personal preference and free will, hopefully based on knowledge. If we choose the simplest form, i.e. r₀=constant, we'll end up running in circles, all the time circling at the same distance from the origin of the complex scalar plane, no matter how many rounds we make there. In that sense, it's perhaps nice to note that nature, on the one hand, and also the C's mentioned it a few times, on the other, shows us so called property or quality of self-similarity (Wikipedia link). If we would include that attribute into our now moving picture or maybe already a movie, we would also account for so called fractality or the fractal nature of the world and most probably reality. In that sense we might recollect our exercise with spirals few days ago.

We could go directly after the gold in the form of Fibonacci spiral, but guided by all the beauty there is in Creation, we might also realize that the golden spiral is just a special case of more general class of spiraling curves called logarithmic spirals, or in singular, spira mirabilis, which all exhibit the property of self-similarity. Of course, we are perfectly welcome to choose any relation r₀(φ₀) we wish for and are inclined to, it's just that if our choice is informed by self-similarity quality then the relationship would probably look like r₀(φ₀)=Ae^kφ₀, where A is distance from the center of the complex scalar plane at φ₀=0, or in our time notation when τ=0, and coefficient k=tanα with α being so called pitch angle (Wikipedia link).

Written all together we get for the complex scalar plane or part of a biquaternion r₀e^iφ₀ = Ae^2π(k+i)τ.
By applying series expansion of the exponential function, playful use of different pitches and perhaps rhythmic swinging or spinning sometimes to the left and other times to the right, we can almost do marvels on this plane or miraculous things as the attribute mirabilis might suggest. In conclusion, we found out what the time very likely actually is, got ourselves acquainted with its real and imaginary parts, and hopefully brought some new information, knowledge, light and life into our everyday lives in the process.

Happy learning or have fun until the next time.