So the compiler on this website is crap. I will rewrite the formulas that did not come out right:

(E/c, p) is the Minkowski four-vector, (p, iE/c) is the Euclidean fourvector.

the next formula is

E^2/c^2-p^2=m^2c^2

the one after is

-(-E^2/c^2)-p^2=m^2c^2

then the formulas come out right.

Oh I understand -- and a big thank you -- Armin --- Yes I do understand a bit better thanks and yes I agree your comments (after the above) weren't meant to be a downer -- thanks for the clarification. And I do actually think they have helped a lot.

I will work on making the presentation of the ideas more consistent. Yours Harri. I did realise that Minkowski used the cEuclidean=ic and that saying "i=c" wasn't exactly what Minkowski meant, but the major point is that what if we make "i=c" then go on from that ... I do feel that making i2=+i and -i has a lot of merit. For example Peter Jackson's red/green sock trick is easy to picture if we use i=c and i=h, and also a version of the "Two Slit Experiment" also is easy to diagram. See attachment on this post if you have time -- easy peasy.

It has been fun actually chatting to you Armin, thanks for the great comments and the technical details in the above post. The first post's FAQ attachment might answer some of your other questions, about areas being numbers and having probabilities within that area.

Yes if I want a new idea heard -- I had better get the basic ideas "more" coherent. And especially notation.Attachment #1: Armin.pdf

One cannot set c=i. "c" is a physical quantity. "i" is a mathematical quantity. Physical quantities are given by the product of a value and an unit. So expressions as c=i are meaningless.

Yes, I saw Minkowski writting (or the people that traduced his work from German) expressions such as "3·105 km = sqrt(-1) Sec", but such expressions are meaningless.

What we can do is reparametrize time as (t --> it) and use a natural system of units just to get a more symmetric expression for the element of line

ds2 = - (dt2 + dx2 + dy2 + dz2)

Alternatively we could just reparametrize the speed of light as (c --> ic) and obtain again a symmetric expression by imposing a natural system of units.

But nothing of this modifies the physics. Physics does not vary by a change in units or by modifying the labels we use to represent things.

The above changes turn the Minkowskian element of line into a symmetric Euclidean form, but other parts of the formalism are antisymmetrized. For example the equation of continuity is broken because the rate term (d/dx0) transforms into an imaginary quantity when we do (t --> it) or (c --> ic).

The equations x2 + 1 = 0 and x2 + 12 = i2 02 are identical. The solution to the second is identical to the solution to the first.

Similar remarks about setting i=h. This is a meaningless expression. Even if we ignore that, when you write the Schrödinger equation as (ihbar ðPsi/ðt = H Psi) and next claim h=i, we can check that replacing h by i in the equation breaks the imaginary term and the equation no longer describes quantum phenomena.

The set of equations in the Hypothenuse box are also incorrect. One can add and subtract the equations and obtain invalid results. One can also just set b=0 and obtain the invalid result i=0.

"Conclusion Winger's question on the nature of physics and mathematics can be addressed rigorously using the fundamental concept -- a number is an area. What is fundamental? A number is an area not a length." A number is neither an area nor a length, a number is a mathematical quantity. Areas and lengths are represented by physical quantities.

    Dear Tiainen

    Regarding your comment at my current essay; https://fqxi.org/community/forum/topic/3143

    Sorry that the changed terms in different feilds of knowledge and interpretations have lost most important fundamental terms of physics discipline, that are necessary to define What is fundamental in physics.

    "Your one indivisible atom sounds very odd to me"

    I didnt mean the chemical atom, that Dalton mistakenly gave to chem.elements

    Indivisible is the original meaning of the Greek word Atom, which Democtratus coine to the Nature's fundamental particle which physics discipline and Natural philosophy are based on. Therefore I strongly propose to keep term to its real meaning.

    I hope you now that the answer of question, What is fundamental? Is somehow depending on physcs. Since physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force.In other word one can't study any effect without matter.

    Although these metaphors in terminology my answer is focusing Nature's Fundamental particle (matter) and energy Force that are still unsolved, or profoundly explained.

    I am readin your essay and will comment more after evaluation. Some points I appreciated are, "Clearly pure mathematical properties (p0,p1,p2,p3,....pn-1,pn,pn+1,......) are matched up with to

    cardinality classes 0,1,2,3,....... so" "Hypotenuse box" (Pythagorean).

    Regarding " bird eye and Frog eye, systems connection,Quantum monogamy".

    Are conceptually included in modelling, though it would be better to use 3D spherical clustering Program.it means that model used can be applied any particle's clustering, ex; electron, proton Neutron, atomic Nuclei, DNA, Dark matter, and so... But since this is summarized basic theory due to contest limitations detailed explanation require a lot.

    I am sure that "Most of the fundamental ideas of science are simple and can be expressed in a language comprehensible to everyone".

    In 2010, my previous essay. http://fqxi.org/community/forum/topic/794

    I explained the Natures fundamental as simplest, smallest thing of all.

    On the other hand, I believe that current physics fundamental problems amongst dealing with fundamental terms such as original meaning of "Elementary" "Quanta" "Atom" .

    I found that biggest and misleading one off all is the term "massless"

    Question related fundental problems of phys;

    What is Elementary Quanta?

    What is Light Quanta?

    What is elementary Charge?

    What is Photon?

    What is Elementary particle?

    What is elementary energy?

    How these terms are related each other?

    Is E=mc^2 fundamentally applicable to all matter?

    Why light is affected by Gravity?

    What are Gravitational waves?

    Why we still discover Einsteins theory?

    Why Newtons simple statements Gravity is still most important of all Physical science?

    Is any scientific theory that we can overall spectrum of physical sciences?

    Which is natures dominant structure/shape at all level?

    Which way philosophical/ scientific idiea from the known history we come to here?

    Any possibility to continue it?.......

    "All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Albert Einstein.

    In general (when dealing with light EM), I have different actions to Feyman's the three basic actions;

    -Action #1: A photon goes from place to place.

    -Action #2: An electron goes from place to place.

    -Action #3: An electron emits or absorbs a photon.

    My opinion

    -Action #1: A photon does not goes from place to place, but its energy is tranfered as wave(force influence/gravitational wave/dynamics).

    -Action #2: An electron does not goes from place to place, but its energy is tranfered as wave(force influence/gravitational wave/dynamics).

    -Action #3: An electron emits or absorbs a photon's energy, but not photon itself.

    Every particle's total energy must contain same quanta (certain quantity), of elementary energy, that equals the total quantity of elementary particle's(Photon's) energy.

    Since elementary mass 1.7x10^-36 kg, by dividing any particle's Mass into the elementary mass, we obtain ratio that equals to quantity of photons (note integer number).

    Every particle's total mass must contain same quanta (certain quantity), of elementary mass, that equals the total quantity of elementary particle's(Photon's) mass.

    Since elementary energy 1.6x10^-19eV, by dividing any particle's energy into the elementary energy, we obtain ratio that equals to quantity of photons (note integer number).

    Proton; 938, 272 081 MeV. 938 272 081 particle (Photons). ODD number of photons.

    Electron; 0.510999 MeV. 510999 particles. (Photons). ODD number of photons.

    Neutron; 939. 565 134 MeV. 939 565 134 particles(Photons) EVEN number of photons.

    You may also discuss following from Gravitational angle;

    Coulumb's constant?

    Universal Gravitational constant?

    G wave and EM wave same speed? Why?

    Pauli exclusion?

    Dimensions in String theory?

    .......

    Best wishes.

    Bashir.Attachment #1: 5_Bashir_Quantum_Mech_and_Relativity_Theory.pdf

    Jouko,

    You have some interesting ideas but they are very speculative. Essay contests such as this are a good place to present such ideas:-)

    I don't think you can set i=c or i=h but I do think you can construct something similar to the following:

    PSI = exp(omega) = sqrt[1 - (v/c)^2] (v/c)i

    Then for v=c, PSI=i.

    I think something similar can be constructed using the Plank Constant.

    You have given me somethings to think about. Many Thanks.

    Best Regards and Good Luck,

    Gary Simpson

      Hiannen.

      I hope you get the point, I'm planning to rewrite a mathematical version (equations) since I must check it will probably take for a while.

      In fact I don't trust mathematics if it doesn't have physical meaning that I can directly tell by words.

      Bashir.

      read the 4-square essay y Gary Simpson here https://fqxi.org/data/essay-contest-files/Simpson_Four_Squares_rev00.pdf

      here is my comment on Equation 1 below the dotted line ---

      ======================================================

      Every time I read your essay I seem to understand, it more and more.

      I have a couple of questions about Equation 1

      (a² + b² + c² + d²)u² = f²u²

      A quote page 3

      "The meaning of Equation 1 is that in a 4-D geometry, if a right triangle is constructed from an integer number of basis lengths in each of the four dimensions (a, b, c, and d), then the hypotenuse (f) that traverses through the 4-D space will also have an integer number of the basis lengths."

      In Equation 1

      Clearly it is the area u² that is common to both sides. Since its area's four squares when summed gives a transcendent "number" to both (a² + b² + c² +d²) and the area f². So if we have a 5-d hypotenuse cut from area f² within our 4-d space-time based on a well understood four squares geometry with an invariant length "the square root of s²". How do you avoid this "cut" being s and not the area s²=(a² + b² + c² +d²) which what equation 1 is saying. That the total area of (a² + b² + c² +d²) times the common area u² equals the common of area of u² times the area f². And ever body knows that (the sign of s²) times (the sign of area u²) equals (the sign of area u²) times (the sign of the area f²).

      "Yes, I am treating an octonion as a bi-quaternion. That is what makes the multiplication table work.

      The matrix multiplication is interesting. If the complex i commutes normally with the unit vectors, the coefficient matrix uses B. But if the complex i anti-commutes with the unit vectors, the coefficient matrix uses B*."

      Bi-quaternions are just directed areas, that is, an area with a + and - sign. Clearly the matrix works because we have the invariant area ijk which then allows us to use octonian logic "based on + and - signs" which are attached to the bi-quaternions' areas. Hence in equation 1 the need of the 5-d hypotenuse cut from the area f² in our 4-d world which is based on an invariant four squares space-time summation.

      Your 5-d area's four squares summation gives us the length of 4-d hypotenuse "the invariant length of the square root s²" not the total invariant area summation. You have 4-d areas with a 5-d hypotenuse length of the four squares for the area f². We have literally have a 5-d hypotenuse length within our 4-d space-time that any four square summation must obey. Since the area of u² is the one common transcendental number that bridges both sides of Equation 1, while the 5-d hypotenuse is an invariant 4-d length that any summation must have available to have closure for the geometry of the area of f².

      A number (which is a perfect square) is the summation of four squares. If the area of f² is n square metres d²ct, then the physical manifestation of that area is a n invariant unit lengths of dct in our 4-d space-time. Not an area. We have an area f² on the right RHS, then on the LHS, equation 1 has a 5-d hypotenuse cut -- length c(metre) -- an invariant length that, by the 4-S theorem and equation 1 - each and every, any and, all - four square invariant summations must obey within our space-time.

      Of course your multiplication matrices Eq 5.4 and Eq 5.5, clearly ties "i" with c(metre), via the common area u² which is on both sides, where we have units of the summation of transcendental i if we use the 4-S theorem on both sides at once but using your multiplication rules A,B*,A,B* for - and + sign matrix Eq 5.3, which is, after all, a + and - sign summation using "octonian" logic directed bi-quaternion areas i.e. the column [C,D], using Eq 4.1 about a stationary "ijk" invariant the area f², using f a length "the square root of the area of f²" to transverse the equal sign, Equation 1 uses a 5-d length, so cannot be associated 1-1 with a summation of four square labelled A,B,C,D thought of as a "a perfect number as an area". It is - the area u² - that is, the common "four square summation" i.e. the perfect square, that spans the equal sign using the 4-S theorem on both sides of Equation 1. A number (which is a perfect square) is the summation of four squares). Your Eq 5.3 is a dance using A,B,C,D where A,B,C,D do integral steps on directed areas ALL on the geometry of the area of ijk. More simply the dance is with the directed areas which have a + or - sign, that is, i and * are not moving, i.e. they don't lead! It is --- i and * --- that are stationary and it is Eq 5.3 that moves areas that equal + or - throughout a basic multiplication table page 6, clearly Eq 5.3 only gives the square root of s², a length not an area for how the multiplication table works in your matrices Eq 5.4 and Eq 5.5.

      The full 4-S multiplication "of the areas on both sides of Equation 1" is:-

      (the sign of the area (a²+b²+c²+d²)) times (the sign of the area u² on the LHS) equals (the sign of the area u² on the RHS) times (the sign of the area f²).

      You will find Eq 5.3 octonian area + and - logic uses only the "square roots for the area u²" on the LHS for the bi-quaternions areas plus and minus signs attachment. That is, it is the common area of the transcendent "number" (a summation of four squares) which transverses the equal sign in Eq 1. as perfect numbers). Not your A,B*,A,B*,-,+ matrix dance Eq 5.3. which is after all + and - sign summation using "octonian" logic directed bi-quaternion areas i.e. the column [C,D]; clearly uses Eq 4.1 a stationary "ijk" invariant the area f².

      More simply, the area of f² is ijk equals -1 and then we take the square root of the area of ijk. that is, √-1 the imaginary unit. Clearly the full 4-S multiplication table for the "equal sign" invariant + and - unit count across the equal sign for Equation 1 is a transcendent dimensional process with "a unit of the square root of the area u² (see below)"; we will call the invariant unit of the times table a "sec"" for the area of the total summation of the area of the four squares of space-time. Then the 5-d hypotenuse cut would have a pure number a "transcendental" 5-d number c=i and it's "4-d length" of the times table is i(sec). The full 4-S sign multiplication times table used for how the LHS and RHS signs of the area u² common area behave across the equal sign, are;

      same signs on the LHS and RHS give +ve while different signs on the RHS and LHS give -ve.

      Or the appearance of the bridge (common area) across the equal sign is in units of -- +i and -i -- that is how we cross the equal sign using the area of u² on the LHS and using the area of u² on the RHS.

      Gary said in my comments

      You have some interesting ideas but they are very speculative. Essay contests such as this are a good place to present such ideas:-)

      I don't think you can set i=c or i=h but I do think you can construct something similar to the following:PSI = exp(omega) = sqrt[1 - (v/c)^2] + (v/c)i

      Then for v=c, PSI=i. I looked at your work instead, to see how you bridged with a common 5-d length (of the square root of f²) the areas on both sides of the equal sign. Your method mixes lengths with areas across the equal sign. While in the full 4-S, it is the four sums of +i and -i that are the "invariant count" lengths of the area u². The hypotenuse of the area geometry of f² is an invariant 5-d length "f" which isn't an area on the LHS.

      =======================================================

      read the 4-square essay by Gary Simpson here https://fqxi.org/data/essay-contest-files/Simpson_Four_Squares_rev00.pdf

      here is my comment on Equation 1 below the dotted line ---

      ======================================================

      Every time I read your essay I seem to understand, it more and more.

      I have a couple of questions about Equation 1

      (a² + b² + c² + d²)u² = f²u²

      A quote page 3

      "The meaning of Equation 1 is that in a 4-D geometry, if a right triangle is constructed from an integer number of basis lengths in each of the four dimensions (a, b, c, and d), then the hypotenuse (f) that traverses through the 4-D space will also have an integer number of the basis lengths."

      In Equation 1

      Clearly it is the area u² that is common to both sides. Since its area's four squares when summed gives a transcendent "number" to both (a² + b² + c² +d²) and the area f². So if we have a 5-d hypotenuse cut from area f² within our 4-d space-time based on a well understood four squares geometry with an invariant length "the square root of s²". How do you avoid this "cut" being s and not the area s²=(a² + b² + c² +d²) which what equation 1 is saying. That the total area of (a² + b² + c² +d²) times the common area u² equals the common of area of u² times the area f². And ever body knows that (the sign of s²) times (the sign of area u²) equals (the sign of area u²) times (the sign of the area f²).

      "Yes, I am treating an octonion as a bi-quaternion. That is what makes the multiplication table work.

      The matrix multiplication is interesting. If the complex i commutes normally with the unit vectors, the coefficient matrix uses B. But if the complex i anti-commutes with the unit vectors, the coefficient matrix uses B*."

      Bi-quaternions are just directed areas, that is, an area with a + and - sign. Clearly the matrix works because we have the invariant area ijk which then allows us to use octonian logic "based on + and - signs" which are attached to the bi-quaternions' areas. Hence in equation 1 the need of the 5-d hypotenuse cut from the area f² in our 4-d world which is based on an invariant four squares space-time summation.

      Your 5-d area's four squares summation gives us the length of 4-d hypotenuse "the invariant length of the square root s²" not the total invariant area summation. You have 4-d areas with a 5-d hypotenuse length of the four squares for the area f². We have literally have a 5-d hypotenuse length within our 4-d space-time that any four square summation must obey. Since the area of u² is the one common transcendental number that bridges both sides of Equation 1, while the 5-d hypotenuse is an invariant 4-d length that any summation must have available to have closure for the geometry of the area of f².

      A number (which is a perfect square) is the summation of four squares. If the area of f² is n square metres d²ct, then the physical manifestation of that area is a n invariant unit lengths of dct in our 4-d space-time. Not an area. We have an area f² on the right RHS, then on the LHS, equation 1 has a 5-d hypotenuse cut -- length c(metre) -- an invariant length that, by the 4-S theorem and equation 1 - each and every, any and, all - four square invariant summations must obey within our space-time.

      Of course your multiplication matrices Eq 5.4 and Eq 5.5, clearly ties "i" with c(metre), via the common area u² which is on both sides, where we have units of the summation of transcendental i if we use the 4-S theorem on both sides at once but using your multiplication rules A,B*,A,B* for - and + sign matrix Eq 5.3, which is, after all, a + and - sign summation using "octonian" logic directed bi-quaternion areas i.e. the column [C,D], using Eq 4.1 about a stationary "ijk" invariant the area f², using f a length "the square root of the area of f²" to transverse the equal sign, Equation 1 uses a 5-d length, so cannot be associated 1-1 with a summation of four square labelled A,B,C,D thought of as a "a perfect number as an area". It is - the area u² - that is, the common "four square summation" i.e. the perfect square, that spans the equal sign using the 4-S theorem on both sides of Equation 1. A number (which is a perfect square) is the summation of four squares). Your Eq 5.3 is a dance using A,B,C,D where A,B,C,D do integral steps on directed areas ALL on the geometry of the area of ijk. More simply the dance is with the directed areas which have a + or - sign, that is, i and * are not moving, i.e. they don't lead! It is --- i and * --- that are stationary and it is Eq 5.3 that moves areas that equal + or - throughout a basic multiplication table page 6, clearly Eq 5.3 only gives the square root of s², a length not an area for how the multiplication table works in your matrices Eq 5.4 and Eq 5.5.

      The full 4-S multiplication "of the areas on both sides of Equation 1" is:-

      (the sign of the area (a²+b²+c²+d²)) times (the sign of the area u² on the LHS) equals (the sign of the area u² on the RHS) times (the sign of the area f²).

      You will find Eq 5.3 octonian area + and - logic uses only the "square roots for the area u²" on the LHS for the bi-quaternions areas plus and minus signs attachment. That is, it is the common area of the transcendent "number" (a summation of four squares) which transverses the equal sign in Eq 1. as perfect numbers). Not your A,B*,A,B*,-,+ matrix dance Eq 5.3. which is after all + and - sign summation using "octonian" logic directed bi-quaternion areas i.e. the column [C,D]; clearly uses Eq 4.1 a stationary "ijk" invariant the area f².

      More simply, the area of f² is ijk equals -1 and then we take the square root of the area of ijk. that is, √-1 the imaginary unit. Clearly the full 4-S multiplication table for the "equal sign" invariant + and - unit count across the equal sign for Equation 1 is a transcendent dimensional process with "a unit of the square root of the area u² (see below)"; we will call the invariant unit of the times table a "sec"" for the area of the total summation of the area of the four squares of space-time. Then the 5-d hypotenuse cut would have a pure number a "transcendental" 5-d number c=i and it's "4-d length" of the times table is i(sec). The full 4-S sign multiplication times table used for how the LHS and RHS signs of the area u² common area behave across the equal sign, are;

      same signs on the LHS and RHS give +ve while different signs on the RHS and LHS give -ve.

      Or the appearance of the bridge (common area) across the equal sign is in units of -- +i and -i -- that is how we cross the equal sign using the area of u² on the LHS and using the area of u² on the RHS.

      Gary said in my comments

      You have some interesting ideas but they are very speculative. Essay contests such as this are a good place to present such ideas:-)

      I don't think you can set i=c or i=h but I do think you can construct something similar to the following:PSI = exp(omega) = sqrt[1 - (v/c)^2] + (v/c)i

      Then for v=c, PSI=i. I looked at your work instead, to see how you bridged with a common 5-d length (of the square root of f²) the areas on both sides of the equal sign. Your method mixes lengths with areas across the equal sign. While in the full 4-S, it is the four sums of +i and -i that are the "invariant count" lengths of the area u². The hypotenuse of the area geometry of f² is an invariant 5-d length "f" which isn't an area on the LHS.

      =======================================================

      Dear Mr H,

      Excellent essay regarding imaginary i. It is something i could never really grasp when i tried to study maths. Its profound that it is so common in central physical theories as you allude to here. I think you have written an excellent paper and i have rated it highly.

      Best,

      Jack

      Hi Jouko Harri Tiainen

      Nice work on imaginary Mathematics..."The area of the imaginary unit is explored and it is shown to be the basis for a new dual mathematics that is fundamental in understand how physics is related to mathematics." Good work sir...

      I hope you will not mind that I am not following main stream physics...

      By the way...Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

      Some of the Main foundational points of Dynamic Universe Model :

      -No Isotropy

      -No Homogeneity

      -No Space-time continuum

      -Non-uniform density of matter, universe is lumpy

      -No singularities

      -No collisions between bodies

      -No blackholes

      -No warm holes

      -No Bigbang

      -No repulsion between distant Galaxies

      -Non-empty Universe

      -No imaginary or negative time axis

      -No imaginary X, Y, Z axes

      -No differential and Integral Equations mathematically

      -No General Relativity and Model does not reduce to GR on any condition

      -No Creation of matter like Bigbang or steady-state models

      -No many mini Bigbangs

      -No Missing Mass / Dark matter

      -No Dark energy

      -No Bigbang generated CMB detected

      -No Multi-verses

      Here:

      -Accelerating Expanding universe with 33% Blue shifted Galaxies

      -Newton's Gravitation law works everywhere in the same way

      -All bodies dynamically moving

      -All bodies move in dynamic Equilibrium

      -Closed universe model no light or bodies will go away from universe

      -Single Universe no baby universes

      -Time is linear as observed on earth, moving forward only

      -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

      -UGF (Universal Gravitational Force) calculated on every point-mass

      -Tensors (Linear) used for giving UNIQUE solutions for each time step

      -Uses everyday physics as achievable by engineering

      -21000 linear equations are used in an Excel sheet

      -Computerized calculations uses 16 decimal digit accuracy

      -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

      - Many predictions of Dynamic Universe Model came true....Have a look at

      http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

      I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

      Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

      In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

      I request you to please post your reply in my essay also, so that I can get an intimation that you replied

      Best

      =snp

      Harri,

      Quite brilliant, I think, Uncertainty isn't entirely eliminated as I'm no mathematician and didn't follow much. Though I have well developed visualisation I never did understand the imaginary number, but you'll understand it looked so right and fundamental I applied a binary code to your score. I kept getting glimpses of important new things I recognised, like holy grail! but mainly out of my reach from this side.

      But I think there may be more. Two essays ago I found Pythagoras in a 3D sphere so he may be ultimately responsible for the complex Cos momentum distributions on rotation. I suspect your dual maths may then prove to be underlain with 'triple maths'. Might that be possible?

      Shockingly (neither of us seem to mind shocks) I falsify Cartesian 'wire frames' and substitute planes forming enclosures, which seems to fit your schema. Each plane is a near/far field transition (or LT).

      So what I really want to chat about and point you to is the door that led me to classic QM, which, was rationalised SR - in my 2011 - 2014 essays. EM propagation is always local c as it is constantly CHANGED by absorption/scattering at local field boundary 2 fluid plasmas (found as shocks, surface charge etc) to conform locally. Law; 'All electrons scatter at c in their centre of mass frame'. That's ok with the postulates but clears away most of the paradoxical assumptions about Relativity!

      Nearly forgot, even deeper down perhaps. It all replaces the problematic Law of the excluded Middle' did you see my replacement '..Reducing Middle'? Gauss & Bayes would be happy. I think that was around 2014.

      I posted my email somewhere near the top here but if you missed it;

      pj.ukc.edu@physics.org

      Top job. I'd be happy to collaborate in any way poss.

      Very best

      Peter

      ps I'm sure you've seen Declan T's but do also see Gordon Watson's essay, and I'll point him to you.

        A nice essay. I think you would be interested in my 2012 FQXi essay titled "A Classical Reconstruction of Relativity" located here:

        https://fqxi.org/community/forum/topic/1363

        And my work on modelling the electron/positron wavefunctions as 3D standing waves, located here: http://vixra.org/pdf/1507.0054v6.pdf

        I also have an essay in this year's contest titled "A Fundamental Misunderstanding" about a Classical explanation for QM entanglement (EPR experiment).

        Regards,

        Declan Traill

        Thanks for encouragement -- yes that is the way to do it Peter -- Shockingly (neither of us seem to mind shocks) I falsify Cartesian 'wire frames' and substitute planes forming enclosures, which seems to fit your schema. Each plane is a near/far field transition (or LT).

        Yes planes (or 2-D areas) that are enclosed is the ticket -- that is the basic idea.

        I'm writing up the technical version (Thanks to Armin and Edwin for their input) which is all maths -- which has whole helps of diagram to help people work out what a S sedenion in abstract algebra is, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals, I actually draw a S as an enclosed area and then I can draw O Octonians and then H quaternions (8-D) and then C then R then N all as areas. Which is what are you saying in the above quote.

        I will send it off and I will look over your links to other essays. Harri -- go the new revolution

        Dear Jouko

        If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

        Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

        My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

        Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

        For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

        My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

        By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

        To steal a phrase from my essay "A world product of evolved optimization".

        Best of luck for the conclusion of the contest

        Kind regards

        Steven Andresen

        Darwinian Universal Fundamental Origin

        Dear Jouko Tiainen Harri, the speed of light as the imaginary unit is very interesting, I bet 10. But I think you don't need to associate a complex number with the geometry of Minkowski is interesting only from an analytical point of view, but not physical. In New Cartesian Physics is the imaginary unit used as an operator of rotation of the radius vector 90 degrees, the square of the imaginary unit turns the radius-vector by 180 degrees. Thus, where the formula is the imaginary unit, we observe a rotation.

        New Cartesian Physics needs your support to develop further. Visit my page and give your assessment there.

        I hope that you are interested in her ideas.

        FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich

        I wish you success! Sincerely, Boris Dizhechko

        Juoko,

        Very interesting and original. I always knew there was something wrong with our mathematics! But don't you maybe need yet one more dim to make it 3D? Good score coming.

        I hope you'll get to read & score mine, not many pages.

        Rich

        Dear Jouko,

        (copy to yours and mine)

        Many thanks for the kind words about my work and for mutual understanding.

        The understanding and appreciation are highly valued.

        I highly appreciate your well-written essay in an effort to understand.

        «I'm happy that maybe you are on the threshold of some new discovery.

        So by reinterpreting the Born Rule, as probabilities |Ψ|2 or (Ψ*Ψ) then the wave-functions of the ket *i and bra i* states respectfully, give us enough mathematical elbow room to accommodate both Relativity and Quantum mechanics in one scheme».

        «Current maths thinking only uses "one" encoding side -- the complex conjugate of the

        Dear Jouko,

        (copy to yours and mine)

        Many thanks for the kind words about my work and for mutual understanding.

        The understanding and appreciation are highly valued.

        I highly appreciate your well-written essay in an effort to understand.

        «I'm happy that maybe you are on the threshold of some new discovery.

        So by reinterpreting the Born Rule, as probabilities |Ψ|2 or (Ψ*Ψ) then the wave-functions of the ket *i and bra i* states respectfully, give us enough mathematical elbow room to accommodate both Relativity and Quantum mechanics in one scheme».

        «Current maths thinking only uses "one" encoding side -- the complex conjugate of the a+ib| side -- to obtain areas. Basically in current maths thinking there is only z=a+ib, with zero=0+i0. We can devise a different set of complex numbers z=a-ib with zero=0-i0. And both can be related to the area of the imaginary unit, to obtain a new dual mathematics».

        As a radio engineer and mechanic, I highly appreciate the idea of a new interpretation of complex numbers.

        In a couple of days, I'll try to answer some of your questions.

        I wish you happiness in your scientific work in search of truth.

        I hope that my modest achievements can be information for reflection for you.

        Vladimir Fedorov

        https://fqxi.org/community/forum/topic/3080

        Dear Jouko,

        A fellow 'finn'? from the name.

        Now first I read your essay, and I get many of my ??? explained. Thanks.

        For me it started with Dirac, but imaginary unit is in so many places, also Planck's constant. But area, dual?

        In some simulations we found the frame to be E6 dual, and the duality is important to get the dynamicity. What if those dual 'boxes' are not symmetric? I have looked for asymmetric solutions of GR, and the covariance/countervariance should then vary. I guess they could, of course.

        Asymmetryor aperiodicity is developed in my essay https://fqxi.org/community/forum/topic/3093

        Ulla Mattfolk.