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RECENT POSTS IN THIS TOPIC

**Ulla Mattfolk**: *on* 2/28/18 at 18:50pm UTC, wrote I found this paper...

**Eckard Blumschein**: *on* 2/28/18 at 6:03am UTC, wrote Dear Jouko Harri Tiainen, Your essay is nearly undigestable, at least to...

**Donald Palmer**: *on* 2/27/18 at 0:38am UTC, wrote Hi Jouko, I echo some of the comments on presentation and also...

**Ulla Mattfolk**: *on* 2/26/18 at 21:09pm UTC, wrote Dear Jouko, A fellow 'finn'? from the name. Now first I read your essay,...

**Vladimir Fedorov**: *on* 2/26/18 at 8:38am UTC, wrote Dear Jouko, (copy to yours and mine) Many thanks for the kind words...

**Vladimir Fedorov**: *on* 2/26/18 at 8:21am UTC, wrote Dear Jouko, (copy to yours and mine) Many thanks for the kind words...

**richard nixey**: *on* 2/26/18 at 1:56am UTC, wrote Juoko, Very interesting and original. I always knew there was something...

**Dizhechko Semyonovich**: *on* 2/25/18 at 13:31pm UTC, wrote Dear Jouko Tiainen Harri, the speed of light as the imaginary unit is very...

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FQXi FORUM

October 17, 2019

CATEGORY:
FQXi Essay Contest - Spring, 2017
[back]

TOPIC: What is Fundamental is the area of the imaginary unit by Jouko Harri Tiainen [refresh]

TOPIC: What is Fundamental is the area of the imaginary unit by Jouko Harri Tiainen [refresh]

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.

Just interested in physics

1. Such as (a+ib) times (c+id)=ac + ibc + ibs +i²bd should be (a+ib) times (c+id) = ac + iad + ibc + i²bd

2. For “That is same a and b but they behave so differently we measured. “ it is “That is, the same a and b but they behave so...

view entire post

The full version of the respond is here -- it seems to have cut of the last section

attachments: RESPONSE_Final_POST.pdf

attachments: RESPONSE_Final_POST.pdf

Sorry couldn't attach file

Harri

The Red/Green sock trick is the top one here;

http://fqxi.org/community/forum/category/31424?sort=communit

y

Glad you liked it, and this years.

I've just downloaded yours.

You asked for my Email to send the pdf;

pj.ukc.edu@physics.org

I look forward to it. Thanks

Peter

report post as inappropriate

The Red/Green sock trick is the top one here;

http://fqxi.org/community/forum/category/31424?sort=communit

y

Glad you liked it, and this years.

I've just downloaded yours.

You asked for my Email to send the pdf;

pj.ukc.edu@physics.org

I look forward to it. Thanks

Peter

report post as inappropriate

Hello Jouko,

I really love those essay which emphasizes mathematics. As soon as I saw your topic containing Imaginary units, I hurried to read your essay. A well-written essay. I had some questions to ask but already found the answer on above post.

My essay is also related to mathematics:Is Mathematics Fundamental?

Kind Regards

Ajay Pokharel

report post as inappropriate

I really love those essay which emphasizes mathematics. As soon as I saw your topic containing Imaginary units, I hurried to read your essay. A well-written essay. I had some questions to ask but already found the answer on above post.

My essay is also related to mathematics:Is Mathematics Fundamental?

Kind Regards

Ajay Pokharel

report post as inappropriate

Hi Jouko,

Wow, I really had to keep concentration to read your essay. I like your way of "logical thinking" and valued it in order to bring you up in the contest. For me, however, the real conclusions were in your appendix.

Some remarks:

“continuous observation” When talking about continuous as a process of time, we are always becoming aware of the results of our observations later as they happen, we are always observing the PAST. The continuity we are conscious of may be an illusion (emergent phenomenon). Does this influence your thoughts?

A little remark on “quantum theory of immortality”. If you are taking more then the normal age a cat survives (for instance 20 years) then the cat will die of age. This theory, in my opinion, hasn’t the right name. It IS all right when we could arrange an infinity of measurements in one moment (whatever length that may have, but take the Planck time)...But...as time is an emergent phenomenon and EACH measurement is taking place in this illusion, we can go on and on....because it is NOT THE SAME emergent cat...

“let there be a superposition of all heads that is pure, allow one impure state for the UWF Universal Wave Function itself, which can act via entanglement as the wave equation for the pure superposition.”. This superposition in my model is just ONE of the Reality Loops available as a probability.

In my contribution, I propose a new model of emergent reality that has not the problems of the MWI, Schrödingers Cat, the double slit experiment, paradoxes of Xeno etc, the collapse of the wave function, etc. I wonder what are your thoughts about my essay “Foundational Quantum Reality Loops”, so I hope that you can spare some of your time-area to read, comment and maybe rate it.

Best regards and good luck

Wilhelmus de Wilde

report post as inappropriate

Wow, I really had to keep concentration to read your essay. I like your way of "logical thinking" and valued it in order to bring you up in the contest. For me, however, the real conclusions were in your appendix.

Some remarks:

“continuous observation” When talking about continuous as a process of time, we are always becoming aware of the results of our observations later as they happen, we are always observing the PAST. The continuity we are conscious of may be an illusion (emergent phenomenon). Does this influence your thoughts?

A little remark on “quantum theory of immortality”. If you are taking more then the normal age a cat survives (for instance 20 years) then the cat will die of age. This theory, in my opinion, hasn’t the right name. It IS all right when we could arrange an infinity of measurements in one moment (whatever length that may have, but take the Planck time)...But...as time is an emergent phenomenon and EACH measurement is taking place in this illusion, we can go on and on....because it is NOT THE SAME emergent cat...

“let there be a superposition of all heads that is pure, allow one impure state for the UWF Universal Wave Function itself, which can act via entanglement as the wave equation for the pure superposition.”. This superposition in my model is just ONE of the Reality Loops available as a probability.

In my contribution, I propose a new model of emergent reality that has not the problems of the MWI, Schrödingers Cat, the double slit experiment, paradoxes of Xeno etc, the collapse of the wave function, etc. I wonder what are your thoughts about my essay “Foundational Quantum Reality Loops”, so I hope that you can spare some of your time-area to read, comment and maybe rate it.

Best regards and good luck

Wilhelmus de Wilde

report post as inappropriate

Dear Jouko Harri Tiainen, The imaginary unit is relevant for physics; It is very interesting - the area of the imaginary unit, however, I think it describes the rotation of space well. Multiplication by an imaginary unit gives a rotation of ∏/2, and multiplication by a square of an imaginary unit rotates the space by ∏, and so on. The wave function describes the rotation of space as a function of the momentum and energy of the particle.The physical space, which according to Descartes is matter, serves as the foundation for the birth of life. Look at my essay, FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich Where I showed how radically the physics can change if it follows this principle. Evaluate and leave your comment there

Sincerely, Dizhechko Boris Semyonovich.

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Sincerely, Dizhechko Boris Semyonovich.

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Dear Jouko,

Thanks for leaving a comment on my blog. I looked at your paper and let me get the bad news out of the way:

If you are working on these ideas for yourself, then more power to you. But I have the impression that you mean your work to be considered and eventually accepted by others, in particular physicists and mathematician. I regret to tell you that in its present form,...

view entire post

Thanks for leaving a comment on my blog. I looked at your paper and let me get the bad news out of the way:

If you are working on these ideas for yourself, then more power to you. But I have the impression that you mean your work to be considered and eventually accepted by others, in particular physicists and mathematician. I regret to tell you that in its present form,...

view entire post

report post as inappropriate

When I listed the math courses I think you need, I left out the obvious one:

Complex Analysis. If you take this, however, after you already have a background in the other three subjects, then, if your fundamental idea really has merit, be in an excellent position to immediately apply it to more advanced subjects involving complex numbers, such as contour integrals, which will then naturally suggest to you ways to incorporate your idea in physics (yes, physicists do use contour integrals).

Armin

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Complex Analysis. If you take this, however, after you already have a background in the other three subjects, then, if your fundamental idea really has merit, be in an excellent position to immediately apply it to more advanced subjects involving complex numbers, such as contour integrals, which will then naturally suggest to you ways to incorporate your idea in physics (yes, physicists do use contour integrals).

Armin

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Thank You for your in-depth comments and for the long long list of the many courses I should take to overcome the conceptual hurdles in my essay and my complete and obvious lack of knowledge in all fields of maths, science and philosphy. I have to thank you for pointing out a few of the many assumptions and "leaps of logic and ad hoc bounds of thought" in the essay. I will consider "these conceptual faults again" after I have done many many years of learning and integrating the ideas in your recommended courses -- in basic maths and elementary science -- and then I will try to start again with these ideas so as to form a more cogent flow of ideas for others to follow. Cheers Thanks ... Harri.

The only point I have to make is that Minkowski was the one who "made c(m)=i(s)" here is a direct quote --- Minkowski's Paper – Minkowsky, Hermann, German paper Raum und Zeit (1909), Jahresberichte der Deutschen Mathematiker-Vereinigung, 75–88. In the 1920 English translation...**We can clothe the essential nature of this postulate in the mystical, but mathematically significant formula 3x10**^{8}(metre)=√-1(second)... www.en.wikisource.org/wiki/Space_and_Time

And since he can do that I thought why not do 6.63×10^{-34}(Joules)=√-1(second) which leads to the idea that space-time and energy-time conjugation come from the same source the indistinguishable "imaginary unit" which then goes to the idea .

Basically the essay is all about what is the "imaginary unit" all about and why it is in all of the basic equations of physics. The basic idea is if you want a dual maths then use an area we get duals easily that way.

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The only point I have to make is that Minkowski was the one who "made c(m)=i(s)" here is a direct quote --- Minkowski's Paper – Minkowsky, Hermann, German paper Raum und Zeit (1909), Jahresberichte der Deutschen Mathematiker-Vereinigung, 75–88. In the 1920 English translation...

And since he can do that I thought why not do 6.63×10

Basically the essay is all about what is the "imaginary unit" all about and why it is in all of the basic equations of physics. The basic idea is if you want a dual maths then use an area we get duals easily that way.

report post as inappropriate

Dear Jouko Harri Tiainen,

I admire Armin's work very very much, but I don't think I agree with*all* of his statements, perhaps because I ignored your use of bra and ket, and also your treatment of entanglement. I pretty much ignore everyone's treatment of entanglement, for reasons I have already published, but as it is a common belief today, I do not generally downgrade essays for...

view entire post

I admire Armin's work very very much, but I don't think I agree with

view entire post

report post as inappropriate

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 "3·10^{5} km = sqrt(-1) Sec", but such expressions are meaningless.

What we can do is...

view entire post

Yes, I saw Minkowski writting (or the people that traduced his work from German) expressions such as "3·10

What we can do is...

view entire post

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

es_rev00.pdf

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

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

Eve

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

I have a couple of questions about Equation 1

(a² + b²...

view entire post

es_rev00.pdf

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

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

Eve

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

I have a couple of questions about Equation 1

(a² + b²...

view entire post

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...

view entire post

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...

view entire post

attachments: 5_Bashir_Quantum_Mech_and_Relativity_Theory.pdf

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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

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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

report post as inappropriate

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

es_rev00.pdf

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

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

Eve

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

I have a couple of questions about Equation 1

(a² +...

view entire post

es_rev00.pdf

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

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

Eve

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

I have a couple of questions about Equation 1

(a² +...

view entire post

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.

report post as inappropriate

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.

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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

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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

report post as inappropriate

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...

view entire post

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...

view entire post

report post as inappropriate

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.

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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.

report post as inappropriate

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

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

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

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

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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

report post as inappropriate

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...

view entire post

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...

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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

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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

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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

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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

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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

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(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

report post as inappropriate

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

report post as inappropriate

(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

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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.

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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.

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I found this paper https://www.researchgate.net/publication/266325108_Energy_eq

uation_in_complex_plane a thesis.

Seems SR also contains the complex field as negative energy. It is removed as unnecessary, because it normally vanish, as you also say. it is an error.

As instance in condensed matter are cases with time reversal, and then the right formula is important.

Thanks once more. Ulla.

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uation_in_complex_plane a thesis.

Seems SR also contains the complex field as negative energy. It is removed as unnecessary, because it normally vanish, as you also say. it is an error.

As instance in condensed matter are cases with time reversal, and then the right formula is important.

Thanks once more. Ulla.

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Hi Jouko,

I echo some of the comments on presentation and also mathematical application.

i is a placeholder for a number. However it represents a specific dimensionless value, not c or h.

X^2 + 1^2 = i^2 * 0^2 = 0 and then x^2 = (-1)^2, which has the solution x = sqrt(-1) = i. In this situation, x is not a variable, but an unknown to be solved.

To consider a^2 + b^2 = c^2 as an area, the values of the variables have to be allowed to vary. This is not the case for the solution of x^2 + 1 = 0 (where x is an unknown, not a variable).

In a different direction, since 'i' is really just a placeholder for an unknown, there is nothing to prevent us evaluating that unknown and defining an actual numeric representation of both i and, by extension, any complex number. In other words, i should be able to be represented in the same way as any other (real) number is - as a single value, rather than x + iy. This would require some new areas of mathematics (like maybe defining what and how a negative base operates) and it could change a lot of equations and possibly some other areas of mathematics by simplifying complex equations. It would need to show that a complex value can be represented and manipulated as a single valued number, not the more cumbersome x + iy representation involving an unknown placeholder. That would change both mathematics and physics in a fundamental way.

Best to you,

Don

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I echo some of the comments on presentation and also mathematical application.

i is a placeholder for a number. However it represents a specific dimensionless value, not c or h.

X^2 + 1^2 = i^2 * 0^2 = 0 and then x^2 = (-1)^2, which has the solution x = sqrt(-1) = i. In this situation, x is not a variable, but an unknown to be solved.

To consider a^2 + b^2 = c^2 as an area, the values of the variables have to be allowed to vary. This is not the case for the solution of x^2 + 1 = 0 (where x is an unknown, not a variable).

In a different direction, since 'i' is really just a placeholder for an unknown, there is nothing to prevent us evaluating that unknown and defining an actual numeric representation of both i and, by extension, any complex number. In other words, i should be able to be represented in the same way as any other (real) number is - as a single value, rather than x + iy. This would require some new areas of mathematics (like maybe defining what and how a negative base operates) and it could change a lot of equations and possibly some other areas of mathematics by simplifying complex equations. It would need to show that a complex value can be represented and manipulated as a single valued number, not the more cumbersome x + iy representation involving an unknown placeholder. That would change both mathematics and physics in a fundamental way.

Best to you,

Don

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Dear Jouko Harri Tiainen,

Your essay is nearly undigestable, at least to me. It is not clearly structured. You didn't even use page numbers. You didn't reveal much in your Bio and no referces at all. You claimed that a number is a square, etc.

Nonetheless, you might have correctly felt that the issue of i and Dirac's brackets deserves critical reconsideration. So far, I see you mainly ignoring the fundamental difference between the basic frog's level of reality and the timeless bird's view level of models that were abstracted from it. Somtimes it is necessary to distinguish chicken and egg duality from a concrete chicken that laid an egg.

Looking forward receiving a comment on my rather contrary essay,

Eckard Blumschein

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Your essay is nearly undigestable, at least to me. It is not clearly structured. You didn't even use page numbers. You didn't reveal much in your Bio and no referces at all. You claimed that a number is a square, etc.

Nonetheless, you might have correctly felt that the issue of i and Dirac's brackets deserves critical reconsideration. So far, I see you mainly ignoring the fundamental difference between the basic frog's level of reality and the timeless bird's view level of models that were abstracted from it. Somtimes it is necessary to distinguish chicken and egg duality from a concrete chicken that laid an egg.

Looking forward receiving a comment on my rather contrary essay,

Eckard Blumschein

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