StrictlyLogical

and that includes relationships between "portions" of the same thing, so to speak. From what I recall in QM probabilities there is never any "absolute" phase, but relative phase is ubiquitous and the foundation for determining interference, and plays much in what the results of the inner product look like (i.e. probabilities). So real numbers we use to quantifying things but "i" and the like are useful for relating things, in particular phase differences.

Real numbers characterize and are abstraction we find useful for quantifying things. Imaginary numbers, as directly as I can relate them to things, characterize and are abstractions we find useful for (some specific) relationships between things.

"Analysis" is a complicated formal construct. That which one builds to surround and is supported by real numbers is not the same as that which one builds to surround and is supported by complex numbers. So no, complex analysis is not "really equivalent" to real analysis. These are two different games played in two different arenas... we can and did make them so. Now the idea of analysis is like the idea of a mathematical expression, how it is used or what symbols are there may be different but what it represents or refers to, is not the same as the expression used. The identity operator helps us understand that although the expressions are not the same what they refer to are one in the same, an identity. So I do not discount the possibility that some form of complicated real number based formalism, using Euler relations etc. cannot create something like an answer, i.e. refer to some quantity, which complex analysis also refers to. When used as a coefficient, a real number can be interpreted as a kind of scaling or "quantity of" operator, so taking i, as operated on by 3 you have three of them, so no 3 times i does not remove the i. i however is like a 90 degree rotation operator in the 2d plane we use to arrange our complicated useful contrivances we call complex numbers. EDIT: The last paragraph seems very important to limit and understand the import of their findings.

No one is proposing that, indeed it would be unnecessary. The potential or purported import of the paper is its implication that *which particular kinds* of abstractions we can choose to use in the context, are somehow actually limited.

That understanding would be incorrect. Particularly that last sentence. Anything characterizable in complex numbers must be characterizable in real numbers, because every complex number is characterizable in real numbers. As for things, any complex attribute of a thing can be represented by two non-complex attributes associated with the thing. In fact the necessity of characterizing an attribute as (specifically) complex is nothing more and nothing less than having to use more than one (specifically two) real number to characterize that attribute. Every operator and mathematical calculation in the complex plane deals simultaneously with two real quantities, phase and magnitude or alternatively real and imaginary parts. A complex number IS two things, and of a necessity is b0th reducible analytically into those two things and cannot be constituted by less than those two things. It can never be a "simple" number, after all it is a complex number, and it has two absolutely independent components, and cannot be thought of as having any less than two components, and therefore it IS two things. So what is the error? Reification. The fact that an attribute (in a particular framework or theory of reality), to reflect reality has two things associated with it, and that the operators must take into account both, say phase and magnitude, means that a thing has a two-attribute attribute. The reification is an erroneous identification of this two attribute attribute WITH the abstractions we use to work with them... it comes from the way we understand and express and work with this two attribute attribute, namely with complex numbers. Moreover, the simplicity with which we deal with the calculations of the two attribute attribute as if it were one attribute (because they always go together)... every phase must have a magnitude... leads one to believe the formalism as expressed is the only way to express that formalism. That when you change the expressions one has changed the formalism... and that "QM based on real numbers" means somehow trying to use real numbers in a framework built for using complex numbers... The idea of a hypothetical "real quantum state" is nonsensical. Why? Because the referent of the modifier term "real" is purely mathematical or abstract, and the referent of the term "quantum state" is supposed to be an entity of reality. This should be a huge clue to how the authors are thinking...or how they are not being careful about what they are talking about, i.e. what refers to abstractions and what refers to reality. The foundation of QM on the idea of representing reality as states in a vector space, and whose inner product corresponds with probabilities of outcomes. We assign states in the same direction when probability is 1 and assign states as orthogonal vectors when probabilities are 0. We have operators to rotate those vectors modeled on causation and interaction. A nice little game no? It turns out that correspondence between these vectors we have concocted to real world outcomes, requires the use of complex coefficients and operators... but what has that done to the formalism? All that has cone is doubled the degrees of freedom. Sure one could not write QM in the standard formulation, the standard way with real numbers, the correspondence between it and reality requires complex numbers but that does not mean one could not rewrite the entire thing, vector spaces and all using real numbers.

How familiar are you with Objectivism as a philosophy? As a former academic of physics, I highly recommend it. Interpretations of physics and in particular of QM are interesting but until we have a complete understanding of the mechanics of measurement (rather than a formalism and assumptions) I think they will remain rather fanciful and mystical… I have found THAT is where the mind goes when it encounters something it does not understand… not merely an acknowledgement of the unsolved but a kind of ecstasy in the “mysterious”. I would suggest you hold onto as much of the solid foundations of thought as possible when you encounter the myriad flights of fancy of both your common and uncommon physicist. Be rigorous and disappointingly real about the distinctions between our abstractions and entities referenced by them. Good luck on your journey!

@Bill Hobba I note a great many physicists completely dispense with philosophy and philosophical theory and the rigours which may be attained therewith… do you bring any philosophical scrutiny to the physics you cite or do you simply take them and the interpretations therein, as true?

Please excuse me I am unfamiliar with the details of Noether’s theories re. fields. If the electric field of an electron has a separate energy which you imply has a mass, then when you expend energy to accelerate the mass of an electron do you need to expend energy to accelerate the electric field of the electron which you imply also has mass? In fact, when you accelerate an electron are you accelerating i.e. moving, its electric field as well? Are you moving two things are one thing... are there two things or one thing? As student of philosophy what is your understanding of an attribute or property of an entity as regards its nature and relationship to the entity? Some would say they certainly are real but are not independently real, they are only always “of” entity or entities.

A funny thing about how we tend to use language, and funnier when we are talking about physicists, “Quantum Mechanics” is sometimes interpreted as referring to what reality does, when it is far more accurate to say QM is something we do, which to the extent it corresponds with observables of what reality does do, is valid and useful. That paper is more about how we process what reality does, not what attributes and properties which are possessed by entities. The third person would point out that a complex number is nothing more than a complicated (not very) combination of real values. They are absolutely and always reducible to real values. We happen to call them phase and magnitude. But again this is mere characterization of the abstraction which is QM, merely interpretations of the abstractions as more or less complex … when in fact it is all the same and beside the point. The processing abstraction is not the referent to which its predictions are directed. Observe there is no absolute phase in the complex coefficients, and also observe that statistical in nature they are not strictly speaking possessed by any single entity, and of course are never observable properties possessed by any single entity. As such, any assumption about complex numbers, I put to you, is more of an assumption about our abstractions referring to physical reality than an assumption about physical reality itself.

@Bill Hobba I should let you know that hearing your interest in these subjects is refreshing. So many mathematicians, physicists, and philosophers stay in their own lanes far too much or hold on to what they have been told by authorities in their field with far too little independent scrutiny. That said, as an analogy I would like to introduce the statement “abstractions are founded in reality” as a generalization which is subject to the same problem. When abstractions are used in a context of referring to reality, with any language, mathematical or not, the system of abstractions should be founded in reality. These sorts of considerations were never really investigated in my training in physics. I would argue the BEST professors admonished us to look at the equations SOLELY as a tool for predicting and quantifying reality… implicitly our way of dealing with reality is not reality… a nice warning about the clear distinction between our abstractions and their referents in reality, without sophisticated explication.

What would happen if second person came along and thought one did not need complex numbers to solve something, but instead thought only that the formulas and equations had to be adjusted… in other words instead of the division of labour for our abstractions being using complex numbers in simple equations, using simple numbers in complex equations? What if a third person came along and said the distinctions of division of labour for our abstractions is really quite superficial and illusory and really either approaches are simply the same thing expressed in different ways. EDIT: and to the extent correct or corresponding to reality, refer to the same things in reality.

Depending on your definition of what constitutes mathematics that statement may be overly broad. Although it sounds absurd, “mathematics” could include both invalid and valid forms, in such a context some mathematics definitely are not founded in reality… and could be floating abstractions at best and wholly based on imagination and irrationality at worst. On the other hand if you propose to define valid mathematics or just “mathematics” as only including that which IS founded in reality then I look forward to your delineation of what falls within and without of that classification. Abstractions are meant to be meaningfully based on and in correspondence to or connected with reality but we all know that anti-concepts, invalid and floating abstractions are all commonly found among the mental contents of a great many people.

I see nothing here which gives rise to a “physical assumption”. The physical things and attributes (observables) are measured as possessing real magnitudes. How we calculate expected measurements involves complex numbers. These are distinguishable. What is the “physical assumption”?

What do you have in mind when you say this? How can a “physical assumption” be that something is from an abstraction? [I am very familiar with complex numbers and vector “spaces” and their applications]

The Dark Ages were a long time ago. Something more recent is Lysenkoism: https://en.wikipedia.org/wiki/Lysenkoism This is the very definition of a "scientific consensus" in Soviet Russia. It's not so much that correct genetics "stood" during that time, but that it was "rediscovered" when the incorrect "consensus" withered away, as it had to. Consensus is not science and in fact has nothing to do with science. The scientific method, when used by independent individual thinkers is, and always has been, that which shatters ideological based consensus, especially when masquerading as "Truth" or "The Science".

Instead of asking about a hypothetical future (which likely is impossible) just look at the reality of the past. When belief in the supernatural as an actual fact was the overwhelming consensus, independent thought in individuals “stood” and in certain circles prevailed.

I think there are important distinctions between the concept of Artificial Intelligence, essentially characterized by being artificial and meeting some kind of definition of intelligence... and something which is truly sentient or conscious. A science fiction writer or a layperson might use these terms interchangeably, but the concepts are not interchangeable... non-sentient machines which experience nothing have been "learning" for decades now, but are nowhere near to exhibiting consciousness, even if they may one day imitate it. Consciousness is not an algorithm, but AI certainly can be algorithmic, as it currently is.

[Emphasis Added] Looks more to me like the Turing test is begging us not to question it...

Unintended consequences for the poor F'ker who tries to "instigate" WW3... He will in fact be setting the spark to wake up and transform of the great masses of Sheeple back into We the People, and instigating in fact the largest Rebellion/Revolution the World has ever seen, by We the People against the corrupt Predator Class and corruption in Global and Domestic Institutions... all throughout the Western so-called democracies. BE assured the People won't send sons to die in order to line their pockets anymore. We will see who gets sacrificed on what alter this time around, if they try to order the People to die in some foreign land for no good reason or if they try to sentence the People to death for refusing to go... I'd like to see them try. This so-called instigation might be just what is needed to start the purification of the world... albeit a consequence unintended by the so-called instigator.

In a proper society one literally cannot punish an opinion. One can disagree with them, one can spend millions of dollars “arguing” … one can Lie in public (as long as it is not initiation of force like libel or yelling fire in a theater). One can choose not to disseminate an opposing view. All of the above… because it is free from coercion … THAT is what makes it free speech. We can wish people were different and we can attempt to persuade them of the correctness of our positions but the marketplace of ideas in a proper society would only be free if people who didn’t believe in free speech were allowed to shout as loud (without amounting to initiation of force) as they want to. I would understand if you propose that in a free society people like us should be strong advocates of reason and even donate to charities and foundations which endeavour to spread awareness and persuade others. I would totally agree with you there. Tara Smith has an excellent paper and a talk on free speech.

AI is the best parrot/yes-man there could be. See and imitate. You'll get from AI what you already get, all the time, nothing more.

If someone claims "mind" means everything that exists, claiming "objective reality does not exist", literally adds nothing, all it does is restate/confirm what they have already baldly asserted. If mind is not all there is which exists, then there is that which is non-mind, being non-mind it is not subjective, i.e. it is objective. The only issue then, is mind then some non-objective part of reality. Then we see the ideas of ghosts and machines, and the like... you should know that some objectivists are dualists. Some are not, while at the same time they are not mechanists, nor determinists. All objectivists (not misidentifying themselves) believe in free will. I.e. that a person could have done otherwise after time 0 ... even given the same Leibniz hypothetical universe (including all that the person is) at Time 0.

So much of culture, society, and its institutions, some of which are machinations of the State, are helplessly flawed, flawed and influenced with error, bias, irrationality, overzealousness, greed and negligence. They pull in different directions, and strike at different populations of individuals, and yes in times of misintegration/activism they take vengeance in active discrimination of perceived so called groups formerly or presently holding power. The infringements on individual rights is alarming and disheartening, whether perpetrated by the system on a wide level or by radicals within the system abusing power. Less government, and proper government are what is needed. The curriculum and the teachers, in this flawed imposed system, are not always guided by interest in the flourishing of every individual child. Agendas, causes, regrets, revenge, rebellion, personal biases all... these tendencies and attitudes now too commonly override and cloud the appropriate needs of children..[so caught up with "imbalance" are the progressives, that they fully self-justify keeping some children down, or actively working to squish their spirit with guilt and self-doubt...]. What I see lacking most is an understanding of True Self-love (and individuality), what it really objectively means, and its nurturing and encouragement. Superficial and political (radical) influence, group-think and categorization of this tribe against that tribe, amplified by social media is now hollowing out the spirit of so many innocent individuals, so that they do not know who they are, why they should make certain choices over others, or what life is. So caught up with trying to fit in they fall apart. This comes to that junior in college, now to all appearances happy. There is no reason that anyone should go through the self-doubt, or lack of self-love, as they are, at such a young age. I think some (not all) less than virtuous high level medical executives ... pharma or surgery - and insurance related... are pushing hard (top down) for wide spread acceptance ... i.e. adoption of the their products (and the attendant flow of money) with insufficient regard for the mental state and maturity of some potential customers, and the impact that the permanent irreparable and irreversible effects can have on those so vulnerable and young, at an age where making stupid mistakes is notoriously commonplace. The religious and medical communities used to push a cure for being gay, they did not need big tech and institutional influence to push their flawed agenda. Whether being A or B is a construct or not, I believe that anyone, any "I am that I am" feeling bad about themselves for what they intrinsicly are is utterly a construct, and a horribly tragic one. One IS utterly unique, and true self-love dictates that whatever one looks like, one looks like what one feels because that is the one that one is, one is not beholden to what anyone else labels one, or what anyone else thinks how looking and feeling should be related. We are not As and Bs or Cs, which should act or feel or do anything in particular, a person is not something that should not have been. Self-love supercedes any and all groups and groupings. Every person, although on a journey, is perfect, as a human being, as a self-soul, an end in themselves... just as they are. That is what needs to be taught.

You missed, or are completely ignoring my comments above. That is your choice.

Hopefully this back and forth will become untenable after a while and the same thing will happen as what hopefully happens throughout government, they get out of areas the left and right disagree on… and leave people alone. The best anyone can hope for a State run system everyone participates in without choice, is that anything taught there consists of what both sides agree should be taught there. If that breaks down hopefully sanity will prevail and the education system will be set free of any government involvement.