Physical Fundamentals, Math Fundamentals, Idea Fundamentals – Have We Spotted Them All? by James N Rose

Steve,

This conversation is so fun and exhilarating, all I can react with is grateful appreciation that I've lived long enough to experience it. I look forward to understanding your physics~cosmology knowledge, but have some distressing news for you. I hope you are sitting in a comfortable safe chair that you will not fall out off as I explain. It is this: you may be a physics~cosmology Specialist, but you are in fact ... a General Systems Thinker. I am sorry to be the one to break the news to you, but it is a fact.

:-))))

(Oh that felt good to write. I am laughing. Hope you are too!!! Intellectual pursuits can really be enjoyable for more than the great 'Eureka' moments that some are fortunate to experience when they discover wonderful scientific insights. Good natured humor balances the intensities of the huntings for knowledge that so many of us are dedicated to. The pressure of 'the hunt' needs a human safety valve of joy and humor ... to balance the intensity.)

Your latest post identifies a side problem in modern science and education. There is SO MUCH data now in all the different fields of study, that to become competent and have viable skills in the separate professions to succeed in life, we have drifted away from the equally important thing. That is: for a well rounded mind, it is important - I would even say crucial and especially important - to be exposed to "other fields / other specialties / other perspectives". It is almost the same way that the fine accomplishment of electromagnetic civilization ... great knowledge .. and ARTIFICIALLY LIT ... night time skies, have extended the hours of a solar revolution to accomplish things within ... we have produced 'light pollution' ... which also affects the mindset of humans.

The fog of light has unintentionally washed out the observed dark-night sky for most people. Science may show beautiful Hubble pictures of what is out there in the universe. Some people may hear about tehe new discovered details of the cosmos. But they have lost .. first person experience ... by seeing stars in a dark moonless night sky ... and really grasped their "place in the universe".

Narrow highly focused limited exposure education results in a similar thing .. loss of 'presence of place' in the expanded knowledge environment around them, around any individual, or group. It becomes more and more difficult to understand, let alone appreciate, the RELATED CO-PRESENT information environment we all CO-INHABIT together.

You asked some posts earlier, what might have set me on my mental exploration journey. It was my mother, Lillian Rose, who told me as a grade school child, that nothing is one thing and one thing only. Her analogy: a tree. (we had a lovely garden and small vegetable farm that the family tended around our home)

She pressed me to reach for and appreciate totality. I can only paraphrase her original words: "It is really important, Jamie (my informal name), to see all the qualities of a tree. To know Life, you have got to see it as a farmer would see it .. for the crop growing, or the land having enough water and nutrients; it gives shade shelter on a hot day; a botanist sees the cells structures, the wood, the leaves breathing CO2 and exhaling O2; a carpenter sees potential timber framing planks, or pieces to make a table or spoon; a bird sees the branch split to hold a nest and bring young into the word, and food .. where insects crawl and eat into; a sculptor artist sees shape-able material to carve into things of beauty; the seed .. that can survive dormancy and yet produce - in the right environment conditions (same as a human 'social community of diversity'), new trees in the future; and chop the wood just-so, break it all down into destroyed structure .. and we produce PAPER ... a rebound re-ordering of the wood from pulp. Know ... -all- of it, Jamie .. the so many 'more' relations inherent in the simplistic reductionist thing~word 'tree'. You have to do your best to be aware of -all of it-, as best you can. It's important."

So I have her to thank. And her boy friend in the 1930's who would become my father, Milton Rose. Among his friends was a brilliant mathematician, Edward Barankin, who was Einstein's grad student for two successive years (no other worked that long with Dr Einstein). And she, as a young non-science trained teenager/young woman, was fortunate to have attended a few parties at Einstein's home, hearing him play violin, listening to the wide ranging conversations they all had together. My father died early, and my mother wasn't a scientist, but she was alert and aware and bright. And her message to me, would be what I would tell every young human, growing into the world. Be open to more than the local, more than the 'familiar', more than the habitual.

Apparently, Steve, someone implanted a similar appreciation in you. Ask questions and explore alternative information and perspectives. "Conventional ideas" -may- prove well done already .. true and reliable. But there is life-filling 'more' to recognize. Which, Steve, :-) brings me to your latest post.

Sometimes, the old phrase, "could not see the forest, because there were so many trees" .. is true. [and another example to add to the list above :-) ]

Your paragraph (5th I think), that starts "Entropy, heat spreads out. ..." is magnificently stated. The fact of centralization~accumulation .. towards MORE ORDER .. in the cosmos, is so obvious, so right-in-our-field-of-observation, and it is a phenomena so oppositionally counter to the (unchallengeable?) "max entropy" rule that physics/chemistry/math thinkers place as 'absolute' .. no one tries to examine or discuss it.

Oh, there are researchers who discuss complexity and emergence... but too few, if any, in astrophysics~cosmology. (except for her the recent hypotheses of Dark Matter; but I am not convinced of the arguments/measures; in any event there is no compelling modeled way to get from Dark Matter to biological emergence). So I totally know your frustration that "nobody wants to talk to me about complexity". [Can you see me? I am raising my hand! "I do!"]

And I will ... but for the immediate day, I will leave it for a next installment of our most excellent conversation. I am quietly chuckling to myself since reading your post. You, the non-biologist, promoting the notion of Darwinian essentialness in the basic dynamics of the universe. Me, a biologist, promoting the notion of examining afresh inner properties of thermodynamics (non-biological relations), that have been overlooked in descriptions and math models. That is laugh-inducing. Not because either of us is wrong in deductions, but I think we form a 'well-formed set', a tautology ... where you point tome me and I point to you, in support of our respective knowledge sets and understandings.

How wonderful.

I need to remark on several important things you wrote: A) I loved your depiction of science methodology as exploration of a crime scene. In our case, there is no 'crime' but exploring the results of events, and back building the history from what's left, is indeed the wise way - if not the only way - to proceed.

B) You identified that behaviors~processes on ALL LEVELS of organization proceed OPPOSITE to conventional ideas of 'entropy' (as the only cross tier driver of events), so that complex entities ...of which stars are a premier ... happen everywhere. Science has so far avoided addressing that pervasiveness .. in the

PRIMITIVE levels of existence. Most thinkers stop because, prior modellers said .. its because of 'gravity' (with the fear mongering admonition similar to old maps that identified "Terra Incognita" and the added warning : "Here be dragons" (don't go there!! we don't really know .. but we think it is probably -dangerous-!)

:-)))))

God bless, Steve. Until next postings.

(This is SO terrific. The best shared intellectual conversation I have had in DECADES.)

Jamie

Feb 15 2018 NV USA - pacific coast time ;

:-) you are a morning ahead of me !)

I re-read my new post --- One correction .. next to last paragraph. I should have written : two bracketed additional word sets {--}:

"You identified that .. [there are some important intrinsic} .. behaviors and processes on ALL LEVELS of organization .. [that can and do} .. proceed OPPOSITE to conventional ideas of 'entropy'

Juan,

I am grateful you are questioning certain content of my essay. Reading your remarks, you quote from the essay, then conclude:

"It is not an interpretation. It can be demonstrated the wave function in quantum mechanics describes an ensemble. Precisely those "statistical renderings" are the ones behind most myths and misunderstandings of quantum theory."

Juan, it was not my essay intention to make more fantasy and misunderstanding.

First, I am new to FQXi and wrote for a general audience, but hopefully with enough academic remarks to resonate with deep scientific mathematic minds.

I had learned in 70 years that questioning valid accomplishments of dedicated researchers, where I might be cognizant of additional relations and data that contribute or mitigate their accomplishments and results .. is difficult mind waters to tread. I have chosen to ask colleague scientists, in all fields, to consider co-present parameters that might have been honestly overlooked before.

Especially with the discontinuity separation of QM vis a vis Relativity.

Re my "Gaussian bell curve" remark, I did not have it in the essay, but did include in a conversation post afterwards, the example of a pachinko machine, where an accumulation of balls falling through pegs, generate a Gaussian distribution curve. Consider related circumstances: almost any series of science event experiments results (done over time) that produce a similar curve. Consider also any school test, where the answers generate a gaussian curve, representing the small number of students who know the material least, to a large group who know -most-, to a small number who correctly know -all- the answers.

What is generating these similar gaussian curves? Beyond our simply identifying them? I use this plausible explanation (by example):

Take the pachinko machine up into outer space .. to microgravity, or as far from a gravity well as possible. "Drop" the balls (if you can at all) from your hand, with the hope they fall through the apparatus. They don't. There is no impetus driver for the activity to occur. No movement, let alone all the batch of balls going anywhere near, let alone into and through, the pachinko apparatus.

This alerted me to something that no Gaussian mathematics includes or considers - the co-present action driver (causation parameter) that must be co-present TO GENERATE Gaussian curve results. For the pachinko game, it is the gravity acceleration field. For school tests, it is the (more complicated of course) presence of a social necessity "pressure" to gauge students' knowledge. For general science experiments, it is a similar quest, the 'pressure' to see the variability of parameters or noise/variability in processes under examination.

Some 'activity driver' is co-present .. always. But no such parameter is ever presented with its own -math term- in the equations or calculations.

The whole of the math done in conventional practice works exceptionally well WITHOUT such terms being include. But, I present the notion that there is more insight and data and knowledge to be gained BY INCLUDING, what I call, the "gradient parameter". By examining the parameter in detail in all its incarnations .. because it is more than a modifying term of the already well established calculations groups. It has its own internal sub-structures and relations .. that result in a net-simple 'gradient term'.

I hope this makes sense to you and others.

There is a variant condition I like to discuss, vis a vis the pachinko game machine. So please bear with me.

It is all well and good to examine activity/event arrangements that produce pretty gaussian curve results. Which confirm our established mindsets.

But instead of small balls and robust immovable pegs, we change the apparatus.

Stay on the earth's surface in the gravity field.

Now use bowling balls, or super-dense lead or uranium balls; and make the pegs out of fragile balsa wood. Drop the sequence of balls through the apparatus -- one at a time and removing balls after they are accounted for - their location logged in.

What is the resulting 'curve'? There is no gaussian curve. There is only one repeated result. The accumulated 'answer' is a large tall single line, graphed at that value.

Does this inform us anything useful? Yes, yes it does. It informs us that the INTERNAL RELATIONSHIPS of events are also critically important. They have to be non-destructively appropriately relatable to one another. In proper proportion. Give a college test to a kindergarten child, and you get a single result: Zero correct answers (if you prevent a random hitting of an answer button .. make it a written test, requiring the skill to hold a pencil and place a check mark in a special location :-) ). {Or test newborns) :-) ok ...

I am more concerned, Juan, with the external gradient parameter. And, if -it's- presence as a math term is something of importance to look at, then I also suggest that our by-habit use of numbers is worth reviewing also. From my years of examination, I concluded that how we use exponents .. and when we choose TO use them as 'dimensions' markers, and when we choose TO NOT use them as 'dimensions' markers, is worthy of better examination and defining. I like using the notion that 'reliable' is akin to the notion 'consistent'. I would feel more comfortable if we made the exponent~dimensions correlation CONSISTENT.

My essay presented, within the limited space allowed, an hypothesis to expand the understanding of 'dimension'; to head toward making it more consistent than we have it now. It requires a deeper review of primary math definitions currently used. I think there is room for improvement.

>Ahhh, almost forgot, there is a larger conclusion that I need to SUGGEST, Juan.

You made remark of strong dependability on statistical mathematics. A fait accompli, because of fine experimental results and internal consistency of the math (as I interpret your well phrased concise sentences).

As my examples point to, 'statistical math' does not occur to map physical events and phenomena, without co-present criteria parameters .. which co-present parameters are NOT statistical. They are activity instantiators. They are present, not statistically present. Not 'maybe they are, maybe they aren't.

[Because such motivating driving parameters exist in so many different forms that I am aware of, I am not going to try and depict them here, let alone write that there might be one and only one shared underlying property they have in common. (though they do, but I am still writing that up) :-) ]

I do NOT CHALLENGE the excellence of statistical mathematics and correlation with phenomena events, especially essential physics. I identify and recommend that there are ADDITIONAL relations -- WITHIN MATH LANGUAGE AND TERMS -- that are the missing associations which are preventing us from better understanding the natural relationship between QM phenomena and Relativity phenomena.

That is why I took the essay question in that direction. I propose that another 'fundamental' relationship exists in mathematics, which few if any have identified, let alone explored or dissected.

***

Now, Juan, you mention time-reversible QM & Hilbert spaces. I have some thoughts on those I would ask you to consider as well.

Your opening pgh, and closing remark, are respected by me. Indeed, extraordinary math has been done in both co-fields ... QM and relativity. I make NO ARGUMENT or question the detail and accuracy of the respective math and math accomplishments. MANY have been confirmed by experimentation, in fact. But noting also, that there is a lot that is not yet confirmed and remains simply hopeful hypothesis.

To be honest and clear, I have discomfort with time reversal ... even though it is an interpreted property / result of some of the math. I was in communication with Ilya Prigogine before his death, discussing and comparing our respective ideas, because I also am most interested in other mechanisms of negentropic complexity building in the universe, that addend to his excellent discovery.

He was generous enough to send me copies of all his final papers, where he had turned from his Nobel Prize winning work on 'complexity arising far from equilibrium', to considering the arrow of time. All I can publicly comment (in absence of his publishing himself) is that he tried to pull forward-time out of bi-directional QM time factors. But not successfully to his satisfaction.

It is my own deduction, knowing what I do about different relationships in the general literature, that time-forward COULD be modeled (not 'explained') by a statistical model. I have an alternative non-statistical preference, but, I have to respect and understand this interesting statistical approach.

Much like multi-verse theorists say that the math 'permits' co-alternative universes (whether we interact with them or not), I suggest that the math 'permits' consideration of precluded/prevented statistically possible time lines sets.

All events loci co-produce sets of available and also precluded 'next options'.

If I jump in a swimming pool, I have precluded next time-moment options of staying dry, of ironing a shirt, of remaining on the ground and walking away, et al. It would be massive to calculate, but I have done some initial calculations and it seems to turn out that as new option spaces open up (in the pool, I can swim with dolphins; I could not do that staying out of the pool), that there is an expanding set on both sides of any bifurcation node or multi-furcation node.

It seems that the statistical set of "no-longer possibles" expands much much faster than the set of "could be possibles". This comparison does not -explain-

forward time, but it at least maps it. From which map we might discover relationships we didn't consider before. I am hopeful.

Also, another relation makes itself apparent in comparing those differentiating sets. Option nodes identify that some events are NOT time reversible. The equations are about more than accounting for conservation of energy, momentum.

This gets back to my description about the commendable internal structure of phenomena systems. We presume and rely on the internal waves~architectures being on the same scale per sizes, energies, frames of reference, etc.

It might be the case that when there is synchrony of those factors, then under those special circumstances, there is indeed time reversal events and relations.

But those scale~matched correlations are very local, special, limited, and may be overwhelmed if not precluded, when the events environments become more complicated.

Juan, I am grateful that you were disturbed enough by remarks in my essay, to write an admonition, warning uneducated misunderstanding of the accomplishments (and therefore the underlying conceptual accuracy) of the high math and deep physics. You wrote with a respectful and tolerant tone and use of words. I hope I have done the same in return.

I am a general systems theorist, so I have had to become familiar with many sciences, many uses of mathematics. Please excuse my use of humanistic descriptions. It has been a dream of mine to get people .. scientists and non-scientists alike .. to patiently appreciate companion perspectives, and maybe use other people's insights to improve each of our own personal ones. And to maybe improve our scientific specialties by considering what has been learned in other specialties.

Thank you for commenting on my paper, Juan. I hope I have addressed, and maybe improved, your impression of what I wrote about. :-) This is an excellent community of minds.

James

2018 Feb 16 3:36PM

Nevada USA

An additional discussion point.

Physics, via Dirac and Planck and Heisenberg, have hit an -apparently- experimental boundary limit regarding deep measurements of 'fundamental' events, architecture and processes of nature.

I understand that ensemble parameters are a limit state for describing active dynamic systems with inherent ongoing motions - that are happening beyond the ability to exactly measure and specify.

This holds for unspecifiable gas motions .. which led to thermodynamics (volume, pressure, density - factors) and entropy (that attempts to track gross system behaviors) .. in spite of the limitation to math-specify particles motion.

Statistics is the only (to date) useful math that maps observed behaviors.

This holds for unspecifiable atomic particles motions also. Statistics is the only (to date) useful math that maps observed behaviors. Also.

My analogies, that you might consider inappropriate to what is happening in physics and chemical systems, I would debate with you and anyone, are exactly the RELATIONS in dynamicslly active physics~molecular system. The relations.

On the macro level, Planck limits and Heisenberg Uncertainty, are not involved. But the RELATIONSHIPS of what are involved in FUNDAMENTAL dynamics behaviors ARE still present at all levels of organization.

I have spent my life concerned with identifying that our limitations in describing events in the universe might be a self-hampering. Because we have left undetailed undescribed ... where information RELATIONS exist .. or are missing .. in our language of mathematics.

The issue is NOT that QM and continuum processes are not compatible. They can't be incompatible. The two different processes co-exist comfortably in the universe. So the DESCRIPTIONS -disconnect- cannot be something essentially found in the processes, the behaviors .. but in OUR DESCRIPTION TOOL instead.

Instead of making more complicated cobbled formula descriptions, using the conventional math as foundationed, I recommend an improved review of the BASICS of our mathematics. A potential improvement -there- .. as uncomfortable and unusual and atypical as that effort might be at first .. could (I would assert: -will-) generate insightful advancements.

In ALL areas of study. Statistics is -wonderful-. Fuzzy Logic is a great extention of it. But statistics is not the end all be all of how to describe systems, how to understand how systems are architected, organized, and behave.

There is more in the essential architecture of the domains of mathematics that need to be explored.

I want to see the discussion, the exploration ... begin.

I hope this makes better sense to you, now that I've expanded on my essay and what/why I wrote what I did there. Thank you, Juan.

James

Many thanks to FQXi 2018 contest readers - supporters and questioners of my essay's ideas - who have posted and made their opinions known. All ideas are important to make public and consider. I feel sad that I see my voting number slowly lowering, but no post or explanation is made to explain why. Science needs open ideas and explicit counter ideas.

I have had wonderful debate conversations over the years - especially at conferences I've been invited to attend internationally and here in the USA - where not every one immediately recognizes the issues I raise and want to be part of research conversation. That is fine. I invite challenges/questioning/explication.

That is the only way we all move forward.

So, PLEASE , anyone who feels they want to rate my paper .. up vote or down vote ... PLEASE post your impressions.

I have had more than my fair share of ... "I don't -like- you challenging -my- ideas" ; or .. "James, you should not be questioning conventional theories or models.". And once in a while I get honesty, "If you are right, then I've wasted my professional career discussing or teaching things that aren't quite right, after deeper analysis. I don't like that, so I'm just going to ignore you and black-ball you. I have no evidence you are wrong, I have no way to debate your propositions, they just threaten me. I will protect my professional stature first, ahead of anything you might enlighten the world with."

I was hoping that FQXi might be a less personal self-interests first forum.

Let the EVIDENCE lead the way ... to an improved scientific cultural future.

I will be the first to admit .. I may not be correct in every notion I propose, but there is merit in there on much of it. Even Newton was an alchemist, who wrote many religious works discussing the accuracy of miraculous events and the factualness of the Bible. Do those ideas disqualify or invalidate his identification of gravity, and theories of "optiks". No of course not -- though he -was- ridiculed by students and peer educators who couldn't parse the chaff from the wheat while he was alive.

I only ask the same respect ... consider the ideas, remark on the ideas. Even if they are novel and different from what you have been used to. You would want the same respect and consideration, I'm sure.

Have the courage to DISCUSS, to DEBATE, to CONVERSE. In the open. Please.

Thank you,

James N Rose

General Systems Analyst

David, Thank you for asking.

First, please understand I am not a high physics specialist, I am a thorough Analyst of Systems Generally. So I study comparative properties and dynamics that are known and modeled in diverse kinds of systems (differently levels of complexity and organization) - especially to appreciate shared (fundamental) aspects, they display.

An example is a piece I webposted several years ago Dean Falk anthropology - Ceptual Institute - web.archive.org that cross discusses metabolic chemistry (RNA/DNA) with physiology, the animal behavior, with evolution.

If you hopefully take the time to read it - about subjects you may not be familiar with - I hope you will understand an un-specified thought: there is much 'evidence' that is gained in every field .. earnest careful scientific research and experimentation. Scientists do their best to identify and comprehend how the data and information fit together. Using two criteria: 1) Can the experiments be repeated, with the same results (at least statistically close, with acceptable minimal variability)... is there reliability in the experimentation? 2) Using prior established knowledge/models about the facts under study .. does the new data make sense and support an hypothesis about 'what is going on', 'how are all the aspects coordinated and accounted for?'.

The failure of the original Hubble main mirror, was finally traced to a minuscule error in surface grinding, causing extreme limits spherical aberration - that was not caught within the original examination tolerances before installation.

I cannot speak to your frustration with the gyroscope malfunction specifically, but deep review of ANY malfunction -should- be a follow-up procedure .. as was done with Hubble, in order to find a repair, a work around, an improvement in the testing equipment. My remark you quoted applies here, apparently. Identified errors, admitted failures, show what should be avoided in further experimentation. "Predictable malfunction" is not a very good excuse, generally. Unless it is something unavoidable -- such as known 'materials fatigue' limits.

So, I would agree with you in general, David. A review of what went wrong, is a time worth it, money worth it, effort to do. With hopefully honest data and explanations; not to identify and hide .. to protect careers. The only goal is - not make the same mistakes ; find improved experimentation methods or tools.

I live in a northern Nevada USA community that is home to Bently Engineering (now a General Electric subsidiary) [I have no financial or professional connection with the company]. Don Bently built the company from scratch after WWII to deal with reducing/eliminating perturbations in high speed rotating systems. Techniques for testing and methods for dampening wobbles and frictions and variances in turbines and gyroscopes .. are studied, known and out there in the scientific literature.

Manufacturing errors due to 'cost cutting' should be avoided as well. Careful finances is truly important, but poor quality - low tolerance - equipment(if better is available) should not be acceptable. That's my opinion.

Especially in modern science and technical equipment, especially in systems where human safety is involved.

The simple precept: reliability~dependability. SHOULD produce prevention of errors, and afterwards .. improved knowledge and wisdom and insights. :-)

Regarding "Science is not a democracy", I have some thoughts on that. "Peer Review" was not, I don't think, originally intended as "let's everybody vote an opinion .. about someone's ideas". It was originally intended for high academic, years of experience, specialists to review interesting theories and experiments .. to shine the best possible 'information light' on propositions and new work. High level critical review. Not moderate experience analyses. And definitely not a 'popularity contest' free for all.

My propositions on shared relationships and properties among diverse systems, has receive both high praise, and cutting derision. The negative responses were disappointing and hurt deeply. But I've grown a thick skill, with confidence in my mental acumen.

The most gratifying experience I ever had was not straight up praise from high placed academics in several fields over the years, but this.

At one conference I got into heated debate with a highly respected University President of a top notch science university. We argued about the notion of "interest rates" in economic systems. My analysis identified that an 'interest rate' was not just a percentage 'rate of return' an investor could expect on an investment, but was also an important measure of 'how fast money flows through an economic system .. changes hand .. moves from one party to the next'.

Quite literally he call me an "a**hole" and idiot. (I was disappointed, saddened, but confident in my evaluation none the less.)

At the next year's conference gathering we ran into each other, greeted each other cordially and professionally, and he opened with, "I'm sorry, Jamie. I had a chance to think more about what we talked about last year, and discuss your notion with other specialists who never considered the kind of thing you suggested, and we realized you are right, a financial interest 'rate', -is- a collateral measure of the 'rate at which'... the "speed" at which, money units flows through an economic system." We shook hands and let it go at that, always happy to see one another at venues ; talking about other things. :-)

It takes time for new information, unconventional information - based on good scientific methodology and practices - to percolate through established preconceptions.

Many 'new ideas advances' take time to resonate (be tested), and eventually accepted. Patience is indeed a virtue, for every scientific researcher. And, respectful communication is one of the best horses to ride, in the journey toward the future.

Thanks, for asking David. Hope my comments help. James

Hello, readers of my FQXi essay.

Does anyone have any specific thoughts or reaction on my proposition that mathematics might be missing some additional important relationships vis a vis base numberline and exponential numberline? Or, that exponents generally could embody dimensional characteristics?

Calculus integration~differentiation accomplishes exponential transforms (typically whole number transforms). I understand that the transforms identify different quanta and geometric forms. Different 'data~information'.

But look at this. Use the polar coordinates equation "r= sin(theta)". The geometric graph is a unit circle. Integrate the equation. The result is AGAIN a unit circle, translated 90 degrees. Integrate that equation and the next result is AGAIN, a unit circle, translated 90 degrees. And so on.

INSTEAD of generating -different- graphic forms (slope at a point along a curve; area under a curve ; et al), the FUNCTION in polar, generates the exact same graph information quanta, simply transformed 90 degrees each time.

Unless some one else has an explanation or argument otherwise, I propose that IN ADDITION to calculus integration and differentiation generating dimensionally related -different- information, that a co-present information group resides in the equations and the transforms ... where certain essential intrinsic "information" is RETAINED, regardless of calculus transformings of DIMENSIONS of the equations.

There is -no error- in current conventional extensive calculus analyses. I am shining an intellectual light on something -else- that is involved.

Physics models are struggling to assert "conservation of information" ... especially in Black Holes ; especially when there is compacted -coding- down to singularities, or to the surface of black holes versus the volume.

So isn't it requisite that we identify WHERE IN THE MATH FUNCTIONS that data is -retained-, DESPITE transformations, and manipulated operators?

Any mathematician in the house willing to DISCUSS -this-?

My thanks. I hope there is some one of courage and curiosity to step forward.

James N Rose