## Friday, December 20, 2019

### What does a theoretical physicist do?

This week, I am on vacation and so I want to answer a question that I get a lot but that doesn’t really fit into the usual program: What does a theoretical physicist do? Do you sit around all day and dream up new particles or fantasize about the beginning of the universe? How does it work?

Research in theoretical physics generally does one of two things: Either we have some data that require explanation for which a theory must be developed. Or we have a theory that requires improvement, and the improved theory leads to a prediction which is then experimentally tested.

I have noticed that some people think theoretical physics is something special to the foundations of physics. But that isn’t so. All subdisciplines of physics have an experimental part and a theoretical part. How much the labor is divided into different groups of people depends strongly on the field. In some parts of astrophysics, for example, data collection, analysis, and theory-development is done by pretty much the same people. That’s also the case in some parts of condensed matter physics. In these areas many experimentalists are also theorists. But if you look at fields like cosmology or high energy particle physics, people tend to specialize either in experiment or in theory development.

Theoretical physics is pretty much a job like any other in that you get an education and then you put your knowledge to work. You find theoretical physicists in public higher education institutions, which is probably what you are most familiar with, but you also find them in the industry or in non-profit research institution like the one I work at. Just what the job entails depends on the employer. Besides the research, a theoretical physicist may have administrational duties, or may teach, mentor students, do public outreach, organize scientific meetings, sit on committees and so on.

When it comes to the research itself, theoretical physics doesn’t work any different from other disciplines of science. The largest part of research, ninetynine percent, is learning what other people have done. This means you read books and papers, go to seminars, attend conferences, listen to lectures and you talk to people until you understand what they have done.

And as you do that, you probably come across some open problems. And from those you pick one for your own research. You would pick a problem that, well, you are interested in, but also something that you think will move the field forward and, importantly, you pick a problem that you think you have a reasonable chance of solving with what you know. Picking a research topic that is both interesting and feasible is not easy and requires quite some familiarity with the literature, which is why younger researchers usually rely on more senior colleagues to pick a topic.

Where theoretical physics is special is in the amount of mathematics that we use in our research. In physics all theories are mathematical. This means both that you must know how to model a natural system with mathematics and you must know how to do calculations within that model. Of course we now do a lot of calculations numerically, on a computer, but you still have to understand the mathematics that goes into this. There is really no way around it. So that’s the heart of the job, you have to find, understand, and use the right mathematics to describe nature.

The thing that a lot people don’t understand is just how constraining mathematics is in theory development. You cannot just dream up a particle, because almost everything that you can think of will not work if you write down the mathematics. It’s either just nonsense or you find quickly that it is in conflict with observation already.

But the job of a theoretical physicist is not done with finishing a calculation. Once you have your results, you have to write them up and publish them and then you will give lectures about it so that other people can understand what you have done and hopefully build on your work.

What’s fascinating about theoretical physics is just how remarkably well mathematics describes nature. I am always surprised if people tell me that they never understood physics because I would say that physics is the only thing you can really understand. It’s the rest of the world that doesn’t make sense to me.

1. re: "know how to model a natural system with mathematics and you must know how to do calculations within that model"

And "mathematics" itself is not some fixed, foundational language, formulated in the past, that all models of the future have to be written in. For example, temporal type theory could be a new language for systems once written as differential equations.

Temporal Type Theory: A topos-theoretic approach to systems and behavior
Patrick Schultz, David I. Spivak
arXiv:1710.10258v3 [math.CT]

"[Temporal type theory] is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. The language is rich enough to allow one to define arbitrary hybrid dynamical systems, which are mixtures of continuous dynamics---e.g. as described by a differential equation---and discrete jumps. In particular, the derivative of a continuous real-valued function is internally defined."

2. When I was in Grad school, I worked in a group physical chemists/chemical physicists that was very experimentally focused. We were very fortunate in that, just down the hall, there was a group of very theory-oriented scientists, and we were able to forge a very productive collaboration. I think there are many, many ways to organize the scientific endeavor.

3. What I do

-drl

“What does a theoretical physicist do?”
----------------
Theoretical physicists...

(at least the “cool” ones)

...write books; create highly informative videos about physics and put them on YouTube; do interviews and lectures around the world; maintain internet blogs in which they graciously respond to the blatherings of their fans;...

...and if they are extremely cool,...

...they write, perform, and record their own original songs of which they turn into music videos.

And that’s just between breakfast and lunch. ;)

5. Happy Holidays!

1. Thanks! Happy Holidays to you too!

6. I think writer don't respond to anyone

7. "It’s the rest of the world that doesn’t make sense to me."

That just made my day! Sabine, you are too cool. I have to go out and immediately buy another copy of your book.

1. But I say the same thing in the book! (Well, kind of.)

8. "Research in theoretical physics generally does one of two things: Either we have some data that require explanation for which a theory must be developed. Or we have a theory that requires improvement, and the improved theory leads to a prediction which is then experimentally tested. "

This omits another option, namely you have a theory and you work on the consequences/predictions/applications of it.

1. Stor,

I see what you mean. I was taking the working out of consequences to be part of "improving the theory" (in the sense that some aspects of it are not well understood and "require improvement"). But I could have expressed that better. Sorry about this.

9. Happy Healthy Holy Days. You forgot the part where you parse standard theory to select those parts that can be reasonably described as being physically real, like in testable, falsifiable, and can predict something. You are among my ten favorite teachers, yours is, for me, the realm of physics for laypersons, which you generously share, in ways that make sense to laypeople.

10. The very nature of the quantum world creates a handicap that only with experiment and the correct mathematics, after many trials and errors, it is possible to express its regularities in mathematics; there is no other way; even, because the classical world emerges from the quantum world, very few things can be used from it to define the quantum world. We dream in a classic way Sabine, hahaha; happy New Year.

11. My current routine for the first week:
9.00 to 5.00 p.m do Euclids geometry
5.00 p.m to 5.55 p.m difficult to concentrate due to the noise outside my house: the school boys verbally abuse me with foul language.
6.00 to 10.00 work on euclids geometry
10.00 till I am go to bed very hard to concentrate because bearded youth outside my house verbally abuse me with foul language

For the remaining three weeks:
I loose all concentration and passion for math. I slowly forget all what I learnt in the first week. General feeling of malaise. Lot of disturbance outside my house. Some sort of psychological external manipulation of the mind which turns me away from my books and makes me lazy and indifferent to studies and life itself.

This pattern, except for the foul language and verbal abuse, that is, bright and steady first week and loss of concentration, laziness, tiredness, sleepiness, and indifference to studies and life has been going on from 9th standard, from 14 years old till date, i.e., for the past 33 years. Right from 14 years old till date I am unable to complete Euclids elements Books I to VI and XI by hall and stevens. I must have restarted a 100 times and failed to complete.

12. But why Euclids Elements? Because Einstein said that the one who has not been transported by this book in his youth is not fit to be a theoretical researcher.

13. A large fraction of the earth's population does not know what defines "theoretical physicist." If a portion of the population has seen Penrose's Road To Reality, they might get the impression that a physicist is a mathematician. If they read Rovelli's Seven Brief Lessons On Physics, they might get the impression that a physicist is a philosopher. But, if they should read Feynman's "QED The Strange Theory of Light and Matter," I believe they approach a proper impression of "theoretical physicist." Feynman says: "I'm going to explain to you what the physicists are doing when they are predicting how Nature will behave." He starts his lectures with an experimental number 1.00118, he returns to that number nearer the conclusion of the lectures, now 1.00115965221. So, when someone asks of me, what does a theoretical physicist do, I hand them a copy of this timeless book.

14. correction not 33 years but 23 years.

15. Kurt Vonnegut said, "Our purpose in this world is to fart around and don't let anyone tell you differently." I see one aspect of something like theoretical physics as that. It involves lots of time just thinking, almost at times even dreaming, of things few people regard.

1. There is s much new stuff (I see every day in science in technology news) coming out of materials science, nanotech, synthetic chemistry and biology, and all of that, but theoretical physics of the so-called fundamental forces and cosmology seems to be in a Dark Age today (with a lot resembling the scholasticism - lots of thinking and dreaming - of a prior dark era), with no Revolution yet seen coming to bring it out of that.

2. The process of embedding known gauge field symmetries into larger symmetry groups seems to be at an impasse. The problem I see is this appeals to larger state spaces and more degrees of freedom. It might be that fundamentally fewer are needed.

16. How do you know when you have read enough? When the time has come to start your own work?
It seems to me one can keep reading forever.

1. In my field there is a rather seamless transition from reading and doing my own research work. When I read something that's very interesting to me, then I'll want to know about the technical details that are usually left out in the article. This then requires me to do the technical work that went into the article myself. So, I'm then already doing my own work on the subject, albeit that I'm not going to get a new result.

Occasionally, I can then get new ideas that have not yet been explored, and I can then also make a good assessment on whether it's worthwhile to pursue these ideas on my own or in a collaboration with other people.

17. Gokul: a still born theoretical physicist. They, who ever they are, love me that way. I read a lot of J Krishnamurti's talks, and they must of thought that it was worthless. But Lo! I came upon Copenhagen interpretation, QBism, the recording part of Quantum Darwinism all myself just by listening to J Krishnamurti's talks--quantum mechanics was not taught at the degree level in college, and never did I read a word of quantum mechanics theory before.

Please think of this: David Bohm is a name in Quantum Mechanics, don't we have theory in his name: Bohmian mechanics? One day Bohm and his wife went to a library and were looking for books on "observer participant phenomenon". Mrs. Bohm inadvertently picked up a book in the rack but the book slipped and fell on the ground opening at the page on "observer is the observed". She found that the book was by J Krishnamurti. She showed her find to Dr. Bohm, who went home and immersed himself in the book, and completed it overnight. He got so interested in J Krishnamurti's work that he arranged for an interview with him. And thereafter, his discussions with J Krishnamurti appeared as books The ending of time, Truth and actuality to name a few. So, for a man like David Bohm to get interested in J Krishnamurti means he saw something relevant to Quantum Mechanics in JK's books.

18. They thought that a still born theoretical physicist in me was an achievement, and that J Krishnamurti was worthless. But without a single equation in math, I arrived at Copenhagen interpretation, and QBism, and the recording part of Quantum Darwinism just by listening to J Krishnamurti's talks.

What does this imply as I see it? That is, without math you can understand Quantum mechanics--I mean without a single equation--just by listening to J Krishnamurti's talks. Proof: I didn't complete even Euclid's elements Book I to VI and Book XI, which is a great victory for them, who ever they are, but I understood quantum mechanics without math. See! how it has all weaved out and brought to the fore "the teachings of J Krishnamurti". Which means there is a more direct perception. See! how "that energy" is weaving itself: there is no God or rest of that bilge. Fear invents God, and the one who knows no fear knows no God. But see! how "that energy" is weaving itself, look what is happening and has happened to me. As a man of science I am extremely intrigued and I want science to get to "it", whatever "it" is.

19. Until physicsforumsdotorg or whatever it was called, I used to think that "theorizing" was just writing what was already on your head upon coming into contact with a question... at no point before that did it ever occur to me that people didn't raise their hands and pick up a ripe theory from the nearest tree!

But I really didn't show up to say that, but this:

Sabine, family, and readers: happy holidays to all.

20. Does mathematics come before physics or after physics?

What I mean is that a theory has to first explain experimental observations and then be mathematically consistent or it has to be mathematically consistent first.

String theory is mathematically consistent with no experimental proof.... If I am not wrong.

1. Physicist formulate theories that explain experimental observations in usually mathematically very sloppy ways. Mathematicians will then later give a rigorous mathematical foundation for the theories. Take e.g. Dirac introducing his delta function in a mathematically inconsistent way, and mathematicians later formulating the theory of distributions that makes the delta function well defined as a distribution.

21. Sabine, you have described very clearly how the process of education and later the work in the physical science is. But regarding the goal which we have in science, particularly in physics, one specific step is missing. One could call it the “Copernican step”.

We have some big open points in present physics like the well-known Dark Energy, Dark Matter, Inflation, the Vacuum Catastrophe. And at conferences I have repeatedly heard the sentence: “We need a new Copernicus”.

The standard process of learning and of research as you have described it does not promote the generation of a “Copernican step”. Maybe this way cannot be formalized. But from time to time there are persons who propose according solutions. But those solutions are either completely ignored or they are formally accepted, but the necessary consequences are not drawn.

An example: W.G.V. Rosser is in my view such type of a Copernicus. He has mathematically shown (in the middle of last century) that magnetism is a relativistic side effect of the electrical field. This is in contrast to Maxwell’s theory which assumes magnetism as an own phenomenon only connected to the electrical force in a specific way. Einstein has stated to have the same view of magnetism as Rosser. And this view is to my knowledge formally accepted by the physical community, but the consequences are ignored. One consequence is that magnetic monopoles do not exist. On the other hand Paul Dirac’s theory demands magnetic monopoles. This conflict should be discussed, but it is ignored.

In my view this is a way as present physical science works, clearly not a good one.

1. antooneo,

It is not so much a matter of needing a new Copernicus, as needing someone in the scientific community with the courage to set aside the foundational assumptions of modern cosmology. Someone, that is, willing to do what Copernicus did, rethink the foundational assumption of the standard cosmological model to produce a better, more accurate representation of the underlying physical reality.

By replacing a geocentric with a solar-centric model, Copernicus opened the door for Kepler to realize that the orbits of the planets were not perfect circles, but ellipses. The result was an accurate, robust qualitative model of the solar system which in turn opened the door for Newton's gravitation.

Sitting around wishing and hoping for a god-like Copernican rescuer to resolve the current cosmological morass, is just a way of avoiding the hard work of rethinking the foundational assumptions of modern cosmology. It's quite obvious that nobody wants to undertake such a task, likely because there is no institutional body willing to pay for the effort.

Thus, the professionalization of science has produced a closed, guild-like, socio-economic system, which has resulted in the unscientific stasis that marks contemporary theoretical physics. Nobody wants to be Copernicus because it doesn't pay to rock the boat, and those who attempt to do so are quickly cast overboard (defunded).

2. antooneo wrote:
>An example: W.G.V. Rosser is in my view such type of a Copernicus. He has mathematically shown (in the middle of last century) that magnetism is a relativistic side effect of the electrical field.
...
> And this view is to my knowledge formally accepted by the physical community, but the consequences are ignored.

antooneo, I am currently working on a monograph on this subject. Your history is more than a bit off. The point was made in 1912 (!) by Leigh Page shortly after Einstein presented special relativity; just copying the reference from the draft of my monograph:

L. Page, “Derivation of the fundamental relations of electrodynamics from those of electrostatics,” Am J Sci, July 1, 1912 Series 4, 34:57-68; available online

To be sure, there are some problems with Page's analysis (and indeed with Rosser's), but the basic idea has been standard textbook material for over fifty years now (e.g., see Purcell's classic book in the popular Berkeley physics series).

antooneo also wrote:
>One consequence is that magnetic monopoles do not exist. On the other hand Paul Dirac’s theory demands magnetic monopoles.

No, you have it exactly backwards: it is the easiest thing in the world to include magnetic monopoles in Maxwell's equations. We do not do that for the very simple reason that, thus far, monopoles do not seem to exist in the real world. If they ever do show up, I assure you we will pop them into Maxwell's equations pronto.

By the way, all this connects with your and my debate a while back over synchrotron radiation: if Rosser had bothered to read and fully understand Schwinger's classic papers on synchrotron radiation, he, like you, could have avoided some foolish mistakes.

For anyone who wishes to pursue antooneo's reference to Rosser, read my monograph when it (eventually) comes out and you can see some simple calculations that show some of Rosser's errors.

In the meantime, Rosser's major papers on the topic are:

W. G. V. Rosser, “ Electromagnetism as a second-order effect (I) The definition of the ampere,”
Contemporary Physics Volume 1, Issue 2, 1959

W. G. V. Rosser, “Electromagnetism as a second-order effect (II) The electric and magnetic fields of a charge moving with uniform velocity,” Contemporary Physics, Volume 1, Issue 6, 1960,
pp. 453-466

W. G.. V. Rosser, “Electromagnetism as a Second Order Effect, Paper III. The Biot-Savart Law,” Contemporary Physics, Volume 3, Issue 1, 1961.

and his monograph is:

W. G. V. Rosser, Classical Electromagnetism via Relativity (New York: Plenum Press) 1968.

22. I liked "We need a new Copernicus". Surely we need one.

23. Man invented God. God is one of the greatest inventions of man. Let us assume that all humans on this planet somehow perish, and there is not a single human left on this planet. Nature will then take over. But most importantly God is gone; with man gone God is gone, religion is gone, ideologies are gone. It is clear that God, religion, ideologies, dogmas, and doctrines are products of the human mind anymore more than airplanes, computers, and spaceships are.

If one has gone deeply into the mechanism of fear at least intellectually, one discovers that fear invents God. And the one who knows no fear knows no God.

24. "The brain can function to its highest capacity only when there is complete security" J Krishnamurti. When this security is denied, there is fear, and fear invents God and seeks refuge in it because there is sense of security which is a false sense of security. Fear invents God. Man created God and not the other way.

25. Sabine,

...you must know how to model a natural system with mathematics and you must know how to do calculations within that model.

There's a step missing here. Before you can make a mathematical model of a natural system, you must first have a well-considered understanding of how that physical system functions. If you misunderstand the system physically, you may still be able to produce a math model that agrees with observations, but it will be able to do so only by invoking the existence of unobservables, i.e. epicycles, dark matter, dark energy, etc.

Such models do not accurately represent the nature of physical reality, they misrepresent it! The great strength and great weakness of mathematics with respect to scientific analysis, is that a math model can always be freely parameterized into agreement with observations.

This agreement can be achieved, no matter how inaccurate the underlying understanding of a given physical system is. Ptolemaic cosmology and ΛCDM are both glaring examples of this mathematical susceptibility to a kind of confirmation bias. As with computers, so it is with mathematics, garbage in - garbage out. Fundamental qualitative analysis has to be reintroduced into theoretical physics if it is to resume making any sort of substantive progress.

1. bud rap wrote to Sabine:

>There's a step missing here. Before you can make a mathematical model of a natural system, you must first have a well-considered understanding of how that physical system functions.

bud, it's more of a back-and-forth process: if you like high-brow terms, it's "dialectical."

One of the things that several of us scientists here have been trying to get across to you is that there are now over four centuries of experience in developing physics. We do know a bit about how this goes.

The classic example here is Maxwellian electromagnetism: Maxwell took Faraday's very visual, physical idea of lines of force and put that into precise mathematical form. When he did that -- only after he had the precise math down -- it became clear that something was wrong, that some term was missing. When Maxwell added that mathematically required term, what he called the "displacement current," a whole new world opened up: it became clear that light was an electromagnetic phenomenon, that there must be electromagnetic radiation we could not see with our eyes (radio waves and such), etc.

Back and forth between the physics and the math -- and take the math seriously.

bud also wrote:
>Fundamental qualitative analysis has to be reintroduced into theoretical physics if it is to resume making any sort of substantive progress.

Oh, there has been lots of (so far unsuccessful) "string theory phenomenology" that is based on "qualitative analysis" without anyone knowing if string theory itself actually is even consistent in any serious mathematical sense.

When Sabine has complained about physicists "lost in math," the problem is not that they have been too rigorous in how they are doing the math, but rather that they have not taken the math seriously enough to get actual, detailed answers that can be confronted with observation and experiment.

Too many physicists have "gotten out over their skies" mathematically: they spout mathy things without being at all clear what they actually mean.

Pretty much like you.

bud also wrote:
>The great strength and great weakness of mathematics with respect to scientific analysis, is that a math model can always be freely parameterized into agreement with observations.

You really think so??? Then you come up with math that replicates the experimental observations in the quantum realm and that also agrees completely with special relativity.

Thousand of very bright people have tried and no one has fully succeeded. But if it is so easy, by all means show us how.

Galileo taught us, "The Book of Nature is written in the language of mathematics.'

Indeed, it is doubtful that anything can truly be described precisely without using math. Those things that cannot be successfully described in math (and certainly no one has thus far given a successful mathematical theory of human society or human psychology) are exactly those things that we cannot describe with real precision.

People like you who will not learn any of the relevant math cannot understand how the physical world works.

Too many physicists are already taking your advice and have become way too cavalier with the math. The time has come to take the math seriously rather than using mathy language to hide their actual ignorance. But the only people who can contribute to that are those people, unlike you, who are willing to learn and fully understand the mathematical form of existing theories.

For, the Book of Nature truly is written in the language of mathematics.

2. ParrotDave

Brigitte Falkenburg pointed in »Particle Metaphysics: A Critical Account of Subatomic Reality (2007)« out...

...“It must be made transparent step by step what physicists themselves consider to be the empirical basis for current knowledge of particle physics. And it must be transparent what the mean in detail when the talk about subatomic particles and fields. The continued use of these terms in quantum physics gives rise to serious semantic problems. Modern particle physics is indeed the hardest case for incommensurability in Kuhn’s sense.”…”After all, theory-ladenness is a bad criterion for making the distinction between safe background knowledge and uncertain assumptions or hypotheses.”...

What do particle physics pioneers think about “today's” particle theoretical physicists respectively “today's” standard model of elementary particle physics. "Today" means here roughly the beginning of the 21st century. A statement by the Physics Nobel laureate (1976) Burton Richter from 2006 gives a “clear” answer.

Quote: “To me, some of what passes for the most advanced theory in particle physics these days is not really science. When I found myself on a panel recently with three distinguished theorists, I could not resist the opportunity to discuss what I see as major problems in the philosophy behind theory, which seems to have gone off into a kind of metaphysical wonderland. Simply put, much of what currently passes as the most advanced theory looks to be more theological speculation, the development of models with no testable consequences…“

Source: »Theory in particle physics: Theological speculation versus practical knowledge«
Physics Today October 2006 https://physicstoday.scitation.org/doi/10.1063/1.2387062

1. Dirk,

I spent a summer working for Burt and know his views fairly well.

I have never seen any sign whatsoever that Burt was skeptical of the Standard Model (aside from the basic point that every physicist should of course be willing to accept in principle the possibility that new evidence would challenge the Standard Model).

I think Burt would only have agreed with Falkenberg to the extent that of course it is a good thing for textbooks and other expositions of the best existing theory to be as clear as possible.

What Burt was quite critical of was string theory, for the simple reason that string theory had and has no prospect in the foreseeable future of making serious, definitive predictions that can be tested and potentially falsified by experiment.

I think that most physicists would agree that this is indeed a very serious problem with string theory. Mathematically, string theory has its beautiful sides, but there really is an issue as to whether, in Sabine's words, string theorists have become "lost in math."

27. "The Book of Nature truly is written in the language of mathematics."

I certainly do not disagree with this, but think it can be stated in more explanatory ways.

I have tried with, "Math is thinking, thinking is math."

I will try again with "Math is rules and the consequences which follow from those rules." So in a universe with rules, math is the way to understand that universe; and in a universe without rules, nothing will work.

It has been commented that perhaps we need a new way of thinking, to work on certain problems. Perhaps so, but I predict that if and when those new ways of thinking are developed, they will be taught by the Math Department.

(Unsolicited opinion on the Internet: 5-euro fine.)

1. JimV,

I agree, of course.

There is an interesting question, as Sabine and others have pointed out, as to why math has been so successful in physical science: this was not what almost anyone expected before the sixteenth-century Scientific Revolution, and I don't claim to have the last word on the subject.

A book I should have mentioned earlier in this discussion is E.. W. Beth and Jean Piaget's book, Mathematical Epistemology and Psychology.

Beth was a Dutch philosopher and logician who was interested in the foundations of mathematics. Piaget was of course the Swiss psychologist who was famous for the study of cognitive development. Among other points, Piaget emphasized the development from the "concrete operational stage" in mid-childhood to the "formal operational stage" in adolescence.

And that is really the take-off point for Beth and Piaget's book: to oversimplify, math starts with concrete actions humans engage in -- most notably counting as well as the drawing and measuring of geometric shapes.

And then true math occurs as we abstract from these actual human actions, removing constraints that seem accidental and contingent.

For example, no human has ever counted sequentially all the way to a trillion! But that seems to be just an accident of the limited human lifetime (and limited human attention span!). So, math treats one trillion as just as real a number as one hundred.

We can count to a hundred. Let's just pretend we can count to a trillion and move forward.

Similarly, no human has ever drawn a truly perfect circle. But, if we abstract away from the imperfections of any real circle, and assume that all the points are exactly the same distance from the center, it actually becomes easier to understand what is going on with circles.

It's not too hard to see how this same process led to higher-dimensional manifolds, to transfinite set theory, and, indeed, to most of the higher mathematics of the last two centuries.

By the way, a detailed history of mathematics along these lines would have to emphasize that this process of repeatedly removing apparently accidental and contingent limitations was, to some degree, an experimental exercise. For example, in the development of axiomatic set theory, Frege tried to use an unrestricted axiom of comprehension: Bertrand Russell showed that this led to a contradiction, and set theorists had to back off and settle for the Zermelo-Frankel axioms. Similar trial-and-error incidents occurred in the development of analysis, algebraic geometry, etc.

Anyway, I think this does accurately describe most of the historical development of mathematics and at least helps to explain why math is so useful: math is just a series of higher and higher abstraction built upon rather elementary ways of dealing with the real world that humans found to be quite useful many millennia ago.

I think that many commenters here, as well as Sabine herself, would find the book thought-provoking, though of course it will not be the final word on the nature or usefulness of mathematics!

All the best,

Dave

2. JimV,

"The Book of Nature truly is written in the language of mathematics."

That is a sentiment, not a definition. The two weak metaphors employed sum to a very flaccid and imprecise statement.

"Math is thinking, thinking is math."

Well, no. It's true that math is a way of thinking, but thinking is not a way of doing math - unless you are doing math.

"Math is rules and the consequences which follow from those rules."

Here's a good working definition of math:

Math is a set of human-constructed, abstract, logical formalisms based on counting.

As to "new way of thinking" arising in the Math Department, that is highly unlikely unless you are simply expecting a new mathematical formalism.

Critical thinking, which is what I think you are getting at, is a reciprocating process. You evaluate theories in terms of facts and facts in terms of theories. Thinking, in that sense, is a dynamic process and that process will, by its very nature, discover new facts and generate new theories.

When you find a situation where either facts or theories are fixed, then critical thinking is not happening and probably not possible. Think about it.

3. Thanks to Dr. Dave and Dr. rap (I am assuming both are at that level) for your replies (which I just now happened to see, belatedly).

In response to Dr. rap:

My definition intentionally applies to soccer and basketball and everything else in which decisions are to be made based on predictions of the consequences.

If I have three errands to do (pick up dry cleaning, buy some ice cream, mail something at the Post Office), and take a moment to decide what order to do them in, I am doing math. Simple math that I can do in my head, but math. In more complex situations, people can't do the math in their heads and need to write things down and proceed step by step, using formal methods so they can understand what they did years later and others can read it also. Each of those formal methods (algebra, calculus, etc.) was the result of deep thinking by brilliant people over thousands of years, so why not take advantage of them?

I am happy with my general definition as I think the more one can generalize a concept the better one understands it; but if others want to split it up into different regions of application and call them different things, that is their prerogative.

The common English phrase when asking someone to think about something, "do the math", sums it up well for me.

Note: the math is not always done correctly. There is good thinking and bad thinking (good math and bad math). I take great solace in my favorite Einstein quote, "All mathematicians make mistakes; good mathematicians find them." Since in my lexicon that translates to "All thinkers" it applies to all of us.

There are also occasions in which assumptions must be made about unknowns in order to attempt a solution, and those assumptions turn out to be wrong. This does not mean we should stop doing math (thinking). Again, if doing the math doesn't work nothing else will either.

(Argumentative on the Internet: 20 Euro fine.)

28. Dave,

...it's more of a back-and-forth process: if you like high-brow terms, it's "dialectical."

That's the way it's supposed to work alright, but that is not how modern cosmology actually functions. What we have instead is a theoretical monologue, in which mathematicists (not mathematicians necessarily), insist on the existence of certain vaguely and imprecisely specified, entities and events, despite the complete absence of any empirical evidence for such.

The dialog is non-existent here, in the sense that the observational results for the claimed phenomena, being unequivocally negative, are functionally ignored by the theoretical community, which continues to believe in its preferred model and therefore in the physical ramifications of that model.

Before going any further, I want to again make clear that it is not the use of mathematics in science that I object to. I have explicitly stated in prior comments, on this blog and elsewhere, that math is a fundamental and absolutely necessary modeling tool for modern science. What I object to is the mathematicist's proclivity for weighting a preferred mathematical model over empirical observations.

You can wrap yourself in the cloak of your historical knowledge of science and pontificate to your heart's content. However, mathematicists, who believe in things that cannot be demonstrated to exist, are not behaving like scientists, despite papers attesting to their pedigree. Mathematicism constitutes a peculiar kind of modern, secular, belief system. It has no basis in science. Here is a typical statement of mathematicist belief:

For, the Book of Nature truly is written in the language of mathematics.

The vague, unscientific, metaphorical imprecision of this statement encapsulates all that has gone wrong with theoretical physics over the last forty years. Galileo's poetic invocation has become Holy Writ. In its modern context it has become a statement of belief, one that ignores the ridiculous train-wreck of theoretical nonsense, like the big bang theory, that has piled up in its wake.

As mathematicism came to functionally dominate science over the last century, our understanding of physical reality has devolved into a pair of standard models that bear, in their particulars, almost no resemblance to the physical reality we actually observe.

Just to reiterate (sticking to cosmology), the big bang and its inexplicable original condition, inflation, substantival spacetime, dark matter, and dark energy are not observed phenomena. They exist only in the model that requires them. ΛCDM grotesquely misrepresents the nature of observed cosmological reality.

Mathematicists have a problem understanding this criticism because of their innate belief that their models somehow define and determine reality. But that belief has no scientific basis and is in fact a profound philosophical error that has made a complete mess of modern theoretical physics. On that I'm sure we can disagree.

(continued...)

29. (...continued)

With regard to Faraday and Maxwell, Faraday's precise, qualitative investigation into the nature electromagnetic phenomena made Maxwell's mathematical elaboration possible. Unfortunately, the modern approach to Faraday's type of qualitative analysis is to treat it as an afterthought - if it is given any thought at all.

Your usage of the term, "qualitative analysis" with regard to string theory, of all things, is instructive. By qualitative analysis, I specifically mean the type of close analysis of a natural phenomenon via observation and measurement (unconstrained by a preconceived mathematical model), that Faraday engaged in. Qualitative analysis, in that sense, has nothing whatsoever to do with string theory.

Nowadays we educate lots of Maxwells but no Faradays. Even experimentalists are steeped in the mathematical framework that shapes their investigations. They are dispatched to find dark matter and dark energy. When they report negative results, they are told to redouble their efforts, and so the necessary dialog between qualitative and quantitative analysis is, on that level, non-existent.

The whole "galactic-rotation-curves-indicate-the-existence-of-dark matter" paradigm rests entirely on an inexcusable failure of qualitative analysis. The Keplerian method was used to calculate the expected rotation curves of galaxies??? Really??? And when that didn't work y'all decided that dark matter was the solution??? Modern theoretical physics apparently, has no idea how to do a proper qualitative analysis of a physical system.

There was no logical excuse for employing the Keplerian method in the first place, to estimate the rotation curves of disk galaxies (galaxies being morphologically complex compared to the solar system). But having failed to even approximate observations, the willingness to simply persist and attribute the model's failure to a shortcoming of observed physical reality (dark matter) was astoundingly obtuse.

On the evidence, theoretical physicists don't know how to think in terms of the actual physical systems they observe, only in terms of their inherently limited mathematical models. Modern cosmology is a mess and the half-baked philosophy of mathematicism is the primary cause.

People like you who will not learn any of the relevant math cannot understand how the physical world works.

That's a ridiculous proposition Dave. If I study the math of your broken model, the one that attests to the existence of things that do not, in fact, exist in physical reality, what do you suppose is going to happen to me?

Do you think I will suddenly experience a true awakening and be given to understand that things that aren't there, really are there, because - its all in the math? If so, you're quite delusional. I am not susceptible to that type of belief, a kind of mindless, mathematical mysticism. When the math disagrees with empirical reality, it’s what reality says that should count most. And I do believe that is the only proper scientific attitude.

1. bud rap wrote to me:
>The whole "galactic-rotation-curves-indicate-the-existence-of-dark matter" paradigm rests entirely on an inexcusable failure of qualitative analysis. The Keplerian method was used to calculate the expected rotation curves of galaxies??? Really???
...
>There was no logical excuse for employing the Keplerian method in the first place, to estimate the rotation curves of disk galaxies (galaxies being morphologically complex compared to the solar system).

Jean Tate can answer this better than I, but if you are trying to imply that astrophysicists naively assumed that galactic dynamics simply followed the exact same laws as Kepler's three laws for the solar system, you are horribly mistaken.

If you are suggesting something else... well, I cannot decrypt what you are saying: I find it impenetrable.

Bud also said:
>What we have instead is a theoretical monologue, in which mathematicists (not mathematicians necessarily), insist on the existence of certain vaguely and imprecisely specified, entities and events, despite the complete absence of any empirical evidence for such.

That is not what has happened. Most physicists supposed the cosmological constant was zero, until "empirical evidence" indicated otherwise (and, as Sabine has documented, the issue is still not completely settled).

Bud also said:
>[Dave] People like you who will not learn any of the relevant math cannot understand how the physical world works.

>[Bud] That's a ridiculous proposition Dave. If I study the math of your broken model, the one that attests to the existence of things that do not, in fact, exist in physical reality, what do you suppose is going to happen to me?

You have repeatedly made claims about the existing models that are false because you are not able to understand the math.

You ask what I think would happen if you did understand the math? Well, if you were able to understand the math and went to the trouble to do so, I think you would abandon some of your erroneous opinions.

But to be brutally frank, I think you lack the ability to understand the math.

Bud also wrote:
>Just to reiterate (sticking to cosmology), the big bang and its inexplicable original condition, inflation, substantival spacetime, dark matter, and dark energy are not observed phenomena.

You cannot directly observe your own hand, What you actually observe is photons reflected from your hand and you infer that you are seeing your hand. All observation is inference, whether of the everyday world or of quarks or the Big Bang.

Inflationary cosmology is, as Sabine has made clear, problematic: it is an interesting speculation. The Big Bang is not problematic: as I recently pointed out, there is enormous evidence for the Big Bang -- not just the CMB and the cosmic redshift data but also the elemental abundances from the Big Bang, the change in elemental abundances in younger vs. the oldest stars, the age of the oldest stars based on stellar structure calculations, etc.

The Big Bang is about as settled as anything can ever be in science. (Yes, we could all be living in the Matrix or brains in a vat. But probably not.)

And, your and your friends' complaints about "substantival spacetime" is just bizarre. I do not know where you picked up the phrase -- perhaps from some bad pop-science book.

What General Relativity says about space and time is that Euclid was wrong. Euclidean geometry is not true in the real world. More fundamentally, spacetime is not Minkowskian -- not the almost trivial combination of Euclidean space with simple linear time that was assumed in special relativity.

The fact that Euclid was wrong was shown by the 1919 Eddington measurement of light deflection by the sun. If space were Euclidean, the deflection would have been half of what was measured. The measured result showed that Euclid was wrong: the curvature of space doubled the actual deflection.

The earth is not flat. Spacetime is not flat. Euclid was wrong.

Get used to it.

2. Dave:

Well, one of us his horribly mistaken, and that would be you.

Thus the smallest Sc's (i.e., lowest luminosity) exhibit the same lack of a Keplerian velocity decrease at large R as do the high luminosity spirals.
- Rotational Properties of 21 Sc With A Large Range Of Luminosities And Radii..., Rubin, et al, 1979

Dave:You have repeatedly made claims about the existing models that are false because you are not able to understand the math.

What false claims have I made? Be specific, skip the hand waving generalities. I'll defend anything I've said against any concrete criticisms you might have. If the past is any guide, your specific objections will take the form of lazy arguments from authority.

Dave: You cannot directly observe your own hand, What you actually observe is photons reflected from your hand and you infer that you are seeing your hand. All observation is inference, whether of the everyday world or of quarks or the Big Bang.

Spare me the sophomoric philosophy. The fact that we now understand the mechanism by which direct observations take place does not mean that direct observations don't take place. Direct observations take place in exactly the same way that they always have.

Hands are directly observed, so are trees and stars and galaxies. Dark matter, dark energy, and quarks and a host of standard model dependent inferences are not directly observed. Mathematicist prevaricators like yourself like to muddy that fact with this disingenuous claim that "nothing is directly observed" in order to provide cover for their empirically baseless claims about the nature of physical reality.

Dave: The Big Bang is about as settled as anything can ever be in science.

In your mind and in the minds of your fellow mathematicist believers, perhaps. But mathematicism is inherently not a good guide to the nature of physical reality, since it is a philosophical stance without any scientific basis. The Big Bang description of its "universe" does not resemble, in any of its particulars, the cosmos we observe

As to substantival spacetime, a rather straightforward concept you seem to have a great difficulty understanding, it is simply the spacetime of Wheeler:

Spacetime tells matter how to move; matter tells spacetime how to curve.

In other words, substantival spacetime both affects and is affected by the behavior of observables. Such a spacetime is, however, not an observed phenomenon, it is only a postulate of the standard model. I'll give the last word on this to Einstein:

Space-time does not claim existence on its own, but only as a structural quality of the field.

The earth is not flat, and spacetime does not exist.

Get over it.

3. bud rap,

You are wrong and Dave is right. We do not ever directly observe anything, except (as Descartes put it) that we directly observe that we think to begin with. If you think otherwise, you are confused and have also missed centuries of philosophy. Space-time "exists" in the only sensible meaning of the word "exist", as I have explained here. If you mean something else by "exist" you are talking past everybody else.

4. bud rap wrote to me:
>As to substantival spacetime, a rather straightforward concept you seem to have a great difficulty understanding, it is simply the spacetime of Wheeler:

>Spacetime tells matter how to move; matter tells spacetime how to curve.

>In other words, substantival spacetime both affects and is affected by the behavior of observables. Such a spacetime is, however, not an observed phenomenon, it is only a postulate of the standard model. I'll give the last word on this to Einstein:

>Space-time does not claim existence on its own, but only as a structural quality of the field.

Wheeler is correct and Einstein is correct, and that you cannot see this is your problem, due to your refusal to learn the math. Wheeler was, after all, doing his best to explain Einstein's theory!

I note that the quote from Wheeler does not, of course, use your favorite phrase, "substantival spacetime."

Yes, both men were simply trying to tell their readers that geometry in the real world is not Euclidean. This has been measured.

You are wrong.

Once again, the real world defeats bud rap.

>Do you think I will suddenly experience a true awakening

No, I don't.

6. Catching up, re galaxy rotation curves ...

Start with this from bud rap: "The whole "galactic-rotation-curves-indicate-the-existence-of-dark matter" paradigm rests entirely on an inexcusable failure of qualitative analysis. The Keplerian method was used to calculate the expected rotation curves of galaxies??? Really??? And when that didn't work y'all decided that dark matter was the solution???"

PhysicistDave: "Jean Tate can answer this better than I, but if you are trying to imply that astrophysicists naively assumed that galactic dynamics simply followed the exact same laws as Kepler's three laws for the solar system, you are horribly mistaken."

To which bud rap wrote: "Well, one of us his horribly mistaken, and that would be you.

Thus the smallest Sc's (i.e., lowest luminosity) exhibit the same lack of a Keplerian velocity decrease at large R as do the high luminosity spirals.
- Rotational Properties of 21 Sc With A Large Range Of Luminosities And Radii..., Rubin, et al, 1979
"

Sorry bud rap, but I'm genuinely puzzled; I hope you can help clarify.

First, I think the paper you are citing, and quoting from, is Rubin+ (1980); here's an ADS link: https://ui.adsabs.harvard.edu/abs/1980ApJ...238..471R/abstract

Second, this Rubin+ paper is all about presenting empirical results, specifically the rotation curves of a sample of highly inclined spiral galaxies (Hubble type Sc).

Third, and most pertinently, I cannot see any "Keplerian method" being "used to calculate the expected rotation curves" of these 21 galaxies (I bolded a particularly puzzling term).

So, start with a specific question: how did you conclude that Rubin+, in this paper, were using a Keplerian method to calculate an expected rotation curve?

Also, what do you mean by "the Keplerian method" (bold added)?

7. Sabine,

I went back and reread your post "Does the Higgs Boson Exist?" and realized we already had an extensive discussion of this issue. I don't want to rehash the same arguments but I want to reemphasize a point I raised, not for so much for argumentative purposes, but as for a basis of thinking about the reason for our strong disagreement on the relevance of instrumentalism to science.

Specifically, you and I seem to have received our scientific educations on opposite sides of a great divide. Time-wise that divide seems to have arisen in the course of the 1970s. I received my formal science education during the 1960s, yours I believe, came several decades later.

What seems to me to characterize this divide is this:

From my earliest interests in science when I was in grammar school in the late 1950s, through high school and college, science was presented as a study of those things that can be observed and measured (broadly inclusive of mechanical extensions of our senses and experimentation).

It was presented so, as a way of distinguishing science from other forms of knowledge, particularly those of philosophy and theology.

This distinction seemed important to me, not least because it seemed to account for the great success of science relative to the other disciplines. To put it trivially, science can launch rockets to Mars, while philosophy and theology can only launch arguments.

From conversations with you and others it seems to me that your scientific education did not emphasize that empirical basis of science. It seems that you were taught an instrumentalist approach to science that deemphasized empiricism as a fundamental basis for doing science. I do not mean to state that definitively - that is only how it appears to me.

I think we share (along with others) a general sense that something is amiss with theoretical physics (cosmology and particle physics/quantum theory). You seem to attribute the problem, mostly to the inappropriate use of arbitrary aesthetic standards (beauty and naturalness) in modeling, where I would say the problems arise from the abandonment of the empirical standard. Those views are quite different, but I don't think they are necessarily contradictory.

So in trying to understand your position better, let me ask you, do you feel I have characterized your science education correctly and do you consider your instrumentalist philosophical views to be dependent on or derived from your scientific education? Do you think your views would be different if science had been presented to you as it was to me - as a fundamentally empirical endeavor?

Thanks, and keep up the good work.

8. Jean Tate,

That's the paper. Did you actually read it? Here's another quote from the same paper indicating that their empirical results did not agree with expectations:

None of the rotation curves have the “classical” shape,
adopted so frequently in the past, of a long nearly Keplerian drop in velocity after the initial rapid rise

Oh, they didn't actually say expected, oh gee. Here:

From:
https://ned.ipac.caltech.edu/level5/March01/Battaner/node3.html

At large distances from the galactic centre the gravitational potential should be that produced by a central point mass and, in the absence of forces other than gravitation, it should be expected that GM/R2 = $\theta^{2}_{}$/R (G, universal gravitation constant; M, galactic mass; R, galactocentric radius; $\theta$, rotation velocity), therefore $\theta$ $\propto$ R-1/2, which is called, for obvious reasons, the Keplerian rotation curve. This Keplerian decline was not observed...

The interpretation of rotation curves of spiral galaxies as evidence of DM halos was probably first proposed by Freeman (1970) who noticed that the expected Keplerian decline was not present in NGC 300 and M33...

From:
https://www.e-education.psu.edu/astro801/content/l8_p8.html

However, astronomers expected that as you got more distant from the center of the Galaxy, the velocities of the stars should fall off in a manner similar to the Keplerian rotation exhibited by the planets in the Solar System.

Here:
https://iopscience.iop.org/article/10.1086/303933/pdf

...to uncover any definitive departures from the standard luminous Newtonian disk Keplerian expectation...

Here:
https://www.mdpi.com/2075-4434/2/4/601/htm

This contrasts with the expected Keplerian decline once the majority of stars and gas are enclosed, providing one of the clearest examples of the mass discrepancy.

I thought you knew this subject.

9. Dave to me:

But to be brutally frank, I think you lack the ability to understand the math.

Once again I have to mention to you that math is not physics and when your mathematical model is discordant with physical reality, it is your model that has failed. But I have to admit that from our conversations, you seem to have no way of grasping physics except through the lens of the one model they taught you back there in school. You learned what to think, but not how to think. That much is obvious from the quality of your arguments. Or, in other words, you don't understand physics, only math. And math is not physics, Dave.

10. bud rap,

I was not taught either this or that approach. I have come to the conclusion that an instrumentalist approach is the only approach that does not require additional meta-physical assumptions and therefore is the only scientific one. I do not think this is in conflict with empiricism and do not know why you think so.

I further have no idea what relevance this has for our discussion because I have not asked you to subscribe to either this or that philosophy (which is the whole reason I am an instrumentalist -- you can keep whatever philosophy you like). If you want to use a different definition of "exist" -- one that is not supported by science -- that is fine with me, in principle. I am merely telling you that you are talking past us, and not in any interesting way, but merely by using a different definition of a word.

11. bud rap,

First, thanks for your comments, intended (I think) to clarify what you wrote earlier.

However, I'm still quite puzzled ... what did you intend this to mean? "The Keplerian method was used to calculate the expected rotation curves of galaxies??? Really???"

Why am I puzzled?

Because this source you quoted from:
https://ned.ipac.caltech.edu/level5/March01/Battaner/node3.html
does a nice job of explaining what "Keplerian" means (in this context). I realize that it contains equations, symbols, etc, and that you seem to have a particularly difficult time understanding such. Here, then, is a simpler description, one that avoids "mathy things":

A Keplerian rotation curve is a plot of rotation speed versus distance from the center of an astronomical system that obey's Kepler's laws. If most of the mass of the system is concentrated at the center, as in the solar system, then the speed of any orbiting body, such as a planet, is inversely proportional to the square root of its distance from the center. The fact that spiral galaxies don't have a rotation curve like this indicates that their overall mass distribution is different than the distribution of matter that can be seen. This is an important piece of evidence for the existence of large amounts of dark matter in the Universe.

Source: https://www.daviddarling.info/encyclopedia/K/Keplerian_rotation_curve.html

While it is called Keplerian, the underlying physical theory is that of Newton ("universal gravitation").

The rotation curves of (spiral) galaxies are what they are (modulo observational uncertainties, which are almost always carefully described and characterized). Interpreting these observational results within the framework of Newtonian physics is common, as is interpreting almost all astronomical observations within the framework of well-established theories of electromagnetism and quantum mechanics (via theories of how atoms behave, for example).

So, if rotation curves are interpreted this way, there is an apparent inconsistency: the estimated mass (from the rotation curves) is greater than the estimated mass (from the light).

What you seem to be saying is that it is, in some sense, invalid to use Newton's theory of gravity in interpreting such observations.

Are you?

12. Jean Tate,

What you seem to be saying is that it is, in some sense, invalid to use Newton's theory of gravity in interpreting such observations.

There is nothing wrong with Newton's theory of gravity. What is completely wrong, is the use of a modeling framework, the Keplerian/Newtonian approximation technique, wherein all of the mass interior to the orbit of a body under consideration is treated as being at the center of the orbit, and all of the mass exterior to the orbiting body is ignored. The system is thus reduced to a two body problem.

That technique is perfectly valid, to a first approximation, in the context of the solar system where 98% of the mass is at the center of the system in the form of the sun.

However, it is a completely invalid technique in a system where the mass is widely distributed as is the case with a disk galaxy. The proof of that statement is simply that when such calculations are made, they do not agree with observations.

Why anyone who understood the basic physical differences between the two systems would expect otherwise, is a great mystery to me. Here you have helpfully laid out a textbook example of the illogical underpinnings of the dark matter paradigm:

I've broken a single paragraph into its two sentences. There is nothing essentially wrong with the first:

If most of the mass of the system is concentrated at the center, as in the solar system, then the speed of any orbiting body, such as a planet, is inversely proportional to the square root of its distance from the center.

The second sentence (emphasis added) contains the faulty analytical reasoning that leads to its illogical conclusion:

The fact that spiral galaxies don't have a rotation curve like this indicates that their overall mass distribution is different than the distribution of matter that can be seen.

This sentence is false as written. Its conclusion is based on the unstated assumption that the conditional of the first sentence (If most of the mass of the system is concentrated at the center, as in the solar system...) applies to a disk galaxy.

To state what should be obvious, that conditional does not apply to a disk galaxy and therefore the conclusion is utterly false.

It is a simple matter to correct this false sentence by replacing the final three emphasized words:

The fact that spiral galaxies don't have a rotation curve like this indicates that their overall mass distribution is different than the distribution of matter that is assumed in the model.

That statement accords with reality. The "missing mass" problem is entirely a result of an inexcusable modeling error, that people like you continue defending to this day. You claim to be puzzled, I'm flabbergasted by the inability of people who claim to be physicists to be that blinded by their mathematicism.

BTW, there are efforts being made by mathematicians with some sense of the physical that manage to properly incorporate what could be called gravitational viscosity (after Zwicky), or disk self-gravity. You yourself dismissed one of those efforts, by FW Cooperstock, on spurious grounds, in an apparent attempt to defend the dark matter status quo.

While Cooperstock used a GR approach, Feng & Gallo (https://arxiv.org/pdf/0804.3203v1.pdf) have been approaching the problem from a Newtonian perspective. Both efforts seem to be reasonably successful in approximating the mass distribution of a galactic disk to achieve reasonably accurate rotation curves without dark matter. Their work, shall we say, is not popular with the dark matter crowd.

In addition to all this, reality keeps beating you people over the head with simple, straightforward facts (Tully-Fisher, Radial Acceleration Relationship) clearly indicating that the rotation curves of galaxies only depend on the distribution of baryonic matter.

It doesn't matter. The new Dark Age of Mathematicism rolls along, as smugly self-satisfied, as it is clueless.

PhysicistDave noted (perhaps not in this thread?) that you seem to have a somewhat adversarial relationship with mathematics (I'm paraphrasing). Much of what you wrote in this comment seems consistent with that characterization. So, please excuse me, but I really don't feel up to even attempting to address how badly you seem to understand Newtonian gravity (maybe PhysicistDave feels differently).

re "You yourself dismissed one of those efforts, by FW Cooperstock, on spurious grounds". Hmm. I thought the main point I made was one I thought you'd be in favor of: the models in the published papers are inconsistent with empirical observations (the Phleps+ paper, for example).

re "Feng & Gallo (https://arxiv.org/pdf/0804.3203v1.pdf) have been approaching the problem from a Newtonian perspective. Both efforts seem to be reasonably successful in approximating the mass distribution of a galactic disk to achieve reasonably accurate rotation curves without dark matter. Their work, shall we say, is not popular with the dark matter crowd."

Hmm. The 2008 arXiv Feng&Gallo paper seems to have not been published in a relevant peer-reviewed journal (unlike at least some of Cooperstock's papers). It has been cited by zero other papers. Among its 28 references are two by the same authors. Both also seem to be not published in relevant peer-reviewed journals.

Perhaps that's a sign that the papers do not pass basic math/physics muster? Perhaps they fail - rather badly - at some rather basic level? And thus that their "reasonably successful" is moot?

But hey, maybe you yourself could have a go at seeing where the Feng&Gallo paper fails, well before they get into trying to make comparisons with observational results?

14. @ Jean Tate,

I do not have an adversarial relationship with mathematics or with mathematicians. However, I do have an adversarial relationship with mathematicism. (https://en.wikipedia.org/wiki/Mathematicism) and its proponents in the scientific community.

As far as I'm concerned mathematicism is an ill-thought out philosophy that has no basis in scientific reasoning and no place in a scientific endeavor. Mathematicism is, unfortunately however, the operational paradigm of modern theoretical physics.

You and Dave, are perfect examples of people who approach science through the mathematicist framework. You are a loss to defend your positions (except with arguments from authority), when that framework is in question.

Take the issue we are discussing in this thread, the Keplerian analytical error as source of the empirically-failed, dark matter hypothesis. Suddenly, you've dropped the subject and wish to discuss peripheral issues. Can I take that to mean that you concede the point or ...?

I'm not going to let you change the subject just because you are unable to defend your position, however ill-defined that position is, beyond being merely an oppositional defense of a failed model. I will in an appropriate thread, address the mathematicist basis for your spurious dismissal of Halton Arp's work.

15. Sabine,

I further have no idea what relevance this has for our discussion because I have not asked you to subscribe to either this or that philosophy (which is the whole reason I am an instrumentalist...

But instrumentalism is a philosophy and on the basis of that philosophy you have declared my position "wrong" regarding the meaning of the term "direct observation". To you and Dave the term apparently has no valid scientific meaning whereas to me, the existence of an objective reality accessible via empirical (direct) observations is the fundamental basis of all scientific endeavors.

Further, I don't see the scientific basis for instrumentalism since it undermines that empirical basis, by essentially denying the centrality, and even the possibility, of empirical observations, and replacing it with a reliance on mathematical formalisms that can be made (via free parameters) to "predict" regularly occurring, observed phenomenon. Doesn't that open the door to Ptolemaic-like errors re the nature of physical reality?

16. bud rap wrote to JeanTate,
>I do not have an adversarial relationship with mathematics or with mathematicians. However, I do have an adversarial relationship with mathematicism. (https://en.wikipedia.org/wiki/Mathematicism) and its proponents in the scientific community.

Well, here is the summary from the source you cite:
>(Mathematicism is any opinion, viewpoint, school of thought, or philosophy that states that everything can be described/defined/modelled ultimately by mathematics, or that the universe and reality (both material and mental/spiritual) are fundamentally/fully/only mathematical, i.e. that 'everything is mathematics' necessitating the ideas of logic, reason, mind, and spirit. ) and its proponents in the scientific community.

I certainly do not think that "everything can be described/defined/modelled ultimately by mathematics." In fact, I am on the record going back decades (if you really care I can dig up some Web links) as criticizing mathematical economics, for the simple reason that mathematical economics has empirically failed to predict economic reality. And this really should not be surprising to anyone familiar with math and with human behavior: anyone who thought the behavior of millions of human beings could be simply modeled mathematically is pursuing a pipe dream.

Nor do I share the view that "the universe and reality (both material and mental/spiritual) are fundamentally/fully/only mathematical." I do know of one physicist, Max Tegmark, as your article notes, who does hold this view, but I (and I suspect most physicist) view Max's views on this matter as a bit loony.

To the degree that my views can be squeezed into any of the little boxes that philosophers have invented, I am, as I suspect most scientists are, an empiricist, specifically A Lockean empiricist (if you want to identify my views -- on politics, metaphysics, or theory of knowledge -- with any famous classical philosopher, John Locke would usually be the closest fit).

What I do think is that all successful theories in physics have been mathematical, going all the way back to Galileo, and that the only precise method humans have come up with for describing the physical world is mathematics.

So, for example, when you and your friends try to attack General Relativity, I and other physicists are going to appeal to the mathematical formulation of GR as determinative, for the simple reason the GR just is a mathematical theory.

There is not and never has been a non-mathematical form of General Relativity!

bud rap also wrote:
>Take the issue we are discussing in this thread, the Keplerian analytical error as source of the empirically-failed, dark matter hypothesis. Suddenly, you've dropped the subject and wish to discuss peripheral issues. Can I take that to mean that you concede the point or ...?

>I'm not going to let you change the subject just because you are unable to defend your position, however ill-defined that position is, beyond being merely an oppositional defense of a failed model.

Well, Jean gave you a reference which said:
>A Keplerian rotation curve is a plot of rotation speed versus distance from the center of an astronomical system that obey's Kepler's laws. If most of the mass of the system is concentrated at the center, as in the solar system, then the speed of any orbiting body, such as a planet, is inversely proportional to the square root of its distance from the center. The fact that spiral galaxies don't have a rotation curve like this indicates that their overall mass distribution is different than the distribution of matter that can be seen. This is an important piece of evidence for the existence of large amounts of dark matter in the Universe.

Exactly. We all agree that the galactic rotation curves are not at all Keplerian, and this is part of the evidence for dark matter!

17. JeanTate,

I think I have finally figured out the source of our friend bud rap's "Keplerian" hangup.

I think bud believes that astrophysicists naively assumed that galactic rotation curves should be Keplerian for a disk galaxy, which of course they will not be, and that therefore when the curves (of course) turned out not to be Keplerian, the astrophysicists immediately started screaming "Dark matter! Dark matter!"

A lot of the pop-science sites do compare the Keplerian curve to the actual curve, when of course they should show the curve you would expect from visible matter compared to the actual curve, hence bud's confusion.

Perhaps you can reassure bud that this is not what happened: i.e, that astrophysicists knew they had to correctly take into account all known sources of gravitating matter and not blindly assume Keplerian motion; however, if you do this with visible matter as carefully as possible, you cannot account for observed galactic rotation curves.

And, so they found the only way to account for those curves was to postulate "dark matter."

I cannot find a layman's explanation of this: here is a technical explanation that illustrates that, yes, astrophysicists do not expect a thin disk to produce a field that results in Keplerian motion, but I assume this will be way beyond bud mathematically (given the elliptic integrals, etc.).

By the way, if our friend bud cherry picks from this site, he will try to convince us that you don't need dark matter (because the author notes that the effect of dark matter is not prominent in the inner parts of the galaxy). It is therefore worth quoting the author's conclusion:
>"These radio observations therefore leave no doubt about the presence of a large amount of dark matter in these galaxies."

If I am reading him correctly, the author is saying that the key data is the 21 cm line from neutral hydrogen clouds beyond the visually bright areas of the galaxy:
>"Thus, we see that the evidence from HI rotation curves of external galaxies is clear: galaxies must be surrounded by extended distribution of non-luminous, dark matter."

Here is an only slightly less technical site making similar points.

For the record: I myself do not know the source of dark matter or even if there is some other explanation for the galactic rotation curves: I am not an astrophysicist. However, I am pretty sure that astrophysicists are not incompetent morons who are making the mistake that bud seems to think they are making. I.e., I do think the sites I have linked to here do prove that, yes, astrophysicists do know that a thin disk will not lead to Keplerian motion.

All the best,

Dave

18. bud rap,

I am aware that instrumentalism is called a philosophy, but it is not. Instrumentalism is a fact. Our theories *are* instruments that *do* describe nature. There is nothing philosophical about it. It would be philosophical to posit that theories are nothing besides that. I make no such assumption. In particular I am not an anti-realist. And instrumentalism certainly does not undermine any empirical basis. I have no idea why you think so.

Try to write down a definition for "direct observation" and hopefully you will see what Dave and I mean.

"by essentially denying the centrality, and even the possibility, of empirical observations, and replacing it with a reliance on mathematical formalisms that can be made (via free parameters) to "predict" regularly occurring, observed phenomenon."

This is complete nonsense. Again I have no idea why you think instrumentalism "denies the possibility of empirical observation". It certainly does not.

19. bud rap wrote to me:
>Once again I have to mention to you that math is not physics and when your mathematical model is discordant with physical reality, it is your model that has failed.

Of course, but theories in physics are presented in mathematics and so to understand what those theories say, you have to deal with the math. You cannot know whether or not the theories are true until you know what the theories assert, and you and your friends here have been refusing to do that with Einstein's theories, which are indeed stated in mathematics. The words Einstein or others use to try to explain those theories in simple-minded terms to non-physicists are no substitute for the math.

>But I have to admit that from our conversations, you seem to have no way of grasping physics except through the lens of the one model they taught you back there in school.

What "one model" is that??? That physics is expressed using math? As old as you may be, that "one model" goes back way before your time, all the way to Galileo.

bud rap also wrote to me:
>You learned what to think, but not how to think. That much is obvious from the quality of your arguments. Or, in other words, you don't understand physics, only math. And math is not physics...

You're just being foolish. As I said earlier, I have used my understanding of math and physics to design and build things that actually worked in the real world, ranging from a drift chamber for a large experiment at SLAC to ICs that won our team an Emmy from the Academy of Television Arts and Sciences to an error-correction system on Adaptec hard-drive controllers that you yourself may have used back in the 1990s on your PC.

I have not only published scientific papers resulting from close collaboration with experimentalists but am also co-inventor on various patents.

You will have trouble finding a STEM person who has had more experience successfully applying high-level math to actual physical systems that were built and that worked.

Your belief that I am a "mathematicist" unable to connect math to the physical world is just your sick bizarre delusion.

You on the other hand...

Again, bud rap, fill in the blank: Bud rap's accomplishments in applying math and physics to building things that actually worked in the real physical world consist of ___________ ?

Not counting the times you replaced light bulbs.

Seriously -- inquiring minds want to know.

You are very good at dishing out insults to people vastly more successful than you, but very, very close-mouthed about your own experience... or lack thereof.

20. Thanks to bud rap, PhysicistDave, and Sabine for all your comments.

Thanks especially to PhysicistDave for the link to "The kinematics and dynamics of galactic rotation". It's more up to date than bud rap's source (https://ned.ipac.caltech.edu/level5/March01/Battaner/node3.html) and a bit more extensive.

I've given up trying to understand your "Keplerian" points, bud. Perhaps you could try again? Start with how astronomers obtain a spiral galaxy rotation curve, then describe precisely where and how "Keplerian" enters into analyses of these observations.

A brief backgrounder on what astronomers think of spiral galaxies; as before, this is mostly from memory, and will likely contain some over-simplifications, omissions, and possibly mistakes.

It's only ~a century since the Shapley-Curtis Debate, after which the nature of spiral* galaxies ("spirals") as external to our own Milky Way became widely accepted.

The major constituents of spirals, that we can see using photons, are stars, dust, and "gas" (which is more accurately called plasma). Other constituents which we largely infer include cosmic rays, objects larger than dust but smaller than stars (e.g. "interstellar comets" and "rogue planets"), and black holes (other than the super-massive ones found in the center of spirals' nuclei; these are inferred from LIGO observations and HMXBs).

A spirals' rotation curve can be obtained from observations of stars, gas, or dust (though this last one is quite difficult); or more accurately, analyses of photons thought to arise from these (or, for dust, absence of photons). In terms of estimated mass, stars generally dominate (and minor constituents' - cosmic rays, stellar mass black holes, etc - combined mass is estimated to be trivial). When you add up the estimated mass of stars, gas, and dust in any particular spiral, you find that in some spirals that mass seems to account for the observed rotation curve (e.g. NGC 801), while in others it is woefully inadequate, especially in the outer parts. Hence dark matter (technically CDM, cold dark matter). And FWIW, analyses of observations of gravitational lenses, where the "lens" is a spiral galaxy, are consistent with the inferred distribution of mass from analyses of rotation curves (there are, sadly, rather too few of such lenses, so far).

Of course you can write hypotheses in which spirals have no CDM, but to do so while keeping consistency with all relevant observations and experimental results is quite a challenge. In particular, you nearly always have to change your theory of gravity; MOND (or a relativistic version) is one such which seems to work fairly well (for spirals' rotation curves); Sabine has written about another (Stacy McGaugh wrote the astronomy paper).

* I'll ignore lenticular galaxies, for now; like spirals, they are disk galaxies.

21. Continued: ...

Now a few words about GAIA, the incredible space mission intended to estimate the "proper motion" of ~a billion stars, most of which are in the Milky Way. Per bud rap's comment (in several places) this is "a mechancial extension" of our eyes, so results from this mission are "empirical".

Eilers+ (2019) "The Circular Velocity Curve of the Milky Way from 5 to 25 kpc" reports estimates derived, in part, from GAIA DR2 observations. I think the paper is careful and clear, in terms of defining what "rotation curve" means and various models tested; in particular, note how they deal with the fact that individual stars' velocities differ with respect to the rotation curve. Note: this paper does not use the word "Keplerian" (at least, not that I could find).

Here's an empirical challenge: GAIA's observations assume that the perceived direction of any star is affected by the Sun's mass, per GR ("lensing" if you will), over the whole sky (in fact gravitational lensing by all solar system planets is assumed, though this effect is quite minor for most observed stars).

If, per bud rap, you believe that the speed of light (in a vacuum) is not constant throughout the cosmos, then your empirical challenge is what to do about the GAIA observations? One the one hand, they must be wrong (because GR assumes constant c); on the other, the derived proper motions seem to be internally consistent.

22. @PhysicistDave, re "I think I have finally figured out the source of our friend bud rap's "Keplerian" hangup."

IMO, bud rap's position seems similar to that of some posters in the crackpot website thunderbolts forum:
- anti-relativity
- "empirical" means "has been observed in the lab"
- dark matter and dark energy are nonsense, lacking empirical evidence
- ditto black holes and gravitational wave radiation
- the mathematics used by theoretical physicists (and astrophysicists) is bunk

Thus bud rap's research program is something like this: scour reliable sources for apparent inconsistencies (e.g. c is not constant throughout the cosmos), and the use of "invalid" analyses (e.g. Keplerian rotation curves). Having found such, write strongly worded comments here.

However, as we have seen many times, much of what is posted is based on mis-understanding or mis-representing the actual physics (or astrophysics or cosmology). And there's considerable reluctance to discuss details.

It's a powerful approach! The only possible crack is, I think, how to square astronomical observations obtaining using GR (etc) with "empirical" (or mechanical extensions of our eyes). Specifically, explaining GR or rotation curves is a weak response (except, obviously to other readers), if only because such explanations necessarily involve the verboten mathematics.

An example: there's a brief discussion of a paper by Lopez-Corredoira+, elsewhere. To me, and I think to anyone who reads it, the case presented (for "discordant redshifts") rests heavily on the statistical model used to estimate the probability of chance alignments. But bud rap did not want to discuss that! Nor even acknowledge that that model is central to the discordant redshift case! (no surprise that the model is inconsistent with the empirical evidence, even without mechanical extensions).

23. @Jean Tate,

Jean says: GR assumes constant c

Einstein says: ...according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.

So either Einstein is right or you are. My money is on Einstein. If, however, you think you can frame a logical, scientific argument in defense of your position, please do so.

As to your intuitive "feelings" re my positions on certain scientific matters you are basically full of crap. In particular, I object to the characterization that I am anti-relativist.

On the contrary, I am what you might call a strict-constructionist regarding Relativity Theory. I believe the theory is sound as written and understood by Einstein. My only objection is to modern interpreters who say dumb things like: "...GR assumes constant c..."

Then, there is this wholesale fabrication: "empirical" means "has been observed in the lab" I have never said or implied any such thing - never. You are a prevaricator, Jean.

Another thing I have not said or implied: the mathematics used by theoretical physicists (and astrophysicists) is bunk Mathematics is not the problem, it is the people, like you and Dave, who cannot distinguish clearly between mathematical models and physical reality who have made a mess of modern theoretical physics.

Lastly, you completely mischaracterize the nature of our discussions of Arp and the Lopez-Corredoira+ paper. I have stated in at least one of those discussions that statistical arguments, whether pro or con, cannot in themselves definitively determine the nature of Arp's empirical observations.

The statistical argument against the apparent discordant redshifts that Arp specifically noted as associating high redshift quasars with lower redshift AGNs with a full galactic structure, is meaningless dissembling. The nature of those observations can only be determined by studying those observed systems closely over an extended period of time. That type of study has been denied telescope time since early on - on the basis of dubious statistical arguments.

24. Dave says:

I think bud believes that astrophysicists naively assumed that galactic rotation curves should be Keplerian for a disk galaxy, which of course they will not be, and that therefore when the curves (of course) turned out not to be Keplerian, the astrophysicists immediately started screaming "Dark matter! Dark matter!

A lot of the pop-science sites do compare the Keplerian curve to the actual curve...

Sure Dave, anything you say. Except that in this very thread I cited a number of non-pop-sci sources, including one of the urtexts of the dark matter delusion:

Thus the smallest Sc's (i.e., lowest luminosity) exhibit the same lack of a Keplerian velocity decrease at large R as do the high luminosity spirals.
- Rotational Properties of 21 Sc With A Large Range Of Luminosities And Radii..., Rubin, et al, 1980

I'm only presenting this again for the benefit of anyone trying to follow along through Dave's dissembling rants. But just for fun let's repeat the citation from a course at Dave's alma mater, CalTech:

At large distances from the galactic centre the gravitational potential should be that produced by a central point mass and, in the absence of forces other than gravitation, it should be expected that (equation removed because of formatting issues - can be found at site below), which is called, for obvious reasons, the Keplerian rotation curve. This Keplerian decline was not observed...

- From: https://ned.ipac.caltech.edu/level5/March01/Battaner/node3.html

I honestly can't decide what to think about Dave and Jean Tate. Are they really as clueless as they seem or only trolling? Most of the time I suspect the latter, but every now and then I think maybe...

The rest of the citations invoking an expected Keplerian decline can be found above at:

bud rap 10:20 PM, January 02, 2020

25. bud rap,

You quote Einstein but clearly do not understand how his theory works. This, I am sorry, is typical crackpot behavior. Go look up a textbook and do a calculation in GR and you will see that Dave is, of course, correct.

Also, this discussion has strayed far off the topic and ends here. If you want to continue it, please do so elsewhere. Thanks.

26. bud rap wrote to JeanTate:
> Einstein says: ...according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.

>So either Einstein is right or you are. My money is on Einstein. If, however, you think you can frame a logical, scientific argument in defense of your position, please do so.

Bud, if GR does not assume a constant c, why do you suppose textbooks on GR routinely set c equal to 1? The number one is about as constant a constant as you can get!

Or, do you once again assume that the textbook writers are all ignoramuses compared to the great genius bud rap?

We have explained to you the Einstein quote in detail: if you use coordinate time that does not correspond to local clocks, then, yes, you will calculate a speed of light less then (or sometimes greater than) one. As I said to you, this is the same as using a tape measure that has its marks spaced twice as far apart as usual and then concluding that you are only 2 1/2 feet tall instead of your usual 5 feet.

But if you use local clocks (e.g., spectral lines) then, yes, the speed of light is always constant. You are just refusing to understand these simple facts.

Trying to talk to you is becoming absurd: even when we explain something to you in simple English, you just act as if you have not read it.

Come to think of it, I am coming to realize you do not read it: you just skim for some sentences you can froth at the mouth at.

As Sabine suggests, we are wasting our time.

If you had a brain tumor, I am sure that you would not allow me to cut out that brain tumor, even though I am in fact interested in neural science and have read various books on the subject.

Yet, you think your judgment is so superior to those of us who have Ph.D.s in natural science, that when we point out mistakes in your thinking, you will not even seriously consider that we might be right and try to understand what we are telling you.

This truly perplexes me: you seem to think it is enormously easier to learn modern physics than to learn brain surgery.

It isn't.

All the best,

Dave

27. bud rap wrote to me:
>But just for fun let's repeat the citation from a course at Dave's alma mater, CalTech:

>At large distances from the galactic centre the gravitational potential should be that produced by a central point mass and, in the absence of forces other than gravitation, it should be expected that (equation removed because of formatting issues - can be found at site below), which is called, for obvious reasons, the Keplerian rotation curve. This Keplerian decline was not observed...

Yes, bud, and that is indeed correct (I thought this was part of your misconception here). Far enough away from any collection of mass, the collection just looks like a point source, and therefore you should see nearly Keplerian orbits.

bud also said:
>Except that in this very thread I cited a number of non-pop-sci sources, including one of the urtexts of the dark matter delusion:
>[quoted text] Thus the smallest Sc's (i.e., lowest luminosity) exhibit the same lack of a Keplerian velocity decrease at large R as do the high luminosity spirals.[emphasis added]

Again, "at large R" is the key here: far enough away from any collection of mass, it should look like a point source and you should see nearly Keplerian orbits. Unless, of course, there is other mass you are not seeing that wrecks things, such as CDM.

I am responding to this so that anyone happening by will see closure to this issue.

bud, you are probably a basically decent fellow, a decent dad, neighbor, etc. But for some reason, you are not recognizing that people with many years of education and experience in a field probably do know some things you do not, and if you would listen to them you can learn from them.

I myself am a harsh critic of much of what is going on in academic physics, even harsher in many ways than Sabine or Peter Woit. But, while I believe, for example, that many string theorists have over-hyped and over-sold superstring theory, I do not think they are simply morons from whom I can learn nothing.

I have in fact learned things from some of the leaders in the string field whom I happened to know -- Polchinski, Susskind, and Schwarz -- on matters not relating to strings. And of course I have learned things from string theorists about string theory, even while I remain more pessimistic about string theory than most of them are.

I haven't learned anything from you, bud, about physics, but no doubt if we were friends you could indeed teach me about something -- car repair, gardening, or whatever else you know about from your work or avocations.

I doubt that there is a person alive who could not teach me something. Perhaps you could consider the same attitude to people who have studied details of natural science that you did not have the opportunity to study.

Sincerely, I wish you all the best.

Dave

28. Dave says:Far enough away from any collection of mass, the collection just looks like a point source, and therefore you should see nearly Keplerian orbits.

Well, that's a nice fuzzy sentiment and but in the context of an actual galaxy with a disk system, it is completely irrelevant. Why? Because in order for the galaxy to appear as point source to an orbiting body, that body would have to be far outside the galactic system (not an orbiting component). Want proof?

Standing here on the planet earth in a completely separate galaxy, several million light-years distant, it is possible, with the naked human eye, to observe the nearby Andromeda galaxy as a fuzzy patch in the night sky. Therefore it follows Dave, that any orbiting body within the disk system of Andromeda will not be far enough away from it, for the galaxy as a whole to appear as a point source. QED

The Keplerian assumption is not physically viable anywhere within a disk galaxy. It was and is an error to assume otherwise. The other obvious proof of this is that using that assumption you cannot calculate the velocity curve properly anywhere within the galactic system.

Without the Keplerian expectation, there is no case for dark matter in galactic systems, unless you count the socio-economic imperative to provide employment for the dark matter contingent within the guild. Dark matter researchers are like firemen on a diesel locomotive.

29. I'm going to try, one more time, to understand what you're saying, bud rap.

I'll start with the Rubin+ (1980) paper already cited in this thread. I find nine instances of the word "Keplerian" in that paper (do you agree?).

In the text (i.e. not Figures), the first instance is the one you have quoted, more than once. Here it is, with full context:

"In general, the rotation curves are characterized by velocities increasing with radius; only the largest galaxies have rotation curves which are flat. Thus, the small Sc’s exhibit in their rotational properties the same lack of Keplerian decreasing velocities as do the high-luminosity galaxies (Paper IV)."

To understand how "Keplerian" is used here requires us to read Paper IV. So I'll postpone that for now.

The next instance comes just a few sentences later (I've put it in bold):

"In many galaxies, positive velocity gradients are observed across a spiral arm; velocities on the inner edges are often tens of kms”1 lower than velocities on the outer edges. Significantly, the velocity decrease from the outer edge of one arm to the inner edge of the next arm is faster than Keplerian in some regions of five or six galaxies, i.e., faster than R^1/2. This is compelling evidence that noncircular velocities are present, in violation of our initial assumption of only circular orbits."

Can you please explain, in some detail, what you think is wrong with this?

30. bud rap, you wrote: "The nature of those observations can only be determined by studying those observed systems closely over an extended period of time. That type of study has been denied telescope time since early on - on the basis of dubious statistical arguments."

First, I think you meant "systems", not "observations" (The nature of those observations). Did you?

Second, what - in detail - would you consider to be "studying those observed systems closely over an extended period of time"?

Third, what - in detail - is "dubious" about the "statistical arguments"?

31. bud rap wrote to me:
>The Keplerian assumption is not physically viable anywhere within a disk galaxy. It was and is an error to assume otherwise.

bud, I gave you two references that you can look at to your heart's content that show they are not doing this.

I am starting to understand where you are coming from: you are taking imprecise or misleading statements from one or a few documents and construing them in a way that makes it sound as if all scientists in the field are doing the wrong thing.

This is clearly what is going on with antooneo and your discomfort with light-signaling synchronization. This is mathematically the simplest form of syncrhonization to explain, so textbooks have a tendency to use it. But, yes, as I have explained in my exchanges with Amos, it is somewhat begging the question -- it could look to a non-physicist as if we are "cheating" by using a weird form of synchronization that brings about the results we want.

That is not what is happening. As I explained to Amos, you can prove that light-signaling synchronization gives the same result, to as high an accuracy as you need, as simply synchronizing clocks the old-fashioned way.

Similarly with your claims that the speed oflight in vacuo varies: as I have explained in enormous detail, if you insist on using non-local clocks that do not keep track of local time (this is what Einstein was talking about), then you will get a non-constant speed of light. But if you use local clocks and distance measurements, the speed of light will be universal. Yes, words (even Einstein's words!) can be ambiguous in making this clear. But is should be clear once I explain it. And the math is not ambiguous.

The main reason you are not getting a response that satisfies you from any of the scientists here is that you are simply saying in effect, "I, bud rap, know scientists are wrong," when the truth is you are misunderstanding some point on which the scientists are not wrong. If you were less antagonistic and instead would say, "I, bud rap, am confused and do not understand this which looks to me as if it were wrong," you would be more likely to get an explanation.

You are taking situations in which one scientist worded something in a way that is confusing to you and then using this to play "gotcha!" with all scientists.

This is not going to get you a positive response. Sabine, JeanTate, and all the rest of us are not responsible for the way that some random scientist chose to imprecisely or ambiguously word what he said in a way that confused you.

If you would try to be polite, we could try to clear up the confusion. But this seems not to be part of your personality.

You should realize that we have no obligation to talk with you at all, and we do have other things to do.

A bit of politeness and, yes, humility on your part would work wonders, but you seem not to have this in you.

32. More on (spiral) galaxy rotation curves.

Jo Bovy's document, which PhysicistDave provided a link to, is a good place to start if you're attempting to understand this topic (link: http://astro.utoronto.ca/~bovy/AST1420/notes/index.html). Quote from the Preface:

"I had various objectives in writing these notes. The first is that while excellent, graduate-level books on this topic exist (foremost “Galactic Dynamics” by Binney & Tremaine, hereafter BT08), in preparing for my class I found that the detailed, deep, and exhaustive treatment of all important topics in galactic dynamics that can be found in BT08 is likely to be overwhelming to students just starting out in the field."

This points to a phenomenon I think is worth spending some time on, namely that written works tend to have a target audience. In the case of Bovy's notes, it is clearly stated. For papers intended for peer-reviewed journals, it is generally fellow professionals. A corollary: if you are not a professional astronomer, it is likely that you will find papers hard to understand (at least in part). Not certain, because you do not, in fact, need a PhD in astrophysics (say) to be able to read and understand such papers. However, what you will almost certainly need is an understanding of key parts of documents like Bovy's if you want to understand papers on spiral galaxy rotation curves.

With regard to "Keplerian", it seems to me you, bud rap, are seeking to impose meaning on how this term was (and still is?) used without trying to understand the context ... but we'll get a better idea if you respond to my earlier comment.

The Rubin+ (1980) paper you cite is a landmark one; it is widely cited as the first to conclude that CDM is a major constituent of spiral galaxies. I certainly hadn't noticed this before, but it may be that the use of "Keplerian" may be declining ... Bovy rarely uses the term, and one of the most recent papers (on spiral galaxy rotation curves) to cite Rubin+ (1980) doesn't use it at all: den Brok+ (2019) "The MUSE Atlas of Disks (MAD): Ionized gas kinematic maps and an application to Diffuse Ionized Gas"

Bovy does use "Keplerian" in Section 9, "The kinematics and dynamics of galactic rotation" (twice, I think); here is one such: "Looking at the rotation curve of an exponential disk in Chapter 6, we see that at 11 disk scale lengths the rotation velocity should be less than half of the maximum rotation velocity and we should see a strong decline in the rotation velocity that is essentially Keplerian. That the actual rotation curve is flat means that NGC 3198 must have a large amount of matter beyond the optical radius: approximately four times as much (van Albada 1985)."

In context, this is perfectly clear ... if Newtonian gravity then lots of mass not seen in the optical.

No mathematicist conspiracy.

30. Did Einstien come up with a thought experiment first and then mathematically described it? Or did math lead to thought experiments?

>Did Einstien come up with a thought experiment first and then mathematically described it? Or did math lead to thought experiments?

In the case of General Relativity, we actually have a great deal of evidence because Einstein published much of his work-in-progress, including quite a few mistakes and wrong turns.

It was a back-and-forth between thought experiments and the math. For example, his initial published prediction on the deflection of light by the sun was off by a factor of two because he went with what you would naively get from the equivalence principle (the falling elevator and all that).

Fortunately, the observations were not made right away, and so Einstein had a chance to correct his error well before Eddington's 1919 expedition.

I know of no way to get the correct result without doing the math. I myself have worked out an easier way of doing the relevant math than what is presented in most textbooks (the second monograph I am working on), which emphasizes more physical understanding and less advanced math. But, in the end, you still just have to do the math.

The same is true for Maxwell's discovery of the displacement current, for Newton's proof of Kepler's laws, for Planck's derivation of the black-body radiation, for Schrödinger and Heisenberg's independent inventions of quantum mechanics, etc.

None of this was possible to anyone who did not bother to master the relevant math (to be sure, Heisenberg needed some help from Born, as Einstein needed help from Grossmann -- but both physicists did realize that they needed the help with the math and went to the trouble to get it).

Physics is not possible without math and a real understanding of physics is only possible for those willing to learn the relevant math.

31. Sabine wrote,
"What’s fascinating about theoretical physics is just how remarkably well mathematics describes nature"
I can't entirely agree to it. Take the Dirac delta. It is used in many physical disciplines. This distribution can only be convolved with extremely well-behaved functions, unlike most fields in nature. Many of them behave well, but not that extremely well (e.g. they do not vanish outside any bounded interval). Physics is an idealization of reality, which is fine with me, but I would rather be able to convolve the delta with any continuous function, for example, because too many idealizations may eventually turn physics not even real. Or take the divergences in QED. The same divergences that prevent gravity from being quantized. They walk the tightrope of mathematical correctness, to say the least. And this is just to name two examples. I actually think that our maths do not describe nature so well, and that this is part of the problem we currently face with HEP.