Thursday, January 22, 2015

Is philosophy bad science?

In reaction to my essay “Does the scientific method need revision?” some philosophers at Daily Nous are discussing what I might have meant in a thread titled “Philosophy as Bad Science?”:
“[S]he raises concerns about physicists being led astray by philosophers (Richard Dawid is mentioned as an alleged culprit [...]) into thinking that observation and testability through experimentation can be dispensed with. According to her, it may be alright for mathematicians and philosophers to pontificate about the structure of the universe without experimentation, but that, she says, is not what scientists should be doing.”
The internet has a funny way of polarizing opinions. I am not happy about this, so some clarifications.

First, I didn’t say and didn’t mean that philosophy is “bad science,” I said it’s not science. I am using the word “science” here as it’s commonly used in English where (unlike in German) science refers to study subjects that describe observations, in the broad sense.

Neither am I saying that philosophy is something physicists shouldn’t be doing at all, certainly not. Philosophy, as well as the history and sociology of science, can be very helpful for the practicing physicist to put their work in perspective. Much of what is today subject of physics was anticipated by philosophers thousands of years ago, such as the question whether nature is fundamentally discrete or continuous.

Scientists though should in the first place do science, ie their work should at least aim at describing observations.

Physicists today by and large don’t pay much attention to philosophy. In most fields that doesn’t matter much, but the closer research is to fundamental questions, the more philosophy comes into play. Presently that is mostly in quantum foundations, cosmology and quantum gravity (including string theory), and beyond-the-standard-model physics that relies on arguments of naturalness, simplicity or elegance.

Physicists are not “led astray by philosophers” because they don’t actually care what philosophers say. What is happening instead is that some physicists — well, make that string-theorists — are now using Richard Dawid’s arguments to justify continuing what they’re doing. That’s okay, I also think philosophers are better philosophers if they agree with what I’ve been saying all along.

I have no particular problem with string theorists, most of which today don’t actually do string theory any more, they do AdS/CFT. Which is fine by me, because much of the appeal of the gauge-gravity duality is its potential for phenomenological applications. (Then the problem is that they’re all doing the same, but I will complain about this another time.) String theory takes most of the heat simply because there are many string theorists and everybody has heard of it.

Just to be clear, when I say “phenomenology” I mean mathematical models describing observations. Phenomenology is what connects theory with experiment. The problem with today’s research communities is that the gap between theory and experiment is constantly widening and funding agencies have let it happen. With the gap widening, the theory is increasingly more mathematics and/or philosophy and increasingly less science. How wide a gap is too wide? The point I am complaining about is that the gap has become to wide. We have a lack of balance between theory disconnected from observation and phenomenology. Without phenomenology to match a theory to observation, the theory isn’t science.

Studying mathematical structures can be very fruitful for physics, sure. I understand that it takes time to develop the mathematics of a theory until it can be connected to observations, and I don’t think it makes much sense setting physicists a deadline by which insights must have appeared. But problems arise if research areas in physics which are purely devoted to mathematics, or are all tangled up in philosophy, become so self-supportive that they stop even trying to make contact to observation.

I don’t know how often I have talked to young postdocs in quantum gravity and they do not show the slightest intention to describe observation. The more senior people have at least learned the lip confessions to be added whenever funding is at stake, but it is pretty obvious that they don’t actually want to bother with observations. The economists have a very useful expression that is “revealed preferences.” It means, essentially, don’t listen to what they say, look at what they do. Yes, they all say phenomenology is important, but nobody works on it. I am sure you can name off the top of your head some dozen or so people working on quantum gravity, the theory. How many can you name who work on quantum gravity phenomenology? How many of these have tenure? Right. Why hasn’t there been any progress in quantum gravity? Because you can’t develop a theory without contact to observation.

It is really a demarcation issue for me. I don’t mind if somebody wants to do mathematical physics or philosophy of science. I just don’t want them to pretend they’re doing physics. This is why I like the proposal put forward by George Ellis and Joe Silk in their Nature Comment:
“In the meantime, journal editors and publishers could assign speculative work to other research categories — such as mathematical rather than physical cosmology — according to its potential testability. And the domination of some physics departments and institutes by such activities could be rethought.”


  1. There does exist a stringy/brane description of topological insulators and superconductors. Such materials are cutting edge experimental science at its best. Magnetic monopoles, dyons, axions and Majorana fermions, which are usually highly theoretical objects, become subject to measurement in the condensed matter regime. Currently, it appears many technological innovations will arise from applying string theory ideas to condensed matter. ( arXiv:1007.4234 [hep-th], arXiv:0908.1537 [cond-mat.other], arXiv:0811.1303 [cond-mat.mes-hall])

  2. Yes, as I said in my post, interesting stuff. What's your point?

  3. Philosophy is often kept in disdain with physicists, but it's true value is actually exactly the same, like the validity of formal math, providing its semantically correct and logical. Not accidentally many heavily mathematic modern physical theories (stringy and loopy models) and concepts (multiverse, antropic principle) don't differ very much in their falsifiability from deep but vague ideas of natural philosophers.

    If philosophy turns out to be nonsense, then from the same reasons, like the formal math: it's not math or philosophy itself, what gets wrong there - it's their assumptions and prerequisites.

  4. I like what Alvaro De Rujula says -
    "... dataphobia - a morbid condition of the brain that turns theoretical physicists into mathematicians ... "

    see "50 years of Yang Mills Theory"
    page 406. "A Phenomenological point of View".

    That said - the problem with physics is that you STILL can not explain exactly what distinguishes a muon from an electron or a tau. You can measure the mass and lifetime - that is nice, but it is not sufficient to explain the mystery to anyone's satisfaction.

  5. A most excellent reply, Sabine. I expected philosophers and reasonably educated journalists to read and understand you. My idealism is foolish I guess. Things that make us sad evoke desire for returning injury (Spinoza) but if we must reply in kind we should not relish or fear it done objectively. Darwin is Great also in this half rational half empirical half blind minds. We are not uncaring robots.

  6. Joel,
    The generation problem and its solution was no surprise to me so how do you know there are not solutions in the world?
    I like what Conway said "calculus is a way to torture wave after wave of uncomprehending freshmen undergraduates."
    Sabines writes clearer English than I do.
    Those undergraduates evidently grow up to be journalists who justify they cannot understand the data. As do some tenured professors who peaked then coasted on their early achievements. You cannot measure that over a lifespan nor assume after hard work nature is so pointless as to have any of us instantly vanish with such work.

  7. I just don’t want them to pretend they’re doing physics.

    I find the wording of statements like this problematic. First of all it gives the impression that you think string theory (for example) is fraudulent, that people working on it have a lack of intellectual honesty. I don't think this is true, and if you do you should be more candid about it.

    Second of all, it gives the impression that you are making a value judgement: that physics is superior to philosophy (for example). (Otherwise why would a philosopher "pretend" to be doing physics?) I don't think physics is "better" than philosophy, and if you do then again you should be more candid about it.

    Thirdly, it feels like a condescending jab and an attempt to seize the moral high ground, the kind of jab that leads to replies in kind rather than leading to level-headed benefit-of-the-doubt discourse about what is after all a difference of opinion among adults who are highly educated in what they believe to be the field of physics (they aren't pretending).

    Fourthly, I don't understand why we can't just call this work "mathematical physics" or some other subcategory of physics. We already have subfields within physics that are very different from each other. We call them all "physics" and if necessary distinguish them by subfield. It seems bizarre to me to get so worked up about whether we attach the word "physics" to a discipline that is after all so heavily physics-oriented, whose members are all highly educated in physics, whose primary goal is consistency with available empirical data, and that is after all just doing its best to "follow the logical trail wherever it may lead," even if that leads uncomfortably to nature possibly being different from how we would like her to be.

    Fifthly, as a follow-up to that last thought. Your side of these discussions seems to always leave out what I think should be a candid admission: that natural law may be anthropic, whether we like it or not. I think it is important for this to be out in the open because we need to be honest about what this (possibly counterfactual) possibility would mean for "physics." I think part of the worry on my side of the argument is that your side has blinders on to this possibility. For instance if hypothetically we do live in an anthropic world, your side of the argument seems to be trying to slow this realization down, even at the cost of the truth, out of what appears to be a disdain for what you characterize as "philosophy." What you don't seem to want to discuss openly is that if nature happens to be anthropic, then what you call "philosophy" has a lot more to say about nature than you seem willing to admit. This gets into difficult waters; of course we don't know whether nature is anthropic, but an open discussion about the possibility would go a long way I think to bridging the divide between the two camps on this issue. After all, both sides should be able to admit the possibility, right? And therefore discuss the possible consequences for the field of "physics"?

    tl;dr: The wording you used is representative of a broader problem in the framing of this discussion.

  8. L. Edgar Otto:
    "The generation problem and its solution was no surprise to me so how do you know there are not solutions in the world?"

    ??? what "solution" are you referring to ? As far as I know it is still a mystery.

  9. Unknown,
    How can truths you do not understand offend you. What side did you read Sabine was in? You cannot throw bull chocolate at her to appease her. But damn man, it is important our children live well and eat. Frustration does not necessarily lead to aggression. But in a reasonably civil society
    psychology is polarized in debate, but you cannot say that science in itself is not a very human enterprise or like free speech unfair to tyranny of imposed slavery.

  10. AdS/CFT? CFT is 2-D chiral math fit into 3-D achiral models requiring parameterization and perturbation. Cinderella's ("Aschenputtel", Brothers Grimm) stepsister chopped off her toes to fit the slipper, the other her heel. Both were falsified.

    Observe what can only be true if derivation is drylabbed. Perform atom-scale chiral geometric tests of spacetime geometry: 90 days in an Eötvös balance or one day in an FT microwave, IR, or Raman spectrometer. Yang and Lee were theoretic piss-ants December 1956. December 1957 was empirically different. Chirality matters.

  11. Too many theorists are not genuinely interested in real effects. The like to play with formalism since this relieves from trouble of thinking.

    A good quite recent example is so is called tau-mu anomaly for Higgs decays. There are 2.5 sigma indications that Higgs decays to tau-mu pair. What is seen as anomaly is that this decay occurs at all.

    Complex superstring inspired models postulating new particles and new parameters are proposed. The motivation of model builders seems to come from the skill of building complex models.

    This anomaly can be however explained by assuming just standard model plus neutrino mixing ('no leptonic neutral flavour changing currents' is coded by these assumptions). Higgs decaying to W pair decaying by neutrino exchange to tau-mu pair! This gives the basic prediction which any reasonable extension of standard model should give. Lubos has referred to this anomaly in a couple of postings and also I have considered it in detail.

  12. This comment is partly related to this and the previous post.I think, one should not complain too much about lack of experiments. Experimentalists have already done a good job of finding CC (Dark energy) and dark matter (indirectly any way).Granted that there is no direct evidence of dark matter. But Quantum theory of gravity will have to explain both dark matter and dark energy. If anyone explains one of these theoretically,there is no doubt, he/she will be on a flight to Stockholm!! So,I think, the ball is in the theorists' court now! It is just that people complaining about string theory are not coming up with alternative acceptable models!

  13. "... research areas in physics which are entirely devoted to mathematics ..." Any form of research that can get funding will be done by someone. Another problem is an unfair system of allocating funds for observational/experimental research. According to Pavel Kroupa, "... a leading member of the scientific community declared last year, as a reaction to the talks of my collaborators and by me, publicly at a conference in California that the Local Group of galaxies cannot be used to test the dark matter models, and modern research papers in which important properties of the distribution and dynamics of galaxies are completely ignored for the sake of a positive argument are not rare. But there are also many researchers who are convinced by the arguments. In some cases they fear of stating this publicly, believe it or not, lest they be subjected to subtle disadvantaging in getting their research grants or telescope time approved or in taking the next step in the tenure-track or career process. Some pretty horrifying stories have indeed come to my ear."

  14. No actual experimental observation was needed for Einstein to come up with its theory of general relativity: it was the outcome of pure thought. It was only later confirmed experimentally. Much of string theory research is in the same spirit: starting from a few basic assumptions one tries to develop the theory to its utmost extrapolations in order to see if it can indeed be verified. Unfortunately we still haven't been able to make such a verifiable prediction because of the complexity of the theory and because we actually don't know what the full theory is. In the process people have however discovered very interesting new structures and relations.It is now true that string theory research mostly resembles mathematics.

    Certain theories (especially strongly coupled theories like QCD) need very difficult calculations in order to compare with the experiments, so it is necessary to develop new techniques for doing the calculations. With the advances of science in the last century the problems left to solve are more and more difficult and no one single scientist or team can do all that is needed. That is why scientists are now much more specialized and we have experimentalists, phenomenologists and theorists.

  15. "No actual experimental observation was needed for Einstein to come up with its theory of general relativity: it was the outcome of pure thought."

    Well, he did ride in elevators, didn't he? I assume that he done so and been able to detect a difference between that sensation and one due to gravity alone that he would not have developed GR, since in such a counterfactual case, GR would not have been true.

  16. Hilary Lawson -The Pitch @ 12:50

    [QUOTE][I]We close the openness of the world[/I][/QUOTE]

    At 32:20 Hilary makes an obvious statement.

  17. Lillegruben:

    "No actual experimental observation was needed for Einstein to come up with its theory of general relativity: it was the outcome of pure thought."

    You are wrong. Einstein's theory of gravity needs experimental input. It needs Special Relativity, it needs the Newtonian limit, it needs energy conservation. Nobody could ever have constructed General Relativity by "pure thought," sitting in a dark room, not knowing anything about observations. What Einstein did was trying to resolve an existing inconsistency. This can work in some cases, but doesn't necessarily work, because such resolutions tend to be not unique.

    In fact, it doesn't really work in GR either, you still need to make extra assumptions, such as the way that gravity couples (via the stress-energy) and that the lowest order is linear in the curvature, not to mention that you want differential equations to begin with. These assumptions are all at the base of it observational based. You don't get them from "pure thought". The "pure thought" story is one of these genius myths that are haunting science.

    Your belief that Einstein's success was "pure thought" is exactly the problem I am trying to highlight, so thanks for demonstrating it. We have absolutely no support for the belief that there is one and only one way to make compatible quantum field theory with general relativity. To make matters worse, many approaches to quantum gravity don't even have these limits, they are even more "pure thought" as you phrase it, they are basically just "consistent things" that might or might not have something to do with nature. String theory at least has the basic ingredients in place. Best,


  18. David: Sadly, I'm not surprised by this at all.

  19. Grossmann is getting his doctorate on a topic that is connected with non-Euclidean geometry. I don’t know what it is.
    Einstein to Mileva Maric,1902

  20. From a early age, young Albert showed great interest in the world around him. When he was five years old, his father gave him a compass, and the child was enchanted by the device and intrigued by the fact the needle followed a invisible field to point always in the direction of the north pole.Reminiscing in old age, Einstein mentioned this incident as one of the factors that perhaps motivated him years later to study the gravitational field. God's Equation, by Amir D. Aczel, Pg 14

    Bold added for emphasis by me

  21. Only a rationalist would understand, that to be effective, one would need to be able "to see."

    A sensor and scientific world belongs to the empiricist and is not the same type of seeing I am referring.

    While it may have been "a mystery" for Einstein, he realize this had an effect on his future life in retrospect. Do we say he did not have thought experiments?

  22. Come on Sabine: now you're nitpicking! What I meant was that no deviation from Newtonian gravity was experimentally observed that led Einstein to consider and formulate his theory. As you say he wanted to resolve an inconsistency. My point simply was that much of string theory's spirit is the same.

  23. Lillegubben:

    First, the perihelion precession of Mercury was well known back then, so why are you saying no deviation was known?

    Second, I understand that string theory is "in this spirit", I am telling you that you are misreading and misinterpreting history to try to justify for which there is no justification. We have no reason to believe that there is only one way to consistently combine GR with quantum field theory. The idea that you can obtain a new theory by "pure thought" is nonsense. There is no historical precedent for this.

    I am not nitpicking. I find it worrisome that many people in theoretical physics today buy into the "pure thought" idea without ever questioning it or looking at the history.

    Besides this GR would never have been accepted hadn't it been for the light deflection on the sun (the first evidence wasn't what it was argued to be, but this is besides the point here). But we're supposed to believe in string theory based on exactly what? Best,


  24. Sabine:

    Point taken: I've learned that I'll better check my facts before posting on the internet. Still I don't beleive Mercury's perihelion procession was the main motivation for developing General Relativity.

    You're also right that the main problem with String theory is that it hasn't succeded in making an experimentally verifiable prediction. The thing is that String theory should be interpreted like a generalization of quantum field theory. QFT is actually not a theory but rather the framework with which the standard model is formulated.

    Is is very well possible that there is another way than string theory to reconcile QFT and GR, however most people suspect that any such attempt will eventually be connected by some kind of duality to some known part of string theory. The string theory community actually embraces the point of view that there is probably not one single definite description (i.e. theory) of our universe that is the truth, but rather that different (but mathematically equivalent) descriptions are relevant in different regimes.

  25. Lillegubben wrote: "Still I don't beleive Mercury's perihelion procession was the main motivation for developing General Relativity."

    It was. Judging from the reference below, Einstein had to change and fudge the equations countless times until "excellent agreement with observation" was reached:
    Michel Janssen: The Einstein-Besso Manuscript: A Glimpse Behind the Curtain of the Wizard

  26. Lillegubben:

    As Pentcho said, Einstein didn't just sit down and derive the field equations. It was a long and windy road, and he wrote down wrong equations more than once, exactly because he did not know a conclusive way to derive them. It was only *after* he had found the right equations that it became apparent just why they are right.

    Be that as it may, it's not really my point. See, Einstein was one guy who did his thing. He had some motivation, that might have been a good motivation or a bad motivation, in hindsight it doesn't matter because he got the right result, and now he's famous. That however doesn't mean that whatever was Einstein's motivation was a good motivation that should be copied by whole communities, and certainly not be used as justification.

    GR is one of the main examples that people like to quote for the "power of pure thought", but it's a bad example. Einstein was very much lead by phenomenology, much more than the later generations of physicists. His whole argumentation style with the thought experiments speaks for that.

    The example that people quote to me most is Dirac's equation. Again, it's a bad example. To begin with Dirac's equation isn't the only way to reconcile special relativity with quantum mechanics, Dirac just was lucky that he hit on the right way to do it at first try (right in the sense that it describes nature). But besides this Dirac's equation was predated by a phenomenological model from two Dutch guys, Goudsmit and Uhlenbeck. Again, it was phenomenology that lead the way, and the derivation came only afterwards.

    There is to my knowledge really no historical precedent when "pure thought" has lead to a correct theory. I am more than willing to hear an example if you know one. I have been giving talks with this argument for some years now and so far nobody has been able to come up with an example.

    I have no clue what you mean when you say that quantum field theory is not a theory. I think you're confusing theory with model. Quantum field theory is not a model. The standard model is a model. (It's one of the cases where the terminology is actually correct.)

    Yes, yes, I know the philosophy, string theory is a language, it doesn't have to be unique, it's a generalization of qft, any theory of quantum gravity in the end is part of M-theory and so on and so forth. Maybe that is so. Or maybe it's not. There's no proof for this, and I'm not willing to believe it just because other people believe it - this isn't how science should work.



  27. Bee:
    If i may pull an example from history. To me, figuring out muons is like figuring out spin. It came out of algebra. Jordan told Pauli about quaternions and out pops the Pauli equation. Pauli algebra is just complex quaternions. Algebra deals with structure - in this case simply that there are left handed and right handed electrons. Who Knew !
    Actually nobody knew, and that is why they were stuck.

    It was three guys - Kronig, Uhlenbeck and Goudsmit. Kronig made the mistake of asking Pauli and got the cold shoulder and never published.

    Once they got un-stuck all hell broke loose and we got spin-statistics and all that.
    So when I refer to physics being stuck today over structural questions - and Generations are certainly Structural, one can logically expect Algebra to come to the rescue. If Nature loves Quaternions, then Nature must also love Octonions.
    OK so it took L.H. Thomas to straighten out the factor of 2 in the Kronig-Uhlenbeck-Goudsmit model, but without spin they were up the creek. Certainly it must be a fact that if we do not know that Nature is making algebraic distinctions like left-right, then we are in that horrible mess that Heisenberg was in before spin.

    Much in Pais 'Inward Bound' and
    Tomonaga 'Story of Spin'

    Can I get an Amen ?

  28. my feeling about supersymmetry, since you mention strings, is that it is an attempt to evade dealing with Octonions ( which look like a complete set of duality oscillators). So supersymmetry always struck me as a hack, and not surprising that we don't see it. It seems like the point of Gauge Theory is to avoid worrying about fermions except for their mass, but nature has to deal with each one specifically.

    i should have mentioned that I think Feynman got away with relying on Dirac algebra because anti-particles going backwards in time is sort of like a signature flip in octonions. But Clifford algebra is nice clean stuff and one can 'get away with it'

    1. There is one more super particle that the SUSY foks can throw in and settle the super symmetric debate once and for all - the towelino!

  29. Some of you repeating the same points over and over have failed to mention Einstein and others made common basic geometry mistakes that they corrected by evidence of observation. It is so intuitively abstract so like any modern QM artist Feymann got a lot from simple stick drawings when like Pollack confronting nature modeling her naked singularity.
    Is there an underlying unified theory or not ? Is there a place where necessary and sufficient become indistinguishable and that not just a zero point of balanced symmetry of signs cancelled in the background including octonions and beyond?

  30. One can be creative and not really understand what cognition is?

  31. We all live on Riemann's critical strip and what Casimir complements that outside it.But we can find deeper resolution on the critical line. Like Feynmann we can turn Riemann on his head axis wise. Logically it is not a matter of convergence or divergence or if his hypothesis is forever an assumption like the parallel postulate by proof or not.
    Ethan Siegel has a delightful description of the debate if there was anything beyond our island galaxy near or far. The quasars were part of a new level of that debate and our deeper observations in our time. Can physics be explainable by pure thoughts? Perhaps in Einsteins day there was only one island universe in fact and the old Greek gods where in actually the only gods. How can we test or think this out as science?

  32. In science, cognition is the set of all mental abilities and processes related to knowledge: attention, memory & working memory, judgement & evaluation, reasoning & "computation", problem solving & decision making, comprehension & production of language, etc. Human cognition is conscious and unconscious, concrete or abstract, as well as intuitive (like knowledge of a language) and conceptual (like a model of a language). Cognitive processes use existing knowledge and generate new knowledge.Cognition

    Why would irrationality rule an empiricist thought train? There is a reason?

  33. Science, is reacting to the Platonist ideal?

    In 1995, Andrew Wiles won worldwide acclaim when he finally laid to rest one of the oldest mathematical chestnuts of the modern era. After more than 350 years, Pierre de Fermat's deceptively simple claim that he famously jotted down in a margin was now unequivocally true: the conjecture had at last become a full-fledged theorem.

    But what, in fact, had Wiles done? Had he actually discovered something? Or had he simply cleverly moved a bunch of symbols around? See: Preview - Plato's Heaven: A User's Guide

    Perhaps mountain peaks will help one learn to mean, "some thing" different( there is a cost to the full download)? You have to be able to get to something called, "self evident," not an infinite regress to infinity, but to the basis of what allows you to move on.

    Hilary Lawson catches Lee at 32:20 of linked Pythagorean Dream, by helping him to "re cognize" what Lee said a moment previous. A realist, no, this is a important distinction when one becomes aware of what they are doing.

  34. "It is known that geometry assumes, as things given, both the notion of space and the first principles of constructions in space. She gives definitions of them which are merely nominal, while the true determinations appear in the form of axioms. The relation of these assumptions remains consequently in darkness; we neither perceive whether and how far their connection is necessary, nor a priori, whether it is possible.

    From Euclid to Legendre (to name the most famous of modern reforming geometers) this darkness was cleared up neither by mathematicians nor by such philosophers as concerned themselves with it. The reason of this is doubtless that the general notion of multiply extended magnitudes (in which space-magnitudes are included) remained entirely unworked. I have in the first place, therefore, set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude. It will follow from this that a multiply extended magnitude is capable of different measure-relations, and consequently that space is only a particular case of a triply extended magnitude. But hence flows as a necessary consequence that the propositions of geometry cannot be derived from general notions of magnitude, but that the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience. Thus arises the problem, to discover the simplest matters of fact from which the measure-relations of space may be determined; a problem which from the nature of the case is not completely determinate, since there may be several systems of matters of fact which suffice to determine the measure-relations of space - the most important system for our present purpose being that which Euclid has laid down as a foundation. These matters of fact are - like all matters of fact - not necessary, but only of empirical certainty; they are hypotheses. We may therefore investigate their probability, which within the limits of observation is of course very great, and inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.
    See: On the Hypotheses which lie at the Bases of Geometry. Bernhard Riemann
    Translated by William Kingdon Clifford"

    Maybe with one's current knowledge, one may only be able to see as far as what the empiricist can see as from an abductive inference, as an hypothesis? One's best guess. But for a rationalist, this is a different process.

  35. "No actual experimental observation was needed for Einstein to come up with its theory of general relativity: it was the outcome of pure thought. It was only later confirmed experimentally."

    As others have pointed out, this is not true of GR. One of Einstein's most famous quotes regards an "observation": something he read that someone said, namely, that when falling one doesn't feel gravity.

    His work at the patent office often involved electromagnetic devices, and at the time there were different descriptions depending on whether the electric or magnetic field was moving. This is directly relevant to special relativity. His parents also worked in the electric-power industry. One thing he always said made a deep impression on him was a compass needle pointing north.

    Einstein was a very down-to-Earth guy, despite the nutty-professor image (not that the two imply a contradiction): he held a few patents himself, was an excellent musician, very much a ladies' man, etc. Rather, what made him special was to work out more consequences of the observed phenomenology than was the case with others.

  36. The Emperor is empirically naked. Frantic efforts undefine "naked" as being invisible clothing that will eventually appear. Children who know no better ask, "suppose the Emperor is naked?"
    Tailoring theory to be empirical.

  37. ......and maybe realize that Gauss being Riemann's teacher, was able to have descendants.:)

    Riemann, was a Rationalist.

  38. Plato Hagel,
    I do not mean to ignore your extensive comments. Rationalism and Empirism are argued as if a pyramid the apex of one the base if the other. Yet is Nominalism not also an opposition to radical empiricism? Science too has such conceptual limits of possibility.
    Are we aware of consciousness in the attention of focused thought while the time or does time vanish contemplating our consciousness?
    Was Riemann such a rationalist he was not aware of multiplicity in geometry and physics grounding a Delta of consciousness a little better focused modest that the greater part of the work of discovery he said he will leave for others?
    I imagine we share the same mental structures in the main when we dream. We are the actors in the dream or we watch ourselves acting from above that.
    My life is a lot easier lately with my 24 HR clock in sight set to London time thus Nepal and Chicago and New Zealand a global compass as to who is awake.
    Time is a strange thing to me to debate or measure both philosophic and scientific. Seconds can expand to hours and they to seconds. OK, so I watched a beheading on fb
    sad for days that this BS is getting real.
    The expression on the victims face in the few seconds, childlike, filled a lifetime. The masked men praised the death of time and one not masked just realigned the display with no sense of emotions.
    In the finite burst of birth as close to worship we can come, or some end burning bright like Riemann taken too soon what is the measure.? Life may not burn as bright over a long lifetime that amounts really to a slow death yet without certainty as the universe itself summed up at an end.

  39. Are Gaussian Coordinates real?

    Einstein's success was due to what Grossmann was studying.

  40. A famous story about the boy wonder of mathematics has taken on a life of its own -Brian Hayes

    Illustration by Theoni Pappas

    In a fanciful drawing done in the manner of a woodcut, the young Carl Friedrich Gauss receives instruction in arithmetic from the schoolmaster J. G. Büttner. As the story goes, Gauss was about to give Büttner a lesson in mathematical creativity.

  41. "it is indeed very clever but of course has nothing to do with reality" -Pauli on spin.

    "Before me lies the April edition of the Proc.Nat.Acad. (US). Not only does
    it contain an article from you under “Physics” but shows that you are now in
    a ‘Physical Laboratory’: from what I hear you have even been given a chair in
    ‘Physics’ in America. I admire your courage; since the conclusion is inevitable
    that you wish to be judged, not for success in pure mathematics, but for your
    true but unhappy love for physics" Pauli to Weyl on his work on gauge theories

    This is how progress was made in physics. Not always by Pauli disparaging an idea which would later become named after Pauli, of course.

    But there does seem to be a phenomenon in which someone for whom physics is their bread and butter assumes they have a superior "intuition" as to what is "physical"- sometimes, these people, like Pauli, make important contributions to Physics. Sometimes they're worse than useless.

    Sure, the world is full of dumb, unphysical ideas. There are also ideas, initially received as unphysical, which went on to become the basis of all modern experimental research.

  42. In addition to the PingPong between Math and Physics, there is the question of how Stern-Gerlach could be done if Thompson hadn't discovered the electron. And how can one do experiments without vacuum pumps and all that. A lot of shoulders have people standing on them. Not to mention that Jordan was working with Courant - so one must not leave out where Courant was doing his work writing Mathematical Methods of Physics. What a time that must have been. And they did not even have TRS-80s, much less decent computers.

  43. I wonder, since algebra ought to put a clamp on axioms, if that idea above would be of any relevance to Axiomatic QFT ? Are they stuck ? I tried reading PCT Spin Statistics - pretty rough going. Speaking of Ray Streater, google "lost causes ray streater" to see his objections to octonions in physics. Ah, but if octonions define particles, do his objections still apply ?

  44. Alice,

    Did Godel assume people are creative?

    Assuming someone will eventually stumble upon a loophole (statement)?

    A loophole (statement) of what?

    A loophole (statement) beyond the internal consistency of any system.

    What does such a loophole (statement) do for the constraints of an internally consistent system?

    Is such a loophole (statement) incompatible with an internally consistent system?

    Anyway the assumption about people is correct.

    People are creative.

    Godel found a loophole too.

    No data, no physics, no evidence, just an unphysical proof for metaphysics and mathematicians.

    Einstein and Godel conversed.
    They still do. Via entanglement.


  45. Weyl sent Husserl a copy of Space-Time-Matter because he thought he was doing phenomenology- he thought the idea of a gauge theory was husserlian.

    I think a distinction should be drawn - while it isn't clear we should call dyons, monopoles, and majoranas ideas from string theory, the invariants witnessing topological order were first constructed to understand ambiguities in certain functional integrals arising in string theory.

    This kind of work, like Weyl's, uncovers truths which are crucial to understanding something about nature, even if the model in which they arose never turns out to be physical or even falsifiable. Such is mathematical physics.

    Now, though it's not for me to say, I do get the sense that there may very well be some kinds of physics which produces neither mathematics nor falsifiable predictions. But it seems like the rancor about bad physics has degraded the intellectual climate more than the bad physics has.

    Truth is, we're just having these arguments because daddy warbucks had a midlife crisis and spent the tuition money on boner pills and a stealth VTOL deathtrap.

  46. InMatrix why are you talking to yourself?

  47. inMatrix,
    As to your first comment I agree fractal reading is part of the philosophic and scientific debate on the philosophy of physicality so to speak.
    I and others more vaguely coined the term 'holofractal' but the more general view would have to include 'Fractoholon'.
    Without a little more general theory, another step really as paradox, philosophy is as confused as science as inquiry stands on turbulent new speculations and evidence. It is the Multiverse -Universe issue and if as biology we are symbiotes or fractal reading DNA as our selfish gene grounding.
    Husserl and Heidegger are important but for time we have to make careful distinction between surrealism and post-modern methods.

  48. inMatrix,
    In Pu239, as atoms have 8 layers of duality known, note that. 240 8D spheres surround one other. Are there islands of stable heavy elements? The observed effect is not total evidence from either its quantitative or qualitative observation. A third concept is needed structurally 'quasicity'. If we are to view or imagine things as rational holiness just beyond fifth dimensional matter.

  49. inMatrix:

    I removed several of your comments. This is a comment section, not a place to write a book. If you have a comment to make, do it, but do it briefly, and don't clog this comment section with unnecessary blather. If you want to discuss the topic in more detail, set up a blog yourself. Thanks,


  50. This comment has been removed by the author.

  51. I quite agree on the notion of formal entropy exhibited by InMatrix but this issue is extremely complex and it is not the question here.

    We must separate two things:

    Utility theories: that is to say, mathematical functions to transfer between experimental inputs (initial state or partial description of a physical system) to other experimental inputs (end state or a full description of a physical system). It is an induction in the traditional sense.

    Unified theories: that is to say, mathematical functions that unify utility theories into one simplified theory. Utility theories are models of the unified theory.

    Both theories are indistinguishable without the historical context of the creation: utility or unifying.

    I believe that the history of science is done by creating models of both types. Regarding physics, the fact that GR does not seem to adequately describe the observable world (dark energy and dark matter) implies that any unification with quantum theory would be equally incorrect.

  52. That whole business of not paying attention to phenomenology regarding quantum gravity sounds downright dangerous to sanity. Too easy to get lost in abstractions and forget the Pauli lesson - if we pay attention to the right stuff, things fall into place. It was as simple as considering that electrons are left or right handed. Of course, that sounds NUTS if you view an electron as a point charge. Thomas had to transport a frame around an orbit, not a point. There still seems to be lots of confusion on this topic.
    Those oscillators i referred to cover all those left-right, and red-green-blue, and matter-antimatter distinctions. None of it affects mass. Algebra won't tell you that but physics does. Each oscillator is just a complex number. If you want a spinor, make a pair, and use Pauli matrices. Or to deal with color, make a triple and use GellMann matrices.
    Heck - one can forget octonions and just use symbols like
    (oa)(bc) and o(a(bc))
    to classify particles. There are 120 permutations and associations. Sort by generation = which slot o is in. We see blocks of 6 - with left-right and color. Double the whole table because of +--- and -+++ to get all the antimatter. It does not affect the form of the oscillator.
    We need another doubling - by exchanging the axial and vector parts of a frame, not exactly evident from notation, but that brings it up to 480 oscillators, and each is a complex number, and each has a multiplication table to preserve its form.
    if quantum gravity has to deal with gluons and whatnot, it seems these guys ought to be dealing with this. Just like Pauli had to deal with the left and right electrons. The table thus constructed deals with muons and taus. Gauge bosons involve relations of, say, colored fermions, annihilating and creating r,g,b quarks.
    Of course, it might take a mind like Pauli to put that all together in a nice equation that relates to gravity - for any oscillator with energy. Gee that does not sound like quantizing GR.
    Nothing about this in Feynman's Lectures on Gravity.
    In fact, it looks like algebra just quantized everything already.
    Have parentheses, will quantize !

    I don't see anything 'philosophical' about permutations and associations.
    This is really elementary stuff and I can't imagine a grad student being clueless about such elementary things. ( well, i suppose Pauli was too, until he was enlightened by Jordan ).
    Evidently if you have supersymmetry doubling stuff, it will make an unholy mess of the table.
    Come to think of it - even philosophers ought to be able to grasp this stuff. There are some tricky things like what about all the oscillators with (oa) - it is not Spin ! Perhaps their contemplations will yield an insight.

  53. Indeed, if you believe, for example, that the mass of particles is hidden somewhere in the axiomatic that you already have, simply shake out the system until the desired theorem appears, hoping that your axiomatic is complete and allows to prove this theorem (Gödel, 1931) and that it allows it with a reasonable number of steps (Cook, 1971).

    By cons, if your system is absolutely or relatively incomplete to demonstrate your theorem you must add axioms. Here, as the Pauli spin, it's a creative act that can take a purely formal form to adapt the system to the phenomenological reality or you need to create a new set of axioms to represent properly the phenomenological reality.

    The latter situation is more complex because you have to take a philosophical position on the issue, for example what determine the mass of the particles or more generally, what is the mass, and then find the appropriate mathematics to create models and test their adequacies with reality.

  54. It is an Einsteinian dream that "pure thought can grasp the real, as the ancients had dreamed", see

    However, Einstein also trusted that " nature is the realization of the simplest that is mathematically conceivable", so the fantasy at least has limits. Suggesting that "the actual creative principle lies in mathematics" he surely didn't open the door for mathematics that are not the simplest conceivable.

    In full agreement with the spirit of this post, Einstein admits that "The theoretician is forced, ever more, to allow himself to be directed by purely mathematical, formal points of view in the search for theories" yet still expects from such search to be " a search for the logically simplest possibilities and their consequences", apart from the obvious expectations that "Such a theoretical structure must be quite thoroughly elaborated in order for it to lead to consequences that can be compared with experience " and that "The theorist must accomplish this Herculean task with the clear understanding that this effort may only be destined to prepare the way for a death sentence for his theory", let Einstein speak for himself:

    "The theory of relativity is a beautiful example of the basic character of the modern development of theory. That is to say, the hypotheses from which one starts become ever more abstract and more remote from experience. But in return one comes closer to the preeminent goal of science, that of encompassing a maximum of empirical contents through logical deduction with a minimum of hypotheses or axioms. The intellectual path from the axioms to the empirical contents or to the testable consequences becomes, thereby, ever longer and more subtle. The theoretician is forced, ever more, to allow himself to be directed by purely mathematical, formal points of view in the search for theories, because the physical experience of the experimenter is not capable of leading us up to the regions of the highest abstraction. Tentative deduction takes the place of the predominantly inductive methods appropriate to the youthful state of science. Such a theoretical structure must be quite thoroughly elaborated in order for it to lead to consequences that can be compared with experience. It is certainly the case that here, as well, the empirical fact is the all-powerful judge. But its judgment can be handed down only on the basis of great and difficult intellectual effort that first bridges the wide space between the axioms and the testable consequences. The theorist must accomplish this Herculean task with the clear understanding that this effort may only be destined to prepare the way for a death sentence for his theory. One should not reproach the theorist who undertakes such a task by calling him a fantast; instead, one must allow him his fantasizing, since for him there is no other way to his goal whatsoever. Indeed, it is no planless fantasizing, but rather a search for the logically simplest possibilities and their consequences"


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