Friday, February 08, 2019

A philosopher of science reviews “Lost in Math”

Jeremy Butterfield is a philosopher of science in Cambridge. I previously wrote about some of his work here, and have met him on various occasions. Butterfield recently reviewed my book “Lost in Math,” and you can now find this review online here. (I believe it was solicited for a journal by name Physics in Perspective.)

His is a very detailed review that focuses, unsurprisingly, on the philosophical implications of my book. I think his summary will give you a pretty good impression of the book’s content. However, I want to point out two places where he misrepresents my argument.

First, in section 2, Butterfield lays out his disagreements with me. Alas, he disagrees with positions I don’t hold and certainly did not state, neither in the book nor anywhere else:
“Hossenfelder’s main criticism of supersymmetry is, in short, that it is advocated because of its beauty, but is unobserved. But even if supersymmetry is not realized in nature, one might well defend studying it as an invaluable tool for getting a better understanding of quantum field theories. A similar defence might well be given for studying string theory.”
Sure. Supersymmetry, string theory, grand unification, even naturalness, started out as good ideas and valuable research programs. I do not say these should not have been studied; neither do I say one should now discontinue studying them. The problem is that these ideas have grown into paper-production industries that no longer produce valuable output.

Beautiful hypotheses are certainly worth consideration. Troubles begin if data disagree with the hypotheses but scientists continue to rely on their beautiful hypotheses rather than taking clues from evidence.

Second, Butterfield misunderstands just how physicists working on the field’s foundations are “led astray” by arguments from beauty. He writes:
“I also think advocates of beauty as a heuristic do admit these limitations. They advocate no more than a historically conditioned, and fallible, heuristic [...] In short, I think Hossenfelder interprets physicists as more gung-ho, more naïve, that beauty is a guide to truth than they really are.”
To the extent that physicists are aware they use arguments from beauty, most know that these are not scientific arguments and also readily admit it. I state this explicitly in the book. They use such arguments anyway, however, because doing so has become accepted methodology. Look at what they do, don’t listen to what they say.

A few try to justify using arguments from beauty by appeals to cherry-picked historical examples or quotes to Einstein and Dirac. In most cases, however, physicists are not aware they use arguments from beauty to begin with (hence the book’s title). I have such discussions on a daily basis.

Physicists wrap appeals to beauty into statements like “this just can’t be the last word,” “intuition tells me,” or “this screams for an explanation”. They have forgotten that naturalness is an argument from beauty and can’t recall, or never looked at, the motivation for axions or gauge coupling unification. They will express their obsessions with numerical coincidences by saying “it’s curious” or “it is suggestive,” often followed by “Don’t you agree?”.

Of course I agree. I agree that supersymmetry is beautiful and it should be true, and it looks like there should be a better explanation for the parameters in the standard model, and it looks like there should be a unified force. But who cares what I think nature should be like? Human intuition is not a good guide to the development of new laws of nature.

What physicists are naive about is not appeals to beauty; what they are naive about is their own rationality. They cannot fathom the possibility that their scientific judgement is influenced by cognitive biases and social trends in scientific communities. They believe it does not matter for their interests how their research is presented in the media.

The easiest way to see that the problem exists is that they deny it.


  1. It seems to me that the problem is not so much that some parameyer value coincidences/fine-tuning are in need of explanation, or that simplicity or unification is desirable in physics. It seems to me that the problem is: there are many many potential explanations to fine tunings and potential ways of unifying theories, most of which we probably haven't imagined yet, and it's a mistake, having found a simple explanation in our contemporary framework, to assume that it must be the right one. Not that "beauty" (or simplicity/unification) shouldn't be a criteria at all, but it's never a decisive one. Would you agree with that?

    1. Hi Quentin,

      It's somewhat worse than this because for most of the problems that physicists in those fields work on we don't even know that there is an explanation in the first place. In addition, strange as that sounds, in some cases the "explanations" don't actually explain anything.

      Take the recent example which we discussed here. Rather than postulating the values of certain parameters, you can postulate a probability distribution from which you then calculate the values of parameters. What does this explain? Nothing. It's just moving around the bump under the carpet.

      Also, what concerns the so offensively small mass of the Higgs-boson that supersymmetry supposedly explains. You cannot actually calculate the mass of the Higgs-boson with it. This "explanation" has zero observational relevance.

      Even after writing and speaking about this for several years, I still feel like this isn't really my territory. It's really something that I wish philosophers would take on.

    2. "It's really something that I wish philosophers would take on."

      Unfortunately for both fields, there is relatively little contact between philosophers of physics and philosophically-minded physicists. For someone to make a splash in the meeting ground between physics and philosophy, they cannot really come at it from one side or the other, due to sociological reasons. As you have no doubt seen, a physicist making philosophical arguments gets ridiculed by the philosophers about as much as a philosopher making physical arguments does by the physicists. It seems like it will require someone to make a career out of being a physicist-philosopher, which is very difficult to do. (Not only sociologically, but just from the sheer amount of /reading/ to be done.) It is a very narrow career path, with nearly double the work to do in order to get to the level at which one can actually contribute. But /someone/ needs to do it - both fields desperately need the other so they no longer are talking past each other.

      "It's just moving around the bump under the carpet."

      I love this turn of phrase.

    3. James,

      I think you are somewhat exaggerating the tension between physicists and philosophers. I have been to quite some meetings that mix the two communities (another one just last week) and they get along more often than not. There are some black sheep on each side, of course, no point denying it, but it's less of an issue than online discussions may make you think. I have to add though that, probably unsurprisingly, most of the philosophers of science who I personally know have a background in physics. (The opposite, someone switching from philosophy to physics, basically doesn't seem to exist.)

      In any case, you are right that there is too little contact between the communities (I also complain about this in my book). I believe the main reason for this is that scientists are very output-oriented and philosophers never seem to come to any conclusions that one could actually work with.

    4. Thank you for your response.
      As I see it, the problem is also that the explanations proposed are kind of ad-hoc, and so we can't even evaluate how good they are?
      This would be (somehow) defensible if they were the only possible explanations... They would be vindicated by elimination. But it seems to me quite presumptuous to think so.

    5. I agree that the issue could be taken up by philosophers.
      It's related to many trendy topics in general philosophy of science: the nature of explanations, the validity of inferences to the best explanation, the interpretation of probabilities...
      I did a quick search and there seem to be a few articles on the subject although some in this list are about theological arguments from fine tuning (somehow related but not quite the same).

    6. I think the main philosophical critique of arguments from naturalness could be along this line:

      1- naturalness arguments presuppose a probability measure on theoretical parameters (=a principle of indifference, not on a priori possible observations, but on a priori possible theories or models within a framework)

      2- this kind of probability measure is very strongly theory-laden, in a way that is generally not preserved by theory change (here historical examples such as Tycho Brahe's could be used)

      3- there's no reason to think that our current paradigm in physics is the last word: future theory change is likely

      4- therefore there's no reason to think that the probability measure used by arguments from naturalness is correct: it's probably not

  2. Einstien said we can get rid of hypothetical ether if only we can think of time as something not absolute. In Aldous Huxely's words "Einstien broke the Newtonian Orthodoxy". Newton was an authority in physics, and if Einstien took Newtons authority for granted he could not have looked farther. Are we inventing hypothetical ethers for mathematical convenience and beauty? I don't know, I am only asking.

  3. If an expert reviews and comes up with a few (namely two) misrepresentations rather than successful debunkings, I become tempted to say that Sabine's book is not a fertile ground of self-contradictions.

  4. Scott Aaronson recently said this, "I’d say there’s a form of “naturalness” that’s almost tautologically true. Namely, when a bunch of huge positive and negative terms almost perfectly cancel each other out, there must be some explanation for it. The explanation might not be supersymmetry, or any other symmetry, or even the anthropic principle. It might be something so strange that no one has thought of it yet. But at any rate there’s some explanation. And probing nature at higher energies is just the most obvious way to look for clues about that or nearly anything else that isn’t explained by the Standard Model."

    What do you think of this argument? Is this what you have in mind when you say that people are not even aware they are using arguments from beauty?

  5. since LHC hasn't seen supersymmetry and the best case scenario for supersymmetry is as a solution to the Higgs hiearchy problem, does Occam's razor to supersymmetry plus LHC null results imply supersymmetry is unrealized in nature?

    1. No it does not because supersymmetry does not predict the masses of the superpartners. They could be anywhere until all the way up to the Planck scale (where, presumably, string theory becomes relevant). The reason that the masses of the supersymmetric partners where believed to be in the LHC range were arguments from naturalness.

      Also note that there is not one supersymmetric model but literally millions of them, and the natural variants of those have not been ruled out in all cases.

    2. oh I know that, but in terms of the null hypothesis, there is no supersymmetry, and Bayesian reasoning, the highest likelihood of SUSY is at LHC accessible energies.

      the data from LHC concludes a failure to reject the null hyopthesis

  6. With this it is maybe worth commenting on what supersymmetry is all about. It is not at all by itself a phenomenology, but more of a theoretical framework that one put phenomenology on.

    For those knowledgeable of physics lore we often employ the idea of raising and lowering operators, a and a^†. The a takes a state of n bosons (say photons etc) |n> and reduces it by a|n> = sqrt{n}|n-1>. The a^† does the opposite and generates a boson so a^†|n> = sqrt{n+1}|n+1>. This comes about from the quantization of the harmonic oscillator, which is a bit involved, but this result is remarkably simple to understand. There is a similar thing with fermions but the raising and lowering operators, b and b^†, obey b^2 = (b^†)^2 = 0. This is the Pauli exclusion principle and it means fermions only have the states |0> and |1>.

    Now supersymmetry at the most basic level is a case where you have operators of the sort b^†a, reduce the boson number of one and replace it with a fermion, or a^†b remove a fermion and replace it with a boson. This is how a boson or fermion acquires so called SUSY partners. Now these operators get “dressed up” with square roots of masses and in general spacetime momenta to define the generators of supersymmetry. The Pauli exclusion principle implies anticommutators of fermion operators

    {b, b^†} = bb^† + b^†b = 1.

    The supersymmetry generators have a similar expression but the masses and momenta mean the anticommutator gives a Lorentz boost. This then connects quantum mechanical properties of spin fields with spacetime.

    There is a lot more of course with superfields etc. However, this rather elegant and simple idea tells us nothing about the superpartners; the formalism has not content with measurable physics, that is something we have to input. It is remarkably similar to Dirac's scheme with the electron and anti-electron, which in the early days had people completely confused, some thinking this positive particle was the proton. Anderson not long after found the positron and this confusion was cleared up. That was the crucial point, nature provided the information found in an experiment. As yet with supersymmetry we do not have this.

    I tend to think supersymmetry is a real aspect of the universe. However, what is clearly in trouble is the phenomenology hung on SUSY, in particular the minimal supersymmetric standard model (MSSM). The LHC has not killed it yet, but MSSM is clearly on life support right now. In some ways if MSSM is false I will say the putative FCC might drive the stake through the heart of MSSM and we can throw it out completely. The remaining days of doing tanβ calculations may be few in number.

    I did a minor in philosophy in college and I know my way around some of that. A nephew of mine abandoned a major in engineering to do philosophy. There is a lot of language in it that scientists find not just confusing but obscuring. The funny thing is the opposite also happens, where a lot of techniques in physics many in other fields such as philosophy find difficult. In many ways this is why I think it is important to distill things down to the simplest language possible, such as my discussion of supersymmetry above is not dense with complicated stuff about Grassmann numbers and superfields. Sort the same happens in philosophy, where a lot of terminology that is really not often that necessary gets used that leads to more intellectual fog than clarity.

    1. In some ways if MSSM is false I will say the putative FCC might drive the stake through the heart of MSSM and we can throw it out completely.

      then how do you connect SUSY to phenom?

    2. SUSY might occur in some completely different manner. There is not so much about SUSY that demands it be a part of the standard model. The standard model, in particular the mass renormailzation of the Higgs, in some ways begs for SUSY to get around some issues.

      There is the sphaleron hypothesis with B - L and it is possible that SUSY is connected with that. This is an interesting, if maybe outside possibility, which in some ways completes the weak interaction as quantum flavor dynamics (QFD). This will require measuring a particle at around 10 TeV mass.

  7. Good to set the record straight, but generally I thought it was an excellent review of the book. He clearly enjoyed reading it.

  8. Would it be fair to say that arguments about beauty in physics always implicitly assume the final truth is about to be uncovered. PV=RT is beautiful (because it predicts so much in one elegant equation) but it is inaccurate. The more accurate versions of this equation aren't beautiful at all, since they are more complicated and also contain coefficients that vary from gas to gas.

    The point is that atoms and molecules aren't the bottom layer of physics and the lower layers of inter-molecular forces and QM spoil the simple equation.

  9. "I think you are somewhat exaggerating the tension between physicists and philosophers."

    I agree. Most of the time, they probably agree more than physicists among themselves, or philosophers among themselves.

    "I have been to quite some meetings that mix the two communities (another one just last week) and they get along more often than not."

    I was there too. One interesting thing was that most of the philosophers actually had a pretty good understanding of the physics they were talking about.

    I neither started it nor participated in it, but at one point a discussion started about Sabine's book. Some liked it, others didn't, some agreed, others didn't, some agreed but thought it was nothing new, and so on. A typical discussion. But then someone said the funniest thing I've heard all year: "I read it for the interviews." Bonus points if you can think of another publication about which that has been often said. :-)

  10. Thank you for providing the link to Butterfield's review. It's clear that he has spent considerable time and thought in assessing "Lost in Math" and his document, in length and detail, reads more like a commentary than a review.

    In your post you reference the phrase “this just can’t be the last word,”. I would say (and I'm guessing this would go for most research scientists) that I'm involved in my research because I consider the current state of knowledge is not “the last word,”. There really wouldn't be much point in carrying on if I believed otherwise.

    Of course how one reaches the conclusion that “this just can’t be the last word,” is a different matter. It involves all the personal and societal pressures you refer to, the education, experience and intuition of the researcher, and technical and - to a degree philosophical - considerations. However the phrase itself is neutral, it simply states why we (researchers) are doing what we're doing. It's a belief, it may be wrong, it may be right but of itself it has no impact on how we do our work.

    There's general agreement that the Standard Model is 'not the last word' and further research is justified. The direction that research takes and the decisions on how it is carried out will be subject to many inputs - some more important than others. Your point about historic considerations of naturalness and 'beauty' having led to limited or no progress is valid and has, clearly, some support. But we are now at a point where further progress is extremely difficult and all possible avenues have to be explored - even those which appear to be of limited use.
    You correctly point out that currently we're at the point where theories are being basically fine tuned (by manipulation of e.g. probability distributions) to postdict results - moving the lump under the carpet - and there appears to be little prospect of either theoretical or experimental progress in the near future. The debate on whether this means - to quote from a previous blog - that "Particle physics may have reached the end of the line" will surely rumble on for some considerable time.

  11. "sixteenth century astronomers over-estimated stars’ size, so that supposing them to be very far away also implied that they were much larger---unacceptably larger---than the Sun"

    There is a crucial point missing: Tycho Brahe didn't know about wave optics. The apparent angular size of a star of about a minute of arc is due mainly to diffraction on the pupil; the true angular size is much smaller. It wasn't "unacceptable" to Tycho that the stars were much farther away than the planets. Rather, he calculated the distance, assuming (wrongly, we now know) that what he saw was the true angular size and the reasonable assumption that they are not vastly larger than the Sun. At the calculated distance, he should have been able to see aberration---but he didn't, hence his conclusion that the Earth is not moving around the Sun and thus his Tychonic model (which is not completely equivalent observationally to the Ptolemaic model). In other words, his mistake was believing observational "facts" like the angular size of things he saw. (Most "measurements" involve some sort of inference as well, though angles involve fewer than most.)

    One might say, well, he could have assumed that the stars have the same brightness as the Sun, rather than the same angular size. However, this would require an additional hypothesis: namely, that stars are distant Suns. (In some, though not all, respects, this is similar to the modern idea of the Multiverse, and suffered some of the same criticisms.)

    1. Brahe's key misgiving wasn't the size of the stars (which he estimated wrongly) but their distance, which he estimated by noticing the absence of parallax, and that was about correct. But that's not the relevant point. The point is that he used the "too large ratio" argument to discard a correct hypothesis, hence a failure of naturalness arguments.

      Even more interestingly, if you think about the reason for why this failed, it's because he implicitly assumed an almost uniform probability distribution.

    2. The Renaissance Mathematicus has longer piece on this. Yes, distance was a problem, but this was connected to the apparent angular sizes. Assuming his estimates of the angular sizes were correct, the lack of observed parallax implied that they must be a) very distant, and hence enormously larger than the Sun or b) the Earth is not moving. In other words, it wasn't the large distance per se, but rather that this distance, coupled with the apparent angular sizes, implied that all stars would be much, much larger than the Sun.

      In any case, he didn't introduce his system because he just couldn't accept the idea of a moving Earth, as the popular myth claims. (Tycho, who---in the sixteenth century!---never married his girlfriend and mother of his children was not one to be too influenced by traditions. It was also his observation of comet parallax which delivered a big blow to the Aristotelian/Ptolemaic world-view.)

      Also, read "parallax" for "aberration" in my comment above.

  12. How mentionned the Austrian-Californian Psychoanalyst Paul Watzlawick?: "Don't be mistaken to take the map for the land that is designed on it!" I'm very glad having seen the author of that book for the first time some days ago in the TV-show "Nano" of the German chain "3Sat". Though psychiatrist&psychotherapist and former theologian, I still am an "amateur" (means "liker") of physics from my fist class in high school through basic education in medical school at the university. She has made me remember and refresh my passion for physics. Another passion she has made me revive in me: scepticism, not to follow the beaten track, to lookbehind each word (ethymology) and to un-disguise wrong usage of words - especially those created artificially by PR and by science as well. You should read once the famous fairy-tale of "the emperor and his "invisible" new clothes...not to forget Abbot's "Flatland".

  13. @Sabine
    I am not so sure that one can do without any notion of naturalness and still do science. Take life for instance. Life is very unlikely. Certainly, most people thought and still think that it "screams for an explanation”. In pre-Darwinian times, many believed that a suitable explanation was an intelligent being (God) that designed it. This is not such an unreasonable solution. Even Richard Dawkins said that, had he been born before Darwin, he might have been a theist for that very reason.
    Other people - Lamarck, Darwin - looked for a scientific explanation, and they found one in evolution, one that explains well the complexity and unlikeliness of life. Had some proto-Sabine been there, she would have probably claimed: this thinking that life is "curious", that it "screams for an explanation”, it's just an argument from beauty, there's nothing to explain here. So let me ask you one question: don't you agree that life is exactly the thing that cries for an explanation? And if it does, what's different from other "unlikely" coincidences, say in cosmology?

    1. Consciousness is something that, in the minds of many, demands an explanation. But many scientists today deny this. A similar situation to the time before Darwin?

      And I note that Darwinian evolution arguably does not explain the actual origin of life, i.e. why it exists as a latent property of matter. Similarly, I doubt that any convincing 'explanation' of consciousness can be constructed.

  14. The fact that the Universe could be essentially "unnatural" and "ugly" is IMO logically consistent. And after more than 30 years of failures trying to move forward it's time to think seriously in that possibility.

    Now that SUSY hypothesis finally seems wrong (together with the rest of "beauties" alternatives), we should start wondering about "uglies" but mathematically consistent postulates. For example, it could be the case that dark matter may be a field whose particles don't interact at all with the "ordinary" matter (nor by the electroweak force neither by strong nuclear force) and that just by deforming the space-time with its mass(in a GR way) it disturbs indirectly our "ordinary" matter.

    In other words, there could exist (transparents) fields unable to couple (in any way) to the known (accessible) ones. There could exist something like a separate set of fields forming a "dark" lagrangian ("dark" to us in the sense this L does not interact with our SM one) and that then this independient set of "dark" fields could be phenomenology presented to us only by the deformation their mass produce in the space-time.

    Moreover, an explanation of this type could be behind also of the dark energy in some way (maybe the equivalent of a "dark Higgs" mechanism with a special & different breaking potential?).

    In summary: in contrast to the WIMPs hypothesis that talks about "interactions only through the weak nuclear force and gravity, or possibly other interactions with cross-sections no higher than the weak scale ", I refer to an hypothetical set of new fields that only interacts (with "ordinary" matter) indirectly though gravity in a general relativity manner (and nothing else). In fact, these fields would have their own lagrangian with no relation at all with the SM one (in low energy scales, possible unifying at very high energies).

    And just to make it clear, I don't talk about the sterile neutrino hypothesis (a "simple" extension of the current standard model) because: "[sterile neutrino would] have Yukawa interactions with ordinary leptons and Higgs bosons, which via the Higgs mechanism lead to mixing with ordinary neutrinos". I.e.; they'd still could interact with (decay into) "ordinary" matter (they are WIMPs after all and I don't refer to that). By contrast, the ("ugly") dark matter candidate I propose would be a really fully non interacting massive particle. Because as I say there could exist a fully independent set of fields unable to interact at all with the SM particles except but the gravity generated by their mass in a GR way (just disturbing the space-time).

    So, what do you think? Do you believe in the possibility of such a two set of (totally separated) fields each one with its own lagrangian conforming a particular (and totally unrelated) gauge interaction model: something like an "ordinary" particle model ("light" standard model) and a independent -and unknown- "dark" particle model ("dark" standar model). We'd have also the classic general relativity that would feel the mass effects of the particles of the two set of fields and that'd be the responsible of the gravity interaction we observe between the "ordinary" matter and the "dark" matter.

    This hypothesis would be consistent at low energy scales but it could unify at very high energies where the quantum gravity would replace the classic general relativity approximation.

    1. Samu,

      First, please do not post your personal theories for something in my comment section, especially not if they are off-topic. I do not normally approve those and you are wasting both your and my time.

      I made an exception for your post because for reasons I cannot fathom people keep asking this question. Is it possible that dark matter is a particle that interactions only via gravity. Yeah, sure, that's an option. It doesn't receive much attention simply because it's difficult to test. And yes, there are loads and loads of theories according to which dark matter and dark energy are manifestations of the same kind of field. Even I have written papers about this.

      So, no, it's not a new idea.

  15. @Sabine
    Brahe based his argument against the Copernican
    system on a naturalness argument:
    "It would be unnatural that the sun is vastly smaller than all other stars."
    And this argument turned out to be CORRECT even though his further argument against Copernicus did not.

    You make a good point. Yes all science starts with
    an argument based on a lack of naturalness as a requirement for a causal explanation that is as simple (a.k.a. "beautiful") as possible.
    Such an explanation is scientific, invoking mere chance is not.
    E.g. if - contrary to the facts - the sun really had turned
    out to be vastly smaller than all other stars, we would
    demand an explanation for this fact.

    1. As I already said, the naturalness argument is that the stars should not be far away to avoid parallax, so it's more natural that the Earth is in the center and the stars are close. That turns out to be bluntly wrong. I don't buy the argument that the size was Brahe's misgiving because at that time it was far from accepted that the stars are suns to begin with. For all I know it would have been perfectly acceptable to just say they're different things entirely. Then again, I am not a historian, so quite possibly my interpretation is incorrect. But it will take more than a link to a blogpost and the opinion of a commenter by name "unknown" to convince me.

    2. Btw, "Such an explanation is scientific, invoking mere chance is not."

      This is nonsense. I strongly suggest you read my book before spreading further misinformation.

  16. Sabine
    what do you have to say about my example that the observed phenomenon called "life" is highly unnatural, and that this unnaturalness spurred the search for a scientific explanation, as is often the case?
    I can provide other such examples if you wish.

    1. As a physicist, I try not to speak about the phenomenon called "life", or at least I will try to hold back until past my retirement. The notion of "naturalness" that I am using refers to theories that have a mathematical framework. If you want to discuss other notions of naturalness, you are welcome, but I'm not the person to talk to.

  17. @Sabine
    > As I already said, the naturalness argument is that the stars should not be far away to avoid parallax,

    Just take a look only at the title of this detailed
    report on the issue:

    It will tell you
    1. that it was about size not distance of "heavenly bodies" (indeed
    they did not know yet whether the stars are suns).
    2. that even in 16th century people agreed
    that an unnatural fact needs _some_
    explanation if not a scientific
    one (as the one of Brahe) then a
    religious one, that was invoked by
    the Copernicans (!).

    Once a Jehovah Witness told me:
    "science claims that life originated by chance,
    that's no explanation!".
    I answered: you're right, THAT'S no
    scientific explanation!
    Sabine you would have answered him:
    "Nonsense! That's an excellent explanation."

    1. Unknown,

      Thanks for the reference, will look at this.

      "Sabine you would have answered him:
      "Nonsense! That's an excellent explanation.""

      This badly misstates my argument and illustrates that you have no idea what I am saying in the first place. Look, if you want to continue talking nonsense, fine. But please stop fabricating things I didn't say.

  18. I maintain that there is not much difference between saying that "the occurrence of life screams out for an explanation" and "the fact that the universe has critical density screams out for an explanation". Perhaps a difference of degree, because life seems to me even more in need of an explanation, but not a fundamental difference. And you do not need a detailed mathematical framework to appreciate that.
    Before Darwin, the existence of life was a crazy thing for all reasonable persons, basically impossible. One must be blind not to recognize that it demands an explanation.
    I would go as far as saying that, in this respect, a creationist is more rational than someone who simply denies this.

    Thus, I quite agree with Unknown's remark that "science starts with an argument based on a lack of naturalness as a requirement for a causal explanation that is as simple ("beautiful") as possible."
    This is not a scientific statement of course (Sabine is right here), but the foundations of science cannot be themselves scientific. However, it is an extraordinarily USEFUL approach. It is, in essence, a more sophisticated reformulation of human curiosity.

    1. You can maintain your opinion all you want but that doesn't make it correct. Your notion of "naturalness" has nothing to do with the notion of naturalness I am talking about. If you want to continue blathering nonsense, that is fine with me, but please leave me out of it.


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