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In praise of scientific error

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scientist drinking comically from beakerMy wife has first dibs on our New Yorker each week, so I only just got around to reading Jonah Lehrer’s piece on the scientific method in last week’s issue, which has been getting so much attention from my fellow science writers. John Horgan calls it a "bombshell" and Charlie Petit a "must-read."

Lehrer describes how many, or even most, published scientific papers prove to be wrong. In a range of examples from biomedicine and psychology, Lehrer tells of a "decline effect." The discovery paper does all the right statistical tests and infers a significant result. Follow-up studies reproduce the result, but find a lower statistical significance. A few rounds later, scientists conclude the discovery was a fluke.

It’s certainly a thought-provoking essay, but I’m not sure what to take away from it. As Horgan points out, it has a certain bait-and-switch quality to it. At first, the anecdotes intimate that the decline effect is an objective phenomenon, as though nature is changing its mind; only as the story unfolds does Lehrer attribute the effect to scientists’ own biases.

Lehrer finds this "disturbing," and his (or his editors’) subhead asks, "Is there something wrong with the scientific method?" Few who are familiar with science would deny that the process has its flaws (on which more later), but the fallibility of published papers is hardly one of them. Almost by definition, a discovery is at the limits of our ability to perceive it, so it is easily confounded with statistical flukes. The only way to tell is to publish the discovery, invite others to replicate it, and let it play out. The difficulties Lehrer describes do not signal a failing of the scientific method, but a triumph: our knowledge is so good that new discoveries are increasingly hard to make, indicating that scientists really are converging on some objective truth.

As Petit points out, Lehrer doesn’t talk much about the physical sciences, apart from alluding to the excitement in the 1980s over a possible fifth force of nature. Measurements of gravity in mines, boreholes, and tall buildings suggested that the gravitational constant, G, was about 1 percent larger over distances of hundreds of meters than in benchtop experiments. Moreover, objects of different composition seemed to respond in different ways to the force of gravity, which they shouldn’t. Theorists suggested that an additional force of nature was operating. Over time, the evidence faded. The anomalous borehole measurements did not go away, per se, but were explained as an uneven distribution of mass within Earth’s interior.

When I read Lehrer’s passing mention of this incident, I couldn’t quite tell what he was getting at. Either he is arguing that the gravitational anomalies were an example of the decline effect, or that physicists are clinging to the law of gravity despite evidence to the contrary. If he intends the latter, whoa. Even when the anomalies were making the news, most theorists saw the law of gravity as so rock-solid—representing the distillation of countless measurements of falling apples and orbiting planets—that any deviations would have to come from some additional force. It seems to me that the process worked exactly as it should. Physicists were alive to the possibility our current theories might be wrong, looked for anomalies, studied those they found, and ended up confirming our current theories. What Lehrer takes as an example of "slipperiness of empiricism" is the exact opposite.

If anything, I’m surprised that such incidents are not more common than they are. Physicists would like nothing more than to find new physics. That way lies immortality. Evidently, their eagerness is balanced by caution. In fact, it may well be overbalanced—a fear of being wrong may sometimes strangle good ideas in their cradle.

I just read Kathryn’s Schulz’s book Being Wrong: Adventures in the Margins of Error, which I would recommend to all my fellow perfectionists. It persuasively argues that error is the flip side of creativity. The fear of making mistakes paralyzes us—we shy away from taking risks and deny errors when we do make them. Science, one might hope, is the one human endeavor that has come to terms with our mortal fallibility. The very word "experiment" connotes a risk; papers are filled with "mays" and "mights"; error bars quantify the potential for wrongness.

And yet scientists still worry about overcaution. Young scientists, especially, can be afraid of asking questions or delving into foundational questions for fear they’ll be thought stupid or loco—with good reason. Granting agencies such as the National Science Foundation and National Institutes of Health are notoriously conservative, and as an article in this week’s Economist lays out, academic jobs are hard to come by.

The history of science suggests that mistakes are not to be ashamed of, but to be embraced. Even wrong ideas contribute to progress. Einstein probably erred when he thought quantum mechanics was incomplete, but was the first to appreciate the phenomenon of quantum entanglement. In 2004, physicist Edward Witten published a paper that sought to develop an exotic version of string theory. It didn’t make much headway, but opened the door to new ideas about how space and time might emerge from deeper physics. More broadly, string theory might be wrong, but oh boy is it an amazing theory—a rich vein of insights and spinoffs that has yet to exhaust itself. Theories that try to explain the universe without dark matter may well prove wrong, but identify patterns in galactic structure that dark-matter models will need to explain.

I’m sensitized to this issue at the moment because I’ve taken flack from some particle physicists for publishing Garrett Lisi and Jim Weatherall’s article in our December issue. Lisi’s ideas for unifying physics are certainly out there; even he admits it. But what persuaded us to publish the article was that, even if those ideas are wrong, they are illuminating—if not for physicists themselves, then at least for aficionados who keep hearing about geometric concepts such as Lie groups and crave an explanation. Whatever theory ultimately unifies physics, it will need to explain the intricate regularities in particle properties that Lisi’s article describes.

So how do scientists encourage productive risk-taking? Several conferences I’ve been to have had brainstorming sessions where scientists were encouraged to spill whatever was on their minds and not worry about being judged. Blogs and online preprints tap into the substratum of hunches, musings, and null results that lie just below the public surface of peer-reviewed papers. Last week I talked with Ijad Madisch, co-founder of ResearchGATE, a science networking website. He says he set up the site to allow scientists to share their unpublished or unpublishable ideas and learn from one another’s mistakes.

Science is not received wisdom, but informed guesswork. It may well be wrong. That’s life. Besides, what’s the alternative? To substitute our own gut feelings for scientific analysis, flawed though it may be? We should always be willing to question the outcomes of science, but we should be even more willing to question ourselves.

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  1. 1. ncomfort 1:52 pm 12/20/2010

    There’s a sense in which mere biases could indicate something wrong with the scientific method. That something is hubris–or perhaps complacency. As Lehrer concludes, just because something can be proved doesn’t mean it is true. Yet I have often encountered the belief that it does.

    I read him as saying that science as currently practiced encourages arrogance about its own certainty. Once the enemy is safely barred outside the gates, you can relax, right? Lehrer’s saying there are always cracks in the walls. Certainty undermines certainty. You can only be confident in a theory’s truth so long as you harbor a doubt about that truth.

    This doesn’t mean that science is bankrupt. Just that we must remain vigilant.

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  2. 2. jtdwyer 2:24 pm 12/20/2010

    I am compelled to continue pressing this simple explanation for the identified principal requirement for additional mass to be provided by the proposed dark matter.

    Around 1970, Vera Rubin observed the orbital velocities of stars at varying distances from the center of spiral galaxies. To her and her contemporaries’ amazement, those velocities did not vary as a function of the stars’ distances from the galactic center, as specified by the laws of Planetary Motion derived from observations of the Solar system.

    There was no real basis for their expectations, since the only similarities between spiral galaxies and planetary systems is that they primarily consist of a rotating planar disc.

    In contrast, planetary systems orbit a dominating central mass (98.8% of total Solar system mass is contained within the Sun), planets are sparsely distributed, bound primarily to the stellar mass. As a result, the further away a planet is from the Sun, the further it is away from most system mass.

    Much of spiral galaxies’ mass is distributed throughout its planar disc. Stars at the periphery of spiral galaxies primary gravitational influences are the billions of comparable stars and gaseous masses nearest to them, not some oversimplified ‘center of mass’ located many tens of thousands light years away.

    There was never any sound, much less proven, basis for expecting the billions of stars in the rotating planar disc of a spiral galaxy to behave like the few planets orbiting our Sun. As a result, there was no need to ‘correct’ this perceived discrepancy by applying undetected mass or modifying gravitational theory.

    I wish I could better explain: there’s plenty more that can be said to elaborate this fundamental error, but it seems to me that the above communicates the essential facts. Can anyone offer any help?

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  3. 3. quincykim 2:59 pm 12/20/2010

    Like the article’s author, I too recommend reading Kathryn Schultz’s "Being Wrong." Wrongness is, in general, our persistent condition, but rightness is our persistent feeling. That feeling of rightness affects a person’s every judgment, even when supplanting an old right with a new one. I doubt that will change anytime soon.

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  4. 4. carlofab 5:24 pm 12/20/2010

    Willard Quine’s introduction to his "Systems of Logic," my text book in college, addressed this. My memory according to Quine: If a theory or model does many things right and is widely accepted for that reason, anomalies on the peripheral of the system tend to be simply noted as such. There are, for example, many living anomalies that should not be there per our current understanding of evolution.

    But if the anomaly strikes at the basic fundamentals of a model, then the model itself is at hazard.

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  5. 5. robert schmidt 7:19 pm 12/20/2010

    @carlofab, "There are, for example, many living anomalies that should not be there per our current understanding of evolution." perhaps you could enlighten us as to which anomalies you are speaking of. I am not aware of any. I suspect the anomalies represent your understanding of evolution rather than inconsistencies with the theory itself

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  6. 6. 5:59 am 12/21/2010

    Provocative article, but conspicuous by it omission is any discussion of the highly contentious debate over the theory of anthropogenic global warming.

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  7. 7. zstansfi 6:33 am 12/21/2010

    "I read him as saying that science as currently practiced encourages arrogance about its own certainty."

    Mr. Lehrer may believe this to be the case, but any scientist who practices his or her research in this fashion is bound to fail utterly at the profession. Science requires a measure of uncertainly–a willingness to accept fault and to try and retry hypotheses, alternate hypotheses and previously unexplored avenues of inquiry. It is true that we may be forced by necessity to battle in support of our findings, to defend our reputations in order to build careers. However, this should not be mistaken as an zealous and dogmatic certainty. Science is as it has always been, a tool for identifying truth: whether this be the indelible, eternal and elusive Truth, or simply a series of facts which apply in only a specifically defined set of circumstances.

    Jonah Lehrer may be an entertaining author, but he is not a scientist.

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  8. 8. MUSKATINHO 12:14 pm 12/21/2010

    Robert Burton’s book "On Being Certain: Believing You Are Right Even When You’re Not" covers this issue well. As philosopher John Campbell says in his review of the book:

    "Philosophers have long puzzled over the nature of knowledge. Burton has a sharp rejoinder: "Certainty is not biologically possible. We must learn (and teach our children to learn) to tolerate the unpleasantness of uncertainty. Science has given us the language and tools of probabilities. We have methods for analyzing and ranking opinion according to their likelihood of correctness. That is enough."

    Anyone hearing this is likely to protest there are plenty of things about which they feel perfectly sure. What is really new in what Burton is doing is his analysis of this ‘feeling of certainty’. It is biologically grounded, and has a definite biological function: to stop reasoning and the estimation of probabilities running on forever. It is rewarding: the feeling of certainty is one of the things we humans crave. Addicts are all around us, but even sober citizens find the taste irresistible. It’s one of our basic motivations – it’s only because we want this feeling that we reason and argue as passionately as we do. But Burton is devastating on the idea that this feeling of certainty is any guide to truth. The schizophrenic convinced his dustbin controls the universe, you or I trying to recall what we were doing on 9/11, the scientist with an unproven hypothesis, can all be equally in the thrall of the feeling of certainty and all quite wrong. It’s somehow less of a surprise that other people can have the feeling of certainty yet be wrong, but it’s always shocking when it happens to you. Burton’s argument is that we have to liberate ourselves from this dependence on certainty, and live with ever-changing probabilities."

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  9. 9. robert schmidt 12:49 pm 12/21/2010, the purpose of the article was not to catalogue all cases where there is controversy, but if they did AGW would not be one. The shrill cries of special interest groups lying and deceiving the general public into believing that they should maintain the status quo in order to preserve the fossil fuel industries does not qualify as debate. It qualifies as malevolence. Similarly the article did not mention the "debate" over mans visit to the moon. There will always be ignorant and evil people in the world who will gladly twist the facts to advance their agenda. The role of science isn’t to convince them they are wrong.

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  10. 10. 12:43 am 12/22/2010

    Robert – Not all who question, (not deny, QUESTION), the extreme projections for AGW proponents are shrill malevolent dupes bent on world destruction for short term gain. Maybe there are a few, but not many, really. I believe that we went to the moon, I find the theory of evolution convincing and I know for a fact that the earth is round. What I question is the alleged certainty that AGW has only one cause and only one solution, and that any who raise any doubt are either soft in the head or subsidized by evil forces. The role of science is to continuously test, reassess, re-examine and when possible, confirm, the theories that best help us to understand how the world works. Time and again theories that seemed rock solid are found to be flawed or incomplete. Global warming theory cannot be exempt if it is to be counted as science. As Richard Feynman once said "My definition of Science is the belief in the ignorance of experts." That worked pretty well for him, and I will stick with it as my working definition. OK I will now stop my shrill cries and go back to counting my oil money while planning the destruction of life on the planet. So many species to kill – so little time!

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  11. 11. jevance 1:36 pm 12/22/2010

    in response to jtdwyer. I seem to recall from my Physics classes in college that the gravitational force of the Earth would be less on an object as it got closer to the center of the Earth (if the object were inside the Earth). The amount of mass inside the radius of the object from Earth’s center was the M used in the equation and the effects of any mass outside this radius effectively canceled (there was a neat geometric proof of this involving cones and the inverse square law). I’m sure that the same reasoning applies to spiral galaxies or other radially symmetric objects. Since the velocity of a star would be determined by letting the centripetal force (F = mass of star(velocity squared)/radius), produced by the effective mass of the galaxy (M) inside the radius of orbit of the star, be set equal to the force of gravity (Newton’s Law F = GmM/(r squared) then the velocity squared of the star would be equal to G M / r. Vera found that the stars velocity stayed relatively constant as the radius increased, I believe. This would mean that the effective mass pulling on the star would have to increase in direct proportion to the radius of its orbit. I don’t think this would be expected to happen for a typical spiral galaxy since the stars in the arms tend to thin out the further you get out from the center. I’m making a few assumptions but I think I’m at least approximately right.

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  12. 12. gmusser 4:29 pm 12/22/2010

    @botbldr I thought about commenting on climate change in my post, but decided not to because I felt the debate has gotten so contentious that it would have overwhelmed the other points I sought to make. But my final sentence is, I think, relevant here. I admire you for seeking to understand climate science for yourself and get under the surface of experts’ public pronouncements, but just be sure you apply the same skepticism to your own feelings on the subject. I’ve gone through this self-examination myself (see my post at and ended up concluding that the globe really is warming, that humanity is responsible, and that it would be to prudent to take action now.

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  13. 13. 9:59 pm 12/22/2010

    The universe big-bang beginning standard model is kept alive by inventing phony dark matter particles to detect. this fools taxpayers in society by wasting spending that falsely explains huge amounts of missing gravity to keep galaxies together. rotation curves to fit actual spiral flat galaxy shapes are explainable by EM forces without dark matter and inferred to exist yet still undetected black holes at the LHC

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  14. 14. jtdwyer 9:44 am 12/25/2010

    Thanks for your comments, however:

    I’m not physicist, but I think that you (and the equations of physics in general) are considering the orbital velocity of (peripheral) stars to be imparted solely from collective galactic mass, generally directed from its center of mass.

    This works fine for for discrete objects of mass, but galaxies are aggregations of up to hundreds of billions of discrete objects of mass dispersed over perhaps a hundred thousand light years.

    A critical issue here is that the vast discs of spiral galaxies are regionally self gravitating, as evidenced by the persistence of their namesake characteristic spiral structures. IMO, this must result in the collective gravitational force of galactic mass is imparted to spiral structures, for example near the galactic center. It is the entire spiral structures that are accelerated by the rotational forces near the galactic center.

    The discs of spiral galaxies are not composed of a few independent objects of mass dominated by a central mass: if they were, they would behave like planetary systems. They are not and therefor do not: no compensatory magic is required.

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  15. 15. mounthell 7:16 pm 12/25/2010

    @robert schmidt, it might be that you are not aware of "many living anomalies that should not be there per our current understanding of evolution" because your perspective stems from that inculcated by the methodology of science. Musser makes the same mistake that (according to the informed/inculcated view) "Science is not received wisdom, but informed guesswork."

    The basis of current understanding as to how we interpret our data can only be received wisdom because that’s how social human beings function. To think that we do not subscribe to the current notions of the herd is to deny that those of us who seek insight into the workings of some part of the universe operate independently is egregiously wrongheaded. Doing so merely reveals we are ignorant of the intricate and intense social infrastructure under which we each operate. Returning to the earlier topic, we see glimpses of that in current perceptions of evolution.

    As an introduction, we might refer to recent work describing how long noncoding RNAs perform key roles in metabolism and development and that epigenetic processes posture DNA sequences for transcription, the products of which are further selected by the aforementioned RNAs (and microRNAs). This is just the ‘tip of the iceberg’ of how biological processes are controlled and not, as is so tediously recited, controlled by "genes" (as repeated by, for example, the noted gadfly and science-fiction writer, Dawkins).

    That life-science disciplines remain balkanized (cubicle-ized) can be seen in the fact that change in a given organism occurs through different dynamics depending upon the disciplinary viewpoint describing it. Compare control of development: devo = genes; neuroscience = cell microenvironment; ecology = environment (food web, life history, complementary species); animal behavior = social environment; cancer researchers make much of DNA sequences associated with cancers, calling them "oncogenes" (there is no such thing).

    Note that we still lack:
    a. an overarching theory of life by which all disciplines can interrelate their data (the "modern synthesis" is inadequate) and
    b. we have no useful and comprehensive definition of the term "life", that is, we don’t know what "life" is.

    Because of these gaps in our vaunted understanding of the universe, we have no cure for cancers (nor tenable insight into their dynamics) or developmental diseases like autism spectrum disorders. The dark-ages organization of the science business prevents us from grasping the underlying subtleties. Darwin was right, but…

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  16. 16. bucketofsquid 4:35 pm 12/27/2010

    Not to intrude but I find the debate between jtdwyer and jevance to be fascinating. What I understand about gravity is that the further an object is from the source of a gravitational force, the less the gravity will exert force on it. This means that in a galactic formation the closer stars exert greater force than farther stars. With the scale of galaxies this would tend to indicate that most of the stars in a galaxy are simply too far away to have much impact on any given star. The scale of gravitational force of stars and interstellar distances is very different than the scale of gravitational force of atomic particles and the distances of atoms in the Earth. I really don’t know the divergence that would occur if we were to scale atoms up to stellar size and measure the space between them but I doubt that it would match the spacing at a galactic level.

    Instead of introducing an invisible "dark energy" or "dark matter" would it not be better to just say that the theory of gravity is slightly off? Any theory that doesn’t scale properly is either missing contributing data (thus "dark matter") or it lacks accuracy. My personal feeling is that the math is bad and the theory of gravity needs refinement. I’ve found a number of situations where measurements didn’t scale well but changing the base unit to something more accurate fixed the issue.

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  17. 17. jtdwyer 10:51 pm 12/27/2010

    Thanks for your interest. IMO the established gravitational equations are adequate within their stated limited domains.

    As I understand, astronomers generally rely on Newtonian gravitation and the laws of planetary motion to evaluate gravitational effects. In an unpublished paper, "General Relativity Resolves Galactic Rotation Without Exotic Dark Matter", F. I. Cooperstock and S. Tieu asserted that the Galaxy Rotation Problem was produced by the inadequacies of Newton’s gravitational equations. This may be true to some extent, but their representation of a two dimensional disk was criticized by Mikolaj Korzynski as being physically invalid. Please refer to:

    Personally, I think the problem of estimation discrepancies is two fold: astronomers tend to apply overly simplified methods of gravitational estimation to extremely complex distributions of mass, and those extremely complex distributions of mass are extremely difficult to adequately represent.

    As I understand Newton’s law of universal gravitation specifies that is is only valid to estimate the gravitational ‘attraction’ effect between two _point_masses_. A point mass can be defined as a single point representing an object of mass. Newton’s shell theorem mathematically proves that spherically symmetrical distributions of mass can be effectively treated as a point mass. Non-spherical aggregations of discrete massive objects cannot be correctly represented by a single point mass.

    While the rotational curve of planets in the Solar system are principally determined by the two-body solution to each planet’s gravitational bond with the Sun, the same does not apply to galaxies. IMO, it is a case of attempting to fit the problem to the solution at hand: to person whose only tool is a hammer, every problems appears to be a nail.

    Unlike spherical objects of mass, galaxies a extremely complex distributions of mass: I doubt that any simple equation can adequately describe its gravitational effects.

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  18. 18. jevance 1:08 am 12/29/2010

    In response to jtdwyer. The (Radius cubed)/(Time squared) = constant relationship discovered by Kepler for planetary motion shows that planets go slower the further they get from any central object (like the sun). I don’t believe astronomers are relying on this relationship to determine the predicted velocities of stars for all the reasons that you’ve stated. Rather, I think they are relying on Newton’s law of gravity alone and a honking fast computer. Because there are so many stars in a spiral galaxy I doubt that they can calculate the force interactions for all two (or so) hundred billion stars but by making appropriate simplifying assumptions, they can come up with consistent answers. One assumption might be that each star’s mass could be represented as a point mass located at its center. Another might be that a small spherical region of stars might be represented as the sum of their masses located at their center (I’ll just call this another big star). Once the entire galaxy has been ‘simplified’, based on data of stellar densities and locations, to the point that the calculations won’t take a zillion years, then the laws of motion are applied. Each element(star region) would have the vector sum of all the gravitational forces of all the other regions on it calculated. This resultant force would point toward the center of the galaxy basically because the left-right symmetry of the galaxy (as you face the center)pretty much ensures the perpendicular components of the forces would cancel out. This resultant force then becomes a centripetal force, causing the star’s motion to deflect out of a straight line. This deflection, repeated for each successive calculation, will produce circular motion only for a single velocity for that resultant force and that radius of orbit. In any case, the acceleration (F/M) of the star can be determined for a small increment of time determined by the programmer, a new velocity calculated and a displacement calculated. Then recalculate everything again using the new positions and velocities. Set the velocities initially as you wish and see what develops. Either each concentric ring of the galaxy will expand, shrink, or remain stable. Stable means you got the initial velocity correct for that radius. The time increment can be lessened to give greater precision. You’ve almost got me interested enough to try programming it for a few hundred stars just to see what happens. There must be some astronomy person out there who has done something similar to this? Any comments?

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  19. 19. ThomasH 2:22 am 12/29/2010

    Lehrer’s article, if read carefully, showed that some scientists are fooling themselves into believing things that they have not proven. Rather than showing that "the truth wears out," he shows that the scientific method works extremely well, that scientists need better training in experiment design and statistical analysis, and that pharmaceutical executives need a better grounding in science. Unfortunately, that message was nearly lost in the sensationalist spin.

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  20. 20. ThomasH 4:50 am 12/29/2010

    @jtdwyer "As I understand Newton’s law of universal gravitation specifies that is is only valid to estimate the gravitational ‘attraction’ effect between two _point_masses_. A point mass can be defined as a single point representing an object of mass."

    This is not true. Newton’s equation F = -G M m / r^2 does seem to imply point mass. However, it is possible to integrate this over an extended object with some mass density function. Analytic solutions are possible within some constraints (e.g. using the Shell Theorem requires mass M to be roughly spherical), and undergraduate physics courses usually demonstrate this for planetary bodies, showing why gravity at the surface of the Earth points toward the center of the planet and how that force decreases as you approach the center of the planet. Numerical solutions, which seem to be more common in astrophysics research, require greater computing power but also offer greater flexibility in modeling non-spherical and "lumpy" masses like galaxies. I suggest that the best course of action is to explore the peer-reviewed literature to understand how astrophysicists actually model galaxies and predict stellar motion.

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  21. 21. jtdwyer 12:56 pm 12/30/2010

    I’m not a physicist or scholar, but a retired information systems analyst. Referring to wikipedia’s entry, "Newton’s law of universal gravitation", in addition to supplying Newton’s gravitational equation it states the definition (referencing a translation of "The Principia"):

    "Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses:[2]"

    I suspect that other practical applications of Newton’s formula to other configurations of mass are mathematically unproven simplifications. But then I’m not a mathematician: aren’t mathematical proofs required for such extensions and simplifications?

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  22. 22. jtdwyer 1:56 pm 12/30/2010

    Thanks very much for your interest.

    I’m not capable of reviewing all the research, so I focus mostly on the establishing report: Rubin, V. C. (1970). Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions. Astrophysics Journal , 159, 379-403;…159..379R

    As I understand, the original definition of the galaxy rotation problem arose directly from the identified observational discrepancy with Kepler’s rotational curve.

    I think that the ‘big star’ estimation approach has been widely used, as has heard mention of initial estimations using a central proxy of estimated total galactic mass located at the periphery of the galactic core.

    I’m not really up to following your description of appropriate calculations, but I think that there are some considerations that are critical to reasonable estimation:
    - The majority of galactic mass is so distant that its gravitational effect is severely diminished. I think this generally accounts for the perceived discrepancy with the ‘big star’ approach, ignoring nearer masses.
    - Most stars in the galactic disc would be surrounded by nearby masses, produced an effective network of local bindings.
    - Local omnidirectional ‘attraction’ effects would not cancel out but rather produce a positionally stabilized, bound structure, I think.
    - This structure may be affected by the inner disc rotational forces as a unit, explaining the seemingly excessive velocity of peripheral stars: if the rotational force of the inner disc is applied to spiral structures, that same rotational velocity may be achieved by peripheral stars.
    - I’m aware that spiral structures are apparently not simply ‘wrapped’ around the galactic core, but a wrapping effect combined with some stretching any many other distorting effects may account for the observed motions.

    I think I’ve just specified a nearly impossible analysis that may correctly represent the factors producing the observed motions, but does not enable simplification…

    There has been some (I think) very interesting unpublished work done by a Kenneth F Nicholson. That may be using the concentric ring analysis approach I think you’re describing. His body of work is presented in "Newtonian mechanics & gravity fully model disk galaxy rotation curves without dark matter", Dilip G. Banhatti;

    I’m not really capable of evaluating Nicholson’s methods – any any additional feedback would be greatly appreciated!

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  23. 23. jtdwyer 2:31 pm 12/30/2010

    FYI – Not all the links to the referenced Vera Rubin abstract page return the PDF: to download from the summary page, click "Full Refereed Journal Article (PDF/Postscript)" near the top of page.

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  24. 24. jtdwyer 3:01 pm 12/30/2010

    By the way, using the ‘big star’ approach to spiral galaxy gravitational estimation is in my view an crude oversimplification and invalid application of Newton’s law of Universal Gravitation (see comment #21 above). That it is invalid can easily be illustrated by the common misinterpretation that the distance specified is the separation distance between to objects of mass: Newton specifies the separation between two _point_masses_, which would generally be the distance between the _centers_ of two spherical bodies. In the case of a vast galactic core being (improperly) represented by a single point mass, the error/difference between its periphery and center would be a significant percentage of total distance. The result of more correctly specifying the distance to the center of the galactic core would amplify the discrepancy, increasing the amount of ‘missing mass’.

    If astronomers are using such crude oversimplifications to invalidly apply established gravitational estimation methods, how can these results be reliable?

    As I understand, accurate application of Newton’s equation to a composite, aggregation of massive objects would require solution the inverse-square attraction between _each_ individual body of mass. The result could then be simplified by using vector summation to determine a ‘net attraction’. However, I suggest that this would eliminate too much information, indicating the production of multidirectional structural bindings.

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  25. 25. phaedrus76 5:55 pm 01/13/2011

    Because I’ve been looking for a solution to the "file drawer" problem for a long time, I eagerly read about ResearchGATE in this post and promptly joined. While it does appear to "allow scientists to share their unpublished or unpublishable ideas and learn from one another’s mistakes," there is no evidence I can see that anyone is actually using the site in this way. I’d like to be proven wrong. Please PM me if you know where the failed studies are hiding on ResearchGATE– or any other outlet (particularly in my field, which is psychology).

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  26. 26. jtdwyer 11:43 pm 01/15/2011

    After a quick look at ResearchGATE, I agree with your assessment: it appears to have been stillborn a couple of years ago. Curious that it was even mentioned in this article, apparently without any investigation whatsoever.

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  27. 27. matty2431 11:11 pm 01/24/2011

    Scientific debate! The true lifeblood of the field!

    In all seriousness, I loved reading everyone’s comments here. As a fellow scientist, I find some flaws within this article… but also some very fundamental gaps that are often taken for granted, especially by those who have been around the block a few times. Right now is a very, very exciting time within the scientific industry which stems from a large changing of the guards. A new crop of young scientists (your gen x/y-ers) are stepping in for the old breed. I am willing to guess nearly everything within the scientific field will be questioned, challenged and possibly refuted or expanded in the relatively near future. For the past century, science has been primarily one track minded and unfortunately for us all that track has delivered the train of war. Now, with the bio/molecular revolution as well as very promising, previously impossible physics experiments and the drive for a more sustainable Earth has lead us, as one race, to use science for its true aims. That being, advancing humanity as a whole… for the greater good so to speak. The scientific method is absolutely the ground level for all scientific experiments, I do not think anyone in their right minds would ever question this. However, the DISCOVERY of the scientific method is only one in a numerous list of scientific DISCOVERIES that mankind has happened upon. Nearly every scientific discovery, given time, will be improved upon by future research, this is a guarantee. So why wouldn’t our beloved scientific method be challenged, peer reviewed and subjected to the same scrutiny that we all must go through for something that may seem insignificant in comparison?

    Link to this

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