Today is another bit of rubbish from viXra! In the comment thread from the last post, someone (I presume the author of this paper) challenged me to address this. And it’s such a perfect example of one of my mantras that I can’t resist.
What’s the first rule of GM/BM? The worst math is no math.
And what a whopping example of that we have here. It’s titled “Spacetime Deformation Theory”, by one Jacek Safuta. I’ll quote the abstract in its entirety, to give you the flavor.
The spacetime deformations theory unifies general relativity with quantum mechanics i.e. unifies all interactions, answers the questions: why particles have mass and what they are, answers the question: what is energy, unifies force fields and matter, implies new theories like spacetime deformations evolution.
This is a theory of principle (universal theory delivering description of nature) and not constructive theory (describing particular phenomenon using specific equations).
The theory is falsifiable, background independent (space has no fixed geometry), not generating singularities or boundaries.
This is hard to believe but a belief has nothing to with it. The real intellectual challenge is to falsify the theory.
So, we’ve got what the author claims is a grand unification theory – the one thing that has evaded the best minds of the last hundred years! And it’s falsifiable! Wow!
Unfortunately, as we’ll see, it’s not falsifiable in any meaningful way, because it doesn’t make any predictions.
One of the important qualities of a genuine scientific theory is that it makes predictions. That is, a theory isn’t a vague bundle of words; it’s something precise, which describes some aspect of reality to a sufficient degree of details that it allows a scientist to make predictions, and then perform a test in reality that checks whether or not the prediction is correct. The most important property of a prediction is its potential to be wrong. A testable theory makes a prediction which isn’t guaranteed to be correct.
As a quick aside, this is the difference between intelligent design and evolution. ID can take any evidence, and say “That’s what the designer wanted”. Mike Behe can predict that there are no “irreducibly complex” systems. But when push comes to shove, he never defines irreducibly complex in a testable way. He can conclude that some system is IC; but if it’s proved that it’s not, that doesn’t invalidate ID. It just shows that that one system isn’t IC – and he’ll just wave his hands and point at another dozen that he claims are. Even if you could get him to accept the idea that IC isn’t a proof of anything, ID remains perfectly fine: there’s nothing that can invalidate it.
Evolution is thoroughly falsifiable. It predicts, for example, that all living things have a common ancestor. And test after test has supported that. If you can show a single species that isn’t derived from the common ancestor, evolution goes down. If you can show a single feature of a single species that really couldn’t have been the result of evolution, then evolution goes down.
In the case of our friend Jacek, he’s got a non-falsifiable “theory”. It’s so woefully vague that there’s nothing in the world that could possibly falsify it. It’s got plenty of problems, but due to its vagueness, any problem that could potentially be used to falsify it can be handwaved away.
So what’s his theory? Basically that everything is a distortion of spacetime. What appears to be a particle is really just a distortion of spacetime – a sort of pinch in the fabric of space around the location of the point. Forces are also distortions in spacetime – they’re just shaped differently.
To quote him:
Any interaction between spacetime deformations we notice as a force: we named them gravitational, strong and weak nuclear and electromagnetic. Any spacetime deformation (a physical object) interacts (a force) with all other objects (being the force itself!)
A differentiation of forces depends only on gradient and size of the deformation subject to our detection. (see exemplary Figure 1).
Read: all interactions (forces) are only spacetime deformations with different geometry!
So – all forces are the same deformations of spacetime. The only distinction between the forces comes from the gradient and size of the spatio-temporal distortion.
OK, here’s one potential falsifier: he’s claiming that gravity and electromagnetic forces are exactly the same thing. Why does a magnet only attract certain things, instead of everything? It’s just a distortion in spacetime, right? He specifically claims that the differentiation of forces depends only on the gradient and size of the deformations. Gravity attracts everything equally. Magnetism attracts some things, and repels others. How can the same distortions behave so differently if they only differ in gradient and size?
Of course, he can wiggle out of that. Throw in a couple of extra dimensions, and claim that different dimensions distort differently. So the difference between forces could be their size and gradients in different dimensions. Presto! Easy.
After this, he gets to something that he seems to believe is profound:
3.11. Finally, we can ask the question: what is pressure? And answer: it is a spacetime deformation.
I’d love to know who asked that question? Or rather, who asked that question without knowing the answer? Since when is the nature of pressure a problem?
Now, we move on to the very best part. He’s got an entire section that’s titled “Mathematics”. It starts off with the statement:
Hooke’s law in simple terms says that strain is directly proportional to stress.
Tensor expression of Hooke’s Law
(The incomplete second sentence is exactly as it appears in the
paper.)
What does Hooke’s law have to do with anything? He never says. The rest of the “mathematics” section is essentially content free.
There’s one drawing that is supposedly an example of a particle in spacetime. What kind of particle? Unspecified. What are the axes? Unspecified. What’s the magnitude? Unspecified.
Then, there’s a couple of bell-curves, which supposedly illustrate the “spacetime density of nuclear matter”. They’re just absolutely traditional illustratory statistical bell-curves, with no unit on the Y-axis, and the x-axis measured in standard deviations. Standard deviations from what? He doesn’t bother to say. (In fact, in the bibliography, he credits the bell-curve illustrations to wikipedia.)
And that’s the end of the paper. That’s it.
For a supposed GUT, it’s really missing a lot of things. For example, it claims to explain the nature of particles – they’re distortions in spacetime. But the problem for the theory is, particles only occur in certain, very limited forms. There are only 12 kinds of particles. If it’s all just continuous distortions in spacetime, then why aren’t there a continuum of particle sizes? Why does charge come in discrete units? Why do electrons only exist in discrete energy levels, instead of a continuum? The theory doesn’t explain this. It seems like it predicts a continuum of particle sizes/strengths. But we can’t falsify it that way, because it’s too vague. He can wave his hands, and claim that there’s some reason for it.
He clearly states that there’s no wave-particle duality: “The wave-particle duality notion is not necessary any more as wave and particle are the same thing. We can assume a particle to be a transverse or longitudinal wave.” And yet, there are very concrete experiments – the dual slit experiment – that can demonstrate both non-particle wave behavior, and non-wave particle behavior. As described, his theory can’t explain that. But we can’t say that it falsifies it either, because once again, there’s just not enough precision here to say, definitively, what he means by “assume a particle to be a transverse or longitudinal wave”.
It’s really quite an astonishingly bad pile of rubbish. And despite the author protestations to the contrary, it’s a perfect example of a non-falsifiable pile of rubbish, because it lacks anything approaching the precision or completeness that would allow it to make a falsifiable prediction.
Any resemblance to the name of Jack Sarfatti is purely coincidental?
Mark, Mark, you really must lay off the viXra, it’s not good for your health. Instead why not spend some time at the other alternative to arXiv? It seems to beat viXra on “scientific value of the average paper”. It even gives some hard-hitting comparisons between its content vs. arXiv’s content!
soulless: You beat me to what I was just about to say! Also, I am worse than a monkey at identifying real physics versus pseudo-intellectual pontification.
In fairness, IC is defined well enough to be falsified. Which is unfortunate for Behe. 🙂
@4:
I disagree. How can you falsify ID?
If there are no irreducibly complex systems, does that mean that there can’t be an intelligent deity that designed things? Nope. You can falsify irreducible complexity as a way of proving intelligent design (which lots of people, including me, have written about). But you can’t prove that ID is wrong. *That* you can’t do – because the way that ID is set up, there’s simply no evidence that you can possibly muster that *can’t* be claimed to be the deliberate work of a designer.
That’s why ID isn’t science: because there *is* no theory. It’s just “goddidit” – and no matter what objection you raise to it, the ID supporter can always argue “goddidit.”
Evolution with common descent predicts common descent, but evolution does not – discovering microbes on Titan with no relation to Terran family trees would not invalidate evolution – nor, for that matter, would discovering that certain protists formed a self contained group with no relation to other life. So long as evolution can be evidenced for each family of descent, the theory (nonrandom survival of randomly varying replicators, at most basic) still stands.
Just thought I’d point that out. The prediction of evolution is that, over time, lineages adapt more closely to their environment, which may include other varying lineages, by a process where the attributes of the more successful members of a lineage are preferentially passed down to the next generation. As a consequence, a sub-prediction is the famous “bunnies in the Cambrian” as the bunny shape is not one suited to the period and belongs in a thoroughly different stratum.
I don’t think that’s strictly true, but point taken.
I am confused. The abstract (and I checked the paper too) says: “The theory is falsifiable”. Not *unfalsifiable*.
Just thought I’d point that out. The prediction of evolution is that, over time, lineages adapt more closely to their environment, which may include other varying lineages, by a process where the attributes of the more successful members of a lineage are preferentially passed down to the next generation. As a consequence, a sub-prediction is the famous “bunnies in the Cambrian” as the bunny shape is not one suited to the period and belongs in a thoroughly different stratum.
It’s not that the “bunny shape” is “not suited” for the Cambrian. Its that the “bunny shape” has many accidental stepwise adaptations from the terapod shape that don’t allow it to appear it as a descendant of Cambrian fauna.
For all I know a trilobite species exists with bunny ears and a growth on its mandible that looks like a cartoon rabbit overbite. But such traits are predicted to arise by stepwise changes from (obviously completely unevidenced) ancestor populations, and without those ancestors the traits are unlikely to occur.
Methinks you oversimplify things here a bit. Evolution as such would not be wrong if it turned out that we had two biogenesis events on this planet. On the other hand, it could be argued that restricting science to only hypotheses making testable predictions would be a tad too narrow. When somebody documents the species composition of a patch of rain forest, or digs up artifacts from a prehistoric campsite, are they not scientists? I think the core issue is (1) to use evidence from the world around you and (2) to accept the most plausible explanation fitting all the evidence. ID fails because the evidence is against it, not because it could not be a scientifically plausible explanation if we had found the evidence to indicate that all species miraculously appeared fully formed in 4004 BCE.
A couple of people have beat me to this, but resist the temptation to use evolutionary theory in your arguments unless you really, really know what you are talking about. Many very intelligent people with excellent training and insight into their own fields seem to feel like they should be able to understand evolution intuitively, on their own terms, without actually studying it seriously. Just my opinion, but I would rank scientific stuff like this: Special Relativity is easy. Fluid Mechanics is hard. Evolution is a %*&#%)@ bitch!
That is what the paper says, but it is an unsupported assertion.
The author really needs to provide some testable predictions that, if they fail, would falsify the hypothesis. (I will *not* dignify this crap by calling it a theory. It very clearly isn’t.)
But, as MarkCC pointed out, that isn’t possible.
It predicts, for example, that all living things have a common ancestor.
So it makes a prediction about the past?
Have you ever looked up the definition of “prediction”?
(I am not an ID believer, but your phrasing here is so vague as to be meaningless.)
@Nemo (#14)
No. It makes a prediction about future observations.
—- further comment redacted due to (possibly) unwarranted snark —-
MarkCC @5 – you’ve changed your argument. I agree that ID can’t be falsified, but that wasn’t what I was responding to. It was to your assertion that Behe’s IC concept couldn’t be falsified. Something is irreducibly complex if it doesn’t work if you take away one part. Behe then claims that such a thing couldn’t evolve, and therefore the Designer diddit.
That can be falsified either by evolving something that is IC, or by show that there is a pathway by which an IC object can be made, where all of the intermediate parts are functional.
@14: As mentioned above, the one common ancestor is perhaps not the best example for evolution per se. But how about: it predicts that you will not find the most complex organisms in the lowest sediment layers (i.e., the famous rabbits in the Precambrian that would disprove evolution).
Thanks to everyone who pointed out that the Rabbit structure is not found in the Cambrian thanks to Parochial structures inherited from other Tetrapods, forgot about that.
Um … genetic engineering?
It may seem like I’m quibbling but I’m not. After all, what ID really claims is that all the features in species were ‘engineered’.
Ooo, you got burned. See, the fact that humans can do genetic engineering is proof that genetics has ALWAYS been engineered. Just like lab grown diamonds prove that all diamonds were created in a lab. Just like synthetic rubber proves that rubber trees were designed by materials engineers.
rni @16: Something is irreducibly complex if it doesn’t work if you take away one part. Behe then claims that such a thing couldn’t evolve, and therefore the Designer diddit.
Miller pointed out to Behe many years ago that this definition was flawed, because what Behe should be focusing on is evolution of new traits, not taking away current ones. Behe agreed with that evaluation of his definition, stated that he was working on a revised definition…then never published one. So Mark’s right; even Behe’s CSI definition is not falsifiable, because right now we don’t know what it (the revised definition) is.
In this respect he (Behe) is mirroring the whole movement; he started out with a clear definition of his hypothesis. When that was refuted, he protected it by getting more vague.
Thank you Mark for you response. I was waiting for a criticism. Thant is the reason I called it the theory and not a theorem. And I’m still not convinced that my publication is a crap. So I’ll try to address some of your comments.
MarkCC: Unfortunately, as we’ll see, it’s not falsifiable in any meaningful way, because it doesn’t make any predictions.
Jacek: “3.9. The spacetime is an elastic medium so we can determine it’s bulk modulus, determining in turn spacetime deformations’ velocity, including speed of light.”
As far the spacetime is not regarded to be an elastic medium. So I’m waiting for experiments or observations that could debunk it. It’s a piece of cake for physicists.
MarkCC: In the case of our friend Jacek, he’s got a non-falsifiable “theory”. It’s so woefully vague that there’s nothing in the world that could possibly falsify it.
Jacek: The fact that you cannot find anything that can falsify it (having only a day) it doesn’t mean it is impossible. A good potential to falsify the theory lies e.g. here:
“3.5. The objects we call particles (or any other objects) do not have sharp (distinct)
boundaries because they are spacetime dynamic deformations (see Fig. 2). They are
wave packets4.
3.6. If the particles have no sharp (distinct) boundaries they also does not have a clearly
defined mass.”
Maybe someone could find a particle having sharp (distinct) boundaries or mass?
or ”3.7. An absolute vacuum in the meaning of not deformed Euclidean space does not exist because all spacetime deformations have non limited range. A result of that property is vacuum polarization.”
Maybe someone will find or create an absolute vacuum? As far it has been not possible.
MarkCC: just a distortion of spacetime – a sort of pinch in the fabric of space around the location of the point.
Jacek: They are not distortions of any kind but wave packets. That’s the difference. And you can easily find a ready to use math on wave packets (Schrödinger equation). And using the math you can calculate properties of any object consisting of so called elementary particles.
MarkCC: OK, here’s one potential falsifier: he’s claiming that gravity and electromagnetic forces are exactly the same thing. Why does a magnet only attract certain things, instead of everything?
Jacek: I claim they are the same in principle. And that principle is what physicists are looking for. I have also showed differences.
MarkCC: Magnetism attracts some things, and repels others. How can the same distortions behave so differently if they only differ in gradient and size?
Jacek: Different size and gradient means that they differ in shape. As we know e.g. Lego pieces of all varieties are a part of a universal system. So the shape is the key. You like the evolution theory so maybe you heard about enzymes. They act only by shape. That is the way they catalyze every reaction. Every enzyme has a specific shape that fits to a specific chemical compound.
MarkCC: Of course, he can wiggle out of that. Throw in a couple of extra dimensions, and claim that different dimensions distort differently.
Jacek: You are talking about a string theory which is really unfalsifiable, but loved by scientists. They can easily publish on arXiv and spent millions of dollars working on this piece of math.
MarkCC: Tensor expression of Hooke’s Law
Jacek: First of all I claim: “This is a theory of principle (universal theory delivering description of nature) and not constructive theory (describing particular phenomenon using specific equations).” Just like the evolution theory. In the evolution theory there is complete lack of equations, but we are sure it is a good theory.
However my theory may be developed using math, so “Tensor expression of Hooke’s Law” is only a hint. There are many brilliant physicists and mathematicians that could possibly go this way. The base is the implication: “3.9. The spacetime is an elastic medium so we can determine it’s bulk modulus, determining in turn spacetime deformations’ velocity, including speed of light. The speed of light c is limited due to the bulk modulus of space, so it represents the possibility of spacetime deformation.”
I’m not so good physicist as you Mark so I need more time to calculate the bulk modulus of spacetime. But I’m working on it for 2 years.
MarkCC: For a supposed GUT, it’s really missing a lot of things. For example, it claims to explain the nature of particles – they’re distortions in spacetime. But the problem for the theory is, particles only occur in certain, very limited forms. There are only 12 kinds of particles. If it’s all just continuous distortions in spacetime, then why aren’t there a continuum of particle sizes? Why does charge come in discrete units? Why do electrons only exist in discrete energy levels, instead of a continuum? The theory doesn’t explain this. It seems like it predicts a continuum of particle sizes/strengths.
Jacek: They are not distortions of any kind but wave packets. That’s the difference.
And my another theory, not published yet proposes an explanation. I called it “The spacetime deformations evolution theory”. One of the postulates there: “Elementary particles and force fields we observe nowadays have been originated due to spacetime deformation self-organization (evolution). Originating objects, like during biological evolution, “tend to” gaining reproduction of their copies productivity (we assume the process to be unconscious in the meaning they are not observers)”. And another one: “Spacetime deformations evolve, resulting in creation of new mutations e.g. new elementary particles having a distinct lifetime duration e.g. different decay timing. We can create them artificially e.g. in laboratory conditions.” And another one: “The bulk modulus of the spacetime is a self-organisation of spacetime deformations parameter”. Maybe this is a crap but it is only a working hypothesis.
As you know the constants’ values in standard model of particle physics and cosmological standard model are determined experimentally and not theoretically.
Mark, maybe you know why it was so hard for scientists (like those publishing nowadays on arXiv) to accept Darwin’s theory? They thought that every organism exists without a change and always in the same shape as we can see it right now. Right now the same problem concerns e.g. recognized particles and chemical compounds.
The Darwin’s theory for many years generated no predictions. Now scientists can find only one. It is more than nothing I know that.
Darwin started explaining his findings with “artificial selection” in contrary to natural one.
Let’s think about LHC as a farm. Does it really produce naturally existing particles? Maybe it is a kind of selective breeding? However there is no real difference in the processes underlying artificial and natural selection.
My response doesn’t mean that I am fully convinced and that my theory is free of faults and completed. So believe me or not I am waiting for more criticism or / and a mind changing trial or both? Thank you.
Jacek, all stable particles have a well defined mass. Ergo, your daydreamings are falsified.
@22:
A proton has a very distinct, measurable mass. In fact, every proton has
exactly the same precise, distinct, measurable mass. It seems like according to your own words, that should invalidate your “theory”. And yet, later in the same comment, you handwave your way past it.
What’s the difference between a “spacetime deformation” and a “spacetime distortion”? You manage to handwave your way past another falsification by using the distinction between those two words as if it had some well-defined meaning.
Like I said in the post: the problem with a “theory” like this isn’t so much that it’s wrong as that it’s so damned mushy that it’s meaningless. It can’t be falsified – but not because it’s right. It can’t be falsified because it can explain anything; it’s got so much wiggle-room that you can handwave your way around any objection. Your comment here is a perfect example of that: first, you say “if there’s a particle with distinct mass, it would falsify”. But then, when you see a particle with distinct mass, it’s not a problem: just wave your hands around, mumble something about cosmic evolution, and presto: you’ve solved the problem!
As for the comparison with string theory:
(a) string theory has a hell of a lot of precision. It makes very precise arguments about how things work, why they are the way they are, etc.
(b) it’s gotten a hell of a lot of flack lately. In the early days of string theory, lots of people were very positive about it. A lot of that has turned negative. Why? Because in the early days, it appeared to explain a lot of things very precisely, and the people working on it thought that they would get to the point of making some falsifiable predictions. Unfortunately, it hasn’t – and a lot of the recent work in it strongly suggests that at least at the present, there’s no experiment we can perform that could falsify it; it’s predictions are so close to those of the standard model that we can’t distinguish it. That lack of falsifiability is exactly what’s caused it to fall out of favor.
And finally: stop the damned arXiv whining. You’re not going to get any sympathy around here. For all the protestations about how awful, restrictive, closed, and just generally mean arXiv is, the fact remains that the submission standards for arXiv are so damned trivial as to be virtually non-existent. All that you need to submit to arXiv is to either be affiliated with a legitimate research institution; or to have one person affiliated with a legitimate research institution endorse you as a legitimate researcher.
If you’ve got a “scientific theory”, but you’ve never talked to or worked with a single other scientist who thinks that you’re doing anything remotely legitimate, it’s pretty safe to say that you’re not doing science.
“[string theory’s] predictions are so close to those of the standard model that we can’t distinguish it.”
This is completely wrong. String theory has many possible vacua which each predict different low energy particle spectra. Most are very different from the standard model. None so far are known to be so close to the standard model that they cannot be distinguished from it.
“the submission standards for arXiv are so damned trivial as to be virtually non-existent”
This is equally wrong.
@25:
WRT string theory: it differs from the standard model, but not in any ways that can be tested today. Every test that we can perform today can’t distinguish between a string-theory universe, and a non-string-theory universe.
WRT arXiv: you keep griping about how awful the standards are. But, as I keep pointing out; the entirety of the arXiv submission standard is “Work at a legitimate research institution, or get one person who works at a legitimate research institution to endorse you as a legitimate researcher.”
What is so unreasonable about expecting a real scientist to be able to find one other scientist who’ll say “he’s a researcher”. They don’t need to say they agree with your work; the don’t need to endorse you work. All they need to do is say that you’re a legit researcher.
How many legitimate scientists never talk to any other scientists? How many legitimate scientists really don’t know a single legit scientist anywhere in the world who’ll vouch for them?
Why, exactly, is that such an unreasonable standard?
MarkCC: “when you see a particle with distinct mass, it’s not a problem: just wave your hands around”
Jacek: Dear Mark,
Thank to your response I found that I was definitely wrong using in my publication the term “mass” without a definition. For me it was too obvious when talking about the spacetime.
The mass definition confuses a lot of people. In modern physics we use terms: relativistic mass and invariant mass (rest mass). Let’s explain what it is all about. The term relativistic mass is used in the meaning of the total quantity of energy in an object or system (divided by c2). The relativistic mass (of an object or system of objects) includes a contribution from the kinetic energy of the object, and is larger the faster the object moves, so unlike the invariant mass, the relativistic mass depends on the observer’s frame of reference. The mass (not regarded as “matter particle”) and energy do not change into one another in relativity. They are names for the same thing, and neither mass nor energy exists without the other. (The very mechanism of that is explained only in my theory). The “matter particles” may not be conserved in reactions in relativity, but closed-system mass always is conserved.
In particle physics, the invariant mass is a mathematical combination of a particle’s energy and its momentum which is equal to the mass in the rest frame. This invariant mass is the same in all frames of reference.
The a.m. statements are not my opinion (except the mechanism statement). That is the modern physics point of view. You can easily check it out in many publications.
Finally what I call a mass in my theory? The relativistic mass. And you are pointing at the invariant mass. But is it possible to find a matter particle in a rest frame?? No!
And by the way think about neutrino oscillations.
And a little thing about a mass. Sheldon Glashow (the Arthur G.B. Metcalf Professor of Physics at Boston University and winner of the 1979 Nobel Prize in Physics): “What the astronomers have discovered is that most of the matter in the universe is not on our list. It’s something else. And we haven’t the foggiest idea of what it is. It may be some kind of supersymmetric particle. It might be black holes. It might be particles with funny names. But we don’t really know what 99 percent of the matter in the universe is made of.”
My theory give the direction and not a ready answer to find it out.
And finally about the mass. Everyone accepts probability in QM (do all the physicists just wave their hands around?), so why do you oppose it in my theory? I’ve put the figure 2 as an example of probability density function. I downloaded the figure because it is easier than to draw it myself. The source doesn’t matter. What matters: you can find a distinct (invariant) mass if you are looking for as well as relativistic one. However the figure 1 is closer to the idea that the mass and energy are names for the same thing. You cannot find one without the other.
MarkCC: As for the comparison with string theory:
(a) string theory has a hell of a lot of precision. It makes very precise arguments about how things work, why they are the way they are, etc.
(b) it’s gotten a hell of a lot of flack lately. In the early days of string theory, lots of people were very positive about it. A lot of that has turned negative. Why? Because in the early days…
Jacek: Let’s look at the theory after the year 2000:
String theory still has a huge number of equally possible solutions, called string vacua, and these vacua might be sufficiently diverse to explain almost any phenomena we might observe. It means the string theory has no predictive power for experiments. Because the theory is impossible to test, a lot of physicists have asked if we can call it a scientific theory. Some of them: a.m. Sheldon Glashow, Lee Smolin, Carlo Rovelli, Philip Warren Anderson, Lawrence Krauss and Peter Woit (I especially like his statement: “The theory has been spectacularly successful on one front, that of public relations. – arXiv:physics/0102051v1).
Another still existing problem with string theory is that it is background-dependent — string theory describes perturbative expansions about fixed spacetime backgrounds. If you think there is something that solved the problem (M-Theory) read a.m. Peter Woit article.
You can easily find a lot of other problems.
Yes, the string theory is a good math, but a bad physics.
By the way you missed what I had noticed about Darwin’s evolution theory.
The spacetime deformations theory brings the new qualities:
– the spacetime properties: homeomorphism and elasticity, which is not obvious and meaningless,
– the geometry being a source of every object we perceive, which is not obvious and meaningless,
– a quite new human being’s perception of so called reality.
And the math behind it is partly existing because GR and QM math are only special cases. And maybe (I say maybe) Darwin’ evolution also is a special case of another more general theory.
MarkCC: If you’ve got a “scientific theory”, but you’ve never talked to or worked with a single other scientist who thinks that you’re doing anything remotely legitimate, it’s pretty safe to say that you’re not doing science.
Jacek: You are absolutely right. So that is the reason I’ve published my concept. I’m talking to other scientists. That is a kind of forum. Why do you think it is worse than a meeting in university restaurant? It can possibly gather more opponents. I count on physicists.
And your contribution is a prove it was worth to publish. However I think you are not a physicist. Doesn’t matter.
@27:
Talk about falsifiability… You’re doing exactly what I predicted you would. As I’ve said repeatedly: you’ve got a theory that’s so vague that it can’t be falsified. And presto – you show up, and get confronted by things that should falsify your theory, and you just wiggle around.
You said, quite specifically, that anything with a specific, distinct mass would contradict and thus falsify your theory. And yet, there are plenty of easily observable things with distinct masses. But that doesn’t even put a dent in your theory: you just wiggle around and obfuscate by playing with different definitions of mass. And yet, that doesn’t change the essential fact: there are specific particles, with specific masses. Those masses are distinct and measurable – and they’re precise and identical, with absolutely no variation.
That contradicts your theory. If all matter is just space-time distortions, and all interactions are wave interactions between moving distortions, there not only is there no reason for things to be made entirely of a small number of fixed-size masses, but in fact, there’s no way that things would be a small number of fixed size masses.
Similarly, you handwave a lot about how the forces are all just distortions with different geometries. But you can’t say anything about what those geometries are, or exactly how different geometries can produce the vastly different effects that we observe. You just handwave and say “geometry”. But how does that work? What kind of observation could possibly falsify that claim? Without any explanation of how geometric variations could supposedly cause those differences, there’s simply no way to actually say whether or not a given observation is consistent with your theory.
Take a gravitational system – two particles orbiting each other. According to you, they’re doing that because they distort space around each other. That’s essentially also what relativity predicts. Fine.
Now, imagine that those two particles are both positively charged particles. According to you, the only difference between this, and the other scenario, is the geometry of the spacetime distortion.
So – how does changing the geometry of the spacetime distortion change the attractive force of gravity into the repulsive force of electromagnetism?
By every bit of physics that I’ve ever seen, it doesn’t make any sense. Electromagnetism and gravity behave so very differently that just claiming that they’re exactly the same thing with different geometries sure seems to be incorrect. But because there’s no actual content to your theory, no precision, nothing of any substance, there’s just no possible way of saying whether that observation *really* contradicts it. No matter what we observe, no matter what experiment we perform, you can always handwave it, and say that it works.
That’s not science. That’s garbage.
There’s a damned good reason why crackpots like you can’t post to arXiv. You can’t get an endorsement to post to arXiv, because you’re not a scientist. What you’re doing isn’t science. That piece of trash that I mocked in this post is not, by any stretch of the imagination, a legitimate scientific paper. It could never, not in a million years get accepted by any peer reviewed journal. Not because you don’t have the right connections; not because real physicists are some kind of closed-minded clique, but because it’s a pathetic, sloppy, meaningless piece of dreck with delusions of grandeur.
@27 As you say near the end of your comment, you have a “concept;” you don’t have a theory. When you’ve worked out the math and made some measurable predictions, you can graduate to having a testable hypothesis. When observational evidence fails to contradict your hypothesis, you can claim to have a theory.
From what you’ve written, it’s clear that you have not worked out your concept in a rigorous fashion, meaning that you do not have predictions that can be tested. For example, you need to calculate the mass of a proton under your hypothesis (given some frame of reference), and how much your hypothesis’ prediction differs from the standard model. Given your concept of “everything’s geometry,” I would expect differences in particle interaction that would differ from the standard model.
In the absence of specific, testable predictions, defined in terms of measurement, Mark is absolutely spot-on in his criticisms. Your concept is free of math, free of testable and falsifiable predictions, and therefore both bad math and bad science. As Mark says, what you call predictions is just a bunch of vague arm-waiving that wastes your time and your reader’s. You only compound your problems by mis-identifying your concept as a theory.
@26, “WRT string theory: it differs from the standard model, but not in any ways that can be tested today”
OK but that is very different from what you said before.
“What is so unreasonable about expecting a real scientist to be able to find one other scientist who’ll say “he’s a researcher”. They don’t need to say they agree with your work; the don’t need to endorse you work. All they need to do is say that you’re a legit researcher.”
But they DO need to endorse the work. That is why the arXiv calls it their “endorsement system”
Furthermore, this is just the first step to getting in the arXiv. They sometimes reject material that has been endorsed. They say it is “inapprpriate” without giving a reason even though it fits all the criteria that they mention on their help pages. What they write seems benign but what they do when an independent researcher submits something is very different. When this happens the endorser faces the threat of reprisals. here is what arXiv says
“We reserve the right to suspend a person’s ability to endorse for any reason. If you endorse a person who makes an inappropriate submission, we may suspend your ability to make endorsements. If you feel uncomfortable about endorsing an author for any reason, don’t do it — ask the person to find another endorser.”
I’ve said these things before but you have not taken any notice, so I dont suppose you will now. I’m just repeating it for the benefit of anyone else who comes across these comments.
Regarding the “rules” for what gets into arXiv, why it is reasonable to talk to at least one recognized scientist; and how Evolutionary Theory and Capitalism overlap in the practice of Science, I recommend:
The ‘science-as-market’ analogy: a constitutional economics perspective
Viktor J. Vanberg1 Contact Information
(1) Walter Eucken Institut, University of Freiburg, Freiburg i.Br., Germany
Contact Information Viktor J. Vanberg
Email: vvanberg@vwl.uni-freiburg.de
Published online: 18 October 2008
http://www.springerlink.com/content/n58t67j468524151/fulltext.html#CR43
Abstract The ‘science-as-market’ analogy has been used in support of the notion that in science just as in markets competition works as an effective instrument for reconciling the self-interested ambitions of individual agents with the social function that science and markets are supposed to serve. This paper examines the analogy from a constitutional economics perspective, drawing attention to the role that the rules of the constitution of the ‘game of science’ as well as the ‘market game’ play in conditioning the ways in which competition works in the two realms.
Keywords Science – ‘Invisible-hand’ explanation – Economic methodology – Constitutional constraints
MarkCC: anything with a specific, distinct mass would contradict and thus falsify your theory. And yet, there are plenty of easily observable things with distinct masses.
Jacek: It is not my fault that you don’t understand the basic notions: relativistic and invariant mass. I tried to show you the difference, but you still don’t get it.
MarkCC: theory that’s so vague that it can’t be falsified. And presto – you show up, and get confronted by things that should falsify your theory, and you just wiggle around.
Jacek: Mark, you are undecided – it can’t be falsified or it can be easily falsified even by you?
MarkCC: you can’t say anything about what those geometries are, or exactly how different geometries can produce the vastly different effects that we observe.
Jacek: Of course that I can, but read once more: This is a theory of principle (universal theory delivering description of nature). The details and equations (however not all of them) you can easily find. But you don’t understand the basics so you don’t know where to go. At the beginning try Schrödinger equation. But that is not the point. There is no sense to copy all known details to my publication.
MarkCC: how does changing the geometry of the spacetime distortion change the attractive force of gravity into the repulsive force of electromagnetism?
Jacek: I’ve never said that gravity is changing into electromagnetism. It’s your imagination.
MarkCC: Now, imagine that those two particles are both positively charged particles. According to you, the only difference between this, and the other scenario, is the geometry of the spacetime distortion.
Jacek: Now, imagine that those two particles are both protons (positively charged particles) and they are packed at the center of an atom. What about very strong repulsive force? No one knows so physicists invented the notion: the residual strong force that bounds protons. What is the residual strong force? Who have measured the force? Don’t tell me about QM calculations. Don’t tell me about fenomenology! Tell what is it?
MarkCC: Electromagnetism and gravity behave so very differently that just claiming that they’re exactly the same thing with different geometries sure seems to be incorrect.
Jacek: What it seems to you is your specialty but not a science.
MarkCC: No matter what we observe, no matter what experiment we perform, you can always handwave it, and say that it works.
Jacek: That fits exactly to your beloved string theories.
I expect discussions with real physicists so I am finishing this conversation. You don’t understand basics like the mass notion and your emotions take control, so bye. Be happy in your world. I can imagine you standing still on your bathroom scale and reading your distinct mass.
Mark and readers,
can you always distinguish arXiv vs viXra ?
I know nothing about physics but it is funny to see a paper with a section called mathematics and with the content this one has.
Mreanwhile, MTH is used in arXiv in something that is falsifiable, even though it might seem as crazy to a non-scientist.
On the geometrization of matter by exotic smoothness
Authors: Torsten Asselmeyer-Maluga, Helge Rose
(Submitted on 11 Jun 2010)
http://arxiv.org/abs/1006.2230
Abstract: Clifford’s hypothesis is investigated: A particle is made up of nothing but a distinct type of a space manifold, differing from the surrounding manifold of empty space. It is shown that this distinct space manifold representing matter differs from the surrounding vacuum by the exotic smoothness of its spacetime. The smoothness structure of spacetime can be described by a tree-like subset — the Casson handle — consisting of immersed discs and connecting tubes between them. The Weierstrass representation shows that the immersed discs are represented by spinors fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. The connecting tubes between the discs realize an action term of a gauge field. Both terms are purely geometrical and characterized by the mean curvature of the components of the Casson handle. This gives a good support to Cliffords conjecture that matter is nothing more but an exotic kind of space.
Comments: 17 pages, no figures, elsevier style
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Geometric Topology (math.GT)
Cite as: arXiv:1006.2230v1 [gr-qc]
Submission history
From: Torsten Asselmeyer-Maluga [view email]
[v1] Fri, 11 Jun 2010 08:30:37 GMT (18kb)
1. Introduction: A geometrical model of matter
1.1. Clifford Hypothesis
It is a daily experience and also a common estimation of physics that matter is an entity independent from space. This strict distinction of matter and space is well known and it seemed naturally, until Einstein in his gravitation theory comprehend space and matter as not distinct: Matter curves space and bended space acts via gravity on matter. Even the Einstein equation
R_μν − 1/2 g_μν R = κ T_μν (1)
describes space and matter with two entities: The left side represents geometry by the curvature tensor. It is balanced with the right side where the energy-moment-tensor
represents matter. The equality sign of Einsteins equation do not mean that “space” and “matter” are the same, it means that the curvature of space (i.e. the energy density of gravitation) is in balance with the energy density of matter.
Thus Einstein’s gravitational theory interprets space and matter as still different but deeply connected things. And so we have to realize, that the natural assumption before Einstein of the duality of space and matter had been replaced by the fundamental dependency of both. But if it was necessary to correct our understanding of space and matter once it could be required once more. This may show the way to a more broader hypothesis namely that matter is nothing more but space of an exotic type.
This idea was argued by distinguished physicists like Einstein, Wheeler and with the most firm conviction Clifford. It was best expressed in the book [1] of Misner, Thorne and Wheeler on page 1202:
“Recall Clifford, inspired by Riemann, speaking to the Cambridge Philosophical Society on February 21, 1870, “On the Space Theory of Matter” [[2], pp. 244 and 322], and saying, “I hold in fact (1) That small portions of space are in fact of a nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them. (2) That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave. (3) That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or etherial. (4) That in the physical world nothing else takes place but this variation, subject (possibly) to the law of continuity.”
Ask if there is a sense in which one can speak of a particle as constructed out of geometry. Wheeler [3] does it in 1962:
“the vision of Riemann, Clifford, and Einstein, of a purely geometric basis for physics, today has come to a higher state of development, and offers richer prospects—and
presents deeper problems—than ever before. The quantum of action adds to this geometro- geometrodynamics new features, of which the most striking is the presence of
fluctuations of the wormhole type throughout all space. If there is any correspondence at all between this virtual foam-like structure and the physical vacuum as it has come
to be known through quantum electrodynamics, then there seems to be no escape from identifying these wormholes with ’undressed electrons.’ Completely different from these
’undressed electrons,’ according to all available evidence, are the electrons and other particles of experimental physics. For these particles the geometrodynamic picture
suggests the model of collective disturbances in a virtual foam-like vacuum, analogous to different kinds of phonons or excitons in a solid.””
On the geometrization of matter by exotic smoothness
Clifford’s firm conviction given by the words of Wheeler builds the basis for our considerations:
Clifford Hypothesis: A particle is made up of nothing but a distinct type of a space manifold, differing from the surrounding manifold of empty space….
[you can download the full PDF from the linked-to Abstract page]
Personally, I believe those thesises to be intelligence test run by alien civilizations on ours. How do you think we’re faring so far?
This seems to be a common response when quacks are confronted by the fact that their ideas are unfalsifiable.
What’s actually happening is that a prediction is generated based on the given idea and a thought experiment is proposed which could potentially falsify the prediction. When the test is followed to it’s logical conclusion it is found to contradict the prediction and thus falsifies the claim. In rebuttal definitions are changed, values are shifted, and concepts are restated using different words, all of which serve to render that test invalid in some way, or to make the results consistent with the reworded idea. The fact that all of these change are still consistent with the original idea is a clear demonstration that it is in fact unfalsifiable.
He’s not claiming that “I tested it AND it’s untestable.” He’s claiming “I attempted to test it, but every test resulting in a falsification is simply reinterpreted in such a way as to render it unfalsified. Since this can be done at will while remaining consistent with the original idea, it is in fact unfalsifiable.”
What a super blog! Keep up the good work. It’s great to see mathematician whisteblowers and those like yourself who help us to separate the wood (good) from the trees (bad) maths.
Cheers
Dr Michael Taylor
http://patternizer.wordpress.com
@37:
Very well said. That’s exactly what I was trying to say, only stated much more clearly!
The problem with “theories” like this one are that they present themselves as falsifiable; and yet, any attempt to do so is easily defeated by the very vagueness of the theory.
If you read his “theory” and reason from it what would make a good falsifying example, there are a bunch of really obvious things that come up:
– It *seems* like the precise uniformity of all of the matter we can observe would be a falsifying counterexample to this “theory”. And yet, Safuta can get around that simply by waving his hands: because the “theory” is so fuzzy, he can always just shift definitions. This is what he does with the “rest mass vs relativistic mass” rubbish. It’s a total, obvious, bullshit handwave: every proton, in every test, every observation, behaves as if it has precisely the same rest mass. There is absolutely no variation. Why would relativistic mass make any difference?
– It *seems* like the very discrete quantum energy levels that we observe all over the place would be a falsifying example. If everything is topologically continuous deformations of space, then energy transitions should be perfectly smooth and continuous as well. And yet, observation shows that it isn’t. But he can weasel around that: since he never specifies the structure of the topological structure of spacetime, and he never specifies the geometry of the deformations within that topological space, he can always wave his hands around and say that it works. Now, my topology isn’t terrific – but, if I’m remembering it correctly, I think that it’s impossible for a continuous transformation/deformation in a continuous topological space to produce discrete steps like what we observe in quantum behavior. But again, because he’s so vague about it, he can wave his hands around and make nonsensical claims.
No matter what you do, you can’t falsify a theory like this. Because ultimately, the theory is so ill-defined that it’s meaningless. You can try to reason from it, but he can simply wiggle out of it, because there is no well-defined meaning to falsify.
To use a metaphor from simple structural engineering. You can build a fantastically stable bridge using trusses. Trusses are amazing structures, and using them you can very easily build a bridge that can withstand a massive earthquake. But even the most perfectly structurally stable bridge will collapse if it’s built on bad foundations. Mount a bridge across a cliff on a thin, brittle stone projection on either side, and the first tiny earthquake that comes along, the bridge is going to fall. You can build a beautiful disproof of this “theory” using math and physics – but because the foundations are so shaky, they can always be pulled out from under your disproof.
@38:
Thanks for the compliment. But just to be clear: I am not a mathematician. When it comes to math, I’m just a hobbyist. I love math, but I’m nowhere near good enough to be a professional mathematician. I’m a computer scientist/software engineer.
That was too much fun. After an initial run of success (7 out of 7!), it was determined that I am a monkey. Maybe I would have done well with nonsense math papers.
The author really needs to provide some testable predictions that, if they fail, would falsify the hypothesis.
I’ve just looked at the vixra site. It’s incredible – stuffed full of bogus math and physics.
But, Mark, stay away from it! There’s enough there to occupy several you for life times in debunking these unacknowledged geniuses.
Quantum physics is a vey succesfull theory This does have its inherent problems though, and that is nobody is allowed to question it. The problem with that is that beliefs become entrenched, and scientific progress may be limited by it.
It is true that his famous equation E=mc^2 has endured the test of time. But has anbody (including Einstein himself) been able to explain exactly where it comes from.
Albert Einstein was also not a great advocate of quantum physics, so he was unable to derive quantum gravity.
Now perhaps both these problems may be resolvable [1, 2] .
Available online
1. String quintessence and the formulation of advanced quantum gravity. Physics Essays 22: 364-377. http://dx.doi.org/10.4006/1.3182733
2. The formulation of harmonic quintessence and a fundamental energy equivalence equation. Physics Essays 23: 311-319 http://dx.doi.org/10.4006/1.3392799
O.K.
So we have a theory based on the deformation of space-time. That’s not dissimilar to General relativity, Sure that must have some merits. BUt where does this start to be a theory of everything, and what does it explain. Does it explain where E=mc^2 come from. Does it give you a theory of quantum gravity. Does it explain dark matter and “dark energy”
Now perhaps both these problems may be resolvable [1, 2], considered comments/questions gratefully accepted .
Available online
1. String quintessence and the formulation of advanced quantum gravity. Physics Essays 22: 364-377. http://dx.doi.org/10.4006/1.3182733
2. The formulation of harmonic quintessence and a fundamental energy equivalence equation. Physics Essays 23: 311-319 http://dx.doi.org/10.4006/1.3392799
Woot! Another one!
Quantum physics is a vey succesfull theory This does have its inherent problems though, and that is nobody is allowed to question it.
You’re allowed. We just don’t think its worth our time to question it. This is a very common complaint / misunderstanding of pseudoscientists. They think its some form of censorship when other scientists choose not to invesitigate their ideas. That’s not censorship, boys, it just means that in the free market of ideas, you have an idea no one wants to invest in.
It is true that his famous equation E=mc^2 has endured the test of time. But has anbody (including Einstein himself) been able to explain exactly where it comes from.
Einstein hasn’t been able to explain it because he’s been dead for over 50 years now. That tends to slow down your publication rate.
So we have a theory based on the deformation of space-time. That’s not dissimilar to General relativity, Sure that must have some merits.
Um, no. You don’t just take a theory that explains one phenomena and splat it across others. GR is about as relevant to electron mass as it is to my hair color.
@46
“In the free market of ideas, you have an idea no one wants to invest in”.
You’re completely wrong. The two articles he is citing cost US$15 each. I would not call that free! XD XD XD
@44
“It is true that his famous equation E=mc^2 has endured the test of time. But has anbody (including Einstein himself) been able to explain exactly where it comes from.”
Of course no, nobody has been able to explain where does the equation come. Einstein just found it one day written on his desk.
Not that the mathematically derived it from its postulated or anything like that. Wait, didn’t I saw that derivation? Bah, noooo.
Actually, E=[(mc^2)^2 + (pc)^2]^(1/2)
E only equals mc^2 if the object is at rest. Pedantic, I know, but it irks me every time. I had to derive the equation as part of a sophomore physics class a few years ago.
@49
you need to read more. m is not the mass at rest
Usually when used in this kind of setting it is, but yes, if m does not mean the rest mass but the relativistic mass E=mc^2 is right. I know most people here know this, but the “famous” part of the equation presumes rest mass. At least, in my experiences with non-scientists.
Quantum physics is a vey succesfull theory This does have its inherent problems though, and that is nobody is allowed to question it. The problem with that is that beliefs become entrenched, and scientific progress may be limited by it.
Who told you that no one is allowed to question Quantum Mechanics?
Anybody is allowed to question Quantum Mechanics…the only catch is that if you do it the wrong way, people might call you a “crackpot” behind your back.
The right way to question Quantum Mechanics is to provide some experimental observations that can’t be explained by the current theory but can be expained by whatever new theory you’re proposing. It also helps if your theory comes with a well-defined set of equations and not just vague handwaving.
It is true that his famous equation E=mc^2 has endured the test of time. But has anbody (including Einstein himself) been able to explain exactly where it comes from.
I wasn’t sure, so I did a quick Google search. The first thing I discovered is that there are a huge number of crackpots out who are babbling nonsense about what the equation means. It was scary!
Finally I decided I’d just see what Wikipedia had to say. Here’s the link I wound up with:
http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Einstein:_Mass.E2.80.93energy_equivalence
I have completed The GUT Theory.
You can find the equations here:
http://www.wix.com/Hyperstig/Hyperstig
0 is a wave function that collapses and re-expands.
I have invented the 1st quantum computer.
I am the failsafe.
You can follow me on Twitter:
https://twitter.com/Hyperstigzero
I adore the way that he proceeds to give a high-school explanation of relativistic mass to actual working scientists.
Hyperstig, you captured the very true and real essence…
I vote Hyperstig for president.
I think you mean poesident. If so, I second 🙂
@52:
Shoot, we derived e=mc**2 from the basic assumptions in high school physics! It was probably a pretty sloppy derivation, but it was a derivation!
Unfalsifiable? Really? Then for all you know, Behe is absolutely right about irreducible complexity and there is no way whatsoever to prove him wrong.
Okay, I’ll take it. Thanks.
@58:
The idea that universe was sneezed out the nose of the Great Green Arkleseizure is unfalsifiable. You can’t possibly prove that it’s wrong. Should we start taking that idea seriously?
Unfalsifiable means much more than just “You can’t prove it’s wrong”. In fact, it also means that you can’t prove it’s right. In fact, it also means even more than that. It means that it lacks sufficient meaning to be able to be scientifically described as having any truth value at all. It’s not just that it’s not true; it’s that the whole idea of assigning it a truth value is pretty much meaningless. Is irreducible complexity, as a theory, wrong? No. Is it right? No! It’s meaningless. It’s a pseudo-theory that’s so ill-defined that you can’t say whether it’s true or false, because what it means for it to be either true or false isn’t really definable. Any meaningful version of
IC that’s been proposed thus far has been rapidly and conclusively falsified. But because the basic version of IC that Behe keeps peddling is so ill-defined, all of those falsifications can just be discarded with a handwave.
Except that when expressed this way, Behe’s IC concept does not need to be falsified because it is trivially false. An arch is an example of something that doesn’t work if you take away one part. Yet nondesigned arches occur in nature. They are formed by subtraction of a natural scaffold–e.g. by hollowing out of a mound by weathering. To deal with this objection, Behe has retreated to what is essentially a circular definition: i.e. a structure is irreducibly complex if the interdependencies of its component parts are such that there is no pathway whereby it could have evolved. In other words, evolution is disproved by the existence of IC structures which could not have evolved. IC theory thus boils down to argument from ignorance: Behe asserts that a structure is irreducibly complex if he can’t think of the pathway by which it evolved.
The proof of E =mc^2 on Wiki starts like this:
The velocity is small, so the right-moving light is blueshifted by an amount equal to the nonrelativistic Doppler shift factor 1 − v/c. The momentum of the light is its energy divided by c, and it is increased by a factor of v/c. So the right-moving light is carrying an extra momentum ΔP given by:
2ΔP = vE/c^2
Since when is that a mathematical proof, when the starting equation is effectively E=mc^2.
Think guys there has to be a better explanation than this!
If you want to get an apriori proof go to reference 2.
Besides there is no point in complaining/commenting about it if you havn’t bothered to read it.
Available online
1. String quintessence and the formulation of advanced quantum gravity. Physics Essays 22: 364-377. http://dx.doi.org/10.4006/1.3182733.
2. The formulation of harmonic quintessence and a fundamental energy equivalence equation. Physics Essays 23: 311-319 http://dx.doi.org/10.4006/1.3392799