(Apologies for the poor audio quality. It improves as it goes.)
Part 1 (Problems)
Intro; Cern & the LHC; A Crisis in Physics; Black Holes & 0d Particles?!; The Atom; Mathematical Physics; more...
http://blip.tv/philosophy/bill-gaede-in-austria-cern-and-the-lhc-part-1-5438667
Part 2 (Solutions)
Definitions; Science vs Religion; Objects & Concepts; 17th vs 21st Century Scientific Method; The Rope Hypothesis; A Grand Unified Theory!; Q&A; more...
http://blip.tv/philosophy/bill-gaede-in-austria-cern-and-the-lhc-part-2-5152635
Some further discussion taking place, here:
The Rational Science Facebook page
There's certainly some pretty big problems in modern physics but from poking around on these sites they look like quacks to me.
Clayton -
You mean youstupidrelativist.com? Yeah, it LOOKS extremely crankish, but that's apparently intentional. The content when you dig deeper is all about clear definitions, so I like it. I don't agree on everything, but no one else is even trying.
Why anarchy fails
You guys are all cranks, this is the real deal:
http://www.timecube.com/
The Anarch is to the Anarchist what the Monarch is to the Monarchist. -Ernst Jünger
@AJ: There was a thread recently on scientific hypotheses and I agree with most of what I saw there but Gaede is simply off the map. I mean, he denies any role for explanation and prediction in science. Then why the hell do science?? If it's not useful for anything, then it's clearly a waste of time. Two hundred years ago, getting paid to be a mathematician was actually a fairly difficult proposition. In the modern world - which doesn't even bat an eyelash at the Pentagon losing $2.3T - not so much.
As far as his arrogance regarding his supposedly awesome consistency, in a few minutes of reading one of the sections on definitions (which themselves seemed quite arbitrary, 1-dimensional and unjustified) I've spotted a few inconsistencies. In the other thread where this topic was treated regarding hypotheses (sorry, I don't have a link to the thread), I mentioned Ernst Mach's excellent book The Science of Mechanics. If you want to see real science, read that book. He spends about 13 pages just discussing the lever - complete with the history of thought and a taxonomy of approaches to theoretical justification of the principle of the lever (force multiplication). He uses diagrams and mathematics but he does not use them to obscure, only to clarify.
Gaede isn't fit to shine Mach's shoes. While I don't think there's much science being done today with the rigor and care that Mach did science in his day, I think that Gaede is exactly what he appears to be: an underinformed reactionary. Just looking at his section on the geometric line, for example, I've spotted several errors. He implicitly assumes that mathematicians do not operate with so-called "completed" infinity (he doesn't even bother mentioning this assumption) but they, in fact, do and we get many important and useful results from such treatment. He presents a 3,000 year old conception of the geometric line as a bunch of geometric points squished really, really close together when mathematicians have known for over a century that such a definition of the geometric line is, in fact, contradictory which is precisely why they've gone to such great lengths to spell out such "absurd" ideas as completed infinity actually mean so they can solve otherwise insoluble paradoxes (such as Zeno's paradox, or the Pythagorean crisis of irrational numbers, and so on).
Gaede doesn't even appear to understand the fundamental discoveries of 20th century logic regarding the nature and limits of deductive reasoning. He seems to believe that his definitions are obviously consistent. He doesn't bother proving they're consistent yet doesn't hesitate to throw out all other definitions in math and science as inconsistent.
It is true that physics is excessively arithmetized but Gaede is essentially presenting his bludgeoned version of Platonism as if it's simply case-closed. The Aristotelean view (which is the dominant one in science) which he critiques may have so many problems not because the world is Platonic but perhaps because it is Pythagorean. He imagines that by debunking the (patently silly) string-theory, he is debunking Pythagoreanism. He is not. There is a resurgence of Pythagorean thought that Gaede is apparently completely unaware of called "digital physics" (most recognizable name: Stephen Wolfram) which has attracted its share of cranks but which actually has a sound philosophical foundation - far sounder than anything Gaede presents.
And then there's this. WTF? That's science? He even contradicts his own thesis that numbers have no place in science, using them liberally to make his Malthusian "case".
He really doesn't deserve even the amount of air-time that I've given him in this post.
Clayton:There was a thread recently on scientific hypotheses and I agree with most of what I saw there but Gaede is simply off the map. I mean, he denies any role for explanation and prediction in science. Then why the hell do science?? If it's not useful for anything, then it's clearly a waste of time.
Of course I agree, but as far as I can tell, so would Gaede. He's just one of those writers that fails to specify the context of his comments much of the time (this is a common theme in his writing for some reason). Actually he says science is all about explanation, but not about prediction. What he means is that prediction is outside the scientific method, not that prediction is useless. He is merely trying to define a better set of boundaries for what constitutes science proper.
I actually agree with him that prediction is a separate endeavor. You explain how something works, and then of course having that explanation is massively helpful in making predictions. That's the whole point of explaining something, as you said.
Clayton:Just looking at his section on the geometric line, for example, I've spotted several errors.
Keep in mind that when Gaede mentions "mathematicians," he is generally talking about modern physicists. Again, he is not good about contextualizing his language. That's why it took me several months to understand his points.
Clayton:Gaede doesn't even appear to understand the fundamental discoveries of 20th century logic regarding the nature and limits of deductive reasoning. He seems to believe that his definitions are obviously consistent. He doesn't bother proving they're consistent yet doesn't hesitate to throw out all other definitions in math and science as inconsistent.
What he means by "consistent" is simply "causes everyone to visualize the same thing" or "non-equivocal," nothing to do with mathematical consistency. See for example:
I don't know where you're getting that he's a Platonist. To me he's Mr. Anti-Platonist. He reviles Platonism almost as much as I do. As to digital physics, that is interesting, and I agree that his rope theory has some issues as well, but at least he's trying to do something with physical explanation - almost no one else is. Gaede's strength is in his criticisms. That's why he most definitely deserves air time. Too bad he's so vitriolic, but hey, beggars can't be choosers. There's no one else doing what he's doing, at the level he's doing it (bunch of Youtube videos, a book, a website, a forum, tons of comments daily, etc.).
Clayton:And then there's this. WTF? That's science? He even contradicts his own thesis that numbers have no place in science, using them liberally to make his Malthusian "case".
Yeah, his extinction theory is silly because he doesn't understand economics. He's great on physics, terrible on economics. As far as numbers, he would probably be the first to admit that what he's doing with his "case" is not science.
So read him for his criticisms of physics, and I'll read Mach. I already had a sneaking suspicion Mach had something good going on. Still I'll be extremely surprised if he is as on top of things as far as physics as Gaede (albeit surely more eloquent).
Gaede's problem, from what I gather from skimming the site (I hate to even admit I've done that) is hubris. He's absolutely right that modern physics has gone off into la-la land. Tesla said, “Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.” But note that Tesla was far more mathematically adept than most of his peers, certainly than Einstein!
See, Gaede implicitly accepts the modernist paradigm... math =/= natural language. The difference is that modernists (falsely) believe that math is a higher language and Gaede (falsely) believes that math is lower than natural language (in fact, he seems to think it's completely useless). The modernists are wrong, math is a subset of natural language, a point which should be obvious.
Even further, the language of mathematics is thoroughly anthropological. Math really always has been theoretical physics because the language of math speaks about the idealizations of the physical world that the human brain itself naturally understands. This is where I think that Gaede is Platonist whether he understands it or not... he banishes idealizations from the real world. The real world is mundane, un-mathematical and speaking of it in mathematical language (the language of idealizations) is categorical error because you are not really describing what is, you are describing what is most certainly not. This strong dichotomy between the perfect world of Forms (idealizations) and the real world is characteristically Platonic.
The difference here is that Plato explained the amenability of the real world to idealization by asserting that the real world is some kind of xerox or imperfect copy of the ideal world of Forms. Gaede ignores the issue by simply banishing Forms from both reality and thought altogether. This is a serious conceptual problem because the very act of engaging in science assumes the existence of Forms/Universals at some level.
As far as "consistency" meaning that it evokes the same thing in everyone's minds, I think that's a pretty piss-poor definition of consistency. Logical consitency is wholly formal, there is no reason for it to be otherwise. As far as conceivability, I think that Gaede is populist about this. His rope explanation of magnetism is fine at first brush but it's not clear if he's making an ontological claim about these ropes or not. If he is, then he is guilty of the same error as the string-theorists.... what are these ropes, how can we see them, etc? If not, then his explanation is metaphorical and is not inconsistent with the "field theory" he despises, it's just a different metaphor.
The fact is that electrical phenomena are superficially so different from mechanical phenomena that it makes perfect sense to treat them as having separate causes (governed by separate physical laws) with the understanding, of course, that all physical phenomena are the outworking of just one, universal Law that governs the unfolding of everything within the physical Universe at all times and in all places. So, it is an obvious mistake to appeal to a mechanical metaphor of entangling ropes.
Furthermore, what is inconceivable about force fields? They feature prominently in all sorts of fiction and the movie producers have no problem adapting what the books have described in words and the audience who has read the books is not surprised by what they see. Of course there isn't literally a "mathematical vector field" surrounding a magnet but it's as if there were.
Prediction is absolutely an essential part of science. It is the flip side of the coin of explanation. You cannot have one without the other, something that pretty much everyone has been horribly confused about since Hume. Prior to Hume, it was intuitively understood that explanations explain things because they are predicting the behavior of the thing in question. After Hume, everyone became great skeptics and threw their hands up at the fickleness of the Universe which could, at any instant, decide not to follow the laws which it has exhibited for all time past. Gaede is just another Humean. The fact is that the Universe is predictable because it is explainable. You can't have one without the other.
Out of curiosity, is he native American? His accent sounds way native to me.
A little too much to address given how much time I have today. I think you're expecting him to present his argument in a logical progression, but he doesn't really. You have to dig for it to see it, but he does address all your concerns in satisfactory ways. The reason I was patient enough to piece together his arguments is that I knew he was on to something, a whole bunch of things, and I was willing to wade through whatever I had to to get at it. I'm very glad I did, though. More later...
ETA:
"Gaede (falsely) believes that math is lower than natural language (in fact, he seems to think it's completely useless).
Quick one: he means it's completely useless for science, by which he means explanation, by which he means a movie of the unobserved mechanisms that are proposed to underly the observed phenomena. With this definition of explanation...
"Prior to Hume, it was intuitively understood that explanations explain things because they are predicting the behavior of the thing in question."
...this takes on a different light and wouldn't make sense. We explain in order to predict. That's what the point of the other thread was.
"Furthermore, what is inconceivable about force fields? They feature prominently in all sorts of fiction and the movie producers have no problem adapting what the books have described in words and the audience who has read the books is not surprised by what they see. Of course there isn't literally a "mathematical vector field" surrounding a magnet but it's as if there were."
Without even getting into the question of whether they are imaginable, more pressing is the fact that they are simply descriptions of what happens, not explanations of by what unseen mechanisms they may happen.
This is all addressed in the other thread more eloquently. Time and time again, I've seen people make some of the same points as Gaede does and get plenty of agreement because they know how to come off less abrasive and brash. Oh well - he's got a 'tude. I wish he were nicer and more eloquent or whatever, but again beggars can't be choosers; he's one of the only people I've ever seen that get the subtleties at play here.
"As far as "consistency" meaning that it evokes the same thing in everyone's minds, I think that's a pretty piss-poor definition of consistency."
Are you kidding? That's the perfect way to characterize consistency (i.e., definitional consistency, which is what he's talking about). That's the whole point of communicating something, and failing at this kind of consistency is probably the No. 1 mistake thinkers make in any field. I've long considered equivocation is the most rampant and harmful habit in the intellectual arena.
Edit: Now I really have to get back to work. I'd love to talk about this more later, though.
As an aside, I'll throw down a few thoughts that have been rattling around my brain on issues of scientific methodology.
Consider the basic objects of geometry: point, line, circle, plane, cube, sphere, etc. These objects, as Plato said, do not really exist because they are anthropomorphisms, they are idealizations which the human brain is capable of operating on in a consistent manner. Steven Pinker has some lectures available online where he discusses the "intuitive theory of physics" embedded in natural language. The way we use language slices up the physical world into 1-dimensional, 2-dimensional and 3-dimensional idealizations each of which are governed by unwritten semantic rules regarding what can be done to them. Edges and boundaries are reified in human language and spoken of as if they were themselves a thing (idealization of idealizations, in essence).
Using these tools, we can construct new idealizations and this is precisely what mathematics since at least the time of Descartes has done. We can speak of the "tangent" "norm" "inflection point" and so on because these are conventional idealizations that have been built up over the centuries. You aren't born with these idealizations and you must acquire them through metaphor based on absorption of explanations of them in terms of the idealizations that you were born with. For example, we can explain the "norm" of a surface at a particular point X as "the arrow which is perpendicular to the surface at point X, in every direction around X (all 360 degrees)". In the case of a sphere, this is roughly visualizable as holding the end of a pencil against a basketball in such a way that the other end of the pencil is "equally distant" from the surface of the basketball in all directions around the pencil.
It is true that the world of mathematics is not the world of physics because the world of mathematics is not constrained by physical law. Infinity is easily conceivable and is extremely useful in mathematical theory. But it is absurd to speak of a physical infinitude. We cannot even imagine what it would mean for a physical quantity to be infinite. It's basically a contradiction of terms... a quantity is observable because it has boundaries (finite), if it were infinite, it would have no boundaries and could not be observed (and hence, would not be real). To avoid errors, we cannot allow the things that are useful in mathematics to seep into physics just because they are useful in mathematics and don't cause problems in the idealized world of mathematics.
However, that doesn't mean that mathematics is useless or ruins physics whenever it comes into contact with it. For example, the world of ordinary experience is, in fact, three-dimensional Euclidean space. We can see this because the theorems of geometry are scale-invariant, at least, up to any size large enough to matter for human beings. Within bounds, it doesn't matter how big or small you make a triangle, its sides will still conform to Pythagorean theorem. Physical space - within the bounds in which this correlation holds - is actually Euclidean three-space because its behavior is indistinguishable from Euclidean three-space.
But I'm skipping ahead of myself. Clearly, the Universe doesn't crunch numbers to figure out what to do next. Our mathematical laws describing the physical Universe, however, require tremendous amounts of number-crunching to figure out the state of the system from one moment to the next. This is one of the areas where we've mistakenly allowed mathematical idealization to seep into physics. I just said above that physical space is Euclidean three-space but I think this is not true in the sense of the Euclidean three-space of real numbers. I do not believe that physical space is real number space and this disagreement might account for a lot of the absurdities of relativity theory (black holes) and quantum mechanics (point particles).
Rather, physical space consists of ratios, it is rational space. There are so many swings of a pendulum per rotation of the Earth about its axis. This is not a mathematical claim, it is a physical claim. We can count the number of swings of a pendulum per a rotation of the Earth. In so doing, we establish a ratio between the swing of the pendulum and the rotation of the Earth. Time is thus measured as the ratio of two different kinds of events. Space is measured in the same way.
To measure time and space is not to say that "time exists" and "space exists" any more than measuring the surface of a balloon with a string means the "surface of the balloon" exists. All of these things are idealizations and it is the nature of human language to reify boundaries and other intangibles when it is useful to do so. Measuring something does not require us to reify it as long as we're careful to consistently maintain the fact that measurement is always the act of establishing a ratio between two physical quantities (objects or events). When we say "the ship is 100 meters long" we mean that if you laid out 100 meter sticks end to end, they would be congruent with the bow and stern of the ship.
In order to establish ratios, the magnitudes we are comparing must be countable (i.e. discretely resolvable by a human observer) - we need a whole-number numerator and a whole-number denominator. Hence, scientific measurement always reduces physical quantities to a discrete or digital form but this says nothing about whether the physical Universe actually is discrete or ratio-like (rational).
However, I think we can make a conceptual leap and make a case for a discrete, ratio-like Universe. The same problems that prevent a human observer from resolving the information in the Universe to its "absolute limit" must affect any physical object in the Universe. Why should atoms or electrical fields have access to more perfect information than we can derive with the most careful instruments constructed to extract every last drop of information about the state of a particular variable in the Universe?
There are two ways to answer this. The first is (essentially that given by Quantum mechanics): atoms don't have better information. A particular atom is unsure about the state information of the rest of the Universe beyond those limits given by the Planck distance, etc. as a result of the uncertainty principle. But there's a second answer which I like better: atoms can't have better information. The second answer is better because it kills two birds with one stone... it explains why we see Planck limits and it resolves the problems that arise with real-number space (infinite information density at every point in space).
What do I mean by "atoms can't have better information"? What I mean is that just like we can only measure the rotation of the Earth down to the nearest whole-number of pendulum swings of our clock, so every physical object is impinged upon by the state information of the rest of the Universe acting upon it down to the nearest whole-number of its sensitivity or "frequency response" to the physical world. Before you think I've gone off into la-la land, please understand that I'm very epxlicitly using metaphor here. Clearly, physical objects do not have little pendulums in them by which they are measuring the time elapse of events around them in order to determine what to do next.
Rather, I mean we should think of the physical world in the small a bit like a metaphor of, perhaps, a spinning gear which can be be spun faster by pushing any one of its teeth or slower by pulling on one of its teeth (think of a merry-go-round). The fineness of the teeth on the spinning gear are what determine its sensitivity. The more teeth, the smaller the changes in physical state to which the gear can respond and the faster it can respond to them. The more coarse the teeth, the larger the changes it responds to and the longer it takes to respond to them. The relativistic conception of the world is that the gears have no teeth at all or, conversely, that they have infinitely many teeth. The quantum conception of the world is that the gears have teeth evenly spaced at the Planck distance (again, I'm liberally using and abusing metaphor, here) but then even the quantum physicists still retain gears with infinitely many (or no) teeth because they use point particles, which leads to their own equations breaking down in the limits.
If a gear with very fine teeth were to briefly spin in the vicinity of a gear with very coarse teeth, there could be no response at all when the fine teeth simply do not meet with the coarser teeth because the time involved was simply too small for another of the coarse teeth to rotate into place. Again, I'm speaking metaphorically, I do not believe the physical world is made up of gears. This is what I mean by the idea that an atom (or whatever) can't be aware of all available state information that is impinging on it from the rest of the Universe. I think this can explain why we observe the (very real phenomenon of) quanta and Plank's limits and it can banish the use of real-numbers from physical theory which leads to the stealth importation of absurd infinitudes into physics.
To summarize, I would like to make the case that the Universe is inherently ratio-like and the fact that we can only measure ratios of physical quantities is simply a manifestation of this fact about the Universe. This would explain why the Universe is quantized... all physical quantities exist as a ratio which is simply two, discrete, whole numbers. Second, I would like to make the case that the Universe does not at all points "utilize" or "act upon" all the state information which is impinging upon it from all other points of the Universe and that this accounts for why we see Planck limits and could also account for the fact of noise, friction and the 2nd law of thermodynamics (disorder increases over time). State information is simply constantly being lost because it did not propagate due to the insufficient sensitivity of the physical system on which that state information was acting.
I really have to get back to work
I'll be online later this evening so we can continue the discussion then... it is fun.
Ah yes, Thread Theory or the Rope Hypothesis. I stumbled across Mr. Gaede a year or so ago and have read his book. He may not have a very tactful approach and his website looks like it's stuck in 1995, but the content is impressive. His arguments against Relativity and Quantum are very compelling and I am convinced beyond all doubt they are complete non-sense. It takes some time to digest what is being said, but once it clicks, you'll never view mathematical physics the same again.
His proposal for Thread Theory is very interesting and far more comprehensive then Relativity or Quantum theories, but still seems to come up short. For all the emphasis on simplicty, clear definitions and visualization of objects, the Rope's inevitably run up against a fatal conclusion; that the rope's must be able to pass through each other. He makes a few half-hearted arguments for justification of the peculiar behavior but ultimately concedes that he has no rational answer for this.
EDIT:
Also, there isn't much point in arguing with him on economics regarding his extinction theory. He is a member (former member?) of the communist party. Some other fun facts, He was a Cold War industrial spy trying to smuggle trade secrets from AMD/Intel to Russia through Cuban contacts. He ended up in the slammer and spent a few years there. He spent that time developing Thread Theory.
http://en.wikipedia.org/wiki/Bill_Gaede
I think Relativity theory (and certain aspects of Quantum theory) are flawed and are giving us wrong answers. But I don't think Gaede's actually doing science. At most, he is discussing the philosophy of science - which is strictly metaphysical.
Take his definition of a line (really a plane or 2-d prism), for example. He fundamentally misunderstands the nature of idealizations. The laws of physics describe idealizations that follow rules very similar to the rules we observe the physical world to be following. Consider finite-element analysis, for example.
The problem is that people confuse the role of idealization. If you're just searching for any damn idealization which fits your data, you may not be explaining anything. Or, if you're over-idealizing the real world (neglecting important, complex behavior as "noise", this happens frequently in economics/sociology), you get meaningless results. Or, if you're dealing with a single sample or a small data set and you're trying to "fit" an idealized model to it (e.g. the NIST model of the WTC7 collapse), you're just data-mining and your idealized model explains nothing.
But if you're not making these noob mistakes and you're taking a humble approach to the study of idealizations as a means for gaining insight into the physical world, then idealizations are extremely helpful. They convert onerous problems into tractable problems. FD = fd is the lever principle, you can use this equation to calculate the forces on either end of a lever. Multiplication itself is a shortcut... you can the calculate area of a two-dimensional rectangular surface from just two measurements.
A physical law such as the conservation of momentum could not even be derived if you bound yourself to Gaede's limitations. Conservation of momentum - inertia - is a wholly "mathematical" idea. But it has a very strong inductive and deductive basis. Read Mach's book The Science of Mechanics to see why.
To extend the discussion a bit further, consider Maxwell's laws of electromagnetism (Faraday's law, Ampere's law and Gauss's law). Anyone who has studied these laws and their application to electronic circuits and RF cannot help but be struck by the ridiculous correlation of the complex numbers and electrical properties, particularly reactance ("resistance" to alternating flows of current) - its behavior conforms perfectly with a magnitude multiplied by the imaginary unit. Electrical engineers design all these amazing circuits using the imaginary unit multiplied by the reactance of the circuit to determine the relationships between power, voltage, current and frequency.
This correlation is mind-bending. If the Universe is not number (as the Pythagoreans believed), then why do physical things act like numbers?
I think you may be missing the point of his argument. He has no problem with mathematics for what it is, he only argues that mathematics is not an explanation of the real world. It is purely descriptive. The fact that electrical engineers can perfectly describe the behavior of circuits or other dynamic processes using mathematics is fine for the purposes of technology and engineering, but this doesn't mean we really understand what is physically happening. Mathematics is meaningless for the purpose of physics.
To illustrate this point, he tries to bring this home by bringing people back to fundamentals. In Quantum physics, we have 2 basic model's of the atom. 1) The electron orbiting the nucleas and 2) the cloud model. They are both different physical interpretations of what an atom looks like. Physicists use the orbiting electron model to explain ionization and electric current, but then they use the cloud model to explain chemical bonding. Well, which is it? It can't be both. If physicists are unable to use one model consistently to explain all behaviors, then we really don't understand anything (with respect to physics), despite the fact we can describe all the behaviors mathematically and apply them to technology and engineering.
mathematics is not an explanation of the real world
This is only true to the extent that natural language itself is not an explanation of the real world - after all, mathematics is just a subset of natural language.
If, in my left hand, I give you two rocks and, in my right hand, I give you two rocks, how many rocks will you have? The answer is that you will have two and two equals four rocks. That is mathematics. It is also natural language. It is also a description of the real world. If we can describe the physical world at all, then we can describe it mathematically, as well. Mathematical description is just a highly ritualized version of ordinary description.
If natural language cannot describe the physical world then what the hell are we arguing about? Reductio ad absurdum, quod et demonstratum.
I guess it comes down to definitions. We can use whatever definitions you like, but Gaede has defined math and physics such that they are mutually exclusive.
Physics: The science of existence or the study of objects. Where exist is defined as physical presence.
Math: The science of dynamic concepts or the study of motion. Concept: A relationship between 2 objects. Motion: Two locations of an object.
Using these definitions, math cannot explain or elucidate anything about your rocks. "4" is a concept and counting is a process. These are man made conventions and do not exist. Physics is the science that deals with the architecture, shape and physical properties of the rocks. Math is then used as a tool to describe any conceivable relationship between the rocks. Does that make sense?
Physics: The science of existence or the study of objects. Where exist is defined as physical presence. Math: The science of dynamic concepts or the study of motion. Concept: A relationship between 2 objects. Motion: Two locations of an object.
There are so many unstated assumptions here, it's difficult to know where to start. I see no reason to suppose that relations between objects are any less "real" or "solid" or "physical present" than the objects themselves. Modern physics does indeed reify time and energy without introspecting about how such a reification is justifiable but this is throwing out the baby with the bathwater. If you follow this to its logical conclusion, you can say nothing at all about the physical world.
Using these definitions, math cannot explain or elucidate anything about your rocks. "4" is a concept and counting is a process. These are man made conventions
OK, and so are the boundaries between rock and non-rock. It is human prejudice that distinguishes between the "solid object" of a rock and the "empty space" between the rocks. The Universe is an indivisible reality that follows one Law throughout but which we perceive as a multitude of substances and laws (relations). The rock is following the same laws of physics as the empty space between the rocks so why do we distinguish between them?
Gaede defines surfaces as if they are really properly basic. They are not. The surface of a rock does not exist any more than the number four exists. It's a prejudice of human perception that is imposed upon the physical world by which we perceive a boundary between rock and non-rock.
and do not exist. Physics is the science that deals with the architecture, shape and physical properties of the rocks.
I can plead ignorance of what "architecture" "shape" and "physical properties" are on precisely the same basis you plead ignorance of what the number four is.
Clayton:Consider the basic objects of geometry: point, line, circle, plane, cube, sphere, etc.
To me, these are just patterns of sensation. They have to be, else humans cannot conceive of them, much less coherently talk about them. All we have is our sensations.
Hence a "point" is a dot on my visual field. A line is a long, thin rectangle (as Zangelbert Bingledack argued), an infinite plane is gibberish, a finite plane is a thin board, a cube is a box (visual sensations + bodily sensations for the third dimension), a sphere is a ball, etc.
Clayton:Steven Pinker has some lectures available online where he discusses the "intuitive theory of physics" embedded in natural language. The way we use language slices up the physical world into 1-dimensional, 2-dimensional and 3-dimensional idealizations each of which are governed by unwritten semantic rules regarding what can be done to them. Edges and boundaries are reified in human language and spoken of as if they were themselves a thing (idealization of idealizations, in essence).
This sounds fascinating, and relevant to my project of creating a visual language. Do you have any links?
Clayton:In the case of a sphere, this is roughly visualizable as holding the end of a pencil against a basketball in such a way that the other end of the pencil is "equally distant" from the surface of the basketball in all directions around the pencil.
I'd say that's not "roughly" how it is, but exactly how it is. Minus the eraser, lead, basketball markings, etc.
Clayton:Infinity is easily conceivable and is extremely useful in mathematical theory.
If it means "endless," as in an endless process. Static "infinity" cannot be visualized, hence is just a meaningless word. (If it can be, draw a pic of it.)
Clayton:But it is absurd to speak of a physical infinitude. We cannot even imagine what it would mean for a physical quantity to be infinite. It's basically a contradiction of terms... a quantity is observable because it has boundaries (finite), if it were infinite, it would have no boundaries and could not be observed (and hence, would not be real). To avoid errors, we cannot allow the things that are useful in mathematics to seep into physics just because they are useful in mathematics and don't cause problems in the idealized world of mathematics.
Exactly. I guess my point above about static infinity is irrelevant if you agree it's an error to carry it over into physical science. Mathematicians can have their formalisms if they want.
Clayton:However, that doesn't mean that mathematics is useless or ruins physics whenever it comes into contact with it. For example, the world of ordinary experience is, in fact, three-dimensional Euclidean space. We can see this because the theorems of geometry are scale-invariant, at least, up to any size large enough to matter for human beings. Within bounds, it doesn't matter how big or small you make a triangle, its sides will still conform to Pythagorean theorem. Physical space - within the bounds in which this correlation holds - is actually Euclidean three-space because its behavior is indistinguishable from Euclidean three-space.
Oh absolutely. Not even Bill Gaede is extreme enough to say that we can't measure using math. He is merely saying that measurement is the observation and characterization (description of the observed phenomena) stage, not the explanation* stage. He is sort of stuck on the word "science" (or "physics") itself, but if he'd just drop it and call it mechanistic explanation he'd communicate a lot better.
*As in, a movie of objects interacting (see the other thread)
Clayton:I just said above that physical space is Euclidean three-space but I think this is not true in the sense of the Euclidean three-space of real numbers. I do not believe that physical space is real number space and this disagreement might account for a lot of the absurdities of relativity theory (black holes) and quantum mechanics (point particles).
This is indeed one of the major problems. In terms of the big picture, I think the more fundamental problem is that the modern physicists don't explain, just describe (the point of the other thread). The undue encroachment of math into physics and the abuse of language is just the means of obfuscating* that deficiency.
*I don't mean to imply it's intentional
Clayton:Measuring something does not require us to reify it as long as we're careful to consistently maintain the fact that measurement is always the act of establishing a ratio between two physical quantities (objects or events).
Indeed, the key is keeping careful track of context. The terrible habit of the modern physicists - so bad that it is almost a culture - is the chronic fudging of this kind of thing. It's not sexy to discuss this kind of thing, doesn't get grant money, etc., but it is the very pith of sound scientific methodology.
Interesting ideas about quantization and Planck length. That's one thing I haven't thought about yet, nor have I looked at Gaede's take on it.
Clayton:A physical law such as the conservation of momentum could not even be derived if you bound yourself to Gaede's limitations. Conservation of momentum - inertia - is a wholly "mathematical" idea. But it has a very strong inductive and deductive basis. Read Mach's book The Science of Mechanics to see why.
OK, this has been really helpful to hear. I just now realized that it is definitely Gaede's use of the term "science" that is the problem. He simply delineates the boundaries of what he wants to call "science" more narrowly than is now common. I think he should just call it explanation, and his entire point is that mathematics has nothing to do with explaining a phenomenon (though it certainly can have something to do with characterizing that phenomenon). The lever equation, for instance, is very useful, but it is just a characterization - just a succinct encapsulation of the observed data.
That is really all modern physics does: it gives succinct (if we're lucky) encapsulations of observed data. Bill Gaede hates that that seems to be the sole goal of science these days, and I have to admit I find it very disappointing as well. Whatever happened to "how it works?" The sense of discovery is totally missing from science these days. It feels empty, unless of course you buy into the fantastical ideas of wormholes, time travel, particle-wave dualities, dark energy, and the like.
The Ptolemaic "explanations" given by relativity and quantum mechanics come in the form of what appear to the layman to be "actual" particles and "real" curvature of space, but that is just a semantic/mathematical blanket covering over the fact that they're only offering descriptions of what is observed, not explanations of how the observed could have come about.
Clayton: This [imaginary numbers and electromagnetism] correlation is mind-bending. If the Universe is not number (as the Pythagoreans believed), then why do physical things act like numbers?
This [imaginary numbers and electromagnetism] correlation is mind-bending. If the Universe is not number (as the Pythagoreans believed), then why do physical things act like numbers?
All sorts of odd mathematical notions are around. It just so happened that imaginary numbers found a use, which is why we learn about them in highschool. Had it been quaternions or something else, we would have learned about that instead. So I think it's more that the concept was there (among many others), and then an application came along. No application came along for the others, so they are forgotten or only studied by mathematicians. Then it looks like the physical world acts like numbers, when actually the physical world acts like one of the many esoteric mathematical entities dreamed up over the centuries.
Re: the discussion with Orthogonal, one inefficiency in Gaede's conception is that he uses the term "exist." He can do without it. Gaede's entire approach to science can be encapsulated in a few words: mechanical movies of what phenomena are proposed to underly observed data.
The word mechanical invokes that basic fact of human experience that there are objects that cannot pass through each other.* They push, pull, and collide with each other. That one fact accounts for most of even a child's knowledge of how to navigate and manipulate the physical world. It is surely hardwired in us to a degree, and even if not, so much of our understanding of the world is based on it. Our very thinking is surely based on physical metaphors as well.
Now, numbers have no place in mechanical movies proper. Of course numbers can tell us if those movies are plausible (for instance, the movie of how gravity works had better show how the objects in the movie interact to produce the inverse square in the gravitational equation), but they have no place in the movies. We use an equation to summarize the observed data (yes, pencil falls toward earth at this rate of acceleration, yes, again, yes, verified again, ok now we have a neat equation that summarizes the data), then we theorize about the (unobserved) physical mechanism by which that data could have been produced. Then we check it against the data (equation) again. And back and forth like that, between data and explanatory theories.
Also, we can visualize rocks, but we cannot visualize numbers (except maybe as movies, or we can visualize 4 rocks, but not the abstract number "4"). Math is useful, but it is not what we put up on the big screen when we want to present our explanation of how we think an observed phenomenon may have come about.
*Unfortunately his rope hypothesis violates this, so it's not yet fully viable.
Everything follows from that. The word mechanical invokes that basic fact of human experience that there are objects that cannot pass through each other.* They push, pull, and collide with each other. That one fact accounts for most of even a child's knowledge of how to navigate and manipulate the physical world. It is surely hardwired in us to a degree, and even if not, so much of our understanding of the world is based on it. Our very thinking is surely based on physical metaphors as well.
*Unfortunately his rope hypothesis violates this, so it's not yet fully viable
The first 20 mins or so of this (but the whole thing is fascinating):
You are aware that Wittgenstein also wanted to create a visual language? He eventually gave up so that might be a cautionary tale. Leibniz was interested in what I believe Steven Pinker has finally begun to do and that is to try to identify the "alphabet of thought", the basic building blocks of human thought present in any human language. Leibniz felt that we could analyze language and strip it down to its bare structure (a kind of mathematical/logical structure) and this structure would be the very alphabet of thought. Nothing more basic than these structures could be conceived. Pinker elsewhere talks about the contrast between his work and Chomsky's works and his description of Chomsky's work sounds a lot like the approach that Leibniz had in mind. I think the evolutionary psychology approach, however, is more concrete and makes more sense to me.
Maybe we have a disagreement about the nature of visualization, then. Even Gaede uses idealizations that do not correspond to mechanical reality to illustrate his "thread theory". Visualization is not simply the construction of miniature models, e.g. a planetarium. Visualization/idealization is the intentional and direct utilization of the features of human language (and, hence, brain) that permit us to "slice up" the physical world into geometric abstractions. Mathematics is "parasitic" on this built-in feature which did not evolve for the purpose of doing mathematics. It just happens to enable us to do mathematics.
My point about real numbers is that physicists have (perhaps unwittingly?) surreptitiously imported an infinitude into the physical world from the idealized world of mathematics - the infinitude of infinite divisibility. Real number space is infinitely divisible, no matter how many times you have divided a piece of real number space, you can always keep dividing it further. This flatly contradicts the Planck distance which means that real-number space is simply a bad model of the physical world, it actually contradicts the phenomena. If the Universe were infinitely divisible, there would be no Planck limits.
This is part of my motivation for proposing a "ratio-like physics" where all quantities in the Universe are in fact whole number multiplies of something else and all relations are ratios between those whole numbers. This limitation would apply at the smallest scales so that we cannot speak of a "physical point", as in, a geometric point that is infinitely small. Such a point would require infinite divisibility which contradicts the Planck limit (an observed property of the Universe).
He is merely saying that measurement is the observation and characterization (description of the observed phenomena) stage, not the explanation* stage.
Yeah, but I think he understimates the power of inference from observed phenomena to extend our resolving power of the Universe itself. Let me explain. Without a microscope, all you have is the unaided eye. You can't see very much. You need a technological tool, a device, to amplify your ability to see small things. This is the microscope. Now, even with a microscope, there are limits to what you can see. What can go past that? Well, we have electron microscopes, interferometers, particle accelerators (basically, these are just ridiculously large and expensive microscopes pointed at fundamental particles). But how can we go past that?
Well, we can use deductive methods to extend our conception of the physical world beyond what is observed with the caveat that such extensions are precarious... a single contrary observation can collapse the entire house of cards. And for a long time, this is all we had... the ancient Greek, Chinese, Indian and later philosophers used deduction from geometry (which was based on scientific observation of the nature of ordinary objects) to speculate about the nature of the physical world beyond what they could directly observe. Democritus, for example, famously postulated that everything in the Universe is made up of tiny atoms (though he wasn't absurd enough to treat them as point-particles as modern physicists do) and that the bumping together of these atoms like billiard balls gave rise to all physical phenomena. Down to the level of chemistry, he would later turn out to have been precisely on the mark.
So, I see two prongs to science, a technological prong and a conceptual prong. The technological prong is dependent upon new devices with greater resolving power. The conceptual prong is dependent upon deductive methods, that is, the state of the art in logic and mathematics. It is the combination of these two that enables us to perform a "heuristic search" of the Universe. Without the conceptual prong to generate speculations by which to guide our observations, we'd have no idea what to look for. And without being able to see things one way or another, we're often stuck saying "Well, it could be A, B or C... or something else completely."
The trouble with modern physics is that it has become wholly obsessed with the technological prong. It's all about building a bigger accelerator. But I don't think we've really digested all the observational data which has been generated since at least the early 20th century. There are other, entirely different ways of thinking about those phenomena which have hardly been explored at all. We're blindly proceeding down one path at full tilt, heedless of the costs of being wrong. What if all this money poured into these accelerators has just been a waste and we should have been doing something else instead if we really wanted to get meaningful answers about how the world operates?
As I've written elsewhere, I believe this is a symptom of public science funding and the "monopolistic theory" or "king of the hill" effect it creates within the sciences. One conceptual framework comes to dominate and sucks up all the oxygen but this actually makes us conceptually blind. That one framework receives basically all funding and the other conceptual possibilities languish, unexplored.
The lever equation, for instance, is very useful, but it is just a characterization - just a succinct encapsulation of the observed data.
Go read Mach. It's more than that, it's a manifestation of a deeper physical principle called moment. Mach specifically exposits the lever principle in order to guide the reader to this deeper (as in, more general) understanding of the mechanical world. He shows how the history of thought about the lever led by halts and starts to this final conception of the moment and how it is the most general and elegant way of understanding the lever principle.
As for the point about Conservation of Momentum, you should read the section where he discusses Galileo's thought-process. You will see that Galileo did not just "encapsulate observed data"... he actually thought-experimentally continuated the observed data beyond what could ever be observed and used this to deduce a generally useful law of physics, the law of Conservation of Momentum. This is an illustration of how the conceptual prong of science can be used to extend the technological/observational prong.
I will concede that mathematics is originally anthropological, that is, human mathematics reflect the built-in circuitry of the human brain and are really a manifestation of our brain's way of thinking about and organizing the physical world.
However, complex numbers are very special. They are different than rational numbers or even real numbers or bizarro numbers (e.g. surreal numbers). Their first special property is that all the basic operations of arithmetic (addition, subtraction, multiplication, division, exponentiation, root and logarithm) can be performed on complex numbers and the result will always be another complex number. This is not true of the real numbers, for example. If you take the logarithm or root of a negative real number, the result is not a real number. The second special property is that there are certain "special" complex functions which have the behavior that every other complex function (with certain natural restrictions) can be "mapped" onto the special function. This means you can choose a single function to represent all possible complex functions which are just parameters to the special function.
There are more interesting properties - fractals and waves (both of which occur very frequently in Nature) are very natural within the complex numbers. And, as I mentioned already, the correlation between electrical phenomena and the complex number system is truly jaw-dropping... it's like the complex numbers have just the right shape to describe electrical phenomena. They are a "perfect fit". To cast that aside as "excessive arithmetization" of physics is as silly as throwing out Euclidean geometry in describing the world of ordinary experience. The correlation is beyond coincidence.
The power of complex numbers and computers together is stunning:
In a metaphorical way, it looks real. It has all the features of the real world as it looks when we investigate it at all scales... a perceptible order that has been slightly skewed and has deep structure as far as you can manage to look. Living organisms, galaxies, ice crystals, all of these and more exhibit this kind of "fractal" structure to them. I believe (as in faith) that the Universe is ultimately something very much like this. At root, the Universe is number because what else could it be other than pure pattern? It doesn't just exhibit structure, it is structure.
And I believe this structure is very "fractal" and "complex-number-like". The laws of the Universe appear at once so mathematical (orbit of the planets) and yet so bizarre (nuclear radiation) because we are dealing with pure structure that is immensely deep. Deep structure can appear very "ragged" and "misshapen". I believe the raggedness in the structure arises from the "lossiness" of the Universe's propagation of state information. Not all information present in a physical system is preserved in time, some of it just "gets lost" and this makes it impossible to run the Universe backwards (time has an arrow) and it causes increasing disorder (entropy) which gives the Universe an "uneven yet structured" appearance.
This is precisely how these fractals get generated... you choose an equation but you don't want to choose an equation that is too elegant, or else the fractal structure is too smooth, symmetrical and repetitive, you choose an equation that is a little "lop-sided" and then you get these amazingly organic-looking structures. I don't think these animations introduce noise into the fractal but you can create even more "realistic" fractal structures by introducing noise... which is just lossiness in the transmission of state information.
</metaphysical speculation>
<quick response> Well if the world were made of some basic building block that had a very simple shape architecture (ex: pyramids), I guess it makes sense that that would result in a lot of fractal structure at every level, and also some simple math would be able to characterize it elegantly since the basic structure is physically simple.