All models are wrong

I’m back in Cardiff for the day, mainly for the purpose of attending presentations by a group of final-year project students (two of them under my supervision, albeit now remotely).  One of the talks featured a famous quote by the statistician George E.P. Box:

Essentially, all models are wrong, but some are useful.

I agree with this, actually, but only if it’s not interpreted in a way that suggests that there’s no such thing as reality and/or that science is just a game.  We may never achieve a perfect understanding of how the Universe works, but that’s not the same as not knowing anything at all. 

A familiar example that nicely illustrates my point  is the London Underground or Tube map. There is a fascinating website depicting the evolutionary history of this famous piece of graphic design. Early versions simply portrayed the railway lines inset into a normal geographical map which made them rather complicated, as the real layout of the lines is far from regular. A geographically accurate depiction of the modern tube network is shown here which makes the point:

geo_tubemap

A revolution occurred in 1933 when Harry Beck compiled the first “modern” version of the map. His great idea was to simplify the representation of the network around a single unifying feature. To this end he turned the Central Line (in red) into a straight line travelling left to right across the centre of the page, only changing direction at the extremities. All other lines were also distorted to run basically either North-South or East-West and produce a much more regular pattern, abandoning any attempt to represent the “real” geometry of the system but preserving its topology (i.e. its connectivity).  Here is an early version of his beautiful construction:

Note that although this a “modern” map in terms of how it represents the layout, it does look rather dated in terms of other design elements such as the border and typefaces used. We tend not to notice how much we surround the essential things with embellishments that date very quickly.

More modern versions of this map that you can get at tube stations and the like rather spoil the idea by introducing a kink in the central line to accommodate the complexity of the interchange between Bank and Monument stations as well as generally buggering about with the predominantly  rectilinear arrangement of the previous design:

I quite often use this map when I’m giving popular talks about physics. I think it illustrates quite nicely some of the philosophical issues related with theoretical representations of nature. I think of theories or models as being like maps, i.e. as attempts to make a useful representation of some  aspects of external reality. By useful, I mean the things we can use to make tests. However, there is a persistent tendency for some scientists to confuse the theory and the reality it is supposed to describe, especially a tendency to assert there is a one-to-one relationship between all elements of reality and the corresponding elements in the theoretical picture. This confusion was stated most succintly by the Polish scientist Alfred Korzybski in his memorable aphorism :

The map is not the territory.

I see this problem written particularly large with those physicists who persistently identify the landscape of string-theoretical possibilities with a multiverse of physically existing domains in which all these are realised. Of course, the Universe might be like that but it’s by no means clear to me that it has to be. I think we just don’t know what we’re doing well enough to know as much as we like to think we do.

A theory is also surrounded by a penumbra of non-testable elements, including those concepts that we use to translate the mathematical language of physics into everday words. We shouldn’t forget that many equations of physics have survived for a long time, but their interpretation has changed radically over the years.

The inevitable gap that lies between theory and reality does not mean that physics is a useless waste of time, it just means that its scope is limited. The Tube  map is not complete or accurate in all respects, but it’s excellent for what it was made for. Physics goes down the tubes when it loses sight of its key requirement, i.e. to be testable, and in order to be testable it has to be simple enough to calculate things to be compared with observations. In many cases that means a simplified model is perfectly adequete.

Another quote by George Box expands upon this point:

Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.

In any case, an attempt to make a grand unified theory of the London Underground system would no doubt produce a monstrous thing so unwieldly that it would be useless in practice. I think there’s a lesson there for string theorists too…

Many modern-day physicists are obsessed with the idea of a “Theory of Everything” (or TOE). Such a theory would entail the unification of all physical theories – all laws of Nature, if you like – into a single principle. An equally accurate description would then be available, in a single formula, of phenomena that are currently described by distinct theories with separate sets of parameters. Instead of textbooks on mechanics, quantum theory, gravity, electromagnetism, and so on, physics students would need just one book. But would such a theory somehow be  physical reality, as some physicists assert? I don’t think so. In fact it’s by no means clear to me that it would even be useful..

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22 Responses to “All models are wrong”

  1. Themos Tsikas Says:

    I don’t understand how that TOE sickness took over theoretical physics. I mean, as Bill Hicks said, “what are the odds” that we’d stumble across it.

  2. “I agree with this, actually, but only if it’s not interpreted in a way that suggests that there’s no such thing as reality and/or that science is just a game. We may never achieve a perfect understanding of how the Universe works, but that’s not the same as not knowing anything at all.”

    Right. This point is often misunderstood by non-scientists, a point Asimov makes in his essay “The Relativity of Wrong”.

  3. I like the example of the tube map. And if they had made the map before digging the underground, perhaps the real thing would have looked like the map (and like an american city). But you wouldn’t draw a street map this way, so why does it work for the tube?

    In the end, the model is not to understand but to predict. String theory seems to fall far short here while GR has a perfect track record. So it should be obvious which one is more useful. But what is the fun working on something that is perfect? There is more career to be had improving something that is (“allegedly”) a failure.

  4. Anton Garrett Says:

    To say all models are wrong is a bit too Popperian; all models are *provisional*.

  5. The Milky Way’s halo is curved spacetime.

    Aether has mass. Aether physically occupies three dimensional space. Aether is physically displaced by matter. There is no such thing as non-baryonic dark matter anchored to matter. Matter moves through and displaces the aether.

    ‘NASA’s Voyager Hits New Region at Solar System Edge’
    http://www.nasa.gov/home/hqnews/2011/dec/HQ_11-402_AGU_Voyager.html

    “Voyager is showing that what is outside is pushing back. … Like cars piling up at a clogged freeway off-ramp, the increased intensity of the magnetic field shows that inward pressure from interstellar space is compacting it.”

    It is not the particles of matter which exist in quantities less than in any vacuum artificially created on Earth which are pushing back and exerting inward pressure toward the solar system.

    It is the aether, which the particles of matter exist in, which is the interstellar medium. It is the aether which is displaced by the matter the solar system consists of which is pushing back and exerting inward pressure toward the solar system.

    ‘Galactic Pile-Up May Point to Mysterious New Dark Force in the Universe’
    http://www.wired.com/wiredscience/2013/01/musket-ball-dark-force/

    “The reason this is strange is that dark matter is thought to barely interact with itself. The dark matter should just coast through itself and move at the same speed as the hardly interacting galaxies. Instead, it looks like the dark matter is crashing into something — perhaps itself – and slowing down faster than the galaxies are. But this would require the dark matter to be able to interact with itself in a completely new an unexpected way, a “dark force” that affects only dark matter.”

    A ‘new dark force’ is more speculative than understanding space itself has mass. What is occurring is analogous to the bow waves of two boats which pass by each other. The aether displaced by the galaxies interacts and ‘piles-up’ as the galaxies pass by each other.

    ‘Ether and the Theory of Relativity by Albert Einstein’
    http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html

    “the state of the [ether] is at every place determined by connections with the matter and the state of the ether in neighbouring places”

    The state of the aether at every place determined by connections with the matter and the state of the aether in neighboring places is the state of displacement of the aether.

    ‘Hubble Finds Ghostly Ring of Dark Matter’
    http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_feature.html

    “Astronomers using NASA’s Hubble Space Telescope got a first-hand view of how dark matter behaves during a titanic collision between two galaxy clusters. The wreck created a ripple of dark mater, which is somewhat similar to a ripple formed in a pond when a rock hits the water.”

    The ‘pond’ consists of aether. The analogy are two boats which pass by each other very closely. Their bow waves slosh back and forth and create a ripple in the water.

    The Milky Way’s halo is what is referred to as the curvature of spacetime.

    The Milky Way’s halo is the state of displacement of the aether.

    The geometrical representation of gravity as curved spacetime physically exists in nature as the state of displacement of the aether.

    Displaced aether pushing back and exerting inward pressure toward matter is gravity.

    ‘Offset between dark matter and ordinary matter: evidence from a sample of 38 lensing clusters of galaxies’
    http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.1475v1.pdf

    “Our data strongly support the idea that the gravitational potential in clusters is mainly due to a non-baryonic fluid, and any exotic field in gravitational theory must resemble that of CDM fields very closely.”

    The offset is due to the galaxy clusters moving through the aether. The analogy is a submarine moving through the water. You are under water. Two miles away from you are many lights. Moving between you and the lights one mile away is a submarine. The submarine displaces the water. The state of displacement of the water causes the center of the lensing of the light propagating through the water to be offset from the center of the submarine itself. The offset between the center of the lensing of the light propagating through the water displaced by the submarine and the center of the submarine itself is going to remain the same as the submarine moves through the water. The submarine continually displaces different regions of the water. The state of the water connected to and neighboring the submarine remains the same as the submarine moves through the water even though it is not the same water the submarine continually displaces. This is what is occurring physically in nature as the galaxy clusters move through and displace the aether.

    ‘Interpretation of quantum mechanics by the double solution theory – Louis de BROGLIE’
    http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf

    “When in 1923-1924 I had my first ideas about Wave Mechanics I was looking for a truly concrete physical image, valid for all particles, of the wave and particle coexistence discovered by Albert Einstein in his “Theory of light quanta”. I had no doubt whatsoever about the physical reality of waves and particles.”

    “any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium”

    The hidden medium of de Broglie wave mechanics is the aether. The “energetic contact” is the state of displacement of the aether.

    “For me, the particle, precisely located in space at every instant, forms on the v wave a small region of high energy concentration, which may be likened in a first approximation, to a moving singularity.”

    A particle is a moving singularity which has an associated aether displacement wave.

    In a double slit experiment the particle travels a well defined path which takes it through one slit. The associated wave in the aether passes through both. As the aether wave exits the slits it creates wave interference. As the particle exits a single slit the direction it travels is altered by the wave interference. This is the wave piloting the particle of pilot-wave theory. Detecting the particle strongly exiting a single slit destroys the coherence between the particle and its associated wave in the aether.

    What ripples when galaxy clusters collide is what waves in a double slit experiment; the aether.

    Einstein’s gravitational wave is de Broglie’s pilot-wave. Both are waves in the aether.

    • telescoper Says:

      Thank you for keeping your comment so brief and to the point.

      • The relativistic mass of an object is the mass of the object and the mass of the aether connected to and neighboring the object which is displaced by the object. The faster an object moves with respect to the state of the aether in which it exists the greater the displacement of the aether by the object the greater the relativistic mass of the object.

        The Milky Way’s halo is the state of displacement of the aether. The relativistic mass of the Milky Way is the mass of the Milky Way and the mass of the aether connected to and neighboring the Milky Way which is displaced by the matter the Milky Way consists of.

        The relativistic mass of the Milky Way accounts for the speed at which the matter in the Milky Way moves.

  6. […] Weinstein’s work is flawed at a trivial level. And even if it is wrong (which, arguably, all theories are) then it may well be wrong in a way that’s interesting, possibly precisely because it does […]

    • “In Weinstein’s theory, called Geometric Unity, he proposes a 14-dimensional “observerse” that has our familiar four-dimensional space-time continuum embedded within it.”

      All this in order to not understand aether has mass.

    • One really does need to read the original post before the first ellipsis here. At first, I thought you had manage to a) find a draft and b) find that it is flawed at a trivial level. 🙂

  7. The Milky Way’s halo is curved spacetime.

    The Milky Way’s halo is evidence of the correctness of relativity.

    The Milky Way’s halo is the state of displacement of the aether.

    Displaced aether pushing back and exerting inward pressure toward matter is gravity.

  8. ‘Comment on the higher derivative Lagrangians in relativistic theory’
    http://arxiv.org/pdf/1305.5759.pdf

    “The relativistic theory of an Aether was discussed several time, see for e.g. [8], [9]. In this paper, our hypothesis is different and gives a relativistic theory of the deformation of continuous media (for which the geometry is described by the metric field).”

    The ‘deformation of continuous media’ is the state of displacement of the aether.

    The Milky Way’s halo is the deformation of continuous media.

    The Milky Way’s halo is curved spacetime.

    The Milky Way’s halo is evidence of the correctness of relativity.

    The Milky Way’s halo is the state of displacement of the aether.

    • Here are a couple of more articles which are discussing the same phenomenon.

      The following article describes a ‘back reaction’ associated with the “fluidic” nature of space itself. This is the displaced aether ‘displacing back’.

      ‘An Extended Dynamical Equation of Motion, Phase Dependency and Inertial Backreaction’
      http://arxiv.org/abs/1208.3458

      “We hypothesize that space itself resists such surges according to a kind of induction law (related to inertia); additionally, we provide further evidence of the “fluidic” nature of space itself.”

      The aether is, or behaves similar to, a supersolid, which is described in the article as the ‘fluidic’ nature of space itself. The ‘back-reaction’ described in the article is the displaced aether pushing back and exerting inward pressure toward the matter.

      The following article describes the aether as that which produces resistance to acceleration and is responsible for the increase in mass of an object with velocity and describes the “space-time ideal fluid approach from general relativity.”

      ‘Fluidic Electrodynamics: On parallels between electromagnetic and fluidic inertia’
      http://arxiv.org/abs/1202.4611

      “It is shown that the force exerted on a particle by an ideal fluid produces two effects: i) resistance to acceleration and, ii) an increase of mass with velocity. … The interaction between the particle and the entrained space flow gives rise to the observed properties of inertia and the relativistic increase of mass. … Accordingly, in this framework the non resistance of a particle in uniform motion through an ideal fluid (D’Alembert’s paradox) corresponds to Newton’s first law. The law of inertia suggests that the physical vacuum can be modeled as an ideal fluid, agreeing with the space-time ideal fluid approach from general relativity.”

      The relativistic mass of an object is the mass of the object and the mass of the aether connected to and neighboring the object which is displaced by the object. The faster an object moves with respect to the state of the aether in which it exists the greater the displacement of the aether by the object the greater the relativistic mass of the object.

      The Milky Way’s halo is the state of displacement of the aether. The relativistic mass of the Milky Way is the mass of the Milky Way and the mass of the aether connected to and neighboring the Milky Way which is displaced by the matter the Milky Way consists of.

      The relativistic mass of the Milky Way accounts for the speed at which the matter in the Milky Way moves.

  9. Erik Andrulis Says:

    The correct and final model of reality is not wrong.

    In fact, the correct model is complete, consistent, and true. It fits all of the data, resolves all the enigmas and anomalies, and explains why things are the way they are and not any other way.

    I welcome discussion on how the complete and consistent theory of the universe is wrong.

    • telescoper Says:

      Is there any such thing as a complete and consistent theory?

      • Maybe there is, but the question of whether we will ever understand it is a different matter. IIRC it was Barrow (the famous writer) who suggested that a universe simple enough to be understood by us would be too simple for us to exist, and that conversely a universe complex enough to contain us would probably be too complicated to be understood.

      • Erik Andrulis Says:

        Yes. Though it is incommensurable with prior theories. the complete and consistent theory proves that you are the theoretician and theory in one:

        Perhaps Phillip, my brilliant critic, would do me a favor and point out the errors in the theory rather than directing me to some hatchet piece.

    • Noted sceptic PZ Myers has discussed your theory extensively:

      http://freethoughtblogs.com/pharyngula/2012/01/27/the-comparison-to-jabberwocky-is-inevitable/

      Read PZ’s take for some entertainment.

      • Erik Andrulis Says:

        When PZ Meyers directs his brilliant towards understanding rather than ridicule, perhaps that would be worthwhile.

        And Phillip, while you’re at it, perhaps you can address the same matter. That’s what a colleague who is genuinely interested in solving the hard problem of life and reality would do.

  10. […] people feel that most if not all scientific theories are wrong.  See here and here, for example.  With this “feeling” in mind, where does that leave […]

    • Complexity is created by the observer. Infinite data streams and associated recursive arguments are caused by the conception of an external material world the nature of which will appear to be unknown. If the observer dismantles the apparatus that causes this artifact-the notion of separation and the creation of limited awareness-the underlying ield of awareness is not obscured. Being perfect connection, it is not subject to division but allows infinite diversity and associated limited systems and concepts of ego and ideation to exist. There is only one truth, but it contains all the possiblility for apparent error and falsehood.
      There is no theory. There is no observation or complexity or accumulated libraries of opinion, just the simple potential for all these to come into being.
      Inspiration is unitary and simple and not bound by logic or language. Explaining everything from a limited perspective can cause infinite and endlessly recursive argument, like the appearance of a universe from a singularity.

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