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It is becoming harder to use just simple theories, where more complex ones are needed e.g. quantum mechanics, super string theory, ...

Are such theories in conflict with Occam's Razor?

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    Occam's razor: "Numquam ponenda est pluralitas sine necessitate [Plurality must never be posited without necessity]", is a "general principle", a sort of "guideline". It is not a logical rule. – Mauro ALLEGRANZA May 4 '16 at 10:25
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    The more complex the phenomena that are to be explained, the more complex the theories with ever more necessary entities that have to be proclaimed for explaining them. As long as there is no simpler alternative, Occam's Razor is served perfectly well, no matter how complex the theory may become. – Philip Klöcking May 4 '16 at 10:27
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    "The simplest explanation" isn't necessarily simple. – BlueRaja - Danny Pflughoeft May 4 '16 at 15:56
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    Occam's Razor isn't a theory; isn't true or false; and it isn't in competition with quantum theory. – user207421 May 4 '16 at 20:10
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    Quantum mechanics is simpler than classical mechanics. – Brian May 4 '16 at 20:53

12 Answers 12

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The more complex and numerous the phenomena that are to be explained, the more complex the theories with ever more necessary entities that have to be proclaimed for explaining them.

Occam's Razor in one contemporary (in his time) formulation is:

lat. Numquam ponenda est pluralitas sine necessitate

engl. Plurality is not to be posited without necessity.

This means that as long as there is no simpler alternative, Occam's Razor is served perfectly well, no matter how complex the theory may become, see e.g. this answer.

The complexity of quantum mechanics and the like is simply due to the vast variety and distinctiveness of phenomena we encountered in experimental environments. They necessitate all these fields/entities to be included because without them, not all of these phenomena could be explained (or rather: described).

On the other side, these theories exclude even more complicated alternatives by delivering a simpler (in terms of plurality) explanation. Here, Occam's Razor can be and has been applied, e.g. in the history of the physics of fields regarding the postulation of 'aether'.

Important aside

What is known to us as Occam's Razor isn't a principle 'found' by himself, it is read out of Aristotle's metaphysics and often reformulated over the centuries, see https://en.m.wikisource.org/wiki/The_Myth_of_Occam%27s_Razor

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    I'd also note that theories like quantum physics and string theory are exceedingly simple. Simple doesn't mean "simple to read", just "few positions"; the whole of quantum physics or general relativity boils down to one equation that's quite easy to understand if you have the required prerequisites. Everything else is making the models that make reality easier to work with - the same is true with all the preceding theories. A big idea behind physics (and science in general, to an extent) is reductionism - simply, the idea that the underlying principles are simpler than their effects. – Luaan May 4 '16 at 14:02
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    Agree with @Luaan. It is not the case that more complex phenomena require more complex explanations. Once we have a simple explanation, the complexity is exposed as only apparent. Newtons laws are pretty simple, but before we had them the phenomena they describe were exceedingly complex. – user20153 May 4 '16 at 21:17
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    @Luaan: While the theory might be simple in the sense that it is expressed in a single equation, the level of abstraction and the complexity of mathematical operations needed to actually achieve a description of particular states of particular systems is what makes it complex imho. Without these factors, the equation wasn't able to describe the vast number of particular phenomena. – Philip Klöcking May 5 '16 at 10:01
  • That's where you mix the two things that shouldn't be mixed IMO - the theory is very simple. Applying it to make useful practical predictions and calculations is much more important, but not really about the theory itself. Models of reality are much more complex than reality itself - we add more complexity to the model to make it more useful. E.g. gravity for "spherical, homogenous objects" is more complex than generalized gravity, but it's also much more useful for e.g. engineering - the equations are easier to work with, and they usually work well enough within the constraints. – Luaan May 5 '16 at 10:50
  • @Luaan: A mathematical equation isn't a theory. A theory must provide and include the interpretational work needed to get from the mathematical description to the particular events they claim to describe. Or at least an image/intuition of what it actually describes. – Philip Klöcking May 17 '16 at 9:38
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Let me post the simple answer.

Occam's razor advises that:

Among competing hypotheses, the one with the fewest assumptions should be selected.

Now the thing is, that the simple hypotheses (eg. Newtonian mechanics) have been proven experimentally wrong. This means they are not competing hypotheses, they are just (very) useful approximations.

And out of the competing hypotheses, quantum mechanics seems to have relatively little assumptions. Compare it for example with the theory that assumes some hidden variables.

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    Hidden Variable Theory is not a competing theory to QM. It is one interpretation of Quantum Mechanics, and competes with the more widely-accepted Copenhagen Interpretation. A better example would be String Theory, which is much more complicated than QM but doesn't provide new predictions (that can currently be tested) – BlueRaja - Danny Pflughoeft May 4 '16 at 16:25
  • @BlueRaja-DannyPflughoeft Are you sre about that first assertion? AFAIK hidden variables theory is always presented as opposition to quantuum mechanics - the wikipedia article (which might be incorrect or biased) only talks about the two as direct opposition. – Tomáš Zato May 4 '16 at 17:37
  • Yes, I'm sure. The hidden-variable theory says that "QM is probability-based because we are missing information". If we had an actual theory that described that missing information, that would be a competing theory; but we don't. See here for more info. – BlueRaja - Danny Pflughoeft May 4 '16 at 18:00
  • @Thunder2709 would have commented as follows if the system had let him (or her): " Re: Hidden variables. QM has been demonstrated to be a closed, complete theory (as mentioned in the wiki article), and as such, the addition of hidden variables does nothing to extend our understanding of QM. What we have here is a legitimate application of Occams Razor. Yes you could assume hidden variables in QM. But seeing as how doing so provides no net benefit, the accepted and rigorously upheld Copenhagen Interpretation should be used instead." – Russell McMahon May 4 '16 at 18:24
  • @TomášZato The theories which oppose to quantum mechanics are "local hidden variable" theories. There are hidden variable interpretations which are experimentally valid, but those variables are non-local. Locality is one of the things you can give up to interpret QM. Determinism is another (this is what is given up by the Copenhagen interpretation) – Cort Ammon May 4 '16 at 23:21
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Quantum mechanics is a theory from physics, while Occam's Razor - see its wording from Philip Kloecking's answer - is a heuristic from the theory of science.

As long as we do not have a better theory than quantum mechanics, the latter fits perfectly well to Occam's razor: There is no concurrent theory which explains at least as much as quantum theory, but employs less entities.

Aside: Whether quantum mechanics is considered complex or simple depends on the background of the person in question. Nevertheless, the interpretation of quantum mechanics is still an open problem.

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Quantum mechanics is a simple theory, you're just trying to understand it from a highly complex point of view!

As any theory explains deeper and more fundamental units of the universe, they get simpler and simpler. The complexity creeps in when you try and infer what any number of individually simple interactions might have at a macro level.

Interestingly, if you ignore a lot of the detail, you can arrive at nicely simplified macro-level theories, such as The Gas Laws, or Newtonian Mechanics. They work nicely because the mathematics tends to cancel out much of the "hairiness" generated by a multitude of interrelated simple interactions.

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Ockham's original formulation goes like this :

Numquam ponenda est pluralitas sine necessitate

Roughly translated, it means this :

Plurality is never to be posited without necessity.

Note the word "necessity" at the end.

In a modern scientific context, Occam's razor is the notion that we should look for the simplest explanation that is consistent with the empirical data. The more empirical data we have to consider, the less explanations remain that are consistent with all data, and the less simple the remaining explanations tend to be.

Basically, you can think of Occam's razor as scientists (1) compiling lists of possible explanations, (2) cross-referencing the explanations with the empirical data available to them, (3) eliminating all explanations that are inconsistent that data and (4) ending up with the simplest explanation they haven't eliminated.

Of course, that process never ends since new findings are constantly published, which is why scientific theories are replaced by other (more complex) theories all the time. That is how one can start with a very simple explanation and end up with very complex scientific theories, all while applying occam's razor rigorously.

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A problem is always examined, and explained, in a particular context. In some contexts, the description can be very intricate, with many adjustments and approximations. Consider the motions of the planets relative to the starfield as seen from Earth. In a description based on the personality of the gods, the explanation must incorporate the entire backstory and current emotional state of the gods, and should include an understanding of why the motions are similar to motions previously seen. By changing context to a theory of epicycles, fewer assumptions need to be made. Shifting context again to the heliocentric model, the description becomes even simpler.

I see it a little like data compression. By transforming the problem to another representation (such as cosine transform space rather than pixel arrays), it is easy to keep what is vital.

Quantum mechanics is a simple theory that makes predictions (and explanations) about physical systems' behavior. It is counter-intuitive, and takes experience and insight to transform the context of a problem into the quantum mechanical realm, but once there the answers are simple.

This is similar to a programmer's error in feeling that a part of a program that was particularly difficult to write must also be difficult for the computer to execute.

For the right problems, no matter how difficult for the brain to make the transition, a quantum mechanical explanation is simpler.

There is no conflict with Occam's Razor, either as stated formally, or as an informal intuition that a simpler explanation is better.

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Note that quantum mechanics is part of the standard model. Even if it is difficult to understand, it is not that complex. With quantum mechanics and relativity you can obtain equations for electromagnetism, weak interaction and strong interaction. Those equation are not that complicated. It might be difficult to solve them, but it is a totally different topic. The idea behind them is quite simple.

String theory on the other hand, appears because the standard model has a lot of parameters. There is a lot of particles, interactions ... One of the reason why people are interested in this theory, is that we could get something simpler. So I guess, the Occam's razor principle is still used and physicists, as far as I know, are still very excited about the possibility to discover a new theory, simpler than any other theory.

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While it seems harder to use just simple theories in some fields, this does not mean that simpler theories do not exist. And many researchers are motivated by grand unification or simpler explanations (even if simpler theories are not known to exist).

Remember for instance astronomy, which became more and more complex with observations, and required to deal with epicycles to cope with Earth-centric model, before Copernicus. In mathematics, some persons with eagle view are able to simplify theories which every people believed untractable before (see for instance How Grothendieck Simplified Algebraic Geometry). From Can one explain schemes to biologists, it is said that:

His unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most abstract level revealed themselves -- and then, like a magician, show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed.

Indeed, testing two different theories sometimes becomes harder too, because they require a lot of energy. When they yield the same explanation on known facts, some researchers use Occam's Razor for the one they prefer to work with. And what simpler, sparsest or more elegant means depend a bit on the person.

And Occam's Razor can apply at multiple scales. You can work within a very complex theory, but still use the razor on small-sized aspects or work in progress.

Finally, the law of parsimony is now used quite often when using instruments. They produce data that should be analyzed to reveal interesting parameters, rare events. In those cases, a lot of data processing approaches are mathematically ill-posed, and sparsity (find the "simplest function" that fits noisy data) has been of help in many situations.

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The post that clarifies that Occam's Razor is a heuristic, or a rule of thumb, not an actual theory is the point. Occam's Razor is a general guide for finding solutions, not an actual part of the solution or theory at hand. Also, the guideline is that the simplest explanation tends to be the right one includes it's own caveat, "tends to be", not "is".

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Occam's razor is a method of doing science. Quantum mechanics is a scientific theory.

Occam's razor is not true or correct, since it is a method, not any kind of statement of fact.

Occam's razor is a kindness. It says: Let's not be cruel to students of science or other subjects by teaching them over-complicated theories that they will go crazy trying to understand. It says that of all the theories which explain the facts completely, we should use the simplest theory. When and if new facts are discovered that disprove an accepted theory, we should accept the simplest new theory that completely explains the new set of facts.

Occam's razor is not about selecting the competing theory that is most "true". It is about not overloading the brains of students with theories that are more complicated than they have to be, and using the simplest theories as well as we can until it is necessary to replace them.

Anybody who feels that the theories that he has been taught are too simple and boring is free to disregard Occam's razor and propose more complex theories. But few other persons will be likely to accept such overly complex theories until new facts make them the simplest explanations that fit all the facts.

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    What? No. Occam's razor has no regard for "students". It's just the observation that given competing explanations, the one with fewer entities is most likely the correct one. Occam used it to show that there's no place for God in science (not that the ideas of science were very mature then) - it's simply another entity that gives no explanatory power to your theory. It's not about making scientific theories simpler - it's about making them correct - if there's something unnecessary, it goes out. "Driving safely is about paying attention and sacrificing a goat" - well, how does the goat help? – Luaan May 5 '16 at 6:57
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Occam's razor says that," Do not multiply quantities unnecessarily" That also mean keep it straight and simple ,dont add anything extra. Quantum mechanics is following the rules of occam's razor, by not assuming or adding something which is not necessary. quantum theory is following scientific method, and occams razor. Occams razor is already followed by quantum theory.

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Suppose, for a moment, that the universe, including all natural laws that govern its operation, arose spontaneously out of absolute nothingness. If such is the case, the natural laws that happened to arise would be constrained by the processes which produced them, and therefore be more likely to be simple than complex. This would mean that Occam's Razor is a law about natural law, and not merely a useful heuristic. Given that we cannot yet disprove the theory natural laws have evolved, it is premature to conclude that Occam's Razor is no more than a heuristic.

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  • If you have any references these would help support your answer and give the curious reader a place to go for more information. Does anyone you are reading take a similar view that you could reference as part of the answer? – Frank Hubeny Apr 21 at 22:06

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