’Tis the gift to be simple, ’tis the gift to be free ’Tis the gift to come down where we ought to be

I’m working on the final exam for my introductory biology course which is laced with Darwinism, but also with the philosophy of science, and early on I’d introduced them to Occam’s Razor. I’d tried to explain to them then that while it’s a useful operational tool in designing appropriate experiments, it’s almost never true that the simplest answer is the correct answer, at least not in biology. And then I stumbled across this article on Simplicity in the Philosophy of Science by Simon Fitzpatrick that summed up that same point nicely.

It should be noted, however, that not all scientists agree that simplicity should be regarded as a legitimate criterion for theory choice. The eminent biologist Francis Crick once complained, “[w]hile Occam’s razor is a useful tool in physics, it can be a very dangerous implement in biology. It is thus very rash to use simplicity and elegance as a guide in biological research” (Crick, 1988, p138). Similarly, here are a group of earth scientists writing in Science:

Many scientists accept and apply [Ockham’s Razor] in their work, even though it is an entirely metaphysical assumption. There is scant empirical evidence that the world is actually simple or that simple accounts are more likely than complex ones to be true. Our commitment to simplicity is largely an inheritance of 17th-century theology. (Oreskes et al, 1994, endnote 25)

Oooh, I’ll have to make a note of that for the next time I argue with an Intelligent Design creationist who thinks complexity is a hallmark of design.

Unfortunately, rummaging around in philosophy articles is not a good way to come up with testable questions for a first year biology course, and I still don’t have a good idea on this topic for the exam. I suppose I could just put that quote on a page and ask them to explain why Crick and Oreskes would say such things, but for the sake of my sanity, I’m avoiding asking for long essays from freshman students. I’m sure my students could handle it, but then I’d have to read 50 such essays, and I don’t think I could.


  1. nomdeplume says

    I’ve always assumed that natural selection will always take the path with the simplest solution to an adaptive problem. But such a path need not necessarily result in a simple outcome.

  2. hemidactylus says

    My quick take on the Razor is not multiplying stuff more than necessary, which is meaning stuff can still get complicated because…well…necessity and pluralism has a wedge or backdoor.

    One would think evolution is exhausted by selection or adaptive considerations, but noooo…! Drift can be important. Gene flow is important and ubiquitous amongst our bacterial nemeses and their low tech phage and plasmid file sharing devices. Doesn’t gene flow impact allelic frequencies in populations over generational time? Bacteria get down to brass tacks with no time nor noggins for social constructs (evil grin).

  3. says

    Easy refutation to the idea that natural selection favors simple solutions: humans exist. If simplicity were favored, we’d all be sleek, elegant, cleanly functional bacteria.

  4. ORigel says

    Occam’s Razor, I’ve heard, is better defined as “pick the hypothesis that makes the fewest unsupported assumptions” than “pick the simplest hypothesis.”

  5. Bernard Bumner says

    Surely Occam’s razor is not about the nature of things, but about the efficiency of explanations? It suggests that no more assumptions should be employed than are necessary to explain all of the observations. If further complexity is required to explain the properties being observed, then fine. If not, then are they actually explanatory and can such hypotheses be falsified? Has there ever been two competing theories that are equally explanatory where one is simple and the other is complex?

    Perhaps what is misleading is to think that it says anything about the inherent properties of nature. That is, rather than being about observers seeking the best conceptual framework to approach such questions.

    Suggesting that simplicity is not a legitimate criterion to weigh competing theories is probably begging the question, isn’t it? How is it possible to legitimately add complexity to an explanation if that complexity doesn’t address a wider scope of observations or better fit the evidence? What reason is there?

    Have I missed the point here?

  6. says

    BTW, I attended the Darrow School in New Lebanon NY, which occupies the site of the first Shaker Community in America. The song you quote in the title, Simple Gifts, is a Shaker song and of course it is about a way of being in the world, not an explanation of the nature of reality. It goes on, “and when we come down to the place just right it will be in the valley of love and delight.” Aaron Copeland quoted the tune in Appalachian Spring. It is similar to the tune of Lord of the Dance, if you happen to know that.

  7. says

    I agree with BB. If the simplest explanation works, there is no justification for adding complexity. It’s a mistake to force observations into a Procrustean framework for the sake of simplicity, but if the simpler theory really does work, it makes sense to start there and see if it extends to more cases.

  8. imback says

    Isn’t a cladogram built with Occam’s Razor in mind, assuming the simplest answer that entities with more shared features are more related? Of course, it’s a statistical assumption and could very well be overturned with more evidence.

    By the way, Wikipedia says the friar William of Ockham used the simplicity principle “to defend the idea of divine miracles.” It seems he bundled any inconvenient complexity into a superior inscrutable being. I don’t see how that helps.

  9. dianne says

    The general rule in medicine is that Occam misses all his appointments and when he does show up, he has a full beard.

  10. Snarki, child of Loki says

    A QUANTITATIVE form of Occam’s Razor:

    Minimize chi-squared per degree of freedom.

    I don’t think it helps in biology, where billions of years of organisms conspire to make your life difficult.

    Okay, maybe not billions of years. But cats. And Humans.

  11. cartomancer says

    I live just down the road from the village of Ockham, where the Venerable Inceptor gets his name from.

    I make a point of buying my shaving razors in the village shop there. Amusingly, this is not the simplest solution to the problem.

  12. says

    “[w]hile Occam’s razor is a useful tool in physics, it can be a very dangerous implement in biology. It is thus very rash to use simplicity and elegance as a guide in biological research”

    I like that. Especially when I think about the mammalian eye, or the fact men have nipples. If God made us he should have done more beta testing. FFS we have to consume ascorbic acid in our food or we suffer from scurvy. Sloppy work god.

  13. skeptico says

    Occam’s Razor does not say choose the simplest. If it did, Occam’s Razor would always choose Goddidit as an explanation. Because what could be simpler than Goddidit?

    Occam’s Razor is: “Don’t posit plurality without necessity.”

    In other words, don’t make stuff up to explain something (posit plurality), when there is a plausible explanation that does not require you to make stuff up (without necessity).

    As I wrote here about Occam’s Razor:

    Suppose I have a cat. One night, I leave out a saucer of milk, and in the morning the milk has gone. No one saw who or what drank the milk. Lets say there are two possibilities:

    1. The cat drank it
    2. The milk fairy drank it

    Occam tells us to reject option 2. This is because option 2 requires us to invent an unnecessary entity – the milk fairy. It is an invention because we have no evidence that the milk fairy exists. And it is unnecessary because there is a plausible explanation that does not require a milk fairy – the cat.

    Both the cat and the fairy are equally “simple” explanations.

  14. PaulBC says

    Simplicity may be the wrong measure, or it may need a more precise definition in this context. There’s no reason to expect global optimality. Evolution won’t deliver it, and in many cases, optimization problems are intractable (or conjectured to be).

    Suppose I put some items in a box and shake it till it settles, then remove anything extending too far to shut the box lid. I have packed the box, though probably not as well as I could. Suppose there’s a way to observe which items are in the box without seeing their arrangement. They could be of different weights such that only a certain set will add to a specific value. So I may know something about what’s in the box without seeing inside, but Occam’s razor is not much of a guide for how they’re arranged. It’s very unlikely to be the simplest arrangement of items. The process was, however, “simple” to describe. Note that the shaking process may have resulted in a better packing than just stacking without shaking, and causes the packing to approach local optimality.

    Given a collection of such boxes of unknown origin, I could conceivably develop a “simple” theory that would allow me to assign a p-value and identify at least some boxes that were packed intentionally and unlikely to have resulted from shaking. That seems like the place where simplicity could be useful. What is most likely to have arisen from a plausible process?

    The globally densest packing might be much simpler than any of the above, but it would be unlikely to result from that process, at least if carried out over a reasonable period of time. It would eventually settle to the lowest energy packing as the gravitational potential energy was converted by friction to heat and dissipated. That would be a simple model of the far future state, but unlikely to give a good prediction for a box of rigid macroscopic objects. Even for ones that settle easily by shaking, like a box of gravel, you’re still really unlikely to achieve global energy minimality.

    Anyway, I think Occam’s razor is a heuristic, not a principle. If there are things you cannot observe, they are not necessarily the simplest that you can imagine them to be. There just isn’t much advantage to speculating beyond this. Work with the simplest explanation and only extend it if it appears necessary to explain something. You also need to be simplifying in the right coordinate system. Predicting the exact arrangement of objects in a box, as above, is not an exercise in finding the packing with simplest description, a but probably something like a class of packings most likely to have arisen in the simplest way consistent with observation.

  15. snarkrates says

    Actually, I do believe that Occam’s razor is pretty decent heuristic, and as Snarki points out, it can be quantified for many statistical models. That, however, requires that the data be reduced to statistics, often not practical.

    A somewhat better quantitative measure of Occam’s razor can be found in Akaike’s Information Criterion AIC, which uses likelihood as a goodness of fit criterion for a statistical model, but penalizes the model with a term that depends on the number of parameters in the model. This is not an ad hoc quantity, but can be shown to be an unbiased estimator of a quantity that measures how much two distributions diverge from one another–the Kullback-Liebler Divergence. AIC selects the model that has the greatest explanatory power, not just the simplest. There are related quantities, including the Bayesian Information Criterion.

    In effect, these are mathematical statements of Occam’s razor, and give us an idea of what is really meant by simplicity in a scientific model. It is the model that provides the most explanation for its complexity. In this sense, GODDIDIT is not a scientific explanation, because the putative god is infinitely complex. Gods cannot be a scientific explanation for anything.

    The information criteria are powerful techniques that allow efficient selection and even averaging over models. Joe-Bob says check it out.

  16. PaulBC says


    “and when we come down to the place just right it will be in the valley of love and delight.”

    So maybe I’m on the right track. This is exactly what happens when you pack a box of rigid items by shaking it! It’s all about finding the most accessible energy minimum.

    Or not… “it’s hard to dance with the devil on your back.”

  17. says

    Yeah, there are a lot of domains where the most likely explanation is “it’s a combination of multiple factors”, whereas Occam’s Razor seems to suggest picking a single cause.

    Maybe there’s a way to fix that by framing Occam’s Razor in the “right” way, but I dunno. How do we know that you aren’t just patching one hole, and leaving open another in a domain of knowledge that none of us are currently thinking about? Ultimately Occam’s Razor is just a heuristic, and not a particularly strong one. “Listen to experts” is a stronger heuristic, and even that one isn’t right all the time.

  18. blf says

    An oft-quoted but perhaps even oftener-ignored form (at least in programming and perhaps other disciplines) is KISS — Keep It Simple, Stupid.

    On the other hand, KISS, when sensibly applied, works great. My current favourite example is how the Nasa / JPL Mars helicopter, Ingenuity, lands (slightly simplified): Fly straight down at a constant speed (1metre per second) until there is no more vertical motion, then stop. The altimeter (a laser rangefinder), etc., isn’t used for touchdown, due to concerns about false readings due to dust being kicked up. Instead, it (essentially) just flies down until it cannot, and then stops. (A fuller explanation is at What We’re Learning About Ingenuity’s Flight Control and Aerodynamic Performance.)

  19. kingoftown says

    I’m not a fan of the version of Occam’s Razor used in animal behaviour, Lloyd Morgan’s Canon, “In no case is an animal activity to be interpreted in terms of higher psychological processes if it can be fairly interpreted in terms of processes which stand lower in the scale of psychological evolution and development.”
    I understand that it’s important to avoid anthropomorphism but I don’t see why we should assume the “simplest” explanation either, especially when it comes to ethics.

  20. federico r.bar says

    This is an interesting thread!
    May I go off-topic for a moment? I cannot help associating the picture saying “When it seems that simple, I get nervous” with my feelings when I see a very low price being announced for a valuable object or service.

  21. Rob Grigjanis says

    A definition as good as any I’ve seen;

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

    Sounds good, but I most often see the term in discussions about it, like this one. Next on the frequency list is naive misapplications of it. Third is situations where a choice is obvious, and doesn’t need a special name,

    So, all in all, worse than useless.

  22. PaulBC says

    kingoftown@19 I’m not sure that’s even a simpler explanation. It sounds more like an enforcement of bias.

    I was thinking about this recently in the process of reading a popular article about hominid brain development, and some fossil evidence about the emergence of some structures. Clearly, the human brain has some capabilities lacking in other mammals, but it’s still the same organ composed of the same kinds of cells.

    To imagine the human brain is all that different from other brains strikes me as the “multiplied entity” than Occam said to avoid. Yes, we can observe that a human brain is larger than the most closely related primates and has some different structures. Humans also exhibit an exceptional language capacity. But the most reasonable null hypothesis is that our brains do more or less the same thing for us as other animals’ brains do for them–consistent with how we think of the heart, liver, kidneys, etc. If we think it does something different, we need evidence for this belief.

    So if we see a chimp acting in a way we can empathize with, the simplest explanation is that its brain is doing something similar to ours. Same with a dog. It may be less likely as the relationship becomes more remote. We may also imagine intentionality that’s not present (a tree swaying in the wind). But there’s no reason to reject the idea that an animal with a brain is mostly using it the way we do–recalling images, visualizing what might happen next, quantifying objects, planning at some level.

    Finding an explanation that interprets, say, the building of a beaver dam into a tropism seems more intended to separate us from animals than to explain anything. For instance, does a beaver merely follow instincts to chew on trees and move sticks, finding by chance that it has created a pond from a stream? Alternatively, does this animal have a memory of carrying out such a process (or observing older beavers) and actually anticipates the existence of this pond as it sets to work? Would it feel frustration and disappointment if the project failed. I suspect that all of these things are true. Though humans have capabilities absent in other animals, there is no reason at all to dismiss things that could very well be present.

  23. says

    an Intelligent Design creationist who thinks complexity is a hallmark of design

    As a hardware engineer, I generally consider complexity a hallmark of bad design.

    In my experience complexity often occurs when there was not enough time (or other resources) to really think about what is necessary in a design.
    Every design is a compromise. But if one carefully considers and weighs the constraints, a solution can usually be found. If it exists, that is. Sometimes requirements simply contradict.

    Alternatively, complexity often occurs when someone tries to to shoehorn in a solution that is not a good fit for the problem.

  24. Pierce R. Butler says

    My heuristic: “Anything that can complicate the situation, does.”

    I call it “Occam’s Whiskers”.

  25. jrkrideau says

    My thought was that the students would wonder about a question about a razer from a prof with a beard like that. Or am I splitting hairs (hares for the biologists)?

  26. PaulBC says

    rsmith@23 It’s definitely true that software development is agglomerative and corrective unless required to be otherwise. This is probably more the case than with hardware, because there are not as many inherent constraints to developing giant, unwieldy systems.

    One of the more laughable ideas coming from ID is Behe’s concept of “irreducible complexity.” It presupposes that the end result must be part of an additive process, and if every part is required, then they must have all arisen together. Really? I can make any reducibly complex system irreducible just by removing parts until it stops working and repeating this process until every part is required (this is apparently called “Muntzing” in electronics).

    However, you still won’t achieve global optimality that way. I’ve simply described a greedy algorithm, prone as they are to settling into a local minimum. In the case of evolution, an agglomerative process can eventually result in function, after which there is no selective pressure to maintain superfluous parts, so the result can eventually be more susceptible to single point failures (i.e. “irreducibly complex”) though it may be more efficient. It may also preserve redundancy if that improves fitness. In practice (I am not a biologist) it seems like we observe a mix of these tendencies: loss of some but not all redundancy.

    An ID/creationist could object that the process of building and removing is less “simple” than one of only building, and hence multiplying entities, but this is a nonsensical objection. Building and removing is observed commonly. If you find, e.g. part of a cow skeleton buried in a field, the simplest explanation is that it was once part of a living animal, not that it is an unusually shaped rock formation. It’s an awfully roundabout way to create a buried femur, but the most likely explanation based on experience.

    The guidance of finding a “simple” explanation is useful, but the notion of simplicity is so ill-defined, that I am not sure how to formalize it.

  27. birgerjohansson says

    Pierce R Butler @24
    For some reason, it makes me think about cats…(picks up shards if a vase).

  28. PaulBC says

    I think scientific induction is a much more useful principle than Occam’s razor. Having made and verified a few observations of what actually happens, the most reasonable explanation when the process cannot be observed is the one that resembles past observations under similar circumstances. It is still not a logically sound form of reasoning, but it has been very successful (and I’m sure there are rigorous reasons to expect it to be). It is what I think most experimental scientists do most of the time rather than finding the “simplest” explanation.

  29. mnb0 says

    “[w]hile Occam’s razor is a useful tool in physics, it can be a very dangerous implement in biology. It is thus very rash to use simplicity and elegance as a guide in biological research”
    It’s very rash to use simplicity and elegance in physics too. Does anyone think the experiments done in particle accelerators are simple? That the math necessary for say General Relativity is simple? Crick is criticizing a strawman version of Occam’s Razor.
    As for biology I found this:

    “In evolutionary biology, the method of maximum parsimony relies on the logic of Occam’s razor, seeking to construct an evolutionary tree that requires the fewest phylogenetic changes along all branches. However, reliance on this method is controversial, because it may oversimplify evolution, which does not always take a minimum path.”
    The however is misleading. What Occam’s Razor means in this case is something like “Given the known empirical data the evolutionary tree that requirest the fewest phylogenetic changes along all branches has the highest probability to be correct. As evolution does not always take a minimum path we never can rule out that there were actually more phylogenetic changes.”
    As you’re the biologist, PZ, not me, it’s up to you to find a few examples of oversimplification. In fact I’d add another rule to Occam’s Razor: things are always more complicated than we assume. This is not a paradox, because the simplest option always can be d**n complicated.

  30. blf says

    It occurs to me that a counter-example of sorts to the Razor is Euclid’s famous fifth postulate (the parallel postulate), which isn’t “intuitively” obvious (i.e., self-evident); indeed for a very long time, people tried to mathematically prove it using the other four postulates (not successful), or to restate it in more a more self-evident form. However, as Ye Pffft! of All Knowledge neatly puts it, “Eventually it was discovered that inverting the postulate gave valid, albeit different geometries.” Those “different geometries” turn out to be both interesting and massively important, with some interpretations very possibly more descriptive of reality than Euclid’s excellent start.

    As an aside, there are mathematical measures of “complexity” — presupposing that is (part of?) the issue — albeit at the present time, I can only think of measures of so-called “computational complexity”, possibly a rather restricted domain? Putting most of that to the side with a lot of vigorous hand-waving, and supposing “simplicity” and “complexity” are inverses, and also supposing the “simplicity” / “complexity” is both measurable and relevant, them a mathematical model might be possible to “formalise” the Razor and the domains (or conditions) in which valid inferences can be drawn. (That is all speculation, after a few drinks, and I am unawares of anything of the sort being suggested or attempted by experts — Sorry for rambling!)

  31. Rob Grigjanis says

    mnb0 @29:

    It’s very rash to use simplicity and elegance in physics too. Does anyone think the experiments done in particle accelerators are simple? That the math necessary for say General Relativity is simple?

    Building accelerators and detectors is complicated. What they do is simple; bash particles together and see what comes out.

    The principle underlying GR is simple; free fall is inertial motion. That leads naturally to the notion of gravity as a geometric phenomenon. The rest is studying differential geometry.

  32. Rob Grigjanis says

    Added to #31: Calculations can be a pain in the arse (I’ve worked with enough Christoffel symbols in GR and Feynman diagrams in QFT to last a lifetime), but I don’t equate that with complexity.

  33. grahamjones says

    mnb0 @29:

    What Occam’s Razor means in this case is something like “Given the known empirical data the evolutionary tree that requirest the fewest phylogenetic changes along all branches has the highest probability to be correct. As evolution does not always take a minimum path we never can rule out that there were actually more phylogenetic changes.”

    That’s still oversimplified. The tree with the fewest changes is not always the one with the highest probability. You could look up ‘the Felsenstein zone’. Or you could consider this simple experiment.

    Put a coin in a box, heads up, and shake it ten times with exactly the right kind of shake to give it a 1/3 chance of flipping with each shake. Observe the result: it is heads up. What is the most likely number of flips?

  34. Reginald Selkirk says

    Yes, the simplest solution may not be the correct one. But the problem here is that the available data supports more than one solution. That can be fixed by TAKING MORE DATA. And not just any data. A good scientist should be able to figure out what data is needed to decide between the available hypotheses, and design an experiment which will produce that data.

  35. benedic says

    One small point, the phrase “Entia non sunt-etc is not to be found in any of Ockham’s writings

  36. DanDare says

    Don’t add explanations to things not in evidence, even if you think they should be there.
    To eliminate cognitive bias.
    So what about a hypothesis that goes outside the shrink wrap?
    A hypothesis is not adding to the minimal interpretation. It is testable and when tested will either affirm that the minimal assumptions was right in this case or provide new data to wrap Occahm around.

  37. Azkyroth, B*Cos[F(u)]==Y says

    My understanding was that “simple” was intended to be interpreted as “has the fewest extra assumptions” and not “easiest to explain to a five year old,” and that the Razor was intended as a heuristic which dictated that, of possible explanations that explain all the data equally well, the one with the fewest extra assumptions was preferable.

  38. bjbjornson says

    Not much to add, but I am rather amused that nearly everyone here seems to agree that the biggest issue with Occam’s razor is that people tend to oversimplify it.

  39. says


    My suspicion is that the people who propose “intelligent design” have never in their life actually done any design. If they did, they would know that (mechanical and electrical) design is very much about using standardized parts and interfaces, and tailoring your parts to suitable production methods. Most people don’t seem to realize how much everyday objects are constrained by the way they are made.

    None of which applies to biological systems which are grown. So how would we even recognize “design” in biological systems?

    the notion of simplicity is so ill-defined, that I am not sure how to formalize it.

    Things that derive from the laws of physics (like mechanics of materials) are relatively easily formalized. By contrast, and to the best of my knowledge, good design and simplicity can only be learned by example. A major factor in that is that what constitutes good design and simplicity can be very situationally dependent. It depends for example on the manufacturing method. A part that is simple to make with machining (milling, turning) is different
    from a part that is simple to make with injection moulding.

  40. snarkrates says

    I would not say that “simple” is ill defined. I would say the definition depends on context. In terms of statistical models, fitting data, the meaning is clear. The simplest model is that with the fewest parameters. The right model is the one that yields the greatest predictive power for future data. Not oversimplified so that it doesn’t fit the data, but not overfitted so that it fits the data exactly.

    In physics, the definition varies, but generaly, it is the model with the fewest assumptions. In biology, it is probably even more contextual, but I think predictive power is probably a good criterion, regardless of the field.

  41. PaulBC says

    snarkrates@41 I agree that “simple” is defined well for fitting data, and too often ignored when overfitting models.

  42. vytautasjanaauskas says

    I don’t understand why so many otherwise smart people struggle with the Occams razor. It does not say that a simpler explanation is more likely to be correct. All it says is that there is no reason to keep adding to an explanation if the existing one is sufficient to explain something. And you can gather that much from Wikipedia?

  43. Christopher Stephens says

    For those that want to see the latest (and in my view some of the best) of what philosophy of science has to say about Occam’s Razor, check out Elliott Sober’s book, Ockham’s Razors: a user’s manual. (Sober’s early book, Reconstructing the Past, also has a nice chapter on simplicity, though some of the biology in the latter book is probably a bit dated).

  44. Numenaster, whose eyes are up here says

    @rsmith, in the realm you are describing the Four E’s are a decent description of engineering goals. They are, in priority order:

    1) Effective: the proposed solution must actually solve the problem
    2) Efficient: the proposed solution should solve the problem without introducing others
    3) Economical: the proposed solution should be the least costly option (to build or maintain, whichever is more important to you) that is both effective and efficient
    4) Elegant: the proposed solution should meet some additional goal that makes it cool to you. Could be extreme re-use of parts, arresting visual design, intuitive user interface, added LED lighting, etc.

    3 and 4 can be reversed for hobby engineering, obviously.

    These are the output of my 17 years as a manufacturing test engineer.