“Understanding” and Occam’s razor

At the beginning of the 20th century, the physicists Hendrik Lorentz and Albert Einstein both concluded independently that measurements of light speed would be the same for all observers. But while both arrived at the same results from their equations, Lorentz’s explanation relied on changes that take place in ‘the ether’. Because Einstein’s paper On the Electrodynamics of Moving Bodies made no reference to a mysterious, undetectable substance, his explanation was accepted as being the most likely.

Even after Einstein’s theory of special relativity had been accepted, Lorentz wasn’t willing to let go of his belief in ‘luminiferous aether’. In 1909 he wrote, “Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter.”

It might seem ridiculous that a serious scientist, steeped in the hard-nosed practicalities of mathematics, could be so convinced of the existence of a things which is both unnecessary and unverifiable. But ether, or aether, had been widely believed to be a reasonable explanation for those physical mechanisms we had not yet explained or understood. It was just assumed that there must be something unseen and unseeable that explained the complexity of the universe.

It’s the same sort of thinking which underpins Descartes’ approach to the division of mind and matter. If mind is somehow different to other kinds of matter, what is it composed of? How does it work? Many serious thinkers have struggled mightily to show that dualism can be made to work, but all explanations ultimately require us to accept the existence of a ‘primer mover’, a homunculus who sits within our minds, directing our responses. The idea that our brains, and therefore our minds, are composed of the same matter as everything else in the universe is too appalling for some to consider. We desperately cling to dualism because then we can argue in the existence of souls and maintain a belief that we are somehow special and different to the rest of creation.

It’s easy to chuckle at the naivety of pre-20th century minds and reassure ourselves that we, in the first quarter of the 21st century, are obviously more enlightened and not prone to such fanciful gubbins. But is positing the existence of ‘understanding’ as being somehow different and superior to mere knowledge any different? Here’s where the application of Occam’s razor can prove so useful. The razor is a heuristic for thinking about competing ideas about the natural world. Essentially the principle is this: Among competing hypotheses, the one with the fewest assumptions is the most likely.

As far as I can see, consciousness is completely explained in terms of memory and knowledge. Our minds have been shaped by thousands of years of natural selection to possess various innate, instinctive capacities. Some things are, perhaps, too vital for the survival of the species not to have carved themselves into our brains. Our ability to regulate various internal physical processes, to balance, to make sense of what we see are overseen by something in our minds, but they are not conscious. Consciousness, the ability to think, is sited in what we’ve come to call our working memory. This is where introspection occurs, and it is the only area of the mind to which we have access. We’re aware there are things we know that we’re not currently thinking about, and we can. with but a little effort, draw them into consciousness, but where do we keep these things when we’re not thinking about them? Where do they go after they have been thought about and our attention has been caught by something new? The best answer we’ve arrived at so far is to speculate that there’s another compartment in our mind which we’ve come to call long-term memory.

Plato thought of long-term memory as a vast bird-cage and our memories as birds. When we wanted to think about one of these memories we’d have to call it to us. Sometimes birds would stubbornly refuse to come, sometimes they’d appear to have escaped the aviary. Instead of this squawking, feathered mass, we’ve come to think that the birds of our memories flock together. These flocks have been named schema. It seems reasonable to suggest that our mind has an unconscious ability to store related ideas and experiences together. We might be able to exert some conscious control over this process, but it happens whether or not we will it. As our experience of our environment grows and is organised, we become increasingly self-aware, until we are able to sort our thoughts and feelings into words.

Is there an ‘ether’ that allows us to do this? In the absence of a more elegant explanation it might be reasonable to think so. Happily, David Geary’s theory of biologically primary adaptive modules of ‘folk knowledge’ and secondary modules of culturally specific knowledge allows us to suggest a less mystical way of thinking about how we learn. Our brains, it would seem, our adapted to learn some things much more easily than others. The modules of ‘folk knowledge’ are so important that they have come to be essentially human characteristics. Every human culture possesses language and has easily acquired systems for learning about the natural and the social world. These are a species-constant, universal inheritance we can trace back to the first appearance of Homo sapiens.

Where human cultures diverge, so does culturally specific, biologically secondary knowledge. Evolutionary biologist, Richard Laland says in his master work, Darwin’s Unfinished Symphony, “Humanity’s success is sometimes attributed to our cleverness, but culture is actually what makes us smart. Intelligence is not irrelevant of course, but what singles out our species is an ability to pool our insights and knowledge, and build on each other’s solutions.” Our ability to share what we know, first through spoken language and, latterly, through writing ensures we have quite remarkable access to a vast accumulation of cultural knowledge.

The magic of how we think can be reduced to something no less magnificent in its mundanity:

  1. Evolution shaped our brains to be able to learn somethings easily. The processes whereby learning is made possible are explained beautifully by Laland but are beyond the scope of this post. Suffice it to say that our genes have coevolved with our culture to accelerate and enhance this process to the point where we have a universal adaptation to learn, amongst other things, culturally specific spoken language easily.
  2. Everything we know – facts, experiences, feelings, procedures –  is stored as memories. These memories are distributed across our brains, but, for convenience, we have invented the ideas of working and long-term memory to explain how this process works. Knowledge is stored in the store house of long-term memory and drawn into working memory when we want to think about it. Everything of which we are conscious – and much of which we are not – is knowledge stored as memory. There is nothing that we can think about that is not accountable for in this way.
  3. The schematic nature of long-term memory can only be inferred, never observed directly. Like gravity, we can see its effects. We can be fairly sure that our memories are self organising, and the more information we store about a subject, the more effective this process becomes. We know that this process must be automatic because we don’t have to do anything to ensure it. More knowledge means more connections and more connects means better storage strength. Better storage strength is probably as good an explanation for understanding as you’re ever likely to get.
  4. There’s no need to invent a special category of mental ‘stuff’ or to suppose a more sophisticated form of reasoning; ‘understanding’ can be completely accounted for by the biological process of storing ever greater accumulations of knowledge as memories.

I’m not so foolish as to think this chain of reasoning provides proof. That is not the point. Each link in the chain can be falsified and, even if we cannot design experiments to test each link, we can subject my assumptions to logical analysis. Occam’s razor allows us to see which explanation contains the fewest assumptions. A simpler theory is preferable because it is more testable. If we posit that ‘understanding’ is different to knowledge, then we have to hypothesise the existence of something as yet unknown. Maybe, in time, such a thing will be discovered. But as things stand today, my explanation is, I think, the least flawed, but if anyone can simplify it further, I’ll happily admit to having been wrong.

25 Responses to “Understanding” and Occam’s razor

  1. howardat58 says:

    But “most likely” does not make something true, or right.
    Evolution is not “right”. It is “more likely” than other explanations.

  2. Michael Pye says:

    I just realised I can know nothing.

  3. Michael Pye says:

    Hang on, how can I know that I “know nothing” as surely that would be knowing something.

  4. This Lorentz character has a common ancestor with me, so I sympathise with him 😉 Also, I live in the town he worked in, Leiden. His house at the Hooigracht has been well kept.
    I guess Lorentz was trying to explain what Newton did not even want to try — his ‘hypothesis nog fingo’. There is this mysterious force (gravity) working over (long) distances of empty space, what a mystery! That mystery has not yet been solved even today. One of the competing theories is that our universe is a universe of information (Erik Verlinde https://phys.org/news/2016-12-verlinde-theory-gravity.html ). There is as yet no way a school pupil can ‘understand’ the three-part formula F = ma. Force equals mass times acceleration. Technically the formula is a tautology. Yet is has been very instrumental in developing our technical world!

    • Tom MS says:

      Definitely agree that lorentz is given a harsh deal in this account of naive ‘pre twentieth century minds’! Lorentz’s work played a major role in the development of relativity, and ether doesn’t seem so much more ridiculous than hyper dimensional vibrating strings now, does it? David you do have a tendency to be rather slapdash with the old pop science and statistics. Well done for ‘solving consciousness’ though!

  5. […] couple of folk, recently, have written about this. @daviddidau and @claresealey. I only want to add one smallish point to what they have […]

  6. Joe Eden says:

    I think there is a danger at talking at two different levels of description – the description at some kind of neurological level of brains functioning and the description of people doing everyday things like remembering. Even if we can (to quote Dennett) get ‘cranes’ to explain how one type of explanation could link to another, it doesn’t mean that what we can say of one we can sensibly say of the other (or that things we can say of one automatically imply things of the other).

    I also wonder if the difference between knowledge and understanding is perhaps a difference between types of knowledge – in your sense. But this wouldn’t need to result in the elimination of ‘understanding’ as a concept, simply a better understanding of understanding as being a certain (vaguely defined, yet nevertheless useful) level of knowledge in a certain area.

    To give some examples, I know that a steam train runs on the increased pressure that arises when you heat water up into steam. I have no idea how to build a steam train – my understanding is limited (with my limited knowledge). Could understanding, then, as you imply in your post, be distinct from knowledge not in kind but just in quantity? Understanding being a high level of knowledge about a subject area that allows successful application, solutions to novel problems, etc.

    So something like:

    Some basic recall Understanding
    _________________________________________________________________________
    Knowledge More knowledge about this area Even more knowledge about this area

    • Joe Eden says:

      I teach Critical Thinking at AS Level. Critical Thinking aims at giving tools to structure and critique the structure of arguments. But these are arguments in any field. Although knowledge in the field is always necessary to evaluate the premises, the inferences can be evaluated field-independently (hence learning about many types of fallacies that can appear in arguments in any field of study). It got me thinking – is some knowledge universally helpful in improving solutions to problems?

      Another example is that I teach RE, and some of the students quickly are able to get high marks not through careful building of knowledge (that is a successful strategy too) but simply through the sensible application of a bit of knowledge to answering the question (they write clearly and relevantly and they quickly see the links between the knowledge they do have and the question). This seems to be a skill (which might be a set of knowledge) which is independent of their knowledge of RE – e.g. Knowledge of the core concepts, Bible quotes and Church teachings on the topic. If it is a set of knowledge, it is a set of knowledge that seems independent of the field of study. And such students seem to be able to do this in other classes, as when I discuss their work with others, teachers are likely to say they are ‘nimble thinkers’ or ‘just get it’ (in terms of exam skills). Or perhaps this is the inherited part of intelligence at play?

  7. Ok, so let’s say that understanding is simply an increment of knowledge. Why have we then developed a separate word for it? We still need to distinguish between the different degrees of function between distinct forms of knowledge, and between the best ways to acquire such distinct kinds.

    A person who can use a Haynes Manual to fix a car isn’t synonymous with someone who can simply quote it. Not all knowledge is equal.

  8. A personal anecdote, on ‘understanding’.

    I had this strong experience of ‘understanding’ in preparation for my analytical geometry on the very last day before for my matriculation exam. This geometry has some peculiar features that obstructed my understanding, even while my technical mastery was pretty good. I knew perfectly well that I did not have what it takes to ‘understand’ this geometry, so I rehearsed pretty much the whole stuff on that day. And yes, it resulted in that peculiar moment that one realizes: Now I understand! The viva voce exam was a fast conversation on analytical geometry, thoroughly enjoyed bij all three participants, and resulted in the highest possible grade.

    What happened? I had all geometrical knowledge available already, yet there was something still lacking. I guess my knowledge was still not sufficiently ‘connected’ to give me the feeling to really master the subject. The one day rehearsal established full connectivity, enabling me to outsmart my teacher and external assessor. No, I am kidding. The feeling was there, though.

    Understanding is somewhat more than just knowing things. It is the connectivity of that knowledge. Or something. I guess.

    • peter says:

      “Understanding is somewhat more than just knowing things. It is the connectivity of that knowledge. ” Do we have any evidence it is any more than knowledge plus linking

    • David Didau says:

      This seems an unfalsifiable distinction. How could we show that connectivity is different to knowing propositional knowledge more fluently? This is where Occam is so useful. Mine is the simplest explanation with the least assumptions.

      • Be prepared for meeting Stellan Ohlsson in November 😉

        Stellan Ohlsson & Ernest Rees (1991a). The function of conceptual understanding in the learning of arithmetic procedures. Cognition and Instruction, 8, 103-179.
        paywalled: http://www.jstor.org/discover/10.2307/3233484 abstract
        article is based on this 1988 report, online http://files.eric.ed.gov/fulltext/ED302410.pdf

        The article is used in Ohlsson’s 2011 ‘Deep Learning’ (seek “Ohlsson & Rees 1991”)

      • With Anders Ericsson ‘understanding X’ might just be something like ‘having mental representations of X’.

      • Joe Eden says:

        Unfalsifiability as a criterion for scientific statements and theories is all fine and good but surely it is limited in scope. To illustrate –
        Ockham’s Razor and falsifiability are principles that are not themselves falsifiable. Conceptual and logical issues are outside the scope of what falsifiability can usefully be used to decide – as, for example, the debate over whether falsifiability is the best criterion for what makes a statement scientific is a debate that cannot be solved by appeal to that principle. I’m all for falsifiability in science, I just think it’s not a panacea and is out of place in a conceptual discussion.

        • David Didau says:

          Falsifiability works very well when applied to empirical questions. Occam’s razor is just a useful heuristic. If you’re going to argue that we can happily ignore either or both then you’re on pretty thin ice.

          • Joe Eden says:

            What understanding is, is not simply an empirical question. An analogy – when scientists reclassified Pluto as a dwarf planet, this was not falsifiable in a simple sense. It was a conceptual decision informed by new empirical data – the discovery of other Pluto-sized objects. Likewise, what understanding is and whether it is distinct from knowledge is not going to be fully determined by empirical enquiry – ultimately a conceptual choice is going to be made. That might be informed by Occam’s Razor, but other principles will also be relevant – such as explanatory power and conceptual usefulness.

            I wasn’t denying falsifiability or Occam’s Razor. Both are useful. My argument was about their scope and therefore questioning whether they were relevant in the domain of this discussion about the concept of understanding, and, if they were, whether alone they would be decisive. One weakness of Occam’s Razor in application is that what can seem most simple might actually diminish what is being explained (I’m thinking of Emotivism in Metaethics – very simple, but reduces ethics down to basically nothing and can’t explain even much that is done with ethical
            language).

          • David Didau says:

            I don’t see your point. Reclassifying something is a semantic issue and, while not unimportant, has nothing to do with selecting between competing theories. *Of course* Occam’s R is not a law, it’s simply a useful heuristic. In this case, very useful as the choice is between my assertion (everything we think with and about is knowledge stored in long-term memory) and the competing theory (understanding is some mysterious other material that ‘glues’ knowledge together).

            Feel free to offer a more convincing competing theory.

      • Be prepared for meeting Stellan Ohlsson in November

        Stellan Ohlsson & Ernest Rees (1991a). The function of conceptual understanding in the learning of arithmetic procedures. Cognition and Instruction, 8, 103-179.
        paywalled: http://www.jstor.org/discover/10.2307/3233484 abstract
        article is based on this 1988 report, online http://files.eric.ed.gov/fulltext/ED302410.pdf

        The article is used in Ohlsson’s 2011 ‘Deep Learning’ (seek “Ohlsson & Rees 1991”)

        • David Didau says:

          I’ve struggled through most of Ohlsson’s book and haven’t found anything that contradicts the position that knowledge, stored as memory, is all there is. Do you think I’ve missed something?

  9. Michael Pye says:

    Knowledge: Facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject.

    Knowledge: Awareness or familiarity gained by experience of a fact or situation.

    This supports your argument David but has left me slightly confused. Surely the argument that knowledge is all there is, must be explicit in the definition. Is this not one, an issue with people mis-using the word, and two if the word is so encompassing surely we are in danger of using it in a circular argument? All we need to teach is Knowledge because knowledge includes everything else.

    Confused.

Constructive feedback is always appreciated

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