What Does it Mean to Comprehend Something?

by: Bruce

December 16, 2010

In my last post I considered Physicist John Barrow’s view of what science is:

So we find that Barrow’s view of science is that it is the process of how we use reason to find patterns in reality and then to algorithmically compress them into finite steps and formula that allow us to represent reality via processes that are computable.

I am going to suggest this as our starting theory of reality, but there is much that can be challenged about this view and therefore refined.

But first, I want to consider the idea of comprehending something. What does it mean to “comprehend” something? The problem with a word like this is that it’s a single word that maps to multiple possible meanings. Harkening back to my first post, if I ask you if you comprehend PI, what would that mean? Is it even possible to “comprehend PI” at all? It’s an infinitely large number, after all. It is therefore beyond comprehension isn’t it?

The Nature of Understanding and Explanation

David Deutsch’s excellent book, The Fabric of Reality, is an exploration on what it means to understand or comprehend something.

He starts his book with the story of how, when he was a small child, he had a dream of wanting to know everything.

It was not that I wanted to memorize all the facts that were listed in the world’s encyclopaedias: on the contrary, I hated memorizing facts. That is not that sense in which I expected it to be possible to know everything that was known. … By “known,” I meant understood.” (The Fabric of Reality, p. 1)

He goes on to give an example of the difference between trying to memorize all the known observational data in astronomy and understanding the motions of the stars. Obviously no one could possible memorize all the observational data, but many people already understand all that is known about the motions of the stars and could therefore calculate out all the observational data, at least in principle. Deutsch goes on to say:

This is possible because understanding does not depend on knowing a lot of facts as such, but on having the right concepts, explanations and theories. (The Fabric of Reality, p. 1-2)

Here we should pause and consider how this sounds oh so familiar to us. It would seem that to understand something is something akin to algorithmic compression. You can’t memorize all observational facts, but you don’t have to. You merely need to understand it and all the observational facts, in principle anyhow, are sort of already available to you.

Therefore, to comprehend PI is to understand that it is the ratio of the circumference to the radius of a circle.

Assuming you also understand what a circle is and what the rules of Euclidean geometry are, then this definition of PI is alone enough to come up with a procedure that encapsulates PI in its entirely, as shown in my first post. Therefore, to comprehend something is to have the right (most right?) explanation of it. This is, in and of itself, a sort of algorithmic compression whereby we can take a impossibly large concept and encapsulate it into a simple set of explanations. (In this case the definition of PI, an understanding of what a circle is, and the rules of Euclidean geometry.)

So I want to propose a slight change to our current hypothesis about reality:

Science is the process of how we use reason to find patterns in reality and then to compress them into explanations that allow us to represent reality via processes that are computable.

However, algorithmic compression and explanation don’t seem to be exactly the same thing, though they are somehow profoundly intertwined. For example, if we actually have a computer program to calculate PI, would we really say the program ‘comprehended’ PI? Probably not. Therefore having an algorithmic compression alone is not to comprehend something. But the reverse does seem to be true. To comprehend something seems to imply you can always algorithmically compress it.

Questions:

  • Can you think of examples of things you comprehend but can’t put into an algorithm?
  • What about ‘justice’? What about ‘beauty’?
  • Can you comprehend yourself?
  • Can you put yourself into an algorithm?
  • To comprehend God would that mean we have to be able to put God into an algorithm?
  • Are there non-algorithmic sciences?
  • What about psychology?
  • Is ‘art’ algorithmic?

Also, don’t miss out on my recent re-print on Millennial Star where I ask “What is Mormon Doctrine?” and try to explain (algorithmically compress?) the incompressible.

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7 Responses to What Does it Mean to Comprehend Something?

  1. Mike S on December 16, 2010 at 6:20 PM

    Can you think of examples of things you comprehend but can’t put into an algorithm?
    I think most “testimonies” fall into this realm. We teach getting a testimony as an algorithm – read, pray with real intent, confirmation. But the algorithm doesn’t work for many people, and for the people for whom it does work, the experiences sound very different. At the same time, people with a testimony of the BofM, for example, would consider it so comprehensible that they say they KNOW it is true.

    What about ‘justice’? What about ‘beauty’?
    Justice is hard because there are several definitions. Is it justice on an individual basis vs justice on a societal basis? These often conflict. Beauty is also hard to compute algorithmically. Many things that I find ‘beautiful’ are opposite to others.

    Can you comprehend yourself?
    I don’t know. I do think that meditation helps one come closer to the underlying reality than many other things. Whether this is comprehension or not is debatable, but it does make sense.

    Can you put yourself into an algorithm?
    I do think that I am fairly predictable. I bet my wife could tell you what I’d do in 99% of all situations.

    To comprehend God would that mean we have to be able to put God into an algorithm?
    If God is Perfect, and if Perfect means there is One way, then yes, God should ultimately be able to be put into an algorithm. We should know what God would do in any given situation. We are taught that Christ’s will is identical with God’s. In that sense, our ultimate goal is to have the same “algorithm” as God. But… I think that our finite minds are so limited that we cannot comprehend God in mortality. Our thoughts are not God’s. But they could be…

    Are there non-algorithmic sciences?
    Not by your definition of science.

    What about psychology?
    Ultimately, yes. It will generally come down to brain chemistry, experiences, etc. At this time, however, our tools for exploring the mind are far too blunt to drill down and determine this.

    Is ‘art’ algorithmic?
    Some art. Music is very algorithmic, and the progressive type of music that appeals most to me has complicated time signatures, etc. Chords and keys have fixed intervals. Anything falling outside these is perceived as jarring. There are patterns that “work” for “hits” – very algorithmic.

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  2. Bruce on December 16, 2010 at 6:25 PM

    Mike S,

    Very thoughtful answers. More than I expected really. Good job. Gave me lots to think about.

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  3. Mark D. on December 17, 2010 at 12:16 AM

    Can you think of examples of things you comprehend but can’t put into an algorithm?

    Making allowances for what we mean by “algorithm”, no. One only comprehends what he understands, no more and no less. One can appreciate, be awed, or mystified by far more than he understands, but that is not comprehension.

    What about ‘justice’? What about ‘beauty’?

    Ditto. ‘Beauty’ is more often appreciated than comprehended, I would say.

    Can you comprehend yourself?

    No. Or, only partially.

    Can you put yourself into an algorithm?

    Dropping the deterministic connotations, to the degree you understand yourself, yes.

    To comprehend God would that mean we have to be able to put God into an algorithm?

    I don’t like the word algorithm here. Substituting the term ‘objective, rational description’ would yield the answer ‘yes’.

    Are there non-algorithmic sciences?

    Not really. Anything beyond that is nomenclature and butterfly classification.

    What about psychology?

    Same deal.

    Is ‘art’ algorithmic?

    When comprehended, yes.

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  4. Mark D. on December 17, 2010 at 1:03 AM

    I have to say that I think the term “algorithmic” is a misnomer here. An algorithm is generally both procedural and deterministic.

    In this context, it is a way of describing what makes a minimal length rational, objective description of something “minimal length”.

    That doesn’t mean that the something being described is “algorithmic”, or even highly compressible. It just ranks objective representations in terms of length, and provides a priority ordering to what one should communicate to convey the greatest amount of raw (uncompressed) information in the smallest number of bits.

    An arbitrarily random system is capable of being described algorithmically, it is just that the description is very long.

    In other words, the applicability of algorithmic information theory to representation reduction has no necessary bearing on whether what is being described is algorithmic per se, it simply says we can convey and process representations of structured systems far more efficiently than unstructured ones.

    So like you say, when we understand something we generally refer to the structured aspects of the system capable of abbreviated representation, not so much the unstructured parts which are not.

    So I wouldn’t call anything that can be understood “algorithmic” at all, but rather “structured”.

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  5. […] post in my ‘Reason as a Guide to Reality’ is available on Wheat and Tares. This one is thoughts on what it means to comprehend something.Here is a quote to whet your appetite:Assuming you also understand what a circle is and what the […]

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  6. […] In my last post, I introduced David Deutsch’s book, The Fabric of Reality. Deutsch’s main interest is in understanding – and by that he means understanding everything. Deutsch believes that understanding something is to have an accurate explanation of it and that this, in turn, serves as a sort of algorithmic compression of all observational data. […]

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  7. Why Scientific Realism Wins | Wheat and Tares on March 10, 2011 at 3:31 PM

    […] has no explanatory power. Deutsch, commenting on the deep relationship between Scientific Realism, comprehensibility, and algorithmic compression, argues: If, for instance, we want to understand why the world seems […]

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