Recently (1 July) I wrote a post on The Mirror Paradox, which arose from my reading of Umberto Eco’s book, Kant and the Platypus back in 2002. The post was an edited version of part of a letter I wrote to Eco; the rest of the letter was to do with epistemology, and that is the source of this post.
Some people think that because we can’t explain something, either it is wrong or it doesn’t exist. Two examples from the opposite sides of philosophy (materialism and fundamentalist religion) illustrate this point very clearly. In a previous post, The Ghost in the Machine (Apr.08), I reviewed an article in SEED magazine (Henry Markram’s Blue Brain project). In the same magazine, there is an essay by Nicholas Humphrey on the subject of consciousness. Effectively, he writes a page-length treatise arguing that consciousness must be an illusion because we have no explanation for it. This is despite the fact that he, and everyone he meets in life, experiences consciousness every day. Humphrey’s argument, in synopsis, is that it is easier to explain it as an illusion than as reality, therefore it must be an illusion. Personally, I would like to know how he distinguishes dreaming from living, or even if he can (please refer Addendum below, 4 April 2010). Another example from the polar opposite side of rational thinking is evolution. Fundamentalist Christians tend to think, because we can’t explain every single aspect of evolution, it can be challenged outright as false. This is driven, of course, by a belief that it is false by Divine proclamation, so any aspect of the theory that is proven true, of which there is evidence at all levels of biology, is pure serendipity. (Refer my Nov.07 post, Is evolution fact? Is creationism myth?)
I’m making a fundamental epistemological point that we don’t understand everything – another, excellent example is quantum mechanics (see The Laws of Nature, Mar.08), where I quote Richard Feynman, probably the world’s best known expert on quantum mechanics (he had a Nobel Prize to prove it), and arguably its best expositor, who said quite categorically in his book, QED, ‘…I don’t understand it. Nobody does.’ There is nothing that makes less sense than quantum mechanics, yet it is arguably the most successful scientific theory of all time. Historically, we’ve always believed that we almost know everything, and Feynman was no less optimistic, believing that we would one day know all physics. But, if history is any indication of the future, I choose to differ. In every avenue of scientific endeavour: biology, cosmology, quantum theory, neuroscience; there are enormous gaps in our knowledge with mysteries begging inquiry, and, no doubt, behind those mysteries, lay a whole gallery of future mysteries yet to be discovered.
None of this was in the letter I wrote to Umberto Eco, but it seems like a good starting point: we don’t know everything, we never have and we probably never will. The only thing we can say with confidence is that we will know more tomorrow than we know today, and that is true for all the areas I mentioned above. As I’ve already said in previous posts: only future generations can tell us how ignorant the current generation is.
Actually, this is not so far removed from Eco’s introduction in Kant and the Platypus, where he hypothesises on the limits of our ability to comprehend the universe, which may include metaphysical elements like God. He postulates 4 hypotheses based on matching items of knowledge (symbols) with items of physical entities (elements), which he calls, for convenience sake, 'atoms', and various combinations of these. As a corollary to this approach, he wonders if the graininess of the universe is a result of our language rather than an inherent feature of it, as all the hypotheses require segmentation rather than a continuum.
I won’t discuss Eco’s hypotheses, only mention them in passing, as I take a different approach. For a start, I would use ‘concept’ instead of ‘symbol’ or ‘atom,’ and ‘phenomena’ instead of ‘elements’. It’s not that I’m taking explicit issue with Eco’s thesis, but I choose a different path. I define science as the study of natural phenomena in all their manifestations, which is really what one is discussing when one questions the limits of our ability to comprehend the physical universe. Secondly, it is becoming more and more apparent that it is mathematics rather than language that is determining our ability to comprehend the universe – a philosophical point I’ve already discussed in 2 posts: Is mathematics evidence of a transcendental realm? (Jan.08) and The Laws of Nature (Mar. 08).
Some people argue that mathematics is really just another language, but I would contend that this is a serious misconception of the very nature of mathematics. As Feynman points out in his book, The Character of Physical Law, translating mathematical ideas into plain English (or any other verbal language) is not impossible (he was a master at it) but it’s quite different to translating English into, say, French. To describe mathematics in plain language requires the realisation of concepts and the use of analogies and examples. Mathematics is inherently paradoxical, because it is conceptually abstract, yet it can be applied to the real world in diverse and infinitely numerous ways. Whereas plain language starts with descriptors of objects (nouns) which are then combined with other words (including verbs) that allow one to communicate actions, consequences, histories and intentions; you could argue that mathematics starts with numbers. But numbers are not descriptors – a number is a concept – they are like seeds that have infinite potential to describe the world in a way that is distinctly different to ordinary language.
Nevertheless, Eco has a point, concerning the limits of language, and one may rephrase his question in light of my preceding dissertation: is it our use of number that projects graininess onto the universe? This question has a distinctly Kantian flavour. One of the problems I had with Kant (when I studied him) was his own ‘Copernican revolution’ (his terminology) that we project our models of reality onto the world rather than the converse. As a standalone statement, this is a reasonable assertion, and I will return to it later, but where I disagreed, was his insistence that time and space are projections of the human mind rather than a reality that we perceive.
I truly struggled to see how this fitted in with the rest of his philosophy which I find quite cogent. In particular, his idea of the ‘thing-in-itself’, which essentially says that we may never know the real essence of something but only what we perceive it to be. (I think this is Kant's great contribution to philosophy.) He gave the example of colour, which, contrary to many people’s belief, is a purely psychological phenomenon. It is something that only happens inside our minds. Some animals can’t see in colour at all and some animals see colours that we don’t, for example, in the ultra-violet range. Some animals, that use echo-location, like bats, dolphins and whales, probably see in ultra-sound. It would be hypothetically possible for some creatures to see in radar, if they ever evolved the ability to transmit radar signals. But, more significantly, our discoveries in quantum mechanics and relativity theory, are proof that what we perceive as light and as time respectively are not necessarily what they really are, depending on what level of nature we examine. This leads to another aspect of epistemology that I will return to later – I don’t want to get too far off the track.
In fact, relativity theory tells us that time and space are inherent features of the universe, and, again, it is only through mathematics that we can decipher the enigma that is relativity, as well as quantum phenomena. But we don't need relativity theory to challenge Kant's thesis on the nature of space and time. We sense time and space through our eyes (our eyes are literally like a clock that determines how fast the world passes us by) and, again, this is different for different species. Many birds, and insects, see the world in slow motion compared to us because their eyes perceive the world in more ‘frames per second’ than we do (for us I think it’s around 24). The point is, contrary to Kant’s assertion, if our senses didn’t perceive the reality of space and time, then we would not be able to interact with the world at all. We would not even be able to walk outside our doors.
I once had an argument with a professor in linguistics, who claimed that 3 dimensional Cartesian axes are a human projection, and therefore all our mathematical interpretations, including relativity, based on Reimann geometry (which is curved), are also projections. The fact is, that we live in a 3 dimensional spatial world, and if we lived in a higher dimensional spatial world our mathematical interpretation of it would reflect that. In fact, mathematically, we can have as many-dimensional worlds as we like, as string theory demonstrates. Einstein’s genius was to appreciate that gravity made the universe Reimann rather than Cartesian, but, at the scale we observe it, it’s not noticeable, in the same way that we can survey our little blocks of land as if they are flat rather than curved, even though we know the earth’s surface is really a sphere.
After all that, I haven’t answered the question: is the perceived graininess of the universe a result of our projection or not? One of the consequences of Kant’s epiphany, concerning the thing-in-itself, is that it seems to change according to the level of nature we observe it at. The example I like to give is the human body, which is comprised of individual cells. If one examines an individual cell there is no way we could appreciate the human body of which it is a part. At an even smaller scale we can examine its DNA, which is what determines how the human body will eventually turn out. The DNA is actually like a code, only it’s more than an analogy, it really is a code; it contains all the instructions on how to construct the creature it represents. So what is the thing-in-itself? Is it the genome? Is it the fully grown adult body? Humans are the only species that we know of who have the ability to conceptualise this, and, therefore, are able to comprehend at least some of the machinations of the natural world. And this, I believe, lies at the heart of Eco’s introductory hypotheses. It’s not to do with matching symbols with elements, or combinations thereof, but matching concepts with phenomena, and, more significantly, concepts within concepts, and phenomena that emerge from other phenomena.
Many people talk about the recursive ability of the human brain, which is to hold multiple relationships within one’s mind, like my friend’s mother’s lover has a cat with an injured foot. I understand that 5 is the norm, after which we tend to lose the thread. In which case, I ask: how can we follow a story, or even an argument, like the one I’m writing now? In another post (Imagination, Mar.08) I suggest that maybe it was storytelling that originally developed this aspect of our intellectual ability. We tend to think of words as being the ‘atoms’ of a story, but, as a writer of fiction, I know better, as I will explain shortly. Individual words do have a meaning of their own, but, as Wittgenstein pointed out, it is only in the context of a sentence that the true meaning is apparent. In fact, it is the sentence, or phrase, that has meaning rather than the individual words, as I’m demonstrating right now. But it really requires a string of sentences, and a lengthy one at that, to create an argument or a story. The shortest component of a story is actually a scene, and a scene is usually delineated by a break in time or location at its beginning and its end. But, of course, we don’t keep all the scenes in our memory for the course of the story, which may unfold over a period of days, so how do we do it?
Well, there is a thread (often times more than one) which usually involves a character, and we live the thread in the moment just like we do with our lives. It’s like when we are in contact with that thread we have the entire thread in our mind yet we are only interested in its current location in time and space. The thread allows us to pull out memories of it, make associations, into the past and future. This is the really extraordinary attribute of the human brain. I’ve no doubt that other animals have threads as well, but I doubt they have the same ability as we do. It is our ability to make associations that determines almost everything intellectually about us, including our ability to memorise and learn. It is only when we integrate new knowledge into existing knowledge that we actually learn it and understand it. To give an example, again, from Wittgenstein, if you come across a new word, you can only comprehend it when it is explained in terms of words you already know. In a story, we are continually integrating new information into existing information, yet we don’t see it as learning; we see it as entertainment. How clever is that?
I argue that recursiveness in the human brain is virtually limitless because, like the cells and the human body, we can conceptualise concepts within concepts ad infinitum, as we do in mathematics. For example, calculus requires the manipulation of infinite elements yet we put them all into one function, so we don’t have to even think of an infinite number of elements, which, of course, would be impossible.
I’ve made the point in other posts, that the reason we comprehend the universe to the extent that we do is because we have this ability to perceive concepts within concepts and the universe is made up of elements within elements, where the individual element often has nothing in common with the larger element of which it is a part, so graininess is not the issue. I don’t believe this is a projection; I believe that this is an inherent attribute of the entire universe, and the only reason we can comprehend it, in the esoteric way we do, is because we are lucky enough to have the innate ability to perform the same trick mentally (see The Universe's Interpreters, Sep.07).
I’ve almost exhausted this subject, but I want to say something about schemas. I mentioned, earlier in this essay, Kant’s assertion that we project our ideas, or models, onto the universe in order to comprehend it. I discuss this as well in The Laws of Nature, but in a different context. Eco also talked about schemas, and while he said it was different to the psychological term, I will attempt to use it in the same sense as it is used in psychology. A schema is a template, is the best description I can give, whereby we apply it to new experiences and new knowledge. We even have a schema for the self, which we employ, subconsciously, when we assess someone we meet.
I argue that the brain is a contextual instrument in that it axiomatically looks for a context when it encounters something new, or will even create one where one doesn’t readily exist. By this I mean we always try and understand something on the basis of what we already know. To give an example, taken from Eco’s book, when Europeans first saw a platypus they attempted to categorise it as a mammal or a reptile (it lays eggs). But, if I was a European, or from the northern hemisphere, I would probably think it was a type of otter or beaver, assuming I was familiar with otters and beavers, because it is air-breathing yet it spends most of its time in river water or underground. Another example: assume you had never seen a man on a horse, but mythically you had seen pictures of centaurs, so the first time you saw a mounted man you might assume it was all one animal.
My point is that we apply schemas to everything we meet and perceive, often subconsciously, and when we become more familiar with the new experience, phenomenon or knowledge, we adjust our schema or create a new one, which we then apply to the next new experience, phenomenon or whatever.
There is a logical connection here, to what I suggested earlier, that we only understand new knowledge when we integrate it into existing knowledge. A schema is a consequence of existing experiences and knowledge, so cognitively it's the same process. The corollary to this is that when we encounter something completely alien, we need a new schema altogether (not unlike Kuhn's paradigm-shift).
I read recently in New Scientist (31May 2008) that someone (Karl Friston) had come up with a Bayesian interpretation of the brain (using Bayesian probability), at all levels, including neurons (they strengthen connections based on reinforced signals). The brain makes predictions, then adjusts its predictions based on what it senses in a reiterative process. He gives the everyday example of seeing something out of the corner of your eye, then turning your head to improve your prediction.
Schemas, their interaction with the world and our modification of them accordingly, is such a reiterative process, only on a different scale. Previously, I've talked about the dialectic in science between theory and observation, or theory and experimentation, which is another example of the same process, all be it's at another level altogether and is performed in a more disciplinary manner.This is where I should write a conclusion, but I think I already have.
Having completed this essay, it has little resemblance to my letter to Umberto Eco in 2002, in either content or style, but some ideas and some arguments are the same.
Addendum (4 April 2010): I may have misrepresented Nicholas Humphrey - please read the addendum to my post Consciousness explained (3 April 2010).