Why is it that people presented with a common world arrive at such drastically different worldviews? Like ants studying a cake: some will see it as hard and icy, some as soft and crumbly, and others as sticky and creamy, although they are looking at the same cake.
(See the story about the blind men and the elephant)
Thursday, 27 December 2007
Wednesday, 26 December 2007
Mind, matter, objects
Can we conceive a situation in which mind exists without matter, or where matter exists without mind?
For Descartes the mind was indivisible and the extended world was divisible, whereas if anything it is the other way round.
The objects of the world partake in the mind that begets them. It’s not that the mind represents an apple that is external to it, but that the mind is the apple, just as the apple is the mind (at least in part). The apple is no less real for this.
For Descartes the mind was indivisible and the extended world was divisible, whereas if anything it is the other way round.
The objects of the world partake in the mind that begets them. It’s not that the mind represents an apple that is external to it, but that the mind is the apple, just as the apple is the mind (at least in part). The apple is no less real for this.
Saturday, 22 December 2007
The plane and the stone
To address the jibe about the idealist philosopher forced to chose whether the parachute they are given when ejected from a plane exists or not: Doubting existence in this case is not taken to mean that objects lack being, form or capacity for behaviour, but that these qualities correlates with our mental view of the world. To a flea that clings to the harness, no doubt the parachute has no existence, even though it will be brought to earth just as safely as the philosopher.
I don’t doubt that kicking a stone will hurt the toe, despite what we now know: that the stone is almost entirely made of empty space and that the atoms of the toe and the stone never actually make contact. This demonstrates, as much as anything could, that the stone, the toe and the pain are products of our mental processing, and therefore entirely real.
I don’t doubt that kicking a stone will hurt the toe, despite what we now know: that the stone is almost entirely made of empty space and that the atoms of the toe and the stone never actually make contact. This demonstrates, as much as anything could, that the stone, the toe and the pain are products of our mental processing, and therefore entirely real.
The mind is real
It would be just as valid, and possibly more so, to invert the standard realist-idealist formulation and say: It is in the mind that experience is most real, while the hypothetical world beyond is imaginary.
It is in the conceptual domain where all the qualities usually associated with ‘realness’ reside: solidity, resistance, tactility, behavioural consistency, causal relations, verifiability, and the like. These are properties of our perceptual activity, our memory and learned experience, our capacity to make associations, to see construct patterns, to organise what our senses detect. It is we who give the world its realness.
Rather than asking how it is that the material world can give rise to the conscious mind, we should ask how the conscious mind gives rise to the material world.
It is in the conceptual domain where all the qualities usually associated with ‘realness’ reside: solidity, resistance, tactility, behavioural consistency, causal relations, verifiability, and the like. These are properties of our perceptual activity, our memory and learned experience, our capacity to make associations, to see construct patterns, to organise what our senses detect. It is we who give the world its realness.
Rather than asking how it is that the material world can give rise to the conscious mind, we should ask how the conscious mind gives rise to the material world.
Thursday, 20 December 2007
The universe discrete and continuous
Is space-time discrete or continuous? Opinion among experts seems to be divided or uncertain. It could be either, both (or neither!).
Prior to the capacity to experience time and space is the capacity to experience distinction and continuum, simultaneously.
Even if reality turns out to be discrete, each discrete part will form a continuum of its own. Reality will always be both.
The dispute about whether the universe is really discrete or continuous reflects the limits of our capacity for conceptualisation. It is really a dispute about the nature of our own minds.
When describing the universe at its deepest levels we tend to use the same kinds of approach that we use when looking at nature at our the human level; we tend to pitch ourselves as external observers, looking at the universe as though it were a rock on a table or lizard in a jar, and make observations or measurements about it from the outside looking in. But this is not a position we can take with respect to the cosmos. Not only are we inside it, we are synonymous with it on the grounds that it is formed in our own mental image.
Prior to the capacity to experience time and space is the capacity to experience distinction and continuum, simultaneously.
Even if reality turns out to be discrete, each discrete part will form a continuum of its own. Reality will always be both.
The dispute about whether the universe is really discrete or continuous reflects the limits of our capacity for conceptualisation. It is really a dispute about the nature of our own minds.
When describing the universe at its deepest levels we tend to use the same kinds of approach that we use when looking at nature at our the human level; we tend to pitch ourselves as external observers, looking at the universe as though it were a rock on a table or lizard in a jar, and make observations or measurements about it from the outside looking in. But this is not a position we can take with respect to the cosmos. Not only are we inside it, we are synonymous with it on the grounds that it is formed in our own mental image.
Sunday, 16 December 2007
Saturday, 15 December 2007
True contradictions
Accepting that contradictions can be true does not mean accepting that all contradictions are true.
Matter, mind and energy
The material world (objects, things, actions) and the mental world (thoughts, ideas, wishes) are unified in that they are both processes of energetic formation and transformation. On this level, at least, they are indistinguishable. This is consistent with scientific materialism.
Friday, 14 December 2007
The world is your mind
Look at an object or listen to a sound: that object or sound is your mind. The world is your mind.
This is not crude idealism. No claim is made about the status of one domain over another; the world is no less real than it appears to a materialist. The proposal is that material reality and mental experience are the same thing, not two sides of a coin or two expressions of a deeper underlying reality. They are co-existent and identical.
They form, as it were, a fractured unity.
This is not crude idealism. No claim is made about the status of one domain over another; the world is no less real than it appears to a materialist. The proposal is that material reality and mental experience are the same thing, not two sides of a coin or two expressions of a deeper underlying reality. They are co-existent and identical.
They form, as it were, a fractured unity.
At the present point in time
Just as there can never exist an actual point in space (see this entry) — only an imaginary one — so I can't see how we can have a present point in time. There can be no immediate moment of any duration; if it is infinitely short then it has no span, and presumably doesn't occur. If it has some duration, however short, then it spans more than a single point and so cannot be a precise moment.
For similar reasons a unit of time — say a second — cannot have an absolute start or end; it is indeterminate in length, or it could even be said it has no length at all, though it has an unspecified duration.
For similar reasons a unit of time — say a second — cannot have an absolute start or end; it is indeterminate in length, or it could even be said it has no length at all, though it has an unspecified duration.
Marx's assumption
Karl Marx remarked that ‘the philosophers have only interpreted the world in various ways, the point is to change it.’ This assumes an essential distinction between the world and the ways it can be represented.
Where's the matter?
It might be asked, 'what then happens to matter, if everything is mental?"
Matter, like any other kind of object, must be brought into being by the mind, since mind precedes existence. It does not follow from this, though, that matter is not 'real' just because it depends for its existence on the operation of the mind.
If we take it that the mind is real, and that what we experience of the world with our minds is real (after all we could not have experiences of the world without a mind) then the materials we confront within that world are clearly also real.
Where confusion might occur is in those distinctions we make between objects of imagination and those of corporeality (such as between forests conjured up in our dreams and physical forests). A dreamt forest feels just as real as a physical forest during the dream, but we cease to regard it as such when we wake up. Likewise, we might vividly imagine unicorns, without committing ourselves to the belief that they exist outside of our imagination.
The distinction between the imaginary and the corporeal is a valid and useful one (and indeed necessary if we are to socially integrate), but it is also a product of the self-same mental processes that allow us to distinguish between, say, a memory and a fantasy (although not infallibly), or between yesterday and now.
In other words, although the distinction between the 'real physical' world and the 'imaginary mental' world is habitual, valid and necessary it does not point to some deeper underlying bifurcation within the universe. Rather it is but one of the many distinctions we make as part of our moment to moment operation, a conventional way of organising our beliefs and behaviours — one that is so conventional that we find it very hard to think of ourselves and the world without it.
Matter, like any other kind of object, must be brought into being by the mind, since mind precedes existence. It does not follow from this, though, that matter is not 'real' just because it depends for its existence on the operation of the mind.
If we take it that the mind is real, and that what we experience of the world with our minds is real (after all we could not have experiences of the world without a mind) then the materials we confront within that world are clearly also real.
Where confusion might occur is in those distinctions we make between objects of imagination and those of corporeality (such as between forests conjured up in our dreams and physical forests). A dreamt forest feels just as real as a physical forest during the dream, but we cease to regard it as such when we wake up. Likewise, we might vividly imagine unicorns, without committing ourselves to the belief that they exist outside of our imagination.
The distinction between the imaginary and the corporeal is a valid and useful one (and indeed necessary if we are to socially integrate), but it is also a product of the self-same mental processes that allow us to distinguish between, say, a memory and a fantasy (although not infallibly), or between yesterday and now.
In other words, although the distinction between the 'real physical' world and the 'imaginary mental' world is habitual, valid and necessary it does not point to some deeper underlying bifurcation within the universe. Rather it is but one of the many distinctions we make as part of our moment to moment operation, a conventional way of organising our beliefs and behaviours — one that is so conventional that we find it very hard to think of ourselves and the world without it.
The known universe is the extent of the mind
This galaxy, located in the constellation Pegasus, is 4 billion light years from Earth. UCLA, Department of Physics and Astronomy: T. Glassman & J. Larkin.The release comes when we no longer think of the mind as isolated within the frame of our body, when we recognise it extends into the world; when the distinction between ourselves and the world is overcome, and the experiences we have of the 'out there' do actually occur 'out there', as well as 'in here'.
Then it is less hard to see how our minds, our imaginations, reach out into deepest space to 'create' distant galaxies, as we find some means of conceiving them using the 'extended senses' of space probes and telescopes. Such galactic entities literally 'come into being' as they are discovered, being oblivious prior to that point.
We still need to imagine them, reconstruct them in our own minds from the blurry data our astronomical devices send back. They remain objects that are sensed and conceived like any other, no matter how old or distant. But in being imagined they become our minds. The known universe is the extent of the mind.
It's not that there's nothing, but neither is there something.
It is not even sufficient to say that what lies beyond perception is the 'unknown' since this implies there is something 'there', albeit something we can know nothing about. In the absence of a mind, the function of which is to impose discrete boundaries on a boundless ***, categories such as 'knowability' and 'unknowability' can have no purchase. It's not that there's nothing, but neither is there something.
Unfamiliarity and validity
We habitually take existence to be such a fundamental condition, in fact the fundamental condition, so that we cannot accept its negation. To say planets and stars 'did not exist' prior to human minds is taken to mean, in some vulgar sense, that they evaporate or vanish when we don't think about them, or that they suddenly sprang out of the void at the point in history when human minds were first 'switched on'.
In other words, we try to apply our daily experiential criteria to that which is before or beyond it. This is akin to the way we have trouble applying criteria of macro-level behaviours to the quantum level, or conceiving relativistic space-time distortions in relation to the standard domestic environment. But in each case the fact that it is difficult (some say impossible) to conceive these behaviours in familiar terms cannot be used as grounds for denying their validity.
In other words, we try to apply our daily experiential criteria to that which is before or beyond it. This is akin to the way we have trouble applying criteria of macro-level behaviours to the quantum level, or conceiving relativistic space-time distortions in relation to the standard domestic environment. But in each case the fact that it is difficult (some say impossible) to conceive these behaviours in familiar terms cannot be used as grounds for denying their validity.
Different kinds of minds
To other kinds of minds the laws of physics might appear entirely different, because to them the cosmos would appear entirely different. Our notion of existence might be entirely absent to them, as might the notions of 'appearance', 'reality', or even 'mind'.
We should not be so conceited as to believe that the way brains, bodies and behaviours have evolved on Earth are the only ways in which minds, intelligences and consciousnesses might emerge. Laws that we take to be universal may be limited in application to our level of perception and capacity for thought. To the man who spends his whole life upside down the action of gravity appears inverted.
We should not be so conceited as to believe that the way brains, bodies and behaviours have evolved on Earth are the only ways in which minds, intelligences and consciousnesses might emerge. Laws that we take to be universal may be limited in application to our level of perception and capacity for thought. To the man who spends his whole life upside down the action of gravity appears inverted.
Mind precedes existence
Despite the scientific credibility of the claim that all that exists of the world is what we can perceive, we remain unsatisfied. There is an irresistible sense of an independent world made of solid things that truly exist, obey physical laws, and have integral properties that are reflected in our sensations. To deny their existence seems like folly.
Furthermore, to deny we can know anything more about them than our perceptual apparatus permits — that they are forever immune to being known 'in themselves' — seems to ignore the vast progress made by science in recent centuries in probing, understanding and controlling natural phenomena at ever deeper levels. Our abstract descriptions of the world (e.g. e=mc2) are empirically verifiable, which suggests that they way we represent reality in our minds is an accurate depiction of how it really is 'out there', and we continue to find out ever more about the brain, the sub-atomic world, the cosmos, which we can investigate at levels of resolution barely imaginable to those working in, say, the 18th century.
Does all this not mean we are digging behind perceptual appearances into the hidden realm of the 'things-in-themselves', the obscure levels of reality we may not be able to sense with our own apparatus, but which we can divine through powerful calculations or sophisticated measuring devices? Does this not show these things exist in a world of their own, whether we perceive them or not?
What is disputed is not that any of these objects exist, but that they do not exist in the way they are apparent to us without our particular mental processes.
Mind precedes existence.
Furthermore, to deny we can know anything more about them than our perceptual apparatus permits — that they are forever immune to being known 'in themselves' — seems to ignore the vast progress made by science in recent centuries in probing, understanding and controlling natural phenomena at ever deeper levels. Our abstract descriptions of the world (e.g. e=mc2) are empirically verifiable, which suggests that they way we represent reality in our minds is an accurate depiction of how it really is 'out there', and we continue to find out ever more about the brain, the sub-atomic world, the cosmos, which we can investigate at levels of resolution barely imaginable to those working in, say, the 18th century.
Does all this not mean we are digging behind perceptual appearances into the hidden realm of the 'things-in-themselves', the obscure levels of reality we may not be able to sense with our own apparatus, but which we can divine through powerful calculations or sophisticated measuring devices? Does this not show these things exist in a world of their own, whether we perceive them or not?
What is disputed is not that any of these objects exist, but that they do not exist in the way they are apparent to us without our particular mental processes.
Mind precedes existence.
Thursday, 13 December 2007
Schopenhauer and the thing in itself
"Thing in itself signifies that which exists independently of our perception, that which actually is." Schopenhauer
The error here (mainly attributable to Kant) is to bestow qualities onto the 'thing in itself' that do not apply, i.e. the quality of 'thingness' and 'selfness'. Nothing exists, or does not exist, independently of our perception. 'Things' do not count without minds, nor do 'selves' — in the sense of self-contained, discreet objects — count.
The best that can be said (possibly) is that prior to or beyond the scope of perception lies a teeming cosmos of fluctuating energy that with the right biological apparatus can be rendered as discrete 'things' (perhaps Schopenhauer's 'will'). Even saying this is not sufficient, but may be as close as we can get with ideas, which in themselves are products of this process.
The practical questions are: how does the perceptual apparatus convert this teeming cosmos (which is not a 'mind-independent' thing, and neither does nor does not exist) into the things we perceive as existing, and how do we then become aware of them?
The error here (mainly attributable to Kant) is to bestow qualities onto the 'thing in itself' that do not apply, i.e. the quality of 'thingness' and 'selfness'. Nothing exists, or does not exist, independently of our perception. 'Things' do not count without minds, nor do 'selves' — in the sense of self-contained, discreet objects — count.
The best that can be said (possibly) is that prior to or beyond the scope of perception lies a teeming cosmos of fluctuating energy that with the right biological apparatus can be rendered as discrete 'things' (perhaps Schopenhauer's 'will'). Even saying this is not sufficient, but may be as close as we can get with ideas, which in themselves are products of this process.
The practical questions are: how does the perceptual apparatus convert this teeming cosmos (which is not a 'mind-independent' thing, and neither does nor does not exist) into the things we perceive as existing, and how do we then become aware of them?
Monday, 10 December 2007
Artists' reputations
Artists must make a reputation for their work before it can make a reputation for them.
Sunday, 9 December 2007
Studying painting
Students of painting need to learn to see their work not as they would like it to appear, but as it appears to others.
The mind in action
All distinctions seem to be contingent on the mind, including that which distinguishes the mind itself.
Objects actually exist in the mind, although they appear to exist in the world. However, there is no conflict here since the world is the mind in action.
Objects actually exist in the mind, although they appear to exist in the world. However, there is no conflict here since the world is the mind in action.
Access to minds
If we cannot have access to our own minds then we can at least observe the minds of others, which in effect then become part of our own minds — to which we cannot have access.
Painting and the mind
Using the mind to try and understand the mind is like trying to paint painting.
The contradictory nature of consciousness
We perceive the world as simultaneously fragmented and unified, full of parts and wholes, differences and associations. To be conscious is to experience neither unity nor fragmentation alone, but the co-presence of these opposing qualities.
Inhumanity
Nothing characterises humans more than inhumanity. We can never accuse animals of behaving as badly as humans.
Descartes' certainty
Descartes holds that to think is to be certain of one’s existence. But do we still exist if we stop thinking?
Locating consciousness
Trying to locate consciousness is like looking for a needle in a needle-stack .
Confirming what we believe
If we want support for our opinions we should read those with whom we disagree.
The impossibility of knowing our own mind
It is impossible to know our own mind in the same way it is impossible for a camera to photograph itself. Of course, the camera can always be pointed at a mirror, and in essence that's what we do to establish our own sense of self.
But what is seen in the mirror is remote and inverted — an external rather than internal view. The camera cannot turn upon itself and photograph itself from its own point of view, and we cannot think about what we are thinking about, except to render our thoughts as remote and temporally displaced.
But what is seen in the mirror is remote and inverted — an external rather than internal view. The camera cannot turn upon itself and photograph itself from its own point of view, and we cannot think about what we are thinking about, except to render our thoughts as remote and temporally displaced.
Humanism vs. posthumanism
Humanists regard humans as distinct beings, in an antagonistic relationship with their surroundings. Posthumanists, on the other hand, regard humans as embodied in an extended technological world.
Un-desire
Indifference towards what you desire will significantly increase your chances of getting it.
Thinking beyond the mind
It is impossible to think of that which cannot be thought, except to think of it as that which cannot be thought.
What is not part of the mind? Nothing that can be thought.
What is not part of the mind? Nothing that can be thought.
Jokes and the irrational
So I said to the Gym instructor, "Can you teach me to do the splits?" He said, "How flexible are you?" I said,"I can't make Tuesdays."
Tommy Cooper
Jokes (like puns and double entendres) frequently exploit the dual meanings of words, in this case two senses of the word 'flexible', but do so in such a way that we have to hold both senses at once. It is the simultaneous appreciation of two conflicting ideas bound together by a single word that gives rise to the psychic discharge we experience as funny.
Jokes are a cardinal case of irrational conception: we conceive two conflicting, incompatible states of mind at once, without one canceling out the other. If this were to happen, or if the meanings were to occur sequentially, then the psychic disturbance would not happen. For example, if the joke was rendered as:
So I said to the Gym instructor, "Can you teach me to do the splits?"
He said, "How flexible are your limbs?"
I said,"My work schedule is not flexible and I can't make Tuesdays."
...little humour is evident, because the two meaning of flexible are not made to co-exist but to follow sequentially. Rationality (if not conversational convention) at this level is preserved.
Jokes are not funny when explained, probably because explanations neutralise the conflict by drawing the sense back into the realms of the rational.
Jokes seem to provide evidence that normal conscious states can accommodate distinct and irrational thoughts, and so resists the widely-held assumption that consciousness is unitary and rational.
See Koestler's 'bisocation' or 'double-minded' theory. He defined humour as: 'the perceiving of a situation or idea in two self-consistent but mutually incompatible frames of reference or associative contexts."
"D'you know, somebody actually complimented me on my driving today. They left a little note on the windscreen, it said 'Parking Fine.'"
Tommy Cooper
Tommy Cooper
Jokes (like puns and double entendres) frequently exploit the dual meanings of words, in this case two senses of the word 'flexible', but do so in such a way that we have to hold both senses at once. It is the simultaneous appreciation of two conflicting ideas bound together by a single word that gives rise to the psychic discharge we experience as funny.
Jokes are a cardinal case of irrational conception: we conceive two conflicting, incompatible states of mind at once, without one canceling out the other. If this were to happen, or if the meanings were to occur sequentially, then the psychic disturbance would not happen. For example, if the joke was rendered as:
So I said to the Gym instructor, "Can you teach me to do the splits?"
He said, "How flexible are your limbs?"
I said,"My work schedule is not flexible and I can't make Tuesdays."
...little humour is evident, because the two meaning of flexible are not made to co-exist but to follow sequentially. Rationality (if not conversational convention) at this level is preserved.
Jokes are not funny when explained, probably because explanations neutralise the conflict by drawing the sense back into the realms of the rational.
Jokes seem to provide evidence that normal conscious states can accommodate distinct and irrational thoughts, and so resists the widely-held assumption that consciousness is unitary and rational.
See Koestler's 'bisocation' or 'double-minded' theory. He defined humour as: 'the perceiving of a situation or idea in two self-consistent but mutually incompatible frames of reference or associative contexts."
"D'you know, somebody actually complimented me on my driving today. They left a little note on the windscreen, it said 'Parking Fine.'"
Tommy Cooper
Saturday, 8 December 2007
Conceptual dissonance
Cotán, Quince, Cabbage, Melon, and Cucumber, 1602Art frequently exploits the conceptual dissonance between what is present and what is absent. The degree of similarity between the painted surface and what it depicts is proportional to the degree of dissonance.
The excitatory potential of vivid representations (trompe l’oeil, etc.) lies not in the fact we see something that could really be there, but that we see something that is there and not there at the same time.
Perceptual dissonance
Art frequently exploits the perceptual dissonance between what is seen and what is recognised. The degree of disparity between the form and what it suggests determines the degree of dissonance.
State Art
After Mark Wallinger, State Britain, 2007"Mark Wallinger was shortlisted for State Britain at Tate Britain, a direct representation of the banners and paraphernalia of Brian Haw's protest in Parliament Square. The jury commended its immediacy, visceral intensity and historic importance. The work combines a bold political statement with art's ability to articulate fundamental human truths."
Extract from Tate press release, 3rd December 2007
If one of the purposes of art is to present the world back to us in surprising or extraordinary ways then too often in practice it amounts trying to find surprising and extraordinary ways to present art back to us. But the strategies and moves in this game are becoming increasingly circular, and so less effective.
The objection is not that the form of the art deviates too far from what is expected, but that it deviates too little.
By drawing a visible and embarrassing totem of political dissent into the arms of state patronage, Wallinger has conspired to more effectively neutralise this oppositional act than those who sought to impose a crude ban on the protest in the first place.
Friday, 7 December 2007
The trouble with unified theories
The goal of much contemporary research in physics is to discover a 'grand unifying theory' of the structure of the universe, which unites theories about the behaviour of particles at very small scales (quantum physics) with the behaviour of objects at large levels (classical physics).
But why is such a 'GUT' sought? Why is it believed it is 'there' to be discovered?
I once heard Ravi Ravindra talk about the comparison between western and some asiatic approaches to science. Western culture is largely monotheistic: one God, whereas some asiatic religions are polytheistic: many Gods. He noted that western scientists tended to seek singular solutions to problems: the singularity and big bang, the grand unified theory of the universe, a unifying theory of consciousness. Scientists brought up in the Hindu tradition, however, were more likely to accept multiple solutions to problems.
Why can there not be many overlapping and co-existent theories of reality that apply in different contexts or to different aspects of phenomena?
But why is such a 'GUT' sought? Why is it believed it is 'there' to be discovered?
I once heard Ravi Ravindra talk about the comparison between western and some asiatic approaches to science. Western culture is largely monotheistic: one God, whereas some asiatic religions are polytheistic: many Gods. He noted that western scientists tended to seek singular solutions to problems: the singularity and big bang, the grand unified theory of the universe, a unifying theory of consciousness. Scientists brought up in the Hindu tradition, however, were more likely to accept multiple solutions to problems.
Why can there not be many overlapping and co-existent theories of reality that apply in different contexts or to different aspects of phenomena?
The trouble with dimensions
We are used to thinking about reality as a 3-dimensional space, perhaps with an added 4th dimension of time. But is this realistic?
3-dimensional space is commonly assumed to be composed from lower-dimensional spaces, consisting of 0, 1 and 2 dimensions. So a 0-dimensional space is a singular point that does not extend in any direction. Extend this point along one axis as you get a 1-dimensional space — a line. Extend this line at right angles to its length and you create a 2-dimensional space — a plane. Extend this plane at right angles to its surface and you get a 3-dimensional space — a cube. The process can continue, by extending the cube across all of its surfaces you get a 4-dimensional space — a tesseract.
While all this is mathematically consistent, how does is relate to reality, i.e. the world beyond our mathematical conception? In the first place, there can be no real (non-imaginary) 0-dimensional space. If the point has any existence at all (other than as an imaginary proposition) then it will have some spatial dimension — however small. The same would be true of the line and plane, which, however thin, would still have to have some depth and width, and therefore would really be 3-dimensional.
So there are no 'real', substantial objects that exist solely in 0, 1 or 2 dimensions. It would seem obvious, though, that substantial things really do exist in 3-dimensional space, but is this so? If the 0, 1, or 2 dimensions are useful conceptual conventions but ultimately insubstantial why should the 3rd-dimension be any different? Could it be that the 3rd dimension has only conceptual existence too? I would argue yes, that what we take to be the 'realness' of 3-dimensional space is just as conceptual as 0, 1 or 2-dimensional space, which is to say it does not really exist outside of our conception.
To look at it in one way: in order to establish 3-dimensional space you need axes in fixed relation to one another. You need a 1-dimensional x-axis, a 1-dimensional y-axis and a 1-dimensional z-axis (using the standard notation). Since none of these 1-dimensional axes have any substantial existence outside conception (as already shown) then we can say 3 insubstantial things added together cannot produce something substantial: three zeros make zero.
To look at it another way: a line cannot be extruded from a point with no extension; a plane cannot be extruded from a line with no extension; a cube cannot be extruded from a plane with no extension, and so on.
To look at it another way: The traditional 3-axes of space require a fixed viewing position. Each moves away from a fixed origin, and in fixed relation to the observer. In order to see a cube in the way we are used to we adopt a particular viewing position which looks at it from one angle, the spatial co-ordinates being fixed in relation to that. But this singular viewing position is a very limited view of the cube, which in fact can potentially be viewed from all angles at once, including all internal as well as external viewpoints. When considered from all its potential viewpoints simultaneously the standard axes no longer apply since there is no fixed viewing position to which they relate. When viewed from all directions at once there is no 'up', 'down', 'forward' or 'back'.
Consequently I would argue that 3-dimensional space is just as much an ideal conception of reality conceived from a single viewpoint as the lower dimensions. It has no more substance than these.
3-dimensional space is commonly assumed to be composed from lower-dimensional spaces, consisting of 0, 1 and 2 dimensions. So a 0-dimensional space is a singular point that does not extend in any direction. Extend this point along one axis as you get a 1-dimensional space — a line. Extend this line at right angles to its length and you create a 2-dimensional space — a plane. Extend this plane at right angles to its surface and you get a 3-dimensional space — a cube. The process can continue, by extending the cube across all of its surfaces you get a 4-dimensional space — a tesseract.
While all this is mathematically consistent, how does is relate to reality, i.e. the world beyond our mathematical conception? In the first place, there can be no real (non-imaginary) 0-dimensional space. If the point has any existence at all (other than as an imaginary proposition) then it will have some spatial dimension — however small. The same would be true of the line and plane, which, however thin, would still have to have some depth and width, and therefore would really be 3-dimensional.
So there are no 'real', substantial objects that exist solely in 0, 1 or 2 dimensions. It would seem obvious, though, that substantial things really do exist in 3-dimensional space, but is this so? If the 0, 1, or 2 dimensions are useful conceptual conventions but ultimately insubstantial why should the 3rd-dimension be any different? Could it be that the 3rd dimension has only conceptual existence too? I would argue yes, that what we take to be the 'realness' of 3-dimensional space is just as conceptual as 0, 1 or 2-dimensional space, which is to say it does not really exist outside of our conception.
To look at it in one way: in order to establish 3-dimensional space you need axes in fixed relation to one another. You need a 1-dimensional x-axis, a 1-dimensional y-axis and a 1-dimensional z-axis (using the standard notation). Since none of these 1-dimensional axes have any substantial existence outside conception (as already shown) then we can say 3 insubstantial things added together cannot produce something substantial: three zeros make zero.
To look at it another way: a line cannot be extruded from a point with no extension; a plane cannot be extruded from a line with no extension; a cube cannot be extruded from a plane with no extension, and so on.
To look at it another way: The traditional 3-axes of space require a fixed viewing position. Each moves away from a fixed origin, and in fixed relation to the observer. In order to see a cube in the way we are used to we adopt a particular viewing position which looks at it from one angle, the spatial co-ordinates being fixed in relation to that. But this singular viewing position is a very limited view of the cube, which in fact can potentially be viewed from all angles at once, including all internal as well as external viewpoints. When considered from all its potential viewpoints simultaneously the standard axes no longer apply since there is no fixed viewing position to which they relate. When viewed from all directions at once there is no 'up', 'down', 'forward' or 'back'.
Consequently I would argue that 3-dimensional space is just as much an ideal conception of reality conceived from a single viewpoint as the lower dimensions. It has no more substance than these.
Sunday, 2 December 2007
Brought into being by the mind
Stars and gases are ideas, just as existence is an idea, and ideas are an idea; they are all products of human conception (itself an idea) and as such only come into being with the evolution of the human mind.
Arriving at the truth
It is usually possible to arrive at the truth by inverting what is most widely held to be true (including this proposition).
Starting a painting
It's often said a painting is never really finished, but it's just as true to say it's never really started.
Painting unknown
Still from What is A Picture? (16 mm film, 1986)The Impressionists wanted to paint what they saw, not what they knew. The Cubists wanted to paint what they knew, not what they saw. I want to paint what we know we don't know.
Art and wrongness
Cézanne, Bathers at Rest, 1875.Great art needs sufficient wrongness — what Picasso called Cézanne's "anxiety."
Another kind of consciousness
One can imagine another kind of consciousness that perceives the world not as made of bounded material objects but of continuous, variegated flows of energy.
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