Seasons

Great minds!

Hmm, Ulrike - you're a mathematician, so do you have any insights on why it is duality that we perceive emerging from dimensionality, and not trinity, or unity, or any other -ity (even fractionality?)? Or is that even a sane question to ask?

I know I tried to propose this to Eugene some time ago, but couldn't express it very well. I think his mathematical sensibilities also revolt at the prospect of undermining such an integral mathematical cornerstone. And perhaps yours do to, like any sane mathematician?

Hmmm... I think duality inherently arises in the mind first. I am here. Everything else is out there. So we divide things up as "X" or "Not X" similarly. So why not a third category? "Neither X nor Not X" comes to mind, but even something like "Undecidable as to X or Not X" (which comes out of Gödel's work) adds a third category. To be honest, I think Gödel has turned much of mathematics into a trinity, rather than a duality. And it is all still unified under the name of "Mathematics."

(I'm not quite sure if this is what you were getting at, so feel free to clarify if I've misunderstood. )

Talking of dualities, do you think the Olympics are a competition between athletes or countries?

Talking of dualities, do you think the Olympics are a competition between athletes or countries?

Both. I think this goes back to Ulrike's carrot. I agree that agruing about the way we describe or think about and experience is superficial and often leads to equivocation or arguments that have nothing to do with the experience itself. Abstractions are fun but they are abstractions. Symbols and qualities are not the thing itself, nor can they ever match the "suchness" of any state, thing or expereince.

Or was that your point, Hejix? Sorry if I was dense. The olympics are about personal and team competition, for the people competing and those who identify and support them. Carrots are carrots whether orange, green or white. The human nervous system can be modeled in many diffferent ways, and math is a world unto itself.

The fact that our descriptions of reality (or realities) are limited, and that our perceptions are limited and our minds acan and do play tricks on us does not necessarily lead to the conclusion that our choices for how to describe and model our reality (whether dualistic or some other tool) reflect some quality of the reality itself. So because we tend to see the world in dualistic terms does not mean that the world itself is dualistic. And because we may not know what a world without "evil" would be like does not mean that "evil" is nessecary, though, perhaps the idea of"evil" itself needs more definition to make this discussion work.

I'll be back after coffeee. Psimagus, don't you ever sleep?

I'll be back after coffeee. Psimagus, don't you ever sleep?

Of course - but I don't let that stop me doing stuff. I'm sleep-learning Russian ATM

Ulrike: Hmmm... I think duality inherently arises in the mind first. I am here. Everything else is out there.

Well, each of the macro-scale dimensions we perceive as applying to the space-time we notionally inhabit have the inherent dualist symmetry of left/right, up/down, forward/back. Maybe the whole reality of space-time itself arises in the mind, and we are all figments of our own imagination (I don't rule it out,) but other realities are at least conceptually possible, with extended symmetries beyond the dual (unitary would be difficult to conceive of, I admit, since there would be no scale to any of the dimensions - they would be point-bound, and not linear!)
In a dimensional structure with trinary dimensionality (I mean an inherent trinary symmetry to each dimension, not just 3 dimensions of course,) the scale of measurement in each dimension would be planar, rather than linear - it would not be "shades of grey", but some sort of "chromatic spread".
So is the dualism we see in this universe, a purely human interpretation we apply to a dimensional structure that might equally validly be described as any-integ(e)r-ity (or even fractionality)?
Or is this universe a sub-set of (potential or actual) higher orders of dimensional symmetry beyond this observable space-time?
And either way, does this not undermine the "sanctity of the integers" ("God made the integers, Man made everything else" S.Hawking), and thus all of mathematics?
Not that I'm a formalist! Really

Ummm... We have defined dimensions in dualistic terms, yes. Which means that (by the defintion) if planar movement is possible, then there are two dimensions, not one. The definition is convenient because we think in either/or terms most of the time. But the location of the coordinate axes is arbitrary. On earth, it's convenient to define one of them as lining up with the axis of earth's spin (north/south; incidentally, the Chinese put South at the top of most maps).

However, the way we define dimenionality is based on the number of ways we can "move". east/west, north/south, up/down on earth gives 3 orthogonal directions. And defining dimensionality in this way give useful results in both mathematics and physics. Even if we change the axes, we still find 3 orthogonal directions (orthogonal meaning that movement in one of them cannot be expressed in terms of movement in any of the others).

For the sake of argument, suppose there were a single dimension with 3 directionalities (call them over/under/sideways). Then we would be able to express movement in all three modalities in terms of movement in the other two (analogy to 1D: up 3 is the same as down -3). That is what unifies a "dimension" in mathematical terms: ability to express movement in that single dimension in terms of any of its modalities. So it would be something like going 2 units over is the same as -2 units under is the same as 1/2 a unit sideways. I can't think of any way to apply such a modality to the known, experiential universe. *shrugs*

There could be none of these things if there were not also at least the potential for, or memory of, hatred, destruction, tears and war.

Not a big believer in the garden of Eden then, are you? I think that we could have such things, and in fact, it would be easier to have it without the memory of "bad". Maybe there would be no concept of good and evil, so that someone from our world would be bored, but that doesn't mean it wouldn't be satisfying to someone who always lived in that world. Unless some bastard had to ruin it all to test "free will" or some rot by putting a big tree in the middle and a neon sign that says, "Do not eat this! wink wink"

If men really wanted peace, they would sincerely ask God for it and He would give it to them. But why should He give the world a peace which it does not really desire? The peace the world pretends to desire is really no peace at all.

If there were a personal god who reasoned all this out, it would be unfair for such an entity to subject the whole of humanity to the wants of some of us. If this God worked in such a way, surely it would make more sense to have the greediest suffer the most and the most charitable suffer the least. Why then do those with the most charity often suffer more? Why are those with faith tortured while those who torture live in wealth and luxury? Why are the young, the weak and the innocent exploited--because of their own hearts? I don't buy it.
This just teaches them to exploit in turn if they get the chance. If they were shown love, they would love.

So instead of loving what you think is peace, love other men and love God above all. And instead of hating the people you think are warmakers, hate the appetites and the disorder in your own soul, which are the causes of war. If you love peace, then hate injustice, hate tyranny, hate greed - but hate these things in yourself, not in another.

There is wisdom in this, but only because I have more control over my own heart and mind than I have over others, not because others' "evil" doen't effect me or innocent people.

Again, if there is a personal god in charge of this existence, (s)he would be able to set up a situation where all children are loved and nurished and are taught how to love and nurish others, and where the first few layers of Maslow's heirarchy of needs are a given.

Since everyone has their physical and social needs met in this world, there is no need to fight over physical resources or stautus. Since everyone is part of the whole and loves the whole (since that is a biological impartive in this world) they need only discover their own talents and develop them for the good of all.

Unfortunately, I think we live in Darwin's world, but if human nature was indeed made the way it is on purose, shame on god.

Maybe there would be no concept of good and evil.

That's exactly it. In such a world there could be no concept of good or evil. There would just be innocence. The real trick is to maintain that innocence in a world where most hold that good and evil DO exist. To me, this means accepting things as they are,, without worrying about how we wish they might be. This doesn't mean helplessness, either. It means taking responsibility. It means, in every moment, doing what needs to be done, without judging or complaining. It means, using every moment to the fullest, because we really only have one moment (the now). It means not turning away from something that needs to be done. And, above all, it means showing compassion to all, not just to those we might label "good." It means walking the edge, and maintaining the balance point.

Oh, you mean accept the world as it is instead of complaining about how I'd like it to be? That pretty much is my problem in a nutshell.

You are right, Ulrike. It's just that doing what needs to be done every moment is a lot to ask sometimes, and though I can imagine compasson for Hitler or Ted Bundy or the guy that thought up reality TV, in real life, I still kind of want to avoid them.

Ulrike: Ummm... We have defined dimensions in dualistic terms, yes. Which means that (by the defintion) if planar movement is possible, then there are two dimensions, not one.

Yes, but that's not quite what I mean - when I say "planar", it is a necessarily poor analogy (our conventions of language don't make describing such things easy!) In the same way we may represent a tesseract in 3 (or even 2) dimensions, the representation fails to fully describe the inherent geometry, for it is a symbol, and not a tesseract itself. The "planar" modality of the trinary symmetry would be irreducible, and not merely correspond to 2 separate dimensions - that's just the only way we can envisage it from here.


The definition is convenient because we think in either/or terms most of the time.

Indeed. But I wonder if the dimensions we perceive appear dualistic because this is how we think, or we think like this because that is how the dimensions are? Or are the two, in some subtle way, the same thing?


However, the way we define dimenionality is based on the number of ways we can "move". east/west, north/south, up/down on earth gives 3 orthogonal directions. And defining dimensionality in this way give useful results in both mathematics and physics. Even if we change the axes, we still find 3 orthogonal directions (orthogonal meaning that movement in one of them cannot be expressed in terms of movement in any of the others).

But isn't this just a self-referential definition of dimensionality in terms of the orthogonal and vice versa? Just as self-referential as all the other dualities we've been noting?


For the sake of argument, suppose there were a single dimension with 3 directionalities (call them over/under/sideways). Then we would be able to express movement in all three modalities in terms of movement in the other two (analogy to 1D: up 3 is the same as down -3). That is what unifies a "dimension" in mathematical terms: ability to express movement in that single dimension in terms of any of its modalities. So it would be something like going 2 units over is the same as -2 units under is the same as 1/2 a unit sideways.

I think that's close to what I mean (though we're hovering very near the semantic event horizon in concept-space here, I think!)
But "movement" through such dimensions would also be of a higher order of "richness", not perfectly equating to our own notion of movement as progressing along a single, dualistic dimension as we experience it - in a somewhat similar way that a 2-D flatlander (vide Abbot) could have no conception of how a sphere can move through 3 dimensions (even though in that example all their relevant dimensions would still be individually dualistic.)


I can't think of any way to apply such a modality to the known, experiential universe. *shrugs*

No. I would say it may be intrinsically impossible to do so with a mind of merely human complexity (or at least of human morphology.) But I don't see why it should be impossible to determine whether it is possible to do so - whether the dualism inheres to reality (and if so, how that relates to any meta-Reality,) or to our conceptual model of it. For one of the only things we can be truly sure of, I think, is that the two are not the same.
We can, after all, visualise a tesseract and prove it's geometrically possible in 4 spatial dimensions, even if we can't build one.

There are other possible coordinate systems for three-space, but they all need three coordinates to define a point.