Hey Recon,
Interesting thoughts.
Sadly, my mathematical ability pretty much grinds to a halt with anything much past balancing my bankbook. And even that's always a few bucks off.

Have you ever watched NOVA's "The Elegant Universe"? If not, you might find it interesting, in regard to the whole dimensional thing.

Cheers from psychospace,
Tock.

Apropos of nothing, perhaps, but just for grins:
flashback

If we have one dimension (like length, height, width, magnitude), we always also have 2 directional possibilities within this dimension.

We have 6 directions in three dimensional space, for instance. Our number line (excluding just now the complex plane) is one-dimensional, and therefore bi-directional. Numbers are bigger or smaller, negative or positive.

Also, and perhaps just as interesting, we have the notion of power sets.
There are 2 to the power of set-members power sets.
Every member of a set can either be or not be a member of a subset. And this is the source of the 2.

The word doubt comes from the word for 2. Philosophy is full of dualisms. Thought itself, considered as distinction, is the imposition of dualism. Is this why our concepts of Being and Totality are so paradoxical, because thought as distinction implies an "other"? Must all attempts at monism incorporate negation or simply founder? How does duality tied into negative theology, negative ontology? N of Cusa presented God as the union of opposites. He tries the smash the 2 into a 1.

Here's a strange quote.
TLP

It might be too poetic for some, but can we imagine a dimension as a matrix (always dual/bifurcated) on which singular/"male" number exists? And can they exist apart? Of course we can combine dimensions, and end up with 3-dimensional coordinate systems, but the essence remains. Is this why Mary and Jesus are so often painted together? Even numbers have been called feminine numbers.

Don't mistake this symbolic dot-connecting for mysticism. I suspect that logic has often been mistaken for mysticism, and that the beauty of truth has been held against it, just as metaphor is often turned into superstition.

You can't have a number system with more than one number unless you imply at least one dimension which is always 2 directions. Can we conceive of a dimension with more than two directional possibilities?

Just think of one dimension as a line, and two dimensions as a plane, and three dimensions as a volume. Height, width, depth. So you have two directions for each dimension. up-down, left-right, forward-backward. And it seems if we add time or some abstract dimension, we would be doing the same thing.

Yes. Hat problems consider three situations: a number can see all subsequent numbers in either the positive or negative direction or it can see all other numbers.

Yes, I too have my lay suspicions that mathematics has gotten time rather confused: somewhere I think t may have lost or gained something such that it no longer represents time in reality. I cannot imagine what it means for time to be a spatial dimension. My tendency is therefore to say that it is not. It is as if someone tells me 'the bicycle is moving yellowly' - perhaps that true, but it means nothing at all to me, so I will have to reject it.

Interesting subject though, almost makes me want to revisit higher math...almost :bigsmile:

As far as time though, I can picture moving forward and backward in time, but I am having a difficult time conceiving of moving up, down, or sideways in time.

Conscious thought, about anything, seems to naturally demand the positive and the negative. There is no way for our minds to conceptualize a mountain without a valley for example, or of light without darkness.
This makes a concept like god or infinite space somewhat impossible to even imagine.
That which can be spoken is not eternal.

"I can picture moving forward and backward in time, but I am having a difficult time conceiving of moving up, down, or sideways in time."

I think this is a misconception of time.
Time is relative whereas spatial dimensions are not. Of course, spatial dimensions can seem relative, when two people of differing sizes see objects as relatively smaller or bigger than they appear to the other person, but the quantifiable size of those objects are the same regardless of the size of the observer.
With time, however, it differs slightly from object to object, thereby making it subjective. It's simply a measurement of the rate of change of objects in 3 dimensional space, not a dimension of existence itself.

I think that this is all completely off topic though, my apologies to reconstructo. After recently discussing time in great depth, I saw his comment and couldn't help myself.

In response to the OP, I think you're on to something about the way we conceptualize, and therefore the way we are capable of understanding reality.
Conscious thought, about anything, seems to naturally demand the positive and the negative. There is no way for our minds to conceptualize a mountain without a valley for example, or of light without darkness.
This makes a concept like god or infinite space somewhat impossible to even imagine.
That which can be spoken is not eternal.

Taoism 101.

I keep a copy of The Tao teh Ching with me at all times. (Shambhala Pocket Classics, John C. H. Wu translation.)

I also have a pocket copy of Tao Te Ching oddly enough, and it's one of my favorite things to read.
If only our brains weren't so under equipped to deal with the topic of the eternal. It seems that our brains are only as capable as the world in which they evolved demands.
The ultimate nature of reality is irrelevant to the evolution of the human genome and the development of the human brain, so now we face a series of unanswerable questions.
Let's just create a computer with more cognitive power than our brains and let it tell us a few things. We'll have to make sure we keep it off the internet though.

I'm of the belief that consciousness is a product of biology, in which case it would be plausible that we could replicate a human brain via computer engineering that would be fully conscious upon powering it up.
If we could engineer a brain with more cognitive faculties than our own or more computing power, it could potentially answer some of our more puzzling conundrums that our limited human minds are incapable of even conceptualizing.

I'm not sure I get what you're saying. Biology as a product of consciousness - is that in reference to the notion of god as creator?

Go into this, if you will. It sounds like we are just moving the fulcrum of negative and positive. I don't see how we can escape the dimensions times two equals directions formula.