2

Get Email Updates Email this Topic Print this Page

Reply Sun 18 Apr, 2010 05:39 pm
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.
Quote:

In mathematics, given a set S, the power set (or powerset) of S, is the set of all subsets of S, including the empty set and S itself.
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.
Quote:

Contradiction is the outer limit of propositions: tautology is the unsubstantial point at their centre.
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.
 
Reconstructo
 
Reply Sun 18 Apr, 2010 07:48 pm
@Reconstructo,
Unified quantity can only vary within a dimension. 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? Of course we can stack dimensions, but this is not the same thing. Dimensions times 2 equals possible directions. Is this transcendentally true?
 
TickTockMan
 
Reply Sun 18 Apr, 2010 11:33 pm
@Reconstructo,
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
 
Reconstructo
 
Reply Sun 18 Apr, 2010 11:48 pm
@TickTockMan,
TickTockMan;153841 wrote:
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

Thanks. I haven't seen that program, I don't think. I should prob emphasize that I'm not making a point about the dimensions in nature, for instance, as in string theory or something. While I'm somewhat interested in that, I know I am far from qualified to address that subject. I'm looking at how we think about dimension, how we experience it. It's really simple as far as the nesc math goes. 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.

Good to hear from you.
 
TuringEquivalent
 
Reply Mon 19 Apr, 2010 03:44 am
@Reconstructo,
Reconstructo;153751 wrote:
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.



Can we imagine a flower as a matrix in which the "male" number exist? Of course, we can combine the dimension of male, female, matrix, and baby into hyper-dimensional space-time, where mystery, beauty, and truth hol:bigsmile:d.
 
ughaibu
 
Reply Mon 19 Apr, 2010 03:51 am
@Reconstructo,
Reconstructo;153802 wrote:
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?
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.
 
TickTockMan
 
Reply Mon 19 Apr, 2010 10:48 am
@Reconstructo,
Reconstructo;153844 wrote:
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. This is what I do when I am doing 3D modeling. Everything is done in the virtual space of X, Y, and Z.

Is this what you're talking about?

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.
 
BrightNoon
 
Reply Mon 19 Apr, 2010 03:41 pm
@TickTockMan,
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:
 
Reconstructo
 
Reply Mon 19 Apr, 2010 03:48 pm
@ughaibu,
ughaibu;153907 wrote:
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.


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.

---------- Post added 04-19-2010 at 04:52 PM ----------

BrightNoon;154126 wrote:
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:


We do seem to think of time spatially. It seems that Newtonian physics is based on an implicit conception of time. We can't calculate speed without quantizing time, and we can't quantize time without counting some other change than the one we are measuring. I can imagine graphing time spatially, and I can imagine a 4 dimensional graph being viewed by choosing an angle and sitting there, watching the the other three dimensions change. But this is an abstract leap. It's nice, but not convincing as to the real nature of time....which for me is concept, and not just mathematical concept.

---------- Post added 04-19-2010 at 04:56 PM ----------

TickTockMan;154024 wrote:

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.


Right! That's exactly what I mean! Two directions per dimension. I like the notion of 3d graphs. I love the visual aspect of math. The formulas for volumes of spheres, cylinders, etc. The polar graphs of functions. I'm not expert, but I feel a deep connection to what I learn as I continue to study it. it really is intuitional. And this intuitional aspect is the protologic. I seriously don't think we can picture a dimension with more or less than two directions, with the exception of the zero dimension, and this would be the Euclidean point. And it's sort of a special case, and really it's a cheat, isn't it? Because I don't think we can imagine zero dimensionality, but only a point that is not allowed to move. Just as we can imagine 2 dimensions from our spot in 3d by negating one of our three bidirectional dimensions.
 
Mentally Ill
 
Reply Mon 19 Apr, 2010 05:00 pm
@Reconstructo,
"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.
 
TickTockMan
 
Reply Mon 19 Apr, 2010 05:25 pm
@Mentally Ill,
Mentally Ill;154151 wrote:

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.)
 
Reconstructo
 
Reply Mon 19 Apr, 2010 05:36 pm
@Mentally Ill,
Mentally Ill;154151 wrote:
"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.

Hi there. Yes, it's an investigation of how we can't help thinking. It seems that all dimensions are dual. The numbers 0,1,2 all interests me quite a bit, as they seem related to our supposedly non-numerical thoughts, like progress and opposites, etc. It seems that you can build the entire math system from one's and zero's if you had to. And this is to use 2 digits. So two is implied. The matrix itself is dual, while number seems to be essentially unity. It's just that number in relation requires a spectrum....Smile

---------- Post added 04-19-2010 at 06:38 PM ----------

TickTockMan;154159 wrote:
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 love that quote. I have a pretty good translation, and that seems like one of the best lines, and like you say: 101.
 
Mentally Ill
 
Reply Mon 19 Apr, 2010 05:48 pm
@Reconstructo,
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.
 
Reconstructo
 
Reply Mon 19 Apr, 2010 06:46 pm
@Mentally Ill,
Mentally Ill;154177 wrote:
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.


Here's another twist. What if there is no eternity outside of the human experience? In a way, we have little pieces of eternity. Consider the volume of a sphere. I don't expect it to change or to have ever have been something else than 4/3 pi r cubed (if I remember right).

The Tao is a great book. I like a good paradox now and then. Strange, but the Tao and Oscar Wilde have more in common than is probably noted.

I do love computers. Still, they can only give us numbers or pictures of numbers, I think. I can't just yet imagine another sort of answer from them. I'll agree that there are no shortage of unanswerable questions. At the moment I'm too obsessed with answerable questions to notice the unanswerable questions. Is immersion the key? I feel like metaphor is our central technology, with math at number 2. From these we have our Taos and our computers?
 
Mentally Ill
 
Reply Mon 19 Apr, 2010 06:51 pm
@Reconstructo,
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.
 
Reconstructo
 
Reply Mon 19 Apr, 2010 07:05 pm
@Mentally Ill,
Mentally Ill;154210 wrote:
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 can dig that idea. Here's the paradox for me. Consciousness as a product of biology, and biology as a product of consciousness. I feel like its a moebius strip. What is concept? Could computers have what we refer to "consciousness"?
 
Mentally Ill
 
Reply Mon 19 Apr, 2010 07:23 pm
@Reconstructo,
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?
 
Reconstructo
 
Reply Mon 19 Apr, 2010 07:37 pm
@Mentally Ill,
Mentally Ill;154227 wrote:
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?


No. No reference to god. Just a question as to how language and thought fits into a reduction of consciousness to biology. It seems that skull is within the brain just as the brain is within the skull. For the dead, presumably, see nothing. What is "consciousness"? And is there such a thing? What is "matter"? Are "matter" and "consciousness" both just clumsy words that work well enough for certain purposes but shrivel under closer scrutiny? (I'm coming from a Kantian/Hegelian angle. What structure does the "mind" add to "reality"?) Perhaps these dualisms are faulty.
 
Mentally Ill
 
Reply Mon 19 Apr, 2010 07:58 pm
@Reconstructo,
You're wondering to what extent our perceptions mold reality, and to what extent reality feeds our perceptions?
Now I think I understand. This perspective is seemingly the byproduct of quantum theory - electrons exist in multiple places simultaneously.
It reminds me of an experiment I was told of. Imagine this set up in a laboratory: There is a machine that fires particles in a straight line, into a sheet of metal that the particles can not move through. The sheet of metal has a single slit cut into the center, a vertical slit. The particles are fired through the slit, splattering against a back drop, creating a pattern that looks like a vertical line made up of dots (the intuitive result of firing particles through a vertical slit).
Then, they use a new sheet of metal which has two parallel vertical slits, resulting in a pattern that looks like two vertical lines made up of splattered particles.
So far, so good? Pretty obvious results.

Now, those events were all observed by cameras and then the end results were observed by scientists. The scientists, however, repeated the exact experiment without videotaping it.
The results were that instead of the particles moving through the slits and creating a pattern similar to the shapes of the slits, the particles splattered against the backdrop in a chaotic mess, resembling nothing whatsoever.

The conclusion of this experiment is that the simple act of perception changes reality.

Is this along the lines of what you're considering?
 
ughaibu
 
Reply Mon 19 Apr, 2010 11:07 pm
@Reconstructo,
Reconstructo;154132 wrote:
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.
There are no negatives in hat problems, there are only smaller or larger numbers than any given number, plus a first number, and a last number of it's a finite hat problem. Numbers are considered to be players, who dont know what colour of hat they're wearing. Ordinarily, the conditions state either that a player can see all hats (other than their own) or only all hats in the positive direction, seeing all hats in the negative direction is another way of stating the algorithmic induction problem.
 
 

 
Copyright © 2021 MadLab, LLC :: Terms of Service :: Privacy Policy :: Page generated in 0.02 seconds on 09/16/2021 at 04:49:33