ok..

[Dil12a]

please feel free to rip apart what i said and point out what was shite etc. since i just scrapped a pass in a level physics and maths i am eager to learn, this is what i posted on another forum when we was discussing it

ok so this is my thorghts with the recent wowness of the holographic theory:

Ok the holographic theory and the forth dimension

Holographic theory came about due to some due about ten or so years ago in numerous experiments found that small particles such as electrons could "communicate" with each other over large distances apparently breaking Einstein’s law's of relativity. Such as nothing can travel faster than light.

The solution is the fact that they are still connected via the forth dimension.

The forth dimension is pretty much like the first two except with another perpendicular property. The forth dimension is well pretty much beyond my understand, as well as 99.99% of peoples understanding. We can imagine it but not understand it. The easiest way to understand things in the forth dimension is to look at the relationship between the 2-d world and the 3-d world.

Imagine now we have a happy 2d world. The easiest way for you to imagine this, is as if you are living and moving between two narrow walls. You cannot move left or right, only up, down, backwards and forwards.

In the 3-d world we can move left, right, up, down, backwards and forwards

In 4-d you can do them all. As well as two new kinds of movements.

Imagine now as a 3d observe you are looking at a 2-d world. The world is a very interesting place. For one, everyone is slim. People can only be tall or short. In the 3d world people can be tall, short, slim, fat, etc. and in the 4rth dimension. Well I wouldn't know. But maybe the people there come in radically different lengths, or something?

Now imagine you cut a 2-d square in half. You get a rectangle half the area of the square, but no matter how much you halved it you still would be left with some area. This could probably be plotted with the Lin function. now imagine a cube cut in 3-d. it also halves the surface area, and halves the volume, again no matter how thin the materials in a cube you cannot cut it into oblivion, you will always be left with something, with a ever decreasing surface area and volume, presuming you check away the other parts.. Now a 4-d cube you could never cut into half. Why, imp not entirely sure, but you would be able half the area, or half the volume, but you would be left with a complete replica of the original, to the same specifications.

It kinda works as if you have an infinite amount of cubes making up this 4-d cube. Cutting it up just makes more cubes, of the exact same size as the original, but only as many as there is in the new direction.

For example we have a 4-d cube with the 4-dimension value being 16.cutting the 4-d cube into halves, would leave you with 16 identical sized cubes. The easiest way to get around this is imagine your MR 2d, and in front of you is a really big rectangle. Us MR 3d slices it vertically down. Invisible to his eye. But this rectangle multiples. In exactly the same proportions as before. Much like the 4-d cube would be. It isn't infinite, buts it’s infinite to us.

Now getting on to the whole holographic theory point. It says it’s communicating infinitely fast between each other, even though they are separated. In the 3-d dimension they are separated, but in 4-d they are still connected. Just like every 2-d object exists in our 3d world, every 2-d and 3-d object exists in the 4-d world.

Now lets says MR 2-d runs to the far edge (right hand side if you was looking into the 2-d world) of the world and witness an object being put there, by say us a 3-d observer. In his world we place a straw. Vertically sticking out of the page. He then runs to the far left of the world and sees the other end of the straw. Now just to frig with the little fellow we wiggle the straw at both ends. For him his brain has just exploded, how can two objects move in unison when they are a great distance apart? That surely breaks the speed of light rule.

But it doesn’t. All we have done is bend the straw. Or even better bent his little 2-d world in half. The poor little shit would not be able to tell if his world was being folded in half or not. For him there is no left and right. Everything would stay the stay up, down, left and right wise but in fact his world is now bent over, meaning in fact the distance isn’t even that great. Its allot smaller than he can possible perceive. Now imagine this translated into the 3-d world. If they electrons are still connected in the forth dimension (by which I explained above, how we could keep splitting them for a near infinite amount almost) then our simple space time 3-d world is just being bent in half to allow this communication.

In case you didn’t know our space time continuums rather elastic. Imagine our galaxy as a giant rubber mat. Larger mass have a larger gravitational effect by pushing down on the mat. Of course the mat can bend and wiggle, and because we are attached to the space time continuum we don’t wiggle or feel its effects. this also means that black holes will not go on forever as some people suggest, but imagine at some point this elastic will revert to its original position, basically making the black hole disappear, of course it would leave behind a lasting memory such as a large gravity "dip" but the black hole is gone. This means that no more matter is being "destroyed" but instead will circle around this gravity mass. giant dust cloud would be formed round this increased gravity, which could easily explain how we not only have nebulas, but also how the stars are created, as only a "former" black hole has the gravitation strength to start nuclear fusion.

I know I kinda got distracted from the point but I was typing as I was thinking. But yea, the universe isn’t a hologram, that each atom is basically a mini-universe. In fact it’s more likely to be true, that we are at the bottom of a much large universe, as imagine our a 3-d world and 3-d atoms. Being nothing more than a rather nice but large display is the 4-d world. As after all they can walk around our universe, even in theory look at us like 2-d objects, just look at a slice of the universe.

I tried explaining this as best as I could but its kinda difficult subject. Feel free to pull apart my argument. Also I apologise for the not so perfect spelling and grammar

[jinydu]

Whoa, what a first post! If I try to read the whole thing, then comment, I'll probably forget some things, so I'll look at each individual part of your post.

The first thing you talk about is holographic theory, which (if I've understood it correctly, and that's a big if, because I haven't read much about it) claims that information can travel faster than the speed of light (in a vacuum), a claim with contradicts Einstein's Special Theory of Relativity. An important point is that Special Relativity doesn't say that "Nothing can travel faster than light". Instead, it only prevents information from travelling faster than light. For instance, if you shine a flashlight at Pluto, then wag your finger across the flashlight, a shadow will move across Pluto, faster than light (provided that you wagged your finger fast enough). However, information itself is not being sent faster than light, since the light emitted by the flashlight needs time to reach Pluto, and the light travels at, well, the speed of light.

I do remember reading about an experiment (I think it was led by someone named "Aspect" and related to the polarization of light, or something like that) that appeared to send information faster than light. However, it should be noted that his conclusion (that such superluminal communication is possible) isn't fully accepted by physicists; some doubt that he truly sent information faster than light.

One phenomenon that is generally accepted, however, is something called quantum entanglement, where the quantum states of two particles become "entangled". Then, when the quantum state of one particle is changed, the quantum state of the other particle also chances, instantaneously, even when the two particles are far apart. Quantum entanglement greatly troubled Einstein (he dismissed it as "spooky action at a distance). Although it appears that one particle is "telling the other particle to change its state" infinitely fast, some physicists question whether any information is truly being sent. If not, then Special Relativity is not being violated. In general, these apparent "faster than light" phenomenon are still be researched, and I think it would be premature to draw any final conclusions at this point.

Next, you go on to talk about "the fourth dimension". In reality, four-dimensional space isn't all that mystical; although it cannot be visualized by humans, it can be studied on paper, just like 3D space.

While discussing 2, 3 and 4 dimensional space, you seem to have made a common error: you assume that there exist mutually perpendicular directions with a unique, well defined, ordering. For instance, you claim that in 2D, up-down and backwards-forwards are the only mutually perpendicular directions, while in 3D, we have left-right, up-down and backwards-forwards. However, a moment's thought reveals that the distinction between left-right and forwards-backwards is itself arbitrary, since your left can be someone else's forwards. Similarly, left-right and up-down are interchangeable (if you don't believe me, tilt your head 90 degrees). In short, it doesn't matter which direction you choose to call left, or forwards, or up. The only thing that matters is that in 2D, you have 2 such mutually perpendicular directions; in 3D, you have 3 such mutually perpendicular directions, etc.

You claim that in 2D, being can only be tall or short, while in 3D, they can be tall or short and slim or fat. Then, you wonder about 4D. As I said in the previous paragraph, it doesn't matter which direction you call the "tall-short" or "slim-fat" direction. However, if you insist on fixing a particular direction as the "fourth direction" (so long as you remain within a particular point of view, this is possible, although arbitrary), and you want a new length analogous to "tall-short" or "slim-fat", you are free to give this new length any name you want. Whatever you choose to call it, it is perpendicular to both "tall-short" and "slim-fat".

Next, you talk about cutting a 2D square and 3D cube into ever smaller pieces. You mention a "Lin function"; I really don't know what you were talking about; I've never heard of a "Lin function". However, if you considered the number of cuts as your independent variable and the area or volume as your dependent variable, you would have an exponential decay function. In any case, your claim that it is impossible to cut a 4D "cube" (it's usually called a tesseract or hypercube, by the way) in half is incorrect; it can be done, so long as you have the right tool. Just as a line cuts a square in half, and a plane cuts a cube in half, a 3D "hyperplane" would cut a 4D tesseract in half (so long as you positioned them correctly). If you cut a 4D tesseract with 16 units of hypervolume in half, you will get two 4D objects, each with 8 units of hypervolume.

Some people make the mistake of thinking that all 4D objects are infinite. While it is possible to think of a 4D object as being made up of infinitely many 3D objects, this isn't really that exotic if you think about it; since 3D objects can be thought of as themselves made up of infinitely many 2D objects. So cutting a 4D tesseract (with infinitely many cubes) in half creates two other 4D objects (each with infinitely many cubes). Thus, infinity = infinity + infinity. As my physics professor often said: "True but useless".

You have a paragraph about cutting a 4D cube that has 16 units of 4D space. Unfortunately, I don't really understand it, especially because I don't want what "MR" is supposed to stand for.

In any case, you then give the example of a 2D being and a straw. I don't think you've described the scenario very clearly (for instance, is this 2D world supposed to be "horizontal", like a ceiling or floor, or vertical, like a wall? This is important, because you say that the straw is vertical, so we have indeed chosen a particular point of view), but I'll take my best guess as to what you mean. I think you have in mind a horizontal 2D world. Above it, you have a straw, bent in the shape of an arch, one end touching the "right" edge of the 2D world and the other touching the "left" edge of the 2D world. Then, you're claiming that if the 2D being is standing at the right edge, next to one end of the straw, and if we wiggle the straw, the 2D being will observe both ends of the straw wiggle immediately.

However, this reasoning (assuming that a 2D version of Special Relativity holds in the 2D world) is incorrect. First of all, if you wiggle one end of the straw, the other end does not start wiggling instantaneously, it takes time for the "wiggling" to be transmitted to the other end. A straw is not a rigid body. In fact, if Special Relativity is correct, there are no rigid bodies. Of course, we could wiggle the middle of the straw instead, so that both ends of the straw start wiggling simultaneously in our frame of reference (remember one of the conclusions of Special Relativity: If one observes sees too events, seperated in space, occur at the same time, a different observer may not seem them occur simultaneously); this brings me to my second point. Even if this were to occur, the 2D being would not see the straw ends wiggle simultaneously. Since he is standing far away from the left-end of the straw, there is a time delay between the instant at which the straw end begins to wiggle, and the instant in which he sees it begin to wiggle. This time delay corresponds to the time needed for information to travel from the left edge of his world to where he is (the right edge), and according to Special Relativity, the maximum speed at which this information can travel is the speed of light. But suppose for a moment that the 2D being did observe both ends of the straw begin wiggling simultaneously. At the moment that this happens, the 2D being could reason: "Since I'm seeing the left-end of the straw start to wiggle now, and since it takes time for light to reach my eyes from the left-end of my world, informing me that the left-end of the straw has started to wiggle, this must mean that the left-end of the straw actually began wiggling some time in the past (to be more precise, that time is the distance between the edges of the 2D world, divided by the speed of light). Therefore, the right-end of the straw must have sent a signal back in time to the left-end, so that it could start wiggling in time for me to see it wiggle now". As you can see, sending information faster than light is essentially sending it back in time, according to Special Relativity.

On the other hand, folding the 2D world in half is another matter altogether. If we do so, it is possible for the actual distance between the left and right edges to become arbitrarily small (from the perspective of a 3D observer). Thus, if information is sent through our 3D space, outside of the 2D world, it is possible for this information to travel between the edges in an arbitrarily short time (so long as the edges are close enough in 3D space), and the 2D being will be able to see some truly bizarre things. However, it is not true that the 2D being would have no direct way of knowing that his world had been bent. If you had read about non-Euclidean geometry, you would know that in curved space, geometry is different from in Euclidean space. Thus, for instance, the 2D being could draw a triangle, measure each of the angles, and upon finding that they do not add up to 180 degrees, conclude that his world has been bent.

In your next paragraph, you seem to be invoking the "rubber mat" analogy of General Relativity (itself a different topic from Special Relativity), an analogy that is often made to explain General Relativity to nonscientists. However, you should keep in mind that it is just that, an analogy. If you really want to understand General Relativity, you have to actually study it, which means learning lots of mathematics. Although the 2D rubber mat requires a 3rd dimension into which it can curve, this is not true for Einstein's spacetime. Mathematically, it is possible to describe the curvature of spacetime without reference to a higher dimensional space into which spacetime curves. If you want to know why, you'll have to study the mathematics. You then go on to talk about black holes do not live forever. Even if the "rubber mat" analogy were a full description of General Relativity (which it is not), I don't see how it follows that a black hole cannot live forever.

In any case, you shouldn't take this too seriously. Remember, this is not how physicists come up with new physics theories in the real world. In reality, a theory looks more like this: http://www.hyper-ad.com/tutoring/math/a ... ation.html
than what you have just shown. (Ok, that link is about mathematics, not physics, but you get the idea. Real physics theories involve lots of equations. No serious physics theory relies mainly on qualitative, written descriptions, although popular press accounts of those theories usually do, since most people are not well educated enough to handle the mathematics).

[thigle]

jinydu my friend. i cannot understand how you, who's been on these forums for quite some time, how can you write (to a newcomer) that "...four-dimensional space...; ...cannot be visualized by humans..." ???!!!

[removed]

so listen, everybody:

humans CAN visualize (=see in mind's eye, imagine, ...) nDIMENSIONAL SPACE !!! not just 4d, but also 5-, 6-, 7-, 8-, and even infinite-dimensional space.

what's needed is openess to possibility, curiosity, diligence, and playfulness of your mind.

[Keiji]

Jinydu meant that we cannot visualize flunespace in the same way a tetronian would. But we can imagine it if we try hard enough.

[jinydu]

Jinydu meant that we cannot visualize flunespace in the same way a tetronian would. But we can imagine it if we try hard enough.

Essentially, that's what I meant.

However, I should add that since I can't read people's minds, I'm not sure how good these imaginings are. It seems quite clear that some users have managed to form pictures of 4D space in their minds, but I'm not sure how accurate they are.

[thigle]

thanx for editing my post, whoever

jin: if that's so (you can't read people's minds) than you should not generalize and act as if you could. leave open. and sorry for the rant

actually, most people cannot visualize 3d accurately either. and many people cannot 'visualize' at all. (I mean 'visualise properly', meaning having actual sight-like perception, in phenomenal space, which is neither objective, nor subjective).

imagination is not a matter of dimensionality, nor of seeing images as such (by mind's eye). it can be of different form for differnet people. visual imagination is what is usually (but not always) meant when major aspect of imagining experience is pictorial. consider the following quote by Einstein about this "visual thinking."

"The psychical entities which seem to serve as elements in thought are
certain signs and more or less clear images which can be 'voluntarily'
reproduced and combined...The above mentioned elements are in my case of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be
reproduced at will." (quoted in Jan. 1985, Byte, p. 114). (italics added)

the magnitude of the ability to form clear mental images is the degree of clarity of the mind.

on the other hand, the dimensionality of the imagined percept is rather conditioned by imaginer's understanding, or refinement of intention, of what he is imagining. (btw, check the etymology of i.mage & magic). that means that difficulties that people encounter when dealing imaginatively with 4 (or more dimensional space) and objects in it, is the infamiliarity, and lack of precise understanding of WHAT and WHERE of the imagined percept. this lack of precision, or refinement of knowledge is the reason for the many difficulties of imagining 4&more dimensional objects, and also for the MYTH of inherent human inability to visualize 4(&more)d.

one should also note, that it's different to say 'to imagine 4d objects' & 'to imagine 4-space'. compare with 'to imagine 3d objects' & 'to imagine 3-space.' most people have hard time visualizing 3-space as such either. although it serves as unseen condition for any 3objects imagining, it itself is hardly graspable in its totality by ordinary people. at best they imagine a 'chunk' of it.

love you all.

[jinydu]

Of course, although human ability to accurately visualize 4D objects or 4D space may be in doubt, the ability to logically derive conclusions about them isn't. That's one of the great characteristics of geometry (when done rigorously): Deriving conclusions does not require that one be able to visualize the objects (although this ability can make the task easier); all that is needed is the ability to follow a logical argument.

[houserichichi]

...in fact if you were to take a course in algebraic geometry/universal algebra you'd learn that there are "shapes" that just can't be visualized period no matter what space you're working in.

[thigle]

houserichichi: ...in fact, that is not very probable. so, could you please give some exemple(s) ? if these are not 'drawable', why calling them "shapes" ? also, how come that "...no matter what space you're working in" ? i am very curious.

jinydu: in logical argument, possible logical values (and thus the whole argument) depend on the kind of logic. kind of logic depends, at the bottomless bottom, on the imagination of the one who is pre-imagining and using the logic. it's you or me or anyone who choses to follow any seemingly pre-given and selfconsistent logical frame of reference.
the very simple aristotelian logic, excluding the middle, is a prime exemple of reductive kind of logic. and that's what you were using when you wrote "...four-space...CANNOT be visualised by humans." you excluded possibility, by the unprecision of your languague, or rather insufficiency of your logic. as logical value of possibility in 'aristotelian logic' is either CAN or CANNOT, and one excludes the other, you excluded paradox of simultaneity because (not having another choice because of the logical frame you were operating in) it's more comfortable not to deal with paradoxes and it's also very simple. it's a logical simpleton. a digital approach. but now ask yourself: is YES and NO all there is to existence? is existence monochromatic ? your experience, (and thus at least a part of what's observable), is surely (even though I cannot read people's minds) polychromatic and multimodal.

so when I pointed out, down this thread, that humans CAN visualize >3d, i was not trying to change logical VALUE of your statement, i was just trying to EXPAND your logic, your mind-frame. at least to 4-valued logic, where AND is allowed. I was and am not trying to make your NO into YES. I am counter-balancing your over-estimation of NO. O & 1 can stand together without contradiction. there exists AND relationship. ! check any boolean or modal logic. or any programmable pocket-calculator. or >12 hundreds years old logic of Nagarjuna (and you might find that some can understand relativity without studying all the math, as you like to accentuate. btw, why do you think Einstein read Bhagavadgita? to derive logical conclusions ? no way. just IMAGINE, my dear friend: 9 years it took him to figure out what he did. and he says: "...psychical entities ... elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined...". he surely was not deriving his conclusions by not thinking. and if he did it by though, than he did it by 'images' too).

but to sum up:
logical values in dual aristotelian logic : 0 OR 1
logical values in 4-fold logic (under many names): 0; 1; 0 AND 1; neither 0 nor 1 (=NOR)
...can you state the 5th logical position ? whoever does, i send him kisses.

so for exemple: you say first that "...fourspace...cannot be visualized by humans..." (=OR), then next post you say "...quite clear that some users have managed to form pictures of 4D space in their minds, but I'm not sure how accurate they are". so non-finaly climaxing, you got to 3 valued logic explicitly, so you can state 2 contradictory statements, and not contradict yourself. (=AND). very healthy.

- - -
now check out (with this new knowledge) the inconsistency of your last statement (trialized for better navigation):
1: "Of course, although human ability to accurately visualize 4D objects or 4D space may be in doubt, the ability to logically derive conclusions about them isn't."
2: "That's one of the great characteristics of geometry (when done rigorously): "
3: "Deriving conclusions does not require that one be able to visualize the objects (although this ability can make the task easier); all that is needed is the ability to follow a logical argument."


1> very ridiculous, not rigorous at all, but pre-cognizable. even though you occasionally, or discontinuosly, allow the possibility, your rational mind have hard time accepting the simple reality of openess, and continuously re-states inconsistencies in it's own understanding by objectivizing them as seemingly objective doubts about yours & others abilities. this IS and ISN'T is just another unnecessity. nervousness of must:
there IS NO doubt about human ability to accurately visualize 4D objects or 4D space >3d, and there IS NO doubt about human ability to logically derive conclusions about >3d. AND, there IS doubt about human ability to accurately visualize 4D objects, and there IS doubt about ability of logically deriving conclusions. doubt and no-doubt are co-present. therfore unnecessary.

2> greatness of the characteristic you chose is just that: greatness of your choice. it's your preference of this characteristic. ask for exemple why Hilbert calls one of his most famous books "geometry & imagination" or why Conway made a course called "geometry & imagination". these maestros of geometry (which is doubtless) didn't use "geometry and logic(al conclusion)" as names. their great characteristic of rigorously done geometry might be quite different from yours. and maybe closer to the imaginal side than to the rational one.

3> as was said above, one cannot follow a logical argument about ideal objects (such as 4d) without imaginal faculty. however latent its form might be, in the stream of experience, due to unawarenes of the "conclusion deriver", it must be present for mind to function. even numbers are "visualized" in core. analytical thinking requires memory, and retrieval of memories and concepts is through i.magination.


to sum up (1,2,3)> it is not true that for doing rigorously geometry it is necessary to derive only logical conclusions. nor does it require only visualisizing objects. visualisizing objects doesn't necessarily require deriving conclusions. you can simply SEE and know right away. i guess that's the difference between gnosis and logos, between in.sighting & conceptually grasping. for rigorously doing geometry, all that is needed is
all there is: both clear thought AND clear vision.

saying that humans cannot visualise 4d is unnecessary and violent to our essentiality. re-stating difficulties in a task is a waste of spacetime which could serve as boost and opening, an easing.

some can sometimes some cannot. depends on people, depends on their context. but ESSENTIALY, human possibilities are open. just because 99.99% of the time I cannot succeed at some task and just because 99.99% of society cannot do something, doesn't make any good reason to believe that it cannot be done or suceeded at at all. it just makes it habitually harder to think it can.

logical argument is imagined. like this one. it's a creation of the one who's making it. you can derive conclusions, but there's no consclusions to make about if there's nothing to make them about in the first place. and (not only) this 'whatness' has to be imagined.

people with heavy mono-rational habit very often don't realize how dependent they are on their imagination, even in their most rationally appearing conclusion-deriving acts. that's because their imagination has been rationalized - i.e. conceptualized, thus hypostased into abstraction - torn apart from living embodied experience: OBJECTIVIZED.

so sometimes, some events/entities can appear rigorous, but actually, they can be full of LOGICAL INCONSISTENCIES (HOLES), SUBJECTIVE AFFECTIVE TONING, and non-rigorous PRESUPPOSITIONS. giving primacy to logic is just some 2000 years old & funny (well, not really) trait of western-worldview. our perspectival logologism. if interested, check out these, for exemple:
barry sandywell: Reflexivity and the Crisis of Western Reason: Logological Investigations (Logological Investigations, Vol 1)
barry sandywell: The Beginnings of European Theorizing: Reflexivity in the Archaic Age : Logological Investigations (Logical Investigations, Vol 2)
barry sandywell: Presocratic Reflexivity: The Construction of Philosophical Discourse C. 600-450 Bc (Logological Investigations, Vol 3)

expressed myself, now i shut up and go to sleep (took me way longer anyway).

[houserichichi]

Some affine and algebraic varieties just cannot be represented graphically as they are truly abstract concepts. Turns out much of modern physics is worked via abstract concepts that eventually give real-world results. Funny how that works out.

[thigle]

houserichichi: i am not persuaded at all, although that is not the point. i'd like to hear an exemple, specific one, not a general statement about 'some affine & algebraic varieties'. truly abstract concepts are specific actually.

and that much of the modern physics is worked via abstract concepts that eventually give real-world results is a result of the fact that abstractions are specific indeed. the doers of the abstractions are part of the real-world on which they do their abstractions. in other words, dynamics of our perception, our minds, of our abstracting mechanisms, are patterned by the same world as the world on which they abstract. the energy is self-patterning. virtual organic. also, it works out like that because of the prevalent formalisms. if, for exemple, the major trend in education of physic & math would be geometrical algebras (clifford's), and if quaternions and octonions would be used where appropriate instead of not so clever vector calculus, modern physics might seem quite different. maybe much more graphic. but it is changing slowly already. from logologics to videologics (& 'haptologic'). some domains of human knowledge as social practices already started to visualize themselves. brightest can touch the image already. the brightest minds always realize that Vision is much more optimal than analytics. very funny indeed.

and check this out:
http://www.brown.edu/Administration/Bro ... ework.html
or this one: George Lakoff: Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being

[wendy]

don't know

i never had problems looking in 7D.

[thigle]

good for you wendy. hopefuly, more & more people will dream together...

[houserichichi]

Varieties are, in their own rights, abstract concepts just like bordisms, bundles, and sheaves. They have no graphical representations in their purest forms. If you honestly want examples I'll spit some out but they're going to be no more descriptive than if I was to spit out examples from a masters thesis you haven't read (unless you've studied algebraic geometry in which case you should already know what varieties are). Truly abstract concepts are just that, abstract...they describe as much as possible in concise a form as possible with as few limitations posed on them as humanly conceivable. That's why one learns arithmetic before college algebra before field theory.

My point in the matter was that there exist things outside the realm of reality. Some of these are used in modern physics (gauges, tensors, actions, differential forms, to name a few) that ultimately give results that we can measure and compare to experiment. Heck, many of the spaces that modern theoretical physics is performed in are abstract. It has moved well beyond the realm of advanced calculus and into those of abstract algebras, geometries, and the like.

[thigle]

well, if you don't want to imagine gauges, tensors, bundles or actions, then do not. that doesn't make them uinmaginable. it's up to you to try.

actually, did you really have to take a course in algebraic geometry/universal algebra to know what varieties are? i didn't. and you might have misinterpreted something if you learned there that 'there are "shapes" that just can't be visualized period no matter what space you're working in'. or you have a semantic problem with "shape". am not picky, I just like precision. and aha, i did take a course in universal algebra & I am not a stranger to algebraic geometry at all.
and yes. i honestly want an exemple, why else would i write i do ? why would i spent my timespace by typing it ? you think i attend this forum to waste my energy, just for the shit of it ? i appear here to learn/teach, not to repeatedly pose questions whose answers i am not interested in.

you write: 'Truly abstract concepts are just that, abstract...'. and i can disagree again. i would have to agree if you would omit 'truly' from the sentence. 'abstract concepts are just that, abstract.' because truth, (together with reality you talk about later), is just 2 of 4 aspects of Being, and are thus multileveled in possible meanings - there are Kinds of truth (& of reality & of presence & of identity). 'truly truly' or 'true truth' is beyond simple truth (of truth & lie).
...'...point in the matter was that there exist things outside the realm of reality.' well, depends on your conception of reality (& things). is there a math definition of 'reality' ? not really. there are Real numbers, but those are as insufficient as a line.

also: 'Heck, many of the spaces that modern theoretical physics is performed in are abstract.' actually, what spaces do you consider specific ? the very conception of SPACE is the most abstract abstraction. very specific. abstracting is space-like, one could almost rename it to 'space.ing'. it is seeing a lot of particulars from space, so that general trait(s) of the set on which abstraction is made comes to the fore. but every abstraction is specific, made in specific context. abstracting is specifying generalities. abstracting is higher-level specification, or 'meta-specification'.

what about for example Kent Palmer's aspects/kinds of Being to disambiguate its paradox (he made it by applying Russel's theory of higher logical types, the following is just a region from wider ontological scale):

Being_Kinds(meta-levels): ...pure...process...hyper...wild...ultra(existence)...?
Being_Aspects(types): reality...truth...identity...presence...? (=grammatical uses of Being in Indo-European languagues)

now make a matrix of these and you got:

for truth:
...
pure truth_verification
proces truth_Showing / Hiding of unconcealement that brings forth the truth
hyper truth_what we see when the Unconcious reveals itself; truth never manifested, haunts truths uncovered
wild truth_final level : revealed truth is ultimately the same as the secret truth
hyper truth_emptiness of existence where truth itself becomes an empty construct
...

for reality:
...
pure reality_a product of testing, like verification, needs to be repeated often
proces reality_occurs in a continual testing that never ends
hyper reality_where the simulation or test is more real than `realiity` itself; game more real than normal `mundane` reality
wild reality_real /not real no longer discernible, what is game and what is reality
hyper reality_ultra-reality of existence itself
...

(freely adapted from http://dialog.net:85/homepage/kent_palmer.html)

[jinydu]

Admittedly, thigle, your post (the one that followed after my second one) is far too long for me to fully respond to at the moment. But I will say that most of real mathematics, and certainly all of what I have studied up to where I am now (just finished my first year at university as a Mathematics major) deals with statements that are either true or false. If you start dealing with statements that are neither true nor false, then proof by contradiction, one of the major methods for deriving theorems, is lost. I have heard about a certain mathematical system that assigns truth values to statements, anywhere from 0 (completely false) to 1 (competely true). Nevertheless, I'm quite sure that this can be dealt with using a well-defined set of rules; such is a common feature of all areas of mathematics. I will also admit that only a relatively tiny portion of my time and effort is spent thinking about this issue (the details of the underlying logic of mathematics) since I consider it to be well-established and because it is relatively far away from what I usually study: solving equations, doing integrals, investigating infinite series, etc.

I will also add that neither Mathematics nor rigorous logic can answer every question about the world. Although it seems to me that you consider this to be a problem, and this be a factor to your using your "4-valued logic", I do not consider it to be a problem. Questions that cannot be answered using logic can be set aside to be dealt with using other (usually less certain) methods, or not dealt with at all. So the math I learn in university cannot fully describe my experience? So what? Neither can any other subject in university.

so for exemple: you say first that "...fourspace...cannot be visualized by humans..." (=OR), then next post you say "...quite clear that some users have managed to form pictures of 4D space in their minds, but I'm not sure how accurate they are". so non-finaly climaxing, you got to 3 valued logic explicitly, so you can state 2 contradictory statements, and not contradict yourself. (=AND). very healthy.

That's not what I was doing... I was changing my earlier statement to take account of your critique. You can safely consider my first statement, overwritten.

[houserichichi]

Let me give a better example. A mathematical group has no realistic worldplace. Yes, I could draw a little bubble on a piece of paper, include all the elements of the group, verify properties within the bubble, and maybe perform actions on and inside the bubble to see what happens to the group but what I'm looking at isn't the group itself. Groups, gauges, tensors, bundles, actions, and the myriad of other abstractions of applied, real-world mathematics do not exist, they are constructs of the mind. As such any visualization, so long as it follows the rules associated with the object in question, depends on the individual. So in that regard I suppose I'll concede. I believe it was Feynman who said something to the extent of you can't see the inside of a brick. Any time you crack a brick open to see its inards you're still only getting a view of its exterior. The "inside" of a brick is a concept that we use, something we can't actually see. The same goes for mathematical ideas, they are purely concepts that exist in the mind, though a great many of them have real world analogues, applications, and the like. If you can visualize addition, the operation (and I really do stress the word "visualize") then please, be my guest to draw me a picture, or have we been using some other derivative of the word "visualize" the whole time? If that's the case then I'll rethink my argument.

One doesn't need to take a course in algebraic geometry to learn what varieties are as the information is quite accessible via the internet. I did, however, take classes in it not only to complete a degree but to further my understanding and ultimately abstract my mentality toward objects that we every day take for granted. Now really, if you're going to accuse me of playing with semantics then explain to me what you would define as a "shape" and we'll move on there. As an example of something that can't be drawn, feel free to give me a picture of n-dimensional projective space over a general field. That's an algebraic variety that you should know quite a bit about.

My definition of reality is something that can follow the laws of science, that is all "entities" in the universe (for lack of a better word) that can be measured, tested upon, and experimentally verified to "exist", or at least follow the rules we associate with them. "Real" things should follow the laws of physics. Pink elephants are not real and if they are we haven't seen them yet so we assume they're not until one comes about. Addition, as I mentioned earlier, is not a real "thing". It is a tool, a mind's construct that helps us operate on, amongst other things, numbers which are also constructs. If someone could hold the number two in their hands I'd love to see it. I don't know what two looks like but I know what two OF something looks like.

I'll give you this much, "space is the most abstract abstraction". What I was referring to was spaces abstracted from our every day intuition, that of three dimensional Euclidean space. Specific examples include Minkowski and Lorentz space, the de Sitter spaces, heck, even a simple 4-dimensional Euclidean space is an abstracted version of 3D or, at the very least, an extension which I would argue is still an abstraction.

[thigle]

ok.

you wrote: "Let me give a better example. A mathematical group has no realistic worldplace. ... actually it happens what I'm looking at isn't the group itself...".
>well, having a place is not a necessity for imaginary percept. the imaginal worldspace is alocal. it's not here, or there. it's similar to color perception - you cannot say that it is on the things themselves - it is not placed. color is essentialy placeless, however it is perceived/it appear as localized due to interpretation. it arises as interpretative play of our minds/senses/their fields, but actually it happens what I'm looking at appearing as red cherry is not the cherry itself, but my representation of it. so i'll concede you're right that 'actually it happens what I'm looking at isn't the group itself' with addition that nothing YOU(orME) are looking at isn't the thing itself. and with specifying the context as one where subject/object structure is present. because in nondual view such mess doesn't arise.

"Groups, gauges, tensors, bundles, actions, and the myriad of other abstractions of applied, real-world mathematics do not exist, they are constructs of the mind."
>well, i still am pretty sure they do. but in what mode ? the mind is of the same nature as so-called objective nature. thus how it constructs is of the same order as what is it constructing about(or from, or rather in). i think mathematical ideas are archetypes. jungians would say that archetypes are precisely that which is not imagined, but what expresses through imagination (among other ways). you then say "The same goes for mathematical ideas, they are purely concepts that exist in the mind, though a great many of them have real world analogues, applications, and the like" and i think exactly because of that, they have this applications because they are these concept which are from minds which are nature. very simple.

"I believe it was Feynman who said something to the extent of you can't see the inside of a brick. Any time you crack a brick open to see its inards you're still only getting a view of its exterior. The "inside" of a brick is a concept that we use, something we can't actually see." i like more feynman's thought on the discrete nature of space under plack scale, scattered somewhere on Tony Smith's site (maybe 240thoughts section?). I to be honest believe we can see the inside of a brick. maybe not by purely by physical-bodily interface, but by consciousness (or soul you might call it in some contexts) ridden by duality-free (=nondual) awareness.

"If you can visualize addition, the operation (and I really do stress the word "visualize") then please, be my guest to draw me a picture, or have we been using some other derivative of the word "visualize" the whole time?"
>I don't know. any sym.bol is a visualisation of addition. does + work for you ? or two facing intentions, or forces: -><- or whatever.
imagination can be invisible as in the case of spatial imagination, or kinesthetic imagination. visual imagination (aka"visualisation") is the ability to summon up object of sight-consciousness together with awareness of this inner-eye consciousness. it's inner vision. internal soul-sense. clarity of the mind - mindsight. check it out every night.

while visual mental imagery is purely sight-consciousness without necessity of external object of seeing & having inner light of spirit in some form as its object, imagination (or imagining if you prefer event-like expressions to entity-like) is the very free activity of the mind, existing as pure possibility. as casey says in 'imagining - a phenomenological study': mind is free, indeed most free, in imagininig. blake says our divine bodies are of imagination.

"My definition of reality is something that can follow the laws of science, that is all "entities" in the universe (for lack of a better word) that can be measured, tested upon, and experimentally verified to "exist", or at least follow the rules we associate with them. "Real" things should follow the laws of physics. Pink elephants are not real and if they are we haven't seen them yet so we assume they're not until one comes about. Addition, as I mentioned earlier, is not a real "thing". It is a tool, a mind's construct that helps us operate on, amongst other things, numbers which are also constructs."
>well, firstly, reality is not something that can follow the laws of science, the laws of science [are ways of knowing that] can follow reality. reality is manifestation as it is. it depends on your ontology and awareness. people tend to classify as unreal things which are illogical(beyond the scope of their logic) or not easily expressible, as if that qualifies for unrealness. rather it should qualify for logic-scope expansion. according to Kent Palmer, you can enlarge your ontological scale by considering not just 1.things(entities, structures), but also 2.events(or eventing, processing), 3. eventities 4. instantatons 5. something like space/energy fusion.
real is just an aspect of Being, occuring at each of meta-levels, always constructed according to where at. thus if reality is construction, then site-specific - topological.. pink elephants are real as illusions, that's their realness. they are hyperreal. real things don't have to follow laws of physics. laws of physics are here because the way the reality is before we project schemes on things. imagination is precisely that which is by unrealness of its being. it's like you find imaginaries by accepting what is not real from the level of reals: that an entity squared is negative. realness is not a qualifier of being real. numbers are constructs which fit reality because they are reality - they are of the same stuff as that on which they act - it's one wild mess. like you say "If someone could hold the number two in their hands I'd love to see it. I don't know what two looks like but I know what two OF something looks like." in my experience which is not mine but just is, because nowhere can i find myself in it, 2 looks like all anythings that come in pairs, as dyads. so you cannot hold 2 in your hands if you separate 2 and 2ness. it doesn't have to be of specific form, it can be formlessness - an open imagination. not-yet visualisation. like a manifold before embedding.

as for "a picture of n-dimensional projective space over a general field", how can i post images here ? although i am not completely clear about this one, let me give a try & get some feedback & constructive critique.

>jinydu> i do not consider inadequacy of specific logics to whole range of world-questioning a problem. rather an inspiring factor for not using exclusively dual logic. university aside, is your mind & body one or two ? none of those, nor both nor neither. 4-valued logic is as insufficient as 2-valued one. it's just more finely applicable. there are as many logics as ways of thought. yoy got even fuzzy logic... just that some are more reductive and some more creative. btw, wendy has XOR in polygloss.

[RQ]

Thigle, you're confusing concepts with physical properties. Yes math can be a textbook, but math itself is a concept. Just because scientists haven't discovered all the theorems doesn't mean all of math is incomplete, or if there's a paradox unsolved doesn't mean math is wrong. Don't give physical properties to nonmaterial concepts.

[houserichichi]

RQ...did we just agree on something?

[thigle]

rq, sorry but i am not. that distinction doesn't have to apply. i am clearly aware that energy & information are not the same. physus & logos are 2 co-flowing streams of unfolding of manifestation. however, it happens concepts & physical properties, these two levels of existence, are perceived as necessary, or even pre-given conditions of all that is. but actualy it's other way around.

math itself is a concept, as you say, but concept itself is concept too. what then is this conceptualizing quality ? concept it if you can.
i didn't state anywhere that math is wrong, or all of it incomplete, because some scientists haven't discovered all the thorems.
presence of paradox just means that not wide-enough consideration is given to thing appearing as paradoxical. and, yes, i do like paradoxes, they lead to non-dualities.