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Our perception of Euclidean space

  1. Apr 2, 2010 #1
    Ok so I was just thinking and realised that instead of a Cartesian plot, you can represent points in an n-dimensional space by drawing n parallel lines and marking a point on each line. Of course this is less appealing than the traditional plot because we perceive 3d space in a way more similar to a 3d Cartesian graph.

    But of course, what we perceive is a construction created in our brain in order to understand the world - we do not perceive things directly but rather we see a representation of the information received in our brains. So this got me thinking, is our perception of space as a Cartesian plot rather than a set of points on parallel lines simply our brain's interpretation of the information, or do we see it like that because that's the way it is physically and independently of our perception of it? I've always been interested in trying to understand to what extent the world exists independently of our perception of it and this serves as a good example to discuss the issue.
  2. jcsd
  3. Apr 2, 2010 #2
    Short answer? We don't know.

    How would you even describe an independent world though? Would you talk about the true colors and sounds out there? Without eyes and ears there is no such things as color or sound. And of course there's more to it than that.
    Last edited: Apr 2, 2010
  4. Apr 2, 2010 #3


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    Brains already model worlds and maths just takes modelling to a greater level of generalisation or abstraction.

    So brains, yours or animals', would learn to see a world of depth. Something small on the retina has to be interpreted as either something actually small and close to (like an insect) or instead large and far away (like a buffalo at a distance).

    I mention this particular example because there is the famous story told by Turnbull...

    So already, a sense of space is based on modelling - it is constructed via generalisations. And the ancient greek philosophers realised this, using the example of a small ship seen crawling along the far horizon.

    Cartesian co-ordinates are a more abstract way of representing space. And the idea of flat dimensionality is general enough to then concieve of n-dimensions and non-euclidean geometry. To allow a step up to even more generalised impressions.

    So we are moving further away from a subjective sense of space (relating very directly to the world of forests and plains) to an objective one (a maths description of our actual flat 3D world). Then this turns out to again be too subjective and we move to an even more general level of description which "sees" n-dimensions and curved dimension. And does the modelling even end there?
  5. Apr 2, 2010 #4
    Yeah well it's actually quite hard to think of anything at all that does exist independently. If space is really a mental construction (as in the first post) you might think time is too.
  6. Apr 2, 2010 #5
    I agree with most of what you said. Although a mathematical description of space is objective, it need not correspond to objective reality. I'm trying to understand if space is objective in the sense that it exists independently of our perception of it, and if so whether it exists in the same sense as this perception.
  7. Apr 2, 2010 #6


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    Of course time too.

    But my point is, if you really want to answer the question about what may exist independently of our mental experience, the place to start is an understanding of how minds construct mental experience (and how metaphysical modelling, as a socially constructed human enterprise, arises as an extension of that process).
  8. Apr 2, 2010 #7


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    But is the maths description "objective"? It is certainly more general and more abstract as a level of description. So it is more formal. But this is a separate kind of property. It just means that given these axioms, these outcomes "must" follow.

    The formalisms are used in modelling and then prove themselves "objective" - less subjective - in their measured correspondence with the world.

    So n-dimensional space is just an idea (how much more subjective can you get?). However once employed in actual modelling, that is used in physical theory and judged in terms of its measurable predictions, then it gives us what we commonly call "a more objective view".

    Maths is all about inventing ideas, with strong self-consistency, that may or may not be useful in the modelling of reality. Science then goes out and checks these ideas.

    This is the modelling relation (cf: Robert Rosen). We have to go further in both directions (both deeper into the subjectivity of ideas, and deeper into the objective measurements of reality) to feel we are raising out point of view from the highly local and emboddied position (which is our naive conscious experience) towards a global and disemboddied state of "view" - the god's eye view.

    And it is a process. With its pitfalls as well as its promise. And to be completely clear about what we are doing, we need a model of the epistemological process itself. Which is the reason for studying stuff like psychology, and then advanced theory in the form of Rosen's modelling relations.
  9. Apr 3, 2010 #8

    The cutting edge in physics points to the landscape being emergent(though it's still not clear from what spacetime must emerge). I think there are similar problems with LQG as they also treat the background as an emergent feature, and not a fundamental feature of the world.

    Of all the physicists that i know of, that have tried to tackle this question, David Bohm seems to have gone the furthest in answering the questrion in his "Wholeness and the Implicate Order".


    In the enfolded [or implicate] order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the "explicate" or "unfolded" order, which is a special and distinguished form contained within the general totality of all the implicate orders (Bohm, 1980, p. xv)."

    As is usual with the big questions, you should take everything with a grain of salt as the problem of induction is as great as ever. Because of the nature of the scientific method, there is always the possibility of observing a phenomenon that will challenge all previously established theories.

    The problem calls into question all empirical claims made in everyday life or through the scientific method."


    While science is the best kind of knowledge that we might have, it's worth noting in certain domains(or maybe all):

    “If you thought that science was certain - well, that is just an error on your part.” - R.Feynman

    To sum up, our notions of what's out there are contradictory and hardly sensible(when viewed outside our 5 senses). And it's only possible to say how things are not, not how they really are(though the problem of induction renders even that statement more or less worthless). Something like a unified picture of reality(a master TOE) might shed some light on how things really are, though you'd have Godel's incompleteness theorem in your way and the ever as big Problem of induction. Conclusions and interpretations drawn on the basis of the hypothetical TOE will always be challenged by the Problem of Induction.

    Because of the above arguments, IMO your question will never be answered in a satisfactory manner. But if there is a way to see how things really are, it seems we first have to understand how consciousness works and as Frame Dragger pointed out we may not like what we find(not that we ever had the say in whether to be here or not, or how things really ought to have been).
    Last edited: Apr 3, 2010
  10. Apr 3, 2010 #9


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    Not sure how this post followed as a response to mine, but anyway. The approach I was talking about, based on a logic of vagueness, prefers abduction to induction.

    Last edited by a moderator: May 4, 2017
  11. Apr 3, 2010 #10
    Sorry apeiron, i meant to quote madness's first post :blushing:
  12. Apr 3, 2010 #11
    I've always had a problem with this concept of perception (especially when it comes to space) because it suggests that there are pseudo-realities that exist outside the limit of our ability to experience them. Especially with space, which has been an obsession of mine, because it is something---even though it's nothing. And I refuse to believe that it behaves independently of our perception.
  13. Apr 3, 2010 #12
    Even within the image of reality you hold, you should be able to see that all your sensory perception is the result of something beyond your sensory apparatus that you CANNOT access directly WITHOUT the senses you are relying on.

    Now, what you do have in addition to your senses is the ability to process and synthesize them into a reality image. So why should you assume that the reality-image you have synthesized is something different from whatever is outside your senses causing your perceptions, even if it is separate, distinct, and not directly accessible to you?

    When you use the internet, do you wonder if what you see in the browser window is the same thing on the other side of the modem? If you don't, it's probably because it doesn't matter. As long as the browser window behaves according to your expectations and desires, you don't need to go further. Still, you probably know that what appears in your browser window is a user-interface that translates signals that are unrecognizable to you into ones that are.

    The question is why you would be obsessed with proving the existence of space (and time) outside of perception. Why would it be insufficient for you to think that space and time are just cognitive tools for organizing sensory signals for processing?
  14. Apr 3, 2010 #13
    I disagree. I think that if things like time and space are just a mental construction and its hard to even think of something which does exist independently, then we should treat these mental construction as fundamental. Why suppose the existence of these objective entities if we can't even imagine what they could be? And after all, our physical theories are all based on concepts like time and space and so they describe these subjective phenomena rather than anything objective (independent of our perception).
  15. Apr 3, 2010 #14
    Because it's true. You can treat them as fundamental, but why deny the truth that you are treating them as such WITHOUT denying the knowledge that you CANNOT know if reality outside perception and cognition resembles that which is perceived?

    I don't prelude every statement of observation with the phrase "I perceive that," but I am aware that I could.

    Ultimately I think it is most rigorous to recognize all statements and claims and all observations as perceptions. You can move from this level to the level of truth-power by asserting claims as statements and being prepared to argue your position and reasoning, but the truth is that you only know the knowledge you have without having any direct access to the referents of your knowledge.
  16. Apr 4, 2010 #15
    Yes, I know. But I still have them. Then what good are the senses if they're deceiving me.

    Doesn't matter. Whether I can directly see infrared with my eyes or use special glasses to see it---I'm still experiencing something from EMR that exists.

    There's a difference. I don't know what the 1's and 0's mean, but I do know what the end result is because that's the way it was designed.

    Because it exists and it is tangible and it must have properties---just like everything else. I truly don't understand why something that routinely exhibits a set pattern of behavior would automatically be seen as being a ruse from my perspective. I firmly believe that as long as it is contained within this universe---we can find out what it is and how it works.
  17. Apr 4, 2010 #16
    I don't understand what you mean here. I'm not denying that I'm treating them as fundamental, I'm just saying that any objective "thing in and of itself" is superfluous and necessarily something that we can't even imagine. It can't even exist in space or time in the way that we understand them, so why should we assume its existence? Supposing the existence of something which we can't even imagine and exists outside of space, time and cause and effect seems a lot like assuming the existence of God to me.
  18. Apr 4, 2010 #17
    The very idea that they are "deceiving you" if they're not transparently giving you direct access to what's outside you is problematic. Senses are receptors for unsynthesized information. The information becomes meaningful when it arrives at the processor. Coordinating motor-responses to sensory data is facilitated regardless of whether the image you're working with is a transparent representation or not. The point is that it is more accurate to say we can't know what exactly the form of things outside the senses is, rather than getting into debates about what that form is.

    But you know that the imagery of the browser window doesn't travel through the wires in the same form you see it on the screen. That is a level of truth beyond believing that when you click a link it is projected through a fiber optic cable to your screen without disassemby, encoding, and reassembly.

    It's not a ruse. It's a data field that is only accessible to you to the extent that your senses can perceive it, at it only appears and makes sense to you in terms you cognitive/neural network can process. You can investigate the patterns you discern in sensory data and theorize and test how things you perceive work. That is science. There is no need for transparent, direct access to reality to practice science.

    For whatever reason, cogntive-consciousness is capable of the range of thoughts, ideas, perceptions, etc. that it is capable of. It is capable of generating thoughts and then later interpolating those thoughts as wrong. It can imagine object things "in and of themselves" and then recognize that such things cannot be established objectively. It can imagine the idea of God and reason that if such an all powerful being or force/power exists, then it would also be capable of camoflaging his/her/its own existence as natural phenomena.

    The way I see it, you have the cognitive tools and your senses at your disposal to use them. You have a capacity to feel and the ability to empathize to develop and practice ethical judgment. Imo, you are a soul stuck in a body with whatever capabilities yours has and the only thing you can do is use what you have to try to accomplish your will. If you choose to observe ethical judgment, part of your will will include the will to avoid harm and possibly even increase positive experiences for yourself and others. If you are skillful and lucky, your choices and actions will have a positive result for yourself and others - but more than likely some negativity will also result; after all you are only human!
  19. Apr 4, 2010 #18
    I thought there was a general agreement here that the Physics Forum banner on top of this page does not exist in the same way we usually take for granted. I mean, the electrical current wired to the RGB diodes is what is really "out there" for the banner, though had it been possible for you to be trapped on the screen, you'd hardly be able to understand.

    Just because it intuitively seems like everything is interpreted 1:1 by our brains, doesn't make it so. If it's just some abstract, mathematical, probability fields out there, and everything else is a mental construct, I don't think many people would want to know.
    Last edited: Apr 4, 2010
  20. Apr 4, 2010 #19
    But why assume the existence of some "abstract, mathematical, probability fields" that are really "out there", rather than just saying your experience is what exists and these mathematical probability fields are a construct which models our experience?
  21. Apr 4, 2010 #20
    They are both. The experience you perceive is constructed by synthesizing perception via cognition. The "probability fields," or whatever you want to call what exists prior to sensory interpolation, are also a cognitive construction insofar as you are conceptualizing them as something or other. What it comes down to is that you can't get around the radical situatedness of perception and cognition within the living tissue of the body; EXCEPT to the extent that you construct reality as transcendent of its material basis.

    BTW, it's confounding to assume that whatever is going on outside sensory-perception is somehow mathematical, governed by probability or otherwise. Both mathematics and probability are synthetic abstractions constructed by cognition. Really, you have no choice but to make knowledge claims based on observations, synthesis, and reasoning. There is no transparent or direct access to a reality outside of that.

    The good news is that no one has ever done anything more that that - except perhaps to the extent that they were unaware of the impossibility of having direct access to the realities they thought they were describing transparently.
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