The ‘geometry’ of existence!


The lower level dimensional space enveloped by the higher space above and so on…


During this holiday season, I wish to leave the readers with some thought on the shape of existence. Probably, despite my intention to bring light upon this subject, I might leave you in doubt or confusion. But remember, it is upon the eyes of the beholder to make sense of what they see, and interpret to their utmost pleasure.

‘Geometry’, the mathematical science of the shape or curvature and arrangement of the internal structure of an object. It measures how the internal features of an object change and differ along its surface and volume. Topology in contrast, is a study of objects that might differ in geometry, but somehow appear to be similar, such that the union of objects under consideration are members of the same family. For example: A sphere and a cube are topologically similar, as they both can be inflated or deflated without addition of any external object or feature, in order to be transformed into each other. Whereas a sphere and a donut are not similar, because you cannot transform them into each other unless you carve a hole in the sphere or vanishing the hole in the donut, I.e without subtracting or adding something, they are not interchangeable. Though geometry may differ in all cases.

I suppose, the difference has been established above, as tersely as possible. I wish to move to its application on our existence and the universe. Now I will start with the topological aspect of things. There is a metric called chern class, developed by the mathematician S.S Chern. I will not go into the technical explanation, but for the purpose of my intended topic, I will try to simplify it in lay words to the best. It describes the number of dimensional objects that can fit into another particular dimensional object. It somehow tells us more about the nature of the bigger space that holds the smaller ones inside it, which will facilitate my elaboration of this math to the Universe itself.. For example: A one dimensional line can accommodate a zero dimensional point or the line itself, I.e zero or one degree of movement. Similarly a two dimensional sheet of paper can accommodate, a point, line and even a drawing of any two dimensional like a square or a circle I.e x-y axis movements.

Moving to our universe, it supports all the sub-objects or I would refer to them as sub-manifolds, from three to zero degrees of movement. The highest level of sub-manifolds it supports is three in accordance to its own physical dimensions of three. According to this geometrical observation in existence, we can understand that there always exists a manifold with dimensions that are equal to or higher than the highest dimensional sub-manifolds it can support. In short, if ‘n’ if the number of sub-manifold’s dimension then there always exists a space or more accurately a manifold of the dimensions ‘n+1’ to contain it. So if our universe supports 3-dimensional objects there has to be a space that is holding this 3-dimensional in a 4-dimensional arrangement. And a 5-dimensional arrangement holding that 4-dimensional space and so on, who knows this goes on till infinity.

Now geometry of space is the internal arrangement and shape of the universe. This geometry is defined by how it it is being stretched apart in that higher (4,5 or x-dimensional) space. As the universal space is stretched, it decides the shape of the space at any point and hence the shape of the object that is formed at that point. Remember it is always the vessel that defines, what shape the fluid that is filled in it, will take. So for believers of higher power in an objectified form or energy, that exists outside our universe, from this I wish to demonstrate that if that higher power is external species sitting outside our universe creating and affecting it, then they must be sitting in the 4,5, or x-dimensional space. Then as geometry and topology works, there has to be a space above encapsulating them. The most rudimentary understanding that can be gained from our existence and the space we inhabit is, that without a containing vessel, what could take shape and form. So, technically there might never be a God, as there always be a vessel of higher dimension containing above and above in layers, deeming the lower dimensional being, always lower in rank. Even the multiverses concept require a space of high enough dimensions to hold all the multiverses.

I do not intend to preach any idea, or offend anyone’s belief, it is only my intention to put light upon basic observation of existence and what it could mean for our understanding of it. Even if there is a higher power, we could never understand it, especially if it extends to infinity. And that true higher power might not have an objectified form.

The shape of things and the surface they exist on, are the determining factors for the physics that prevails in a system. Everything that may exist might be a geometry of infinite or unknown layers of dimension, something ever unfathomable by human mind.

10 thoughts on “The ‘geometry’ of existence!

  1. Ah yes, the long awaited post! 🙂 A sensible, simple concept, yes. But whoever said God/ Source sits at the top of it all, looking something like a glowing Dumbledore, overseeing everything like some overlord 😀 God may or may not, at the same time, be anything, in any state/ form, does not necessarily have to encompass the universe in it’s entirety just bcoz He/ She/ It is the source. I think that if such a thing as God/ Source/ Energy gestalt could create everything in existence today, I’m sure this supreme being can figure out a way to cut a corner for itself amidst it’s creation 🙂
    All in all I really enjoyed the post, thank you for that! 😀

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  2. Why do theoreticians always conjure new dimensions? We don’t experience any dimension but the three spacial dimensions of the universe. You are looking at equations when you should look at the real world around you and try to explain it – that would be science.


  3. Thanks for reading Swetha :). The thing is, I did not discuss this idea, with the intent of just saying that God sits outside our space, but many religious belief do support that. And technically to create something, for example for the sake of humor. Say if I might be a God, in objectified form, I could create a universe in these dimensions like create in an external box like or something or I could like create if possible a 2-D universe on my skin like a tattoo, or may be something within my body if since that’s possible. The highest number of dimensions I could create would still remain 3, and then above that something has given shape and form to me, I.e the bigger universe itself and then something might have given form to that universe and so on. anyways I feel you are seeing this post from the perspective of a God still in objectified form. Whereas I merely discussed it as an addendum to my idea, which originally was, that our space could just be a subspace of another and that outer space might be further a subspace of another and so on. Because as per geometry a manifold can exist only if there is some other bigger manifold to contain or express it. due to this virtue, we could never really point to a true creator, especially if some believe in an objectified God, as there always be a superior space.

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  4. Thanks for reading Mr Hall! whether you believe or know it or not. mathematics is the language of the universe. All the science we know about our existence and the universe today, was first mathematically expressed and then realized in practical nature. Though undeniably a lot of things have happened vice-versa. We do not experience a lot of things that doesn’t mean they don’t exist. Our body is so unreliable at experiencing nature that we cannot differentiate the most subtle of phenomenons that shape bigger events. In our own body, one can never tell that he/she is going to be sick day after tomorrow, something that has started to brew may be a week ago. A lot of things are claimed but mathematics provides a way to establish something through symmetry and consistency in its realization. geometry makes sense, only if you wish to see it that way. Just by observing the shape of daily life things you can figure the pure geometry at work. My intention was not to discuss dimensions in this post as I have done that in previous posts, it was to consider an idea that there may be something holding our universe inside it, as an implication of geometry and then that something might be held inside a bigger space and so on. An infinite process probably beyond human understanding, maybe because we are represented by just 4 dimensions , 3 of space and 1 of time. A limitation of the space that we are contained inside.

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  5. Dimensionally then, lesser dimensions fit in higher dimensions ad infinitum. One logical response to this paradigm is that what is lesser is an integral part of all that is greater as if the greater universe is always observing itself from its lesser parts.

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  6. Yes that is the other side of viewing it. That could quite be a possibility but it would still create infinitum as it is also about geometry, on what do we think is our universe expanding, I’m sure you’d not disagree that our Universe expands as its already realized. It needs a manifold to contain it’s expansion and not just contain but experience that expansion. That bigger manifold facilitates that. And then if you think, that bigger manifold must have a higher container to hold it and that gives infinitum. But obviously there must be more to it but how will we ever know. The physics that we experience evidently does require the need of higher dimensions.

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  7. Hey Prateek! Thank you for the elaborate explanation. Actually, I did understand your post with the meaning you intended. I do agree with the idea that our universe could possibly be infinite sets of containing space, each containing one and in turn being contained in another. Now, I am not talking of God in connection to your post content. This is a very general, out of context, supposition on the idea of a Creator. I do not really have any thoughts or ideas on Source’s/ God’s form/ formless existence or its existence at all. The reason being, there are many things we do not know of or understand yet. We are perpetually in a state of learning and discovering. Anything is possible and that also includes God’s non-existence! However, what I do feel is that everything around us including the observable universe is systematic and not the least bit random. It functions coordinated on some laws/ forces/ constants and all of it had to be just right in order for everything to exist and in the way it does today. To assume that all this came into being randomly/ accidentally is just something that does not resonate with me. Whatever it came from, however it exists, need not be from and regulated by this God, the image religion offers us anyway. But, in my opinion there must be some source out there. 🙂

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  8. A great comment Swetha 🙂 you are absolutely right that there is order in the universe, but it is derived out of chaos. The mathematics is infinite, out of unimaginable number of quantum combinations, the one that can survive at the energy state of our Universe, leads to the bigger picture and the flow of universe that we see from our naked eyes and understand with our coarse senses. I can never say for sure myself what could be driving this super sophisticated mathematics, strings, fluxes and fields or may be even something above that nothing is guaranteed to absolute certainty. but it sure is a perfectly coherent mechanics and in ways a work of ultimate art.

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  9. I couldn’t agree more with you. It is a wonder and perhaps a puzzle that will take a long long time for us to make sense of 😦
    I must admit I do enjoy, at least as much as I can comprehend..hehe.. reading your posts. Look forward to many more!

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