“The universe is inside us. It’s in you and you’re in it.”
There it is; my “spacescale” theory of cosmos! Not because the atoms of our bodies come from other stars, and not based on any other spiritual propaganda.
The universe may be inside us, literally.
I don’t have time to elaborate on this mathematically right now. Therefore, I briefly touch upon the informal concept only so I won’t forget this. I will get back to this at a later occasion.
This is just a theoretical (and yet informal) gameplay with axioms. But you can think of it as the main idea of a theory that its math can be written rigorously and its predictions can potentially be tested by experiments. The whole thing is new to me, too. So I just set out to document the idea.
I am sane and sober. This post is serious and not ironic. And no spiritual or metaphorical bullsh*t is intended.
If someone is raising eyebrows reading this, I would be happy to discuss the topic with them in more precise terms.
If you decide to go through this post, please read it with trust and patience. And with as little prejudgement as you can about me and my mental condition (!) as well as all of the perceptual biases fed to us by the dominant scientific culture of our civilization. Please bear with me carefully throughout this passage and read it with a very very open mind.
1. Conscious realism
Before going through the passage, watch this TED talk by Donald D. Hoffman. His work may turn out to be one of the most ground breaking studies of our time. And the implications of this approach to sciences are huge.
Hoffman claims that reality can have nothing to do with our perception.
Objective reality can exist as the source of cause and effect in the world, but to our counter-intuitive surprise our perception has NOT necessarily mapped it in any “real” way, but only in a useful way for fitness.
According to this approach the fact that we can “map” the reality and make a useful “autocad”-like software that others can also use, still does not mean that our very basics of geometric perception had anything to do with the reality. They are just one practical approach of interacting with it for survival.
His main thesis that evolution may favor fitness and not the reality is hard to grasp for two reasons. One that it is in contrast with our dominant scientific belief system and we are not used to do science that way. But a greater problem in my opinion is that his radical ideas are difficult to grasp for us humans, since we may have been deceived by evolution from the very early stages all the way till now. Thus this deception may be deeply rooted in us.
I must say I used to carry similar thoughts and thus I wrote this (Persian) for the philosophy section of the most popular reformist newspaper in Iran back in 2003, though the article was vetoed being labeled as an idealistic subjective viewpoint.
2. Relativism of geometry
I always thought that the geometry of our perception must be deceiving, simply because we have thought and worked it out with our brains. But I never imagined I would go this far to question the whole set of perceptual and intruitive axioms of geometry. And I am intending to do it here.
Let’s break the foundation of a geometric construct, such as any modern axiomatization of a geometry, into two sets:
1. Logical rules of deduction
2. Geometric axioms
Where did we get group 2? From our intuitive perceptual assumptions. They are intuitive so they must be right, we thought.
Playing with these two sets we have constructed intuitive (but not real) geometries that gave us engineering that – so far – helped us to survive better, so we assumed they must represent some sense of an objective truth. What went wrong? We took the latter too seriously. Our “intuitive/perceptive geometric assumptions” did not have to do anything with reality!
Evolutionary biology is the base of geometry, not the other way around.
Evolution is not probably the base of reason and logic (group 1), but it is the foundation of some of the intuitive axioms of geometry (group 2). Because of the intuitive and useful deception of this group, the resulted geometry and thus the whole physics and engineering we built on top of that was only a construct of our basic perceptions. Self-consistent, intuitive, and useful. But not real.
The catch is that the intuitive geometry that we built could be just a random artefact of our evolutionary path. Its axioms come from our profoundly biased perception, and we never fully doubted them, with a systematic and comprehensive map.
It was a historic choice. From Ancient egypt to Pythagoras and then Euclid we based our reasoning and built our sciences on top of a deceiving set of axioms about time, space, scale, and other fitness arteficts of our evolution. They were axioms of survival, not axioms of reality.
Did we make science on top of the most intuitive, yet most deceiving branch of it, geometry? Geometry is not pure math and reasoning. It did not have to be as universally as valid as logic, number theory or algebra. But it was assumed to be. Very simply put, the axioms of group 2 were just the artefact of our evolution and could be theoretically undermined, rewritten or completely deconstructed.
Omar Khayyam of the pioneers of Geometric Algebra said a millennia ago:
“Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved by propositions five and six of Book two of Elements.”
Khayyam was deceived himself and thought it in vain! Attention must be paid to the fact that algebra and geometry are different, in appearance, and in essence. Algebra *may be* a universal base for reasoning but geometric facts are just deception of our perception thatappear intuitive, to us. He even got the word “trick” right, but mistakenly refered it to “algebra”, instead of the “geometric facts”.
3. Deconstructing intuitive axioms
How on earth the “unified entity of space and time” and the whole concept of spacetime was intuitive?
It was not.
A century ago Einstein assumed this very weird axiom and deduced some theoretical, exotic and non-intuitive results from it:
Things get shorter and more massive when they move? Simultaneity is relative? Mass is energy? Gravity is a property of space and time?
None of this was, has been, and will ever be intuitive. You read them in books and newspapers. And Einstein was only brave enough to assume time and space to be the same thing, despite such a profoundly counter-intuitive sense. You are now used to it so you can’t percieve how crazy it may have sounded back then. Then he played around with the theoretical implications of this assumption and got even more non-intuitive results. Some of them were verified by objective experiments long later.
The weirdness of early quantum mechanics came from the same place, but the opposite order. Objective experiments showed results that did not satisfy our perception. Ever since theories and axioms has been rewritten in an ever increasing pace so they cope up with the experiments.
No matter in which order the axiomatic theories or the objective experiments arrive to us, after they are in agreement with each other, they are – both – to be trusted, not the intuition.
Relativity and quantum mechanics hinted us conservatively that the geometry of cosmos may diverge from our intuitive thinking of it. Or that the reality may be a generalization of our deceived range-limited perception. It may be far worse than that. The reality may have actually nothing to do with our perception after all.
This is not trivial. If you think this is what quantum mechanics has so far claimed, you are still deceived. This is far more radical. Thinking of cosmos, did we ever manage to remove our basic ingredients of intuitive perception from our written objective math? Even in the context of modern geometries, although we constructed slightly different topologies and geometries (say Riemannian) , weren’t they all still profoundly biased due to some of our wrong yet intuitive axioms?
In my manuscript on higher dimensional Euclidean geometry 20 years ago I touched upon the relativism of geometry. But I – sadly – did not deconstruct the Euclidian axioms and only generalized them to higher arbitrary dimensions. Historic mistake in sync with the society.
It is hard to think and not intuit [perceptually], but setting ourselves free from our perception and knowing that this may actually be a more scientific and “real” approach, although less intuitive (biased), brings new possibilities and we were unaware of those possibilities, as Hoffman says too.
In my interpretation, we never reconstructed it all perception-free. Until recently, and may be in string theory, or M-thoery may be we find axioms that are borrowed from objective experiments more than the perceptual bias? It’s not enough if you ask me.
Reality is not intuitive. But the good news is that it is achievable and objectively testable.
Now, let us deconstruct some basic intuitive axioms in new ways in disagreement with our perception, and still use reason and logicalcomputers (useful Turing machines) to rebuild new profoundly different geometries for cosmos. Then we double check its theoretical results and implications with old or new experiments.
And things start to get interesting:
4. Theory of spacescale
And now, ladies and gentlemen, let me deconstruct one of the most profoundly intuitive axioms of all geometries and sciences that you know of. And then briefly build on it to surprise you with its exotic implications. My time is short to elaborate now, so spitting out the short story:
I am asking, what if “small” and “large” are the same thing?
Of course counter-intuitive, but ignore your bias for a moment and read this:
Hoffman compares the faith of two organisms with simulation: One organism with a realistic perception of the truth, a “linear” fit-ness function of a given resource. The other with a non-realistic, wrong perception of the truth, a bell curve fitness-function. The truth sends the first organism to extinction, because it takes too much or too little of that resource. The deceived organism which has the bell curve fitness function, responds to the “just right” amount of that resource due to the distorted bell curved perception, whereas the organism who saw the truth, dies!
The organisms who could intuit about relativity, quantum entanglement, or wave-particle duality (things that we know from our experiments), die if their true vision did not help them fit from early days. Instead, we, deceived creatures who don’t even understand that time is space, reproduced and survived.
Back to the bell curve perception: We have intuitions about ”left and right” directions, “cold and warm” temperature, ultra and infra” light frequency, “in and out”, “past and future” time, “small and large” size, etc. They are not necessarily telling us how the nature works, but they are two asymmetric sides of a stimulus and have evolved in us to fit and survive.
Now I ask you what if “small and large” are actually the same thing in two different directions? Such as “back and front” in space.
Let’s deconstruct the basic intuition we have about “scale” and build a geometry on top of that exotic axiom where scale is a dimension in space.
Roughly speaking you get what you may call a 4D manifold, made of three spatial dimension, and one “scale” dimension. It’s like spacetime but “time” is replaced with “scale”. And they are unified.
I will get back to you why, with more accurate and formal description of this manifold and possible metrics on it, but for now accept from me that from which ever direction you move on the surface of it you get back to where you are. (the 3D surface of a 4D sphere, as an even-dimensional space can be combed due to the Hairy Ball Theorem, it has no singularity.)
If we simply assume the non-intuitive axiom that “scale” is “space”, despite the fact that just like “time” we perceive it very differently, then it has mind blowing theoretical results. Here’s one of them.
5. The universe is inside us!
This can simply be an implication of unifying scale and space on a combable 3D surface of a 4D sphere (3 space + 1 scale):
Choose a direction around yourself, literally any direction. Up or down, it doesn’t matter. Then zoom in it.
Look at your hand for instance. Say you zoom into one of your cells, any of them. You just keep straight and don’t turn. Then you zoom into it till molecular level. Then atomic level, and you see quarks and what not and when you zoom enough guess what you get: The whole universe! The one and the only universe. The exact same universe that you are in it. And you can repeat.
This video was probably made to demonstrate this visual effect of zooming from intergalactic to sub-atomic levels, but can actually be an implication of the spacescale axiom. Ignore the tilts and the cheats and the wrong microscopic objects that it shows, it is a good visualization of what you may expect from this theory.
And yes, it should have approached the woman on a side of the earth when the planet became visible. We expect to lend in the same eye of the same woman, not elsewhere, if we go on a straight line (a geodezy) on the surface of the 4-ball.
This video may be a bit better. It doesn not tilt and its sub-atomic particles seem more size-realistic. But it does not loop.
Here, zoom in scale may be just like moving in a physical dimension. It is not believable, but the theoretical predictions of this theory are objectively testable by experiments.
Just like space and time being the same thing was never intuitive. But was predicted by theory and then approved by experiments.
What if I claim “space”, “time” and “scale” can be all the same thing, and interchangeable? Despite our perceptive bias.
You zoom in something and it gets bigger, and you get close to something and it gets bigger. Same, same. Don’t stay biased. Remove your euclidean axioms.
Scale is just a direction in space? Is it just like “forward and backward” althought we percieve it differently as “in and out”? Just like time that is a dimension but we sense it as “past and future”, although they are just the same and interchangable?
The universe is inside us?
It’s in you? And you’re in it?
It’s not intuitive. But can be real.
In fact a one-sided space (such as the Klein bottle) you would actually look into your own eyes, face to face. May be that’s where we all came from.
I set a mirror in front of your mirror.
To build an eternity,
out of you.