Our e-dimensional universe

Here’s the layman’s explanation of my theory that physical space is e-dimensional (e = 2.71828…) (for links to the papers, see [1][2]).

It is easy to see that it is a surprising new idea that could lead to new physics, but how can physical dimensions be anything but 3? And the most troubling thing is that it is not even a rational number!

The answer is that three-dimensional view of physical space is merely a convention that we have gotten used to. We use this convention to mark points on Earth, but we can’t really check this easily at either the local or the cosmological levels.

In the big bang model, the universe expanded from a singularity (initial state of extremely high density and high temperature) which explains the cosmic microwave background (CMB) radiation, and together with gravity (whose origin is unknown but which is seen to work through either Newton’s or Einstein’s theory) it is consistent with the large-scale structure of the universe with its patterns of galaxies and matter on scales much larger than individual galaxies or groupings of galaxies.

There is divergence between the expansion rates obtained from early universe (captured by CMB data) and the late universe (considering the receding of stars and galaxies) aspects of the universe.

The divergence can be explained away of we accept that space is not quite three-dimensional, but rather e-dimensional

Why hasn’t it been thought of before?

The three-dimensional nature of space is an implicit assumption in Western physical thought and so it has not been questioned. When the idea of information is probed deeply we realize that mathematics compels us to abandon the assumption of a three-dimensional space (References[3][4][5]).

The beginnings of the universe and the nature of space are connected to many deep questions concerning not only physics but also philosophy. These include:

What is the origin of space?

What are the ultimate components of the universe?

What is the relationship between physics and consciousness?

What is space?

The formal use of three-dimensional space is part of modern physics. We can also speak biological space within which biological structure evolve.

Newton took space to be absolute and to be three-dimensional. This was extension of the Aristotelian view of the universe as a container in which the sun, the moon, planets and stars are embedded in perfectly concentric crystal spheres that rotate at fixed rates. In the observer-centric Indian physics that goes back to Kaṇāda, physical laws must be based only on substances, their properties, and their motion, but the experience of time and space is a consequence of the relation between the observer and the world being observed.

There is striking similarity between physical and biological structures. This must be the result of the commonality in the nature of physical and biological spaces, or perhaps the two are identical. Patterns in brain structure and the filament structure and distribution of matter in cosmology are quite similar.

But how morphogenesis may be related to biological space is not known. Indeed this could very well become an exciting new field of research connecting physics and biology.

A new theory of gravity

The new papers provide an explanation for gravity that has been missing in physics, for Newton’s law was based on experiment. The new theory doesn’t change the inverse square law of gravitation but explains why it has this form and suggests that gravity has weakened by about 20% in the last 4 billion years (Reference [6]).

According to current theory, about 96% of the universe is dark matter and dark energy (of which there is no direct evidence) and what is observable is only 0.5% (because another 4.5 % is interstellar gas). Although some scientists are confident that dark matter and dark energy will be eventually discovered, there is no observational evidence in support of it. My theory shows there is no need to speak of dark matter and dark energy.

It shows that the currently accelerating expansion of the universe will eventually slow down and finally reverse. This ties up many loose ends in current physics.

Meaning of e-dimensionality

What is the meaning of an e-dimensional universe? To answer this, we must ask what we mean by the word “dimension” (see References [2]–[7]).

Dimension 0 is a point, dimension 1 is a line, dimension 2 is a plane, and dimension 3 is a solid. An object with dimension between 2 and 3, or e-dimensions, is like sponge or cheese. Another way of seeing it as an object whose density in the limit is less than that of a three-dimensional object.

Fractals have dimensionality that is often noninteger. Two examples of fractals are the Whirlpool Galaxy and the Nautilus shell shown below.

But how can space be like a sponge, with holes? The answer to this is that the sponge-view is one way of looking at space; another is that dynamics itself is an expression of this sponge-like nature. Such disparate views can be harmonized by the principle of complementarity, which is one of the deepest philosophical ideas in science (see [8] and references therein).

The most astonishing thing about noninteger dimensionality is that it can be shown to be the origin of gravity. If gravity is a property of space, it solves a puzzle for which science has had no answer until now.

This research also explains the counterintuitive idea of asymptotic freedom [2].

It can have uses for the military, for space travel, and for the understanding of turbulence that Feynman called “the most important unsolved problem of classical physics.” It can also lead to insights that help in the design of novel metamaterials.


  1. Kak, S. Information theory and dimensionality of space. Scientific Reports 10, 20733 (2020). s41598–020–77855–9
  2. Kak, S. Asymptotic freedom in noninteger spaces. Scientific Reports 11, 1–5 (2021). https://www.nature.com/articles/s41598-021-83002-9
  3. Kak, S. Information, representation, and structure. International Conference on Recent Trends in Mathematics and Its Applications to Graphs, Networks and Petri Nets, New Delhi, India (2020).
  4. Kak, S. The base-e representation of numbers and the power law. Circuits Syst. Signal Process. 40, 490–500 (2021); https://doi.org/10.1007/s00034-020-01480-0
  5. Kak, S. The intrinsic dimensionality of data. Circuits Syst. Signal Process. 40, 2599–2607 (2021); https://doi.org/10.1007/s00034-020-01583-8
  6. Kak, S. Information theory of evolutionary stages in noninteger dimensional spaces. TechRxiv (2021); https://www.techrxiv.org/articles/preprint/Information_Theory_of_Evolutionary_Stages_in_Noninteger_Dimensional_Spaces/13775005
  7. Kak, S. Fractals with optimum information dimension. Circuits Syst. Signal Process. 40 (2021); https://link.springer.com/article/10.1007/s00034-021-01726-5
  8. Kak, S. Epistemic view of quantum communication. In Quantum Foundations, Probability and Information. Khrennikov, Andrei, Toni, Bourama (Eds.). Springer (2018).


For a deeper discussion for the layperson, see here: https://www.academia.edu/49175956/The_Measure_of_Space



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