In 1884 an English country schoolmaster wrote a book which still enthrals today. Mathematicians and physicists such as Carl Sagan, Michio Kaku, Ian Stewart and Stephen Hawking have all used the amiable inhabitants of 3D Spaceland, 2D Flatland and 1D Lineland from EA Abbott’s ‘Flatland: A Romance of Many Dimensions’ to show how geometric dimensions build and interact. In a completely original treatment, William Brown takes the simplicity of Abbott’s structure to another level by nailing down a set of universal principles and delving into the way the characters perceive their world.
The question is then asked...
Could such a structure undergird our world?
Today’s physics is at an impasse. Roger Penrose, Lee Smolin and many others write that we stand on the brink of a new paradigm. With waning confidence in String theory and the refusal of time to divulge her secrets, stuck with the arbitrary fix of Inflation theory, embarrassed by the refusal of dark energy to show up, and dabbling in science fiction with the multiverse, the Standard Model of modern cosmology is in trouble.
In addition, modern science has sidestepped all the richness of consciousness by answering the question What is life? with the simplistic assertion that aliveness is physical complexity, with little suggestion as to how such a process might operate.
Building on the thought that by taking for granted our ‘spatial’ dimensions of length, width and height we may have missed something of great import, the book describes - by extrapolation and analogy - a geometrically consistent nested hierarchy from which a whole new paradigm emerges, and out of which fall in an unforced way answers to many of our deepest questions. The shape of the universe, the nature of time and gravity, and the ascending complexity of life all take their place within an observer-centric dimensional structure which never deviates from the simplicity of Flatland principles.
The originality and logical consistency of this carefully considered and meticulously crafted application of EA Abbott's 'Dimensionality' to the real world could light a fire that may never require to be put out.
“The observer-centric model of the universe is very consistent.”
Dr Charles Wang, theoretical physicist, University of Aberdeen, Scotland
“I commend you on the persistence and energy you’ve invested here.”
Rudy Rucker, US mathematician and author
CS Lewis' words to Kingsley Amis on loaning him his copy of Flatland, December 1962:
"The original manuscript of the Iliad could not be more precious."
The Observer-Centric Universe
With the hemi-ball surfaces in full contact at every corresponding point, the lines that radiate away from and into each hemi-ball connect Centres A and B. The outer circle represents the distance of Centre A from Centre B, as viewed by the observer spherically in every direction by the 'Antarctica effect'.
It is not possible to depict or visualise this in reality because our minds can only picture spherical surfaces touching at a single point (as illustrated). However, in the manner of the 'rolling balls' experiment (Chapter 27) they touch simultaneously at every point on their shared surface, which constitutes the 2D equator. Note that, by rolling the balls, Centre A may be viewed from Centre B at the same distance in every 3D direction. This distance is the radius from the observer to the spherical surface of the observable universe.
This observer-centric model, although derived by extrapolation of the Flatlander's perception, is identical to Einstein's finite spherical model comprising the 3-sphere surface of a 4-ball (hypersphere), with the addition that the Big Bang origin is located at Centre A whilst the observer is at Centre B. This adjustment, derived from Flatland principles, holds great explanatory power.
"Took some time last night to look at what is happening currently in cosmological research. A lot of work is going into numerous theories on dark energy, dark matter, variable gravity/speed of light. The thing that struck me is the sheer gulf between all this and the observer-centric model, and it occurred to me that it may be very difficult for the world of physics to adjust.
This is not an unusual event in science. It happened with the luminiferous ether, phlogiston, caloric to name but a few. Unfortunately scientists, being human, become emotionally invested in particular theories and in many cases spend their careers on them. The most recent one to go would appear to be TeVeS (a relativistic version of MOND) which died on 17th Aug 2017 when LIGO got a result which showed that gravity and light both travel at c.
The thing that I don’t understand is this… what will it take to get them to go back and re-assess their interpretation of the 1998 distant supernovae projects? 20 years on cosmologists have all forgotten something: all that was discovered was a light anomaly – nothing more – from which they DEDUCED an accelerating universe, from which they DEDUCED dark energy, which 'makes up' 74% of the universe. Nobel prizes all round.
But where is it?
The model in terms of which the results were interpreted is, sadly, WRONG. There is no dark energy. I suppose that will eventually be realised. The observer-centric model is perhaps just too simple. It could have been hit upon 100 years ago had Einstein simply placed observer and origin at antipodal ‘poles’. However, although he described the model in 1916 (the finite 3-sphere), he didn’t take this critical step.
Carlo Rovelli informed me he is ‘skeptical for so big claims’. So skeptical that he hasn't got round to reading it (although he says he will). But I’m not surprised because, without altering constants, GR, or QM, the model
solves the horizon problem of CMB uniformity
explains the 1998 distant SNe Ia light anomaly
shows the universe to have net zero gravity (explaining so-called dark energy)
reveals the correct mechanism behind expansion
shows in terms of information transfer why both gravity and light exist at c
describes the mechanism by which the universe diminishes to a Big Bang singularity, and
provides a theoretical basis for the Equivalence principle.
In the process it dispenses with
the G/DE knife-edge
recent acceleration, and
the cosmological constant.
Read all about it… (start with Appendix 2 for a quick overview)."