Dimensions and Creativity: Part Two

I include here a letter I sent to Professor Max Tegmark at MIT outlining the ideas, mine and other people's, that got me thinking and prompted Part One and the upcoming Part Three of my Dimensions and Creativity posts.


1-Dimensional Mathematics, The Echoes of the Universe, Roger Penrose and the Endless Loop of Time





Abstract

Below I will put forward several ideas; from a question on the validity of mathematical infinity, to the Universe existing as a cycle with no beginning or end.



I will suggest that Heisenberg’s uncertainty principle is the arbitrary behaviour of unobserved particles and their ‘echoes’ in potential realities which, when observed, can be specifically located only because other possible but less probable locations are cancelled out and disappear without trace. I will suggest that the double-slit experiment can be explained as what happens on the rare occasion when we are able to detect two possible universes at once.



I will describe multiple universes consisting only of ‘potential’; a single pattern of probability in a wave of the most probable ‘reality’ expanding toward heat death and zero mass before eventually looping back on itself to create the beginning of space-time from its own end. Not, as Roger Penrose has suggested, a new universe, but the very same universe; its cause, in the absence of any measurable time or space required for a sequence to form, being its own death when the end gives rise to the beginning in a closed loop of Time.





Dear Professor Tegmark,



I recently saw the Horizon programme “What is Reality?” on the BBC and was interested to hear you say the Universe is not simply described by mathematics, but actually made of mathematics.



As you have a standing invitation on your website for people to contact you with their ideas I’ve sent you mine. I included an abstract above so you can see at a glance where I’m going and decide if it’s worth reading on.



With relation to how maths is embedded within the fundamental structure of the Universe, it occurred to me that maths could be said to have direction without width or breadth, which, by my understanding, would make it one dimensional. Could it be that maths is the 1-D aspect of the physical universe? I may be way off here, but isn’t maths, when you cut it down to absolute basics, a continuum with only increase or decrease in value as possible directions and no ‘sideways motion’ to produce additional dimensions?



If the Universe exists on a mathematical framework that’s being discovered piece by piece, is it possible the first dimension is where we find that framework? A blueprint from which the other dimensions of space-time emerge? That’s my starting point, from which I head towards a far bigger picture along the way taking in a few other ideas I think are related.



The title of this e-mail includes so many big ideas it would take too long in this format to convey in any detail everything I’m weaving together, so I’ll sketch out an overview of the points. The list below maps out a progression of ideas as I see it, some are mine and some are not. Much of it has been gathered from many places over many years to form a wider concept that seems to fit together quite well. I’m sure there are many flaws, but I’d like to offer it to the experts in case it is of any use or interest.



At the risk of sounding like a Lewis Carroll character, I’d like to start with infinity.





On Infinity:



Infinity is used happily by mathematicians, but to a physicist it indicates a serious error in their equations.



If the Universe is built on a framework of mathematics then ‘pure’ concepts like infinity are idealised and not functional. Perfection doesn’t seem to exist in this universe as the physics of non-uniform dispersal through inherent imperfections appears to be the root cause of diversity.



There’s a mathematician (whose name unfortunately I can’t recall) who claims numbers don’t increase +1 to infinity, but at some very big number they somehow return to zero.



It would be impossible, even for an indestructible counting machine, to add +1 infinitely without the end of the Universe interrupting. Infinity seems to me to exist only in manufactured spaces, like halving the distance between an arrow and its target so that it travels forever without hitting its mark; always a fraction closer. This isn’t what happens of course, so is it any more realistic to say numbers are infinite if space-time is finite?



If the above is true there must be a ‘maximum number’. Perhaps if you take the smallest possible division of Time and multiply it by the full length of Time, i.e. the full duration of the Universe, that yields the largest possible number that could ‘fit’ into Time before somehow resetting to zero. As odd and counter-intuitive as this sounds, it would parallel what Penrose suggests for Space.





On Waves of Universes:



In Creation Revisited Atkins describes the behaviour of light waves through air and water and the resulting refraction. Light waves, he says, travel by the quickest route from A to B, but to find it they must first try everything then eliminate all the ones that aren’t the quickest. Light has a short wavelength so any waves deviating far from straight lines quickly interfere with each other and cancel out. When light travels through different media the wavelength is effected.



I’ve heard that anything that can be described as a single object with momentum can be thought of as a wave, including the Universe itself. (I think this relates to deBroglie’s ‘matter wave’.)



If the Universe described as a wave has an extremely short (near imperceptible) wavelength it may create multiple possibilities that, from our perspective, instantly cancel themselves out leaving just one wave as the optimum, most thermo-dynamically probable, configuration of everything.



I suggest the medium the universe-wave travels through consists of the vast number of possibilities that exist (the total potential energy of the Universe) and that all thermo-dynamic occurrences and choices of humans and animals affect the ‘direction’ of the wave. Where choice occurs the wave would take on a local characteristic, perhaps of a specific complexity (could this one day be used to detect life in distant galaxies somehow? A good plot for a sci-fi story). This doesn’t argue for Determinism as it doesn’t imply causation.



The interference that cancels out the other waves and leaves the one that is our Universe, what we call Reality, is according to probability. The improbable doesn’t happen, the probable does. Where this is arbitrary it can go either way and gives us an opportunity to detect it with experimentation. These areas of our reality appear ‘fuzzy’ to us, as in the double-slit test.



If the probability of an event (e.g. the location of an electron, the path of a photon) changes due to interaction such as measurement, observation, etc., the wave behaves differently and becomes less ‘fuzzy’ as the number of probabilities reduces. If an electron is unobserved it has the potential to be in more than one place due to equal probability of being in any specific location; but once observed that’s no longer the case. The extra waves of probable universes interfere with each other and cancel each other out until just one is left in a single location. If the electron’s velocity is measured, rather than its location, the Universe has no need to be so definitive and location can remain ‘fuzzy’.



In the double-slit test, while the photons aren’t measured, they can be in two places at once because they always were. The photons appearing on the screen are those that aren’t cancelled out by interference. No photon is split in two, no new universe is created, in fact one of many possible universes is revealed to us. When the photons are measured as they pass through the slits the probability changes and we can see the edges of Reality change. An echo normally hidden from us disappears. Measuring the photons applies the laws of physics at an increased local level, reducing the probability to one location per photon. Wouldn’t this fit with quantum mechanics and go some way to explaining the apparent paradoxes?



In current multiple universe hypotheses each universe begets further universes and each of these begets even more, increasing exponentially. This requires a limitless capacity for creation; and surely that would include the creation of energy. But energy can’t be created. Taking Occam’s razor to the problem, if the same energy is recycled again and again as the waves are cancelled out and return to potential energy state, we don’t need to explain anything new. The standard model fits.



In this hypothesis however, each new universe exists only for an infinitesimal amount of time (is there a lower limit on splitting Time, and could the duration of the new universes define it?). If events in those universes are possible yet not probable they cancel out. They wouldn’t occur over noticeable distances because the wavelength is so incredibly short. This occurs at the quantum level yet is simultaneously occurring throughout the Universe, each wave contributing to the universe-wave, the tiniest and largest scales linked together. The particles of the whole falling into place individually to create Reality as we understand it. Schrodinger’s cat now begins to make sense.



For us to be able to do anything we have to ‘move through’ the medium of what is possible, but we’re confined by the laws of physics and directed by what is statistically probable. In the medium of time-space I can get up from my chair or stay put. For those potentials to exist there has to be something for the variant universes to ‘fit into’ or ‘flow through’, but each choice or variation doesn’t have to be the cause of a whole new ‘Reality’ in its own right. If the potential that forms the possible is recycled back into the whole the problem disappears.



The ‘flow’ of potential begins to explain Time’s singular direction and why things bigger than an electron don’t spontaneously appear from nothing. The laws of thermo-dynamics dictate what is possible and what is most probable. If physics theoretically allows for time travel or the spontaneous appearance of conscious minds such events don’t occur because the probability of them happening is negligible at every moment a universe-wave cancels out and the possibility never becomes Reality. We’re misinterpreting the statistics by thinking the odds get better as Time goes on. Each moment is in one sense a new universe and the odds are the same for each one as it comes into being. The reset button is pushed. The chances of a bowl of petunias and a sperm whale suddenly springing into being are small enough to be discounted.



Time doesn’t need to flow in a specific direction, an illusory arrow may have come about due to the nature of statistical probability. A cup falling off a table is statistically weighted to keep falling because gravity bends space making the probability of it not falling zero. It smashes when it hits the floor because entropy says it will. The number of permutations the molecules can take other than as a fixed cup are so many, breaking is so probable, that nothing else can occur in the brief moments where the universe-waves come into being and cancel out. We experience Time as the flow of events towards the unavoidably probable, it can’t flow backwards or be perceived backwards without violating probability. There’s no ‘rule’ against it, but the capacity for it to happen isn’t there.



On the End of Time as its Beginning:



Roger Penrose has theorised that the end of the Universe and the dissipation of all matter and energy into potential energy is the catalyst which creates a new universe via its own Big Bang.



Penrose may have overlooked that it doesn’t need to be a new universe. A sequence of universes implies a continuum occurring within a timeframe, yet Time only occurs within a universe. To put the process into a procession of one universe following another is simply to imagine our universe within a bigger universe that behaves the same. But that doesn’t address the issue, it just moves locus, I believe incorrectly, further out. I can’t see how a sequence can occur outside Time.



A thought experiment: Compare the life of a universe to a train journey; the train itself represents space-time in any form (temporal sequences, matter, energy, potential energy), and Passenger A represents an immortal traveller who loves riding on trains and is able to survive the birth and death of universes. Each train runs exclusively on its own track and the tracks all run in large circles so that all journeys begin and end at the terminus. The terminus is at the South Pole and all tracks run up the lines of longitude, cross at the North Pole and return to the terminus. Other stations along the way are not relevant, remove them and there is still a journey. Direction of travel is irrelevant. Imagine a journey ending; the train stops but Passenger A doesn’t need to board a different train travelling on a separate track to begin another journey.



Our universe may be a closed loop. Time ends but instantly begins again, the whole Universe returning to the start. In the final moments of space-time dimensions become immaterial and it becomes possible to return to the point of beginning without moving. With no mass, no distance and no passing of time what in one moment were the furthest reaches of the void in the next are indeterminate from every other point in space-time. Time as we understand it no longer functions with nothing physical to affect. The entire Universe dissipates to potential energy and is reduced to a single point in Time and Space, an indefinably tiny speck of nothing containing literally everything. The Big Bang is the beginning of Time, but also marks its end.





I’m not a physicist or a mathematician. If I had the skills to express these ideas as equations I might be able to spot the (no doubt many) faults in them and understand why no one has made these connections before or come to these conclusions. Maybe I’m totally wrong…



…but about ten years ago I had an idea that universes could repeat, this was coincidentally about the same time Roger Penrose began thinking about it, but I only heard about his theory this year. That gives me confidence at least some of my ideas are respectable and make some kind of sense.



I hope you’ve had time to read this email and maybe, just maybe you’ll decide to respond. I’d love to know if I’m way off or if there’s anything interesting in there.





Regards,



Richmond Strange BSc (Hons), BA (Hons), MBPsS

Dimensions and Creativity: Part One

In his latest book Stephen Hawking says philosophy is dead, claiming that it’s scientists who now make all valuable discoveries. The comment prompted a debate on BBC Radio 4’s The Infinite Monkey Cage (available to download on iTunes) where Brian Cox showed his less often seen dismissive and impatient side, usually reserved for astrologers. Prof. Cox begins the discussion from the perspective that Hawking is right and goes on to challenge the usefulness of philosophy, saying that science is the best if not only means to deduce and reason our way through understanding of the universe. I disagree with them.

What do we mean by philosophy? Maybe “the study of the fundamental nature of knowledge, reality, and existence” (OED online), but I think that definition misses something. To me philosophy is thinking a problem through at a time when there’s no available empirical research, constructing thought experiments where no physical experiments can be performed. Until the raw thinking is done there’s often no clear starting point for research to begin, but thought experiments can provide them through logical, axiomatic reasoning unhindered by the limitations of the laboratory. Einstein’s daydreams about the subjective experience of a man falling from a building prompted his theories of Relativity, but they have no place in the world of objective demonstrable data as experiments involving interviews of people thrown off buildings isn’t exactly ethical.

In the study of human consciousness psychologists often talk about a “black box”, by which they mean the unknown inner workings of the mind. At this point science leaves the stage and takes a long walk into the gathering dusk, hands in pockets and whistling tunelessly. It takes a philosopher to step up and take over the challenge because philosophers deal with exactly this type of problem. Daniel Dennett digs deeper into the matter than most psychologists have been comfortable to go. He has assembled data and opinions from multiple scientific disciplines, each of which have criticised him for wasting his time with the others, and he suggests that the black box is in fact a very poor and misleading way to frame the problem as there’s nothing within the brain that equates to it. It’s bad thinking and a trap easily fallen into (see Dennett’s book ‘Consciousness Explained’). When scientists run aground it’s sometimes philosophers who push on. Unbounded creative thought can sometimes lead to entirely new ways of seeing things.

In response to Hawking’s dismissal I wrote a blog entry almost entirely without scientific research. The introduction to that blog entry took on a life of its own and became the one you’re reading now. To avoid overkill I’ve split them into two parts, the first to introduce the background and inspiration for the thought processes in the second. Also to explain why I’ve gone off on a total flight of fancy in an area about which I know almost nothing and without benefit of information or calculation. In my deliberate eschewing of the scientific method I used creative thought to find my direction and logic to steer by. I was especially encouraged by my discovery that about ten years ago Professor Sir Roger Penrose started working on a theory describing the Big Bang as following on from and being caused by the end of a previous universe. It’s now in the public domain:

http://www.physicsforums.com/showthread.php?t=201377

And it happens that at around the same time I had come up with something that was essentially a scaled-down and maths-free version of the same thing. Go me! It all came about when NASA telescopes discovered that distant galaxies are increasing in velocity as they move further away from us, leading to the proposition of so-called ‘dark energy’, now thought to be the cause of the universe expanding at an increasing rate. You don’t need to be an astrophysicist to work out that if there’s a mysterious energy pushing everything apart then eventually all matter will dissipate; nor that once all matter cools to pure, massless energy, or even prior to that when all that’s left is a sea of photons, that the passing of time will no longer occur and the four dimensions of the universe will disappear, with Time going right alongside the other three spatial dimensions and leading, literally, to the end of all things. At that point time and distance become meaningless – all energy eventually becomes potential while mass and dimension are entirely absent from the universe. Imagining everything spread over near-infinite distance or concentrated into a single point are both errors. But it seems that even well-respected scientists have trouble getting to grips with this.

In the first episode of Wonders of the Universe Brian Cox describes the fascinating and awe-inspiring depths of time after the death of all stars and evaporation of the last black holes, but he trips up on his final point while stating that the arrow of time will cease to exist and the universe will continue in a perfect order of maximum entropy and total heat death “forever”. “Forever” is after all a direction in time which requires not only space but mass. A sea of photons has no mass and a dimensionless universe devoid of time removes itself from such pedestrian concerns as past, present and future, its here and now is indistinct from its beginning or its end. Roger Penrose takes this to be the clue to the birth of a new universe. I take it to be a clue to the birth of our own endlessly cycling universe, looping like the Ouroboros symbol of antiquity and of multiple unscientific cultures worldwide, which Plato, a philosopher, described as the first living thing in the universe.

Philosophers have always had far more freedom in their thinking than scientists and early philosophers lived in times dominated by imagination and symbolism. Scientists now often live in a world devoid of imagination. Philosophy has been shut out of science and science is the poorer for it. Creative thought is a fundamental part of human development yet it’s so often side-lined. People lack cross-discipline thinking and guard arbitrary territories behind lines drawn only for the sake of convenience:

Knowledge may be infinite and it may be borderless, but for practical purposes, we slice knowledge up into pieces and apply convenient labels that help us segment it into manageable portions for pedagogical purposes.

M. E. Kabay, PhD, CISSP

http://www.talkreason.org/articles/science.cfm

There are often good reasons for the doors being shut. The art world too demands a pedigree to show an artist is ‘qualified’ to contribute to the field from some deep-rooted personal value system and aesthetic understanding rather than applying themselves randomly. The difference is at times very hard to spot but is an essential aspect of modern art. Nature is quite capable of abstract beauty without human assistance so it’s possible to dupe unknowing art critics into heaping praise on an elephant with a paint brush. That’s not to say the elephant’s work isn’t of aesthetic value, only that the elephant is no more aware of the effect of her painting on others than a spider is aware of humans that stop to gaze at a web bejewelled with dew. It’s not the intrinsic value of a piece of modern art that resonates, it’s the value added to it by a human being holding it up and putting their name to it as a thing they wish others to be aware of and experience. The assumption, perhaps correctly, is that anyone (or anything) that hasn’t already proved themselves as a creator of art for art’s sake should be treated with caution. The world of science is not dissimilar. There are barriers and trials one must overcome before becoming an accepted member. There are uniforms, strange languages and obscure symbols. Scientists at times conduct themselves like a priesthood, custodians of the mysteries of the universe dressed in white vestments. It’s understandable, even forgivable, but their altar is sanctified by logic, reason, intellect and deduction. They seek evidence not proof, as nothing can ever truly be proven scientifically, only verified by repeatable demonstrations. Their beliefs are founded on demonstration while faith is anathema to the process, but an amount of faith is in fact enshrined within the most fundamental concepts of science: faith that humans must possess the ability to comprehend reality with some practical degree of accuracy, and faith that the process used for deduction, the scientific method, is the only correct way to go about it.

Neither of those tenets are arrived at scientifically. It’s not possible to do an experiment using the scientific method to determine if there are alternatives to it, neither is it possible to discover the limits of our comprehension through experimentation. We can’t manipulate the necessary variables or appoint a non-human control group for study. It’s easy to forget that before the endless waves of faultless logic begin a small leap of faith is required. What this means is, despite assurances that science is an entirely objective discipline, it cannot be so. It also means that science is a very human discipline and one that cannot remove itself from its human origins. To my mind that’s one of it’s strengths, not a flaw. Without it scientific research would lose its sense of wonder, its practical applications, its greatest achievements; it would become no more than a cataloguing exercise in patterns of matter and energy. As meaningless and directionless as nature, which despite a wealth of aesthetic beauty is devoid of intent or human message and is not art.

The most awe-inspiring, fascinating and beautiful thing in the known universe is simply this – to be human and to experience life here. It transcends individual disciplines and the territorial approach to knowledge, it cannot be categorised as any one thing or coherent collection of things. And it isn’t separate from the universe, life on the Earth, or even the matter and energy from which everything is made. The boundaries are ours and they are false.

*EDIT 06.04.11*

"I know Stephen Hawking well enough to know that he has read little philosophy and less theology, so I don't think his views should be taken with any special weight."

Sir Martin Rees, astronomer Royal

http://www.guardian.co.uk/science/2011/apr/06/martin-rees-templeton-prize

So Hawking was just sounding off against philosphy without doing any research.

"If I have the time and I'm not totally overwhelmed with things to do, then my mind constantly and gently chews over problems and often an answer or idea will pop into my head almost at random. Having the space to think is a genuine luxury, and vitally important if we want people to be creative in any job."

Professor Brian Cox

http://www.guardian.co.uk/science/2010/sep/11/science-stephen-hawking-brian-cox?INTCMP=SRCH

What is it Brian Cox is doing if not philosophising? To me the finger-pointing 'my dad's bigger than your dad' attitude shown by otherwise respectable and brilliant scientists is just an argument over territory - 'You leave the thinking to us and we'll just call it all science, even when it's not.'