Essay on Psi, Synchronicity, and Space-Time

#2
Here's another recent article (not mine) that asks the questions whether space-time is like a superfluid. I believe EthanT started a thread focusing on this idea a while back, but I think it's worth revisiting for this discussion if anyone cares to go there. This idea is rather old, but the modern-day formulation of it has probably been around since the early 1970's (P. Tewari and K.P. Sinha) or so, and every once in a while someone or some article chooses to revisit it. While I think space-time is too exotic to simply label it as "this" or "that", I think a superconducting superfluid is a pretty darn good analogy.

http://earthsky.org/space/is-spacetime-like-a-liquid
 
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chuck.drake

#3
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Sciborg_S_Patel

#5
Good stuff as always John. Couple points:

He defined science as “A method of thought which obtains verifiable results by reasoning logically from observed fact.” Only when curious amateurs and professionals alike pursue scientific truth in this way can meaningful answers concerning the origins of synchronicity (aka sync) be uncovered.
This is important. I think there's a somewhat disturbing trend to make scientists into high priests and humanism/materialism into a religion where we wait for revelations. Yet when looking for livable truth, at minimum, people should use a combination of caution, reason, and personal gnosis to guide them.

And who knows? In the search for personal truth one can live the seeker might find some fruit of communicable truth to bring back to the rest of us.

All too often however answers to questions concerning the mechanical underpinnings of synchronicity devolve into tired new age rhetoric and vague references to quantum physics.
I share this sentiment, and mentioned it when Tucker started talking about how QM could explain reincarnation. I find this will end up weakening the proponent case as QM is very complicated and many assumptions made by laypeople may not pan out in the future....or even in the present upon closer examination.

The world may simply work according to laws or principles of which QM is a subset or a convenient & temporary tool. Makes me more partial to Conscious Realism and the Implicate Order you subsequently mention.

Despite the noisy objections of most neo-Darwinian materialists, observation tells us we live in an ordered world pregnant with purpose and underwritten by cooperative interdependence.
I think you may want to link to some of these observations. I realize synchronicity is a well documented phenomenon, but I think many people may not follow you past this point without some evidence to read up on.

That said, I do like your consideration of anecdotes. I think the dismissal of all anecdotes of the Numinous as flights of fancy is an overreach, or at the least doesn't give one a path to livable truth.

For example the rapidly advancing field of Quantum Biology is revealing that most of the bio mass on planet earth, including our own DNA, function as coherently connected quantum systems. Human beings, birds, and even bacteria are making use of complex quantum effects on a macroscopic scale; something considered to be science fiction as recently as a decade ago.
Some links would be great here. I actually made a list of possibilities here if you need them!

Furthermore Chaos Theory and analysis of Non-Linear Systems have revealed the Universe to be a fractal order-building ecology far from equilibrium. This directly contradicts the Newtonian worldview of a clockwork machine spiraling toward inevitable entropic heat death.
My understanding is heat death is still all the rage among physicists? Curious about the importance of Chaos Theory & NLS here.

Personally, my intuitive sense tells me Penrose's idea of cyclical contraction & expansion is closer to the Truth than heat death but I admit I'm not basing that on any real math I've looked at!

So the million dollar question remains: What accounts for this stranger than fiction reality we find ourselves embedded in? The answer is revealed once we revive the concept of a Cosmic Ether.
This is the meat of the essay, and it's definitely interesting stuff. Will get into that portion in a bit. :)
 
#6
This is important. I think there's a somewhat disturbing trend to make scientists into high priests and humanism/materialism into a religion where we wait for revelations. Yet when looking for livable truth, at minimum, people should use a combination of caution, reason, and personal gnosis to guide them.

And who knows? In the search for personal truth one can live the seeker might find some fruit of communicable truth to bring back to the rest of us.
Right. It's that age-old debate whether science is a method or a position. When it becomes a rigid position that haughtily dismisses alternative possibilities, and refer to not looking at the relevant evidence as a "lack of evidence", it is no longer science.

I share this sentiment, and mentioned it when Tucker started talking about how QM could explain reincarnation. I find this will end up weakening the proponent case as QM is very complicated and many assumptions made by laypeople may not pan out in the future....or even in the present upon closer examination.

The world may simply work according to laws or principles of which QM is a subset or a convenient & temporary tool. Makes me more partial to Conscious Realism and the Implicate Order you subsequently mention.
QM is definitely important, I think it hints at the mechanism for psi for example, but yes I think its taken too far sometimes. I don't even mind that it's taken into goofy directions, as long as you can argue a good case for your point of view. But often people don't really understand what it is they're saying exactly, because most people's understanding of QM = Observer Effect & Quantum Uncertainty and little more. If you're going to enter into these sorts of debates, its important to be quasi-well-read on them. Don't have to be an expert, just read a serious, more "down to earth", book or two beside the new age stuff.

Bohm's interpretation of QM, in my eyes, is the clear best option. It is beyond logical. John Bell himself was a huge proponent of Bohm's interpretation of QM, and it motivated most of his EPR work, which he would've won a Nobel for had he lived long enough. Einstein even once said of Bohm's ontological interpretation, "I like what David has done."

But even Bohm gets knocked on by copenhagenists and many-worlds folks. I got into a quibble with a house-skeptic a little while ago who basically called Bohm's interpretation a "cult". That's the level of prejudice aimed at challengers to the status-quo, no matter how reasonable and well-developed the challenge is. If it's not popular, it must be a "cult".

I think you may want to link to some of these observations. I realize synchronicity is a well documented phenomenon, but I think many people may not follow you past this point without some evidence to read up on.

That said, I do like your consideration of anecdotes. I think the dismissal of all anecdotes of the Numinous as flights of fancy is an overreach, or at the least doesn't give one a path to livable truth.
Honestly the list would be too long. Purpose = Teleology, and teleology is obvious in biological systems. I think Paul Davies and Thomas Nagel both argue for this convincingly. Neo-Darwinists even believe in purpose in nature, they just think it is purely to propagate the "information" in our "selfish genes".

Most scientists want to do away with anecdotes because they require a certain amount of value judgment. It means you have to actually understand people, their motivations, biases, etc. and be able to arrive at an answer to their credibility from there. It's basically too much work, so the "objectivists" basically resort to a "fuck it all" type attitude.

My understanding is heat death is still all the rage among physicists? Curious about the importance of Chaos Theory & NLS here.

Personally, my intuitive sense tells me Penrose's idea of cyclical contraction & expansion is closer to the Truth than heat death but I admit I'm not basing that on any real math I've looked at!
It absolutely is. Most argue that self-organization is a temporary aberration and nothing more, even though clearly the universe has become far more complex since its beginning. I think cosmology is by and large a pretender science. Not "pseudo" necessarily, just totally lacking the ability to say anything definitively about beginnings. Maybe it was a one-time BB, maybe the universe cycles between expansion/contraction, or perhaps its eternal. Nobody knows, and all the "evidence" for one thing or the other is easily explained by the other model, with no definitive way to tell them apart in many ways.
 
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Sciborg_S_Patel

#7
Getting to meat of this essay, but wanted to mention three things I think might be relevant to you personally:

1) Nobel Winner Brian Josephson discusses the Pathology of Disbelief, touching a bit on how this halted Cold Fusion research.

2) F.David Peat discusses acausal principles and how this relates to synchronicity.

3) Kauffman discusses how creativity transcends mechanism, and avoiding the Galilean Spell of reductionism.

Okay, on with the show:

From this point on all further attempts at elucidating an objective ordered view of the Universe were seen as hopelessly naïve. This emergent paradigm provided fertile ground for a probabilistic interpretation of quantum mechanics to take hold soon after, further entrenching the idea of a random indifferent Universe governed by atomistic serendipity.
This is interesting - many proponents of free will often turn to the injection of Chaos offered by randomness but here you mark it as a challenge to the notion of higher order. Of course most people aren't familiar with Bohm's Neutral Monist take on reality via the Implicate Order in the way you are, but it is a nice "judo flip" against Bohmian mechanics shutting away any sign of human freedom.

He felt that what we perceive as randomness is an illusion; that what we actually experience as random happenstance is in fact a highly complex form of deterministic chaos.
Ah, that makes me think of Chaordic systems:
"The mix of chaos and order is often described as a harmonious coexistence displaying characteristics of both, with neither chaotic nor ordered behavior dominating. Some[who?] hold that nature is largely organized in such a manner; in particular, living organisms and the evolutionary process by which they arose are often described as chaordic in nature. The chaordic principles have also been used as guidelines for creating human organizations -- business, nonprofit, government and hybrids—that would be neither centralized nor anarchical networks."

Within this quantum underworld Information is exchanged faster than the speed of light between subatomic particles by what are called Pilot Waves. As a result coherence and mind-like behavior emerge on a macroscopic scale. Bohm’s Implicit Order provides a theoretical explanation for the “spooky action at a distance” that so troubled Einstein and accounts for the mysterious phenomenon of Spontaneous Self-Organization. Unfortunately these profound ideas are only accepted by a minority of the mainstream physics community despite their rigorous mathematical underpinnings and logical consistency.
Definitely check out Josephson's stuff, he's used the Implicate Order as well as Wheeler's ideas about consciousness giving rise to physical law to construct a consciousness centric view of the universe. If Psi ever gets established academically, he might be in for a second Nobel Prize in Physics. :)

If we come to accept the idea that everything was born out of a highly ordered Cosmic Ether, and that we have a dynamic relationship with the fabric of space itself, strange notions like synchronicity begin to make a lot more sense.
McGinn ponders similar notions in Consciousness and Space.

"I am now in a position to state the main thesis of this paper: in order to solve the mind-body problem we need, at a minimum, a new conception of space. We need a conceptual breakthrough in the way we think about the medium in which material objects exist, and hence in our conception of material objects themselves. That is the region in which our ignorance is focused: not in the details of neurophysiological activity but, more fundamentally, in how space is structured or constituted. That which we refer to when we use the word 'space' has a nature that is quite different from how we standardly conceive it to be; so different, indeed, that it is capable of 'containing' the non-spatial (as we now conceive it) phenomenon of consciousness. Things in space can generate consciousness only because those things are not, at some level, just how we conceive them to be; they harbour some hidden aspect or principle."

In innumerable ways the Ether seems to exhibit the properties of a Superconducting Superfluid, or a Bose Einstein Condensate. Superfluids are truly bizarre macroscopic entities that demonstrate a wide array of quantum effects when brought to sufficiently low temperatures.
This was really interesting stuff - I'd heard of superfluid but was not familiar with, frankly, how awesome it was. :)

The notion of fluid reality is one I'd heard before - that we are on the 3-D surface of a 4-D object. I think the 4-D objects may sit in 5-D fluid or something...was definitely over my head though it seems to align with your comparison of superfluid to ether.

Am I understanding correctly that this fluid precedes notions of space? Or just our 3 spatial, 1 temporal notions of space-time?

We may not be fully conscious of it, but we are engaged in a constant dialogue with the sub-quantum Ether itself. As components of an imponderable organism that we are forced to refer to as “Space”, we are analogous to highly self-aware cells. Despite their short shelf lives all cellular life serves a purpose, all cells have an important role to play, and all cells receive subtle signals and cues from their host environment. We too must pay attention to those subtle signals and cues if we hope to discover our higher calling. Otherwise we are likely to become nothing more than a cancerous growth.
Thoughts on this higher calling would be interesting. You mention the Great Work, which made me think of the spiritual goal of the alchemists:
"The image to be held before one is that every act by every person has an effect on all, changing the delicate balance that keeps the universe in motion. Therefore, it was considered necessary by the alchemists to so conduct their work and their lives, which were really the same thing, as if the salvation of the world depended upon it.”
-June Singer, Androgyny


I'd be interested in your familiarity with the subject of alchemy, or whatever spiritual ideas you have in mind here.

Understand that I am not implying that our lives, and the future, are completely deterministic. If complex systems analysis teaches us anything, it is that future states of a system are ultimately determined by some novel unpredictable X-factor. As humans we possess the unusual capacity to break old habits and create novelty. Therefore we are the X-factor. That is our collective purpose in the co-creative evolutionary process that lies before us.
This seems to be in line with Penrose & Lucas's ideas about creativity being more than mechanism without being reduced to randomness. Lucas even offers a similar conclusion to yours at the conclusion of his Godelian argument:

"Thus, though the Gödelian formula is not a very interesting formula to enunciate, the Gödelian argument argues strongly for creativity, first in ruling out any reductionist account of the mind that would show us to be, au fond, necessarily unoriginal automata, and secondly by proving that the conceptual space exists in which it intelligible to speak of someone's being creative, without having to hold that he must be either acting at random or else in accordance with an antecedently specifiable rule."
 
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Sciborg_S_Patel

#8
Comparison of Bohm's ideas with the ancient Hindu idea of Akasha - article by two time Nobel Peace nominee Ervin Laszlo:

The Akasha

The dimension that generates the holographic spacetime we experience is the Akasha. The Akasha harbors the geometrical relations that govern the interaction of quanta and of all things constituted of quanta in space and time. It is the seat of the fields and forces of the manifest world. The Akasha is the universal gravitational field that attracts things proportionately to their mass; it is the electromagnetic field that conveys electric and magnetic effects through space; it is the ensemble of the quantum fields that assigns probabilities to the behavior of quanta; and it is the scalar holofield that creates nonlocal interaction among quanta and configurations of quanta. The Akasha is the integration of all these elements in a unitary cosmic dimension that is beyond space and time. It is the fundamental, if in the everyday context hidden, dimension of the world.
 
#9
Sorry taken so long for me to respond but here goes:

Ah, that makes me think of Chaordic systems:
"The mix of chaos and order is often described as a harmonious coexistence displaying characteristics of both, with neither chaotic nor ordered behavior dominating. Some[who?] hold that nature is largely organized in such a manner; in particular, living organisms and the evolutionary process by which they arose are often described as chaordic in nature. The chaordic principles have also been used as guidelines for creating human organizations -- business, nonprofit, government and hybrids—that would be neither centralized nor anarchical networks."
Interesting. Had not heard of that term...I like it a lot. I also stumbled across "Chaosmos" recently as well listening to Robert Anton Wilson. I think it comes from Finnigan's Wake, but not 100% sure.

Definitely check out Josephson's stuff, he's used the Implicate Order as well as Wheeler's ideas about consciousness giving rise to physical law to construct a consciousness centric view of the universe. If Psi ever gets established academically, he might be in for a second Nobel Prize in Physics.
I will definitely get to your links. Thanks for putting those up, you always find the most provocative material in regards to these subjects. Josephson is a hero of mine, and while he gets much derision amongst mainstreamers nowadays, there are still a few who are brave enough to call him a "hero" as well for his work on superconductors back in the day (Steven Strogatz for example). I have even more respect for Josephson based on the fact that he successfully defended his theory of super-currents and Josephson junctions against the almighty John Bardeen in front of a crowded room for hours when he was only a mere graduate student (Bardeen being a two-time Nobel winner at the time if I remember correctly). That takes guts and an ungodly intellect to achieve.

This was really interesting stuff - I'd heard of superfluid but was not familiar with, frankly, how awesome it was. :)

The notion of fluid reality is one I'd heard before - that we are on the 3-D surface of a 4-D object. I think the 4-D objects may sit in 5-D fluid or something...was definitely over my head though it seems to align with your comparison of superfluid to ether.

Am I understanding correctly that this fluid precedes notions of space? Or just our 3 spatial, 1 temporal notions of space-time?
I think it works for both 4D & 5D. I think it precedes space, but I'm still not decided on whether time is foundational/irreversible or emergent/reversible. I lean toward it being foundational/irreversible (in line with Prigogine and Smolin for example). I think that anything that precedes space has to be a self-organizing entity that is all pervasive. Therefore, I find a self-organizing superfluid to be a good analogy. Others compare it to an exotic superconductor (like Nobel Laureate Frank Wilczek), or a self-organizing nodal cellular automata network (as in Quantum Loop Gravity or Ralph Abraham's model of pre-space), or an exotic virtual plasma (Moray King), or a liquid crystal (Aspden). There are so many models, and they are all useful analogies in my eyes, but I just picked the one that appeared to me to fit best. But to say space or pre-space is literally any of these things is probably incorrect. The absolute truth about space and pre-space are unknowable in my view. All we can do is work with models and theory craft and stay open-minded to new evidence.

Thoughts on this higher calling would be interesting. You mention the Great Work, which made me think of the spiritual goal of the alchemists:
"The image to be held before one is that every act by every person has an effect on all, changing the delicate balance that keeps the universe in motion. Therefore, it was considered necessary by the alchemists to so conduct their work and their lives, which were really the same thing, as if the salvation of the world depended upon it.”
-June Singer, Androgyny

I'd be interested in your familiarity with the subject of alchemy, or whatever spiritual ideas you have in mind here.
My knowledge is somewhat superficial, but good enough to understand the basics and understand how to integrate it into the material I'm better versed in. There are definitely certain truths existing in nature that inspired Alchemy (alpha-beta decay & even transmutations in cold fusion systems). And my view is that what the true Alchemists were interested in was not transmuting metals, but transmuting the human being. I've always viewed it as a methodology for personal transformation by playing with the information of the universe and transforming it into new models, etc. Somewhere along the way it got perverted, like all belief systems, and people think it was only about material wealth and transmuting physical elements.

This seems to be in line with Penrose & Lucas's ideas about creativity being more than mechanism without being reduced to randomness. Lucas even offers a similar conclusion to yours at the conclusion of his Godelian argument:

"Thus, though the Gödelian formula is not a very interesting formula to enunciate, the Gödelian argument argues strongly for creativity, first in ruling out any reductionist account of the mind that would show us to be, au fond, necessarily unoriginal automata, and secondly by proving that the conceptual space exists in which it intelligible to speak of someone's being creative, without having to hold that he must be either acting at random or else in accordance with an antecedently specifiable rule."
Other philosophers have spoken on the transcendent nature of creativity. That it is the thing that allows us to transcend the mechanical part of our being. Bohm, David Peate, RAW, Curtis White, amongst others.
 
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#12
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Sciborg_S_Patel

#13
More stuff that made me think back to your excellent essay:

Unbroken Wholeness: The Emerging View of Human Interconnection

The notion of a separate organism is clearly an abstraction, as is also its boundary. Underlying all this is unbroken wholeness even though our civilization has developed in such a way as to strongly emphasize the separation into parts. –David Bohm and Basil J. Hile, The Undivided Universe.1

"I suddenly developed a severe headache in the back of my head," the nurse said tearfully. "It was so painful I could not function and had to leave work. This was strange, because I never have headaches. When I reached home and was lying in bed, the phone rang. I learned that my beloved brother had been killed from a gunshot wound to the back of his head, the same place my terrible headache was located. My headache began at the same time the shooting occurred."
It's not just happiness that gets around. The team also found that depression, sadness, obesity, drinking and smoking habits, ill-health, the inclination to turn out and vote in elections, a taste for certain music or food, a preference for online privacy, and the tendency to think about suicide are also contagious.26, 27

Christakis and Fowler published their findings about the spread of obesity in large social networks in the New England Journal of Medicine, widely considered the most influential medical journal in the world. They showed that obesity in people you don't know and have never heard of could ricochet through you. They attributed the contagiousness of obesity to a "social network phenomenon" without proposing any specific physiological or psychological mechanism.28

To label something, however, is not to explain it, and to merely call this sort of thing a "social network phenomenon" has all the explanatory value of saying "what happens happens." In the commentary that accompanied the article in the New England Journal of Medicine, the experts who weighed in took the same tack. They discussed the genetic factors that influence obesity and the connections within and between cells in an individual that may contribute to overweight, but they too were mute about how distant humans might influence one another when they are beyond sensory contact.

Some suggest that the ripples work through the action of mirror neurons, which are brain cells believed to fire both when we perform an action ourselves and when we watch someone else doing it. But when people are remote from each other, there is no one to watch, and therefore no stimulus for the mirror neurons to fire. Others suggest that the spread is through mimicry, as when people unconsciously copy the facial expressions, body language, posture, and speech of those around them. There is a hint of desperation in these attempts to find some sneaky physical factor that mediates changes between distant individuals. However, when all is said and done, Fowler and Christakis 29 say they don't really know how happiness, obesity, etc. spread. The fact that your friend's friend's friend, someone you've neither seen nor heard of, is affecting your health has begun to rattle many of the gatekeepers in medicine
eta:

One such case reported to Playfair involved identical twin boys, Ricky and Damien, only three days old. Anna, their mother, would feed them during the night in her bed, propping herself up with pillows. On this particular occasion she had one twin, Ricky, in front of her, while her other son, Damien, lay on a pillow to her left. As she was changing Ricky's diaper, he suddenly began screaming. This was surprising, for even though only three days old, "he was a really good baby," Anna said, as was his brother. She could not figure out what was wrong, as he had been cleaned and fed. Then, still screaming, Ricky's body began to shake, as if he were having a convulsion. Anna reports that the thought suddenly popped into her head that "twins relay messages to each other." She looked down to check on Damien and, to her horror, saw that he wasn't there, but was face down in the pillows behind her. She immediately grabbed him and saw that he was blue in the face with his mouth clamped shut. Damien was suffocating. She and her older daughter began artificial respiration and called an ambulance. The terrifying event had a happy ending. Anna concluded, "Without a doubt, Ricky saved his brother's life. Had it not been for him screaming and shaking, I never would have looked for Damien until I had finished with Ricky, and by then it would have been too late."41
 
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Sciborg_S_Patel

#17
McGinn ponders similar notions in Consciousness and Space.

"I am now in a position to state the main thesis of this paper: in order to solve the mind-body problem we need, at a minimum, a new conception of space. We need a conceptual breakthrough in the way we think about the medium in which material objects exist, and hence in our conception of material objects themselves. That is the region in which our ignorance is focused: not in the details of neurophysiological activity but, more fundamentally, in how space is structured or constituted. That which we refer to when we use the word 'space' has a nature that is quite different from how we standardly conceive it to be; so different, indeed, that it is capable of 'containing' the non-spatial (as we now conceive it) phenomenon of consciousness. Things in space can generate consciousness only because those things are not, at some level, just how we conceive them to be; they harbour some hidden aspect or principle."

The Experience Of Space: Chaos Theory and the Evolution of Consciousness


I. INTRODUCTION
A. This paper is the beginning of a meditation on the notion of phase space.
B. I have the intuition that the notion of phase space is much more than a computational convenience I believe, rather, that it is a pivotal notion in the development of Western thought. If I am correct, the contemplation of the notion of phase space can bring clarity about both the explanatory power and the blinding limits of the scientific enterprise in general, and about the science of complexity in particular.
C. This paper attempts to begin the meditation on phase space by contemplating the evolution of consciousness which makes the notion of phase space possible, and by defining phase space within that context.
 
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Sciborg_S_Patel

#18
Thinking Straight About Curved Space

For in contemporary physics, space is curved, or non-Euclidean. In non-Euclidean space, the sum of the angles of a triangle may be greater than 180°; more importantly, the shortest distance between two points may not be a straight line, but a curved one. Matter, it is asserted, warps space (strictly, spacetime): its gravitational field bends space (and dilates time). Any change in the amount and distribution of matter will change the curvature of spacetime. Euclidean geometry is the geometry of a space whose curvature is everywhere zero – the geometry of the imaginary space of a matter-free universe.

When we first hear talk of ‘curved space’ we rebel. The least we should ask of something said to be curved is that it should have edges, surfaces, and parts that look or feel curved, which space itself does not. Analogies are offered to make the idea less counter-intuitive. We are invited to think of a journey over the surface of the earth or any spherical object: the shortest distance between one point and another will inevitably be (or rather be represented by) a curved rather than a straight line. A straight line in the Euclidean sense doesn’t exist in curved two-dimensional geometry. And the sum of the angles of a triangle inscribed on the surface of a sphere will add up to more than 180°.

Those willing to think for longer than two seconds will see this explanation as a fudge. It is entirely possible, for example, to connect two points on the surface of a real spherical object such as the earth by a straight line, if you are willing to dig a tunnel. What’s more, while the earth may have a curved surface, it is not curved ‘through-and-through’, as curved space (which lacks surfaces) is supposed to be. The earth’s surface is curved, but within this surface, its substance, the material of which it is composed, is neither straight nor curved. That is why we can take straight or curved pathways through it.

Physicists will smile at taking the analogy too literally. But if it is not taken literally, it lacks explanatory force. And taken literally, it is seriously misleading. The curvature of an object such as the earth is extrinsic – evident in its surface. The putative curvature of non-Euclidean space is intrinsic: it is present at every level above that of an infinitesimally small spatial point. So resistance to the idea of curved space does not arise from a superficial misunderstanding that can be cured with the help of a simple analogy. Rather, it is resistance to the odd idea that emptiness can have any topology, curved or straight.
We are now in a position to understand the origin of the counter-intuitive – indeed unintelligible – notion of space being curved (or indeed, having any kind of topology). It arises from projecting into space our mathematical portrait of the influence of gravity on the trajectories of objects. However, by using an everyday term such as ‘curved’, we are conflating an appearance, as exemplified in the surface of a spherical object or the parabolic flight of a thrown missile, with a mathematical abstraction capturing the change in the position of an accelerated object with time. This is a prime example of what in The Concept of Nature (1920) Alfred North Whitehead called, “the muddle of importing the mere procedures of thought into the facts of nature.” In this case, we are translating handy ways of depicting (and hence predicting and calculating) the influences of gravity on the motion of objects (and indeed of light) through space – bending their trajectories – into the structure of space itself. Nevertheless, the fact that the mathematics of motion in space and the curved shape of graphs of position against time are congruent does not mean that space is itself curved, nor that it makes sense to say so.

The Distortion of Space
The unintelligible idea of ‘curved space’ is the product of misidentifying a system of representation with that which is represented. This habit has a long history. From Pythagoras onwards we have been prone to the illusion that our ways of geometrising space capture space itself – perhaps even believing that the mathematical logic of pure quantities is somehow ‘out there’. However, the immense power of mathematical physics – which requires abstracting from phenomenal reality and the reduction of experienced and experienceable reality to mere parameters to which numerical values are assigned – does not justify uncritically accepting concepts such as ‘curved space’ that attempt to re-insert phenomenal appearances into its abstractions. On the contrary, we should acknowledge that ‘unreasonably effective’ mathematics (to borrow Eugene Wigner’s phrase) can take us to places to which nothing non-mathematical corresponds. For instance, consider the assumption, central to modern cosmology, that space itself is expanding. It is not idiotic to be puzzled by the very idea of expanding space, given that ‘expansion’ is usually of stuff into relatively empty space. Thinking of emptiness expanding into something that is not even emptiness is more than a little odd.

Physics, and the technology based on it (and indeed our civilisation), has flourished by being prepared to set aside the common sense that tells us that the earth must be flat otherwise people will fall off it, that a small object will always fall slower than a big one, and that the state of rest and motion in a straight line are fundamentally different. But we should not conclude from this that the mathematical portrait of the world is the last word on what is really there, or that everyday experience of lived space is in some profound sense defective or even wrong.

In The Production of Space (1991), Henri Lefebvre, the ‘philosopher of everyday life’ reflected that, “Not many years ago, the word ‘space’ had a strictly geometrical meaning… In scholarly use it was generally accompanied by some such epithet as ‘Euclidean’… and the general feeling was that the concept of space was ultimately a mathematical one. To speak of ‘social space’, therefore, would have sounded strange.” We should recognise that the notion of ‘curved space’ is less legitimate than that of ‘social space’, however useful the former might be for the development of mathematical physics. And we should not be pressured into thinking that the space of daily life, which is neither Euclidean nor non-Euclidean, is somehow not the real thing.
 
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