There is a school of thought in cognitive science, sometimes known as "Quantum Interaction", which tries to model aspects of cognition with the quantum formalism. See Diederik Aerts, Peter Bruza, and especially Keith van Rijsbergen's "The Geometry of Information Retrieval", among many other people. They hold conferences, so there are plenty of papers to read.

Maybe the Many Minds Interpretation has some mileage in it for your purposes

I do want to think about the overall theme for a bit before commenting, but I want to point out that one group many of whom would be happy not to be stock brokers and most of whom have senses of humor that may seem to most other people as rather strange are mathematicians. Physicists may have strange senses of humor, but I know far too many of them who've become quants, if not brokers.

Also, many of the scientific-minded people I know who have senses of humor that are odd (like mine, I must confess) are jugglers. Just saying.

With regard to the essay: "Since magnetic fields can easily penetrate the brain and do not collapse wave functions, one possible candidate for an oblivious link between two brain centers might be a slowly varying magnetic field. Two humans with their heads immersed in the same oscillating magnetic field may be the first people to actually experience the pleasures of rapprochement, a new kind of quantum-mediated telepathy."

Sounds very easy to do the experiment - has he tried it?

Quantum thinkers will be awesome at finding parking places.

Feynman always rubbished the idea of: "the collapse of the wave-function" IIRC Again, you are not confronting the duality represented by the double-slit results, now we can fire individual photons, sequentially over time. Displaying an underlying order, on which we have no "handle" (yet)

QC is a wonderful MacGuffin, but I seriously wonder at its supposed real power - I predict that P = ? NP problems will remain intractible for instance.

What QC add-ons to humanity might/would do is give us extra senses and hightened perceptions. That in itself would open a lot of closed or only-just openable doors?

This reminds me of Greg Egan's "Quarantine" where the protagonist, with his brain in a non-wave-function-collapsed state, conducts a house to house search of an entire city. All at once.

And a little later, EVERYONE temporarily gets a non-collapsed state, and things get weird.

Your drawings are like colored Rorschach tests.

Quite a lot of people seem to disagree with "the collapse of the wave function" as a real thing. In Penrose's book that inspired Anathem (I have to wonder how, given the difference in quality between the two) Penrose discusses the collapse of the wave function as an artefact of our currently limited and incorrect understanding, or some such phrase. Given it was still in the section where he was discussing things about which he did know something, I assume he was broadly right.

I did, however, watch Brian Cox's recent BBC show "A Night With The Stars" and although a lot of it was old hat to me, he explained something about the Pauli Exclusion Principle in a way I'd never heard it before. If we could tap into whatever mediates that, computing just takes a huge leap or five forwards. And while it's not QC as I normally think of it, it would be a fair name for a useful McGuffin.

Every object supports a very intricate quantum computation. Think of a septillion or so particles hooked together by intricate forces, all of them vibrating. Clearly any object is a universal computer with a very rich range of readily accessible states.

Most objects I encounter seem to be special-purpose computers at best. This rock on my shelf can only execute Room Temperature Lump of Granite 1.0 in its current environment. The advantage is that it's extremely efficient compared to general purpose computers; it would take more than 10^40 floating point operations per second on a classical programmable computer to reproduce the atomic-scale behaviour of one small rock with good fidelity.

Along the same lines, guessing the floating-point "equivalent" of human brains is Not Even Wrong. Human brains are notoriously bad at performing floating point operations and computers are notoriously good at it. Just like the mathematically rich atomic-scale dynamics of a room temperature rock aren't fungible for some other kind of mathematical work, the rich dynamics of the brain are not fungible for fabulous numbers of floating point operations or SQL queries.

The question going the other direction is at least not ill-founded: how many floating point operations per second does it take to simulate a human mind indistinguishable from the original? The hard upper limit would seem to be whatever it takes to run dynamic quantum chemistry for a human central nervous system at atomic scale resolution; something out of reach even in the unlikely event Moore's law continues another 100 years. The much lower estimates I've seen, in the petaflop-exaflop range, can be regarded as wild-assed guesses hopefully papering over large unknowns.

Cox seemed to be saying something about the Pauli Exclusion Principle that I've never heard anywhere else, and I'm deeply sceptical about it: that no two particles may have the same quantum state at the same time. Anywhere. In the entire universe.

If that's so, then yes, there's something deeply weird going on.

My previous understanding was that they can't have it in the same place - so within a single atom, you get the energy shells, you get volume, and so on. But his version would lead to the theoretical possibility of an Ansible. Not to mention that our observation of what appears to be the same state within different atoms must be different states, so what prevents the different electrons within a single atom having those apparently indistinguishable states.

Should the quantum state include the position though, then fine. But that doesn't then require magical across-the-universe communication with other particles that don't share the same position.

That's what I understood him to say too - and in several different ways at different times.

That's really what made me wonder - a slip of the tongue in a lecture to give that impression incorrectly is one thing. But when he essentially repeats it in different ways, seems like he's either completely wrong about something or he's saying something I didn't know that's new understanding.

He's certainly in a place to have far better understanding of it than me, particularly new interpretations - and yes it certainly suggests ansibles and the like. But he could have been talking rubbish of course.

I strongly suspect that he was trying to say something a lot less controversial, but was faced with a comprehension gap between him and, say, Sarah Millican.

Which is not to say I wouldn't spend money to see Millican - I'm currently waiting for some tickets to arrive - but she's a stand up comic whereas Cox is a boy-band keyboard player, and they don't always connect.

One very interesting modern result with regard to the double slit experiment is that by performing weak measurement one can determine which slit a particle goes through without collapsing the interference pattern.

"My previous understanding was that they can't have it in the same place - so within a single atom, you get the energy shells, you get volume, and so on."

If it is in a different place it is in a different quantum environment which also helps to uniquely define it. I don't see the problem.

"The SF dream is that there's some new and exciting angle, a different tech, a clear and simple insight,..."

There is, Rudy, there is... people keep forgetting that neural nets are pattern recognisers and no more. They need other techniques added to them, and there is a lot out there. So many in fact that not all the avenues have been explored... They only need to be put in the right order with the right connections...

I always understood the Paul Exclusion Principle as "no two two fermion particles (particles with spin n/2 statistics) may have the same quantum state" where the quantum state included position in space-time. For instance when we talk about the state of a proton, we speak of its momentum and position as complementary parts of its state.

In any case, we don't need to remove position from the Exclusion Principle to get nonlocal connection between particles: bosons don't have an exclusion clause in their contracts, and so you can cram a lot of photons into a single state (which is pretty much what a Bose-Einstein Condensate is).

Oops, that should be "particles with spin n/2 statistics for n odd", since n even refers to bosons.

wonder if thats what 'being in the zone ' is

This being sf and presumably "better at math" is doing yeoman's work as a stand in for "more intelligent", why not go with the premise that the Platonic realm of mathematical forms is real and that different people can more or less directly perceive it through some QM hand-waving? When certain gifted individuals explain that they just "see" the results rather than arriving at them through baroque chains of induction or massive and intricate numerical computations, they really mean it.

Nothing new under the Sun, of course. Hardy with his tongue firmly in cheek speculated thusly about Ramanujan's facility with numbers, for example. The QM hack is just a new coat of paint on an old, old idea.[1] One that doesn't get enough attention as an sf trope, imho.

[1]Don't give it much account, myself. But it sure is entertaining to read about :-) Actually, if I'm not mistaken, RR has done this one already in White Light.

I am a person of Little Mathematical Quantitativeness and so i am inclined to say.. if That is ' True ' Then, Why Do Two and Two make Four?

It gets plenty of attention from Penrose

I'm reminded of one of Jill Bolte's descriptions of her damaged brain when she said that she couldn't sense where her body ended and everything else began. This seems similar to the descriptions of "everything is connected" some people express when part of their brain is disrupted.

Could your protagonist have some sort of similar disorienting sense when accessing the uncollapsed mode?

If the brain has a relatively discrete module that gives one the impression of separation from the environment, could a module connect you to another module that accesses an uncollapsed state and also triggers the collapse in order to read it?

I also can't help feeling that this might be related to "jaunting" (The Stars My Destination).

The powers shown by the "the Fraternity" (Wanted) in the movie might well be based on determining the best outcome for any action and collapsing just that state. One episode of tv's Fringe was similar too.

"Surely some revelation is at hand..."

Perhaps it always was present, just unnoticed until careful experimental design showed it up?

It gets plenty of attention from Penrose

How does this follow from Penrose's ideas?

I tend to break with the Buddhists and the dude who wrote The Self-Aware Universe.

The idea is that God is the observer in the quantum interaction. God is also the observer in our lives. We have problems with this notion because we spend much of our lives getting socialized that there's this entity called "you" that's doing all this. Instead, it's a bunch of conditioned behaviors that helps us get along with everything else, know where to take a crap, what to eat and not to eat, speak a language, and do all the things necessary to keep living as a human.

I like this one because it makes sense of the soul as observer. Of course it's immortal, it's a basic function of the universe that will survive our death. It's just not a personal part. It also accounts for all those mystical experiences people have. They simply slip their conditioned mind for a few minutes.

The problem with AI (or IA) isn't particularly making it a better observer. It's already got that part of "I," just as every other part of the interacting universe does. The thing is, as with any child, we want to burden infant AIs with all the conditioning that lets them be functioning members of human society, under the mistaken assumption that this will make them more aware.

Considering how much of personality is clutter and conditioning, it's also really worth questioning how much more of it we need in our lives, and whether it's a good idea to rope in other sentient beings to expand the amount of mental clutter and conditioning we deal with. If being transhuman just means that my messy desk has four more virtual dimensions of junk to lose important stuff in, is that an improvement?

How about everything is just probabilities interacting, and thus the reality that we sense is not a collapsed one but merely the most 'probable' events manifesting themselves within our consciousness.

Perhaps there is not true collapse that completely erases previous 'entanglements', but merely degree's of dampened/enhanced probability.. a sea of thrashing, interacting probability patterns that we surf for meaning. Over time a dampened probability event might fade to effectively zero (i.e. take longer than the age of the universe to increase in likelihood).

So at what level do these probabilities collapse to create our consensus reality? How far up the macroscopic do these effects go ? We now know plants use quantum effects to improve photosynthesis: http://www.nature.com/news/2011/110615/full/474272a.html

Maybe we'll discover chess grand-masters actually do a bit of quantum superposition to figure the best move, versus pruning leaf-nodes as a computer might do.. But say we want to add that feature to a brain. The plant use was to more efficiently channel the exciton to the reaction site. In the case of our brain we might want to either explore different neural paths at the same time (superposition) or to boost the Axon efficiencies (say a graphene sheet inside the myelin sheath: http://physicsworld.com/cws/article/news/23538 ) The problem with these hacks is we know so little about how the brain works we risk insanity or worse.

If we could biologically model a chess grand-master's brain perhaps we would know if they have trained clusters of neurons into superposition states (makes a good story anyway) or at least have a biological target for a room temperature superposition hack.

The target goal would be a human that could 'sense' probabilities.. which circles back to the question I posed earlier about the level at which probabilities collapse to create reality.

On one level the superposition could be limited to information retrieval/manipulation within the brain, while on another level it could extend out from the brain.

Extension out from the brain would be a tennis player modded where they unconsciously create a superposition of ball states and create corresponding high-probability responses (positioning themselves).

Sadly we don't know enough about how the brain does these calculations to say much about where you could take it. Still it would be cool to be able to always be at the 'right spot' to hit that ball...

"I also can't help feeling that this might be related to "jaunting" (The Stars My Destination)."

Also puts me in mind of A. E. Van Vogt's "The Pawns of Null-A".

On a slightly more serious note, I have often wondered about the physics of the neuron - there are nanometer sized structures critical to their functioning, but this size is within the limits where quantum effects are significant, effects such as tunneling. Coupled with a hypothesis that consciousness is an emergent property riding on the oscillatory substrate of nerve behavior, and that these structures play a large role in determining when a neuron fires, and therefore the frequency (and FM) it does that - maybe some SF traction therein?

Of course if you use some quantum characteristic of neurons or the EM fields generated by the brain or some such you can use some brain hack like a special kind of cognitive training (and this sort of thing has been done many times in SF, from van Vogt through Heinlein and Gordon Dickson, and so on). Or you use a drug that does something exotic to the nervous system, like Ted Chiang. But I kind of like the idea of a coprocessor for the brain (and you can see how this would work for AI too). So you build this quantum computing gadget that fits in a small case attached to a head band, and the band has TMS circuitry in it that entangles the gadget and some part of the brain.

The gadget might be true quantum computer that allows some very fast processing, with parameters set up by your brain, so it's like thinking about a problem and then suddenly seeing the solution (in great detail) in your mind's eye. Or the gadget might allow your brain to query and modify the quantum states of objects at some distance to you, giving you both clairvoyance and a way to get your environment to do computation for you. Or maybe it connects two brains together and allows you to borrow computation from your buddy's brain.

Or if you're in the mood for a Thorne Smith pastiche, maybe it turns out that alcohol molecules allow easy quantum computation, and people can sit around in bars telling tall tales while using their drinks to think deep thoughts. Hmm ... that could make an R. A. Lafferty pastiche too.

Sorry, what is this "Collapse of the/a function" nonsense? The Q-states ARE, they do not collapse upon observation. Copenhagen is wrong. It is our understanding of the Q-states that is faulty & incomplete.

Oh & @ 21 I think B. Russell & A. N. Whitehead managed to prove why 2+2=4 didn't they? ( Principia Mathematica )

Penrose is big on the idea of the mathematical Platonic Realm and our interaction with it via QM, most notably via Hameroff's tubules hypothesis

I thought that Gödel had proved that the "Platonic Realm" was a construct, like Mathematics itself, and not a separate, actual reality ???

I am reliably informed that mathematicians are still working on 1+2=3, let alone the dizzying heights of 2+2=4. PM showed that 1+1=2.

As for the rest of the content of your post, just declaring that Copenhagen is wrong without providing a proof is a grave disservice to the scientific community.

Sorry but if 1+1=2 then 1+2=3 & 2+2=4(= 1+1+1+1) surely? I'll stick with Feynman's pronunciation on Copehagen, thank you! AND the recent double-slit results, previously referred to. ( IIRC R. P. F. called it, the Copenahagen interpretation, "mystical claptrap")

Godel proved no such thing. If anything he showed that mathematics is infinite. The constructivist position is has many problems, not least of which is why everybody comes up with the same number for Pi regarding circles in flat space. Or, do large primes exist before we compute them?

"God created the natural numbers, all else is the work of man." -- Kronecker

So, yes, primes exist, but someone had to invent irrationals and complex numbers and transfinites. I can point to 5 cows, but I can't point to something that's exactly 9.3̅ centimeters long.

And since flat space is an abstraction, the limit of the space we know as curvature (i.e. the presence of mass-energy) is reduced to zero, I'd say π is something we built on top of what exists. Many uses of π aren't geometric at all; it turns out to pop up in mathematics and physics in a lot of places. Which, I think, just goes to show how inter-related much of mathematics is.

And what Gödel proved was that no logical system as powerful as integer arithmetic could be both complete and consistent. Yes, mathematics can be considered "infinite" in that you can continue to prove an infinite number of theorems from some base set of postulates, but there are necessarily true theorems that cannot be proved with that same base set.

" And what Gödel proved was that no logical system as powerful as integer arithmetic could be both complete and consistent. "

ERR ... Proved? Proved in what sense that is comprehensible to the average Politicians Struggles with Maths, beyond Quadratic Equations in his Public/private Schools for Kids of the Privileged Classes ..bearing in mind that the Political Minds that hold control of the Purse Strings of MONEY for Research.

So .. where's the benefit in terms of His/ Her kids/offspring being given a Decent Job .. Big Salary .. in say, a Nationalised Power Company or a BANK /Investment of that kind ?

Explain this to the POPE of ROME, or to the US of Americans Religious Right Politician of your Choice at this season of the year .. my teeth ache with the vibration of sodding Xmas Carols.

Not that the Music isn't good - who could object to Mozart? - but it's the underlying ' OBEY or Else! ' that gets on my tits.

If your simplistic 'proof' had been sufficient, then Principia Mathematica would have been unnecessary, rather than possibly the most important mathematical work prior to Gödel's.

As for the Feynman statement, why, if you're going to argue from authority, why not use the sainted Einstein? He also didn't like Copenhagen.

if you're going to argue from authority, why not use the sainted Einstein? He also didn't like Copenhagen.

The problem with arguing from authority is you have to figure out who the more trusted authority is. Bohr and a whole host of other physicists were quite happy with Copenhagen. And most physicists today follow the "Shut up and calculate" interpretation. On the other hand, the need to understand how to make quantum computing work is forcing a showdown on QM interpretations.

Now it's true that I don't like the Copenhagen Interpretation, but I realize that as a non-physicist with only a basic knowledge of quantum mechanics I'm not competent to make a judgement on something that physicists have been arguing about for almost a century. That doesn't stop me from voicing my opinion, but it does stop me from insisting that my opinion trumps other argument.

In fact, Principia Mathematica's work on arithmetic was based on work by Pierce, Dedekind, and Peano, starting from Grassman's realization that the natural numbers could be defined using the successor operation and induction. So it's not as if it was really surprising. See this for reference.

"Think about it over Xmas and share your thoughts in the comments. How would it be to think in an entirely new way? What routes might take you there? Can you stop collapsing the states of your mind?"

Transcendental meditation and yoga are age old techniques to accomplish just that. In fact the reported siddhis of accomplished masters hint at the possibilities of access to the uncollapsed wave function:

See Wikipedia definition of Siddhi: "In the Samkhya Karika and Tattva Samasa, and hence in Tantric Buddhism, it specifically refers to the acquisition of supernatural powers by magical means or the supposed faculty so acquired. These powers include items such as clairvoyance, levitation, bilocation, becoming as small as an atom, materialization, having access to memories from past lives, etc."

Now let's say through the invention of a new device (e.g. nanobot swarms that take residence at key regions of the brain and inject a precisely measured cocktail of hallucinogenic drugs to allow entry to the quantum substrate) this capability becomes accessible without a lifetime of practice. Let's say a sect or class of people suddenly has the ability to seriously mess with reality, like materializing or dematerializing objects at will... um Jedi Knights anyone?

I'm at least partially with bruceohenpdx ... Gödel showed that maths contains undecidable propositions - which is directly contrary to the "platonic" ideal/model.

Sorry about argument from "authority" but ... "Copenhagen" appears to insist on the so-called collapse of the wave function - pure mysticism in fact. Even if one hews to "shut up & calculate" one can see given the more recent double-slit results I have been referring to, that this (C) interpretation is quite simply wrong. In fact we are still with Feynman, back in the 1950's: "We don't understand QM" BUT we do know, additionally, such is the power of scientific enquiry, that certain possible interpretations or proposed explanations are wrong (as stated).

My personal take on this is that until some resolution of the renormalisation problem(s), allowing a match between, and consistent results from BOTH QM & Relativity (And one or both of those will certainly require modification) are achieved, then we will not have a consistent explanation, that fits all the known facts.

"Gödel showed that maths contains undecidable propositions - which is directly contrary to the "platonic" ideal/model."

I don't see how you come to this conclusion

Lots of good comments here, I'll go through them carefully and formulate a coherent summary/response in a day or two.

===

I don't quite know why Godel is mentioned in this discussion, but I might as well clarify his relationship to platonism in math. I discussed this with him in person a couple of times.

(a) Godel WAS a platonist, he thought of mathematical objects, including the infinite ones, as having as solid and unique existence as any physical ones.

(b) His celebrate Incompleteless Theorem proves that that no finitely describable theory of mathematics is complete and consistent in the sense of proving all the true facts about math and disproving all the false ones.

(c) Even so he still thought there was a complete set of objectively true facts about math, and that we could make partial advances in learning these facts by opening our minds to the possiblity of directly perceiving infinite sets.

===

Long day of Chrismtas over, great fun, tiring, intense, like a movie that just runs and runs and runs. Twelve hours of reunion! Hope you all had wonerful, good or at least tolerable Xmases.

Interesting that Gödel was a Platonist, given that said stance cannot be squared with actual, experimental, messy reality.

Wishing it were so (whatever it is) does not actually make it so - as we all know, but religious believers refuse to even acknowledge this uncomfortable truth. Are "platonists" religious bleievers, I wonder? Especially given the way some parts of the teachings of Plato & Aristotle were taken up by the church (& the rest of classical philosophy and knowledge was carefully trashed)

I will certainly look forward to RR's later comments!

"I don't quite know why Godel is mentioned in this discussion, but I might as well clarify his relationship to platonism in math. I discussed this with him in person a couple of times."

If there is a Platonic Realm, this must be pretty close to the ideal forum response.

"Interesting that Gödel was a Platonist, given that said stance cannot be squared with actual, experimental, messy reality."

Because the latter is a subset of the former

Imagine that you can run infinite simulations but the skill comes in when you try to execute one of the simulations. Try to get the waves to collapse in just the right way to get what you want.

The rare in this world is reality. There is only one. Infinite possibilities that you and others can see but only one will exist when the waves collapse.

Reality becomes what people want to own, not money or fame, those are easy to get if you can get the reality you want to occur to happen. Since they are easy, they have no value.

Start small. Running the simulations is technical but collapsing the waves is a skill, you will need to learn it.

Your in a bar hoping to go home with someone. You can determine instantly the right approach that will get you home with who you want. Now you have to collapse the waves to implement what you know. Depending on the scenario, this could be complicated or simple.

Of course there are other people who can do what you do. Some times there are in the same bar at the same time you are trying for the same outcome. Then the fun begins.

Once you have mastered the basics, art comes into the process by how you get what you want. It is too boring to do it easy, you like to show off, it becomes a game.

One trick is to get artifacts from rare scenario's to show up in situations where they dont belong. They become the signature for the scenario. They are how you know which scenario became reality. Who won. Of course if you are trying to compete in a long complicated scenario, you would want your opponent to think they are winning when they are not. You would try to forge their signature.

Some people simply become focused on the rare occurrence, the unusual event, they become addicted to being surprised.

In a world where a subset of people can do this, the subset would begin to think of regular people as just players in a drama, not real. The games would be played for those in the know. What happens to regular people is just collateral damage.

Dirk Bruere @ 49 No It isn't. That is the whole point. A line of infinitely narrow (zero) width (The perfect, "Platonic" line? ) for instance.

What's the minimum size for anything? The Planck length isn't it, or similar? 1.616199(97)×10−35 metres.

The Platonic realm is a MODEL, it cannot be reality, unless QM is seriously worng, and I don't mean disagreeing-with-Relativity wrong, either, I mean WORNG.

Oops.

jib @ 50 Err ... are/were you paying attention? WHAT collapse of the wave function(s)? This is a figment of the imagination, rather like the Luminiferous Aether.

Isn't Rudy's superposition of states idea pretty much the plot (ok a plot) in Dune?

"What's the minimum size for anything? The Planck length isn't it, or similar?"

The actual answer is: apparently not. Nobody knows. http://www.physorg.com/news/2011-06-physics-einstein.html

As for mathematics and physical reality http://arxiv.org/abs/0704.0646

Things can be wonderful, and not be true. I you are getting into the thinking that CARL SAGAN wrote about in THE DEMON-HAUNTED WORLD. I wonder if people are starved for good things to believe in.
"Insight, untested and unsupported, is an insufficient guarantee of truth." Bertrand Russell.

Err, so is FTL. It is science FICTION after all.

Well, the FTL thing remains to be seen. Results next year.

Brains are engines for steering probability towards desired outcomes, it doesn't take quantum magic to recognize this fact.

Personally I suspect that the mechanism of the brain will turn out to be the basic feedback loop, like the spinal reflex, only brains are able to build complex responses to complex stimulus via pattern matching and memory. I base this suspicion on the observation of all other organs in the body, which are all made up of the accumulation of the basic repeating units: Nephrons for kidneys, alveoli for lungs, etc, etc

In a world where a subset of people can do this, the subset would begin to think of regular people as just players in a drama, not real.

You mean rich people.

Does the mental framing context matter as long as the math's right?

Look at Newton- probably thought that Calculus was helping him discover insights into the mind of God. Remove God from consideration, and calculus still works just fine. God, Platonism, platypuses, whatever.

C Unfortunately, even if the math is right, SOME people will use the "mental framing context" to do very nasty things.

Dirk I find the GRB-polarisation results very interesting. As for the "external mathematical reality" model, this is just religion - looking for the crystalline Empyrean (note), so to speak. Not buying it without some evidence, which comes there none.

(note: reference is to last few cantos of vol III of Dante's "Divine Comedy")

Yes, the bloody conflicts fought over geometry have soaked battlefields for centuries.

Well there was "48"40 or Fight" as a war slogan in the US in the dispute with the British over the Pacific Northwest.

Although they did compromise that one, so no blood soaked battlefields until the NHL expanded into Vancouver.

C Very funny & clever - NOT. Your knowledge of directly relevant history obviously needs a good kicking.

1: Will you look through the telescope to see the moons of Jupiter? 2: Will you burn someone at the stake, for daring to suggest that stars (in the night-sky) are very distant suns, and they might have planets? 3: Then there is the fate of the female mathematician from the Library of Alexandria, murdered by a christian mob, set on by the bishop of that city, Saint Cyril ..... These were some actual historical examples of the sort of mental framing that I was thinking of.

Very bloody conflicts over geo-metry indeed!

A current example is: "There is no cause & effect - things only happen by the will of allah".

Tegmark says in that arxiv paper:

I hypothesize that only computable and decidable (in Godel's sense) structures exist

Which is what I was trying to imply when I quoted Kronecker upthread. If there is a single Platonic Realm, then ISTM that it must have some basic postulates, and that it can't contain structures that are mutually inconsistent or are undecidable from the postulates. Conversely, if there are inconsistent structures in mathematics, I think that means either that there must be multiple Platonic Realms, or none. As an apostate Platonist of many years standing, I vote for none.

oh, God. Peano's Axiom. I had a Maths tutor whose idea of a jolly introduction was to set us all a task which was basically, "Given Peano's Axiom, re-produce Principia". And of course he did this without naming the mathematicians or the problems. Then he'd sit there in tutorials knocking our "proofs" to bits with a grin.

I think he intended a sort of Kobayashi Maru test. Me, I decided if I couldn't even do the first assigment I'd better leave the course quickly.

So Peano was instrumental in my arts career.

@Greg, 62. I completely agree. Of course Galileo wasn't content with being right, he had to publicly call the Pope a simpleton - while the Pope was under pressure to show that Galileo wasn't under special protection as an old crony of sorts.

Most "ideological" conflicts are perhaps best re-framed as struggles over resources and competition for influence amongst factions - in the case of St Cyril, the struggle for the ear of the Roman prefect Orestes. From different sides, Hypatia "fell a victim to the political jealousy, which at that time prevailed" (Socrates Scholasticus), or alternately "beguiled the people of the city and the Prefect through her enchantments" (John of Nikiu).

In any case, pretty much as you state - it's the framing, not the picture.

@ general discussion - It's very tricky to get quantum physicists to talk about how brains might work - they've had their fingers burned before, and sadly a legitimate line of enquiry is mainly left to the purveyors of woo out of fear of contamination of reputation. Penrose has had a lot of stick, for one example. I know the only quote I could get from a nearby quantum theorist was "hmm". He was more forthcoming about the non-existence in his opinion of a Platonic Realm in any real sense.

"Conversely, if there are inconsistent structures in mathematics, I think that means either that there must be multiple Platonic Realms, or none."

Or a Platonic Realm that can embrace contradiction

"A current example is: "There is no cause & effect - things only happen by the will of allah"."

Determinism v Free Will. Jury is still out on that one

I have trouble understanding how a Platonic Realm could embrace contradiction. Does that mean there have to be multiple Platonic Ideals for the contradictory concepts and for all Ideals in the chain of proof from the postulates to them? After populating a contradictory Realm, how does Platonism offer any explanatory power or simplification? And if it doesn't, why believe in it?

Here two examples of 'alternate ways of thinking' from other books - noting them in the hope that they help spark further ideas:

2.Robert Persig explores a potential alternate state in his book, 'Zen and the Art of Motorcycle Maintenance'.

Suggestions:

"I'm feeling lucky" theme: People in this frame of mind:

-- Are hyper-aware, of both memories and possibilities. -- Tend to surf their probabilities waves into happy/lucky circumstances, and spread the luck onto those around them. -- A leet subculture goes for humor via arranging extreme incidents in can-you top-this fashion. -- Things get more complicated when they're near each other's spheres of influence. Tensions arise in both actuals and meta-possibilities.

" After populating a contradictory Realm, how does Platonism offer any explanatory power or simplification? And if it doesn't, why believe in it?"

Because if we do not believe in it we end up with the idea that prime numbers do not exist until we calculate them. Or do you prefer a half-Platonic Realm where only "parallel lines never meet" is true, and its negation does not?

Another thought: I've had the pleasure of doing some fairly intensive personal development programmes (Landmark Education)over the years. I seems to me that how they work is by helping people 'think' in different ways - and they do so in a relatively quick period of time (2-4 days). It's not a fundamental change (same old neural net pattern-making machinery in place - but it does feel like a very liberating 'upgrade' each time (especially as they are very transparent about the process and say 'this is all made up, it's not the truth, just try the models on and see what new results and experiences become available etc). David Gerrold does a wonderful job of exploring this in his War of the Chtorr series ( I think he based it on the old EST training that I presume he participated in back in the 70's).

“Genius is only having a superior power of seeing.” - John Ruskin. Perhaps your AHA is entirely to do with the way these people change the way they 'see' things...

The Mandelbrot set image in your painting reminded me to dig through the Big Box of Stuff I have in the corner and I found this still in its shrinkwrap.

Did you ever do anything else with Autodesk apart from the Cellular Automata software?

Well, if you really want to think seriously differently, and in some ways in a dramatically improved manner, try taking 400ug of LSD in a controlled environment

Prime numbers, like any other positive integers, exist by nature of the fact that it's possible to count things, and the integers represent the equivalence sets of the counts. I'll grant that a lot of the structure of the universe is determined by number theory, but that doesn't mean there has to be a abstract realm to hold the numbers. It could be all in our heads. But in what way does a complex number exist?

As for Euclid's 5th postulate, it's true for some geometries and false for others. How can it be an ideal if it's only conditionally true? If you look at the structure of modern geometry, it goes back to Klein's Erlangen Program, and is based on the notion of symmetries and constraints. So each geometry is determined by the set of symmetries that are conserved by the transformations of that geometry. Which geometry is the Ideal? Euclidean, because that's the closest to what we see in daily life (even though it's only close)? Inversive, because that's the one with the fewest number of symmetries? Projective, because that's the one computers understand best?

And here I was thinking mainly of the time Pythagoras killed three guys in a bar fight with a hypotenuse.

Anyhow, you're overgeneralizing- the one point you've got problems with is people who think "I shall kill or otherwise forcibly silence people who disagree with me."
Barring that little meme, framing context is just the window-dressing of thoughts, and different frames don't matter- you can think that only matter and energy exist, I can believe in a Platonic ideal realm, the Dream of Brahma, a super-advanced computer at the end of time, etc, etc. As long as neither one of us decides to pull a knife, we're all just skippy.

Now, yes, the times of disagreement that get violent get all the attention, but consider the vast number where they don't- "What? You think that we should focus on renewable energy for automobile transportation rather than investing in reduced suburban sprawl and improved public transport? DIE, BASTARD!"

The contemporary sources indicate Hypatia was killed because of political and personal jealousies, not ideological conflict. Over the centuries, she has obtained what might one call certain Platonic identities as the trope of the female scientist, the fall of Hellenistic thought to Christian dogma, the embattled and sacrificial rebel female, etc.

Ironically enough, as a Neoplatonist, she would have subjugated empirical though to ideal forms; so she might have approved your abstraction of her historical reality to "truer" expressions for the purpose of arguing about science and religion. However, she would not have supported your specific argument in this thread.

And she also clearly did not die in a dispute over geometry per se, anymore than Archimides did.

Apologies for the typos. I meant to write "empirical inquiry" not "empirical though" and of course, I did not mean to mis-spell Archimedes.

To show the power of abstract forms over reality, it was the Church recasting her as a witch or intellectual seductress a few centuries later that enabled her to become a powerful figure in rebuttal. Powerful city figure, who happens to be woman and the equivalent of a University President, is rumored, accurately or not, to be interfering in the power struggle of two other powerful city officials and gets murdered by a mob of partisan cronies (a common occurence throughout Classical times)...does not have the same metaphorical zing.

C, that's a wonderful, memorable line: "And here I was thinking mainly of the time Pythagoras killed three guys in a bar fight with a hypotenuse."