What are we allowed to change? Here and throughout this book, I shall keep the mesoscopic alone. Things of medium size are way too visible in our cognition for us to be able to change them in an interesting way without loosing track completely, going completely bonkers. From the size of teeth to the size of stars, I’d better not touch what is visible about physics.

How It Should Be in Utopia: The changes we should consider here are of two kinds, those that would make the world more practical, and those that would make it more beautiful. These notions start to pull in opposite directions after a point. As a study by (XXXX) shows that our aesthetic preference dodges from both too much complexity, and from too much simplicity. Subjects were given three classes of paintings, with different degrees of shape complexity in them. They spent most of the time looking at the most complex one, but rated the middle one as more beautiful. This makes sense, compare the sight of a savannah with the sight of a deep forest, there is more to look in the deep forest, so you focus longer on it. One of the reasons you do it is because there may be snakes somewhere around, or fellows of an opponent tribe hiding there. The savannah has widespread visibility, so you can check out for lions long before they arrive nearby.

Trees are a perfect example of the reason why evolution has given us a desire for mid-level visual complexity. If there are none, you are bound to fry, freeze, or in the best case, be found by those you’d better keep away. If there are some, you have shadow, perhaps some fruit, shelter and a hiding place. Now if there are too many, you are lost and anxious, for anything faster than a slug will take very little time between being seen by you, and getting to you. Not by coincidence, some architects found a lasting school of design a while ago called ¨modernism¨ which tries to simplify a lot the designs that surround us. Long, very, very long before this school of thought there was a style called baroque, and it was characterized exactly in the opposite way, having intricate designs, twists, edges, curves, forms, sculptures, shapes, eye lines, shadows, wings, stories, kings, gods, priests, angels, girls, animals, wheels, hair, clothes, expressions, positions…. among other things….and a few more….. you get the hang of it….. emotionally at least…. when you read this final part….. and feel that you can’t stand anymore…. those little dots….

One of the things that separates this two schools, and one I think is highly responsible for the difference between their designs, is the average visual complexity of the surrounding environment. Life was way more simple, with fewer objects and less propaganda in the baroque times. In that time, the more, the merrier, when it came to visual processing. Those brains were craving for more, for most of their visual life was an experience of more of the same. But in the time of the modern school of art, it was all different, life was rushing through our eyes, the experience of the impact of thousands of daily images, like a movie that changes it’s scenes every twenty seconds. Cars, business, industry, art everywhere, cinema, buildings, trains, and lots, lots and lots of people. When the baroque school was in vogue, we were still living in a visual Savannah, but then came the jungle, deep, intricate and metallic, and that was just too much. We needed less. We needed something that reminds one of either a plains or the ocean, the skyline not the skyscraper… and as such, the memes of modernism achieved power within the human society… but I digress…

So, we have two kinds of changes to apply to our non mesoscopic physics, those that would make it more beautiful, and those that would make it more practical. Let us start with the latter. There is no reason why a high-school graduate should not be able to describe the fundamental physical laws in a conversation in a party, in the same vein as there is no reason why he shouldn’t be able to talk about a beautiful TV series he just watched. So we must provide some simplicity to our microscopic and macroscopic physics, this is not very hard. Before Einstein, space was thought to be very simple, three dimensions, four if you count time, things from the past go to the future, things from the future go to an even further future, and things in the present become past before you know it. Light (photons) traveled in a straight line (thus not according to probabilistic waves). If the physical macroscopic world worked like the predecessors of Einstein thought it did, high school would be a much deeper experience, we’d actually be learning almost all there is to know about the mechanics of the world in those few years! Physicists would definitely feel a warmth inside, once they settled the fear that they themselves wouldn’t be personally able to find out the most important physical laws, since they had already been discovered. Some, readers of Feynman perhaps, would protest against a simplification of physics, since the pleasure of discovery is the the pleasure of doing physics. This is partially true, and it is interesting to imagine ourselves in a territory in which it is always possible to create anew and make innovative discoveries. But we must not assume that the pleasure of discovery must be possible in each and every domain of knowledge. Something as fundamental as physics should not take eight years to be learned, and discoveries can always be made in other realms, such as applied physics, botany, or computer science, if that is the case.

There are shortcomings in choosing to live in a Newtonian world… The first one is that Quantum computation would be indeed impossible, since the behavior of micro objects would be mostly a tiny mimic of their bigger counterparts. Our current (2010) computers would not suffer, but our computational prospects would suffer a little bit. Take for instance these predictions of the possible computing power available per cubic inch (SANDERSXXXX) (KURZWEIL XXXX) (BOSTROM 2001)

According to the Many-World interpretation of Quantum Physics, when we do quantum computing, what we are doing is basically computing in many, many worlds at once, using their computational resources, and then recovering somehow this information into our world as a final result of the computation (DEUTCH 1997). If the universe was Newtonian, we’d have to abandon this dream, and accept a limited amount of computer power per parts of matter, energy and space available. This can be made unproblematic in one of three ways. First, accept, as some are starting to, that the level of isolation of a quantum computer necessary to do quantum computation is such that the dream would not only be unachievable in Utopia, it would also be unachievable here, in good old Earth. This may seem sober, but is quite insane, it depends on the belief that one can decide how reality behaves, and this is one of the distinctive properties of Utopia, not of reality. Second alternative: Start thinking about taking the dream of getting to know how the world works to an extreme, what is the dream of a physicists, or of an analytic philosopher? ¨To find out how the world is.¨ – Well, yes, but what do you mean exactly? – ¨ To find a set of equations that, given all the information of the behavior of all particles at a given time, it shall give you the physical behavior, future and past, of the whole of existence, everything, from the tiny speck of dust, to the grand mammoths, passing by that day in which your mum told you not to forget to bring a coat.” – Okay, suppose I gave you this set, would you be happy with it? – Why, of course! I hold in my own hand the whole of Man’s knowledge, right before my eyes are the eyes of tiger, the bright blue sky is at my command, I have found out the power through which number holds sway above the flux, as Russell remarked. – ¨What is is about the equations that you find so enlightening, so marvelously soft and warm and fulfilling? – ¨The whole truth is subsumed on it, once I know it, I know everything that matters!” – Do you know when is your girlfriends birthday? – ¨Well, no¨ – Do you know the feeling that inspired the poet when he composed his love poem? Do you know the courage it took for the conqueror to forget about his religious upraising and start killing in the name of vengeance? Have you any grasp of what is a family, or a master piece of art? – “No, you see, the level of description you are talking about it too high, I will only know the position of atoms, planets and similar things, for the things you are talking about, I’d have to have an idiom of translation in-between levels, so that I could find those objects among the numbers and vectors” – Then you struggle for a bunch of numbers that will give you more numbers, sometimes greek letters. It is an enormous pleasure to understand the rules that govern that which is tiny, and that which is enormous, and I do not wish to affirm that there isn’t value in knowing these things, but what worries me is that, since this particular task is so difficult, many of the world’s most intelligent people spend a live dedicated to it, *as if* once they had found and held strongly to the final theory, the very doors of paradise would open to them – ¨Our dream is, partly, to know everything there ever will be. We seek for more and more knowledge because it feels good to know, and it feels better to know more, why would we not want to know it all?” – Richard Rorty once said that the dream of the analytic is that there would be a moment where a part of the universe, in a finite time, would compute every single property the whole universe will ever have, once this is done, the traveling will have been complete, our journey is finished. But what about after that? Let us suppose the computational dream actually is the purpose of the universe, as knowledge seekers many times suppose. We develop a brain/mind/computer that is so enormously powerful that for a moment, it has a glimpse of all there is. In a tiny set of moments, all the computations that calculate everything, before and beneath, above and behind, around and within will be executed, the feeling that everything is what it is will be felt. Aristotle said that to say the truth is to say of what is, that it is, and of what is not, that it is not, after the completion of the dream of Understanding, the complete truth will have been known. I see some beauty in that, but it is beauty the size of a marvelous, uniquely inspired movie, it is not beauty worthy of worship as being *the one path*. Douglas Adams has put a machine, in his own Utopia, that gives one the ability of contemplating the universe (probably the observable universe) in all its vastnes, way and well beyond what we can imagine. The only survivor to entering the machine, and contemplating one’s relative size to the whole universe was Ford Beeblebrox, and the reason he survives is that he enters the machine in a simulated universe made for him, and discovers he is, indeed, the most important creature there ever was in the universe. To me, sometimes, depending on my mood and level of existential anxiety, it seems like the dream of physicists, and of analytic philosophers is that they would feel like Beeblebrox, that once all the equations are there, right in front of them, they will all magically unite into a picture of an egocentric universe, that cares about you as much as the God of believers cares about them. ¨What you bring is shocking on the one hand, but part of what I believe remains intact despite of it, there is something about those equations that will not be taken away from them, it belongs to them alone, and it allows them to hold sway above the flux, to be that which we always dreamt of. It is the property that them, and themselves alone have: Permanence. All of our lives, we struggle, in one way or the other, to persist, all we know about the world, we know because genes that were trying to persist created brains, and minds wanted to persist. We search for persistence in our children, in our jobs, in our emotional lives… we want the world to bear our craved marks in the most solid rock, we want to live on through our work, our ideas, and our beloved ones. Our hearts, most of all, wish to remain beating, to experience deep and profound happiness, peace. All this may be, partly, a distortion of our true wish, that few times escapes peoples minds, but did once, from Woody Allen’s: ´I do not want to be immortal through my work, I want to be immortal for not dying!´ The dream of immortality may not be possible for our minds, since personal identity isn’t what it looks like[1], and also, unfortunately, we know that mesoscopic objects do not last long enough. No matter how deep our encravings (??word exist??) in the monolith, air and water shall erase our markings upon this world. No matter how many read our books, or saw our movies, memory will fade away. But the equations! Oh, they are not as fleeting! You can trust them as you can no other thing. They are valid here, as are there, they are now as will be when our galaxy hits Andromeda, they hold no matter who is on power, they stand beyond the reach of kings, queens, supercomputers and tsunamis… If our dream is a dream of persistence, and it is, there is nothing that will persist for longer, for all else changes. It changes, in fact according to them, and they describe all possible routes of change. But they themselves stay. When offered the dream of power, instead of the dream of persistence, Einstein said (????): “Politics may be for a decade, but an equation, is for eternity¨ this is what your shattering argument can’t take from us. I agree though, that all the rest it has swept, and I see, finally, the reason why would anyone *not* dedicate his life to figuring out the underlying physics of the cosmos.¨ – The message of persistence is a beautiful one. Persistence though, is, like Computation, Truth, and God, still a messiah. Surely, as a messiah, persistence far surpasses in muchness the dream of Power, so much the worse for Nietzsche, Ghengis Khan, and Eric Cartman.

The second alternative, when we are considering good reasons to accept the trade-off of having no quantum computing, versus having no one understanding physics seems to lead us to having no quantum computing, and abandoning the dream of the Complete Computation. It is a high price to pay, having to give up on the ultimate grasp into microscopic physical reality, but we can rest assured that the dream of Persistence, and many others, will still be strong, steady and with a soft fur in the world of utopia. Physicists do not learn the equations only if they think there is a change they will be able to one day perform the one computation, their eyes will still glare to be in the presence of those symbols that describe that, which, uniquely, and, in a sense, above all things, persists…

The third alternative consists of establishing within Utopia something very akin to what a very old philosopher thought. Leibniz conceived of a notion of Universal Harmony. He had strong within the dream of the total computation, but for reasons somewhat different of those that our physicists will offer. Leibniz was concerned with the problem of how does one thing influence another, and he concocted a worldview in which all things actually are separate, monads, he would call them. All the matter is made of monads, sort of like little balls that don’t have contact. Each and every of those would contain in itself all the determinations of movement and happenings of the whole world (that is the dream is taken for granted *as a premise*) and in such a way it would know when it was time to move or be moved, without actually having to touch or be touched. Things were not allowed to have relational properties, only instrinsic ones. Suppose you push something with your hand, how can it know that you are pushing it? If there is movement, we must account for it, but if two adjacent particles move one another, either one moves first (therefore occupying a space where the other one isn’t, which would give the other one no reason to move) or both move at the same time, in which case there would be some sort of precognized move on the part of the second one. This is the sort of issue that Leibniz was dealing with when he conceived of universal harmony. He decided (as old philosophers used to do) that the world was made of this simple entities, monads, each and every one of them was simple, not decomposable, and therefore it had to contain within itself all the relations it beared to other monads, present, past, and future. Basically all things inside the cosmos were simple substance achieving the Understanding Dream. His reasons for his decisions are far outside the scope of our scrutiny, but the general sense is that since he thought all true propositions are of the form (Subject)*(Predicate) and that all truths were analytical (true in virtue of their meanings alone) then it meant that all predicates were contained in their subjects, and therefore relations had to be containted in monads, not have a separate reality as relations. Once he settled for himself this interesting project of creating a world of separated stuff that contains it all, he had a very rough problem to deal with. For one, under his doctrine all sex was masturbation. How could he make sure that all the monads were acting as their inner relations would describe if there are no real relations between them? How could he make sure of the truth of what each of them contained, if those pseudo-relations did not imply the existence of any real relations such as touching, pushing, demanding from, having an orgasm in the presence of etc…? For this he provided the notion that we will be needing here, in the third alternative, the notion of Universal Harmony. As its name implies to a great extend, within this doctrine, there is a harmonic tonus to our world, the monads behave as they should, even though nothing relates to nothing. A *deus ex-machina*, the notion of Universal Harmony comes simply as a holy savior, that will once again bring consistence to a very interesting doctrine of substances. It is unfortunate that since the times of Leibniz much has changed, philosophers don’t get to decide many doctrines anymore, *deus ex-machini* are strictly forbidden, and worst of all, one cannot invoke the three letter word as the explanation of why is it that something in particular takes place, ’God’ has stopped being an explanation that guarantees that, deep within simple substance, non pecaminous masturbation is sex after all.

Merrily for us, Utopias are allowed their share of *deus ex-machina *solutions, the third alternative is to postulate a different kind of Universal Harmony to our world, that is a complete mapping of the better part of it into a smaller part of it, we allow the property of the Monads, and of the dream of the Understanding to exist, once, in a mind/brain/computer vast and highly accessible for mere humans to see. This computer will be able to do it not because it bears enough causal relations with the world around it that it can actually compute, through sheer empirical fact plus equations, the ultimate fate of the universe, but by equations plus chance… It is a given that the shape of the universe is such that it will compute right, and we do not have to worry about the causal details that would render the operation impossible. Not only this computation will be accurate to the finest level of detail about what is outside the computer (after all, if it computed itself there would be some trouble lurking within the math) but it also will be accompanied by the corresponding ¨Ahá!¨ feeling, which, being computationally much more simple, will be transmitted to all those scientists gathered around the machine, in proportion to how much their cognition is able to feel it. This way we can remain Newtonian, achieve, at least once, the Computational Dream, remain able to see and understand those few things of the world that actually do *persist*, and watch the show of all there is.

———–

By picking the third alternative, and letting quantum mechanics fade into the abyss of all that never was, we loose something that to some could be very valuable, and to many others, terrible, almost unbearable. These are the many-worlds of quantum mechanics. If we abandon Quantum Mechanics, we must abandon many-worlds, there is nothing else we can do. Either it is a probabilistic universe in which split experimenters at time_{2} only get to be in one place each, or it is a deterministic universe, in which no splitting occurs, and, among other fascinating things, light travels in a straight line! There are many reasons we would like to keep the many worlds, I will now try to argue that they are insufficient or false. The first reason is because we want to have more choices, in the sense of more possible futures, and it feels nice and warm inside when we think there *actually* is an open future out there for us. There are some mistakes already in this reasoning. When quantum worlds split, there is no fact of matter about yourself_{1}, that is, yourself before the splitting time, that decides that yourself_{1} will become yourself_{2a} and not yourself_{2b}, that is, there is no fact of matter as to which of the two actually is you, they both are, in all possible senses. All your descendant selves, lets call them, are equally you. All your ancestor selves, in the same vein, are you. But that does not mean that all your parallel selves are you. Yourself_{2a} is distinct from yourself _{2b}* even though both are the same as *yourself_{1}, only living a few moments later. Sameness is not a transitive property when it comes to your-quantum-selfity, one might want to say. If A is the same as B, and B is the same as C, it does not follow that A will be the same as C, just like if Brazil won most games against South Africa, and South Africa won most games against China, it does not follow that Brazil won most games against China. What this all implies is that when you thought quantum physics was allowing you to believe correctly that there are open futures for you, you were wrong, unless your definition of ’open’ ranges over cases in which everything is determined, but more than one thing happens at the same time. In my personal target for the operations of the expression ’open future’, it includes very near the middle of the target the idea that there is one single future which is contingent, that is, is not necessarily going to happen, but is probabilistically going to be determined as time moves along. Even closer to the middle of what I understand by ’open future’ is the idea that I get to decide, above and beyond the scope of all physics, out of my pure biblical will, what I will do and how my future will be. This picture sounds as open as possible. So in almost all cases where I say ’open future’, this could be what I’m meaning. In most of the cases, but not almost all, I could be talking about probabilistic futurology, in just a few of them I would be referring to the kind of branching that many-world purports.

In even fewer, I’d be referring to the idea of an epistemically open future, one in which all is determined, but since we do not know the determination (because aren’t currently achieving the computational dream) we count our subjective probabilities as open-ness regarding the future of the world. Here I suggest we stick to the definition of ’open futures’ that ranges over biblical will and probabilistic futures, but not over determined branches or subjective probabilities of a determined future. So, if we do, then you didn’t have options in the first place while you were living in quantum world, you have no reason to miss options in the all renewed Newtonian Utopia. This gets ¨What the Bleep do We Know¨ and similar quantum mysticism out of our way.

There is still work to be done, since in the Many-Worlds there is still the sheer amazing, interesting fact that we are actually living in Many-Worlds! I mean, how awesome is that? Isn’t it way more interesting to be living in a gazillion places at once? To be able to dream of the version of you (that is not you, because it is parallel) that won the lottery, wrote a bestseller, played with Yo-Yo Ma in a concert watched by billions and debunked the record holder for the 100mts? Yes, any utopian must account for that. There is no way you can say you’ve just made the ideal world and you took all those worlds away from us. There is a dream that dies when you kill parallel worlds, this is the Dream of What Never Was.

Wait a minute, there is a paradox here! If this is Utopia, you don’t give a damn about what there isn’t, after all, of all configurations of what there is, you are sitting atop the best of them…

As the Architect remarks in Matrix: Although your question is the most pertinent, it is also, the most irrelevant. It is patently false that dreaming of worse worlds cannot be a property of the best world. For one, the best world, being the best for (pick your choice between) everyone/most people/everyone that matters/me and my friends is a world in which there are beings that do not live in *their* best world. It probably does not coincide with anyone’s personal best world (except if there are those whose true emotional standard for a best world is that it is the best for the chosen set). It is generally taken for granted that it is good for people to dream about their lives as better ones, and I do not see reason to fight this intuition. If it is correct, than we know that the best world differs from the best world in which no one dreams of world worse than this one in exactly the fact that people are not able to dream of their personal best world. Not only the very best, but all in which things are better for them. Not only those, but those in which the things they are currently concerned with are best for them, regardless of how those would have turned out in the long run. With that behind us, we must now find space in a Newtonian world for parallel worlds, so that the Dream of What Never Was can be fulfilled, and surround the impounding fantasies of the Utopian peoples. Sometimes, solutions are so easy you don’t get to see them, for they are right before your eyes. We need to find space. Space, isn’t that something we have an infinite supply of already? We do not need quantum truthfulness to have an infinite universe, we do not need to protect our bubbles from much. There is no conceptual contradiction in having an infinite space with bubbles like ours inside. There would of course be some changes. Even though we have destroyed probability in the level of where is a particle going to be tomorrow, we must keep a little probability happening. We need for it to be finitely probable that a cube of 10^{x} meters will give rise to a bubble, otherwise, there would be no bubbles and only empty space. We might want to add a proviso that no bubble shall appear within another bubble, and therefore we maintain all the Newtoneity our Computer/Mind/Brain/Dream-achiever might wish for, since he is only calculating what happens in our bubble (or a bit less, our observable universe). Also, there would not be 10^500 different possible bubbles, because all those bubbles were inter-differentiated by facts pertaining to either string theory (Wooo!) or quantum theory, and both of those were abandoned due to average high school stupidity, as you may remember. There would still be many possible worlds out there, far, far away, farther away than Far, Far Away itself, where Shrek and Fiona are wondering if their world is or not Newtonianly possible. These are the Newtonianly possible worlds. I do not know how many are them, but they are sure enough to, literally, make our dreams come true.

By now you may have noticed that in contemporaneous cosmology, and in contemporaneous speculative philosophy of physics, the meanings of a few words started to blend. Universe means three different things. Observable-universe, Universe containing bubbles (also called ’Multiverse’), and bubble. That is because usually people mean bubble when they say ‘universe’, since they are not aware that there are other bubbles out there. ‘World’ has the same problems. To make things easier, I shall establish what, from now on (but *not* until here) I mean by those words

Universe: By universe, I mean our bubble. If two bubbles fuse, then I mean by universe the sum of them.

Multiverse: By multiverse, I mean the all the things there are in the same level of physical reality as we are, all the bubbles. All the space in-between, if there is, all properties instantiated In this space.

Bubble: A bubble is something that looks like our observable universe, having objects, time, matter, etc… it does not have the constraint of having to be visible by a particular civilization at time, so it is not contained within a light cone, it may or not have been generated by a big bang, and contains at least energy, if not more sophisticated stuff like Helium, Cadmium, Gold and those nice people who sell ice-cream at the beach just when you need it.

World: By World I’ll mean the physical multiverse, all quantum branches that may come from it, and in general everything that can be causally related to something within this branching object, physical or otherwise. Since there are parts of the object (such as separate bubbles) that bear no causal relations to each other, we provide that will be included all the non causal stuff there may be in-between the bubbles (if such a notion makes sense. In Utopia, it does) like void, empty space, gunk, points etc…

So in utopia we have a multiverse with many bubbles, one of them being our universe, just like here. We currently do not know if the level of quantum splitting spans across the whole multiverse, just the bubble within which that particular quantum thingy is, or only the future light cone of that thingy. We do not know the size of the structure that divides when a division occurs. In any case, we have lost the many-worlds, but subtracting an infinite quantity from another does not leave us with zero. Just think of the analogous case of subtracting a line (infinite points) from a plane (infinite points). We remain with infinite points, or, in our case, infinite possible dreams being actualized elsewhere in our very own cozy multiverse. Martin Luther King can rest in peace.

——————————————

I have cheated a little bit, because we need another quantum provision for all this to surely take place. Either that, or another deus *ex-machina* to come save us. Just like it is true that I can extract infinite points from a set of infinite points and remain with infinite points, it is also true that I can have an infinite space, with a finite probability of generating a bubble for a finite subset of it, and not get all the bubbles I might wish for. There are two ways in which this can happen. There can be too few bubbles, or too many. Let me guide you through this… Too few is quite easy. Just imagine that there are only three possible bubbles, meaning that for any finite sphere within infinite space, only the probabilities of insurgence of these three bubble kinds are finite. No matter how big you make the sphere, it is still only likely it will generate one of these three worlds. This once again depends on what can an what cannot vary, and, as I hope we agreed in earlier reflection, we have no idea how to determine that, we just make the educated guess that some constants and arbitrary values can vary, and that is that. The other way is by having too many possible bubbles. In this case, it won’t be true that a huge sphere will ascribe a finite probability for a bubble, say, ours. In this case we are actually going to delve into domains a bit beyond our knowledge of the World, sorry for this. Let’s get going: There are infinites (called cardinal numbers by mathematicians) of different sizes. Imagine all natural numbers (yeah, like someone could do it!), they are infinite, and yet, for each of them, there are infinitely many real numbers (like square of two, Pi and some others), the math concerning transfinites is a bit too complicated, but it can be found here:

http://www.cogsci.ucsd.edu/~nunez/web/SingaporeF.pdf

Either take a look or believe me in that there are infinites of varying sizes. Also, there are no infinites that differ by a finite amount, only by infinite amounts. The total number of natural numbers is the same as the total number of natural numbers plus 7. Since those infinites can be organized into different sizes, they can be put in order, just like their finite cousins. The number of natural numbers has been called Aleph0, the number of real numbers Aleph1 and the sequence of Alephs is infinite, like the sequence 0,1,2,3,4 … All of this is standard math (or standard set theoretical based math, for precision), but here we are about to hit a wall. *No one knows *if there is a number between Aleph0 and Aleph1. We know no finite additions to Aleph0 will give us Aleph1, because any addition would give us Aleph0 again, same for subtractions of Aleph1, *but this does not imply* that there are no such numbers, there may be more complex operations that give us a number, *previously unknown*, that actually fits in-between Aleph0 and Aleph1. That is, a number that is bigger than the number of points in Natural numbers line, and smallet than the number of points in a Real line. If the notion of an *unknown number *sounds too heretic to fit what you consider as acceptable about the world, you may want to review your acceptability standards before finding out that there are (spoiler alert!) *Illegal Numbers*. Yes, you heard it right. There are numbers outside the law. This are numbers it is illegal to sell, possess, or even, under some circumstances, know! Just imagine the following scene:

Class, how much is 25399 times 8883?

Linus, 214736417, mm almost

Bill, 216736382, no no Bill, try again

Larry, 216736317!, very good Larry!

Alan, 216736327?, you have the right to remain silent, anything you say can and will be used…..

There are awkward things in the world, and I think illegal numbers stand right besides laws about bringing lions to the cinema in Illinois (?????). So let us accept unknown numbers as a possibility, and proceed with why it is not enough to have an infinite space to be sure there will be someone just like you somewhere else drinking the finest tea and playing with soup bubbles instead of taking care of the dog.

1/3 is aproximately 33,33%, ¼ is 25%, and there are many interesting fractions, such as 22/7 a number that people used, for a long time, to believe that was the result of dividing the circumference by the diameter. Let us focus our interest in those that are between 0% and 100% for these are the only ones you can use in probability (there cannot be something 110% likely). The question that concerns us at the moment is, what happens when I have one over infinite? More specifically, what is the result of dividing one by aleph0? The answer is, nobody knows. There is no such math. Same for 100 over Aleph2 etc… when we intuitively say that one over infinite tends to zero, we are talking about the concept of limit, which involves finite numbers, not real infinites, these are useful for mathematical operations, they are cheaters, not the real deal. No one knows how to do the real deal, division operations with infinite cardinals as their divisor are not defined. This is not only true for numerators like 1, 100 or 10^7+56, it is also true of other infinite numbers. So Aleph0 above Aleph0 is undefined in our mathematics, same for Aleph1 over Aleph0, Aleph0 over Aleph1 and Aleph232 over Aleph27. Now you may be beginning to see our trouble! What if there are infinite possible configurations for a Newtonian bubble, and we live in an infinitely extend space? Are we to maintain that *all *the possible configurations of bubble will be realized? Suppose for illustration that the number of possible Newtonian Configurations is Aleph1, that is, the same amount as the amount of real numbers, and that total number of finite cubes of 10^{100}mts size is Aleph0, now it seems ridiculously implausible that all the configurations will manifest themselves, there simply is no space for that to happen. The very definition of Aleph1 is that you cannot map Aleph0 into it in a one-to-one correspondence, so how can a space containing Aleph0 points instantiate Aleph1 universes? It *seems *like hell it cannot. But what are we to say of the opposite situation, what if there are Aleph1 points, Aleph1 finite regions, and only Aleph0 possible configurations for a Newtonian bubble[2]?

What if :

Aleph1 / Aleph0

…correctly describes the probability for a specific configuration of bubble to turn up actual, to be realized?

It seems like this should give us a probabilistic value of one. Yes, one, not infinite, because probabilities range in between 0% and 100% which is one. We *want* to say that if there are more finite spaces available then configurations, and they outnumber them by infinity, obviously all configurations will be instantiated, but behold the mathematical unproven intuition. The same reasoning might have lead us astray into the doomy lands of dividing by zero. Let us here maintain a skeptical position, accept that the question is open, and protest, with Bostrom (2006) that with so many mathematicians someone should have invented by now a non-contradictory math that allows us to think of infinitarian probabilities when we have to. Bostroms problem deals with ethics and infinite space, ours deals with probabilities and infinite space. To an extend, his approach to the issue using hyper-reals (a kind of number in between reals, a kind which, by now, you may even find perfectly ordinary) may prove helpful to our case, but there would still be many unsatisfactory results.

There is one more mathematical intuition that we have when talking about randomness that is quite dangerous. We always assume that all available outcomes have the same odds, that is, we always assume the die has sides of the same size. We are talking about real randomness here, not man-made artifacts that were *specifically designed to equalize the chance of possible outcomes. *It is a widespread vice to think that if something is random, truly random, then all outcomes have the same chance. This is false.

Think of a common die with two sides painted yellow, and the others with numbers one to four. Yellow is 1/3 likely, and any number is 1/6 likely, yet, it is completely random which of those possibilities will be actualized. Random means[3] you have no idea what will come up, not that you have no idea what is the likelihood distribution between possible outcomes. So even if it were established that Aleph1 / Aleph0 is a defined value corresponding to more than zero, and that the amount of configurations is Aleph0, and that the amount of finite spaces is Aleph1, this would still not guarantee that *all* configurations are instantiated, for they could be distributed in an evil way, with a part of them being way more likely than others, so that the operation of division among this others would not render values above zero.

One particularly implausible but nice looking scenario is that in which not only there are, say, Aleph0 configurations and Aleph0 spaces, but also there is an exact match between them, that is, no configuration ever repeats itself, and all, by infinitesimal chance, manifest. This is so absurd, in probabilistic terms, but so absurd, that it is completely compatible with one of the principles Leibniz used to build up his monadic system, the principle of the identity of indiscernibles, according to which it is impossible for two things to be exactly the same in all characteristics, and yet be numerically distinct[4].

We fortunately have no commitment to mathematics and transfinites when building our Utopia, we have a commitment with the mid-level world, the world of trees, glasses, love, sex, lust, 3D movies, fingers and music. We are allowed to create and abandon mathematics, this will be discussed in the chapter concerning the mathematics of Utopia, so, for now, let us just guarantee that there will be many bubbles around us looking a lot like us. To do that without having to interfere with the domain of math, we must quantize our Newtonian world, all objects and events that take place within it will take place in a finite amount of space, and there will be none that can be infinitely divisible. This guarantees that the total amount of possible configurations is finite. Let us do the wrong thing (counterfactually it is not wrong) and decree that the likelihood of any possibility arising is the same, and this will guarantee us a mathematical operation in which we multiply a finite number by an infinite one. The finite one is the probability of a bubble with configuration X appearing in a finite space, the infinite is the number of finite spaces. This operation is well defined in current mathematical theory, the result is the same as the infinite number. We do not even need to decide between infinite sizes to find out our needed Dreams within Utopia. Utopia may have an undefined infinite number finite spaces, as long as we don’t find any other reason to establish one, pick your choice. Mine is Aleph227.

So we can dream in peace, in Utopia, there are infinite universes, in some of them you are the prettiest girl in the prom, there is some epistemic uncertainty (which of those universes is the one I’m in?) which makes you feel like you have choices, even though deep in your heart you know you don’t. As Alexander Vilenkin puts it, “Many-Worlds in One”, this is the cosmology of Utopia. And the best of it, the equations fit a T-shirt! If that was not enough, your average high school student can grasp them, and a bunch of scientists and analytic philosophers can rest assured that the Dream of Computation will one day be achieved, thanks to Leibniz’s Universal Harmony, discrete physics, some ad-hoc principles of computation, and infinitely extent space, in our cozy and cuddling Newtonian-ish universe. Welcome to Utopia.

——————-

These were only the practical requirements, but by now, we may have realized that the borders dividing practical, useful, interesting, sweet, cozy, and beautiful are not as well defined as we might have wished for. When we postulate infinite bubbles, are we looking for the practicality of dreaming? Hardly likely… we are seeking the beauty of dreaming within reality. It is indeed practical to abandon Quantum Physics, so no trouble here. What about simplifying equations? I hope baroque and modern art were both right, and for that to be true, it must also be true that the visual and mental environments became much more populated in the centuries that separate them. Our century brings with it accelerating information, accelerating people, and accelerated lives, there is no doubt we are in an age in which beauty lies in simplicity, and it is perfectly marvelous to find out that the equations that best fit our practical requirements also will turn out to be the most beautiful.

What else do we need in our physics to have beauty? There are at least two non-classical phenomena that are in the desires of most: Teleportation (aka non-local travel) and Time Travel (aka non instantaneous travel). A few sophisticated ones might also be wishing for a zero-energy machine, a machine that theoretically produces work and therefore useful energy forever. Let us consider all of those separately.

[1] The reason for the impossibility of immortality has nothing to do with the fact that one in every two billion people reaches 118 years old. Immortality in this sense

*is possible*, not as in living forever, but as in living some 255466 years of healthy life. The real impossibility has to do with a question underlying philosophy of mind called personal identity, and it is not time to talk about it. Not yet.

[2] Note that all the concerns about Newtonian bubbles here also apply to Einsteinian and quantum bubbles, unless there are strictly no features of space that are not-quantizable, that is, absolutely every property of the multiverse that can vary is perfectly discrete, not infinitely divisible, nor gunky (if you are not a philosopher of physics, do not bother about finding out what “gunky” means…).

[3] The word ’random’ usually ranges over both kinds of cases, but I pledge guilty to anyone who would accuse me of semantic dictatorship, since it is true that the case where all outcomes are equally likely is nearer to the center of the target of the word’s possible ranges. Since we do not have two words, I encourage people to use ’random’ to mean any distribution of outcomes, known or unknown, and ’equally distributed random’ for what happens in fair dice, coins, and other casino devices. “objectively random” means that a Laplacean demon, or our physicists super computer, would not be able to know in advance, “subjectively random¨ is the kind of randomness that the die has, it is your state of knowledge that is undefined, not the outcome itself (at least in a Newtonian bubble). Since you are less powerful than a supercomputer, it follows that that which is objetively random is also subjectively random, but not otherwise. Your subjectivity cannot see deeper than objective reality, for there is nothing deeper to be seen.

[4] Too see why this is absurd, consider a spheric World with only four identical spheres exactly a hundred meters away from its center, and exactly the same distance away from one another. Since there is no up or down in the universe (no outside reference), there are no properties to distinguish the spheres, except their relational properties to one another. If this still bothers you, then imagine an infinite universe in all directions, with an infinite series of spheres occupying it in perfect density and homogeneity, any two of them are now not only intrinsically identical, but also identical in all the relations they bear to any object within the universe, yet distinct. Credits to Lewis (XXXX)

O mesmo

very badargumento de pintar as faces do dado e ainda considerar a distribuição aleatória… ¬¬’Quase iniciou a terceira guerra mundial em pleno II-EI, rs.

Se há mais faces pintadas de um cor, e menos faces pintadas de outra cor, é claro que

em relação a corexiste uma causa atuante (a saber, a distribuição desigual de cores) contando, além da pura aleatoriedade. E isto explica a diferente probabilidade dos resultados.E pro diabo se a “tradição” não vê essa coisa óbvia.

I sadly lost some 9 pages describing Time Travel and Teleportation…….

It took away the motivation to keep writing about the physics of Utopia. So I’ll probably start another topic and then go back to physics…..