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This equates to answering the question "what's the difference between white and black?" with: "White is white because it shows no colour; black is black because it is black." That's the "physicist's" answer isn't it; absolutely right, but completely useless. It's only apparently useless to you :) For science it answers our questions we need answered some of what you are seeking is outside the domain of science. That which is outside science we care not about. However, let’s take a closer look at your logic. The space is infinitely small indicates there is no space.
Again we don't have a problem with no space. Its stuff thats smaller than plank distance it doesn't exist in our realm. Again I think you are talking about well what is the stuff thats smaller than plank distance and we go you may never know why get hung up over it, it's not in our space we cant access it. Space is infinitely great means the space is infinite. We cannot have an infinite number of finite particles.
Again at science I have told you consistantly from QM we agree with you on that. Space is only infinite to us in terms of observation and travelling ... physically it is most certainly finite. Space without matter represents the physical reality of nothingness.
We disagree totally. If you read the articles I linked it is quiet clear from QM eventually all matter must disolve based on radioactive decay. All matter seems to have a decay constant it is just very very large but not infinite. That does not mean the universe ceases to exist just because matter doesn't exist it simply becomes a universe devoid of matter. So if no forces conspire to kill the universe inbetween time QM would say the universe will continue until it dissolves into a empty matterless place. What happens then or whats governs things from there at this stage that is outside the realm of science as we have doubts we can have physical access to test that realm. Nothingness is the only thing of which we can have an infinite amount.
An infinitely large amount of nothingness = nothing.
An infinitely small amount of nothingness = nothing.
Ergo, infinitely small = infinitely large.
Thats all an esoteric argument. The same argument exists in mathematics ... prove to me you have zero. The argument goes you have +5 and 5 or you have +10 and 10 etc how can you prove zero. Zero can occur by balancing infinite negative numbers versus infinite positive numbers. So zero mathematically is also an enigma it can never be proved to exist as you don't have zero of anything. In the end this all falls to occum's razor (http://en.wikipedia.org/wiki/Occam's_razor) What you say may be true Bill S but it is unimportant from empircal studies point. At science we apply the razor and simply say what you may well be true it is totally unimportant for the same reason as the mathematical use of the razor on defining zero, your argument leads nowhere and provides no workable framework. You may find that uncomfortable ... so be it ... there are antirazor groups.
Last edited by Orac; 11/04/11 03:07 AM.
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Again I think you are talking about well what is the stuff thats smaller than plank distance and we go you may never know why get hung up over it, it's not in our space we cant access it. Planck distance is a finite distance. I'm not asking what is smaller than Planck distance. All I am saying is that if something is infinitely small it does not exist in the material world. Space is only infinite to us in terms of observation and travelling ... physically it is most certainly finite. The first part requires a very specific definition of "infinite", which I would not argue with, as long as we are clear about the context. I see no reason to argue with the second part. That does not mean the universe ceases to exist just because matter doesn't exist it simply becomes a universe devoid of matter. Presumably this universe is not devoid of energy, so it is not nothingness. Zero can occur by balancing infinite negative numbers versus infinite positive numbers. Undoubtedly this is mathematically true, but since you can never demonstrate that you have a positive or negative infinite number of anything, the argument is pointless in reality.
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Planck distance is a finite distance. I'm not asking what is smaller than Planck distance. All I am saying is that if something is infinitely small it does not exist in the material world.
Then you agree with science .. plank distance is a bounding condition for us. Presumably this universe is not devoid of energy, so it is not nothingness.
Correct at science we would simply a universe devoid of matter and full of energy and possibly dark energy and matter if such things exist. Undoubtedly this is mathematically true, but since you can never demonstrate that you have a positive or negative infinite number of anything, the argument is pointless in reality.
But I can have +5 and 5 and +10 and 10. I urge you to read (http://en.wikipedia.org/wiki/0_(number)) It evokes the same problem Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "How can nothing be something?", leading to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum
See I assure you it is exactly the same argument ... infact I did this exact dialog with my mate socratus (Israel Sadovnik Socratus). I have seen this exact argument many times and it dates back to the medieval times. Infinity in many ways is just a more modern version of the same dance over zero. Hence the solution for science is that infinity can only be valid with a given context and zero falls to occum's razor it means the lack of something.
Last edited by Orac; 11/04/11 09:22 AM.
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And therefore according to QM your theory is not the theory of everything as we state
"If a theory featuring renormalization can only be sensibly interpreted as an effective field theory, i.e. as an approximation reflecting human ignorance about the workings of nature, then the problem remains of discovering a more accurate theory that does not have these renormalization problems"
You require renormalization so therefore even if you were right you must by definition be only an approximation.
My theory does not require renormalization. The physical world comes into the picture only when matter is present. For matter, everything is finite. Even the number of universes is finite, but with an arbitrary limit (may be one or very very large number). Thus basically, my theory qualifies as a candidate for the theory of everything.




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That's the "physicist's" answer isn't it; absolutely right, but completely useless. .... Ergo, infinitely small = infinitely large. I agree with you that the answer is useless as far a physical world is concerned. Whether the space without matter is infinitely large or infinitely small, it is physically nothing and so of no use to us. Whether both are equal or not is a question that has no logical answer. Science requires logical answers, and so science cannot answer that question. We have to leave it to the philosophers. However, once we have matter (which is grainy), a physical world just exists; everything connected with the physical world is finite. Science is expected to answer the structure and the interactions (of this physical world) at all levels, starting from the quantum level to the cosmic level. How space, time and matter (with their respective qualities) came into existence is beyond the scope of scientific explanation. That is, there will always be something arbitrary, and you have to say 'white is white and black is black' because they are so. This arbitrariness will be the minimum in a real 'theory of everything in physics'.




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My theory does not require renormalization. The physical world comes into the picture only when matter is present. For matter, everything is finite. Even the number of universes is finite, but with an arbitrary limit (may be one or very very large number). Thus basically, my theory qualifies as a candidate for the theory of everything.
It does you just don't realize it if your using standard unlike charge attraction theory or do you have a does your theory have a different way on how that works? .
Last edited by Orac; 11/05/11 12:26 PM.
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Part 3
So far we have looked very briefly at infinity as it is used by mathematicians, scientists and philosophers. For the present, at least, I propose to let the philosophers’ views take a back seat, and try to concentrate on the more scientific aspects of the infinite.
In general, scientists seem to be quite comfortable with the ways in which they use infinity, and if these definitions serve the purpose of making scientific calculations and theorising easier and more straightforward, as long as long as they do not lead to errors, I am very happy to leave them alone. There is no need to look for any reality that might underlie QM in order to use it; similarly, there is no need to look for deeper meanings of infinity if the “shut up and work” ethic is all that is needed in a given situation. However, for those of us who neither work in science, nor shut up readily, questions must remain.
When considering infinity, one of the major questions that must be asked relates to the nature of the Universe. Is the Universe finite, or infinite? I have already raised the possibility that it might be both, but this possibility needs to be examined rather more closely. If we accept the Big Bang theory, it looks as though the Universe must be finite; it had a beginning when it was infinitesimally small, but it was, nevertheless, finite. However much it grows, it can never become infinite. Would that it were that simple! There are those in scientific circles who propose that the Universe was infinite, even when it was small. On the face of it this seems selfcontradictory, but we must remember that, to the physicist, infinite may simply mean that there is nothing outside it, or even that there is no limit to the extent to which it can grow. However, outside that specialised usage, we have to ask if that is what infinity really means.
In visualising a Universe that grows from a miniscule speck to the vastness that we observe around us it is easy, especially for the nonscientist, to picture a sphere with a clear boundary. Today, most cosmologists accept that the Universe has no boundary. Does this mean that they think it is infinite? Apparently it does not. Current thinking is that the Universe is a hypersphere with a very slight (perhaps imperceptibly slight) positive curvature. If this is the case, it could be finite, but have no boundary. Scientifically, there is no reason to argue that a finite space must have a boundary.
What is a hypersphere? The simplest explanation is that it is the 4dimensional analogue of our familiar 3D sphere. The surface of a 3D sphere is often cited as an example of a finite surface that has no boundaries. This is fine as an example of something that is finite and boundaryless, but, unfortunately, many popular science books describe this as infinite; which, manifestly, it is not. The surface of a sphere is a 2D entity which requires a 3D object for its existence. It follows that the surface of a hypersphere must be a 3D entity that relies on a 4D object for its existence. So, we are asked to accept a fourth dimension of space if the Universe is a hypersphere, but that may be the lesser of two evils, as we are about to consider.
Next we need to ask what the situation would be if the Universe were flat – absolutely flat. Would this mean that either it had a boundary, or it was infinite? Is there any way in which a zerocurvature, boundaryless space could be contained in a finite volume? Is it logically or mathematically possible? Unintuitive as the answer may seem; it is “yes”. This is because cosmology is a mathematical science, and space is represented by a mathematical concept called a differentiable manifold which does not have to be surrounded by a higher dimensional space. A manifold is a topological space that equates closely to Euclidian space when considered on a sufficiently small scale. A manifold is said to be differentiable when, on a sufficiently small scale, it is close enough to vector space to permit the application of calculus. Space simply has to look right in any location you might choose, and the locations have to be smoothly compatible where they join. By way of example; take a square sheet of paper; mark North and South at top and bottom, and East and West on either side. If you now glue the North and South edges together, and the East and West edges together in such a way as to form a torus, you have no boundaries. You might also object that your paper is no longer flat, but cosmologists assure us that there is no need to perform this difficult gluing job; all you have to do is specify the neighbourhoods at the East and West edges as if they were joined, and do the same for the North and South edges, and you will have a flat space which is finite, but has no boundaries. If you think this is taxing the credulity overmuch, you are in good company. It appears that very few cosmologists are working on this line of reasoning, and most of those who are are trying to establish that it is not representative of our Universe.
What about a universe that is both finite and infinite, depending on the point of view of the observer. As mentioned above, this would have to be a context related universe, which, generally speaking, is what we would be dealing with if we were talking to a physicist. The context may be existence within the Universe. The Universe is expanding, but we have no evidence that it is expanding into anything. As far as we can assess our Universe is all there is. We could never visit all parts of it, nor could we travel all round it, because of its vast extent, and the speed at which it is expanding. For all practical and observational purposes it might as well be infinite. Physicists are content to refer to this as being infinite. Once again, as long as we are aware of the context in which we are using the term, that is a legitimate use of “infinite”.
The same physicist might also describe the Universe as finite if he/she is discussing a topic in which something outside the Universe designates the context. The concept of the multiverse, for example, might provide such a context, as might certain concepts in QM. Again, provided the context is clear, this seems reasonable, but we are still left with the question as to whether this is all there is to infinity.
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Bill, in your first post you say, Part one:... Once one has grasped the various ways in which the term “infinite” is used it becomes possible to work with it in much the same was that many scientists work with quantum theory, simply by accepting that it works ... This prompts me to ask the following: Various ways? You mean used in mathematics? And in physics? Used? By whom? Who are some of the "many scientists" who simply acceptI presume you mean blindly?that quantum theory works? You comment, "without asking how, or why." Why not? What is wrong with asking: How? And Why? Bill, you add, Infinity becomes a tool which can be used to express ideas and concepts. What kind of ideas and concepts? You also add, "The physicist can then say, Beyond this, we are not dealing with science. So then, what do you suggest? Bring in the clowns? Or is there room for philosophers and theologians?some of whom may also be careful scientists.
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This prompts me to ask the following: Various ways? You mean used in mathematics? And in physics? Used? By whom? Who are some of the "many scientists" who simply acceptI presume you mean blindly?that quantum theory works? "various ways….by whom?": In mathematics; e.g. look at the work of Cantor. In physics; look at Orac's contributions to this thread and in Is the physical world real? It should not be necessary for me to point you to examples of the use of infinity by philosophers and theologians; you are probably better acquainted with those than I. I presume you mean blindly? I think, if I had meant “blindly”, I would have said “blindly”. You comment, "without asking how, or why." Why not? What is wrong with asking: How? And Why? What gives you the impression I was saying that anything was wrong with asking how and why? What kind of ideas and concepts? How about singularities, infinite curvature, infinite speed, infinitely small particles and infinitely large space for a start? So then, what do you suggest? Bring in the clowns? Or is there room for philosophers and theologians?some of whom may also be careful scientists. Just in the two threads I mentioned, Orac has protested that aspects were “not science”. In your opinion, does that put him among the “clowns”? There is plenty of room for philosophers and theologians, but simply because I acknowledge that scientists may express opinions about what is or is not, in their view, science, does not mean I am trying to exclude anyone.
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.... Just in the two threads I mentioned, Orac has protested that aspects were “not science”. In your opinion, does that put him among the “clowns”?
There is plenty of room for philosophers and theologians, but simply because I acknowledge that scientists may express opinions about what is or is not, in their view, science, does not mean I am trying to exclude anyone. Bill S: Please accept my apology if in my questioning I came across like as if I think of myself as a prosecuting attorney. My intention was to get my own understanding and own thinking clear, not to question the sincere thoughts of others. It is my sincere hope that the day is not all that far off when the borders between body/mind/spiritmatter, thought and willwill no longer be there; that we will soon be able to travel from matter, to mind, to spirit like we can now travel from water, to land, to air and even to moon.
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I am happy to be a clown I am a QM scientist these days we have thick hides ... goes with the territory.
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Absolutely no need for an apology, Rev, a lively verbal exchange tends to clear cobwebs from places where cobwebs shouldn't be.
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Part 4
It is easy to think of renormalisation as just a device for getting rid of troublesome infinities in QM, but, as usual in modern science it is not as straightforward as that. In classical electrodynamics a problem occurred because – for example – the electron was considered as a point particle, but the electromagnetic field associated with it had to be described by a more continuumlike field theory. Essentially, this problem was overcome in QED, because both could be treated as quantum fields. However, a related problem remained, because if calculations try to take into account a particle’s reaction to its own EM field, runaway solutions are encountered which go to infinity. These infinities are embarrassing because they make nonsense of the calculations. Renormalisation involves some complex calculations and clever mathematics which effectively replace the infinities with finite physical values for the quantities involved. Although, in some scientific circles, renormalisation is regarded with considerable suspicion, it seems to be an essential process if physicists are to make any progress with important calculations in QED. Practically the process seems to work and has generated predictions that have been confirmed to a high level of accuracy. It may be just a mathematical device, but some wiggleroom has to be allowed, in the same way that it is considered acceptable to invoke extra dimensions in order to make theories work. The important lesson to take from this is that infinities that are not constrained by specific contexts, or limited by mathematics do not fit into finite, physical calculations. Every infinity that finds its way into scientific endeavour must be, in one way or another, “renormalised”.
Have we reached a point where we have to accept that any nonrenormalised infinity is outside the scope of science? I think not. A final point we have to consider before plunging into the complexities of the infinite is the nature of nothing. It is often said that the Universe came from nothing, but when one looks more closely at this “nothing” it inevitably begins to look very much like “something”. Like infinity, nothing seems to be quite a flexible term in science, especially in cosmology. For the sake of clarity, I must stress that when I refer to nothing I do not mean some quantum fluctuation of the vacuum, or anything else that might turn out to be something; I mean absolutely nothing.
I am going to start with an assumption. Obviously any assumption must be open to challenge, but without making some basic assumptions scientific progress would stagnate. The assumption is this:
There can never have been a time when there was nothing; otherwise there would still be nothing now.
In other words, something has always existed. Asking what that something might be is probably a shortcut into philosophy, but there is no need, at least at this juncture, to ask that question. All we need to do is to accept that something has always existed – something is eternal. We need to start by looking at the nature of eternity and how we might try to understand it. The popular image of eternity is that it stretches infinitely far into the past, and infinitely far into the future, but can this really be how it is? It is often said that in eternity, anything that can happen will happen, an infinite number of times. Let’s try to equate that with our image of eternity. Eternity stretches infinitely into the past; so an infinite amount of it is behind us. During that past time, everything that can happen will have happened, an infinite number of times. If everything that can happen has already happened an infinite number of times, how can these things happen again? How can things happen more than an infinite number of times? Here we have a paradox. If we regard eternity as linear, things have already happened an infinite number of times. An infinite number must, surely, be unsurpassable, yet there is still an infinite number to come. Undoubtedly there would be a way round this if we were dealing with mathematical infinities, but here we have a physical infinity. If we need a context for it, that must be the absolute need for something to be eternal. Am I confusing things by using “eternal” and “infinite” as though they were interchangeable? Is something that is infinite necessarily eternal? Until someone can demonstrate a mechanism by which something finite can become infinite, we are forced to conclude that anything infinite must always have been infinite, and must, therefore, always have existed. This brings us to a logical conclusion:
Nothing can become infinite; therefore any infinite thing must always have existed, and always been infinite.
Can there be change in infinity? As long as we regard eternity as being a beginningless, endless procession of time it is quite reasonable to accept that change can occur within “subsets” of that eternal time. However, we have already looked at a major problem involved in regarding eternity that way. The problem does not go away if you try to divide eternity into subsets. Because there must already have been an infinite number of subsets, and every change that can happen in every one of those must already have happened, an infinite number of times, again we are faced with the problem of having to add to that unsurpassable infinity. The only reason that time seems to us to have any connection with eternity is that we are creatures of time, and the only way in which we can come near to visualising eternity is to imaging it as an endless expanse of time. We coined the word “eternity” to describe that limitless expanse of time, but our understanding needs to evolve. A similar thing has happened with the word “Void”, which originally meant a vast expanse of nothing, but is now understood as a seething mass of energy and virtual particles. We are unable to imagine nonlinear “time”, and seem to have become the more so as our science, technology and sophistication have progressed.
In the same way that it makes no sense to try to divide eternity into portions of time, so it makes no sense to try to divide infinity into a collection of finite objects. At first sight, it seems logical to suggest that infinity might consist of an infinite number of these finite objects. However, as we considered earlier, it cannot have become infinite, so it must always have been an infinite number of finite things. We need to build change into our model, so finite, material objects must be subject to change. If this infinite collection of objects has always existed, then every possible change must have happened an infinite number of times, so we are back with the old familiar problem. We seem to have reached another logical conclusion:
Eternity is not a vast expanse of time. Infinity is not an extremely large number.
It is probably time to return to the question I sidestepped earlier on the grounds that it might involve philosophy, rather than science. The question was asking what the something might be that has always existed. The nonspeculative answer must be “everything that exists now”.
This leads to the question: Have I “painted” myself into a corner? I am proposing an infinite cosmos in which there can be no passage of time, and therefore no change; yet we live in a finite Universe in which we observe constant change. I suspect that there are those who would object that any speculation along these lines would be outside science, and such may be the case, but having made a proposal it seems necessary to defend it. That means there will have to be a “Part 5”, but, hopefully, I can keep that short.
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If everything that can happen has already happened an infinite number of times, how can these things happen again? How can things happen more than an infinite number of times? Here we have a paradox. Not really a paradox, Bill. That infinite number isn't a fixed number. You can add to it an infinite number of times. http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel "These cases demonstrate the 'paradox', by which we mean not that it is contradictory, but rather that a counterintuitive result is provably true: The situations "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms. Some find this state of affairs profoundly counterintuitive." Am I confusing things by using “eternal” and “infinite” as though they were interchangeable? No confusion, Bill. There are two dictionary definitions of the word eternal: (1) time without beginning and without end (2) timeless. Clearly, we're discussing (1)
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That infinite number isn't a fixed number. I have to go a step further and say: That infinite number is not a number at all. If you regard it as a number, it is only a mathematical infinity. If it were truly an infinite number, it would have to encompass all the numbers that could exist, which is manifestly nonsense. Outside of mathematics, infinity is not a number. Hilbert’s Hotel is something I have given quite a lot of thought to. It is clever, but it works only if you apply mathematical principles to infinity. You have to treat infinity as though it were a very large, flexible number, which it is not. (1) time without beginning and without end (2) timeless. Clearly, we're discussing (1) There are two definitions because eternity is used in two distinct ways. (1) is equivalent to mathematical infinities. (2) is the nonmathematical definition and is equivalent to real infinity.
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You know you would have been burned at the stake if rede and I had our way. http://www.youtube.com/watch?v=yp_l5ntikaUBEDEVERE: Tell me. What do you do with witches? VILLAGER #2: Burn! VILLAGER #1: Burn! CROWD: Burn! Burn them up! Burn!... BEDEVERE: And what do you burn apart from witches? VILLAGER #1: More witches! VILLAGER #3: Shh! VILLAGER #2: Wood! BEDEVERE: So, why do witches burn? [pause] VILLAGER #3: B... 'cause they're made of... wood? BEDEVERE: Good! Heh heh. CROWD: Oh, yeah. Oh. BEDEVERE: So, how do we tell whether Bill S is made of wood? VILLAGER #1: Build a bridge out of him. BEDEVERE: Ah, but can you not also make bridges out of stone? VILLAGER #1: Oh, yeah. RANDOM: Oh, yeah. True. Uhh... BEDEVERE: Does wood sink in water? VILLAGER #1: No. No. VILLAGER #2: No, it floats! It floats! VILLAGER #1: Throw Bill S into the pond! CROWD: The pond! Throw Bill S into the pond! BEDEVERE: What also floats in water? VILLAGER #1: Bread! VILLAGER #2: Apples! VILLAGER #3: Uh, very small rocks! VILLAGER #1: Cider! VILLAGER #2: Uh, gra gravy! VILLAGER #1: Cherries! VILLAGER #2: Mud! VILLAGER #3: Uh, churches! Churches! VILLAGER #2: Lead! Lead! ARTHUR: A duck! CROWD: Oooh. BEDEVERE: Exactly. So, logically... VILLAGER #1: If... Bill S... weighs... the same as a duck,... Bill S is made of wood. BEDEVERE: And therefore? VILLAGER #2: A witch! VILLAGER #1: A witch! CROWD: A witch! A witch!... VILLAGER #4: Here is a duck. Use this duck. [quack quack quack] BEDEVERE: Very good. We shall use my largest scales. CROWD: Ohh! Ohh! Burn the witch! Burn the witch! Burn him! Burn him! Burn him! Burn him! Burn him! Burn him! Burn him! Ahh! Ahh... BEDEVERE: Right. Remove the supports! [whop] [clunk] [creak] CROWD: A witch! A witch! A witch! BILL S: It's a fair cop. VILLAGER #3: Burn him! CROWD: Burn him! Burn him! Burn him! Burn! Burn!... BEDEVERE: Who are you who are so wise in the ways of science? ORAC AND REDE: We are Orac and Rede, keepers of the sacred infinity.
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Looks like you've been weighed and found wanting to be a duck Bill (hehe, sorry, couldn't resist that).
"Time is what prevents everything from happening at once"  John Wheeler




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My wife says: if I weigh the same as wood, does that mean I'm a blockhead?
I just shouted "Duck!!!"
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Orac, that's the best link you have posted; the science is impeccable!
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