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You might argue that you would have eternity in which to perform the manoeuver, but in eternity you would already have done this an infinite number of times, and since there seems to be a distinct possibility that you cannot add to infinity, how can you perform the manoeuver again?

Quote from: alancalverdThe "endless digits" business is irrelevant to infinity.Would you also apply this to the “endless digits” of number lines? I look for clarification here because it is so rare to find someone who doesn’t insist that these are examples of infinite series.

The "endless digits" business is irrelevant to infinity.

Infinity may be an illusion caused by our experience of passing through the material world. We do not really understand the fundamental nature of time and it may be the case that a dimension or dimensions underlie the classical world that are non-local in the sense of existing without separation in space or time, therefore, time as we normally define it would not be necessary. It has already been proven mathematically that nature at the quantum level is non-local so time could be simply an emergent property of the macro-world. Actually, this is a more logical approach than to assert infinity exists because how would you ever prove it? It is only because time is a common sense experience that we assume it has to go on forever but common sense is not a good guide to the true nature of really. People used to think the earth was flat based on common sense or that it was impossible to float about but now we understand how gravity works we are much wiser about things.

Apparently, there may exist other universe within a multiverse that have no or little resemblance to ours and where our mathematics would simply not apply.

In the case of pi this is also true such that even if the value of pi never terminated during the life of our universe it would probably not apply in another future possible one.

Infinity doesn't necessarily have anything to do with time - were you thinking of eternity?

Quote from: webplodder on 04/10/2013 17:06:14Apparently, there may exist other universe within a multiverse that have no or little resemblance to ours and where our mathematics would simply not apply.Says whom? I can see the laws of physics being different, but mathematics is an axiomatic system; how could it be different in another universe ?QuoteIn the case of pi this is also true such that even if the value of pi never terminated during the life of our universe it would probably not apply in another future possible one.Can you explain how or why? Pi is a ratio whose exact value depends on the chosen geometry, but on the Euclidean plane it's irrational, so it seems to me that its decimal representation in any universe will be the same, given a Euclidean plane.

QuoteInfinity doesn't necessarily have anything to do with time - were you thinking of eternity?This is not a meaningful question. For a start, how do you define infinity and eternity and what is the difference, if any?

Mathematics inevitably reflects the way the laws of our spacetime universe work but not necessarily other kinds of universes where there exist very different laws, if any.

What if there existed universes that were like the way the quantum world is, i.e. completely random?

Pi only works based on the axioms of maths but such axioms originate from consistent features of nature which may be peculiar to the universe we happen to find ourselves in.

Quote from: webplodder on 04/10/2013 17:42:59QuoteInfinity doesn't necessarily have anything to do with time - were you thinking of eternity?This is not a meaningful question. For a start, how do you define infinity and eternity and what is the difference, if any?I'll defer to Merriam-Webster: Infinity: the quality of having no limits or end : the quality of being infinite.: a space, amount, or period of time that has no limits or end.: a very great number or amount. Eternity: time without an end.: a state that comes after death and never ends.: time that seems to be without an end.The difference should be obvious - eternity can be considered a type, subset, or instance of infinity, specifically relating to time.

Time and space are inextricably linked, therefore, I cannot see how any separation between them is possible. Matter, and the laws governing the way matter behaves, operate within a space time framework so it seems false to me to attempt to give separate definitions to them.

Quote from: webplodder on 04/10/2013 17:49:49Mathematics inevitably reflects the way the laws of our spacetime universe work but not necessarily other kinds of universes where there exist very different laws, if any.The laws of physics are expressed using mathematics. They don't determine mathematics.QuoteWhat if there existed universes that were like the way the quantum world is, i.e. completely random?Ours is a quantum universe - and it has stochastic (probabilistic) randomness; that too can be expressed through mathematics, but doesn't determine mathematics.QuotePi only works based on the axioms of maths but such axioms originate from consistent features of nature which may be peculiar to the universe we happen to find ourselves in.Which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?

Many physicists regard nature as deeply mathematical in nature so it would indeed appear that maths is determined by the way physical reality works.

Ask yourself why maths arose in the first place. It arose because it precisely reflects reality and another kind of arrangement would not.

What would be the case in a universe with 6 dimensions, for example?

So: which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?

Our universe probably has more than 6 dimensions; but regardless, what would the case be with 6 dimensions? how would that affect mathematics?

were you only considering the potential for physical infinities?Just trying to clear up why you feel time is necessarily involved.

QuoteSo: which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example? Well, for example, 1+1 always equals 2, or the square of the hypotenuse in a right angled triangle is equal to the square of the sums of the other two sides. Pi is another example, although we only have an approximation of it though, for practical purposes, it is predictable enough. So, in the real world adding 2 apples together always results in 3 apples and calculating heights using trigonometry is reliable.

In another kind of universe where the surface appearance might be any number of dimensions our maths would fail.

dlorde, we can only try to conceive of other types of universes in terms of our brain physiology which has been shaped by evolutionary forces peculiar to our planet and the geometry of our spacetime universe. It may be, as far as I know, that if other intelligent forms have arisen in other kinds of universes they would possess an entirely different way of perceiving their environment than us and so their symbolic representation of such could be so bizarrely removed from the way our brains work that we simply could not relate to it.

Even our maths are fundamentally three-dimensional since they are the result of electro-chemical processes with the biological brain.

... it has never actually been proved that consciousness is the result of brain activity, at least, not entirely.

It has been assumed by most scientists that consciousness is an emergent property of the brain's electro-chemical activity but what if this was not correct? That would mean that we would have to introduce the idea that consciousness could exist outside of the brain and possibly beyond physical death. If so, then ideas and concepts might exist in a kind of ethereal 'Platonic' realm which interacts with physical reality.

In what way is mathematics 'fundamentally three-dimensional?

... given a reasonable level of complexity, any set of mathematical rules, or axioms, can be shown to be self-contradictory at some point by anyone expert enough in maths.

What this means is that we can no longer regard the brain as a kind of computer operating on strictly logical lines but something more which seems to be produced by consciousness. An ordinary computer would not have the ability to 'see' anything outside of its axioms because a computer does not possess consciousness.

This is why it is questionable as to whether we can regard the brain as the seat of consciousness and that consciousness cannot simply be based on a set of simple electro-chemical processes.

It was Godel who showed that any non-trivial axiomatic mathematical systems can generate statements that are not provable within the system, and cannot include statements of their consistency without being inconsistent.

Also, let's not forget that a digital computer can emulate a neural network, as can any universal Turing machine, and the brain is, basically, a linked assembly of biological neural networks.

No, it says nothing at all about the brain as the seat of consciousness. Consciousness is neither complete nor consistent in the mathematical sense, so is not, in that respect, different from any non-trivial axiomatic mathematical system, so that doesn't disqualify it from being based on a such a system; however, the brain itself isn't based on such a system. It's nonsense whichever way you look at it.

QuoteIt was Godel who showed that any non-trivial axiomatic mathematical systems can generate statements that are not provable within the system, and cannot include statements of their consistency without being inconsistent. Yes, I'm aware of that, but I simply wanted to state the case in uncomplicated terms for general understanding.QuoteAlso, let's not forget that a digital computer can emulate a neural network, as can any universal Turing machine, and the brain is, basically, a linked assembly of biological neural networks. I'm sorry, but a Turing machine is nothing like a biological brain since a Turing machine has no potential for creativity. A Turing machine needs a set of instructions to follow provided by a human programmer.QuoteNo, it says nothing at all about the brain as the seat of consciousness. Consciousness is neither complete nor consistent in the mathematical sense, so is not, in that respect, different from any non-trivial axiomatic mathematical system, so that doesn't disqualify it from being based on a such a system; however, the brain itself isn't based on such a system. It's nonsense whichever way you look at it.Documented near-death experiences tend to support the idea that consciousness can exist independently of the biological brain. I'm not claiming the case has been proved, however, anyone who cares to look into the evidence would seriously consider the possibility.

I'm sorry, but a Turing machine is nothing like a biological brain since a Turing machine has no potential for creativity. A Turing machine needs a set of instructions to follow provided by a human programmer.

Documented near-death experiences tend to support the idea that consciousness can exist independently of the biological brain. I'm not claiming the case has been proved, however, anyone who cares to look into the evidence would seriously consider the possibility.

As for pure mathematic it's only your imagination and logic webplodder that restricts it I think. You can create all sorts of logic, and it does not have to fit this universe, to be self consistent. To make the assumption that theoretical mathematics must be a result of the way we find our universe to work, as coming from that, will need to prove that all mathematics in existence today are subsets of the physics we find. Myself I don't think that is possible to prove.

It must have occurred to others that there is a striking similarity between QM and thread drift.Feynman would like it because it takes a topic from A to B by every possible route,Heisenberg would approve because there is a distinct uncertainty that the topic will ever arrive at B.Schrödinger would be pleased because the thread, like his cat, remains neither dead nor alive until a Mod takes decisive action.

... I might formulate it such as whereas humans make both bad and good choices a quantum computer only will make the most probable fit to a question.

And that seems ultimately to become a question of free will. In a way it becomes a sort of 'clock work' universe, building on a assumption of there being a 'ultimate answer', for each and any question asked.

Individually we find indeterminacy, and with consciousness involved also the ability of making 'wrong choices'. So whereas a 'universal quantum computer' might ignore the ability to make a wrong one, meaning that 'free will', it does not imply (to me at least) that it can't have a consciousness, as being self aware.

dlorde, how does an artificial intelligent system manage to integrate and synthesise information resulting in completely novel paradigms? I have yet to see this being achieved today, even with the most powerful computers which are really just huge number crunchers.

It seems to me that a Turing machine lacks some vital element in processing data which I would call 'thinking.' It is safe to say that so far we have much to learn about how the brain processes information so it would seem over optimistic to assert that a Turing machine would be capable of multi-level operations when we don't even know how this is achieved with people, or indeed, animals.

Are you saying a Turing machine is conscious and self-aware? Can Turing machine reflect and make critical evaluations and draw from experience? I tend to doubt it.

I accept that the evidence surrounding NDEs is anecdotal, however, those instances where NDE patients have recounted information they could not possibly have been aware of during the time of their NDE has yet to be explained.

Those critics who maintain a NDE patient is just that - near death, but not actually dead so that they might still retain some awareness of their surroundings - overlook the fact that a flatlined brain would simply be unable to experience the rich imagery involved in observing incoming data like images, audio sensations and touch. These are something that require the use of the higher brain functions located in the forward lobes of the brain and other areas which, in a brain that is showing virtually zero EEG activity, would seem implausible.

Pete, infinity doesn't bother me. There was a time when I felt I needed to take issue with the use of the term infinite for things that were obviously not infinite, but that is no longer the case.

I have tried on a few occasions to clarify my position, but either I don't do a very good job, or others are reluctant to pick up the idea. As this thread demonstrates, discussion diverges into all kinds of other things. There may be a link between NDEs and infinity, but I wonder about its scientific pedigree. Perhaps, if I state my starting position as three simple points it might help.1. There can never have been nothing, otherwise there would still be nothing now.2. If there has always been something, that something must be infinite/eternal.3. If there has always been something, what is the relationship between that something and the Universe we observe?

1. There can never have been nothing, otherwise there would still be nothing now.2. If there has always been something, that something must be infinite/eternal.3. If there has always been something, what is the relationship between that something and the Universe we observe?

Bill, I'll voice my objections again, but I feel like I'm a broken record at this point. Quote from: Bill S1. There can never have been nothing, otherwise there would still be nothing now.2. If there has always been something, that something must be infinite/eternal.3. If there has always been something, what is the relationship between that something and the Universe we observe?These are all making way too many assumptions about how the universe would be created. You seem to be enforcing the physics within this universe onto whatever existed that created the universe. For example, could the creation of the universe involve a creation of infinite amounts of space and time instantaneously? You could argue that would violate causality, but causality is something that exists within the universe in our space and time--it isn't defined and shouldn't be expected to hold for an event that occurred outside our space and time. You're coming into asking these big questions with a lot of preconceptions. You may be right and your view is certainly one way of looking at it, but it certainly isn't the only way of looking at it.