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Author Topic: Is infinity an illusion?  (Read 68707 times)

Offline webplodder

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Re: Is infinity an illusion?
« Reply #200 on: 04/10/2013 16:51:29 »
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 reality. 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.
« Last Edit: 04/10/2013 17:08:10 by webplodder »
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #201 on: 04/10/2013 17:00:44 »
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?
It depends what assumptions you make. If you assume that the lobby can tannoy every room at once to tell them to move to room 2n (or whatever), then the whole move can be done in the time it takes to move one room. Of course, if you insist on the tannoy message travelling at the speed of light or less, it will take an infinite time to complete the whole move (but to each occupant, it will seem as if everyone is moving at the same time). If it takes half an hour to move rooms, you can repeat the whole move every half hour - although the guests might complain - best give them a half-hour rest before moving again if another infinite coachload turns up ;)
« Last Edit: 04/10/2013 17:02:46 by dlorde »
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #202 on: 04/10/2013 17:06:14 »
Quote from: alancalverd
The "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.



I don't think it is very meaningful to say something is infinite, even mathematically speaking, because the mathematics we use today only exists within the context of the material universe we find ourselves a part of with its particular laws. Apparently, there may exist other universes 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.
« Last Edit: 04/10/2013 17:10:19 by webplodder »
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #203 on: 04/10/2013 17:06:49 »
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.
Infinity doesn't necessarily have anything to do with time - were you thinking of eternity?
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #204 on: 04/10/2013 17:16:32 »
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.
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 ?

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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.
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.
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #205 on: 04/10/2013 17:42:59 »

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Infinity 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?
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #206 on: 04/10/2013 17:49:49 »
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.
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 ?

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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.
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.


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.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #207 on: 04/10/2013 21:45:39 »
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Infinity 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.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #208 on: 04/10/2013 22:37:12 »
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.
The laws of physics are expressed using mathematics. They don't determine mathematics.

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What 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.

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

 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #209 on: 05/10/2013 00:35:16 »
Infinity:

 "the quality of having no limits or end" : the quality of being infinite.  OK.

 "a space, amount, or period of time that has no limits or end."  This definition is so tied to our 3+1D world that it is of very limited value with respect to any thoughts beyond the finite.  However, it does establish a sort of relationship between eternity and infinity, such that it is quite reasonable to use “infinite” when making reference to “eternal”, although this relationship is not necessarily reciprocal.

 "a very great number or amount."  This is simply a mathematical approximation; valuable in mathematics, but not really infinity.

Eternity
 "time without an end."  This is valid only if you accept that an unbounded sequence is really infinite.
 
 "a state that comes after death and never ends."  This is theology/philosophy, not science.

 "time that seems to be without an end."  “seems to be”:  Precisely!
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #210 on: 05/10/2013 09:51:31 »
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Infinity 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.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #211 on: 05/10/2013 10:07:18 »
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.
OK, but what has time to do with an infinite amount of something or a numerical (mathematical) infinity - or were you only considering the potential for physical infinities?

Just trying to clear up why you feel time is necessarily involved.
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #212 on: 05/10/2013 10:13:54 »
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.
The laws of physics are expressed using mathematics. They don't determine mathematics.

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What 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.

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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.
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. It is true to say that our universe is finely tuned in a way that permits the development of life and that a slight mathematical shift in the way it works would produce a very different universe. 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?

 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #213 on: 05/10/2013 14:15:45 »
Many physicists regard nature as deeply mathematical in nature so it would indeed appear that maths is determined by the way physical reality works.
So: which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?

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Ask yourself why maths arose in the first place. It arose because it precisely reflects reality and another kind of arrangement would not.
So you keep saying. I'm asking for some plausible argument or explanation, preferably with hypothetical examples. 

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

Offline webplodder

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Re: Is infinity an illusion?
« Reply #214 on: 05/10/2013 15:08:51 »
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So: 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.



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

Indeed, but what I meant and should have made clearer is the day to day experience of 4 dimensional spacetime in our universe where classical maths works. In another kind of universe where the surface appearance might be any number of dimensions our maths would fail.

 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #215 on: 05/10/2013 15:23:01 »
It is easy to assume that because mathematics seems to be the “language of the Universe”, the Universe is “governed” by mathematics.  Perhaps it is better to reason that mathematics is the best language we have found to enable us to understand the Universe.  There may be a better language, we have just not found it yet.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #216 on: 05/10/2013 15:44:45 »
Quote from: dlorde
were you only considering the potential for physical infinities?

Just trying to clear up why you feel time is necessarily involved.

Obviously I can’t answer for Webplodder here, but I would like to be clear where I stand. 

Mathematical infinities are approximations for very large numbers, so they can be used with time, space and any numerical quantity.

I have yet to be convinced that something physical can come from nothing; therefore something must always have existed. .this something must, therefore, be infinite/eternal.  To avoid infinite regression, which is infinitely pointless, it becomes necessary to consider a number of possible attributes of infinity. 

Is this science?  In so far as it appears to involve a sine qua non of the existence of everything, I think it must be.  Surely this makes a consideration of the nature of infinity as much a part of physics as, for example, extra dimensions, multiple universes or the reality that might underlie QM.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #217 on: 05/10/2013 16:31:37 »
Quote
So: 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.
Those are examples of maths in this universe. I'm curious to know how you think it could be different elsewhere. As I mentioned previously, geometric relationships may depend on the topography in which they're used, but given a Euclidean plane, they will always be the same.

Are you suggesting that in another universe 1 + 1 may not equal 2 ? 

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In another kind of universe where the surface appearance might be any number of dimensions our maths would fail.
Why should maths fail? we might find it difficult to express the physical appearance of a strange universe through mathematics, but that doesn't affect mathematics. Also, physicists have already mathematically described a variety of multidimensional universes.
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #218 on: 05/10/2013 16:35:12 »
If the universe or multiverse is non-local then time would not be a necessary property because everything would exist simultaneously, both past and future events and communication would be instantaneous. I'm no expert but aren't there experiments which show that photons can travel back in time to reflect a delayed decision on the part of the experimenter in a variation on the double-slit experiment?
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #219 on: 05/10/2013 16:49:54 »
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. We inevitable are forced to use a three-dimensional brain to describe something outside of our ability to describe. Even our maths are fundamentally three-dimensional since they are the result of electro-chemical processes with the biological brain.

I would like to make another point, however. Notwithstanding the foregoing, 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.
« Last Edit: 05/10/2013 17:06:31 by webplodder »
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #220 on: 05/10/2013 18:20:44 »
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.
Potentially, yes.

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Even our maths are fundamentally three-dimensional since they are the result of electro-chemical processes with the biological brain.
In what way is mathematics 'fundamentally three-dimensional'?

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... it has never actually been proved that consciousness is the result of brain activity, at least, not entirely.
It isn't something that can be proved, any more than the existence, or otherwise, of god. In these cases, science generally assesses the evidence for and against to generate the most plausible (provisional) explanation. In the case of consciousness, the vast majority (and the most reliable) of evidence is entirely consistent with it being generated by the brain. I'm not aware of any robust evidence to the contrary. This, and the absence of any plausible suggested mechanism (particularly one consistent with the laws of physics), suggests to me that it is beyond reasonable doubt.

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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.
Or not. If we had some ham, we could have ham & eggs, if we had some eggs...
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #221 on: 06/10/2013 09:47:48 »
dlorde, Roger Penrose has pointed out the problem with regarding the brain a kind of computer consisting of essentially an immense number of on/off switches when we look at the non-computability of mathematics. What is meant by this is that 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. I'm not suggesting there is compelling scientific evidence to support this view but that things may not be as straight forward as many scientists seem to think.
« Last Edit: 06/10/2013 09:50:13 by webplodder »
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #222 on: 06/10/2013 09:59:37 »

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In what way is mathematics 'fundamentally three-dimensional?

Mathematics is produced by a brain that has a three dimensional architecture (or to be pedantic, four dimensional spacetime).

 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #223 on: 06/10/2013 10:26:32 »
... 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.
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.

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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.
No one seriously considers the 'brain as computer' to be more than a clumsy and limited analogy. The brain is clearly is not based on an axiomatic mathematical system, and there's no requirement for consciousness to be mathematically complete and consistent.

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.

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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.
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.
 

Offline webplodder

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Re: Is infinity an illusion?
« Reply #224 on: 06/10/2013 11:46:14 »
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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.

Yes, I'm aware of that, but I simply wanted to state the case in uncomplicated terms for general understanding.

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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.

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.

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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.

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.
 

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Re: Is infinity an illusion?
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