Yes, I was thinking of dual aspect monism. I favour the thought that number is something that comes with manifestation, like time, or extension. This is not to say that they do not exist in Platonia, eternity, or other forms of manifestation. But I don't think we can make any hard conclusions about what happens elsewhere, or that we have stumbled upon anything fundamental.

When it comes to Platonia or eternity my intuition is that number is present more in a form of geometry, wherein it is an expression of something more transcendent and fundamental. A kind of divine geometry.

Yes I think it depends on your personality type. I always had very positive results, except for a few brief episodes of paranoia, cased by external circumstances causing my body to want react defensively, or evasively. Well into the hedonistic world in my experience though.

isn't it more a case of the words are alluding to something considered or believed in, but which is inconceivable to us. So rather, a humble acknowledgement of our cause, even if done in ignorance.

...and your point is?

I don't think we can deconstruct Platonism, but we don't have to accept it either it's just part of philosophy. If Plato hadn't come up with it, someone else would have, I probably came up with the rudimentary idea myself before I read Plato.

However I am not an idealist as such, so I can take it or leave it. The idea of letting abstract numbers fall back on the concrete world does appeal to me, which is why I am using the analogy of grains of sand. Also I am reluctant to ontologize number too, I see it as a natural quality of manifest existence, but not exclusively in the form we find it.

I already know about Hilbert's hotel etc. What is your point again, there doesn't seem to be one?

Ok let's try the odd and even numbers and see where that takes us.

Odd numbers = even numbers = odd and even numbers = ( odd numbers and even numbers munis even numbers) = infinity.

There you go, you can subtract infinity from infinity.

You still haven't either described this continuum, or said where it is, in realation to us?

Are you not able to discuss a simple hypothetical, such as the grains of sand I described? I know it is probably an impossibility in physical reality, but that is not the point.

I'm interested in these ideas about an existing continuum, is this in the field of mathematics, or astrophysics?

So you are suggesting that number, i.e. Integers are not fundamental. Does this mean that there are places where 1+1 doesn't equal 2?

Yes you raise a good point about Aliens interfering with us is some way. But we would only be likely to trip them up if they are very prolific throughout the universe. We are not likely to visit more than a few local star systems any time soon.
My point is that our first priority should be to establish a base of some sort in orbit so that if a catastrophic event happened on the surface of the planet, there would be a few people able to recolonise and more importantly retain the technological and scientific knowledge for the survivors. Thus enabling a fairly rapid recovery of civilisation. Currently all it would require to wipe us out to the extent that the few lucky survivors are thrown back to the Stone Age, is a fairly large asteroid impact in one of the deeper oceans. Perhaps an asteroid about 500metres in diameter would have that result and there are plenty of those wandering about in our vicinity.

There is absolutely no way an infinite number of anything of any size can occupy a finite space.

Who said it was finite? I am discussing a hypothetical situation, in which there is sufficient space.

Reality takes place in the continuum, which is Aleph1or 2^(Aleph0) if you have reason to reject the continuum hypothesis.

Nice idea, but that is a mathematical form, we are talking about life and existence, where is this continuum? And how does it produce these finite things I see before me?

I did point out when I brought this up that I am aware of the difficulties in applying infinity to reality.

Also, the experience of Psilocybe dreaming is anything but static! ;)

I was going to say something along those lines, but thought it was to hedonistic for such a polite audience.

I was thinking of a notional infinite quantity of grains of sand. Or do you think there cannot be and infinite quantity of anything, even hypothetically?

to scratch the surface. Reality takes place in the continuum, where denumerable infinity is not big enough

I'm all ears, what is infinite about reality?

I believe that life on Earth is at an ever-increasing risk of being wiped out by a disaster, such as a sudden nuclear war, a genetically engineered virus, or other dangers. I think the human race has no future if it doesn’t go to space.
— Stephen Hawking

Yes he's right, also about what he said recently about A.I.

We will have to go into space, or at least colonise a neighbouring planet. Hopefully we will have a few hundred years grace before it is necessary as our space technology is still very clunky. Perhaps the first priority should be to develop a self sufficient space station. So that should a large asteroid hit the earth, there will be some survivors. Even this is some way off.

In the meantime we just have to survive the crises brewing at the moment and try not to commit hari kari.

It's going to be a rocky ride the next 1or 2 hundred years.

I expect that what is more likely is another fall of civilisation, followed by another dark age. It does have the feel of a post apocalyptic novel though.

Yes I understand this(although I'm not a mathematician), I dont see a cardinality though in the grains of sand. Unless the set of all grains of sand (green and blue) has a higher cardinality than the set of green grains?

I think this is as far as I can go in abstract mathematics, my interest is more in the direction of maths in the real world or where it is to be found, or relevant in/to existence.

Yes, perhaps if each grain is infinitely small, then they would fit on the head of a pin;)

If you can't find two literally infinite piles of sand of different colours, why not use the odd and even numbers instead?

Yes, but numbers are ideas, so susceptible to human frailty. An alien, or a monkey, can count the grains of sand and can only come to the same conclusion, because they are not ideas.

am a believer that actually infinity is a number.

Can this number be counted?

Also, I am aware how many grains there are;

blue grains = green grains = green plus blue grains = (green plus blue grains minus green grains) = infinity.

Yes, Russia seems to be going into a dark place at the moment.

Why do you say that?

Well can't say what would have happened, but the U.S. would probably have got stuck in Syria and would have been accused of waging war on a legitimate sovereign nation, not to mention supporting rebel groups which could be labelled militants. It would all have been very unpopular back home. An unholy mess and that's not to mention getting in a mess with Russia.

What decision made in the 40's influenced the present situation? It's interesting that you bring up the post-WW2 world-scene. To me, this question is really about what we owe one another on a global scale... and what we don't.

Well take your pick, the alienation caused by U.S. involvement in the Middle East has been building bit by bit since the paranoia over the creep of communism after WW2, led to a cat and mouse game between the U.S. and Russia all around the world.

I can't say if the Arab spring would have happened otherwise, but I doubt it would have been so incendiary.

My first thought was that Veritas represented fire, which represented pain.

Yes, Paul Klee was a big influence at one point, this was before I had learnt to paint. I wasn't going to let that hold me back from being creative. I like those landscapes (Moth creek, Govetts leap), I am beginning to see an Australian style, perhaps its due to the bright light.

Yes I get that, but the fact that it is undefined is not really saying anything about things that might exist. The use of undefined in this maths seems to be more a case of, encountering an unspecified(undefined) value and then concluding we can't go any further because we've lost the content. Out there in the world of things that exist, you can't just deny something that exists simply because it doesn't compute.

Let's say there is an infinite amount of grains of green sand and there is also an infinite amount of grains of blue sand, both exist. We know that if we theoretically count them as one group infinity + infinity and that we will then have an infinite amount of grains of sand, which we know are green and blue, but which are still seperate, because we are only imagining them as grouped together. Now let's imagine we mix them up so that they are all randomly mixed in together, a set of an infinite amount of grains of sand, of undefined colours. Now we could theoretically sort through this set and put all the green ones in one place and all the blue in another until we are back were we started. So we have subtracted an infinite quantity from an infinite quantity.

I am by the way aware of the problems of applying infinity to existence.

I wouldn't be surprised if Deutsche Bank is hiding a gaping casm somewhere with the German paranoia.

l am not a mathematician, so can't get involved in discussing equations. However I don't see the necessity when considering infinity.

You say an "indeterminate form", yes I can see that, but isn't an infinite quantity also indeterminate? I don't see how it is significantly different. You could add infinity to infinity and get infinity. Can't you then take that same infinity away again and leave the first infinity as it was before. I agree that addition and subtraction might come from the finite realm, so in a sense this is trying to discuss an unknown in another room, you can't see into.

Anyway, the Hindu's describe Brahman as infinitely infinite(I'll look for a reference), so there are plenty of infinites around in there for one to be subtracted without diminishing his omnipotence.

I would point out that I don't use infinity much, I find eternity much more fruitful.

I do feel sorry for Cantor, that he was not able to progress further in the direction of the continuum. I think he was lacking some transcendent insight, which might have helped.

Regarding the Hilbert's hotel illustration. It occurs to me that infinity - infinity = infinity. I say this because the Hindus define Brahman as that which is the same if you take something away from it, subtract it, it remains the same infinity.

Yes I'm sure there are some important things to be found out as yet. For me the area of interest is in divine geometry. I have developed some concepts, but they are not fleshed out yet.

Regarding absolute infinity, I feel it is an over simplification. This is not to say it is not the case, rather that it's intricacies may be beyond us at this time. The idea of a kind of transcendent continuum is interesting, but primarily within the sphere of being, rather than anything external. I have developed a thought experiment which attempts to illustrate this.

Imagine you are looking at a transcendent being, like the Christ, a bodhisattva, a god*. As you focus, you feel you are only seeing the surface, the external body of them, the real person is further back(metaphorically), under the surface. You refine your conception to peel back the layers a bit. You imagine a purer more transcendent being, on a higher plane, in a higher dimension. But equally present next to you in your plane, in the same body. It is just your conception which has changed.

So you repeat the process, imagining an even higher purer form, perhaps in a divine realm next to God. Again you are seeing exactly the same person, in the same place nothing has changed other than your perception. Then you repeat the process and begin to realise that each time you peel back a layer it curls up and folds back behind the being like a hair on his head. Then you notice there are many thousands of hairs alongside it. The being becomes in your imagination transcendent. Traversing many dimensions, even realms worlds, times. While all the time absolutely present in this one place. You realise that the dimension they inhabit is of another order another kind and for them to step into the manifest world's we find ourselves in is like dipping their toe into the water. You look again and the being is as before before you looked closer, just another person standing next to you, all along it was your conception which had changed.

* I have experienced something along these lines in person with a guru, I once new, which helped me to develop the idea.

Yes, 2D abstract ideas around concepts of skin/membrane/change.

Thanks, I don't seem to have much time for reading at the moment. To much time spent painting, or restoring my house.

I was at the old site and still am a believer that actually infinity is a number. We just don't have the correct definition of a number. Because infinity and it's counterpart, which we avoid by talking about limits, are so useful and so obvious in mathematics that the former shouldn't be just taken as an axiom an left there. (And I do believe that there's an absolute infinity, actually)

Interesting, I do play with the idea of an actual infinity from time to time, it always ends with with some kind of fractal. Although when I contemplate Brahman, as defined in Hinduism I can conceive of that kind of infinite in the sense of infinitely transcendent.

Are you thinking of something multidimensional, or transcendent in some way?

Well I don't know what his reasoning was for pulling back from the conflict, but in hindsight it looks to have been a good call.

As to whether the U.S. caused the war and the destruction of Syria. I think they are certainly culpable, but the causes go back to the first gulf war and before. A legacy of foreign policy decisions in regard of the Middle East going back decades, perhaps even to the late 1940's.

I love Japanese gardens!
I happened upon an interesting Australian artists the other day, Sydney Long, I'm already drawing inspiration from his work.

Some of my abstract pieces.

If we could generalise the notion of an "observer", an act of measurement or individuation, with matching rigour, then we would really be closing in on a fundamental view of things. We could finish what the Greeks started.

This is simple enough, one is simply required to accept that "Platonia", or number, is appealing to the conception of mental or abstract forms which have a reality(presence) in a divine(transcendent) reality, as well as our reality. In which all forms in that divine reality are as fundamental as number appears to us. Another such form is the form of self or being, which is both present in the divine reality and the world. So in measurement we find the divine witnessing the divine in concert with the person waving rulers around. Hence the fascination of the Greeks with number and Platonia, they can intellectually sense something absolute going on.

Mind~world dualism treats consciousness as some definite Cartesian substance - a concrete soul stuff. While divine~world can ease you back towards a more pantheistic and immanent rendering of the situation. It starts to sound more like my organic and pansemiotic conception.

This is only superficially a duality, there is always a third veiled component, of spirit. Or an imminent divine self, or being. This being is simply a witness, eye, a lense. So we have a triad, world, mind, spirit. Mind, body, spirit. Spirit being as universal as number, but immutable, so is essentially veiled to us. In the absence of specific tutoring to know the spirit for what it is.

As I see it what the OP is thinking of is not whether idealism or realism is indicated, or supported. But rather the possibility that we, the personal self, might through some unknown, or veiled mechanism in our reality be able to be switched, or transferred to another reality, rather like we seem to be when we have a dream.

I don't think an idealist ontology is required for this, there could just as well be "real" structures in our existence which are a mechanism for this to happen. For example a mechanism for the process of the transmigration of souls, enabling our "self" to be reborn in a newborn after our death. Or the mechanisms employed by enlightened beings to inhabit more than one place at a time, or walk between worlds, times.

It occurs to me that God would have to follow the rules on this one. I don't know what the implications are for so called omniscience.

That was an early painting it didn't turn out as I intended, apart from that it is a nice painting. I should do it again and it should turn out right now, the idea was very much in the Turner style.

Oh, my images have disappeared, I'll try and get them back. The've mysteriously returned.

Yes I know the extent of the chaos. I wouldn't stress the proxy war to much though. It might be going on in some level within the respective armies of Russia and the U.S. But their administrations are not in that game.

Anyway I am more concerned about the carnage in Allepo at the moment, because there is a large trapped population. Allepo is(was) the largest city in Syria, so if the supply lines are cut there may be mass suffering of the civilian population. I heard a Syrian in Allepo on the radio this morning claiming that there is heavy cluster bombing going on in some neighbourhoods. Specifically designed to kill people hiding in buildings.

Oops! I didn't intend to put the cybosh on the thread. I will discuss the war in the thread on the Third World War in the politics section.

Nice, I used to do doodle art, very enjoyable. Also it developed into abstract art for me.i'll fish some out.