PeterJ

Okay, I suppose I'm not understanding it all yet.

Oh man. How can this gave become so complicated? I made some mistakes and that certainly didn't help. My apologies. But I have described just one process and have not cherry-picked. I'll try to put it staighforwardly. We count the products of primes >3 in R. We do not need to count the products of prime factors larger than sqrt p2.because there aren't any. We then count how many 6n numbers there are in R. We then deduct the former from the latter. That is, for each product that 'lands' in R at 6n+/-1, we assume that it prevents one twin prime from occuring. (In reality two products may occur side by side at 6n+/-1 and only prevent one twin prime from occuring, but we are always taking the worst case scenario because we want a lower limit on the twin primes in R, not the actual quantity of them), I hope this makes things more clear. I know I'm coming at it from an odd angle. The calculation becomes ever more lengthy as p grows larger, but there's no need to calculate anything except to establish the principle. I'm not sure there cannot be any exceptions, but I'd be astonished if the quanity of twin primes in R did not increase with p1. (Would it be possible and a good idea for someone to delete the two or three early posts that referred back to my original messy terminology, which disappeared when I re-edited my first post? They'll completely confuse anybody starting out at the beginning of this discussion, Just at thought.)

There seems to be a difference in their result if we are rounding up, as we are here. The second version can produce a slightly greater total. But this can be ignored. . The division by 6/p works like this. By using the 6n numbers as a metric it is possible to map the remaining products of the primes against it. One inviolable rule is that the products of p >3 that effect the distribution of twin primes (ie. occur at 6n +/-1) always occur at 6np+/-p, Thus there are always two relevant products of p in every 6p numbers. All other products can be ignored. Thus there can never be more than R/6p x 2 products of p in R. I can't see quite what you're doing in your second para. You would only need to divide R by 15 and 21. There could be no relevant products of primes >7 in the range.

Yes, It goes by at high speed and then suddenely you're 70. I'm not there yet but can see it coming. I think it;s a very good idea to develop your own ideas and not be too swayed by other philosophers. Few of them solve major problems so we need to do it differently. But, the problems they identify are genuine problems. For a theory of everything these problems would have to be solved. My objection to your idea is that it does not address any of them. For instance, such a theory would have to solve the problem of consiousness. If it did not do this it would not be a theory of very much. As it stands your idea seem to concern only physical mechanisms and processes, so even if it worked it would be a purely physical theory and would run into the same trouble in metaphysics as all purely physical theories. A plausible Toe would not leave major problems unsolved. I think you;re being very unfair on physicists by asking them to accept your idea, It isn't close-mindedness, it's the lack of testable consequences, predictions and solutions, it isn't that it';s wrong, it's that it does not make a difference. A Toe should be controversial and directly threaten current ideas. Then it becomes interesting. Or that's how I see it. You say that you 'do not think the world beyond my fingertips is an illusion. Its real and its amazing . Its not a giant clockwork machine unwinding'. But you do not need to choose. It could be an illusory clockwork machine. .

There are two products of 5 at 6n+/- in every 30 numbers. So 72/30 x 2 gives the total. (Or 72/15 - which gives not quite the same result but may be better). Where R =72 the only primes factors we need consider are 5 and 7. No need to count 11 and 13. So 48/15 + 48/21 = 7. Here R/6 -1 = 11, so 11 - 7 = 4. So there are at least 4 twin primes in R where p1 = 7.

Yes. This is exactly correct. But this extension would be a mistake in my view. You are taking a limitation on your intellect to be a limitation on the world. I would say we think we are a self because we are not aware that we are the all. You may not agree, but you do not know that it is not the case. If you could establish an independent self then you would have to conclude that Buddhism is nonsense. .

I depends exactly what you mean. If a part really is a part, and not just an arbitrary region of a continuos whole, then it would have a boundary, while the whole would not. So they'd have this different characteristic. But this is probably not what you mean. If you mean that each portion of a line looks the same on any scale as we zoom in and out then I understand that. If you mean that the parts are not truly separate from the whole, which would be indivisible, but are notional or conceptual, then I cannot conceive of such an entity, but I know what you mean.

Weirder and weirder...

Not quite. If p = 7 then R = 72. R will always be a number divisible by 12. I see what you're saying. But these objections can be met. I just need to clarify what I'm saying. RP would be R/3p ( a neater way of putting it) for each p up to sqrt p1. This would exhaust the prime factors that we need to consider. The final formula should be R/3p for each prime up to p2. This might be an arbitrarily large series of calculations. I'm hoping this clarification answers the problem in your example. Thanks to you both for taking an interest. Is the idea clear yet? It should not look obviously wrong. .

John Re that 2nd sentence "Totalling 2R/(6p) for each prime up to p2 gives the maximun qty of relevant products in R." This works because the products of a prime occur at 6n+/-1 twice in every 6p numbers. So R/(6p) x 2 gives the products of p that affect the distrubution of twin primes. Ie. the relevant products of 5 occur at 25, 35, 55, 65, 85, 95,.. Using this it is possible to calculate the maximum number of prime products that can occur in R. We already know the maximum number of twin primes in R (assuming no prime products it's (R/6)-1). So from this we can produce a lower limit for TPs in R. I'm afraid I cannot follow your maths so can't comment on that. Imatfaal - An example. Where p1 = 5 R = 24 (49 - 25. This gives the max qty of TPs in R as 3, which is (24/6) -1) RP = 2 (relevant prime products in R, Given by 2(R/6p) or 2(24/30) ) Ergo, where p1 =5 there is at least one TP in R. The trend is then always (on average) that for each increase in P1 there is an increase in the minimum qty of TPs in R. It is only 'on average' because the calculation is very sloppy lower down the number line.and will underestimate TPs. Another way of saying this might be - If there is a TP in R for some pair of consecutive primes, then there must be a TP in R for any larger pair. I would have liked to do the calc for TPs up to N, which would have been a more common approach, but I couldn't make that work. .

I can agree with a lot of that. But why approximations and estimations? These can never be truths. It seems to me you're overcomplicating the issues. But it's hard to know what to say about it all. I'm not sure I understand your view yet. You say - "Point being, that it is both true that we are capable of imagining "no divisions" and true that it is impossible to actually acheive such a state. Not while being a living human. The mere fact of being a living, conscious human, separates us from the rest." We are not capable of imagining 'no divisions'. The intellect requires divisions in order to operate. These are the categories of thought. Also, why do you say it is impossible to achieve such a state while being a human being? This is not a finding based on experience or logic. This is why I referred to guesswork. A guess cannot be presented as a fact. . Guessing is fine as a guide to research, as you say, but it is not a result. I feel that your guesses are getting in the way of the facts.

Yes. Many apologies. The original post was very messy. I don't know how I made so many mistakes. I've edited it and hope it's now more clear. In short ... R/6 gives the maximun qty of twin primes in R. Totalling 2R/(6p) for each prime up to p2 gives the maximun qty of relevant products in R. Taking one from the other gives a lower limit for twin primes in R. It is a mechnical argument derived from the behaviour of the products of the primes. I hope it's beginning to make sense. It can be made more accurate but this will do to get the principle established.

Hi John. It;s because there are two products of p at 6n+/-1 (therefore 'relevant') in every 6p numbers. We only need to take account of the primes up to P^2 since products of larger primes will not fall in R. Oh hell L is a hangover from a previous attempt to sketch it out. I'll go back and change it to R. Pr is the quantity of relevant prime products in R. I'm afraid I don't know the conventions for the use of the letters.

Imatfaal - I've just been following up your reference to Weyl's work on the continuum. I found myself reading this essay. http://publish.uwo.ca/~jbell/Hermann%20Weyl.pdf It completely amazed me. I can't thank you enough for pointing me at Weyl. I can now say 'what he says' when anyone asks what I think about all this. Well, what you would call a continuum would to me be an impossibe object. If it has no parts it could not be 'boundless of extent'. I read Weyl as saying the same thing. A boundless continuum can only be a concept, not a real object. I would define a continuum in two ways, following Weyl as far as I can tell. 1) An intuitive continuum would not be a mathematical object. It would continuous and would not have parts. In Weyl's co-ordinate system as described in the essay above it is described as a point. It would a uni.. oops. 2) A mathematical continuum would be an extended series of points or locations. It would have parts. It would be a conceptual construction, and within the limits of intelligibility and usefulness we would be fee to define it how we like, Weyl suggests that this is not an idle matter of definition but has implications for the reality of time and space. In a far more muddled way I am suggesting the same. . I could not follow the entire essay but it is interesting to watch Weyl try to reconcile these two version of the continuum. He seems to end up with the view that both contain an aspect of the truth, and that the law of the excluded middle must be questioned for a resolution. This is roughly my suggestion, that there are two valid ways of looking at spacetime, contradictory but also complementary to each other, and the problem we have with it is that we assume that there is only one correct way. . His explanation of the distinction we require between the continnum of intuition and experience (which I have been calling 'pure' or 'ideal') and the continuum of the natural sciences and everday thought, (the continuum of the 'transcendental' or imputed world) is brilliant. It annoys me when people say in a few words what would take me a few thousand. It's the second best essay I've ever read on the mathematics of Buddhist cosmology. Many thanks again for mention Weyl. How about we follow his terminology?

Mike - I don't think you have a theory but maybe you have an insight. I have tried a similar experiment, motivated by a quite similar idea. It worked on the two occasions. I tried it, and each time the chances of it working were approximately zero by my calculations. So I have some sympathy with your idea and the story of the pebbles. I just don't see how you can make anything of it without developing a overarching cosmological theory for which it is just a very small part. To say that anything that can happen must happen does not seem to get us anywhere.

The Twin Primes Conjecture Sometime ago, when my hasty first attempt went wrong, I promised to come back sometime and give my ‘proof’ of the twin primes conjecture. As was rightly pointed out in the initial discussion it is not a proof as a mathematician would use the word, so I’ll call it an heuristic argument. Or, if you like, it's just a thought. I make no claims for it other than that I think it correct as far as it goes. All that matters to me is whether I have made mistakes. I’ll try to state it as briefly as possible. It is painfully simple. Please excuse the clumsy termimology. I have tried to be clear but clarity is not one of my talents. . As I make use of the 6n numbers for the calculations it simplifies things if the primes below 5 are ignored. So ‘primes’ here will mean ‘primes >3’.. The proposition: There is always a twin prime between the squares of consecutive primes. Call p1, p2 consecutive prime numbers. Call R the range P12 to P22 Call RP the quantity of prime (>3) products in R (those that occur at 6n+/-1 and thus affect the distribution of twin primes). Call RL the lower limit for twin primes in R. RP is calculated as 2R/6p for all primes below P2. Where for any p this produces a fraction we would round up. This is clumsy but it can be refined. It need only produce a lower limit, not a quantity. It becomes increasingly accurate as R grows larger. RL is R/6 - RP. (Count the potential locations and deduct one for each 'relevant' prime product in R.) The calculation will overestimate RP and thus underestimate RL. This is fine as its accuracy increases with P.. As long as it does not overestimate it is useable. If we do the calcs. we find that LL increases with P. Thus the quantity of twin primes in R increases with P and may be arbitrarily large. It can never fall below zero. End. Okay, it’s clumsy, but I don’t think this really matters. It can be made less clumsy but then it gets harder to present. At present I cannot see what is wrong with the basic approach. The increase in R for each increase in P grows exponentially, while Pr as a proportion of R grows ever smaller. Even if the calculation is clumsy for the lower reaches of the number line the trend is unmistakable. Or maybe not. I’ll wait and see. I have two questions. Have I made a mistake? How can I make the presentation tidier so that it’s easier to see what I’m getting at? EDIT: Tidied it up a lot after the first comment. .

One problem is that it the only proof we can ever have that an event is possible is if it happens. It would be impossible to find an event that was possible but did not happen. Thus evidence and counterevidence is impossible. Also, I cannot see what this theory is for. How does it help? What does it say about specific problems?

I see. So you know it all already. Even though you know that you don't know that what you are saying is true, you say it as if you know it is true. This is not science or philosophy, It's a lottery ticket in the great game of guess the truth and then argue for it. It's a game I have no intention of playing. .

Interesting stuff Mike, and good pictures. I also have little interest in a theory that merely unifies some forces by some mathematical procedure or other. But the big picture would have to be bigger than this. You do not explain matter or mind, its existence or creation, not answer even one philosophical question. A correct theory of everything would explain everything. But 'everything' is a very difficult concept. I would recomment Paul Davies book Mind of God for an initial discussion of this. Also, incompleteness becomes an issue for theories of everything, as Hawking points out, and needs to be dealt with in the theory. Russell's paradox also arises, for it is the same problem in a diffterent form. You show 'everything' as contained within a blue line that marks the set. Is this line inside the set? In this case you need another line in the diagram to contain this, and so on to absurdlty... . You seem to have a strictly physical theory on the go, and this cannot be a theory of everything. Even Hawking agrees about this, although his essay on the topic ('The End of Physics') seems to have disappeared recently from the Internet. Perhaps he changed his mind.

I was not defining 'you'. I was suggesting you examine your 'you' in order to answer your questions about what is inside and outside rather than jump to conclusions. . Well shucks. I'm just someone whose had time to study things that few people bother with. Most people are specialists, and have no time for exploring the connections between areas of knowledge. Thus I can become an expert in my field without being a genius. There's little competition. I know of no 'logical' walls and do not switch modes in order to defend stances. Yes, most philosophers run into logical walls, more usually called 'barriers to knowledge' or 'ignoramibuses'. But I know know how to get around these barriers. As far as I know there are no barrriers to knowledge. Tar - This is my main argument against Immortal. PJ - No main argument is required. As you say, he was perfectly capable of shooting himself in the foot with his own arguments. Tar - If you start with my defintion, that TAR2 is a particular living body/brain/heart group, living on Earth, and PeterJ is a different and distinct, unique living body/brain/heart group, then inside and outside have distinct and meaningful meaning. PJ - Yes. This is clearly true. Tar - Anything of PeterJ inside TAR2 is imaginary (specially since I'm straight). I do not have the actual PeterJ in my head, in the chemicals and neurons, I have an analog representation of you. Incomplete and inaccurate to be sure. PJ - Yes, but this is irrelevant. The suggestion is not that you and I are merged inside our heads. The suggestion is that you and I are a conceptual overlay on the unity of awareness, a distinction that is not ultimate or fundamental, and can be reduced just as Kant suggested. Inasmuch as you are you and I am me, then we are distinct centres of experience with distinct physical forms. Only at a level of awareness beyond 'you' and 'I' would this unitification of identity become apparent. Or 'by reduction' might be a way of putting it. Thus by reduction many well known philosophers arrive at this idea. But in philosophy it is a conjecture derived from logical analysis. In religion it is a knowledge claim from direct experience. Tar - One should not use what is known to be an image, as the real thing. Nor call a real thing an image. PJ - Amen to that. Now you just have to discover a phenomenon that is not an image. I would suggest that there is only one. Tar - The thing and the image of the thing are already understood by virtue of the two pure intuitions Kant figured we each are endowed with, that of space and that of time. And any understand occurs at the now, and at the here. And the only place and time I have, is where the body/brain/heart group of TAR is. And the only here and now that you have is where the body/brain/heart group of PeterJ is. We can coincide, as in being on the same talk board at the same time, or being in the same place, should we run into each other. But there is a clear distinction between what goes on inside TAR2 and what goes on inside PeterJ. And we each are on the the outside of the other. PJ - Kant was clear. The intellect cannot be understood unless we assume that it reduces to a phenomeon that is not an instance of category. Such a phenomenon could not belong to you or me, it would be the orgin and destination of you and me. The suggestion here is that from absolute viewpoint there is no 'Tar' who can be distinguished from anything else. Tar - I know this to be true because every single one of us knows there are billions of "other" body/brain/heart groups wandering around the Earth. PJ - Yes. Of course. Tar - We have already correctly parsed this inside outside thing, even if the parsing is all done inside our heads. We already know the difference, base on our equipments ability to know the difference. To know the difference between memory and prediction. To know the difference between a hamburger sitting outside on the plate, or inside in the stomach. We must have already figured these things out. They are not a mystery, or a logically impossible stance to take. PJ - Hmm. I think you are skating over the issue here. You do not speak of a knowledge, of things but of the appearance of things. Solipsism is unfalsifiable because what you are referring to is only relative knoweldge. It is only when you attenpt to develop a fundamental theory based on this 'knowledge' that the logical difficulties become apparent. This is why it is a non-topic in physics but the central issue in philosophy. Mind you, the idea that the universe is one interconnected entity is gaining ground all over. Tar - What is impossible is for you, not to be you witnessing what ever you are focused on. PJ - Have you ever spent some time trying to see exactly who is doing the witnessing? Tar - And if there were to be no you, who would you ascribe the point to, should you reach such a point as you were successful in dissolving your Atman into Brahman? With no separate PeterJ to consider, there is no one to acheive a high score, in PeterJ's estimation. PJ - Yep. I wouldn't put it in the same words,but something similar. There is nothing to be attained and nobody to attain it. This would be a crucial insight for those who study awareness. . . Tar - But we are WAY off thread, and I am off my rocker. This stuff is really silly to argue about, because we are already both assuming the existence of the other,(you existing outside me, and me existing outside you) to even be arguing the point with each other. PJ - I don't think it is silly or off-topic. I think you are on the right track and think about these things seriously and honestly, which is fairly unusual, but that you haven't quite seen the real subtlety of the view you're opposing. I am not assuming the existence of anything at all. For my view, which in one of its forms is Middle Way Buddhism, nothing would really exist. If it did then Buddhism would fall apart as a metaphysical theory. I've often wondered if the claim that nothing really exists is testable in physics but I suppose not. It is testable in logic, however, and it works very well as a solution for philosophical problems. But the proviso 'really' would be crucial, since obviously things exist in a sense. I don't want to argue about these issues, you can believe what you like, but I'm happy to explore it. Perhaps the Matrix is an interesting case study, because it is debatable whether Neo's world is inside or outside of his mind. This is all relevant, because the suggestion would be that for Neo to understand his reality he would have to go well beyond faith, language and even the intellect. Then we are not beset by theory-laden perceptions and intellectual preconceptions and can see past the images to what is actually real and true. Then we see what the writers of teh Upanishads meant when they said that if we see the voidness one thing we see the voidness of them all. You might like to check out Beaudrillard's 'Desert of the Real'. This would be very relevant here. It is the title of the chapter of the book in which Neo hid his computer disk. .

This is not quite what I said. What I said was correct. A fundamental theory would require a phenomenon with some godlike properties. Being absolute would be one. This is not a controversial idea but commonplace. pretty much common sense. The word 'God; would be innapropriate, but it's in the ballpark. Okay - you won't;agree. But then you don't need to agree, or even examine the issue, as long as you can make do without a fundamental theory. If you can do this the issue does not arise.

There is no scientifically recorded observation of consciousness inside of a living organism either, so this tells us little. By the usual definition of 'scientifically' used in the natural sciences no such observation would be possible. For physics conscious stars is as useless an idea as conscious human beings.

Hmm. It seems we are on different planets. I'll leave you to talk to some physicists about your idea. It doesn't seem to have anything to do with philosophy.

What problems does your idea solve? It certainly won't solve any philosophical proplems, and it is therefore noreductive, It is therefore not a TOE. But I can't make head or tail of it.

Okay. Thanks for explaining your position. I can't see what problems it solves, but then as yet I can't understand it, and that may be just me.