PeterJ

For what it's worth I'm with the OP. A gnostic interpretation of the teachings of Jesus would not require us to believe in God. Or, at least, the God of the NT would be nothing like the god of the OT. I also am an atheist who believe Jesus (fictional or otherwise - who cares?) knew what he was talking about, or at least the wrrters of the books that survived the purge that have come down to us as the Nag Hammadi library. The western Church failed in its attempt to wipe out the gnostic interpretation and its practices in favour of the Roman heresy but it was a close run thing. It is incredible that I was fifty years old before I even heard of the Gospel of Mary, but the news was always bound to get out. There is a passage in the library that suggests that one day the teachings will be properly understood, and that with that undertanding will come a great healing. Nice thought.

Maybe it is not a maths question but it has some interest in metaphysics. (Thus the theological connection). Here it is zero as a concept, or as representing a void, that is interesting, rather than its role as a number. We might say that zero is a concept, so it is not nothing. Thus a void would be something and not nothing etc. From this kind of thinking we get to Lao Tsu's point, 'the zero begets the one'. Not mathematics, no, but it's this kind of thinking that stoned high school kids may get into. Especially since it implies something prior to zero. 'The Nothing That Is - A History of Zero' by Stuart Kaplan is worth a read. Mostly mathematics and social history. He leaves the metaphysics mostly to the very end but he does make the connection.

The idea would not be that human beings created the universe. It would be that consciousness created it, or that consciousness is it. It is not so odd. One physicist I have read (Greene?) proposes that with no observers to admire it the moon would gradually dissolve into it's atomic constituents. Don't know if that's a wild idea or orthodox, but it seems interesting. At any rate, it is hardly a new idea that everything in the universe is immediately connected, as if sharing a common identity. Re. black hole projections, is there something about Berkenstein bounds here? Never got to the bottom of what these are but wondered if they're relevant.

Qualia are qualities. They are defined as not being patterns in the brain. Patterns in the brain would be neural correlates of qualia, not qualia. There is no evidence that qualia can be reduced to neural correlates and many researchers find it an incoherent idea. The whole point of the term' qualia' is to distinguish the phenomonon from patterns in the brain. We might believe that qualia are the outcome of patterns in the brain, and there is clearly a causal connection of some sort, but even if smoke is caused by fire they are not the same thing. It would be impossible in principle to show scientifically that we can create qualia in a neural network. It would be impossible to show that qualia even exist. To say that qualia are patterns in the brain is to make a category error. Abiogenesis I know nothing about. But I always wonder why life only started once. This seems very strange to me.

You're clearly right about this. People will believe almost anything. But I'm tempted to ask 'so what'? We can't dismiss God on the basis that some people have a daft idea of Him. I also agree that books proposing a link between, say , 'chi' and what physicists call energy tend to be woolly and vague and not much use to man not beast. But this would not in itself show that there is no connection, or nothing to be gained by exploring the relationship. There's much handwaiving on both sides of this argument, and on the whole people seem to make up their minds long before they look into the issues.

I'm very surprised to hear you say this, immortal, but I couldn't agree more. Except maybe for the word 'perfection'. "Therefore we should look for new schools of philosophical thought which can achieve the perfection that natural sciences has achieved over the years."

My apologies. At one point I wrote 6p+/-p when it should have been 6np+/-p. This rendered one sentence a bit meaningless. Ho ho. I won't rise to this. I've talked to maybe fifteen or so mathematicians about all this and you're the first to interpret my words in such a way. I'll go with the statistics and assume you have some axe to grind. But sorry about the silly mistake. That confused the issues.

I think you've gone right to the heart of our mutual irritableness. In philosophy, where I am more comfortable, an argument is sometimes called a proof, albeit that it might be a failed proof. That is, a proof does not have to succeed in order to be called a proof. A syllogistic argument may be called a proof and also be invalid, unrigorous or successful. A proof or argument may may be correct and yet still be unrigorous and fail. I assumed the same would be true in mathematics. Apparently not. My proof is correct in the sense that it works, that it would be a way of proving, or perhaps demonstrating would be a better word, the TPC, but it is not yet successful becase it is unrigorous, there are one or two loopholes. Dr. Booker was of the opinion that mathematicians already knew of this method of proof, but had never managed to close the loopholes. I think I can see how to do it. We'll see. No. He was polite, and took the trouble to reply with a very thoughful and helpful letter, perhaps because he heads up an external mathematics education project and is used to talking to amateurs, congratulating me on my correct heuristic proof. He clearly did not expect me to make this proof sucessful, or to derive from it the sort of abstract proof that you would call a proper proof. I don't think he was either drunk or patronising, but you'd have to ask him. I'm more suspicious of you, mate, to be honest.

Okay. But there are clearly proofs that some mathematicans think are correct and heuristic. I'm sorry but I don't know anyone here or their background, so I must assume that Dr. Booker is right. I do not usually try to second guess such people. His letter to me was the best written piece I have ever read on the topic. Interesting though. Why do you say there is no such thing a s correct heuristic proof? Is it in the nature of heuristic proofs that they cannot be correct, or is it the nature of correct proofs that they cannot be heuristic?

Oh c'mon. You wrote... "The difference is that they are being polite and not wishing you to stop your investigations and thoughts by being brusque. DrRocket on a forum is not held back by those limitations of society." This is patronising and it is a personal comment. You have no reason to jump to this conclusion. You have no idea of what happened but just assume I am a fool. How did you expect me to react? What? When I said 'I have not suggested otherwise" it was in response to your statement "maths proofs must be rigorous, a heuristic in maths is only of a bit of explanatory use." Why are you persecuting me like this, with deception and trickery? Yes, I have managed a correct heuristic proof. And yes, I agree with you about maths proofs. Okay. This is not my problem. I did not attempt a rigorous maths proof. I did not pique your curiosity, as I intended, I only aroused your anger. I aroused Shadow's curiosity, but not yours. For you it is clearly personal. I'd rather it wasn't. Your words are there for anyone to read. I think maybe this would have been a better starting point than the assumption the people who I've talked to were being kind to me or are poor mathematicians. I'm not annoyed by the way. I know exactly why you reacted as you did. But it's not much fun to have to deal with such reactions, being continually forced to defend my sanity in this way, and I'd rather just deal with the issues.

How astonishingly patronising. But yes. That's why I was so surprised. His area is statistics, so perhaps he'd never thought about it. He probably figured it as soon as I put the phone down. I have not suggested otherwise. I do happen to believe otherwise, but I have not suggested it and will not here. I don't know exactly what you would count as a proof and what not. Are you saying that you're not sure you can rigorously prove that the products of 2 and 3 are not prime? Thanks for asking. Despite the vast implausibility of it I'm not quite sure that my full argument won't end up being interesting in some way, so I'll keep one or two important bit back if that's okay. But here's the idea. It could hardly be more simple. I am not claiming it is a proof of anything. I am saying that I have been told by someone who should know that it is a correct heuristic proof but not yet rigorous. He did not suggest I had changed the world, and neither have I at any point. I know that an heuristic proof is not a mathematical proof. I use the 6n numbers as a metric against which to measure the behaviour of the products of the other primes. This means ignoring 4 numbers in every 6 and examing only the two possible twin prime locations. Two products of p (>3) occur at 6n+/-1 in every 6p numbers. These will occur at 6p+/-p. So, for instance, 2 locations in every 6 cannot be twin primes since they are products of 5. Etc etc. Some fiddly corrections terms are needed, but these become increasingly unnecessary as p increase. Roughly speaking... For the range p1 squared to p2 squared, call it R, there are R/6 possible locations of twin primes. We know how many products of any p will be created in R for each prime up to sqrt p1, so we can deduct one total from the other. Of course, very often these products will occur where there is already a product of a prime, i.e 35, but this doesn't matter. I do not count twin primes, just set a lower limit for twin primes in R. It is never less than 1, and the calculation always underestimates it. R increases with p, while the quantity of products of primes below sqrt p1 occurring in R decreases with p. Ergo, on average the quantity of twin primes in R increases with p. Quite where it goes to I'm not sure but it's always on the increase. Nothing very fancy. I treated the the number line as a vibrating string and examined the combination wave created by the music of the products of the primes. As a result I would happily bet my life that there an infinite quantity of twin primes. But I would not be able to put together what you guys would call a formal proof. An heuristic proof is easy enough though, since it just means describing the mechanics. Please note that it was not me who made such a big deal out of this. I mentioned it only because I was being accused of being a dunderhead.

I think the OP's original argument goes wrong because it stipulates a physical phenomena that cannot be included in physics. If it stipulated just a phenomena of any kind it might work better. Stephen Hawking arrives at much the same conclusion as the OP but for what seem like better reasons. With my hazy understanding I concluded that Hawking's idea concerns theories, not empiricism or understanding, which by their nature are prone to incompleteness. That is, we may be able to understand it all even if we cannot include it all in a formal descriptive theory. His essay was called 'The End of Physics'. I note that he has withdrawn it from the Internet, so maybe he later changed his mind. Is it not more simple just to say that every theory must, like every dictionary, contain an undefined term?

Oh dear. I'm not impressed that you have not asked even one question and just dismiss what I say out of hand. I'm beginning to realise this is a common practice on this forum. The arrogance is surprising and very difficult to cope with. Perhaps it's my inability to speak as a mathematician that leads you to this dismissive view. Where p1, p2 are consecutive primes there must always be a twin prime between p1^2 ans p2^2, and as p increases so, on average, does the quantity of twin primes in the range. This can be established by simply examining the combination wave of the products of the primes up to p1. It's not my fault. It's the way the primes work. You remind me that I once phoned a professional mathematician I knew slightly to discuss the primes and in the course of the discussion happened to mention that the primes >3 must always fall at 6n+/-1. To my utter astonishment he did not believe me. I had to spend five minutes trying to convince him this was not baloney. I did not succeed. Ridiculous. Exactly which bit was baloney? Do I believe you or the most prominent mathematician I have ever spoken to? Hell, another time I discussed this with a mathematician who was the wife of a Field Prize winner. The word 'baloney' did not come up. Anway, let's leave the TPC. The RH is the topic. I'd like to thank everybody for being so helpful on this. I've veen asking some of these questions for a long time elsewhere and this is the first time I've had some answers I can understand.

Oh dear. Please read the discussion before posting silly objections. My point was that Buddhism is mysticism, ergo the view being expressed by immortal would not represent mysticism. Logic alone can prove that the the doctrine of mystcism is the only metaphysical view that is not logically absurd. But you're right, it cannot do any more than this. Not can it prove that all apples fall own, or that the world outside your mind actually exists, or that there is not a Lazyboy recliner orbiting Neptune. My last post on this thread.

They are different things, yes, but not mutually exclusive things. Hell, if they were we'd have to choose between them. Wisdom comes from knowledge. It is no good stating things as facts when they are opinions. Show me a wise man who has no knowledge. Where they always were, lost under your complex way of thinking about this. How would you know what pain is if you have not felt it? Pain is not accessible to third person observation. Of course Mary would recognise red in your version of the situation. As you say, she has already experienced it, and is hardly likely to have forgotten the experience. But the whole point of the original thought experiment is that she has not experienced it. We cannot just change the experiment to avoid the difficult issues. Do you see that this is what you have done? If that's true, yes. If not, no. If you could win your argument there would be no problem of consciousness. Unfortunately the problem is precisely that your argument is is unwinnable. Were it winnable then philosophy of mind would be a piece of cake.

Oh. I didn't realise you have such a low opinion of mysticism. I suppose it wouldn't matter to you that all Buddhists would disagree with you. Have you not even read Nagarjuna? He logically proves that you are wrong. But enough is enough.

This is why i added a note at the end opf my [previous [post. We verify empirically that the theory would accord with the facts, but this is not verification in a full sense. In mysticism we verify our theories empirically in a full sense, but not in physics. I'll have to stop here. Clearly you believe I am an idiot. I'll break the rule I made for myself and suggest you go to philpapers.com and look far an essay called 'From Metaphysics to Mysticism'. This gives my view. I am not prepared to argue with you about it since you make no meaningful objections just send up endless flak.

Many thanks. That's the most useful article I've ever read on the topic. My understanding of the primes is almost entirely musical, being more a musician than a mathematician. I wish this had been a chapter in his book. Now I'm starting to get it. Or maybe. Is it possible to say anything very simply about what the RH actually does? Probably not. I recognise all the chains of reciprocals from my attempts to count primes, but most of it is meaningless to me. What are its basic operations and stages? Can they be summarised? I appreciate your help by the way. This must be like going back to primary school.

No. that's not it at all. Logic shows that all partial or positive metaphysical theories are logically indefensible. This is demonstrable. It is the most famous result that metaphysics produces. The only remaining theory would state that the universe is a unity. All this can be logically proved. Whether the universe is a unity cannot be established in metaphysics but would be an empirical matter. I wonder why you are so anti-logic.

Yes. Scientific theorising works as you say. But empriricism is not theorising and it works by verification. That is, we verify theories by the use of empiricism. In the same way, metaphysics is theorising and works by falsification, or what Peirce calls 'abduction', (inference to the best explanation), while mysticism proper is all about empriricism and verification. I think we agree about all this. Yes. I would just add that the scriptures would not be necessary. Aristotle pointed out that logic cannot prove anything about reality, and he is quite obviously correct. Certain or true knowledge does not come from logic. We agree about this. Neither does it come from books, in my view, but here we seem to disagree. This appears to me to be a complete misunderstanding. I have never even heard such a thing said before. Maybe this the correct approach to practice for those in some tradtions who repeat mantras, but it is not true that mysticism, or the practice of understanding reality, requires the saying of mantras. You cannot put such views on behalf of mysticism. It is misunderstood enough already. If you re-examine your words you will see that they state that Zen Master Hongzhi's method of 'silent illumination' is not part of mysticism, nor the method of counting the breaths, nor a million other methods. Mantras are optional, like this or that way of gripping a golf club. Of course, all roads lead to Rome. It would be inevitable that we will all have similar experience along the way to the truth since we're heading in the same direction, and in the end we will all arrive at same destination. But every journey will be unique as we all start in different places. It is very clear form the literature that it is wrong to say that this method or that method is necessary, as if there is a rule book. There is no 'should' about it. A form of practice may require a consistent approach, such that the method 'should' be followed if it to be effective, but there are endless methods and we can make up our own if we like. It is just a question of what works best for us. Yes. Books like the Bible are so difficult to interpret that their longetivity is only a quite weak indication of their truth, at least in science and philosophy, but it is certainly telling that the perennial philosophy remains perennial to this day, since as a philosophical scheme it is more clear and is testable in metaphysics and even to some extent in physics. Yes. Logic cannot prove anything about reality. I expect everybody here would agree. Being led to water is not the same as drinking. I thought we'd agreed about this a few times already. I'm afraid I have no idea what 'one to one correspondance' means here. One discipline produces a theory and the other produce empirical knowledge. How can these be in a one to one correspondance? They can only be consistent or inconsistent, and only as far as metaphysics is able to go. It does not need saying that having a theory about the truth is not the same as knowing it. And of course we cannot conceive of the truth. If we could then the doctrine of mysticism would have to be nonsense. Given its nature, a phenomenon that is not an instance of a category, that in no case is 'this' or 'that'. that is never 'Lo here or Lo there' , to paraphrase the Gospel of Thomas, it is not difficult to work out why we cannot conceive of it or understand it by doing metaphysics or physics alone. It would be what we are. On reflection, perhaps it was not quite right to say we verify theories by empiricism. Not sure about this. Maybe 'verify' is the wrong word. Not important.

Well no. Reading a book gives experiential knowledge of reading a book, and praying for revelations gives experiential knowledge of praying for revelations. As you know, mysticism is about rather more profound revelations and realisations, and these are reported as being directly consistent with the results of metaphysics. My point was that mysticism and metaphysics are consistent in their conclusions. Iow, experience and logic do not lead to different places. But 'one to one correspondance' is not how I'd put it. I think the difference between us is that I can prove what I am proposing.

Actually metaphysics produces a very clear result. It is only that metaphyscians rarely accept it as being a result, preferring to believe that it does not produce one. Mysticism is precisely consistent with metaphysics and neither mysticism nor metaphysics is inconsistent with science. I wouldn't expect anyone to believe this without a proof, but such proofs exist. Mysticism establishes in experience what metaphysics establishes in logic, and the natural sciences, as far as they go, produce results consistent with both. I don't know why anyone would think otherwise these days, given the availability of the necessary information. But I don't think metaphysics produces any answers to the 'why' question, anymore than science, unless it is where the answer is a simple matter of causation and therefore leads to an endless regression. Kant puts the result of metaphysics as that all contradictory pairs of propositions about the world as whole are undecidable. Equivalently, Bradley concludes that metaphysics cannot produce a positive result (and not no result at all). Nagarjana shows that all positive metaphysical positions are logically indefensible. This is the perennial result of metaphysics stated three ways. But not everyone wants to call it a result, so the layman is often led to believe that metaphysics does not produce one. Only in mysticism and dialethism is its result accepted at face value. Elsewhere a paradigm shift would be required if metaphysics is not to be dismissed as producing no result.

Yes. this is what I thought to start with. It took me a while to figure out how it could be correct but unrigorous. This seemed to be a contradiction. In the end I saw that it is correct in principle but that I have not quite ruled out the possibility that it might go wrong eventually if the numbers behave in a very particular way. I can do this, I think, but I haven't got around to doing it yet. The mathematician in question is fairly senior and well respected. (Being at Bristol I imagine he knows Berry quite well). You can look him up if you want. I rather think he is right. In fact I know he is. The proof is too simple to be confusing. I'd put it up for comment but I want to finish it first. I still cannot grasp what the significance is of the non-trivial zeros. What does the output value of the Z-function actually tell us about the input value? Or is that another misguided question? To me the zeros are as meaningful as 42 is as an answer for 'life, the universe and everything'. Is this explicable to someone without a PhD? I've heard the zeros described as tuning forks, but why?

A proper answer would have to be too long for here. But briefly, if the world is a unity then all positive metaphysical positions are false. In no case could the universe as a whole be characterised as this or that, just as Lao Tsu tells us. If all such positions are false, then all metaphysical dilemmas, (where inevitably one positive position is positioned in a contradictory and complementary relationship to its counterpart), are undecidable, just as Kant and Hegel proposed. That all such positions can be logically refuted is shown formally by Nagarjuna and informally by Francis Bradley. It is also consistent with the conclusions of almost all philosophers, not one of whom has ever proved otherwise, and would explain why metaphysics appears to many people to be virtually pointless. Only if the universe is a unity, such that all phenomenon share a common identity, would the knowledge claimed by mysticism be possible. This is true regardless of whether we have a clue as to what we really mean by 'unity'. This is not something that can be conceived, and in thought we can only investigate its logical ramifications. These ramifications are often very clear. I would not want to argue that God does not exist since this is much too simple an idea to capture what I believe to be true. After all, never mind 'God', it is even difficult to known what we mean by 'exist'. But in logic it can be demonstrated that if there is a God then He cannot be wholly distinct from ourselves, any more then we can be wholly distinct from each other. According to logic the universe as a whole is a unity, or, to put it differently, reduces to a unity. Whether it actually is a unity cannot be established in logic, which does not produce true knowledge. It can only be established empirically. Yet it is suggestive that logic and three thousand years of reported experience coincide so exactly. So please don't dismiss logic as useless. Although it cannot make us drink it can at least drive us to water.