PeterJ

That's about it, Strange. I can see that in many scientific discussions it is possible to ignore the phrase you put in italics, and it would be impractical to keep repeating it. But when it comes to the ontological priority of matter and consciousness this is the cutting edge of debate and research. There is nothing like a consensus, and whichever view we take it is untestable in the sciences. On such highly debatable and fantastically important philosophical matters there is no case for making dogmatic statements as if we've already done the research. Just the addition of the phrase, 'it seems to me' would do the trick. 'Here's why' would be a bonus. Otherwise the speaker will appear to be a closed-minded fundamentalist not worth talking to, Such statements do not flatter the reader's perception of the author's clarity of thought. Admittedly, it is common for people to state their preferred metaphysical conjecture as if it is a fact, but no amount of wrongs make a right.

Okay. It's not my forum. If we are going for informality and lack of rigour that's fine by me. Just change the name to 'pubchatforum.com so people don't get the wrong idea about the forum. I see no problem in making assumptions either. I assume that people here are interested in science and the scientific method. So why not use it? The method is not to 'reify' opinions and assumptions as if they are facts. People regularly do this, of course, but it's a personal; thing. To state in public that 'consciousness is like this or like that' when we have no idea which it correct is just plain daft. It causes discussions to turn into shouting matches, and it certainly does not help our understanding of anything. We could be sharing knowledge rather than arguing dogmatically for our unfounded opinions. Besides, to conduct our research by assuming that we already know the result is not a sane thing to do.

Oh no! I'm not going to start getting into the details. Certainly not the numbers. All I'm concerned with here is the question of whether a proof as described would be old hat, trivial, interesting or useless. If it is not trivial then I may move on to say some more, but there's no need to open another can of worms at this point. I suppose I could restate the question in case it helps. If we could prove that no finite quantity of primes would produce sufficient products to ensure that there is a highest twin prime pair (two consecutive twin primes), then would this be of any use to anyone?

It doesn't matter a damn to me what people assume. What matters is that they know the difference between an assumption and a fact. This was my simple point. The relevant posts above are full of assumptions presented as facts, display a poor knowledge of consciousness studies and have no respect for rigour. Is this really a good way to discuss consciousness? It's not a discussion I'd join, except to complain about the woolly New Age approach that's being taken. Prometheus - I'm not asking for proof of anything. I'm not making any claim about consciousness. I'm making a claim about ignorance. I'm suggesting that most of the statements people are making here about consciousness are unscientific, unproved, display a lack of scholarship and are not dispassionate.

Now we seem to be on the same wavelength. I hope it's not trivial, but I'm still uncertain. If it is not, I'll have a go at formalising my casual attempt. It can definitely be shown that there is only one instance of three twin primes in a row, and that this is the longest sequence possible, but I've been presuming that this would not be news.

My main problem with the OEIS list is that I don't speak the languge. Even that article is beyond me. Where it starts, 'A *prime gap* is an integer ...' I have no idea what the formula that follows means. As far as I can understand it though it doesn't seem to help. Yes, I do think this seems to be a special case of the prime gap problem. I thought it was a simple little idea, but it seems not. I'll say more about it in my reply to John. That's it. We're talking about consecutive pairs of twin primes relative to the set, i.e. consecutive pairs of numbers not having one of the primes in the original set as a factor. It's a trivial thing really, but I find it intriguing. The proof may not even work, but at this point I;m just trying to see what it would mean if it did. This would be nothing like Euclid's proof. It would not prove that any particular case of n,n+2 is a twin prime. It would state only that insofar as it is possible to predict the density of primes from the general rules governing the behaviour of the products of the primes, (which is the only determinant of the density), the possibility of two consecutive twin primes occuring infinitely many time can never be ruled out. NB. It would NOT state that there is an infinite quantity of pairs of consecutive twin primes, just that if there is not we'll never know it. I suppose it is a proof that the claim of the TPC cannot be refuted, but there must be many ways to prove this.

Urgh. Going through the OEIS dbase is painful. I've checked 30 pages without finding anything relevant. Trouble is that even if it is relevant I may miss it, due to the technical language used. I'll go back later and do more checking. No, nor me. I wish I could express myself more clearly, but surely what I've written already is enough to make it clear that I am not suggesting there is a proof for an infinity of twin primes. I mean really, a person is hardly likely to come on a maths forum and ask if a proof of the TPC would be interesting.

Sorry John, I don't see your objection.

I'm talking about consecutive twin primes. That is to say, a twin prime at 6n+/- followed immediately by another one. I don't know how to improve on this explanation. The TPs at 6+/-1 and 12+/-1 would be an example. I'm asking if it is would be interesting if we could prove that no amount of primes on a list, (whether they are sequential or not), would be sufficient to generate enough multiples to prevent there being an infinitude of consecutive twin primes. (NOT consecutive primes, but consecutive twin primes.) The quadruplet thing seemed relevant because I noticed (or thought I did) that OEIS includes data on pairs of primes at p and p+4 under the twin primes section. So I wanted to make it clear that this is not what I'm talking about.

Okay Acme. Got it. Thanks. OEIS is doing my head in but I'm going through backwards looking our for anything that sounds relevant. John. It would be the first of your two formulations that I'm concerned with. Two adjacent twin primes each at 6n+/-1. The vital word in my OP was 'consecutive'. Without that a proof would, as you say, be trivial. I didn't know that two primes at p and p+4 could be considered a twin, and perhaps should have made it clear that this is not what I mean here by 'twin prime'.

Acme- Unfortunately I'm not able to understand the quote you give at the end of your post. But I will go have a look at OEIS link. I had no idea such places existed. phyti - I think maybe you need to read the thread again.

Great stuff! Thanks for hanging on in there.

Okay. Perhaps I should have said 'prime quadruplets'. My thought is this. On the face if it, it is possible that there is only a finite quantity of prime quadruplets. This is regardless of the truth of the TPC. It could well be that the first 10,000 primes are enough to ensure that there is a highest quadruplet. A proof that it would not be possible to prove that this is the case seemed like it might be useful, or would at least be a curiosity. But maybe not. I just wondered. Am I be misreading your proof above? It appears to relevant only to single twin primes, and to more or less restate Euclid's argument.

Yes! I'm talking about consecutive instances of twin primes. Two twin primes in a row, the longest sequence there can ever be. The TPC asks whether there are infinitely many single twin primes. I thought it might be slightly interesting to show that it is at least possible, no more than that, that there are infinitely many consecutive twin primes. Or, if you like, that it would be impossible to prove that there is a highest instance of two twin primes in a row. I didn't mean to make a big deal about it. It may have been proved a thousand times for all I know, or it may be completely useless.

I thought this was a science forum. Yet apparently rigour and method is to be abandoned, and we should just shout our opinions as if they are facts. It is ridiculous, How is one supposed to have sensible discussion under the circumstances? Do we just keep insisting that our guess about consciousness is true, and then try to shout each other out? What about gravity? Might the same method work? Or do we admit what we do not know and consider the possibilities calmly and rationally. But this is not the point. My complaint did not mention my view on consciousness and it is irrelevant. What matters that we don't go around a science forum stating that we know the truth about some issue when we very obviously do not. If we are not able or willing to distinguish between what we do and do not know then this is probably not a good place to demonstrate it. . For goodness sake. It's like a nest of angry hornets. . .

Thank you John Your example seems to refer only to single twins. I'm speaking about adjacent pairs of twins. Is this not something quite different, and a little more difficult to prove?

Not at all insane or offending, but not proven. You are assuming that biological life must be prior to consciousness, but this is a very big assumption and it there could never be a way to confirm the truth of it. So feel free to hang to to your opinions, but note that they are not known to be facts. To simply take it for granted that matter is prior to consciousness is contrary to the entire spirit of physics and philosophy. To state that it is would be a certain mistake. I could just as easily state that consciousness is prior to matter. Then we may as well arm-wrestle for who is right. These wild statements get us nowhere. Better to ask: How would we go about proving that matter is post or prior to consciousness? If we cannot answer this then obviously the jury must remain out until we do. .

Sorry. I have no idea what you're saying here. What has your point about 'no infinite set of natural numbers within a set of natural numbers' got to do with anything? You say, 'While it is one thing to say how likely a prime character is on an interval, it is quite another to say what interval or where on it the prime character may appear'.. This may be so, but I have no idea what this sentence means or why it's relevant. I'm asking a very simple question. A yes or no answer would be fine. Would a proof be interesting or trivial, it's a multiple choice question with just two possible answers.

As nobody else has commented I can't be quite sure that I've put myself clearly. Maybe not. Take a large but finite set of primes, the primes up to 10^50, say. Is this enough primes to ensure that there is eventually a highest consecutive pair of twin primes? Bear in mind that the products of the primes in the set are the only numbers that can have an effect on the answer to this question. If these products are always insufficient to prevent consecutive twin primes from occurring, then it at least possible that there are an infinite qty of such consecutive pairs. I have no idea whether a proof of this possibility would be trivial or interesting, so I thought this was a good place to ask. .

I'm sorry, but your statement, 'matter existed long before the universe has any concept of life or consciousness', makes it clear that you do not make calculations but indulge in conjectures. The analysis of such issues is called metaphysics, and no competent metaphysician would make such a statement. If you'd started 'In my opinion...' then I wouldn't have said a word. You certainly cannot post the statement above and hope to avoid a religious argument. This seems pretty obvious. What you call 'common knowledge' is nothing of the sort. It is a common conjecture but nothing to do with knowledge. It will be a disaster for your research if you mistake popular opinion for the facts. The more rigorous approach would be to avoid such dogmatic statements until you can prove they are true, or at least are able to refer us to someone who can. That one statement would be enough to ensure that your post could not be published in a decent journal. So it's not that I'm arguing about how the universe began. I just react badly to dogmaticism and lack of rigour. The topics warrant a more scientific approach. I think you could get away with saying that matter is prior to life, although I can think of a couple of possible objections, but whoever first proves that matter is prior to consciousness will be on for a Nobel prize.

Yes. There is my proposition to prove. If it's interesting enough to make it worth bothering. I think maybe you should read the proposition carefully. Are you suggesting that you can prove it? I think you'll have a struggle, but if you succeed you'll have answered my question.

The case I gave is was intended merely as an explanation of 'relative primality'. There are , of course, an infinity of examples.

Okay, but I'm not sure where the problem is yet. Say the set is (2,3,5,7,11,13). The number 289 is not prime, but it is prime relative to this set. Perhaps I could put it differently. P: No finite set of primes produces sufficient products to prevent the occurrence of an infinite qty of consecutive pairs of twin primes. Note that this is not very exciting. It is obvious that no finite set of primes P could prevent the occurrence of a twin prime at P!. I just wondered if by extending a proof to cover consecutive pairs of twins things became more interesting.

So, you have learnt that matter existed long before the universe had any concept of consciousness. Not a lot of people know this. I suggest publishing the experiment that confirms it. You shouldn't have any trouble getting into Nature with such a breakthrough. It seems you also know that consciousness can be explained in a 'zero religious' way. Your knowledge seems to be well ahead of physics. Excuse me for saying so, but I have sneaky suspicion that you are mistaking guesswork and wishful thinking for science and analysis.

None of the primes in the set are factors of the two aforementioned adjacent pairs of numbers (n, n+2). .