NortonH

Neither do I. I just refuse to accept religious arguments for something in place of the scientific method. If you believe in something just because other people do then, whether that thing is right or wrong, your belief is religious. If you have seen a model make predictions which are validated then that is scientific. So without a quantitative model able to make usefully accurate predictions you have nothing. Not sure what you are talking about. ??

OK so what is the scientific method about - claims by individuals with reputations or is it about models, predictions and evidence? I do not believe that people, institutions, reputations, trust or authority get any mention in the Scientific Method. I am no expert, however.

So you are saying that the starting conditions need to be known to a high accuracy because small errors propagate and increase with each iteration of the model. It is an interesting idea. But surely a mere 30 balls cannot present that hard a problem with todays computers. I believe people are making accurate predictions and when they make incorrect predictions they can use that information to modify the algorithm.

I am thinking of scientific claims made without any reference to a quantitative model. Sometimes we hear some claim about the future state of some system or other but without any reference to a model that can be scrutinised. Obviously no scientifically rational person would give such a claim any credence but there are a lot of people around who do. They seem to be caught up in the general mood and tend to go along with the crowd rather than adhere to the scientific method. It actually comes down to the decision - do I follow the scientific method or do I follow popular opinion? Since humans are humans it is not always so easy do separate out human nature. I guess such situations can only be described in terms of religious faith - "I believe this because a lot of other people claim to believe it and if I disagree will be subject to ridicule and abuse." I do remember the events a few years ago when the speed of light was called into question. I had little doubt that it would soon be discovered that the experiment was flawed but I did note the way in which the matter was discussed calmly and scientifically and without any abuse of the people who performed the experiment which threw up the apparent contradiction.

Sorry I was just trying to be precise. It is so easy to go off-topic if one is not careful. I am a total supporter of the scientific method but i believe it needs to be adhered to rather than just recited. ie If you have a hypothesis you need to apply the Scientific Method rigourously, even if that means that a beloved and popular theory is found to be inadequate. Obviously is is hard for a human to let go of a cherished idea but if it lacks some necessary quality (eg fails to meet the requirements of the SM) then that idea has to be deemed false. That is an important matter. If it cannot be replicated it is not science.

Sorry, but I am unclear. Is this thread about climate science?

How? Are you saying that the laws I mentioned do not cover the scenario I detailed? How is what I wrote nonsense? I am sure it is more complicated in 3D but so what? That is the problem we have to solve unless they start selecting lottery numbers using a billiard table. The laws of physics are the same every week. It is just the initial set up and the environment that changes each time. Anyway, people are making accurate predictions and so, no matter what objections you have, it shows it can be done.

A very important paragraph in a very important article. Sorry, Strange. I am not sure where your comic fits in with this thread. Please enlighten me as i am a bit slow sometimes.

The lottery does not have to let you do anything. It is easy to estimate the size of the box and a ping pong ball is pretty easy to find. There need only be thirty six balls. THIRTY SIX. That is nothing in terms of numbers that computers can handle. In any case I happen to know more than I have let on. There are already people doing this and making accurate predictions.

You have been asked by others to show where the proof is flawed and have refused. Thanks for playing.

I am not talking about balls rolling along a surface I am talking about balls colliding in air. Have you seen the lottery number generator? It does not look like a billiard table. Do you get it yet? So you say that the problem cannot be solved because of the initial conditions but surely if we took thousands of accurate measurements and used massive computers that would not be a problem.

It occurs to me that the principles behind the selection of the lottery numbers are quite simple. We have a near spherical box containing about thirty ping pong balls which are rolled around and then one at a time is selected. The physics is very simple. 1. If two balls of equal mass collide then they move off at ninety degrees to each other. 2. When a ball strikes a solid surface the angle of reflection is the same as the angle of incidence. 3. Gravity operates. Surely with those three very simple, irrefutable laws of physics it should be easy to predict next week lottery numbers.

If you think it is wrong then say wrong.' Then say why. It does not matter how much historic data you have or how far into the future you 'extrapolate' if you do not have a credible model. Do you have one?

That is why evolutionary scientists do not try to make such ridiculous predictions. This should be a lesson to climate 'scientists' who, for some reason, DO make ridiculous predictions way into the future.

Studiot or someone listed a few but it is pretty easy to demonstrate that between p,q irrational there is z rational. YOU are the one claiming that the hypothesis is false so I asked you for a counterexample. Do you have one? If not, then what is your reason for claiming that it is not always possible to find a rational between two irrationals? If you are here just to troll and waste everyone's time i will ignore you. No doubt I will be suspended for 'failing to answer relevant questions' or some such crap but that doesn't matter. I am not really interested in indulging clowns.

Yes. That is a good example. A countable number of removals (of rationals) leaves behind an uncountable number of irrationals. I guess we can remove the algebraics as well and get the same result. OK. So now i am still stuck on the conundrum of the 2^n and 2^aleph0. Why does one not approach the other as n approaches aleph0? The only thing I can think is that the set of end points is well ordered and the set of rationals is not. But then the set of integers is... So I am still not sure how to resolve that conundrum. Any ideas? So can you give us a counterexample? Show us a couple of irrationals with no rational between them? If not then it seems clear to me that the original proof stands.

OK, I understand what big N means but for some reason my browser was displaying it as /"mathbb{}/" or something. It has resolved it now so that is clear. I am happy now that your function 2^n maps end points to naturals so that is OK. That just means that my conundrum has moved to the contrast between the power set of N and the number of end points. I am happy with Cantors clever argument that the power set cannot be mapped to N so the problem is the cardinality of the sets. The power set has cardinality 2^alep0. Now I can only assume that this has been extrapolated from finite sets where it is 2^n. So that gives me the impression that as n approaches aleph0 we can say that 2^n approaches 2^aleph0. Yet this seems to be where the problem is. The Cantor set still baffles me. A countable number of cuts produces an uncountable set. Only the end points experience a cut firsthand and yet somehow an uncountable number of points are left behind separated from all other points.

I have no idea what \(\mathbb{N}\). means. I am warming to your idea of the mapping of the end points to the 2^n integers as you described above. So I am almost comfortable with the idea of the end points being countable but I will need to think about the difference between the cardinality of the power sets and the end points. I will reacquaint myself with the original argument used and then return.

I believe your statement but I just point out that the same argument can be made about the power set of each of the sets I listed. Your argument is not rigorous. I can see the attraction of thinking that at each stage the sets are finite and countable but I do not see how they are any different from the power set cardinality at each stage.

I am not convinced. I can make exactly the same statement about the power sets of the sets {1}, {1,2}, {1,2,3} ... as they continue towards aleph null. So it seems that we have two possible hypotheses. 1. It is possible to map the set of end points to the integers 2. Such a mapping is impossible. I believe it is not possible so I am now obliged to try and demonstrate that such a mapping is not possible. You will need to try and demonstrate the mapping you believe exists.

There was definitely collusion with the Russians by the Clinton campaign - eg the Steele Dossier, but I am not sure what the Russians are supposed to have done for Trump. It seems more like a case of trying to wish something into existence. Sorry, but if there was a Bigfoot he would have been found by now. Same with the 'collusion'.

The Mueller search for evidence of 'collusion' reminds me of the endless search for Bigfoot.

After each stage of removal the number of end points doubles. After n stages the number of end points is 2^n As n approaches infinity this becomes the cardinality of the power set of N does it not? So that must be uncountable.

I say they are not.

If a business fails then it fails. That is reality. I guess Trump is the only person in history to ever have a business failure. By the way, four of the five failed ventures were in the gaming industry. To be honest I think that if you are investing in casinos and you lose there is a certain natural justice in that. In any case as far as character, integrity and affection are concerned at least you can console yourself with the fact that he is way ahead of the other contender for the 2016 presidential race.