abskebabs

I feel that I could have asked this question in either the physics or mathematics part of this forum, but as the context of my question is very general, I decided to place it here. We often talk about dimensions in different circumstances and situations describing different phenomena, both abstract and "physical". My question is there a rigorous single definition for what we call a dimension? If so what should it be? For example in physics we refer to spatial dimensions, and time as dimensions, and these seem to be because of geometric relations that unify them which are not trivial. One only needs to mention the spacetime invariant interval, or Pythagorean theorem to recognise this. However, in my brief knowledge I am also aware of different notions of dimensionality, such as similarity dimensionality, as well as many others that can be applied in a useful way when analysing fractals. These are also defined in a way that is self consistent. As well as this, I know of, or more accurately am vaguely aware of other types of dimensionality like those in things like Hilbert spaces etc. Can all these be "reconciled", so as to provide us with a single rigorous definition of dimensionality? Or is this a mistake, and not feasible or worth doing; and we should recognise the inherent differences between the notions, and perhaps it is just a mistake of our intuition mixed with our everyday experiences and notions to expect there to be an underlying connection. I expect my questions may sound a little naive to those more seasoned with the topic under discussion, but oh well:cool:

I think you may need to be a little more careful with your words and research regarding this matter in order to avoid misunderstanding. 1st of all, joining the European Union is a trifle in comparison to the longstanding democracy Turkey has had for decades. In fact it has been like this for a long time, before the world started to acknowledge and widely use this notion of an "Islamic world". However, it like other countries(Thailand comes to mind:rolleyes: ) doesn't have an apolitical military. So when it comes to protecting the country's founding secular ideals the Turkish army takes issue. The same is probably sadly true with how the secular nationalists and army have dealt with minorities in the past and could have dealt with kurds in the very near future if they had been elected. I'm sure you're well aware of the military buildup on Iraq's border, and the fact that the vast majority of the politicians proposing an attack inside Iraq were were these secularists. Imagine the quagmire that would have created, turning a relatively stable region of a very unstable country into a war zone? Also it's important not to take such a black and white approach when looking at the politics of the country. It is the so called Islamists that have been pushing for entry to the European union, political and economic reform, even reducing the persecution of minorities! Obviously, I like many others who support the ideals of secularism would be rightly concerned if a leader who is suspected of wanting to mix religion with state is elected. But the rest of the world and especially the Turks, who this chiefly concerns should and probably will just be a little wary developments, as you say time will tell. If things go out of line, the people will respond if they don't like it, it's the essence of democracy. On another note, a big deal is made in Turkey over women wavering a veil in public places and institutions. Similar activities are carried out in staunchly secular countries like France. Now I ask you the question is the forced removal of a veil, or religious peace of clothing any different in the treatment of an individual than its compulsory wearing in states such as Iran, when judged by our metric of Enlightenment liberalism? I know Iran is much worse in many other ways, but we should not employ double standards in our comparisons. Personally I hope the army stay out of the whole affair. Interestingly, similar sentiments seem to come form EU officials. It's almost a litmus test of Turkey's majority as to how it handles this crisis, for lack of a better word. It may risk losing brownie points if the army does decide to take action. But then again, this is really symbolic. I don't know why Turkey or anyone for that matter is so enthusiastic about joining the EU, it's wholly overrated. However if you want bureaucracy, infighting, regulations, gradual loss of sovereignty and like funding untenable agriculture subsidies join the Club:-p !

Thanks for the help everyone. Pre-edge; what is it you are proposing removing?

Well done my friend, you are correct;) . I must say I'm pleasantly surprised at how quickly an answer was found. I had a very similar method using algebra like you have shown to solve the problem. It would be good if the answers could have been covered up so more people could try this problem. Personally however, I do not know how to do this either.

Here's one I think people may enjoy. I would recommend using pen and paper to solve it. "Keith is twice as old as as Joseph was when Keith was half as old as Joseph will be when Joseph is three times as old as Keith was when Keith was three times as old as Joseph. Their combined ages make forty eight" How old are they? Enjoy:D

As a person Dawkins does irk me a little, especially when he talks about the "vastness of the universe" and how great science is, I mean don't get me wrong but it's like he's trying to instill a kind of religious sense of grandeur. Overall though, I don't think he's so bad, I just hope he and other people don't take themselves too seriously. People do get a little over the top emotional about this sort of thing on these forums I think. Whatever conclusions we make, we have only our universe to ridicule us:cool: He strikes me as a bit of a logical positivist, and it would be nice if he were to expand on his own thoughts and beliefs in one of his documentaries, as even logical positivism has to be founded on elements of faith, and is not self consistent on its own(Please correct me if I am wrong). I guess the argument on black and whiteness kind of has a point, and I guess perhaps a serious documentary on the history of reasoning and logical systems would be a good contribution that he could make, but I'm not sure it's his area of expertise. Also:D , I don't think it is helpful if people start to look at someone like him as the "voice" of science. Hell, it would be nice if people weren't throwing around slogans like belief and "faith" so much and tried to look at what they actually mean. I can only say what it seems like from my own perspective, but often it seems like he's antagonising people rather than trying to make them think, but I'm sure those are probably not his intentions.

I think thats generally more advanced than what I was looking for. Basically, I know the geometric definition for the basic conic sections, and I know, or I can find the algebraic formulae to represent them on a plane(not going 3d yet!). What I want to do is be able to relate the 2 and therefore derive the algebra using the geometric notions as starting points.

I think I may have seen the first site, but it seems to just list the formulae like other sites rather than explain and derive them. Thanks for the 2nd site though;) . I would still be willing to look at others as well, if anyone else can offer resources they think will be good on the subject of this thread.

I feel this is (yet another:rolleyes: )area that I need to work on and familiarise myself with in maths. I know about conic sections, what they are; hyperbolae, parabolae, ellipses etc, and I have a very rough idea but not a working memory of the formulas that can describe their functions in a Cartesian coordinate plane. In order to understand them better and to gain some personal satisfaction for myself that I do; I would like to derive the formulas. I have already looked on the Internet for something of the sort, but I don't feel I have found what I was looking for. I intend to get an elementary geometry book so I can revise my knowledge of this and other related areas soon. In the mean time however, I would like to ask if anyone knows proofs or derivations of these formulas, and if so, could they kindly try and explain them to me? Alternatively, I would be very grateful if someone could point me in the direction of a resource that does address the issues I have. Thanks in advance:-)

I study physics as my course, though I do like to dabble in a little mathematics recreationally. It's also quite beneficial to do this.

It's depressing that I'm not at all surprised by that video. Who knows...

Hmmm.... I have a few friends who are interested in making films, and in fact I know one person who's just finished making 2. They're not very major or famous(yet!), but if you want I could tell them. As for making films, this is something I have been much interested in myself. However I acknowledge there is a very big difference between having a fanciful desire to do something and pursuing and putting a lot of work into bringing it to fruition.

Yes:doh: , I was dreading when you'd get round to responding to my post... I realised too late to edit my mistake! My mistake, I was referring to your "signature" at the bottom of your posts(not insulting your intelligence of course;) ). Also I must admit I was frankly unawre of the "internets" being a cultural reference. I guess I should stop taking you seriously:-p ...

Not that I feel particularly sorry for child molestors or sex offendors, but it does seem they are ostracised by society in this way, in a fashion that is slightly illogical when you look at the bare facts and figures. I was under the impression, that the reoffending rates for these kinds of crimes was actually very low. In fact the biggest danger for women, children(perhaps men too) comes from those that are close friends and family. The truth may hurt, but I think people ought to start facing up to it and question themselves more. In such a light the opening proposal could be taken more seriously, but I'm still in doubt myself whether it would be useful. The reason for this is because a peopdophile's sexual desire may be temporarily satiated by this, but they may want more and more to "satisfy" themselves. They could soon find that this "virtual child porn" is not enough for them, and thereby creating a spiral of supply and demand, not removing the problems we still have today. Also, we need to really find out more about what determines our sexual desires and orientations; whether the phenomenon is purely psychology, something in nature, or more likely; lying in the difficult gray area in between. Then we can begin to look for ways to deal with it more effectively.

If you want to learn trig the best way to do it for the long run IMO, is to prove the identities so they make sense to you and then memorise them. It might be good to just skip and memorise them(especially if you're in a rush), but I think proving them or at least appreciating why they are valid gives you some context in which to remember them, and more importantly; try to gauge some meaning. Admittedly, it will be pretty hard for you to come up with a proof on your own(though impressive if you do), but if you'd like; I know one for the addition of angles of cosine, sine and tan, so PM me if you'd like me to tell you it in more detail. I guess I'm just feeling too lazy to make a thread on it:cool:

I have strong suspiscions your statement is incorrect. I may be wrong, but I think girls tend to have much more of a preference for social networking sites as opposed to forums like these. Then again this just a hunch, can't be sure of anything really.... Besides your contradicting your own avatar:rolleyes: . "Internets"....Sheesh!

I've tried to find a proof but I haven't got it yet. I'll keep trying.... Meanwhile in the process I found an indirect way of proving the sum of a geometric series! In fact I'm surprised I didn't realise this earlier.

I guess, I am equating believing something absolutely a 100% and knowing it for a fact in terms of certainty for a person. In such a case proof would be erroneous. Thereby, what you are referring to as having "faith" could not really be called believing, as the fact that the notion of proof is even entertained shows doubt and disbelief. In short why would something that is fully believed need proving? I'm sorry if I'm going nowhere, I'm now thinking about withdrawing from this thread and having a deep long think(some sleep would be good too!)....thanks for the responses though.

I take your point.... I guess the problem is partly a semantic one. From my inference it doesn't seem that the argument about WMDs necessarily relays an absolute belief. For example, I will swap the word belief with one I think will provide more amenable connotations to carry my point: "I reckon that there are WMDs hidden somewhere on Earth, but due to financial limitations, I cannot search every cubic centimetre to find out; thus I cannot know for sure." Such a statement shows doubt, and I guess, I may be wrong with this but I thought strictly; if you believed something you had to be absolutely sure about it. Now, logically I can see such a belief being untenable(regardless of the phenomenon under discussion), but that is what I thought the definition was. Hence this is why I would stress the difference between the word belief and "reckon", that I have used as a device to help illustrate my point. Also, though it could be pursued arbitrarily, the perspective of proof from such an absolutist perspective would be irrelevant. I apologise if I have made errors along the way, but to me, it seems if we try and apply rigorous definitions to the words we are using; then the statement "agnostic theist" does not hold well.

I'm not sure if this works the other way round, but basically to be an agnostic theist you have to believe in something you're not sure of. Isn't such a stance contradictory?

Hallelujah! I concur;)

Martin, I was under the impression that Causal sets was separate to LQG. I was intrigued by the general idea, and will read up on it at some point at this website:http://www.einstein-online.info/en/spotlights/causal_sets/index.html What is its relation to LQG though? I would guess background independence, but what else?

Woohoo:-) ! Iraq have won the Asia cup! I offer my congratulations to the Iraqi pople and their team. http://www.afcasiancup.com/en/tournament/mtindex.asp?aid=50768&cid=1377&mt=12049&sec=105&ssec=246

Hiya. I found 2 papers talking about what I have mentioned in the title. They are accessible via the links: http://www.springerlink.com/content/h107848j00l9u6q2/ http://www.springerlink.com/content/r74733p30331785k/ As they have been fitted into the category of "experimental biology" and "experimental genetics", I figured this would be an appropriate place to post. I do not have access to the relevant journal, so I was hoping someone here would be able to have a look at this and give me their make of this. The reason the these documents have piqued my interest is because the subject seems to be about distant inter cellular electromagnetic interactions(as a physicist, I guess that's inevitable:-)) . I'm not sure of the mechanism, but I think it could be UV radiation. Actually I give up trying to give a layman explanation of this, I just wonder, is there a mechanism for the effect they are describing, and could someone explain to me what is being discussed, in perhaps a more elaborate way then is alluded to in the abstract? I would love to see for myself but I don't have access to this journal. Also I guess I have to ask, has anyone heard of this before? Has any further research been done on such an effect? Is this stuff bogus??

I've recently been working through a book called "Mathematical puzzling" and during the time I was tackling a problem investigating whether the identity [math]{2}^{n}-1[/math] could produce primes. During the analysis I came up with and derived an equation that seemed to hold generally, and this made it very interesting. In fact tbh, when I found it and realised it's general validity, it made me so excited I felt like hopping up in the air in some sort of stereotypical Archimedic fashion:-p ! It just seemed to give that kind of joy you can only experience when you find something like this in the field of mathematics or mathematical sciences. Also to note how this relates to primes; all powers of n that are odd can produce primes, though this isn't at all always the case. Whether this is ture or not can be determined by the character of the RHS of the equation. This is as opposed to when the power is even; the only even power of n that produces a prime is 2, and this fact can be proved as well. I guess even though I felt this way at the time, it's strange, I looked at the same equation today and thinking of the way I derived it, I couldn't feel more blase about it. In the end I think most mathematicians would probably think it trivial. Still, I'd like to share it with you: [math]{2}^{n}-1=\sum_{k=0}^{n-1}{2^{k}}[/math] What do you think? I guess also people could contribute their own results and share how they felt when they found them too;) . I encourage people to do so.