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Convergent matrice=divergent constant ?

  1. Apr 13, 2006 #1
    I am doing research into brain systems.

    Does anyone have any examples or links to existing equations where a a convergent matrice is the reverse of a divergent constant, such as log or phi ?
     
  2. jcsd
  3. Apr 13, 2006 #2

    matt grime

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    That makes no sense at all.
     
  4. Apr 13, 2006 #3
    I kind of anticipated that might be the response. i got to start expressing the problem somewhere.

    Basically this idea was proposed elsewhere by a japanese physicsts as an elegant mathematical representation of a dipole. Who he is i cant pronounce his name so having problems googling it.

    The idea is that the physics of a dipole North side pull can be represented by the mathematics of convergent matrices and the south end push by divergent irrationals or power laws. The dipole itself is an elegant reversal system of the two, so i'm looking for the equation which describes how the two ends equivocate for the whole dipole system. Does that make it clearer ?

    Its for a paper on microtubules. (neuron structural components)

    Not sure what i can do in return ? sure aint math. Considered pretty good on queries regarding most of the current stuff in brain sciences and neurochemistry.
     
  5. Apr 14, 2006 #4

    matt grime

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    The phrase 'divergent irrational' does not make any sense, nor does the phrase 'convergent matrix'. Just repeating them doesn't help.

    "irrational" used as a noun like that means 'irrational number' like the square root of 2, or pi, as such it is a number, it does not diverge or converge or do anything of the sort at all.

    Convergent matrices has some hope of meaning something. I could invent a meaning for it, say one whose eigenvalues are all less than one in abs value. This would not be a stupid or bizarre thing to do if you wished to model a 'sink'. However, I don't know of any standard meaning for it. And as I presumed you already googled for it and didn't find any information I won't bother to search.
     
  6. Apr 14, 2006 #5

    HallsofIvy

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    phi is a constant but "log" is a function. In addition, I have no idea how a constant (i.e. a single number) could be divergent. I don't believe "reverse" has a mathematical definition. If you meant "inverse" then I don't see how a matrix could be the inverse of a number.
     
  7. Apr 15, 2006 #6
    A constant such as phi represents the fibonnaci series.

    http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/

    which is divergent

    http://milan.milanovic.org/math/english/divergent/divergent.html


    sorry bout that, I mean "inverse". for some obsessive reason i dont like the sound of the word. I had to cut it from your text rather than type it.

    so this is quite helpful so far. Now i have some directions for both sides of the equation.

    What i'm trying to get at is the equation which represents the poles of north/south electromagnetism. It appears to me that the north pole has a bias towards the magnetic components and the south pole has a bias towards the electrical component( for the south pole this is borne out by the divergent fractal nature of fibonnaci and phi. http://www.infinitetechnologies.co.za/articles/geometry1.html ) I cant say much about the north pole, but have reasons and presumptions which i'm pretty sure about. So this has lead me to start beginning on the maths.

    I'd be even more delighted if someone else has been through this area, in fact i'm astounded if this is not the case, considering the prevailance of electromagnetism through every cell of our brain.

    Do you think this thread should be-redirected to the physics sections ?
     
  8. Apr 15, 2006 #7

    matt grime

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    Your definition of 'divergent irrational' is nonsense: any number can be made to 'represent' in that manner a divergent sequence.

    The inverse of a matrix (if one exits) is a matrix, not a real number (unless the matrix also happens to be a non-zero real number, ie 1x1), nor is is a function such as log.

    I suggest you actually try to find out what the meanings of the words you're using are, and then try to find out what the meanings of the words you're trying to explain are.
     
    Last edited: Apr 15, 2006
  9. Apr 15, 2006 #8
    did i use the term "convergent matrix" ? I was always referring to matrices. Anyway thats not important.

    I just posted a reply on this to HallsofIvy. The irrational number phi, (which is represented within the structure of brain microtubules as fibonnaci) definetly represents a divergent series. It can also converge but primarily seem to be divergent.

    http://milan.milanovic.org/math/engl...divergent.html

    Does this make any better sense ?

    Modelling a sink, is a good analogy for the north pole pull, so for the divergent side of the equation thats exactly what i'm trying to do.

    From wikipedia and relevant to electromagnetic dipoles.

    "As the Earth rotates, every arrow pointing outward from the center of the Earth also rotates, except those arrows that lie on the axis of rotation. Consider the transformation of the Earth after one hour of rotation: An arrow from the center of the Earth to the Geographic South Pole would be an eigenvector of this transformation, but an arrow from the center of the Earth to anywhere on the equator would not be an eigenvector. Since the arrow pointing at the pole is not stretched by the rotation of the Earth, its eigenvalue is 1."

    so for the purpose of a convergent system why do you propose the eigenvalue has to be less than 1. Is this something that occurs when the eigenvectors are stretched ?
     
  10. Apr 15, 2006 #9

    matt grime

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    And I posted a reply to your reply: give me any real number and I will produce a sequence that diverges that is perfectly in analogy with you

    phi <---> golden ration

    rule.

    Reading back I see you used the phrase 'convergent matrice' and not 'convergent matrix'. Now, what the hell is a matrice (apart from the french for matrix)? And matrix is the singular of matrices by the way.


    Your link (the version that works) is not helpful at all. We all know what the fibonacci sequence is.
     
  11. Apr 15, 2006 #10
    if it can be made to do so, why is it nonsense ? Anyway i dont really like discussing in this kind of tone. I certainly wouldnt do it anyone else, within my own field if the situation were reversed.

    The real point here moving beyond bad definitions, which were really just a beginning point, and having now discarded logs and moving on to phi as relevant to the divergent part of the equation, is to find a usuable represenation for electromagnetism and fibonnaci structure found within brain microtubules. (structural components of neurons)

    Perhaps you mean that insert a number into a function like log it becomes divergent. good point. Decided to leave log behind now, for the two reasons. Its input dependent function and i dont come across it much in biological structures (yet).

    vital irrationals such as phi, which as previously pointed are divergent and occur without functional input. Also i'd be interested on your personal opinion on the prevailance of phi throughout living structures, and from what i believe lately has been found in astronomy

    http://goldennumber.net/cosmology.htm


    Now thats interesting, arent primes combinations of non-zero real numbers. And primes corellate to phi

    http://mathworld.wolfram.com/Phi-Prime.html

    not sure, of other ways to do this except the method of loggin on and discussing with those in the know. Theres a limit to what a beginner can glean from wikipidia and wolfram mathworld.
     
  12. Apr 15, 2006 #11
    as previously stated phi wich represents fibonnaci is divergent

    http://milan.milanovic.org/math/english/divergent/divergent.html

    and is also irrational

    from http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html

    Can we write Phi as a fraction?
    The answer is "No!" and there is a surprisingly simple proof of this. Here it is. [This proof was given in the Fibonacci Quarterly, volume 13, 1975, page 32, in A simple Proof that Phi is Irrational by J Shallit and later corrected by D Ross - see below.]
    ...........Here is the contradiction if both p and q are 1, then p/q is 1 and this does not satisfy our original equation for Phi, the one marked (*).
    So we have a logical impossibility if we assume Phi can be written as a proper fraction.
    The only possibility that logical allows therefore is that Phi cannot be written as a proper fraction - Phi is irrational.

    what then is the problem with inventing the term "divergent irrational" to describe phi ?

    in regards to "convergent matrice" i did in fact find papers using this term from french mathematicians. Hence the mix up. I then cannot use the term convergent matrix without causing more confusion, although I have come across the term convergent matrix many times in reference to the result from statistics programs like SPSS.

    Convergent matrix comes up a lot in google

    http://www.google.com/search?client...rgent+matrix&sourceid=opera&ie=utf-8&oe=utf-8
     
  13. Apr 15, 2006 #12

    matt grime

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    The simple problem is that the term 'divergent' is pointless. Any irrational, or rational number is 'related' to a divergent sequence in exactly the same as phi is to the fibonacci sequence. Thus there is no point in using the appellation 'divergent' since it adds nothing to the description. It is pointless, it is meaningless, geddit? Every irrational number satisfies your attempt to defining 'divergent', by which I am formally using the assocation: satisfies the recurrence equation of a divergent sequence since you have been unable to provide a proper definition. If you cannot define your terms properly then you are engaged in pointless crackpottery. As it is your posts are indistinguishable from trolling, hence the negative tone from me that you don't appreciate.

    Why are you proving phi is irrational? I assure you most people here are sufficiently mathematically well informed as to know that all rational algebraic integers are integers.

    Since you are using the term 'convergent matrix (or matrice)' you ought to therefore have a definition of what one is. You haven't given one.
     
    Last edited: Apr 15, 2006
  14. Apr 15, 2006 #13

    Hurkyl

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    On the physics end, you're way off on magnetism. Magnetic North and South are completely symmetric -- the only possible way to tell them apart is by appealing to some standard to which we've arbitrarily labeled "North".

    To put it differently, if I secretly went throughout the universe and replaced every magnetic North pole with a magnetic South pole, and vice versa, it would be absolutely impossible to notice that anything has changed.


    On the math end, we (justifiably) aren't particularly receptive when people come in who don't really know much about math, and yet are willing to tell us how things are.
     
  15. Apr 15, 2006 #14
    This is an interesting subject. YEss i know that we have always thought that solely magnetic systems were symmetrical, but when we get to "electromagnetic" systems things start to get a little strange. I have good reasons from looking at biological dipoles (which are more complex and hence reveal more detail than planetery ones) that the electrical component squews the south pole to assymetry for the electrical component and for the system to remain balanced the north pole squews its magnetic component to become stronger. Hence it has pull.

    Anyway i'll leave this for a physics threads. I'm just trying to grasp some maths for the time being.


    I would say the problem is more one of trying to get to grips with definitions. I'm sure of what i've come across in many kinds of biological dipoles, and its not in agreement with the less complex dipoles used in physics. So i would say yes in that sense i am sure of how things are. there is a mismatch.

    i'm pretty sure, you wouldnt want to read my book on the subject of biological dipoles, So what i am doing is looking for mathematical descriptions, which can describe the findings briefly. These may be original, and yes my math is crap. My biology was crap three years ago, i self learn very quickly and now correct the work of professors in this subject. I had just the same kind of reactions when i began neuroscience .now several years later i am taken very seriously and get a lot of respect on the neuroscience forums. That is evident by the fact i get queried myself on many neuroscience subjects. When i do so, i certainly avoid trying to make the person asking me questions feel inferior. A particular couple of people that used to do this to me in the neuroscience area, now avoid discussions with me, purely because they cannot get their cheap kicks as i can correct them without feeling i need to resort to tyrades. Must be something about the internet. that brings the worst out in some people. Perhps it takes extra effort to fight this tendency we have, while anonymous.

    To sum up, yes i am very confident of what i am trying to do. which is looking for elegant descriptions for a real problem. my current lack of maths skill is just a current problem, which will grow better over time. I knowing nothing much of maths 8 weeks ago and now can start this discussion in which i feel i made salient points, and can discuss these abstract concepts. I answered criticsm from people here with what looks like a lifetime of calibre. Is that trolling ? isnt trolling about going online with a destructive agenda ?

    what i'm trying to do is is Find the equation which describes biological dipoles. Any links to those for planetary ones would be a helpfull beginning point.
     
  16. Apr 15, 2006 #15
    Well at least thats a progression from "nonsense". You also said the term "convergent matrice or matrix" was "nonsense", yet i googled you loads of references for the term, "convergent matrice" or "convergent matrix" .
    I could just copy the many of definitions of "convergent matrice or matrix" from the french mathematicians or SPSS specialists.

    Why bother ? I get the feeling bringing up a definition isnt of any value to yourself. Its certainly getting me nowhere with the problem i'm trying to solve. For yourself It seems like being superior and calling suggestions "crackpot", "nonsense" or worse has a greater priority.



    such pleasantry.

    Many great mathematicans spent a great deal of time on diverent series.

    http://www.amazon.com/gp/product/0828403341/103-7960634-1663035?v=glance&n=283155

    http://en.wikipedia.org/wiki/Divergent_series

    http://blogs.msdn.com/reuvenlax/archive/2006/01/09/510732.aspx

    Anyway to reput this back in context you were criticising me when i asked what the problem is with inventing the term "divergent irrational" to describe phi ? so its putting the term together thats the problem and not divergence in itself. From what i can make out from wolfram divergence is simply the absence of convergence, but also from wikipedia more interestingly the inverse of convergence. Which brings me back the question that beget this thread. figuring out that equation for biological dipoles.

    Anyway what you said to me was

    Now what i'd really like to know is this (put in bold for plea to an answer) does this also apply inversly ? Could you also say The simple problem is that the term 'convergent' is pointless. Any irrational, or rational number is 'related' to a convergent sequence in exactly the same as phi is to the fibonacci sequence If so then either statemement is pointless, so why bother saying it ?

    phi keeps recurring when examining neurological systems. i'm not proving its irrationality, that was someone elses work, i quoted. I'm just interested to find out what phi is. Now i know its irrational.

    Now you stay stuff like this

    I kind of respected you, because you have a logo which says maths guru and obviously a lot of time put in this forum. You know little about me to say to what percentage of this pursuit is "pointless crackpottery".

    isnt a degree of time spent "pointless crackpottery" a well known part of the creative process ? Its been observed throughout history. Creativity begins with concepts founded on reason and experience. I already have these. Now i'm in this direction. Why do you have a label on this forum as a teacher ? I have done teaching myself. These kinds of comments are uneccessary and destructive.

    go back and quote me where i posted some of this kind of verbal tyrade. From what i can see its purely one directional. Trolling as far as i know is an aim to cause destruction on a forum. I thought it was clear my aims are creative and to solve particular results i got in biological dipoles.

    like i said elsewhere, as we are online and anonymous, and some of us in particular areas are obviously in a postition of superiority its justs presents a bad reflection of yourself if you have some kind of drive to speak this way. However you are still having a dialouge which is providing me with direction, so for that, i'm very grateful indeed. I certainly wouldnt refer to you in this derogatory way if you had some creative ideas in the areas where my strengths lie.

    Anyway enough of that. I still got some good stuff to reflect on. Unpleasantness aside. I am sure there are plenty of people i can have a discussion without this kind of diatribe. If you want have the last word, and we'll just leave it at that.
     
  17. Apr 15, 2006 #16

    tmc

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    just to chime in about the definitions...

    Yes, googling "convergent matrix" will yield results. If I write a book, I can create a new concept and call it a "convergent matrix".

    Someone else may then create another book, create a new concept, and call it also "convergent matrix". It will be completely different than the one I wrote in my book, but he can feel free to use it, as long as it is understood that he is not using my definition (ie, if he were to start quoting me, then things might start to get weird, but as long as his book has no contact to mine, there will be no confusion).

    Now, if someone were to start a forum post about "convergent matrices", the forum readers might be confused as to what hes talking about. Is it the definition from my book, or from the other guy's book? And then the guy decides to google for definitions, and posts BOTH definitions on the forum without reading them and checking that its the correct definition (because he only knows the name and has no idea what it defines).

    Thats the problem here. You speak of "convergent matrices", but have absolutely no clue as to what a divergent matrix is. How are we supposed to know?
     
  18. Apr 16, 2006 #17

    matt grime

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    Here, let's try again to explain why labelling the irrational number phi divergent is pointless. And bear in mind that we're having to guess what your definition of a divergent irrational is since you still have not defined one. All you have said is that it is divergent because it is somehow linked to the fibonacci sequence.


    Lemma: any number can be linked to a divergent sequence.

    Proof: given any number t consider (x-t)(x-s)=x^2+Ax+B, if either s or t are in abs value greater than 1 then the sequence defined by x_n = A_x_{n-1}+Bx_{n-2} for some choice of x_0 and x_1 will be a divergent sequence.

    So, why is phi divergent? It is a legitimate question, and mentioning that 'many great mathematicians have studied divergent sequences' means nothing and is incredibly patronizing (as are many of your replies, if you want to level accusations, which imply you know a great deal about mathematics and we should listen to what you say). Your refusal to address criticisms in a way which indicates you've understood what has been said, and blindly believing what you say is correct without seeming to understand it is a sign of a crackpot. So listen to what people have said and respond to them, don't just ignore their perfectly valid criticisms. This is indeed an internet message board (though what makes you think it is anonymous?), and has been the focus of a lot of crackpots posting their own private ramblings and using it as a platform to espouse their crackpot views. Don't fall into the trap of sounding like one.

    For instance, I meant what I said when I said you need to look up these definitions. You are bandying the word inverse around again without seeming to realize that we used it to mean the inverse of a matrix. And the mathematics usage of the term matrix is different from the biological usage. I hope you're taking all these things into account.
     
  19. Apr 16, 2006 #18

    Phi is more than linked to fibbonaci. Phi is the description, which produces fibbonaci sequences and is also irrational.

    Fibonnaci is prmarily divergent, although it can be limited by a function. The definition of a divergent sequence is that it is not a convergent one. It has no limit. Fibonnaci is intrinsicaly infinite. As you say its possible to create infinite series from many conjurations. Phi is somewhat different for these is its produces

    entering 5 into (1+√n) / 2 produces phi.

    As you say you could enter anything into this, but only 5 produces a reciprocal.

    Phi + 1 = Phi 2

    This gives its a natural inverse series without resorting to convulation.

    The example you gave to do this appears require a convulated expression.

    Phi is elegant, and elegance aside from being a holy grail of maths is a good indicator we are on to something vital. This bears out. Phi being somewhat prevalent through every cell of yourself, and the structure of the major organs such as your brain, the number of fingers you use to type. Not only that just about every living structure, every system that humans organize for themselves, every planet and what is now being proposed the structure of the universe itself.

    I could rattle a whole post of about assymetry in life and power laws in complex systems. Considering the mildy abusive tone so far, i aint going to bother.

    Thats a reply to saying the term divergent was meaningless as if nobody should even discuss the subject.

    The only accusations i leveled were regading your human preference to be mildy abusive whenever you get the chance.

    If beleived i was correct would i be here asking questions, trying to come to a solution to a problem ? No i would have a webblog pronouncing my ideas in one direction. so far is i made it clear already just how limited i am, and have made several requests for paradigms to assist understanding of patterns, number and equation like representations that keep re-appearing in the research of brain and human systems. Once again you shame yourself by abusing your position (if you really have one here) by using such low and derogatory terms.


    Stop using cheap and derogatory terms and such an interaction might occur.


    Its anonymous and a bad reflection on yourself, that you are sitting at a pc and can make cheap jibes at a person that would get you a sore face IRL. Is there a trap to sounding like a crackpot ? interesting idea. Most of the people i know that like to revert to attacking someones state of mind at the drop of a hat, are usually a little crazy themselves. Hence its such an ongoing issue.

    Not that this denies you may be correct in regard to myself. i'll admit when i'm wrong. We all get things wrongs. Its part of trying to get things right. Is there a need to revert to mild ridicule. I never actually got to the stage of discussing my results on living electromagnetic structures and why they appear to produce an inverse equation that appears to be mathematical.

    Thats my goal. The stage has not occured that i can say to myself ok i've got a few things wrong here and there.


    fair enough regarding definitions. This is my learning process. No need for it to be unpleasant. How did you get that teacher icon ?

    it was myself that introduced the questions regarding what the inverse of a matrix could be. That was one of the main points of this thread.
     
  20. Apr 16, 2006 #19
    i dont recall even discussing the topic of divergent matrix on this thread. My references to divergent are all related to series and sequence.

    The problem here was that just mentioning the term "convergent matrice/matrix) produced in mr Grime the need to totally negate the very existence of the term as nonsensical.

    Refer to post two of this thread by mr grime

    Obviously its not, is real and as i then presented is used in a variety of situations. Having begun on that kind of footing i was then not in much of mood to pick any of these for discussion, not with this person anyway. He had a label which indicated he had teacher status on this forum.

    I doubt whether he should have this at all. He does not present much hope of a decent kind of interaction and has a preference to be mildly abusive.
     
  21. Apr 16, 2006 #20

    matt grime

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    mathematically you have many things wrong.

    you have for no reason decided that convergence and divergence is a property that a real number has and you have offered no mathematical explantion of what this means. you asserted that phi and log are examples of these. one of these is a real number, the other is a function. you asserted that you think they are the 'reverse of convergent matrices' without explaining what you think a convergent matrix is. now you assert they ought to be the inverse of a (convergent) matrix. The inverse of a matrix is a matrix (when it exists). Do you know what a matrix is? An mxn representation of a linear map on a vector space? Do you know what a non-singluar matrix is for these are the only ones that have inverses. If M is nonsingular do you udnerstand that the inverse, M^{-1} is the unique matrix satisfying MM^{-1}=M^{-1}M=Id? I doubt it. But you persist in the same vein without checking what other people are telling you.



    I have no idea. I didn't ask for it. And who says that everything I post here is done as a 'teacher'? Actually I believe it says homework helper, and science advisor, I don't see the word 'teacher' at all.

    You also should bear in mind that this is the mathematics forum. It is perfectly valid to call something nonsense, or gibberish if that is what it is. It is not any comment on the other person, but precisely a comment about what they have written. If it makes no sense, it makes no sense; it is nonsense. And your posts are indistinguishable in many ways from those of the cranks who have posted here.

    But we know that; it is a matrix, not a 'divergent irrational' whatever that might be. Complaining that you never mentioned 'divergent matrices' is missing the point. Whatever combination of divergent, convergent, irrational, or matrix you used, you have at no point offered any mathematical definition of any of these composite terms as *you* are using them, beyond patronizingly linking to a definition of a divergent sequence. And? I said that your use of the qualifier divergent in regards to a real number was meaningless (if it is meaningful, what is it?), not divergence itself, for pity's sake. Simply write here, in the forum, in your own words what you are taking the definitions of these things to be. A google link to pages which mention the words 'convergent matrix' (or is it supposed to be convergent matrice, I forget now) doesn't tell us anything. If you don't know what the inverse of a matrix is then you really do need to go and look up these things. They aren't what you want to know, so using confusing terms like this is not going to help your cause, and is only going to make more people frustrated at your repetition of these things without explaining what they are.

    The words convergent, divergent, irrational, matrix and inverse all have mathematical connotations. Connotations which make a reference to phi and log as divergent irrationals nonsense (something which makes no sense). And, no, concatentating words with mathematical meanings is not 'doing speculative mathematical research' anymore than picking words at random from a political textbook is making a speculative attempt to write a constitution for Iraq.

    By analogy, what would you think if I wrote: I have this idea in your area: quasi-heriditary microtubules. They are the reverse of macroscopic symplices....
     
    Last edited: Apr 16, 2006
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