Convergent matrice=divergent constant ?

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The discussion centers on the relationship between convergent matrices and divergent constants in the context of brain systems research, particularly regarding the mathematical representation of dipoles. A Japanese physicist's proposal suggests that the north pole's pull can be modeled with convergent matrices, while the south pole's push relates to divergent irrationals like phi. Participants express confusion over the terminology used, particularly "divergent irrational" and "convergent matrice," with critiques on their mathematical validity. The conversation highlights the need for precise definitions in mathematical discussions and explores the implications of these concepts in understanding electromagnetism within brain microtubules. Ultimately, the thread emphasizes the challenge of bridging complex mathematical ideas with biological structures.
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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 ?
 
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That makes no sense at all.
 
matt grime said:
That makes no sense at all.

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 can't 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.
 
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.
 
sprinklehopper said:
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 ?

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.
 
HallsofIvy said:
In addition, I have no idea how a constant (i.e. a single number) could be divergent.

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


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.

sorry bout that, I mean "inverse". for some obsessive reason i don't 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 can't 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 ?
 
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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.
 
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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.

did i use the term "convergent matrix" ? I was always referring to matrices. Anyway that's not important.

"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.

I just posted a reply on this to HallsofIvy. The irrational number phi, (which is represented within the structure of brain microtubules as fibonnaci) definately 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 ?

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'.

Modelling a sink, is a good analogy for the north pole pull, so for the divergent side of the equation that's 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 ?
 
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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.
 
  • #10
Your definition of 'divergent irrational' is nonsense: any number can be made to 'represent' in that manner a divergent sequence.

if it can be made to do so, why is it nonsense ? Anyway i don't really like discussing in this kind of tone. I certainly wouldn't 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 don't 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


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),

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

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

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.

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.
 
  • #11
The phrase 'divergent irrational' does not make any sense, nor does the phrase 'convergent matrix'. Just repeating them doesn't help.

as previously stated phi which 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
 
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  • #12
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.
 
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  • #13
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.
 
  • #14
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".

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.


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.

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 wouldn't 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 ? isn't 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.
 
  • #15
The simple problem is that the term 'divergent' is pointless. 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.

Well at least that's 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 isn't 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.



Thus there is no point in using the appellation 'divergent' since it adds nothing to the description. It is pointless, it is meaningless, geddit?

such pleasantry.

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

https://www.amazon.com/gp/product/0828403341/?tag=pfamazon01-20

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 that's 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

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.

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 ?

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.

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

If you cannot define your terms properly then you are engaged in pointless crackpottery.

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.

As it is your posts are indistinguishable from trolling, hence the negative tone from me that you don't appreciate.

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 wouldn't 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.
 
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  • #16
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 he's 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?
 
  • #17
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.
 
  • #18
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.


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.

So, why is phi divergent? It is a legitimate question.

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.

and mentioning that 'many great mathematicians have studied divergent sequences' means nothing and is incredibly patronizing.

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

(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).

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

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.

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.


So listen to what people have said and respond to them, don't just ignore their perfectly valid criticisms.

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


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.

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 occurred that i can say to myself ok I've got a few things wrong here and there.


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.

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.
 
  • #19
tmc said:
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 he's 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?

i don't 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

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

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.
 
  • #20
sprinklehopper said:
Thats my goal. The stage has not occurred that i can say to myself ok I've got a few things wrong here and there.

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.
How did you get that teacher icon ?

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.

it was myself that introduced the questions regarding what the inverse of a matrix could be.

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...
 
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  • #21
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.

i don't recal saying, thinking or seeking anything about real numbers and divergence. I did for convergence, just because there was plenty of stuff already availible, and it fits with my biological stuff, which we had better not get into. I haven't offered an explanation of convergent matrix, because its been done by others and so exist to be taken when the time is right for that to happen. My present focus is primarily conceptual which is how to get a convergent matrix to invert in some kind of way to a real number like 5 which can produce an irrational divergent series.


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).

I don't think they are inverses, reversals, or i believe now the correct term is reciprocal. I'm looking for likely candidates, and those two looked like promising beginnings. conceptually, I think a convergent matrix decreases itself to a binary systems. Correct me if I'm wrong. Also along those lines previously you stated

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),

so what is the inverse of this kind of binary matrix, you suggest its then real number. ?


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.

Well i looked it all up. wasnt hard to grasp. Would i be correct in saying that's its basically a binary matrix ?

http://mathworld.wolfram.com/NonsingularMatrix.html

this in fact is perfect for what I'm trying to do in neurobiology. Its binary or digital matrix or matrices that keep appearing.


your posts are indistinguishable in many ways from those of the cranks who have posted here

i'm now considered a creative genius in my own context. I certainly feel just as annoyed to be called so, as i a crank or crackpot. However, since you want to use a derogatry extreme yet again, i'll just stick up for myself by informing you that such a reciprocal extreme is applied to me by well heeled people in a variety of scenarios. Personally all of these tems piss me off. genius, crank, crackpot..none of these words are good.

I was called a "crank" when i began in neuroscience, because i brought an original agenda of electomagnetic symmetry and a total lack of ability to converse properly. his then grew into something pretty amazing. Basically because i knew what my experience told me, and i had the latitude to do so.

Thats how creativity works, of you know much about creativty. Several years later my lastest book on brain structure and electromagnetism has astounded many professors. It took four years of creative incubation and several years of persistance to climb the ability hill,. where i could speak the language of genetics and neuroscience. And the friction here is similar to that time several years ago within that field. However the crank or what others may more positively call creative idea bit, is what this thread is all about, not proving my ability to converse at your level. Take that attitude if you like. I already came up with the goods in neuroscience and the results which arose are descriptions which seem to be mathematical. So for draft three this maths hill is the next self teaching stage. I know what I'm trying to do.

It hardly likely after coming through all i just described, and just beginning maths 8 weeks ago,while doing a day job, that i'll be up to speed. however regardless, i am steaming ahead anyway. Whats the point in calling me a crank ? or was it crackpot previously. What you mean is you don't understand me, my lack of ability is pissing you off, and you don't think I'm listening. However i know what I'm trying to do, and that's not going off track from a biological dipoles, and an academic support system that tells me I'm heading in the right direction.

Simply write here, in the forum, in your own words what you are taking the definitions of these things to be.

Its not possible, its coming from genetics and biology, and appearing as maths. My support system is prevented me from discussing the primary concepts online

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.

it was just a reply to your insistence that the term itself was nonsense, as if it never existed and was made up.


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,

Well i do now thanks to yourself, and it I'm right its binary, you can't know how exciting that is, because it was binary results that arose from the analysis of "areas" of brain structure which posess convergent networks that operate with a structure that is visually a "matrix".





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
...


cant argue with that. That just seem like what I'm trying to do. However my agenda is very deep, so thrashing out defintions is just a current process.

if you had seven years of reason to tell you that microtubles had qualities and results which resulted in mathematic terms, you are sure off, you might find yourself visting a biology forum, trying to grasp how mathematical terms translate to that discipline. This is all I'm trying to do.

i'm not ready to define either side of the equation, convergent or divergent, i originally proposed, as I'm still trying collect a whole load of stuff i can stick on either side, till i finally see which definitions do the trick. I am encouraged however by these non-singular matrixes your proposed.

Anyway if up to could you or yanyone else tell me if

1. a convergent matrix tends towards binaries.?
2. a non-singluar matrix i.e. the only ones that have inverses are binary. ?



Sprinkle
 
  • #22
Yet you're still not explaining what you mean.

1. a convergent matrix tends towards binaries.?
What is a binary? Is it a binary matrix? In one of his posts, matt pointed out what it could possibly mean for a matrix to converge. Using that definition we can see that a matrix can indeed converge to a binary matrix, but it can also converge to other matrices just as well.

a non-singluar matrix i.e. the only ones that have inverses are binary.
No. There are many nonsingular nonbinary matrices.
 
  • #23
Again, you haven't understood what I wrote. I did not say that any of the individual terms or phrases must be meaningless, or nonsense, but that your use of them was. You cannot explain what you mean when you use them. And as I have said before, when someone asks you to explain a new term such as 'divergent irrational', examples of which you claimed were phi or log, then it is prefectly correct to demand an explanation of this term, and that since phi is a real number and log is a function, and neither of which is divergent in any sense of the word, it is more than understandable to label that as nonsense (mathematically you thread title just does not make sense, or is false; talking of a divergent constant *is* nonsense, a constant is exactly that: constant; it doesn't 'do' anything like converge or diverge. That does not however preclude you from offerning a definition for it that does make it make sense. It is for instance, superficially, nonsense to say 'let h bar tend to zero' since h bar is a constant, but it is now an accepted abuse of terminology that means some quantization variable (usually q) is allowed to tend to zero which ought to give the classical case; q=h bar gives the ordinary, real life, quantum case). Further linking to a definition of a divergent series (neither of phi or log are such) and saying many great mathematicians have studied divergence (as if we didn't know this anyway) is not helpful. And try to bear in mind that the people who might answer a post such as yours will have at least a degree in maths, probably a masters and sometimes a phd, so telling us what divergent means (week 1 in undergrad analysis) is not what you need to do. You need to state what you think it is not what we know it is.

How about, instead of trying to use mathematics terms on a mathematics forum you used the biological ones? I mean you say

"you might find yourself visting a biology forum, trying to grasp how mathematical terms translate to that discipline"

but that isn't what you're doing. You're already using the terms as if they have some mathematical meaning. So what mathematical meaning are *you* giving them? As it is you are writing as if you have decided what the mathematical interpretation is already. Terms whose meaning you freely admit to not knowing. So try using the biological terms and then try to let someone say if there is a mathematical formulation for what you want to say.And I have no called you a crackpot or a crank, I have said that your posts are close to making you sound like one. You haven't, evenn now, addressed the mathematical issues with your posts, and you keep slightly changing the subject to avoid discussing them, for instance when someone, following my mistake, points out that you've not defined 'divergent matrix' when it should of course have been 'convergent matrix' you point out their mistake but still you don't state what a 'convergent matrix' is in this context. Try looking at this to see what kind of things physicists (and mathematicians, but mainly physicists) see a lot of on internet forums (Jon is a moderator at sci.physics.research amongst other things):http://math.ucr.edu/home/baez/crackpot.html

(point 14 in particular)

Sadly we cannot point you to the Theory Development section to see what kind of things were routinely posted here.

But you aren't thrashing out definitions: you're abusing them (just thrashing them if you will), and causing confusion because of your misuse of terminology."My present focus is primarily conceptual which is how to get a convergent matrix to invert in some kind of way to a real number like 5 which can produce an irrational divergent series."

Right, now that is how you should write maths (and no, not because of some personaly belief of mine). There are still problems: you have still not explained what you want a convergent matrix to be in this context. And if it is indeed a matrix, you do not want to use the word invert. You will simply be applying some function to yield some (real) number. There are many ways to do this. However, you've now switched to the phrase 'irrational divergent series' (fromo just 'divergent irrational') which is also unexplained.

So far you've not been able to explain what these things ought to be or do."if you had seven years of reason to tell you that microtubles had qualities and results which resulted in mathematic terms, you are sure off,"

if you're so sure of these terms then surely you know what they mean? How can you assert you're sure something is a convergent matrix when you don't know what a matrix is? (Judging by the fact that you've not written what you think it is)

(nb I am assuming you meant to write 'if you had seven years of reason to tell you that microtubles had qualities and results which resulted in mathematic terms you are sure of')

Finally, 1x1 means a 1 by 1 array, nothing to do with binary numbers; matrices are defined over any field, or ring and invertibility or non-singuilarity has nothing to do with 'binary'ness.
 
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  • #24
sprinklehopper said:
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.

There is lots a beginner can do besides logging onto the internet and cribbing free yet only vaguely valid knowledge from anonymous people.

I would suggest that you find a local college and take a few math courses first, such as a linear algebra or a number theory course. If that is not possible, then at the very least find yourself a good linear algebra or matrix theory text and work through it before doing anything else (there are tons of them available cheap and used at Amazon or Powells Books). You seem to be a bit hazy on fairly well-established concepts as the inverse of a matrix or the limit of a sequence or even real numbers.

Why pay for something that you think you can get for free? One, flesh-and-blood people will provide quicker and more meaningful interaction; and will give you a better idea if you're onto something or not. Two, the best books provide an excellent resource and will generally contain valid arguments that you can check yourself. And will provide assignments that help you explore and understand the material better.


The fact is that phi is much less important a number than e or pi or 0 or 1 or even 10. It shows up every so often for physical reasons -- a friend of mine at CWRU has a nifty argument as to why the Fibonacci sequence shows up in phyllotaxis -- but then again so does pi and the square root of 2, which has the "mystical" property that its reciprocal is exactly half of it.
 
  • #25
The occurence of phi, or Fibonacci, when it is genuinely there, is usually completely explicable. And essentially because of the equation x^2=x+1. I suggest trying to find an article by Keith Devlin on the American Mathematical Association's website about it.

One thing I find very odd is that people who have a misconception about how amazing these facts are (don't get me wrong there are some very importatn things one proves about phi) is that they always ignore the other root of that equation.

As for its apocryphal uses, I'd like someone to demonstrate that it does indeed occur in odd places like Greek art or the ratio of parts of the human body any more than any other number which happens to be about 1.6
 
  • #26
First, one more plug for definitions. In mathematics, if you want to discuss anything at any depth, you need to start with your definitions. Starting with someone else's definitions is acceptible if they are consistent with the other definitions and you understand them. Without understanding the definitions of the words you are using, a mathematical discussion is pointless.

Now, to put up the mirror :rolleyes:

sprinklehopper said:
i'm pretty sure, you wouldn't 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.

I, for one, would rather read your book on biological dipoles before continuing this mathematical discussion. Without any context, I can't make any sense of the ideas you are apparently trying to communicate. I have my ideas about what's happening regarding the part I bolded. My feeling is that those people avoid you not because they can't get their cheap kicks in, but because they think it's pointless trying to have a meaningful discussion with you. I've seen fools get a lot of attention on other forums. I can't prove this is the case - maybe you are a shining star in the field of neuroscience. I can only go by what I see in this thread. I don't see anyone trying to make you feel inferior. Just a lot of people who have little to no idea what you are trying to say, and would rather spend their time with something fruitful.

Just my observations. And so that there is at least a little mathematical content in this post , it is interesting that the other root gets ignored, especially when you need it to write the formula for the nth fibonacci number.
 
  • #27
By the way, I did google on "convergent matrix" and got a number of hits. In every one that I checked, they were really talking about a matrix function or sequence of matrices. It was the function or sequence that was convergent (as a limit) not the matrix. Largely, this was where they were using a recursive algorithm to solve some numerical problem.

Once again, there is no reason to refer to phi as "divergent" just because it is associated with (or can be used to create) the divergent Fibonacci sequence. As matt grime showed, any number can be used to create (or be associated with) some divergent sequence in exactly the same way as phi is with the Fibonacci sequence.
 
  • #28
BAck from my other job and got a load of books on algebra etc.


No. There are many nonsingular nonbinary matrices.

Quote: from matt grime :
a non-singluar matrix i.e. the only ones that have inverses are binary.


It was in context with inverses unless you know of non-singular matrix that have inverses and arent binary ?
 
  • #29
then it is prefectly correct to demand an explanation of this term, and that since phi is a real number and log is a function, and neither of which is divergent in any sense of the word,

Not divergent as a singular term. When you look at their real life applications, they mostly spin out divergent sequences. Surely that can be conceded ?

(mathematically you thread title just does not make sense, or is false; talking of a divergent constant *is* nonsense, a constant is exactly that: constant; it doesn't 'do' anything like converge or diverge.

The thread title is just a beginning point. i don't expect me to really figure this problem just like that. Let's move beyond where i began from. That seems like long time ago to me



That does not however preclude you from offerning a definition for it that does make it make sense.

It is for instance, superficially, nonsense to say 'let h bar tend to zero' since h bar is a constant, but it is now an accepted abuse of terminology that means some quantization variable (usually q) is allowed to tend to zero which ought to give the classical case; q=h bar gives the ordinary, real life, quantum case.


Lost me a bit there. I'm not doing quantum level neurology. Look what happened to stuart hammerof. I couldn't find a reference to quantization variable that wasnt at quantum level, but i think what youre saying is that an operator is required to reduce the constant



Further linking to a definition of a divergent series (neither of phi or log are such) and saying many great mathematicians have studied divergence (as if we didn't know this anyway) is not helpful. And try to bear in mind that the people who might answer a post such as yours will have at least a degree in maths, probably a masters and sometimes a phd, so telling us what divergent means (week 1 in undergrad analysis) is not what you need to do. You need to state what you think it is not what we know it is
.

did i use the term divergent series ? from the beginning of this project, my results are always about divergent sequences.

How about, instead of trying to use mathematics terms on a mathematics forum you used the biological ones? I mean you say
"you might find yourself visting a biology forum, trying to grasp how mathematical terms translate to that discipline"
but that isn't what you're doing. You're already using the terms as if they have some mathematical meaning.So what mathematical meaning are *you* giving them? As it is you are writing as if you have decided what the mathematical interpretation is already. Terms whose meaning you freely admit to not knowing. So try using the biological terms and then try to let someone say if there is a mathematical formulation for what you want to say.

Thats exactly right. Thats what's going on here. But its too complicated to present the biological stuff, so let's pick a tree as really good example, that requires the equation I'm looking for. As its basically tree like systems that keep appearing in brain research and genetics.

This however would require you me to get some images which refer to the divergent/convergent numberings in microtubules and plant / tree phylotaxis. Visually this might make what I'm trying to get at clearer.

http://img55.imageshack.us/my.php?image=tyreytry9mc.jpg



so what you are saying is crackpot is acceptable and standard verbiage in mathematics in general, or was this just a one off joke page ? Many great creative theories would have began with a maximum crackpot score then.


"My present focus is primarily conceptual which is how to get a convergent matrix to invert in some kind of way to a real number like 5 which can produce an irrational divergent series."

Right, now that is how you should write maths (and no, not because of some personaly belief of mine). There are still problems: you have still not explained what you want a convergent matrix to be in this context.

I want it to end up as a your definition of a a non-singluar matrix, The binay one. That is the only one which yields inverse.


And if it is indeed a matrix, you do not want to use the word invert. You will simply be applying some function to yield some (real) number.

Whether is is a function is not relevant. The primary mission is it has to invert to explain why the quoted biological structures are inversions.


There are many ways to do this. However, you've now switched to the phrase 'irrational divergent series' (fromo just 'divergent irrational') which is also unexplained.

I am now at the stage now where the right hand side of the equation has to be a "divergent sequence" which expresses as a phi sequence. I can't call it irrational now as phi was disproved to be irrational.

Quote from Bennet briggs book

"The word irrational, literally means inexpressible as a ratio"

yet phi which is called the golden ratio here is proven to be irrational

from http://www.mcs.surrey.ac.uk/Personal...nacci/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."


Can you make sense of that. ? Those are contradictions from respected mathematicians.

So far then to summarize how this is moving along

The left side of the equation needs to be a convergent matrix, your definition of a a non-singluar matrix, The binay one, as that is the only one which yields an inverse.

The right hand side of the equation has to be a "divergent sequence" which expresses as a phi sequence. I can't call it irrational now as phi was disproved to be irrational.



so is this acceptable in terms of definitions at least.

Convergent non singular matrix= fibonnaci divergent sequence

So far you've not been able to explain what these things ought to be or do.

I want to be able to enter binary numbers into the left hand side of the equation which will yield fibonnaci numbers, that are inversions of the binary numbers in terms of symmetry. To explain, That means i need the design of a non singular matrix that will yield the fibonnaci sequence. So that it balances in either direction to explain the graphic i posted. The equation has to push and pull in the sense that if i input bigger integers into the left side equation matrix (perhaps using phi function) then i'll get a decease in the sequence of real fibonnaci numbers, in the right side. Similarily if i incease the amount of numbers in the fibbonaci numbers in the left it will equal a reduction in the size of integers to which enter the matrix function.

This is a beginning. Now i can try and attempt my first equation. Which is a beginning because if each side inverts properly i should be able to stick an inverse of each mathematical expression onto either side.

"if you had seven years of reason to tell you that microtubles had qualities and results which resulted in mathematic terms, you are sure off,"if you're so sure of these terms then surely you know what they mean? How can you assert you're sure something is a convergent matrix when you don't know what a matrix is? (Judging by the fact that you've not written what you think it is)

Bad expression on my part.


Finally, 1x1 means a 1 by 1 array, nothing to do with binary numbers; matrices are defined over any field, or ring and invertibility or non-singuilarity has nothing to do with 'binary'ness.

dont recall trying to say this. I was just referring a binary matrix from this

http://mathworld.wolfram.com/NonsingularMatrix.html

the final one in the table is a binary. a non singular matrix does have something to do with a binary matrix

http://mathworld.wolfram.com/01-Matrix.html


This is quite good. i'll need to go read up on binary matrixes now.
 
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  • #30
**** another three replies. My brain has had it for tonite.


later.
 
  • #31
This is getting ridiculous. I've let this thread run longer than it should have.

Sprinklehopper: whether your a crackpot or seriously trying to learn, this format is inappropriate. It is unduly combative, and potentially misleading to other students of mathematics. I'm actually embarassed to see that this thread makes the front page of a google search for "convergent matrix".

When you're willing to be more receptive to others' responses, then you can start a new thread. But if you intend to keep the same attitude, then don't bother.

Willingness to try and learn the concepts, and what kinds of objects are being discussed is good. Willingness to try and learn what words mean is good. Continuing to speak what amounts to gibberish despite being repeatedly told so is bad.


Before I close the thread, though, I will answer some of what you've said:


[2] is an example of a nonsingular matrix that is not binary.


Imprecisely speaking, the usual usage of the term "rational number" means any number that can be written in the form a/b where a is an integer, and b is a nonzero integer.

And an irrational number is a real number that is not a rational number.
 
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