studiot

Sorry my mistake. My posted table came from Ott ch9 multifractals. Ch10 Many Dimensions and Multifractals is in Holborn. (I picked up Holborn whilst Ott was left on the scanner)

I don't care what copilot put up (it doesn't think). This nonsense is as bad as Pope Gregory v Bruno or Galileo or Plato's cave shadows and about as far from the original topic as one can get.

Ott Ch10 is entitled Many Dimensions and Multifractals. In Relativity treatments start with one spatial dimension and then move on to 2, 3 and 4. Fractal geometry is no different. Remembering that the much of the activity in fractal analysis take place in phase space of some sort, not ordinary x,y,z geometrical space we define a multifractal as An object with a multiplicity of fractal dimensions. In ordinary continuous analysis we start with at least to variables to define a calculus eg x and y to get dy/dx etc. We then define multivariable calculus as the calculus of 3 or more variables and the derivatives are partial and one needs 3 axes or dimensions to place or embed the system in. A similar scheme takes place for fractal dimensions, except the 'derivatives' are all these fractal limits based on some 'measure' or another. One such measure is called the box (or box counting) measure which counts the number of 'boxes' of side epsilon needed 'cover' the fractal set. This echos the epsilon delta argument in continuous analysis calculus. And a limit count is taken as the epsilon becomes smaller and smaller (as in ordinary calculus if such a limit exists) Ott provides a very good motivation for multifractals in chapter 11 where he examines the Physics of Diffusion Limited Aggregation, Electrodeposition, Viscous fingering and how and why simple 2D linear partial diff equations (Laplace) lead to fractal behaviour at moving boundaries, thus developing the patterns we see in Nature.

This book from the same publisher and about 40% cheaper is more elementary and may suit your need more. https://www.worldscientific.com/worldscibooks/10.1142/12345#t=aboutBook Its content coverage is roughly similar to the Oxford book I quoted or this one form Cambridge University press Chaos in Dynamical Systems Edward Ott In Chapter 9 he calls f(alpha) the singularity spectrum and discusses the application to Thermodynamics. It should be noted that the notation in this field is very new and very fluid.

I agree with this, but only if the fourth axis is ct or ict.

This is where you disagree with the Cambridge Encyclopedia of Language, which has a whole chapter on various forms of sigh language, as procedural. Further you keep talking about communicating a message, yet contradicting yourself by saying that only the 'receiver ' has means to understand the meaning, implying that the generator of the message has no control over the message and ignoring intent. Also you keep ignoring my poet who uses language to generate meaning in the receiver's mind, a meaning that may not be the same as intended, but nevertheless acceptable to the receiver. For instance the poet may intend the receiver to happy or sad or whatever and succeed in that but not for the reasons he originally though of.

I suggest it would be productive to widen the scope of the discussion. Consider the statement 'A kiwifruit is delicious.' This is true for some people but not for others so is not a fact, but a value judgement. But the statement 'A kiwifruit is a fruit' is true regardless of how it tastes and is a fact. Which brings me to the observation that English offers the ability to distinguish between Truth, a Truth and the Truth. Another factor is time. The statements Mars is 150 million miles from Earth Mars is 50 million miles from Earth Can both be true, but are either facts ? The statements Churchill was born in 1874 was true in 1875, but not true in 1873. Then again there are other ways than comparison with reality to establish veracity. For instance 'A triangle has three corners' is true by definition. So the tense of the verb is significant, and can cause confusion in those languages that do not have a present tense of this verb.

I don't suppose your definition of parse is any more consistent than your definition of symbol, procedure, equation, meaning, receiver etc coincides with ours.

Hi Markus, I'm just going out so very quickly this might be a start for you Chaos and Non Linear Dynamics page 448 ff Scaling and f(alpha) indices Robert C Hilborn Oxford University Press. Sternberg has some stuff in his Dynamical systems book but I think you mqay have to find pieces of information in lots of different palces. (Non linear) Dynamics is a key phrase. I have some more to check so will post again later. Let us know how you get on.

It is obvious that we have a clear problem. You have stated several times that the meaning is determined by the 'receiver'. This leads to the obvious paradox that no meaning can ever be transmitted, discussion is impossible and that it is pointless me writing these words since only the reader can determine the meaning and I, the writer cannot set it. Hence communication is impossible. Good day to you.

Of course they do. But you are so narrowly focused on procedural v symbolic that you are ignoring the inputs and thought of others. You are not receiving their messages. For instance swansont asked you about intent. When I go to a cafe and order a cup of coffee, my intent is clear and comes from me, the speaker, not the waitress who is a listener. No 'interpretation' is necessary. I have asked you for examples of some of your statements and classifications, and am still waiting. I will go first. A good example of a procedural language (in my opinion) is sign language.

Excellent idea. +1 Your notion is intriguing but needs to be worked through carefully so you don't mistransfer definitions between space and spacetime, you require to set up a suitable transformation to do this. Yes, so long as you keep distance and time separate, as in space and time. What does distance mean in spacetime ?

Let us compare this discussion with an earlier 'scientific' quest. Act 1 Galvani discovered electricity causes frogs legs to twitch. Act 2 Mary Shelley writes a famous scifi book based on the human conviction that. following Galvani, electricity induces life. Electricity is just the wrong agent for that job. Today Many folks dream of nuclear rockets based on human conviction that fission / fusion will solve all ills. Fission/fusion is just the wrong process for the job. And not only do we still not know what the right process is to induce life, we don't know what the right process would be for interstellar travel.

+1 for being prepared to say "I don't understand" or words to that effect. Chips today are 2 dimensional so are measured by area, not length. So reducing linear dimensions by a factor of 10 reduces the area by a factor of 100 and so on. Quite a significant reduction in its day. but IBM are proposing 3 dimensional chips, making an even more dramatic saving. So 1/3* 1/3 * 1/3 =1/27. Obviously not as goo as 1/1000 would be, but not to be sniffed at even so.

Time we had some new chip technology. And good to see IBM backroom boys still on the job.

All you are doing here is proving my contention as to how wonderful the English Language is, as compared to most others. Yes is there are more factors to consider then English allows you to add qualifiers and quantifiers indefinitely. But just maybe @npts2020 has only one oak tree at the end of his drive. If there is only one tree he doesn't even need the 'oak' adjective or the 'old' one. And of course the driveway could be made specific by use of the first person possessive pronoun my.

This paper gives the rules for summing series of P-adic numbers and some tests for convergence, in section 4. I haven't checked your series, but remember you can form P-adics from Q, and Z https://math.uchicago.edu/~may/REU2020/REUPapers/Pomerantz.pdf

I am very glad you made this second post because it explains a lot. Everybody is a bit different from 'normal' in some way or other. Mathematically it is perfectly possible for there to be no actual instance of the average in a sample set. In the last few years there has been a move to use real people with a particular difference instead of actors in works of drama. For instance there is a deaf actress who specialises in parts exploring social interplay with a deaf person. In the same way there is a French actress who plays an autistic girl working for the police. The original was 'Astrid in Paris' and is in French, but there is an English version spin off called 'Patience'. Both characters are fumbling their way through social relationships and friendships, you might find it interesting if you can get to see some of the episodes. Not sure if you like Mathematics, but you have posted elsewhere a question about p-adics. I can tell you that dancing is a most interesting demonstration of one of the more fundamental areas of Maths, called group theory, which is about patterns. (do you like patterns ?) In fact one Professor uses these patterns to introduce the main aspects of group theory (which nowadays pervades many areas of chemistry and physics) . I can post some details if you like.

So is the letter A spiky or cuddly like a ? Incidentally Was this a joke ?

More play upon words in place of an answer to the question I asked. Please define your words more specifically. I can't see how you can get far in the scientific world if you keep using different definitions from everybody else. Before you told me you define a lightyear as a distance. Now you tell me you define it as a difference in time. How is this playing around not self contradictory ?

None of these are part of Language. I do however there is more to symbolism than the alphabet punctuation etc. For instance the international symbol(s) on public toilet doors. The meanings are well understood. You have said it before and I disagree. Further this view directly contradicts the communication model. Either the receiver receives an intended message or does not. Procedural communication is less what the lawyers call "An invitation to treat" than symbols (eg Special Offer! £1) Surely if there are any thought processes at all they are generated by the originator and communication has been successful if the receiver that message, not one of his own generation. What about my Poet ? He expresses something as a result of his thought processes. If this generates the same mental image in the receiver then communication has been successful. Art like this is about the only example I can think of where the image in the generator's mind is different from that in the receiver's and yet his generation can still be called Language.

That is why they are so good at doing your homework for you or polishing your 'paper'. But that is not the only thing they do and should not be classified as such. There is more to language than procedural thinking and symbolic thinking (which is really only representation / repackaging already formed thoughts). It is instructive to present the statement to you favourite AI "Mr Green is green." I expect most humans would have little trouble understanding what I might mean by this but a quick go in Google produced nothing remotely connected to it. It is also fruitless to try to associate a two part entity (language) with one part entities like procedure, structure, representation etc. It should be further recognised that each of the two parts of language may be broken down into more parts.......... So a poet will have thoughts and expresses these as a poem which may not be in 'proper' English But is proper nonetheless. The second part of this is communication which may be to a specific individual (as in a conversation) or it may be to people in general, none of whom the poet will ever address directly. Of course the meaning though by the poet may be different from the meaning inferred by the beholder which opens another can of worms.

What distance function (metric) are you employing in making this play upon words ?

Your most recent passage above contains several fallacies. Yes LLM's work with language, but that is like saying the man who takes your ticket works with the railway network. Both his work and that of LLms only occur in a very limited way as compared to the whole railway network The whole purpose of Language is the communication of meaning. So much so that I was taught that in the English Language a sentences is only a sentence if it makes sense. Some words strung together (which is what an LLM does) may or may not be a sentence. Even the LLM itself acknowledges that although it doesn't know it has done that. The LLM has no access to the meaning of its responses, although I grant you that the algorithm makes a very clever pretence. Further it can be quick enough to give a 'spoken' response in real time as in a conversation. Just as an some earlier computers could print out a sine wave or actually generate an audible version. It treats output media as the same. I also disagree that verbal communication is somehow 'better' than written communication. Both forms have their uses and abuses, advantages, drawbacks and pitfalls.

I'm not sure about these ideas of 'Truth' as something standing separate from other parts of reality. Although medical matters are often debated in courts, I don't think it is germane to this thread about AI. However it would be interesting to discuss 'Truth' in the light of idiopathic diagnoses and statistics.