Eternally returning to the virtual

On page 244 (Ch.11: The Narrative Adventure) of The Blank Swan, Elie Ayache wrote that "to capture (...) the singular 'how' of creation as such" will provide for "our perception of the creature as a result of the act of creation, our perception of it against the backdrop of the virtual it is emanating from, will allow us to read, in the static and actual and settled creature, a continual and eternal return to the virtual. As it actually, definitely, 'eternally' exists, the creature eternally returns to the virtual."

Nietzsche's idea of the "Eternal Return" is often borrowed by various thinkers and adapted to their need, which is fair indeed, because Nietzsche himself did not close this idea (that he himself borrowed from various sources: mythologies and poets) into a strict interpretation, leaving ample room for his readers to comprehend it in their own way.
A few years ago, I myself pondered over this idea, and came to consider it as a return to the materiality of the body, a necessary and eternal travel from the abstract to the material, where thought (I personally used the word "regard" in french, I don't know how to translate it in english, in order to convey its polysemy, associating the ideas of seeing, considering, thinking, caring, guarding, absorbing, mirroring, repeating, ..., Nietzsche would perhaps talk of "will to power") eternally returns to the body in order to reaffirm itself (by again moving away from the body, in order to later return to it) in its freedom, in acting. It seems to me that it adheres to the sense of the following sentence from Elie Ayache found on page 234:

"Thought wakes up with the body pushing it from behind, and it is soon to be itself literally pushed outside of the room."

This eternal return of the "regard" to the body from which it comes, is also the return, I believe, of the thought onto the creature from which it emanates. It eventually is through the consideration by thought of the negation of the body that is its origin, that body and thought are articulated into a relationship of eternal return. But the negation of the body can also be seen as the affirmation of contingency (and its necessity), it is therefore an eternal return of the actual to the virtual, which is the perspective described by Elie Ayache.

Furthermore, I think that this ability for us "to read, in the static and actual and settled creature, a continual and eternal return to the virtual" is particularly well-represented in chinese art. Calligraphy painting, for instance, is all about enabling the viewer to enter and to experience the process of painting, that is the virtual:



This is the character li, which means strength, but there is no depiction of strength here, nothing substantial differentiates this painting from 力. What is apparent however is the way this painting has been realised. We can easily imagine ourselves drawing this exact character, the brush strokes are clearly visible, Wen Shen, the author of this calligraphy did not do anything to conceal his technique, on the contrary, he's displaying it, we can imagine the tension of his hand, the speed of his strokes, even the angle of the brush on the paper. This painting does not represent 力, it represents itself, it is a painting of the painting.

Similarly, chinese landscapes do not represent a landscape, they again represent the painting of the landscape:



Again, Chen Jun here doesn't make any effort to conceal his technique, on the contrary, sharing it is the whole point of the painting.
This philosophy of art is further developed in the works of Zao Wou Ki, whose explicit ambition is to paint the Dao, which is nothing else than the virtual:



The stress on the process of actualization that underlies chinese art obviously has its counterpart in chinese philosophy and most importantly in the Dao De Jing (道德經).
Interestingly, just as virtue and virtual shares an etymological connection, the Dao De Jing relates both concepts quite closely in the first chapter of the De (德, virtue):

上德無為而無以為也 (shang de wu wei er wu yi wei ye) (1)

which translates literally (and according to Henricks whose book is referred above) as:

The highest virtue takes no action, yet it has no reason for acting this way.

Or, in other words: The highest virtue remains virtual

This idea is of course pervasive in all traditional chinese philosophy, it is sometimes referred as the "Wei wu wei"(為無為) principle, and it can be found to some level in the teachings of all Daoists, but also in Confucianism. The De Dao Jing (to use Henricks order), that is, the Book of the Virtue and the Dao, or to use a purely western vocabulary, the Book of the Virtue and the Virtual, is unique in linking both the notion in such an explicit manner. It indeed seems to say that to be virtuous is to remain in constant proximity with the virtual, at the edge, one could say, between the virtual and the actual.
It is, in this sense, that Art has an educative function, it is what formed the thought or the "regard", to remain virtuous, by not interrupting the eternal return to the virtual away from(and pushed by) the actual, by remaining not in the "can be" (The Blank Swan, p.437) which is already too much on the side of the actual (into an ontological beingness), but rather in the "also can". This expression which is often found in Singlish (Singaporean english) obviously comes from the chinese ye keyi(也可以), the "ye"(也), meaning also, acts as an untotalizer of the range of possibilities. Indeed, this expression often comes as an answer to a request, which assumes implicitely, that the demand was rather out of the range of what is normally requested, the interlocutor then replies that it can also be done (even though, in practice, this expression is more pervasive and exceeds this context).

也 is also found in the above verse (1) of the De, here it is widely believed to just be an emphasis, an affirmative marker, as it is only found in the MaWangDui version, and not in the more commonly used version of WangBi , its importance is therefore neglected. However, I believe that it should also be understood here as an untotalizer, a differentiating operator, that extends the meaning beyond its literalness. Far from emphasizing then, I think it may well be a de-emphasizing marker, a prompting to forgetting in the sense Elie Ayache is proposing on page 248:

"Forgetting is the point of inflexion and reversion to the surface that is necessary for writing. By contrast with the sum total of possibilities, clear and yet confused, forgetting makes the writing thread obscure yet distinct."

A lot could be said now of these ideas of clarity and obscurity, in relation with chinese thought, I leave it to the readers to appreciate for themselves, maybe through the works of Francois Jullien, or maybe by looking also at the works of Zao Wou Ki.

Igor Markevitch: Le Nouvel Age

It's been a while that I wanted to publish a post on Igor Markevitch's works. Although he's better known as a conductor, he's one of my favorite composer. I could have chosen more famous pieces of his works such as Rebus or L'envol d'Icare, I may discuss some of them in the future, but as it happens, right now, I can only listen to the CD starting with Le Nouvel Age of which 1mn extract of each movement can be listened and the whole piece can be purchased here.

A presentation of Le Nouvel Age (the new age), the one that can also be found in the CD, can be read here.

To me, one of the most striking feature in Markevitch's music is its self-restraint, which is contrasting with the futuristic elation found in Mosolov's "Iron Foundry" for instance:



The programatic subtext, provided by Markevitch himself in his autobiography and reproduced in the CD leaflet, reflects this in toning down the pride of a youthful wrath with:

"Présence sous-jacente de la vulgarité." (underlying presence of vulgarity)

This presence seems to instill a lingering sense of shame in all the piece, and this leads to a fundamental questioning(the unresolved dominant seventh) that comes to dominate the third movement: Isn't the New Age the age of shamelessness, and therefore the age of vulgarity?

The Medium of Contingency

“The medium of contingency”(shortly available in volume 22 of pli) clarifies many points that remained implicit in “The Blank Swan”, it particularly precises the divergence that exists between Elie Ayache’s (EA in the following) and Quentin Meillassoux’s (QM) thought. In that, it does answer my earlier comment, somehow confirming it, but also, strangely, I came to disagree with this one to the extent of now holding the contrary belief that EA’s and QM’s thought do merge into a seeming compatibility.


I-THOUGHT: FROM DOUBT TO AXIOMATICS

The following passage (on page 2) from “The medium of contingency” seems to assume a certain conception of thought, or at least of its placement in order to think speculatively, in QM’s sense:

“If a speculation like Meillassoux's must bring our thought flat against the matter of absolute contingency, with a flattening of the depth where we would have searched for the reason why things are what they are and not otherwise and with the flipping of ontology from the side on which things are to the side on which things can be and if, correlatively, contingency has to be thought independently of any division of underlying states in which the contingent thing possibly can be something or other, then the step back from contingency - for only by stepping back from its absolute strike are we able to make sense of it and unfold the expanse where it can be thought speculatively - should take place in a direction and through a medium that maintain the absence of reason and the absence of states.”

I am not sure there is any depth to be flattened in the way thought relates to any of its object, and in the way thought is really, since I can’t conceive of a thought severed from its object (in the way I can conceive of an objectless desire, for instance). On the contrary, I tend to believe that thought is flat, what does have depth is its manifestation via language, but thought is largely independent of it, and it is independent naturally “of any division of underlying states”, which are just tools used to express itself (i.e. its object).
As such, thought can easily criticize these divisions, these states, while it may lose itself in it every now and then, it always retains the capacity of freeing itself from their influence, of turning against them, of staring at them in an inquisitive manner. Language can even help thought in its rebellion against language, as any natural language contains its own meta-level. In that, thought can easily turn itself (and its object) upside down.
So I am not convinced that “a medium that maintain the absence of reason and the absence of states” is all that necessary, provided that states are not taken too seriously, too heavily so as to place us in “a world that is repelled by gravity”(The Blank Swan-p.152, Après la finitude-p.149). As long as the totalization of states in not given too much credit, the philosophical debt can easily, and instantly be repaid.
That being said, “a medium that maintain the absence of reason and the absence of states” may not be necessary, but it may be useful, but more on this later.

The condition for thought to stay in control of its fate, and thereby, be speculative, is doubt, which may just be the historical root of QM’s factuality, as just like facticity cannot be said to be factitious (Après la finitude-p.107), doubt itself cannot be submitted to doubt.
Doubt seems therefore to appear as the psychological form of facticity (see Après la finitude-p.101), or to go further, as the subjective face of it, and to extrapolate a bit more, one may wish to consider the equivalence between the necessity of facticity and the necessity of doubt, wherein the former does imply the object (principle of factuality) and the latter, the subject. I will not follow this line of thought now however, and I genuinely don’t know whether it leads anywhere.

Doubt is nonetheless dated, and often distorted beyond recognition by a mundane usage, whereas axiomatics propose a modern mathematical formalization of doubt. It may then be through axiomatics, and mathematics (and maybe indeed topology, to follow Jeff Malpas along with EA, The Medium of Contingency-p.18) that speculative thought can progress. Mathematics, in their axiomatized form, also present the great advantage to be a very flat language, containing its own meta-language, and providing an unmatched clarity to the extent of being tautological (as it is fully explicit).


II-USEFULNESS OF THE MARKET

While I don’t think the market is the only available medium for factual speculation to develop, I wholly follow EA’s analysis of the market as being a genuinely “contingent and immanent place”. As such, it is therefore useful, but not only because of what it has done, but more because of what it promises to do.
Looking at the market, not as the medium for factual speculation but as just one of many such media, we should expect all these media to communicate with each others, to exchange and nourish their respective speculation.
Clearly for instance, and some works may already have started on this matter, that I still have to get acquainted with, the derivatives market should be a fruitful domain for the factual speculation on probability axiomatics, which itself could lead to topological and therefore ontological results.
It may also be that a speculative resolution of Hume’s problem (as stated by QM in Après la Finitude-p.176) could draw some insights from the material un-totalization of contingent claims by the endless complexification of exotics contracts.

Furthermore, the market may not be the only one, but it appears, in some important regard, to be the purer, the most devoid of faux-semblants, it will therefore act as a useful reference for the other places of factual speculation. Not unique but central, it may play the role of a singularity, a repelling or an attracting one, it does not matter but it will be instrumental in the development of factual speculation, and it may even be more than that, as I believe it also has a political and ethical relevance which is not foreign to its immanence, but that is another matter.

The Blank Swan

I already have published a review of “The Blank Swan” on Amazon site, I will not repeat it here, rather, I wish to further an analysis (which I outlined on Amazon’s review, but in very vague terms) of some of its thesis in relation with those of Quentin Meillassoux in “After Finitude: An Essay on the Necessity of Contingency”(the original version of this book being in French: Apres la Finitude).

I- SOME OF MEILLASSOUX'POINTS

1. Hume’s problem and its probabilistic inference
In “After Finitude”, Quentin Meillassoux takes on Hume’s problem which investigates the possibility of grounding rationally the observed stability of natural laws, or, in Meillassoux’words, our capacity to demonstrate the necessity of causal connections. Meillassoux lists three types of answers to this problem: a metaphysical, a skeptic and a transcendental one.
I am only interested in the latter here, I leave to the interested readers to check on the others in Meillassoux’ book.
The transcendental solution to Hume’s problem is typically the one proposed by Kant. Kant’s argument is a reductio ad absurdum, starting from assuming that there is no necessity in the causal connections, it results, according to Kant, in the complete destruction of the possibility of representation, as the very categories of representation would lost all meaning in a world where causal connection would keep changing. From there, Kant infers that therefore, since we have representation and consciousness of phenomenon, causal connections are necessary.
However, Meillassoux notices that Kant’s argument hinges on a probabilistic assumption, the one according to which if causal laws could change, they would change often, to the point where all representation would become impossible. It is this assumption that Meillassoux does criticize, by proposing the concept of untotalization, inspired by Cantor’s work on transfinite numbers.

2. Cantor’s transfinite and the concept of untotalization
Cantor’s theorem establishes that the power set of any set A (finite and infinite alike) has a cardinality superior the the original set A, in other words, the set of all subsets of A has more elements that A itself. That leads Cantor to introduce transfinite numbers to account for the cardinality of various infinite sets: aleph-null is then the cardinality of the natural number, while aleph-one is the cardinality of the set of all countable ordinal numbers.
From the work of Alain Badiou, who interpreted Cantor’s theory in ontological terms, Meillassoux argues that such a concept of the transfinite invalidates Kant’s argument, as probabilities are valid, in their frequentist interpretation only insofar that a totalization of the cases is not problematic. In Meillassoux’words:
“We are completely ignorant of the legitimacy there is in totalizing the possible, as we totalized the faces of a die. Such an ignorance is sufficient to demonstrate the illegitimacy of extending an argument about uncertainty outside of a totality given by experience.”
The possible, because of Cantor’s theorem, may therefore escape, according to Meillassoux, a totalization compatible with its treatment by probabilistic means, and that is enough to invalidate Kant’s argument. Meillassoux does not provide however a positive demonstration of how Cantor’s theorem, applied to the possible, makes probabilities invalid, he simply raises the question, and concludes, rightfully in my view and for the problematic he’s looking at, that this is enough to reject Kant’s argument.


II- THE BLANK SWAN

Elie Ayache’s book is subtitled “the end of probability”, and its central thesis is indeed, following the trail opened up by Meillassoux, to assert that probability theory is unable to account for the reality taking place in Finance.
It would be presumptuous to summarize here all that there is in “The Blank Swan”, just as the previous section can in no way be taken as a summary of Meillassoux’ work, I just wish to precise a few concepts, in order to point out an ambiguity which, in my opinion, is left unresolved by Ayache.

What Ayache proposes to do, in his book, is to apply Meillassoux’ conclusions about the physical world and our relations to it, to the world of derivatives trading. For that, he asserts, in convincing terms, that the market (of derivatives) is a medium of contingency. Therefore, the market is untotalized, in the very same way that Meillassoux says possibilities in the material world are, and in the market, this untotalization can be derived from the non-redundancy of derivatives contracts, as indeed, if a contract is redundant, its market would simply vanish; or in the words of Ayache:

“If there were an established law, then some derivatives would never be exchanged.”(p.167)

This is indeed true, if valuation were exact, there would be no room to exchange a contract at variance with this valuation, and therefore no market. The existence of a market clearly points out to the inadequacy of the valuation process, and therefore to an untotalization of possibilities.
All this is still very much in line with the thesis from Meillassoux, however, Ayache goes a step further when he writes:

”In ‘thinking’ contingency as absolute with regard to the material world, Meillassoux is thrown into the exchange. His speculation is untenable in ‘pure’ thought and the corresponding detachment or transcendence.
(…)
All I am trying to do is to carve out the space that is adapted to speculative factual thought.”(p.190)

Here I see a divergence between Ayache’s and Meillassoux’thought. Elsewhere, Ayache wrote:

“Speculation thus recovers its absolute meaning. It surpasses even thought itself.”(p.175)

Such a stance seems to assert speculation (which, in Ayache’s terms, means the act of inverting the model, whatever it is, for valuating an option and engaging into “the trading of the derivatives at variance with its replication plan”, i.e. the writing of the market), as a process that exceeds thoughts, that reaches to a point beyond thought. But then, one of the main point of Meillassoux being the re-appropriation of the domain of the absolute by thought, isn’t Ayache positing a new absolute which he again places beyond thought?
Another way to put it is: Isn’t Ayache falling into a new kind of Fideism, which is properly a target of Meillassoux’work?
By proposing such a radical criticism of probability, positing not the end of some interpretation or axiomatization of probability but of probability itself, Ayache may have hypostatized a reality beyond thought, only accessible through speculation. What then differentiate speculation from a magical ritual, that one must perform in order to access to a higher level of reality? Aren’t we driven into a fideistic way of relating to the world (be it the world of the market) and to give up any illusion of grasping it with an analytical apparatus?
That matter doesn’t find any treatment in “The Blank Swan”, and it is, in my opinion, its major defect. Because of it, an atmosphere of ambiguity does linger over the pages, becoming more and more persistent.

I shall stop here for now, not that I’ve said it all, and I will likely come back to comment on some other ideas from the book, such as the logic of place, that I wish to analyse further, in relation to Nishida Kitaro’s ideas of the logic of basho, for instance, though I still have some study to do before that.

From Spot FX to FX Options (maybe)

Sorry for having been a bit absent these last few weeks, I am considering moving towards FX options trading, and I have therefore been studying this very different area.

This idea came to me quite accidentally. A few weeks ago, I bought "The blank swan" by Elie Ayache, out of curiosity really; I started reading it and after about 30 pages, even though, I got the gist of his ideas (which are more philosophical than technical), I nonetheless realized that I may enjoy the book more if I was a bit more knowledgeable in Options Trading. Until then, I had browsed through some mathematical finance books, but never went into much of the details.
I therefore did that and acquired Espen Gaarder Haug'"Derivatives: Models on Models", I am still reading it, but I already have realised how powerful Options trading can be.

As I see it, traders are to face two unknowns: the volatility and the direction of the move. So far, I don't think analytical tools provide for a very good prediction in terms of the direction, but I tend to think that volatility can be foreseen in a better way, albeit far from perfect.
Nonetheless, it is very possible to make money in Spot FX, the uncertainty about direction can indeed be compensated by a proper money management strategy (that can be found in many trading books, see those by Van Tharp for instance), but Options trading seems to be able to do that more efficiently by hedging the risk by means of a combination of options, diminishing thereby the exposure to direction while maintaining a profit potential out of the volatility variations. And this is only one aspect of Options Trading, as it appears to offer a rich range of other approaches to trading.
And last but not least, it also proposes rather stimulating intellectual challenges.

My knowledge of these combinations is still too incomplete for me to detail much more at this level, I shall therefore continue to explore this area in the next few weeks, and will confirm whether I chose to trade FX Options in the future. If so, one must expect some changes in the content of this blog, even though I will continue to look at technical tools to analyse the "underlying" time-series, I may concentrate as well on some portfolio strategy issues.

Variation of the Hurst Exponent

While playing around with various strategies, I came to consider that an interesting way to use the fractal dimension is to look at its variations rather than its absolute value. Furthermore such an approach makes sense at a mathematical point of view: from equation (1) in this post, applying the functional power rule of derivation, we can see that:



Rearranging it, we get:



Asymptotically (for t sufficiently high), we can then see that the sign of the variation of H with time gives us the sign of the variation of the variance over time, and when this variation is positive, it indicates an increasing volatility and is therefore the best time to enter a trade. It must be noted that this indication does not say anything about the sense of the trade we should enter, and it therefore ought to be combined with a directional indicator in order to be fully operational.

Even though most of such variations can be seen by just looking at the FGDI graphic, it is just as easy (and possibly adding some precision) to program a new indicator that displays the variations of H over time, the script of this indicator can be found here on MQL4.
Below the indicator Hurst_Difference is displayed in the lower window on a 1hr chart for EUR/USD:



Whenever this indicator display a value above 0, it indicates a potential entry for a trade.
The parameters of Hurst_Difference.mq4 are:
f_period (integer): This is the period considered for calculating the fractal dimension, default is 30.
type_data (0,1,2,3,4,5 or 6): This is the type of price the indicator will consider (0=CLOSE, 1=OPEN, 2=HIGH, 3=LOW, 4=MEDIAN, 5=TYPICAL, 6=WEIGHTED), default is 0.

Self-similarity and a measure of it

Following an exchange via emails with a fellow trader, John Last, in which he made some remarks about the interest of some kind of self-similarity, I came to conceive a new indicator, which can be used to detect some convergence of behaviour between different timescales, in the sense outlined below.
____________________________________________________________________________________

I-General Remarks

Self-similarity is a well-known feature of fractals, it may however be useful to precise a few things about this concept.
The classic examples of fractals such as the Cantor Dust, the Von Koch Curve or the Sierpinski Gasket display an obvious self-similarity that is the direct consequence of their recursive mode of construction. However, when one comes to consider real-life applications of fractals, one should not expect to find such a perfect self-similarity.

Furthermore, when it comes to random fractals and their applications, which is the case of financial markets, self-similarity should not be taken as meaning a repetition of the exact same pattern, not even as a repetition of a pattern close enough to the original to warrant the use of "repetition".
Rather, what is meant in the case of financial price variations by self-similarity is really a "statistical self-similarity", which is more of a similarity of behavior between different timescales.

What should be compared therefore in order to measure the level of self-similarity at a given time, is not how the price curves at different timescales are "similar" to each others, but rather whether their behaviour, and particularly their volatility displays a level of self-similarity across timescales.

II-Dispersion of the Fractal Dimension across various timeframes

To measure this statistical similarity, I will only consider the dispersion between the FGDI of various timeframes around the FGDI of the longest timeframe considered.
For instance, considering the TimeFrame of 1hr, whose FGDI is fgdi(60), and the other shorter timeframes of 5mn (fgdi(5)), 15mn(fgdi(15)) and 30mn(fgdi(30)). The dispersion will be given by:



Which is basically the formula of the standard deviation around the value of the longest timeframe.
This calculation seems rather straightforward, except that we must take care of a little technical problem: if, at the present instant, the value of the FGDI is actual for all the timeframes, the value of FGDI 30 bars ago in the 5mn timeframe is not corresponding to the value of the FGDI 30 bars ago in the 15mn timeframe. Indeed, the 30th bar back from now on the 5mn TF corresponds to 150mn ago, which on the 15mn timeframe corresponds to the 10th bar in the past.
Clearly therefore, to re-establish a correspondance that makes sense in equation (1) above, one must apply a change of index, whose general equation between a given timeframe (TF) and the reference timeframe (TFref) has the following form:



'newpos' is the new value of the index to be considered in the shorter timeframe in relation to the index 'pos' from the reference timeframe. Notice that in MQL4, the further a bar is in the past the higher is its index, in order to have the past index available, the main loop should be a decreasing one in terms of index, starting from as far as necessary in the past and calculating the bars towards the present.

That being said, I am aware, that the simplicity of this transformation does not ensure a perfect match between the different timeframes and an error of a few bars is still possible in the past, but the complexity of implementing a full check in order to ensure a perfect match is not warranted given that it will modify the final calculation in a negligible manner.

III-Implementation in MT4

I then wrote this indicator as MTF_FractalDispersion11.mq4, the script is available here, and here is what it looks like on a EUR/USD chart, in orange, in the bottom window:



For clarity purposes, the value of the dispersion is multiplied by 10, a low value is indicative of a high self-similarity, between the different timeframes.
For instance, in case of a trendy market (FGDI below 1.5), a low dispersion (corresponding to a high self-similarity) is a positive indicator to enter a trade in the sense of the trend, provided the said trend is in the same direction in all the timeframes considered.
The available timeframes are 5mn, 15mn, 30mn, 1hr, 4hr and 1 day. Each timeframe can be weighted as desired (but by an integer value).

Important remark:
From an excellent remark by John Last, I came to realise that the graphical representation of the Fractal dispersion is only aligned temporally to the prices graph (and therefore also to the Fractal Dimension graph) for the reference TimeFrame (the longest TF selected, with a weight above 0). On all the shorter TF, this representation will appear as contracted towards the right (proportionally to the distance we are looking at in the past from the present, rather than the Fractal Dispersion being contracted, it is the price, and therefore also the Fractal Dimension, that are dilated, taking more values than in the longer TF, within the same time interval), and the movements of the FractalDispersion will therefore appear to have taken place at a time later than at which they really did happen (the correct time will be the one displayed on the reference TF, i.e. the longest one selected).
The only time all the graphs will coincide on all TF is the present. Any analysis of the past should therefore take this into account.
This effect of contraction/dilatation is particularly well-illustrated on the following graph, sent to me, by John:



Here, by comparing the two lower windows (ignore the difference in numerical values, they are due to another mistake I did in the first version and that I also corrected), we see that the yellow curve MTF_FracDisp11 is nothing else than the contraction towards the left (with the present as the fixed point) of the green curve MTF_FracDisp.
Incidentally on this graph, the correct representation, except for a multiplicative factor of √2, is given by MTF_FracDisp, this is however exceptional and solely due to a specific setup, the 15mn TF is actually not the reference TF.
In all cases, MTF_FracDisp11 gives the proper value of the fractal dispersion and does coincide with the timescale only for the graph on the reference TF. And this indicator should only be used as such.

Notice that this indicator needs to access FGDI.mq4 on your PC, and that this one should therefore be present and compiled properly.

The parameters of MTF_FractalDispersion11.mq4 are:
e_period (integer): This is the period considered for calculating the fractal dimension, default is 30.
e_type_data (0,1,2,3,4,5 or 6): This is the type of price the indicator will consider (0=CLOSE, 1=OPEN, 2=HIGH, 3=LOW, 4=MEDIAN, 5=TYPICAL, 6=WEIGHTED), default is 0.
M5w (integer): This is the weight to be applied to the 5mn timeframe, default is 1.
M15w (integer): This is the weight to be applied to the 15mn timeframe, default is 1.
M30w (integer): This is the weight to be applied to the 30mn timeframe, default is 1.
M60w (integer): This is the weight to be applied to the 1hr timeframe, default is 1.
M240w (integer): This is the weight to be applied to the 4hr timeframe, default is 0.
M1440w (integer): This is the weight to be applied to the 1day timeframe, default is 0.