Valentino Straser you are asking "the big question" which may not have an answer as such. What can be done is to review where we are, and how some breakthrough away from the "local minimum energy trap" in which we are could occur.

If I look at a fairly recent science, economics, here are some remarks on how recognised breakthroughs happened:

-Adam Smith recognised the interest to look at humans as individual agents, acting at least partially selfishly, to improve their own position: eat, gain access to goods, etc. This view was leveraging on the "sound competition" part happening in the economy. Everyone takes care (at least) of themselves.

Of course, it's not the whole story, but it's better than just wait for everything to come top-down, decided from high above: humans are staged in the play.

-Karl Marx was faced with an economy growing through industrial production. Capital investment in the machines, and payment of salaries were said to be the growth factors. This narrow view actually has actually propagated with no correction to this day, and this is proven by the way the inaugural ceremony of the 2012 Olympic Games of London staged the "industrial revolution". In this staging broadcast worldwide on television, you could see mostly "the capitalists" well-dressed with top hats, as "the heroes who have made the industrial revolution possible". Heroes with their money for sure, but what about the unwilling heroes, child labour (young boys victims of testicle cancer, while working with coal in and out of the mines), men and women living in poverty? This poverty was reported in detail by Engels, and led Marx to analyse what was happening. The result in economics was simple to summarise but very important: recognition of the key role of labour in the economy. Before, labour was there, but not a focus, not a key parameter of the economy.

-John Maynard Keynes, at the time of the Great Depression, identified that consumption would be the key parameter to act upon, to try and shake the vicious circle the world economy had entered into.

Before him, consumption was considered secondary, futile. Now it is clearly important and taken account of.

What can the next breakthrough be in economics?

It has probably to do with data.

Today data is "leaked for free". Some useful internet platforms get their "fuel" (data) for free, from people who do not know that their data may have value.

There are pedestrian considerations describing another world possible, in economic terms, looking precisely at the microeconomics of a possible valued data world as in [1] and [2].

There are also more mainstream scientific steps in this direction, with the recognised work of Jean Tirole (Nobel Prize winner in Economics) and Jean-Charles Rochet [3] on two-sided markets, analysed in [4].

You could build on the structural description above, and ask what radical change in the way we look at the world might lead to new breakthroughs:

-Copernicus, away from geocentrism, towards heliocentrism

-Galileo, first referential-aware description of movement and forces

-Newton, first calculus supported differential equation based approach (somewhat initiated by Galileo) description of movement in forces

-Lorentz, Poincaré, Einstein: enriched look at motion and forces, invariants in changes of referentials.

AND NOW

Look at different scales? Multi-scales interacting (see Mandelbrot's fractals and self-replicating structures, wavelets allowing for multiscale analysis)?

Here are my references for the field of economic science, which I have singled out, and from which I have extracted a single area. There is more to it, but one could try and start

[1] Big Data Economics, towards Data Market Places, by R. Di Francesco https://www.amazon.co.uk/gp/product/B00QD7LMO2/ref=dbs_a_def_rwt_bibl_vppi_i1

[2] Microeconomics for big data, by R. Di Francesco https://www.amazon.co.uk/gp/product/B014N7I4SU/ref=dbs_a_def_rwt_bibl_vppi_i0

[3] Two sided markets, an overview, by J. Tirole and JC Rochet

https://web.mit.edu/14.271/www/rochet_tirole.pdf

[4] How Jean Tirole’s Work Helps Explain the Internet Economy, by Claire Cain Miller, New York Times

https://www.nytimes.com/2014/10/15/upshot/how-jean-tiroles-work-helps-explain-the-internet-economy.html

Dear Renaud,

thank you for having responded to my request. I agree with you on the difficulty in answering such a question. However, I think that the question should be asked by many, especially due to the speed of information and scientific discoveries. I have set myself a reflection on the Galilean paradigm for the study of earthquakes and in particular for the search for seismic precursors. In this case it was not possible to simulate conditions approximating the reality of earthquakes in the workplace and so I preferred to consider a paradigm based on clues, a bit like investigators do, who thanks to them are able to understand a more complex reality. In the didactic field I have also tried to introduce new concepts of a circumstantial type of methodology, but I think it is still premature for its roots in the past. Thanks again for your valuable suggestions. If you think about RG there is my paper for teaching based on the paradigm of clues and how to deal with it in school laboratories.

With best regards,

Valentino

Dear Valentino Straser ,

Let me leave for later the "big question" which you have asked in general terms through your question.

I think I can provide input, as candidate tools, for the more specific but still very complex and multi-faceted problem you are addressing as a sismology expert (and I am not).

I have initially worked in signal processing and detection of biologically shaped events. To do this I have naturally looked at my initial problem: human speech, and detecting micro-events in it (nothing pathological, just expected events). I found a reliable way to detect glottal closure (this has to do with the air flow which happens in our "pipes" as we breath and blow, and also as we speak and make our vocal tract change shape, and perform glottal closure and aperture (vowels).

The real time methodology built upon deriving directly from the input data a short-term model and a longer term model. Measuring the divergence (Kullback-Leibler works) between the two, you detect disruptions, my "disruption" of interest was the glottal closure expected event. Observing the data, and bearing in mind the large deviation theory, I found that there was a convexity issue helping: the divergence related signal had a piecewise convex enveloppe, with jumps at the glottal closure. It's something we find in many places, think of a RLC circuit in electricity, and in particular the charge and discharge of a capacitor, know to all of us with neon tube lights: you have a piecewise convex function appearing in this process.

Let me give you references for this as [1],[2] and [3]

As for an other angle of approach to sismic events and their stochastic nature, maybe you could consider a set of predefined "agents" (to be defined meaningfully in sismologic terms) each with a pattern of response to input probability (a sort of transfer function role from input probability measure to an output probability measure).

After having followed a very interesting course in Behavioural Economics at the London School of Economics, I produced a research paper on a model whereby human agents receiving an input information (say an input probability measure, or a value from a certain source, or a declaration from a politician) transform this source information into an output information. The way they shape it depends on the trust they put on the source ("I trust him", "he's a lier", I trust her a bit here, and less there", etc). To do this in both a humanly interpretable and meaningful way (behaviour readability and explainability) and in a mathematically usable way, I proposed a few very particular "shaping functions".

I am confident that you can build the equivalent of a neural network from these, and hopefully bend the system to make it sismologically useful.

The reference for this is [3]

[1]Real-Time Speech Segmentation Using Pitch and Convexity Jump Models: Application to Variable Rate Speech Coding, by R. Di Francesco, June 1990, IEEE Transactions on Acoustics Speech and Signal Processing 38(5):741 - 748

DOI: 10.1109/29.56018

[2] Conference Paper Detection of the glottal closure by jumps in the statistical...

[3] Article Processing of Uncertain Information by Humans-Behavioural Ec...

General Relativity and Cosmology: Unsolved Questions and Future Directions

Ivan Debono and George F. Smoot

Dear Reanaud Di Francesco,

even very distant disciplines and scientific fields can have connection points. This common thread is the Method. In the deterministic form "the antecedent" of a given phenomenon precedes the "consequent", and it is this link between cause and effect that allows science to make predictions. This concept is intrinsically linked to the laboratory experience and the control of human knowledge about Nature. However, stochastic or even chaotic phenomena pose new questions about the limits of the Galilean paradigm. The need to introduce new concepts into the investigation, such as "the clue", allows to make evaluations on phenomena not directly experimentable in the laboratory that lead to explore new directions in research. An example in this context is provided by cosmology on the question of "black holes", but of course the concept can be extended to other scientific fields. I will read with interest the documents you have suggested to me. Thank you for the interesting debate that has arisen.

Regards,

Valentino

For more than 10 years, forensic science has been at best, criticized for its lack of scientific foundations and at worst, presented as an oxymoron. An exclusive focus on standard operating procedures and quality management could cause forensic science to fall short of addressing the epistemological issue initiated by judges. This is particularly so in rapidly changing times, including digital transformation of society and decentralization of forensic services. As a consequence, the present understanding of forensic science by both scientists and its stakeholders is questioned. It is argued that that forensic science fundamental principles and, more broadly, forensic science philosophy are pivotal to the reliable application of science to address security and justice questions. https://onlinelibrary.wiley.com/doi/10.1002/wfs2.1349

Kindly check https://core.ac.uk/download/pdf/288802614.pdf

Please see the link below

https://www.edge.org/conversation/philip_goff-a-post-galilean-paradigm

Dear Anmar Aldewachi, I did not know Philip Goff's publication and I did not know that the issue of the Galilean paradigm and its limits that modernity poses had already been approached with a similar level of criticism. Thanks for this precious suggestion.

Regards,

Valentino

1)Could I ask a naive question about granularity/scale of events?

In Television, we moved from standard definition through high definition to high definition, then ultra high definition 4K, 8K, and further immersive television (360 degree, whereas 4pi steradian might be enjoyable..., then holographic, volumetric etc)

Now, science has looked at different scales of events, nano, etc, meso...

The changes when scales of observation change are not just homothetic. There is entropy and more happening, see multi-scale analysis supported by wavelets, and the theory developed by Benoit Mandelbrot.

https://en.wikipedia.org/wiki/Fractal

https://en.wikipedia.org/wiki/Wavelet

2) Could I ask another naive question on linear vs non-linear analysis?

We know of first order effects, second order effects, third order effects particularly important in Laser optics.

This is all going back to assuming a Taylor development near a point. That may not be the complete story.

https://en.wikipedia.org/wiki/Nonlinear_system

3) Moving beyond linear/non-linear, there is a very strong framework not yet fully exploited of set analysis: set valued maps (F: x-> F(x) where F(x) is a set), developed by Cellina, and now Aubin and Frankowska [1].

You have many cases where tangent cone sets are available, whereas differentials existence cannot be assumed.

The move from functional calculus to set valued maps can be compared with the move from geometry to topology (core structural properties, weaker and more general hypotheses)

This applies to sciences in general, especially in the current era where sets -data sets- become a core tool, using AI/ML/DL

[1] Set-Valued Analysis, by Jean-Pierre Aubin & Hélène Frankowska, January 2009, DOI: 10.1007/978-0-8176-4848-0_7

Chapter Set-Valued Analysis

I believe that an important concept was expressed by Poincarè regarding the concept of deterministic chaos. To summarize his concept we can say that often the functions and above all the scale of occurrence of certain phenomena are put in function of time, while it is more reasonable to consider it as a function of events. A concept that is closer to reality and more forward-looking, not only in the scientific field. I believe that the complexity and depth of thought of the authors you mentioned can also fall within this context. At least I think so.

I agree with Valentino Straser

Dear All,

Thank you for taking part in this debate and I would like to continue underlining some limitations of the Galilean paradigm and the importance of a "circumstantial" paradigm. A particular case concerns the problem of "global warming" which constitutes evidence for everyone but cannot be reproduced in the laboratory, as foreseen by the Scientific Method.

Interesting ! - https://onlinelibrary.wiley.com/doi/abs/10.1002/wfs2.1349

Thank you for sending me the link and contributing to the discussion on a seemingly simple issue which is instead of fundamental importance for scientific investigation.