Fellow researcher,

This is a very complex question and the answer I offer is even more. Let me start with the use of mathematical statistics to study psychology. As you said, this is a research method for groups, so only group features, at best, can be accounted for in such a method. If you ask the right question that can be really useful as youngian collective unconscious, cultural pressures and changes, emergence of new social-interpersonal structures are all very important collective phenomenon.

On the other hand, to make a statistical analysis at the individual level, you not only at the risk of making inferences of too little data, but also you've got no standard to base your analysis on. Let me explain this in other way. I am a physicist and as a physicist, to understand some phenomenon, I make a simplified model derivative of some known features that are important for the phenomenon. So I can tell if the model is presenting the 'right' results because the model is 'predictable' in what I measure, I have the real phenomenon as a calibrator, and as the model is derivative of some other known model or system, I can break it apart to tell exactly what is happening. This is not possible with humans because, among other things, we do not have any standard for a healthy mind whatsoever. Youngian collective unconscious, cultural pressures and changes, emergence of new social-interpersonal structures are all external features that influence directly in how we perceive the healthiness of the mind necessarily so. For example, for ME the liberal fantasy that everyone is unique and should egotistically pursuit some kind of dream imposed to him at the cost of severing as many interpersonal connections as it takes making the individual, by its own accord, to ostracize its family and friends is crazy. But for some other people even sharing my cultural heritage, to love your family and friends above the money and status is the crazy thing to do. In any case, if you believe that an unhealthy mind is an nonconforming one (as is its definition) and that this nonconformity brings the unhappiness that psychologists must prevent their patients, than to use statistical frameworks to help your work, you should at least be careful on how you interpret your data and not over-valuate the analysis.

Notice that I am not saying it is useless. I not sure if I show the right impression, but I am a applications of statistical analysis in psychology (as well as many other system) enthusiast. I think there is an immense potential in using this tool for these kind of problems, but there is also much work to be done and it is a highly multidisciplinary. From the famous philosophical question "does the individual exists without the society he is inserted in?" to the highly practical and inherently linked to cultural features question (usurped by many 'coaches') "what do I have to have? what do I have to be? what kind of ties should I keep? what should I strive for? To be happy" are all variables that we should take into consideration when we even define what is an individual.

I hope this discussion was somewhat useful.

Ricardo Simão Pereira Lopes

At the individual level, a random process can calculate his next behavior using individual data. For example, a person always likes to go to the cinema on a Saturday and calculate the probability that he goes to the cinema on the next Saturday, which is used to predict his behavior. The same goes with time series, which can predict his behavior using his historical data. I think it's better than counting a large group of people, since it's studying individuals.

Ricardo Simão Pereira Lopes

In fact, I don't think psychology is suitable for statistics, neither group statistics or stochastic processes, can do nothing. One way I recognize is to analyze Psychological activity into programs. I think that "programs" is the same tool as "mathematical equations", it can be used to describe the laws of the social sciences, it can be used to describe complex systems science. For example, "the earth revolves around the sun", this sentence is about a physical program, it is a program.

Ricardo Simão Pereira Lopes

Do you mean that there is no standard for measurement? Unable to measure psychological phenomena? This I feel the same way, the psychological measurement is actually very confusing, the so-called operational definition can not solve the problem. Physical measurements are much more accurate, and the object being measured is very clear. So I don't agree with psychology to use statistical research, even use mathematics, should use something called "program"（Or "instructions", "calculations", "process", etc., as discovered by some scientists in complex science.）In economics, Nicdlas Quesaay's economic chart is the program.

Fellow researcher, if you forgive me the familiarity, calm down. This is a very intriguing topic so let us take baby steps and try to take our time understand each other. You said "At the individual level, a random process can calculate his next behavior using individual data" and gave a nice example, I agree it can be used to predict the probability to a person to make a given decision, but this is not really the issue here. The issue is why would the person goes to the cinema on a Saturday. How this is important to him and why you know? I think this is the real question for psychologists because the reason the person in your example goes to the cinema every Saturday may be similar to what some people goes to church every Sunday, but also can be a similar reason why some people must take a long shower after every day of work. In the first case, may be familiarity or cultivation of its social circle or even 'spiritual healing' through something he really believe is sacred, but in the last case it can be a depression or psychosis symptom, a deep in-satisfaction with his own work. I don't think the action matter much, but the meaning of the action does and for this to be answered through statistical analysis one must at least be sure of what one is really been asking and be very careful on the interpretation.

About the second text, you said "In fact, I don't think psychology is suitable for statistics, neither group statistics or stochastic processes, can do nothing". I got a little confused because your arguments seems to say otherwise. So I disagree a little with this sentence and disagree a little with the argument. The argument I think is in all correct, but it can not be use to place psychological activities into mathematical tools because is just too complex. In the example you gave, even if you predict 9 out of 10 times the person goes to the cinema, why it goes or why it does not goes is still unknown. What you can assert is: given an environment, this is the probability the person will behave this way. This mathematical question is purely behavioral one and not really a psychological one. If I may say so, I think psychology is much more related to complex decision trees in computation than equations because once you understand why the person does what it does given controlled stimuli you get much more precision in behavioral probabilities and behavioral predictions. This is also the reason why I think statistical analysis is very useful, because even if it does not give information for individuals, it hints what are the important decisions in the 'cultural cognitive decision tree'. which can be useful to make new standards for healthy minds in given environmental histories. By the way, this is all speculation from my part, so I'm very glad to be having this discussion and I hope the sentiment is mutual.

Ricardo Simão Pereira Lopes

I agree with you that statistics can only count a "fact," but they do not explain it, and what psychologists really have to do is to study why, That is, why does he go to a movie every Saturday? The mechanism here is the point. So, I'm actually opposed to using statistics as the main method.

But, you write:

This is also the reason why I think statistical analysis is very useful, because even if it does not give information for individuals, it hints what are the important decisions in the 'cultural cognitive decision tree'.

So, do you think the statistical conclusions can at least provide a reference?

You write:

“ I don't think the action matter much, but the meaning of the action does and for this to be answered through statistical analysis one must at least be sure of what one is really been asking and be very careful on the interpretation.”

But, it is not easy to do so, and such an assumption is very difficult. For example, if you assume that "he goes to the cinema because he is alone," or "he just likes watching movies," these assumptions are not easy to verify with statistics. Because statistics are not good at answering why

Ricardo Simão Pereira Lopes

But statistical analysis is hard to answer why he went to a movie on Saturday. It's certainly not easy to use statistics or experiments. It is better to directly ask him why, this is actually a psychological analysis, and directly ask him what he thinks, much better than using statistics or other methods.

Ricardo Simão Pereira Lopes

You write:

”What you can assert is: given an environment, this is the probability the person will behave this way. This mathematical question is purely behavioral one and not really a psychological one.”

Yeah, so I said the statistical method wasn't right. Because the example I give is not a psychological problem, where the example predicts the probability of some of his behavior, and does not answer the "why" of his behavior. You seem to think you can use statistics to study why he goes to the cinema every Saturday? That's not easy. It is not easy to use statistics to find the reasons, statistical methods are only good at counting one conclusion, But for the "why", statistics are not easy to answer.

So, do you think the statistical conclusions can at least provide a reference? Yes really think so!

"It is better to directly ask him why, this is actually a psychological analysis, and directly ask him what he thinks, much better than using statistics or other methods." I know, but the beauty of statistical analysis is in its elimination of personal traits. For example if one asks the person why he goes to the cinema every Saturday, if he trusts the interviewer enough to just tell the truth, he might say "I don't know, I just do it". And this would not be wrong and in fact would be truer than to find some random answer to pick. What I mean by the use of statistical analysis is something like build a data-frame related to the visit. In this example, questions that I think would be useful to build a psychological profile for this guy capable of understanding its action of going to the cinema every Saturday (or how its decision tree works, which can be used in other situations) would be something like:

Why do you come here every Saturday?

Do you have a preferred appointment? How much to be here in time influence Your experience?

What kind of movie do you prefer?

Does your mood interfere in your movie choice? how?

Does your mood interfere in your decision to come in the cinema every Saturday?

Have you ever missed a cinema at Saturday for some reason? For what reason?

When did you begin to come to the cinema in the Saturday?

Do you usually come here alone or in company? Do you like to come alone or you prefer in company?

etc etc

The statistics of the actions of the person gives no clue whatsoever in the understanding of what he does what he does, but a analysis of people answering does questions that present such behavior, or similar behavior, may prove very insightful. I absolutely agree with you, this analysis is not in any way trivial and we are very far from understanding individual psychology as a science easily understandable (at least approximately) by mathematical models, if this is even attainable, but if this kind of analysis helps a little in the improvement of behavioral predictions, I think is worth to ponder a little more about it.

Ricardo Simão Pereira Lopes

You are a physicist, and mathematical equations are very suitable for describing the laws of physics, but not for biology, economics, etc. Do you know why? Why do universal mathematical equations fail in these subjects? From Archimedes on, mathematics became a tool for describing the laws of science, which Galileo and Newton later developed extensively. But why is mathematics now failing in the social sciences? Is that possible? Isn't mathematics just the only tool to describe the laws of science? Is there also a tool to describe economics, biology, psychology, and even political science and history?

I think there is, and this tool is even older than math, it is "program." It's always been there, and humans have been using it, but no one has noticed it. It's very old. In fact, it has been discovered in complex science, but some people call it "calculation" or "instruction", while others call it "process". This tool, called "program", describes the laws of psychology, economics and even biology, and just like mathematical equations to describe the laws of physics, it is also a tool to describe the laws of science. Here are two lines of evidence, one is the economic chart of Quesaay and one is the biological DNA concept. Both are both programs.

What you call 'program' I think you mean logic and it is the founding theory of all mathematics. I did not claim that all is mathematically soluble and it is pretty obvious that the great majority of mathematical problems are not equationable. I don't know what you mean by why is mathematics now failing in the social sciences? because I don't think is falling except where the concepts are ill defined.

This thing you call instructions, which by what I understood if something like "if this do that", is what I called previously a (mathematical construct) decision tree. So I think we are agreeing on that. I'm not arguing that, I'm arguing that statistical analysis can hint the subconscious structure of such decision tree. Understanding why someone always go to the cinema at the Saturdays do not explain other person going to the park at the Sunday, but understanding the 'program', as you call, of the former can hint why the later does what it does, what such action means to him and what it is hoping to get from doing it. That's all.

Ricardo Simão Pereira Lopes

You're right, and I also doubt that a "program" is a "logic."You call it a "decision tree," as it seems possible, because it is like an algorithm, and it makes sense to reveal its structure with statistical analysis.

Ricardo Simão Pereira Lopes

Mathematics is not very applicable in the social sciences

In this way, I hope that switching systems -like markov jupe systems- can reply to the problem of human behavior stability. ......

Issam El Hamdi

You tried it with the Markov process?

@Duan Xian Xiang

Just I think on this idea to model the switching human emotions,

but this need some collaborationsort between math/applied math and psychology

Issam El Hamdi

wish you success

Ricardo Simão Pereira Lopes

Studying psychology with time series or random processes, you can infer the overall psychological activity from each physiological amount of an individual. For example, by measuring the data of epinephrine secretion, and then we use the method of probabilistic statistics to speculate the overall law of the hormone secretion, and then we can speculate the psychological activity of the individual. This is ok to infer the macro (namely the individual psychological activities) from the micro data, but this research direction is very difficult. Microeconomics is used in this way, but because economies are bigger than human individuals, the micro-movements of economies are not micro-movements for researchers. But the psychological research of individual microphysical data, measuring these physiological amounts to speculate that the psychological activity, is quite tiring. This approach is far less than my theory, my theory is to treat the individual as a whole, and then without mathematics, only the human psychology as a system, Psychological programs are analyzed by psychological analysis, and then the physiological responses of these programs can be measured, which is much better than simply measuring the microscopic physiological responses and then speculating as a whole.

Ricardo Simão Pereira Lopes

It's just like touching an elephant. Starting with the microscopic data, it's like touching a part of an elephant, such as the thigh, studying the texture, structure and function of the thigh, and then speculating from these data about what the animal is, and speculating about the behavior of the animal.(here,we didn't know it was an elephant.) This is also ok, but it is more difficult. If it wouldn't be much easier to see the whole elephant and then analyze its behavior or physiological structure? That is exactly what my theory does. Start with the person as a whole and analyze his mental activity, rather than measuring the microphysical response of his body to speculate on his mental activity. As for the human group as a research object, statistics of its group commonality, and then speculate on the psychological law of individuals, this is wishful thinking, because people's psychological differences are far greater than physical differences. This method of statistical group commonality is much more impractical than the physiological amount of individuals. In fact, this is also the difference between the overall thinking and the local thinking. Oriental people analyze from the whole, while you infer the whole from the part, completely opposite ideas.

Hi professors. I hope you are doing well. This is a mathematical article that proves a new recurrence relation that is fundamental for mathematics. The article proves also that four infinite series are equivalent. Hence, this article opens new opportunities to demonstrate and develop new mathematical findings and observations. This is the link: https://www.researchgate.net/publication/364651911_A_useful_new_equation_of_four_infinite_series_and_sums_by_using_a_new_demonstrated_recurrence_relation