The very fact that you've posted your question and I am replying and you can read my reply, I believe, answers your question. The devices we are using to communicate are described mathematically. Effectiveness means that there is(by default) a clear cut way to discern what is coming from where. E.g. graph of communications describing intricate entanglement between mathematics and other disciplines. Otherwise the device would be non operable. Wigner's paper I quote extensively in my book http://www.worldscientific.com/worldscibooks/10.1142/8514   e.g. read Closing Remarks where you will find more recent publications on the same subject. I do not recommend to pay much attention to frivolous talks by Feynman or  Dijkgraaf. The references in my book are written by people whose contributions to mathematics is much more sound/solid than of the people you are quoting.

George (Stoica). You would be surprised to read references in Closing remarks of my book. It happens that very famous mathematicians were unable to reach a common denominator on this issue. They picked up some sort of fight with each other...Reading of these people is very entertaining. Much more so than listening to Feynman or Dijkgraaf.

George, my book is from the same category..It is subversive...Even more subversive is my latest paper "Black magic session of concordance...."(to be published in IJMPA) which you can download from RG at once.Yes, I am a quiet diccident.  Surely, I am paying a big price for my diccident activities...However, I am put into corner by virtues of my life and other alternatives are not available for me...

NATURAL SCIENCES PROVIDE THE NATURAL PHENOMENA, AND MATHS PROVIDES THE EXPLANATIONS.  THIS IS VERY MUCH OBSERVED IN PHYSICS, CHEMISTRY, BIOLOGY, AND OTHER BASIC SCIENCES INCLUDING PHARMACOLOGY.  THANKS.  

If we understand “how does mathematics come from?” and “what mathematics is?”, the answer is no doubt: natural sciences are reasonably effective in modern mathematics. There are many threads on these two questions.

Dear  Dejenie A. Lakew,

I find intersting article and sent you the link.

Regards, Shafagat

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

THE REASONABLE EFFECTIVENESS OF MATHEMATICS IN THE NATURAL SCIENCES

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled “The Unreasonable Effectiveness of mathematics in the Natural Sciences,” claims that “the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”

Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed.

See link for detailed version.

http://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=2265&context=etd

Dear Arkady,

Interesting book you have written on how most laws of physics and almost all other branches can be studied and described exclusively through contact geometry and topology, very small sections in the galaxy of mathematics and we therefore can say they are, not only very effective but languages of the physical science.

The surprising thing is that the same thing is valid in Clifford analysis in which physical laws are obtained from the mere application of the Dirac operator without using empirical conditions,  physics always puts as governing conditions and we therefore  say Clifford analysis to be the new language of nature. We therefore have to champion that nature is discovered and made visible and known through weapons  from the galaxy of mathematics.  

Dear Shafagat,

Thank you for posting the very essay by Wigner,  where Robert Dikgraaf is inspired to prepare his talk and that in turn inspires  me to ask the thread of the discussion.

Yes, natural sciences are reasonably effective in modern mathematics.

Dear Dejenie,

The use of mathematics is indispensable in natural sciences. The troubles are that many cannot properly use mathematics because of their lack of formation and the necessary thoroughness and some relationships in natural phenomena cannot be mathematically approached. The answers to these problems are various and the developed mainstream options accepted in many journals are only approximate and deformed.

I think that R. Feynman has said so much, that it is not worth commenting on them any more.

But the original question about effectivenes has to be answered.

Well, by the term effective we mean:

• answer a question fast and experimentally correctly
• create a theory with the samllest set of arbitrary parameters ('constants' in Physics terminolgy

So, if we see the modern history of sciences we observe:

• an initial expansion of natural sciences due to the mathematics help (calculus--->Newton, differential equations--->Maxwell, differential geometry--->Einstein,probability theory--->Bohr
• a slow down at the second half of 20th century due to the extrmely complexity of mathematical theories involved (super-symmetries, super-strings, M-theory)
• a disappointment at the experimental verification of 100 years accepted theories like general relativity and recent super-symmetrical theories

Now we are at a critical point where old theories, just mathematical beautiful without lab prove, are trying to continue dominate, although they have created un-observed 'monsters'...

If we think that the physical sciences (quantum physics and astrophysics) represent the minimum entropy, instead the biological sciences represent the maximum entropy then it follows that conventional mathematics will be hardly be able to describe / predict  the biological processes (molecular biology etc.).

Do you think that the approach of Gregory Chaitin with metabiology (defined as a field parallel to the biology that deals with the random evolution of artificial software), in some ways very humble, can rappersentare a beginning? Regardless the question of evolution and Darwin.

I read his popular book "Proving Darwin: Making Mathematical Biology"  and I was fascinated (but I do not know math).

I apologize for my intrusion.

https://egtheory.wordpress.com/2012/06/29/proving-darwin/

Yes it is and I believe most contribution have done justice to this

I just found this

http://arxiv.org/abs/1506.07576

Dear Arkady,

Very good article for the discussion. The difficulty I have with Wigner statement : "The miracle of the appropriateness of the language of mathematics

for the formulation of the laws of physics is a wonderful gift which

we neither understand nor deserve"  is that we humans understand mathematics to the partial utilization of it and we deserve  that, it is not a miracle or a magic at all. 

An other important point in the article is the power of the Dirac operator as a new  power that  unifies mathematics and physics specially via the Atiyah-Singer Index theorem - that unified three major parts of mathematics: analysis, geometry and topology. Good source! 

Dejenie, please also read Closing Remarks in my book

http://www.worldscientific.com/worldscibooks/10.1142/8514

In it you will find  additional references  to  papers on the same subject written after Wigner 

Arkady, what you have in your closing remarks is the unreasonable effectiveness of contact geometry and topology in physical sciences and it has been the case that mathematics is effective in understanding physical science. What is unique in the case of your book is that specifically contact geometry and topology took that privilege. It is a remarkable leap. 

Dejenie, all this is fine.Still, take a look at references in closing remarks. They continue Wigner's discussion.Warmest regards, AK

I once heard a pharmacy professor saying that "Pharmacy can do it without chemistry". Of course, the man cannot be serious given that drugs are chemicals made by chemical processes with application of chemical techniques. The same logic applies to the question under consideration. When a physical or natural science does not utilize mathematics, then such science will be dwarfed into qualitative descriptions & interpretations that lack precision & accuracy. Example: When you put the palm of your hand on the forehead of your child to conclude that s/he is in a fever state, your qualitative description must be supported by a "quantitative" thermometer which gives the exact temperature since 37.5 oC is not worrying but a temperature higher than that by one degree requires intensive medical care. Without mathematics, natural sciences will be in deep trouble.

All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

--- Roger Bacon

Indeed, the universe is a mathematically behaving physical reality. Tegmark as a cosmologist, may have a belief in the mathematical universe and extending that  through physical intuition to a possibility of multiverse, people of string theory wants to talk about. The mathematical universe was the belief of Galileo and other thinkers which I have put in my introduction of the thread, and  the belief of several  mathematicians of contemporary and  old. 

I believe with mathematical discoveries the secrets of the physical universe are unveiled.

Solving Wigner's Mystery: The Reasonable (Though Perhaps Limited) Effectiveness of Mathematics in the Natural Sciences -- IVOR GRATTAN-GUINNESS

In i960 the physicist Eugene Wigner published an influential article on 'The unreasonable effectiveness of mathematics in the natural sciences'. I counter the claim stated in its title with an interpretation of science in which many of the uses of mathematics are shown to be quite reasonable, even rational, although maybe somewhat limited in content and indeed not free from ineffectiveness. The alternative view emphasizes two factors that Wigner largely ignores: the effectiveness of the natural sciences in mathematics, in that much mathematics has been motivated by interpretations in the sciences, and still is; and the central place of theories in both mathematics and the sciences, especially theory-building, in which analogies drawn from other theories play an important role.

See through link.

http://www.sfu.ca/~rpyke/cafe/reasonable.pdf

Our science history proves that it is for sure that natural sciences are reasonably effective in modern mathematics but the most difficult thing is to build a “good bridge” between mathematics and its related sources as well as its workshops.

In my own biased view of things I will try to answer the question on whether I agree with Feynman or not. The simple answer is that it depends. I would first like to separate mathematics from the foundational logic system on which it is based(this marriage was not done until Boole, Freege, Russel Godel and others cemented that link). In that sense, I think that the underlying Lingua franca is Logic and not math (we still need reasoning that is not merely quantified but also on how we draw inferences on how do we break elements so that they can be quantified). I would also be haste in saying that progress cannot be made without mathematics(excluding logic) since man has not always been as reliant on strict mathematical principles to make progress, but on sheer luck(I would argue that we still rely on some luck, and we still will, but less so as our understanding of nature continues).

As we progress in science it becomes less probable that not relying on mathematics will accomplish things because we are reliant on mathematics to achieve things. Does this mean that we cannot make progress(whatever that means anyway)? the answer is no. Does this mean that it will be a better progress? maybe. The truth of the matter is that we do not know because we have not diverged into this unknown (in all sincerity  I would be scared to try it, and who wouldn't).

I am always cautious in my wonderment of what we have achieved and assigning Platonistic undertones to mathematics. While it is marvelous, we still need much to learn (especially me) and some of the things that we hold most dear in our respective field might be refuted tomorrow.

Just a thought

Dear George, indeed mathematics includes the fields you mentioned.

Dear Arturo, it is very true that as long as our representation of knowledge regarding truth is relative due to our understanding, we always make progress in doing better approximations, approximations that are more closer to the actual truth than the previous one. 

Regarding the marriage mentioned by the people named above, unless it is a matter of certificate they produced to cement the already existing link, the link is always there from the beginning. There is always a link between a built structure and its founding basis. What mathematics is the structure built on its axioms of foundation, without which there is no the structure of mathematics in the first place. It is not because some one says that something exists or does not exists but because it really exists. 

Indeed it is always the case that rules of mathematics are always strict that follow the unambiguous laws of logic and that may not truly describe the actual happening of things, but it is the most closer and reliable method to access reality, which enable other sciences to validate their intuition of reality and truth.  

Dejenie,

I would first like to say that I appreciate your insights and enjoy the provocative questions and feedback that you bring to the discussion in RG.

I completely agree with you that the link has been there between logic and mathematics. But nonetheless, my emphasis is that it is not a static Platonistic unrealistic relationship.Its link has grown stronger throughout history, and as you so correctly put it, progresses to better approximations.

You highlight a point that none can disagree that based on our understanding mathematics is the most reliable method to describe reality in a quantified manner. however, I could not discard my interpretation of Feynman's assertion that disappearance of mathematics is but a setback and not a crippling event. My division between logic and mathematics is to highlight that even if we did not have the core axioms of Peano, the axioms of set theory or group theory, we could still through logic alone achieve progress in our understanding of nature.

 Ellis,the difference between physicists and mathematicians lies in the fact that physicists eventually have to deal with reality in the form of devices, gadgets, etc. From here is the division into theoreticians and experimentalists in physics.In mathematics this is the division between the applied and pure mathematics. Von Neumann , when asked who he is:pure or applied mathematician,  was always evasive. In both disciplines this division is the source of many problems. Whoever attempts to improve QM will be publishing his/her results in professional journals. Why then nowadays there are so many journals? It is because science is becoming more and more feudalistic. Each journal is "owned" by a local feudal(or bunch of feudals) and readers and contributors  are  serfs... Thus, if it is not possible to publish in journal A (say, in Nature or Science), it will be possible to do so in B or in C and so on.Once something is published, other feudals will pretend that this result is invisible for them. How you can explain the fact, visible very vividly at the Math.Sci.Net. , that a given person had collaborated with 95 others?! This is NOT an exception nowadays.This is becoming an acceptable norm. Incidentally, Feynman falls out of this trend.His record at the Math.Sci Net is indicative that he was mainly working by himself.This is how it should be but this is how it is NOT nowadays...All string theoreticians are having 75-100 collaborators each. Journal of High Energy physics will accept papers only from serfs only known to them. And  administrations  are pretending not to be aware of these facts.Wonderful life for some and miserable for the rest....And this is what is called science nowadays...

Ellis, the trend is this: until and unless you have nothing of significance to present to the rest of the world, you keep some hope, that, AFTER ALL it cannot be that bad. But it can be that bad!! As soon as you have something  new you will feel the pressure from above upon yourself instantly. Latest example. I had submitted http://adsabs.harvard.edu/abs/2015arXiv150707791K to arxiv.org in early June, to the hep-th section. Well, my paper was immediately stopped by the administration of arxiv. According to their self-imposed rules, all submitted papers are to be seen by the moderators-that is by the gatekeepers of truth. Moderator decides if the paper could be displayed at arxiv at all and in which section it should be displayed .You, as an author, are not allowed to send to moderators e-mails since they are being instructed not to reply to e-mails.    Fine...My paper was kept by moderators for more than 1.5 month and was sent to general physics section of arxiv...This was done intentionally. The paper was meant for hep-th section and in general physics section it would sank into oblivion at once.Regrettably for those who run arxiv, I am already too known to the public so that the paper has already collected 28 downloads at arxiv and 55 downloads at Research gate https://www.researchgate.net/profile/Arkady_Kholodenko.   Moral: those who keep strings attached believe that only they are entitled for presenting new things. Everybody who is not from their circles should be mercilessly suppressed....Not only my paper was placed into wrong section of the arxiv, but, in addition, arxiv did absolutely nothing when the paper was accepted for publication into IJMPA-the high energy physics journal...The acceptance also was not made as easy as you could imagine...But this is yet another story for another day

Dear Ellis and Arkady,

From among the many things Richard Feynman has done, the one which particularity cemented him as one of the persons with true scientific minds is - his refusal to be enlisted in a book that chronicles scientists in terms of their ethnic backgrounds. He believes that science and knowledge are results of  true independent and global minds of  free persons of  mankind and rejected in a hate tone  ethnicity.  

Indeed a tool but of a different kind, a language of beauty and rigor through logic and  reason only to validate truth.

I do not see any fallacy from the word logic but a strict principle of reasoning and rational thinking. Indeed mathematics deals with reality when conforming and describing laws of nature that are discovered by human intuitions and validated through empirical testing, but it also deals with abstract structures in which consistency is demanded, truth is proven and yet, a physical reality that has the structure is not  known.

What makes mathematics fascinating and reasonably effective is that the structures developed somehow either describe a physical reality or will describe one in the future and the reason for this is because of the foundations or the fundamental axioms up on which mathematics is established. 

Your example discusses relations between cause and effect and tries to give a meaning to existence. Indeed existence - uniqueness are important  to mathematics  and when a natural cause disappears then the anticipated effect will not exist. If some how a physical reality that exists in three dimensions looses one of its dimensions, then definitely there will not be any behavior that will be observed along the third dimension. But I do not see any larger insights  as to how this example relates to the galaxy of mathematics.   

Dear Manuel,

Mathematics is a broader domain of abstract and applied knowledge  in which mathematical logic is a piece and the field that  specifically studies existence is a branch of philosophy called ontology or in the broader sense metaphysics. Besides most of the things we use to do our jobs effectively, lead our lives and live healthier and better are not results of fallacy but results of truth of mathematics  and science.  

Manuel,

I think that you should decouple the concepts of your argument. Mathematical logic on which mathematics is based does not deal or is based on existence. A formal predicate calculus which uses modus ponens(from which other rules can be derived) does not have anything to do with causality but deals with the validity of how logical statements are chained together. We can have non causal statements in modus ponens and are totally acceptable (for example, in concept ontologies there is an implication without causation).

Further, mathematics does not deal with existence nor its origins, it deals with quantification of abstract entities.

Manuel,

Sorry if I do not get your point  but again, I think that you should decouple the concepts in your argument.

1) By stating that "acts of selection in order to come into your existence" you are implying a subjective reality as opposed to an objective reality. I do not know if that is your intended objective, but it seems to be from your statement and I would be cautious of such statement.

2) The statement "If you cannot select them they do not exist" provides existence of mathematical objects based on a subjective viewpoint. While I am by no means a Platonist, I would rephrase you statement to unactualized possible. Mathematical objects do exist, but existence should be differentiated from:

• Spatio-temporal connotations
• The speech acts of the person invoking those concepts

3) The statement "Mathematics describe the effects of a causal reality" carries too many implications that one should be careful in formulating a conclusion. While mathematics can explain the effects of causal reality it is not its sole objective. Mathematics can be made without referring to causal reality and merely describe quantities.

I also think that you should also make a difference between the concept of mathematics and the actual implementation of mathematics. Mathematical implementation are instances of mathematics and can be formulated incorrectly, that does not mean there is a fallacy in mathematics or logic.

Selection is a process of choosing few from among available things based on conditions of our parameters of choice but mathematics in the contrary uses what are assumed truly exist  without selection. The fundamental axioms of mathematics are not specific facts of truth of intuition  that are selected from among many but the only facts that are observed and used to built mathematical structures. 

Manuel,

May you forgive me, but I still think the point in your initial post and the following posts are missing some key factors.

I will try to summarize my perception thus far:

Given: Papers addressing flawed scientific methods

Given statement summary:"logic we use to perceive reality is based on effects causing effects which says nothing about how effects come to exist"

Given statement:"Gentlemen, mathematics, just like the words you are now reading are solely dependent upon the acts of selection in order to come into your existence"

Given apparent conclusion: 'the "Flawed Scientific Method" document was designed to go with the public invitation to help science self-correct'.

To this last statement there is an implication A->B where A is the first given and B is the apparent conclusion. The other comments are explicatory in nature.

I would say that there are several problems in my view of the implied conclusion.

1) (nature of the problem) The problem is one of experimental methodology and in my view this is an instance of a counterexample, it does not invalidate the current methodological view of science. I would say an implementation problem instance, not a theoretical one, nor does it generalize to all science. See 2 below

2) (logical) In stating a guiding principle of science like the one you are proposing, the methodology has to be an induction proof not an implication. You have found the instance but I do not see the generalization to every possible case so that it becomes a guiding principle. I am not denying the fact that you found a counterexample, but the induction step is still missing.

3)(philosophical) It might be argued that the same experimental setup that was devised in the paper is a subjective view of a more complex system(a very simplistic model) that does not necessarily captures the complexities to draw the conclusion of the implication.while you mention two frames of reference, the one described in the experiment is a subjective one.

4)(pragmatic) In my experience the paper does not account for all variables of choice. While the restrictions are imposed by the scientist, the reality is otherwise when it comes to human beings and especially computers. The experiment has not accounted for people who chose not to play, to cheat, or to hack the system. How does the theory account for the choices in this instances. In computer science experiments with people you have to assume an adversarial setting where people are trying to cheat the system and the distributions are non stationary in describing behavior. While it might be argued that the experiment was delimited in nature, in my view of gathering statistics from computer based systems, there is a strong possibility to account for malicious behavior as part of the choices(especially where there are competitive incentives).

I would first clear these points with you before debating the ontological problem of choice.

Note: This is just my perception of the thread so far

Let me know

Dear Manuel,

Selection is a process of picking from among many, the types some one needs in order to accomplish a purpose, but mathematics is not that and the way it does things is not by selection but by exhaustion. It simply finds what is true and reasonable fact of reality , starting from the foundation and builds consistent structures of provable concepts within, called  truths which are not selected by any means.  

If mathematics was established by selection,  then all those technological products we use that are built based on scientific principles resulted from mathematics could not have function as we imagined. Because nature functions in its ultimate precision and a minute deflection creates unexpected consequences - the chaotic nature of nature - it simply demands precision of the highest order in which selection will not work but exhaustion. 

Christian - indeed there is nothing in the universe that is non mathematical in behavior  and imperatively mathematics is always needed as an eye to see and to describe such behaviors and communicate with nature. Therefore mathematics will never disappear but instead remain indispensable for all time and will grow  as our understanding of the universe and behaviors of phenomena in it  increases in amount and precision with more closer to the truth.

Christian - indeed there is nothing in the universe that is non mathematical in behavior  and imperatively mathematics is always needed as an eye to see and to describe such behaviors and communicate with nature. Therefore mathematics will never disappear but instead remain indispensable for all time and will grow  as our understanding of the universe and behaviors of phenomena in it  increases in amount and precision with more closer to the truth.

@ Christian Baumgarten : "Mathematics is a language of physics - no more and no less." I don't agree. Or rather: I only agree with the latter part: "no less". Actually, it is much more than that.

Since more than 100 years mathematics is *also* the language of a steadily growing part of the social and behavioral sciences: mathematical psychology, mathematical sociology, mathematical biology, mathematical economics, etc. Most of these branches of the older fields are also denoted by the suffix "-metrics", e.g. psychometrics, sociometrics, etc.

Moreover, there is a highly sophisticated branch of mathematics which the physical, social, and behavioural sciences have in common: measurement theory (including metrology). Indeed, the most important and highly esteemed contributors to (if not pioneers of) measurement theory come from the field called psychonomics-psychophysics, a hard-core subfield of theoretical psychology. I should also mention the field of ergonomics, or what is called Human Factors in UK/USA: you can't reduce this field to proper physics, although it might be said that it is on the border between applied physics and psychology.

Finally, I don't agree because immense parts of pure mathematics and logics don't have any immediate applications, yet, so just calling them languages for some empirical sciences doesn't do them justice at all.

It is funny, if not disappointing, that there appears to be so little cross-communication and cross-fertilization among the diverse sciences (physical, social, behavioural and what else you have), that they don't even realize how much they have in common, especially on the deeper, more fundamental levels of those sciences.

Fully agree. For instance, as far as I know, no serious theoretical psychologist - whatever his or her particular epistemological stance - would ever claim such a miraculous thing.

On the other hand I have to admit that there are differences and discussions of a similar - reductionist - sort: how much of psyche can be safely reduced to (neuro-)physiology and how much of it (if anything) has an ontological status of its own, e.g. the so-called higher order cognitive functions like language, memory, reasoning, etc.

Most research psychologists don't care so much, as they are trained in doing small-scale empirical-experimental research for which the choice of the right methodology is more important than epistemology. Not so different from research physicists, who plan and conduct their small-scale experiments within the context of a particular theory, in a given subfield of physics. This is what Thomas Kuhn in his popular book has called "normal science".

In psychology, however, there was a time - not quite so long ago - that researchers wanted to abandon any reference to "mental or cognitive things" at all in psychological theorising, perhaps in the vain hope (a) to expel pseudo-scientists from intruding into the serious business of psychology and (b) to build up a parsimonious body of knowledge from first behavioural principles. That movement called behaviourism was promising, in the beginning, but didn't succeed in the long run.

Still, the mind-body problem  isn't decided, yet, and creeps up again and again, either in its more moderate form ("often, so-called mental phenomena are best explained as-if there exist such a thing as a psyche, but of course some day we will be able to explain them fully in biophysical and neurophysiological  terms") or in its extreme form ("there will always be aspects of human mind which cannot be explained away by reference to underlying physical processes.").

As long as this mind-body-debate is going on, psychologists will be far away from a debate of the sort that's going on here: whether all of what we call reality is just a projection of mathematical thinking or - even stronger - mathematical objects.

The reason that such a debate is possible at all in physics might also be, that theorizing and experimenting in physics are often years out-of-sync, so theory doesn't inform and restrict research and research doesn't inform and constrain theory enough. Each one can go its own way. This is almost impossible in the current habitats of social scientists. But who knows ...

      ---------------------------------   [added 2016.05.25] ------------------------------------

The question is of course, what is worse: being bold and decades ahead of (empirical) research but also being able to make substantive predictions of hitherto unobserved or unexplained phenomena  OR  not being bold and staying close to established theories and socialised facts but not being able to propose and predict substantive new phenomena which may be empirically proved?

Natural sciences take the first route, probably because they have experienced successes with it and take any trouble and risks with it for a fair and necessary price. Psychology and most of other human sciences take the second route, which is much less risky, but isn't thus able to produce really new insights. Worse: if you leave the beaten track, e.g. want to do research in parapsychology, you will risk your professional life. Not so in physics: paraphysics is well and alive, as are its pioneers!

Dear Dejenie and All

I would say that mathematics follows natural sciences; mathematical language in essence describes various aspects of nature. If it was a pure independent science in itself, I believe that it would have found out by now what division by zero is. We fail in it because we cannot conceive, through any natural science,  what this means.

Narayanan