In the introduction to the question" What is the relationship between Mathematics,Science and Nature?" I have concluded that "Nature is innately mathematical, and she speaks to us in mathematics. We only have to listen."

I want now to present an example that illustrates this in a beautifully way and make another equally important conclusion.

Because of quantum theory we now have two kinds of physical theories, those that work at a large scale and those that work at the scale of individual atoms. these theories are incompatible — the very successful theory of relativity isn't expressible in quantum terms, and vice verse.

Currently,we don't have a theory that works at all scales-unified theory. However, an element of such a theory is an equation written by Paul Dirac in 1928. Dirac's equation successfully predicts the behavior of particles moving at relativistic velocities, so to some degree it reconciles the relativistic and quantum views of reality.

While writing his equation Dirac realized it had two possible roots. At that point, Dirac could have decided his equation was only an approximation of reality (there are plenty of those), or he could claim his equation accurately described nature, therefore nature allowed two different kinds of matter, with positive and negative signs. Dirac decided his equation described nature and in so doing his equation implied the existence of a new form of matter, antimatter.

Dirac realized he could rewrite his equation to eliminate the negative root, but that equation would have been complex and unattractive, solely to eliminate the strange possibility that nature allowed two kinds of matter. Acting primarily on instinct, Dirac decided his equation accurately reflected nature, and he described the possibility of something he called "antimatter." Within a few years antimatter had been observed in 1932 by Carl Anderson. Carl discovered a new particle called "positron"(like electron but with positive charge).

Dirac did not invent his equation, if he did then this implies nature subsequently obeyed Dirac' equation and this will make Dirac some kind of a creator! But Dirac is not a creator, Dirac discovered his equation and he found it in nature. This clearly demonstrate that nature speaks to us in mathematics and equally importantly, that mathematics was discovered not invented.

The question of this thread was inspired by the reference below and the above is an extract from it:

http://arachnoid.com/is_math_a_science/index.html

I'd suggest the idea that mathematics is condomain Y, situated in human mind, of function y=f(X) where domain X is a set of nature laws which can be observed by the humans.

The described relation somehow is personal. nature is nature, a part of mathematics try to describe nature. I think the relation between nature and mathematics is as data and tools for modeling. application of tools (mathematics) in description of data (nature) results physics.

Dear Azizi

results science, not only physics!

Dear Sinjab

Thanks for your correction.

None other than Mathematics shall express nature in an understandable format to Humans. Math is basically an expression of human reasoning.

Mathematics throws a lot light on the darkness of nature and even in religion. A very good example is in the area of numbers. The numbers integers between 1-10 and some other have implications in nature. A family unit can be viewed as an algebraic structure where e.g. a ring where the children form the set and the man and woman are the two binary operations of addition and multiplication. Tracing back the origin of humanity using the bible, God created man and created the woman from the man. This action is similar to a cyclic group where an element in a group gives the remaining ones. In fact, mathematics is closer to so many spiritual truths than nature is.

Dear Temitope

Thank you for pointing out some aspects of how mathematics can be connected to religion.This is something I must admit I have not thought about. You have raised a very interesting point and I shall research it seriously.

I am not Christian, but it is very interesting how christianity and Islam share common beliefs. Not only we believe in Jesus and Mary, but we also believe that God created the woman from the man!

In fact, there are numerous thing christians and muslims do that confirms variuos fact in mathematics. Consider the number of times a devoted muslim must pray in a day. The postures when praying (this reveal some facts on geometry). So many. One fact about Jesus was his use of the number 12. He had 12 disciples, started teaching at the age of 12,performed some miracle reflecting 12 (fed 5,000 people with 5 loaves of bread and 2 fishes with 12 baskets remaining, healed a 12 year old girl, healed a woman with 12 year of blood flowing disease) 12 tribes of Israel, 12 hours make a day light, 12 hours make a night day, 12 months of calender make a year.

I think God can use math to restore religious peace on earth.

Well, now we are drifting into the esotheric corner.

No offense meant, but seeking for parallels between science (including math) and religion appears to me as yet another attempt to convince ourselves of some higher purpose behind our being. Which I personally don't believe in.

What would, for instance, be the implication of the integers between 1-10 in nature? As far as I know, people are calculating with base 10, because that's the number of fingers they got on their hands. And computer science has taught us, that other bases are much better suited for efficient counting and calculations.

I agree, that people like Gauss, Newton and others developed mathematics for describing their observations of nature. But I have the impression that mathematics has developed a life on its own, at least the fundamental part of it.

Thinking back to the undergrad lectures in calculus, that we physics students attended together with the math students: the mathematicians were excellent in understanding differential equations and proving them solvable or not. But none of them actually had an idea what you could use differential equations for.

Regards,

Sebastian

Nevertheless, the mathematics are the tools our students need to know to use them in the sciences such as physics, chemistry, biology and agronomy.

Absolutely. There is no doubt that all sciences and engineering disciplines rely heavily on the instruments provided by mathematics. However, many of the mathematicians' beautiful developments, discoveries, inventions, or whatever you want to call it, have not yet found any practical application, and many may perhaps never find one.

Science is nature's mathematics, as nature is God's Art. So, there is not only connection or relationship between mathematics, science and nature but also between mathematics and art, as there are no boundaries in knowledge in the real sense, it is only for our convenience that knowledge has been classified into various fields of studies, so that lesser intelligent ones with limited faculties and abilities can understand and master them and call others as jack of all and master of none.

If you think about the evolution of our brains, you can see that it developed as part of nature. The way we think is dictated by nature. We often think we are apart from nature, but this is a superficial viewpoint.

Concurrent and independent discoveries, breakthroughs, and inventions in many fields that are very similar are indications that we humans share a common way of thinking.

Therefore, there is really no fundamental separation between mathematics, science, and nature.

I don't know whether humans think in a common way or it is by now a long shared scientific tradition with its methods, logical expression and symbolism that is responsible for it. Ask a man living deep in the forest of Africa, you will know better that humans think alike or otherwise. Give an alternative scientific theory that better explain a phenomenon but is unorthodox or unconventional, the reaction of the scientists will show whether a theory not compatible within their paradigm is acceptable or not. It is why many neat and powerful theories by the scientists have been sacrificed on the alter of so-called science. Science is unlikely to listen unorthodox views and methods to find out truth. It is why I pointed out in a thread on ResearchGate that Science is not only undemocratic but bigot also. There is a number of scientists either sacked from their positions for their unconventional views are silenced like Big Brother (1987) or by Big Business Houses.

Mathematics is not in nature, it is in human mind as Pert has pointed out. It was success of application mathematics to motion by Newton that gave boost to mathematics. Einstein strengthened it, but initially it failed in the quantum realm and during last two decades quantum/wavelet algebra is *invented* and advanced to explain quantum phenomena with some success but quantum mechanics still depends heavily on chance analysis (probability).

Azizi and several other scholars are correct that mathematics is a tool to understand nature as we perceive it. As science is a mental construct so are mathematics, language and graphics to help understand the nature. Take out all words from a well written and researched article in any field of science and keep only equations, numbers etc., will it possible to make sense of that research. To me mathematics is simply logic written in shorthand. Similarly visualisation through flow diagrams, animation and other graphic and non-graphic means may so effectively convey the reasoning of a scientist as mathematics or so many words in logical sequence may be used through a shared language to convey the same concept, idea, thought, law whatever it may be. But beauty of the mathematics lies in its parsimony.

However, the claim, "As we learn more about nature, it becomes increasingly apparent that an accurate statement about nature is necessarily mathematical. Anything else is an approximation. So, mathematics is not only science but is also an exact science." does not hold true in that mathematics itself has numerical analysis analysis and theory of approximation.

In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by best and simpler will depend on the application.

http://en.wikipedia.org/wiki/Approximation_theory.

A complex function F(c) is approximated with a simpler function F(s). The original function F(c) is an exact and accurate function not an approximation.

Modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice.The overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but "accurate" solutions to hard problems. hard problems can be described exctly mathematically but not easily solved, or they can be both hard to describe and solve. In either case, that does not necessarly mean in the future they can't be both described and solved exactly.

I submit that there is a difference between "exact "and "accurate" ,but then again not everything in nature is simple! The use of powerfull computers is narrowing the gap.

Dear Pavel

Thank you for your interesting observation. I totally agree with your statement "basic physical approximations underlying theories can be much more interesting".

@Mohammed: We "modern" people are not that removed from "primitive" hunters and gatherers. The elders in such villages are wise, often much wiser than we are, especially in interpersonal in matters. You can also read accounts of verbal fables and religion that demonstrate that much ancient wisdom and knowledge of human nature is very applicable to the 21st Century. Not much has changed in the way in which humans think.

Today, we just have many more man-made inventions to deal with. The ancients dealt with more complex matters in nature (e.g., which plants are medicinal, which are edible, etc.) It is a kind of trade-off: man-made environment vs. virgin wilderness environment.

In all areas of thought (e.g.,science, math, language) when things start getting too complicated, we invent a new term for an entity that is referred to frequently, as a kind of shorthand. We keep doing this, and before we know it, we have reached a higher level in the hierarchy. (In math, this is where we distill mathematical prowess - very few people can understand and feel comfortable in the highest realms of abstract mathematics.)

Nevertheless , as has been shown in some studies, most people can handle,. at most, seven independent thoughts simultaneously. Hence, the need to synthesize new terms to reduce the complexity.

We think in the same way as "primitive" people, we just tend to work at a higher level of abstraction, with the same limitations of thought regarding dimensionality.

@Dear Antonio

I totally agree with your exposition. It is not that I have any disrespect for traditional or conventional wisdom especially as you have pointed out in respect of “in interpersonal matters”. I am also aware of ongoing researches and intellectual property rights of ethno-botany, ethno-medicine etc. But, the point in discussion was about “there is really no fundamental separation between mathematics, science, and nature”. Even educated people unless given a measure of distance find it hard to perceive how far a place is. It is hard for most educated persons to decipher astronomical distances given in light years. In the same way people travelling the same place over the years have different perception of distance, area and direction. As you yourself have pointed out “In all areas of thought (e.g., science, math, language) when things start getting too complicated, we invent a new term for an entity that is referred to frequently, as a kind of shorthand. We keep doing this, and before we know it, we have reached a higher level in the hierarchy. (In math, this is where we distill mathematical prowess - very few people can understand and feel comfortable in the highest realms of abstract mathematics.)” It is in this context that I pointed out that people think differently. You believe in human evolution and I do not. I have found out that it was a government supported and propagated idea because its predatory concepts justified colonialism and situation has not changed. Science has become bigoted, facts are hidden and secrets are maintained, people never know scientific facts. You may say it is my illiteracy or ignorance [I would not be offended], but on this count i.e. evolution of man I do think differently from you. It is not that I am talking about situated knowledge or I am taking constructionvist position. To me science is science and voodoo is voodoo.

If nature is a study object, then science describe it and mathematics prove the description with equations

Science and mathematics are there to make things simple for enjoying the nature. Not in writing/discussing/talking big paragraphs about their relationships. their relationships is so simple so please keep it simple.

Dear Rajneesh Mohan

Thank you for your comment.

Not everything in nature is simple and this is why mathematicians have developed tools to deal with them. You need to read what was said right at the beginning so you could understand!

@Mohammad: Try to separate science from its applications and misapplications. Scientific research follows the SCIENTIFIC METHOD - it is the best invention ever!

When some scientists and politicians apply it to support an a priori position their distortion of the truth is to be condemned.

But I am confident that the vast majority of scientists are true to the SCIENTIFIC METHOD.

Such a great question Issam.

There are those (still a majority) who think that maths is just a descriptive tool (Dieter Zeh, many many many others)

Then there are those (Max Tegmark, many others) who think that mathematics is ultimately the only reality, and that the 'physical world' simply conforms to math, that math maps onto reality and not the other way around.

Those would point to Einstein's astonishment that nature totally conforms to math; they would point to E=MC² working just so that the math equations not be violated, to the counterintuitive Bell's theorem being shown to actually work in reality, to even the Big bang being, under most scenarios, something that happens out of nothing just so that an applicable understandable math equation not be found feckless.

The consequences of the latter approach I find far more interesting and gravid than the former. For instance, Gödel demonstrated that math is necessarily an open-ended system, that a mathematical self-consistent system can never be a closed system. Map this onto the physical world, and it tells you that any universe cannot be a standalone - that there exist other universes outside of the first one.

Food for thought ...

If you take the etymology of science in Greek, it is called 'epistimi' and derives from 'epi'+'istame' which means stand above something.

Therefore science is the action of mastering a study object .

When you 'do science' you try to master the study object. How? By successive approximations.

It is as if you are a blind man, trying to understand the shape of a rock. When you were born somebody gave you gloves of great thickness. Therefore you could understand the size and roughly the shape. As you do science, you make the glove even thinner using your wits only. Therefore you describe the Object even more accurately.

Will you ever understand the Object fully? I doubt it.. And it wouldn't be fun after all if you did.

Now math.. You start finding rough proportions and harmony on the object. This is what motivates your research after all. You need to express them, and thus, math is born. It is as if math already existed and somebody used it to define the Object.

You don't understand it but it intrigues you.

As you delve deeper by doing science, your math evolves along with your scientific approach. And then you discover even more fundamental symmetries..

And you keep going. There is this point when you have done such a good progress that you predict what the next symmetry will be like. And you find it to be real, measurable. And this motivates you even more to keep going.

All this is a self-preserved system. Trying to explain nature by doing science, using math and then discovering that math is not just a tool but something more. You use your math to improve your scientific approach when you discover that your approach unravels a fundamental mathematical structure that you hadn't ever thought of.

All this is the quest of the human intellect to master the unknown.

The most fundamental of quests.

Thank you Chris and Emmanuel for very interesting and thoughtful answers, they show deep understanding of the topic.

I see the problem mentioned this way:

1. There is Nature and we want to know about it as much as possible. Some researchers are simply curious, while others are inclined more to everyday practice (how to? why not?, etc.). We, the people, are a part of Nature

2. There is mathematics - an amazingly versatile tool to describe and simulate natural phenomena. The really great thing is that math is able to describe quite different phenomena with identical equations, see for example the potential theory, game theory, and so on. This simple fact makes our lives a bit less complex.

3. Finally, there is Science. I see it as a specific methodology linking reality (Nature) with its description (Mathematics). Here we have to infer the correct equations but also predict not yet observed phenomena. Doing science we have to abandon any personal prejudices on the one hand but also make our brains to produce wild phantasies to be later validated either by Nature or by Mathematics.

There are still many phenomena not described satisfactorily by math (earthquakes are hardly predictable) and there are mathematical concepts seemingly not (yet?) applicable to the surrounding reality (recall the case of complex numbers?). Science is the way to make the solid bridge between the two.

@ Edwin: Ud. tiene razon, pero la matematicas es mucho mas que el lenguage del universo fisico. La mayoria y el grano de matematicas existe en el abstracto de la logica.

Mathematics is language of science.

I would like to bring up to this discussion an interesting book by Gregory Chaitin (The Limits of Mathematics) in which he cleverly describes how mathematical (and/or computational) models are always inexorably incomplete. So, for me, mathematics provides incomplete definitions of nature's behavior, throughout scientific investigation. No wonder, falsifiability is an essential part of any scientific definition.

@Antonio

In response to my reference to evolution in the context of thinking differently you have pointed out, “Try to separate science from its applications and misapplications. Scientific research follows the SCIENTIFIC METHOD - it is the best invention ever!

When some scientists and politicians apply it to support an a priori position their distortion of the truth is to be condemned.

But I am confident that the vast majority of scientists are true to the SCIENTIFIC METHOD.”

My first question is if people don’t think differently, then why are there so many of philosophies and epistemologies?

Though I am a realist but I do not have such a firm faith either in science or the way it is generated and neither closed to other concepts of reality or deaf to other voices. If I am not wrong, in a thread in Researchgate perhaps you have asked the question, “IS "KNOWLEDGE" ONLY A KNOWLEDGE OF MODELS OF REALITY, NOT KNOWLEDGE OF REALITY ITSELF?” This question generated considerable heated debate and naturally you know well what is the context of question and what does it imply and what are its philosophical and scientific ramifications with respect to the reality? Therefore, without going in details, I would like to point out that what we call objective reality is nothing more than a bit of a giant pie made up of web of trillions of facts.

Even this bit of the reality that we have been programmed with is false, it is a collective myth, a shared programme bound by a false programming language, necessary to the smooth functioning of our current operating system. The survival of humans depends on the choices they make in response to continuous environmental challenges. To make the right choices, they need accurate information about the world. They process the information provided by their senses to form mental representations of the world – models which embed their assumptions about how the world operates and which allow them to run mental simulations of possible actions to assess the likely outcome. It is the existence of these representations (or knowledge structures, or schemas, or beliefs – used here interchangeably) that make subjective reality possible and provide the foundation for its construction. Beliefs can and do vary in the accuracy with which they represent the outside world, which accounts for the factual differences between objective and subjective reality.

The capacity limitations and biases of human information processing guarantee both that our mental models will be incomplete representations of elements of objective reality and that they will contain inaccuracies. It’s our perception of the world that shapes our reality and the absence of certain facts from our collective consciousness can only result in an incomplete perception of reality. Therefore, it is impossible to have a complete knowledge of objective reality. In order to do so we would have to know everything. This means we can only have a subjective view of reality, shaped by the bits and pieces of objective reality that we have gathered.

Further……

What it is that shapes our subjective reality is our perception of all that is around us. If each person was isolated from other people for their entire life then each person would have a completely different subjective reality. This is why each culture is different from the others. They developed separately and so have a different interpretation of the data. It seems that culture works to shape a common perception or a common subjective interpretation of objective reality amongst its members. It is called COMMON ILLUSION of objective reality or COMMON SET OF MYTHS. And this common illusion always changes, different eras, ages and regions have different accepted common subjective realities. Hence, all of us are given this common subjective reality by our culture and by creators of culture. We share a common set of ideas, concepts, language, etc., that allows our society to function. This we generally accept as objective reality. Although we cannot completely know objective reality, we can be led to believe that we do by people who are in charge of what bits of information should get way into our perception. It is not simply a speculation, in fact, observation and compilation of gathered data have led several of us to the fact that THERE IS A CONCERTED EFFORT TO MANIPULATE EXACTLY WHICH BITS AND PIECES WE ALL GET. In this way the regulators of information are free to create whatever pseudo-objective reality they choose, this is the common illusion most of us share. This created common illusion tends to benefit its creators. By design it keeps us prisoners, physically and mentally. If we do not understand this concept, and if each individual’s subjective reality matches that of most others, then most of us will think that it is objective reality, simply because most of us agree that it is.

Culture [or politico-economic system] is not our friend. Everything that exists within this system exists to benefit it. If our understanding of the world around us does not match with the common illusion created by the regulators of information, it may be a problem for the system. It may be an obstacle to its smooth operation. So, this system and those who control it, inherently seek to manipulate our perception in order to better fit us in. In this way, the reality that we have been programmed with is false, it is a collective myth, a shared programme bound by a false programming language, necessary to the smooth functioning of our current operating system. The Departments of Defence in several advance countries and many public relations firms call this technique PERCEPTION MANAGEMENT. We are, therefore, physically and mentally prisoners of this system.

To conclude I would like to remind you what Albert Einstein said about theory which has a direct bearing on my arguments:

“If the facts don't fit the theory, change the facts.”

Nature, Mathematics and Science are beautifully interwoven and according to me, INSEPARABLE! We cannot understand nature without maths and science. Our understanding of nature becomes easy with the basic fundas of Science and maths!

Dear Mohammad, Thank you for devoting so much time to your answers. My only comment is that in reference to the Scientific Method, there are three things that set it apart from other aspects of dealing with our universe: 1. It allows, no - it requires, that others can perform the same experiments, under the same conditions, to see if they can duplicate the same results. So it is not just one's subjective opinion or the results of an error being made. 2. It is the source of all the wonders we see in technology, medicine, etc. And, 3., It is capable of predicting many events, such as the appearance of comets, the arrival of a storm, etc.

No other endeavor can make such claims.

Perspectives may differ,but one cannot deny or ignore the complementary contributions of scientific methods in broadening our understanding of the present and past experiences of mankind- irrespective of ones affiliations or leanings.

Scientific methods as such do not seem to contribute in any way to the present problems of the world.Rather,I find it is the selfishness of humans who manipulate the gifts of scientific processes to further hidden interests,that does all the damage.

As for the topic of interest,I wonder why many of the contributors to the thread chose to by-pass the one posted by Mr.Antonio initially...

When it is accepted that man belongs to Nature,whatever he contributes in terms of maths or science too must necessarily belong to Nature itself.Therefore theoretically,it appears that any relationship in terms of maths or science, can only be as much as what other fields such as politics,religion etc., do have with Nature.

Matematics is only a writing form of human thоught. If we have not intuition, ideas-we can not write matematics formulae. To understand matematical results-also we need inteligence and knowledge of natural lows.

Dear Antonio & k.c.muralidhar

I am not against science as in response to his thread I have very clearly mentioned that science developed through building models and till they are capable of prediction they are useful and on this limited knowledge of reality, human civilisation has reached the present level of progress. As regard so-called SCIENTIFIC METHOD, I have certain reservation which I have spelled out on the following thread in response why is it difficult to discover or get novelty?

https://www.researchgate.net/post/How_to_define_the_concept_of_discovery10

But, I reiterate the position that there is perception management and positions are reiterated for the gains of certain systems. If one breaks the chains of the system and starts telling truth, he/she is silenced. Eminent example is that of scientist of the NASA who was sacked because he believed in intelligent design. Another case is that of renowned scientist Arpad Pusztai who found evidence of intestinal damage caused by genetically modified potatoes, therefore, his funding was suspended for his publication of preliminary results, and therefore the study was never completed.

Nietzsche writes that mathematics does not explain the phenomenon it describes them. So if we have the mathematical form of the law does not mean that we understand the phenomenon.

Jose F, I'd like to comment if I may on your Quote " mathematical models are always inexorably incomplete. So, for me, mathematics provides incomplete definitions of nature's behavior" Unquote

The fact that mathematics can never consist of a closed system was first fully & incontrovertibly established by Gödel, and the subject has been explored thoroughly since. In a nutshell, a mathematical system can only be apprehended and made consistent in its entirety from outside itself. Then, attempts to subsume the previous mathematical environment into the new, wider one, only displaces the problem one step up and creates yet again a new environment - ad infinitum.

I would agree therefore with your ascertainment but not necessarily with your analysis or conclusion that math therefore cannot map physical reality.

It could well be that, reflecting mathematics, nature itself is "incomplete" within any of its physical manifestations (aka any closed universe.) Some current cosmological models deal with this by positing infinitely nested universes - any universe being stable only because it is subsumed within a larger multiverse - and so on ad infinitum. There exist workable possible mathematical mechanisms - although of course thoroughly unproven physically - to model & accommodate an infinity of nested universes.

Falsifiability is also a key step of scientific enquiry for another (and kindred) very compelling reason: mathematical modeling, given enough variables, can always accommodate any physical scenario whatsoever, however fanciful or wrong.

All you have to do to have a perfectly workable mathematical description of any physical theory, is to always have one more variable than the number of your experimental points. (In essence, this is precisely Peter Woit's main whinge about current string theory, for instance.)

So a combination of further experimental data points, Occam's (or Ockham's) razor, and a measure of predictiveness are always needed to vet and anchor a physical theory into reality. Unfortunately, this being an imperfect world, even this combination of conditions has been proved to be lacking in some (admittedly rather rare) situations.

In the introduction to the question" What is the relationship between Mathematics,Science and Nature?" I have concluded that "Nature is innately mathematical, and she speaks to us in mathematics. We only have to listen."

I want now to present an example that illustrates this in a beautifully way and make another equally important conclusion.

Because of quantum theory we now have two kinds of physical theories, those that work at a large scale and those that work at the scale of individual atoms. these theories are incompatible — the very successful theory of relativity isn't expressible in quantum terms, and vice verse.

Currently,we don't have a theory that works at all scales-unified theory. However, an element of such a theory is an equation written by Paul Dirac in 1928. Dirac's equation successfully predicts the behavior of particles moving at relativistic velocities, so to some degree it reconciles the relativistic and quantum views of reality.

While writing his equation Dirac realized it had two possible roots. At that point, Dirac could have decided his equation was only an approximation of reality (there are plenty of those), or he could claim his equation accurately described nature, therefore nature allowed two different kinds of matter, with positive and negative signs. Dirac decided his equation described nature and in so doing his equation implied the existence of a new form of matter, antimatter.

Dirac realized he could rewrite his equation to eliminate the negative root, but that equation would have been complex and unattractive, solely to eliminate the strange possibility that nature allowed two kinds of matter. Acting primarily on instinct, Dirac decided his equation accurately reflected nature, and he described the possibility of something he called "antimatter." Within a few years antimatter had been observed in 1932 by Carl Anderson. Carl discovered a new particle called "positron"(like electron but with positive charge).

Dirac did not invent his equation, if he did then this implies nature subsequently obeyed Dirac' equation and this will make Dirac some kind of a creator! But Dirac is not a creator, Dirac discovered his equation and he found it in nature. This clearly demonstrate that nature speaks to us in mathematics and equally importantly, that mathematics was discovered not invented.

The question of this thread was inspired by the reference below and the above is an extract from it:

http://arachnoid.com/is_math_a_science/index.html

Whatever we understand within our perceived limitations as science or mathematics,is in fact our own patterns of reading the manifestation of perfection permeating Nature.

Nature,whatever it may be said to represent,

speaks through humans,

acts through humans,animals and plants,

plays through humans,animals,plants and inanimate things-

with tools of intelligence-

we call it variously as maths,science,religion etc.,

with all that...It teaches.

It teaches in silence...

Very few choose to learn-variously in limitation.

Some get to hear its harmony...feel it,

but most of us are content with the camouflages-noises.

Self-made-our own-therefore 'sweet' noises.

Cheers.

there is no absolute certainty, and this is absolutely true I read this in Umberto Eco's Foucault's Pendulum (in the heading at the beginning of every chapter), it is already a quote on his novel, but I cannot remember from whom (maybe Descartes?, I'll check tonight and let you know).

@Samuel

You are 'absolutely' sure that that there is no absolute certainty!

Perfection.Is it a myth?

Superficially it is so..in the realms of relative existence -the outcome of self-imposed limitations(seen through the limitations of prism the colorless light appears differently).

We all know that one needs to experience to confirm what one understands and that it does not stop with exhaustive discussions alone.

It is also known that higher knowledge gained through reading helps,but the same becomes an impediment itself when not followed by practice that confirms what one gets to understand at every step of understanding...the theory and the practice need to work in unison.

It is said: like the left foot that follows the right when we walk up,theory is to be followed by practice if it has be assimilated.

Needless to say, one needs to step forward diligently-even just to get a glimpse of it-what we mean by perfection.There is no magic or myth or mystery.Simple facts.

Explanations regarding what kind of practice,whether it is scientific or not,can it be proved or demonstrated etc.,depends more on the need of the individual who seeks it than on the desire of proving it to one and all.

I think nature has a design, with an order (repetitions, cadences) and for that its natural language is maths.

I think maths contains us, but I think that maths seems more exact than nature. (Or only our maths). For that possible we need (we feel need) something more than maths to explain all.

The exactness of Nature is qualified by what we seek to observe and understand in Nature.Perhaps,the narrow view or definition of Nature contributes to the confusion that we tend to view it as something different from mathematics,science etc.,

We know that intelligence of humans(a product of Nature,in a sense) operates quantitatively as well as qualitatively.The exactness of mathematics,therefore invariably depends on how best we employ those aspects of intelligence.

Now.Is intelligence upon which every bit of our maths or science depends,alien to Nature that we get to understand internally and perceive externally?

Can we argue that intelligence that operates variously through science,mathematics etc.,does not represent inherent perfection in Nature even at least by some degrees?

Is it not a fact that whatever laws of physics or chemistry we keep discovering have been converging more or less towards some point of perfection that we keep denying day in day out?

The objectification or tendency to view perfection as an entity(static or dynamic)degrades it and consequently we are bound to label whatever we get to understand as imperfect at every stage.

I think is more "perfection" what I see in nature than maths, but may be we must said stiffness to the perfection of maths (possible for our limitation).

(Issam Sinjab, because I´m woman I want to say you this, I know you want to know, and it is not telepathy, it´s only logical:

About God-man-woman. I prefer to see me near God directly, not with a man in the middle. But I can see Jesus like a God and a man. For that I can think that I am daughter of God, in first term with a man in the middle. (But "this" man... because was the first. Only for this. (And then all men and women before me)).

I never think that this is important, or this implies I´m less than man (God haven´t time limit), because I could not think free. (If I was less I could´t be more than a man, this is not good for woman).

It´s impossible to me not see God directly over me. (But I said thanks to the man).)

We only was waiting for you (artistic)

Look it what you wont.

We (women) only was waiting for you (men).

We (men) only was waiting for you (women).

Dear Ana

I see you are so passionate about God and Jesus, you may not know it but I am if not more passionate than you are, at least I am just as passionate as you are.

However, we have all seen what happened when we were trying to discuss God in a different thread that had nothing to do with religion and/or God!

With the greatest of respect, I prefer to avoid this type of discussion here for fear of upsetting someone( and the love is no longer there--remember Ana!).

I will be very happy to talk with you endlessly about the things we share and love dearly(God, Jesus and religion) , but this is not the place for it. You can either email me or send me a private message to my inbox. It is always a pleasure for me discussing issues of this nature with a highly intelligent lady like you. Better still, may I suggest you start a new thread asking a question about God. That will definitely be a much better place for a public discussion.

Dear Ana, please tell me what is the perfection in my appendix whose only use apparently is to give me appendicitis? Is this intelligent design or stupid design?

Illness is worst.

I cannot say you why I think our body is more perfect than maths (nature complete better) (I don´t say our body), but possible because our body create our maths?

Nature is complex, and greate, science is system to study the nature, mathematics is only an instrument of science!

Dear Ana,

The worst disease perhaps is blindness which prevents from seeing the beauty of nature. Jesus cured several blind men provided that they believed in him. He had the power to heal. If I had that power I would cure every blind in the world without demanding anything in return. Just for the pleasure of making them happier. I am sure that you would do the same. I don't understand what is the reason for your admiration if Jesus did not cured all blind men.

I not continue with God.

Juan, now I a follow you. If you want to continuous with this topic talk me in private message.

'Mathematics is the Mother of all sciences' whether pure sciencs, applied sciences or naturalor biological sciences, Mathematics is playing an equal role in all branches of nature and humanity. No duobt, Nature is very complex but the mathematical tools developed are proving to be boon to solve and prove its complexities.

I am not agree, that mathematic is mother of all sciences! O"k she is plaing great role in many sciences, but she is only an instrument! When Gaus tolking that she is queen of science, that mean that there are many other branches of science, also important

Science = Mathematics X Nature

"Mathematics has been the language of science for thousands of years, and it is remarkably successful. In a famous essay, the great physicist Eugene Wigner wrote about the "unreasonable effectiveness of mathematics". Most of us resonate with the perplexity expressed by Wigner, and also with Einstein's dictum that "the most incomprehensible thing about the universe is that it is comprehensible". We marvel at the fact that the universe is not anarchic - that atoms obey the same laws in distant galaxies as in the lab. The aliens would, like us, be astonished by the patterns in our shared cosmos and by the effectiveness of mathematics in describing those patterns."

---Martin Rees is professor of cosmology and astrophysics and master of Trinity College at the University of Cambridge.

@Patrick Sole , whether a design is "intelligent" or "stupid" depends on its purpose. You seem to assume that any intelligent design of your body would not include your appendix. However, can you truly claim that you fully understand the true design purpose of the body? Unless you can, your assumption seems poorly justified.

@kerry: if u find any purpose to my appendix I ll send u a box of chocolates. On the other hand Evolution theory has answers. It is just the remnant of the time when we were eating grass and needed a longer digestion.

Mathematics has been remarkably successful as the language of physics which is the science of the smallest and greatest scales of the universe. In the middle scales, what is going on in the life and human science has not so far been express elegantly in the language of mathematics. Maybe it will happen one day. Maybe one day we will invent new mathematics for the phenomena of life. But maybe not? I have difficulty to believe that something like the love for your child will ever be express in any language. Poetry evokes this reality of love but poetry does not claim to define it.

I will refer to the message of Louis Brassard mostly though my comment is not exclusively addressed to him. I agree with the view but I would like to add my own perspective. Languages (the common ones English, French etc) are not only means of communication are also means of codification and of sophistication. I can use thousand words to transmit no message in fact; this is a politician escape in a difficult sensitive debate. I can use no words and say a lot; remember the look in the eyes of your parents when you come home late as a teenager.

My claim is that we use language more and more as means of escaping reality, instead of transmitting information about reality. Language has become means of falsifying reality and again Facebook is the best example for that. You can re-create yourself, your neighbourhood a s o just with a digital cam and an internet account. Tell your own story. Remember for some 300 years ago, we could make the distinction between realism and idealism in literature. The realism of written sources in that time was enshrined in the fact that only view voices could be heard, only view people were writers or historians. Now-a-days everyone is a writer, a photo-artist, a reality-mystifier. I do not know where you can go to search for the brutal truths today. Maybe in North Korea, since there the known lies are official truths. Everyone knows that it's a lie but everyone has to act as it were a truth.

We are captive in this socially created realism. My reaction is to search for alternative ways of expression art, poetry, a high degree of abstraction is necessary in order to deliver some genuine, non-mystified, first-thought meaning. An alternative is to speak with a child. Children can give us lessons in sincere conversation until a certain age when this sincerity is corrupted.

The bottom line of my comment is that I crave for genuine meaning in life and because we have expelled the reality from reality, the codification and abstractisation are the only means to convey some genuine thought into the sensorial world (subjective truths expressing an untwisted thought are considered puerile). Since maths is all about codes and abstract expressions, I see an actual potential in using maths to transmit knowledge about reality (even subjective reality) in a less corrupt manner. Maths is not social, this is what I love about it.

Dear Emanuela

I wish I could up vote your answer a 100 times, unfortunately I can't and even if I could I would not have given it the credit it desrves. Thank you Emanuela.

Many coleagues overestimated the role of mathematics. I understand proffesional mathematics-this is sense of their life, but I do not understand other scientists, coming to this conclusion. Mathematics is very important research tool in engineering and pure science, but Nature is very complex and only human intellect is able to understand various trends and laws of Nature. The science is system of creating new knowledge for Nature and needed various instruments.

Mathematics is the voice of pure reasoning; it accepts even the counter-intuitive results as long as the manner of obtaining them is scientifically correct (in contrast to politically correct). This is a big relief to me.

In the legal field, in business law litigations mathematics is important. As long as you can prove not only in words but also with figures (loss of profit, savings, outstanding debt, the temporal dynamic of these economic figures etc) in a comprehensive way before the judges, then your legal arguments will weight much more. The judges start to pay more attention because the other arguments the purely legal ones that you can employ have been heard by the judges on and on. Give me more than just the law, give me something to grasp, some objective fragment of reality, some figures to rely on. The human intellect is complex no doubt but the problem is that the human intellect does not always want to accept the facts and especially in the field of litigation, it is clear that you try to twist the facts in your favour. This is the game to a certain extent, but the ability to twist should not be the determinant one, some substance must be added to it. Otherwise the process will lose its legitimacy.

A good question about the human intellect would be: What is its ultimate pursuit? To survive as an individual, as species? To achieve knowledge? To avoid the uncomfortable facts in a self-defence attempt, in this way avoiding insanity, which also would be a form of the survival motive? Imagine that you would possibly know the objective truths, all of them, about your neighbours, your children/parents, the politicians running the world, the historical events of the past and present etc. How long do you think that you will remain sane under these circumstances or better said how fast will be the collapse of the mind?

The mind (human intellect or which other word fits) is built on some 'Salonfähig' blocks of memory (the socially acceptable reality), if they collapsed, we would be in trouble, all of us. The naked truths are ugly and only the fools and the children can be interested to deal with them for a while.

Mathematics has an impersonal (therefore completely safe and exculpatory) manner to deal with ugly truths by peeling off the unpleasant concrete muddy truths and conveying them into abstract expressions. In this way we can deal with them.

"You can’t corrupt math, although it’s not because there aren’t mathematicians who wouldn’t corrupt it if it could be corrupted.

Numerous mathematicians become just as illogical and biased as the pack, once they stray from math.

What can be corrupted is the application of math, and many people confuse the application of math with math" -------Elbadudedansky Brodudensky

Apropos of what Issam has just told now. I have an easy example: the elections. Watch how the politicians try to twist the statistics (applied maths) in their favour and prove why you should vote for them. But as long as you can reason independently and have access to this material, the twist would be exposed.

The twist is not enclosed in the figures, but in the inappropriate perspective and method of interpretation.

I think that when Kepler found a mathematical correspondence in the cadences of heaven, this must be the most sentimental emotion can feel an human. Check that there is a reason, not just random. We already take it for granted, but not ever was the same.

Dear Emanuela, as much as I love math, it is still a human endeavour and as a professional i can ensure u all the flaws and qualities of human experience are there.

There are schools, there are influences, there is even a variety of political BS we call "motivation". Obectivity is in the eye of the beholder.

In Swedish language, there is an expression that literally (mot à mot) can be translated as the human factor (mänskliga faktorn). When you hear it, as non native speaker you would probably guess that it's a positive value (such as creativity). They mean the ability to fail, to take an incorrect action leading often to accidents.

I love the Swedish pragmatism in this meaning. We have to distinguish between the value of validity of a theory (in law, maths aso) and the interpretation and application adopted by the 'human factor'.

At a philosophical level the key in my opinion is to confront the imperfections of the human existence as an alternative to our usual escape in platitudes. These escapes are illusory in fact and often the confrontation is the only one way to search relief from a negative life experience.

There is a mathematics of the quantities and one of the qualities. The first is more developed, while the second one has only more recently been inquired. I cite from Olaf Diettrich:

'If cognitive evolution made the operators of perception and the operators of mathematical thinking to commute, it would explain both the algorithmic compressibility of the world and the success of induction.'

We are not yet there, but still ...

http://www.vub.ac.be/CLEA/people/diettrich/12.pdf

I have found a good illustration. I don't know how accurate the model is but anyway the idea is that the divorce can be predicted with a certain margin of error.

'Mathematics of Marital Conflict: Qualitative Dynamic Mathematical Modelling of Marital Interaction'

The main point is not to follow the warning signals, but just to realize that our behaviour can be encoded in maths.

http://faculty.tamucc.edu/jchampion/wp-content/docs/Cook-et-al-JFamilyPsyc-1995.pdf

Very interesting reference!

@ Emanuela

I felt almost exactly what Issam chose to convey about your captivating and straight-from-the-heart- observation...

Let me say.A beautiful mind that conveyed exactly what it thought and, rightly so.

Congrats.

Jokes are another way to say the truth. I didn't think about myself because I am definitely a lost case in this field. :) This is my way to confront the reality, admit my own limits or the limits of the institution or both and just live with this less delightful insight.

I am aware of the contractions that we can never fully escape. My solution against the blue feelings is to write poetry, when I have this mood of not fitting in the big picture.

For me science is born in poetry, and when I escape that is where I find refuge! The language may be different but there is no language barrier in poetry, even if you don't understand it you can feel it!

“Poets say science takes away from the beauty of the stars - mere globs of gas atoms. I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination - stuck on this carousel my little eye can catch one - million - year - old light. A vast pattern - of which I am a part... What is the pattern, or the meaning, or the why? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?”

― Richard P. Feynman

Two atoms of hydrogen and one of oxygen have met (observe a ménage à trois) and built something new and essential for our life on this planet. At a deeper level the separation in atoms is irrelevant.

If I could accept the idea of soul, I would never cope with the idea of soul searching. I can barely search for my own reasons and understand myself; the mission of searching for other souls would be an exhaustive attempt meant to fail. What I try to contemplate is the idea of self-irrelevance at the deeper level.

Without dreams we cannot found...

@ Emanuela

Extremely sorry.No pun or joke was intended.I was very much impressed by your scintillating comments and reacted spontaneously-to tell you the truth.

However,I understand now that it did not convey exactly what I wanted.I have rephrased it now and hope you understand.

(soul-searching,hard-hitting etc.,in fact referred the impact that your post would have had on others).

Thank you.

Issam, "para llegar a la última estrella me adentré en el desierto".

Emanuela, "Cuando encuentras el alma ya solo te dedicas a "encontrar"... ya no necesitas búsquedas".

Going back to the main topic of this thread, we have seen a famous example of how mathematics can point the way towards new discoveries in physics. British mathematical physicist Paul Dirac used pure mathematics to formulate an equation that led to the idea of antimatter several years before the first antiparticle was found in 1932.

Two more breakthroughs in physics in the 20th century owed much to mathematics. The first was the formulation of quantum theory in the 1920s, of which Dirac was one of the great pioneers. The theory tells us that, on the atomic scale, nature is intrinsically fuzzy. Nonetheless, atoms behave in precise mathematical ways when they emit and absorb light, or link together to make molecules.

The other was Einstein's general relativity. More than 200 years earlier, Isaac Newton showed that the force that makes apples fall is the same as the gravity that holds planets in their orbits. Newton's mathematics is good enough to fly rockets into space and steer probes around planets, but Einstein transcended Newton. His general theory of relativity could cope with very high speeds and strong gravity, offering deeper insight into gravity's nature.

Yet despite his deep physical insights, Einstein was not a top-rate mathematician. The language needed for the great conceptual advances of 20th-century physics was already in place and Einstein was lucky that the geometrical concepts he needed had already been developed by German mathematician Bernhard Riemann a century earlier. The cohort of young quantum theorists led by Erwin Schrödinger, Werner Heisenberg and Dirac were similarly fortunate in being able to apply ready-made mathematics.

The 21st-century counterparts of these great figures - those seeking to mesh general relativity and quantum mechanics in a unified theory - are not so lucky. A unified theory is key unfinished business for science today.

The most favoured theory posits that the particles that make up atoms are all made up of tiny loops, or strings, that vibrate in a space with 10 or 11 dimensions. This string theory involves intensely complex mathematics that certainly cannot be found on the shelf, and the challenges it poses have been a stimulus for mathematics. Ed Witten, the acknowledged intellectual leader of string theory, ranks as a world-class mathematician, and several other leading mathematicians have been attracted by the challenge.

Finding a unified theory would be the completion of a programme that started with Newton. String theory, if correct, would also vindicate the vision of Einstein and the late American physicist John Wheeler that the world is essentially a geometrical structure.

-----Professor Martin Rees,New Scientist .

Sorry Ana but I didn't see your post as you posted it while I was writing my post!

I don't speak Spanish but why do I have the feelings you are talking about star/s and desert?-Not by telepathy but by looking at similarity with English words?

Am I wrong?

I see a problem with the way of discussing on RG. You can only see 10-12 answers in chronological order and many people react to one phrase without knowing the context. For instance my little chat with K.C. Muralidhar was mostly started as a joke. It was a psychology study based on maths that I have attached to a previous message as a proof that the human behaviour can be described mathematically (predicted with approximation). It was a study on marriage and divorce. Muralidhar made an affirmation referring directly to me and I've answered with a joke.

This simple fact has led to counter-reactions. I am sure that the person who has down-voted the comment has not followed the whole discussion and has no idea on what it has been discussed in that context.

Earlier today I've made an affirmation about maths being an alternative language, making a point similar to the one made by Dimitris. Then we've discussed maths, quantitative and qualitative algorithms, maths and cognitive science a s o.

In the end all it counts is to talk about soul and ghosts and there you have the strong and passionate reactions, both pro and contra. Sorry, but this genre is not my cup of tea!

Dear Emanuela

I also can't understand why such a well structured question is voted down? I just take it in my stride. I suggest dear Emanuela you do the same. It is not worth ruining your cup of tea!

Dear Issam, I agree. In a way I should be happy because the RG confirms the theory that there are no objective truths, but only socially (subjective) constructed truths, this means also changeable. We can always change the mind and evolve from our safe cocoon of preconceived ideas into something else, a bit more free and exciting :)-

Ana Maria, I've asked 'oncle' google to translate for me :)-

It's very easy, not exactly but helps.

all planets stars and the moon fluw sertan orbits calculated by mathmatics

tree growing time need mathmatics cacullation

Finaly .Imprtant disegens in our live have to be cacullated carfuly*

What is mathematics? Mathematics is abstract thinking, which offers an intelligent being. You can teach a monkey to stick touched the banana, but you can not teach an equation of the circle.

We discuss relations between Nature, Science and Mathematics.

Nature is more exciting, great and strange. Science is system to know Nature!.Mathematics is great tool for that, but only a instrument. We can like mathematics, but Man intelect is more exciting, science totaly-too, and Nature-much more!!!

Dear Georgi

This may be is why nature is called mother nature(or mother Earth)! The common personification of nature that focuses on the life-giving and nurturing aspects of nature by embodying it in the form of the mother can be equally used to represent the science-giving and math-giving aspects of nature!

Dear Issam Sinjab! I am agree on 100%! I wrote my ansver because some others told only on mathematics !

Mathematics is a language for expressing relations. Science tries to discover the invariant relations in Nature. Any knowledge is about relations. Any living organism is in relation with a Nature through its body. The structure of this relation is built-in in the sense-acting system of the living organism reflecting as a mirror nature from a certain viewpoint. Leibniz call that a monad. Through biiological evolution, the relations of nature (which are mostly relations among living things) get gradually internalized into the sense-acting systems of the higher living organisms. The stoics thought that the human body is a microcosm that is a mirror of the macrocosm. The very structure of our senses is a kind of implicit theory of the world with all its relations implicitly known. Human we are the only animal which have imagination. What is it? It is similar to dreaming while we are awake. Our awareness field is split between regular animal awareness and self-awareness. Through self-awareness we access to structure of our sense-acting system which is an implicit platonic world of the relation of the world. The core of mathematics and science is built-in and it is why we could later rediscover this by inventing science and mathematics.

I hate to be an iconoclast here, but I believe that mathematics is an invention of the mind, and purely a human description of things. No mathematics is a perfect description of reality. All mathematical descriptions are approximations. A mathematical equation that expresses something in physics is merely a compression of that physics. All compressions are lossy. There will always be Nth order terms that are missing, but we ignore those for practical purposes. I suspect that we will one day find that the inverse square law for gravitation probably has some extremely tiny correction terms that we have missed out, but that we get away without them for most practical purposes.

The diffraction pattern that that light makes when it passes through a slit can be described by a Fourier transform. However, photons know nothing of Fourier transforms, they just do what is in their nature. The Fourier transform is our human description that we have artificially overlayed on the phenomenon and it forms our human way of understanding it.

The number pi does not exist in Nature. It is purely an artifact of the human mind. Think about it: in Nature there is absolutely no such thing as a perfect circle. A perfect circle is a product of the human imagination. So when people say "isn't it wonderful that when we look at all the equations, pi seems to appear everywhere in Nature," I say "no, you are just imagining that." Pi in fact appears nowhere in Nature at all. That is a human artifice.

Scientists who think like me about this are called non-Platonists, and scientists who think mathematics is all part of Nature and waiting to be discovered are Platonists. Probably more mathematicians are Platonists than Physicists. Physicists behave strangely in that when they are together in conferences in peer groups they behave like Platonists, but then when you question them in a quiet room when no-one else is listening they appear to be non-Plationists deep down. Engineers are probably the biggest group of non-Platonists and are more honest about it.

I am essentially a physicist who finally got in touch with his inner non-Platonist :-) I consciously converted to non-Platonism when I was about 18-years old, and it was a very liberating experience. Before then I had huge philosophical problems with physics that have now disappeared, because I take a more practical approach and differentiate between human constructed models and what is real.

Do you think that without human maths no exist?