Does mathematics really exist in nature or is math just a human construct?

No. Necessity and Sufficiency are concepts from formal logic OR the philosophy of causality.

The presence/occurrence/truth of that which is Sufficient requires that which is Necessary also exist/happen/be true.
The absence/non-occurrence/falsity of that which is Necessary requires that which is Sufficient also not exist/not happen/be false.

Depending on your formalization choices, such relationships can be written in terms of logical/causal implication, S→N; logical negation and disjunction, N∨¬S; class inclusion: {x: S(x)} ⊆ {x: N(x)}; or class intersection, {x: S(x)}∩{x: ¬N(x)} = ∅.

I think you have lost the thread. The Lagrangian is a human-made function in the field of human-made physics that describes the behavior of a classical physics system. It is neither unique nor responsible for the behavior of reality. The map is not the territory and even if you bring all the maps, the territory cares not.

You are confusing necessary and sufficient when it is the case that if it were true that the universe were governed by mathematics, it would necessarily be true that mathematics could be used to describe its behavior and it is also the case that if the universe were governed by a function that the universe would be governed by mathematics. and if physics could be reduced to a function then mathematics could be used to describe the universe's behavior. But it has not been shown that the universe is governed by a a function. Quantum mechanics suggests the opposite. In addition, Lagrangian mechanics does not show physics is governed by a function in that a great number of equivalent Lagrangians exist for any hypothetical situation and in quantum physics, the integrated Langranian over the prospective trajectory is a functional which does not dictate the outcome but only the probability of outcome.

 

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Thank you for responding. I understand the human application of *probability theory", a human mathematical concept.
Allow me a few more questions. In view of the following statements,

and

and

https://en.wikipedia.org/wiki/Probability#Summary_of_probabilities

Even if the fundamental functions of the universe are probabilistic, does the *permittive condition* of *near infinite potential* in a "near infinite space* with *infinite time* (or timelessness), result in an inevitable event?
The highlighted red seems to indicate that IF we did know all the conditions present, would we discover that all universal functions are fundamentally mathematical processes?

I have a real problem with being given the choice between *order* as some form of persistent universal mathematical deterministic functionality, whereas *chaos* is a form of persistent mathematical *disorder*. In a persistent disorderly universe how could we even invent the mathematics that describe orderly functions?

 

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Because mathematics is a product of logic, not of observation. That at least is my contention.

Both order and disorder (randomness) seem to be intrinsic features of the universe.

If it makes you feel better, true randomness is a mathematical concept, too.

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But it is still a language and like all languages it's man-made.

 

So? It is used to describe and illustrate the laws of physics, GR and the Universe/spacetime of which we inhabit. They evolved at the BB.

 

"A rose is a rose, by any other name"

 

And more than just GR. GR is infant mathematics. To the Universe.

Mathematics is about shapes and energy.

 

And the inherent potentials (human values) of these dynamic forms and their positive or negative interactions and processes, in accordance to mathematically allowed or disallowed processes (human equations).
The point is, that if you take away the observer, the universe will continue to function as it *must*. A simple language of *If --> Then*, which allows for a near infinite way of expression, of which we can only see a glimpse now and then. A *discovery* of a natural process, translatable into human mathematics.

 

Exactly ; which so few understand

Take the observer out of the picture .

The Universe does what it does.

We discover.

You ; Write4U understand ; excellent

 

No mathematics is not about "shapes and energy".

Energy is a physical concept without any definition in mathematics.

Shapes, i.e. geometry, is a branch of mathematics, but there is plenty of mathematics that is not geometry.

 

a) How many branches of mathematics are there?

b) is the calculation of *potential* energy or the measurement of *forces* also a branch of mathematics?

c) is the geometry of the universe also a branch of mathematics?

d) if everything measurable object or event in the universe is a branch of mathematics, then what is the Mathematical Function?

There seem to be a lot of little branches of mathematics related to universal functions. Does that tell us something about the Mathematical nature of the functions of the Universe?

 

Well, that is a sweeping statement and utterly wrong.

And what is the definition of language? IMO, it is only a means of *information sharing*.
If I spit in someone's face am I expressing a language or exchanging information?
When a dog bares his teeth, is he expressing a language or exchanging information?

Human laguage (grunts and clicks) is just another means of exchanging information. In Science, scientific notation is merely another form of exchanging information. When a positive particle bonds with a negative particle, are they exchanging information? Can that information be translated into mathematical expression?

 

E = Mc^2 is not mathematics?

But is there geometry without mathematics?

http://www.britannica.com/topic/geometry

 

Whut?

The fact that E=mc² is a mathematical expression does not mean that energy is a mathematical concept. I can say, "Elvis était Americain", without it following that Elvis was a Frenchman. Right?

None of the terms in that expression is a mathematical concept. E, m and c are physical quantities, not mathematical concepts. The mathematical concepts are symbolised by the equals sign, the placing of symbols for two variables next to one another to denote that they are multiplied together and the superscript 2 denoting something multiplied by itself.

And the fact that I describe geometry as a branch of mathematics obviously implies that all geometry is mathematics, but not - durh - that all mathematics need be geometry.

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a) Lots, depending on your definitions. Try this for a start: https://en.wikipedia.org/wiki/Lists_of_mathematics_topics
b) No. A calculation of potential energy is an application of mathematics. You might as well ask whether the act of tightening a screw on a door hinge is a tool in your toolkit. Measurement of forces is experimental physics, not mathematics at all.
c) No. See (b). Though if it becomes a sufficiently complex problem, it is possible that someone might decide to devote a branch of applied mathematics to the problem.
d) since every measurable object or event in the universe is not a branch of mathematics (see a, b and c), the question is otiose.

There seems to be something badly wrong with your understanding of what mathematics is. Is that what comes of a career in accountancy?

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On the contrary I think Pluto is dead right. Mathematics is the language of quantitative logic.

 

No, it follows that Elvis had a Nationality other than French and that it can mathematically proven that America is not in the same geometric location as France.

Is the expression E = Mc^2 a mathematical equation?

Clever, but it does mean that all geometry is mathematical. Thus, in view that the universe is a geometrical structure it is, by your own words, mathematical.

Name me a property or a function of the universe that cannot be equated by a human mathematical expression, eventually. You only need one to disprove the concept that everything in the universe functions in accordance to *some* kind of mathematical value or function, regardless if we have discovered this process or will at a later date, or maybe never.

 

On the OP issue, I have a question and opinion in one: Isn't mathematics a special branch of logics?

My argument in support, based only on my own personal understandings of those two things: If I understand correctly, logics is about the relationship between concepts and objects, and the logical consequences of those relationship if the train of logical steps from the starting relationship is followed to some conclusion that is not logically inconsistent with the premise used to posit the initial relationship; while mathematics is about the relationships between objects and quantities, and the operations upon these, following mathematical rules derived from the initial axioms, to give some further resultant object or quantity consistent with the changing or constant values from starting equation and expression to final mathematical consequences of those changes and constants.

Applying this view of mathematics, I can only see the universe in logical terms only, not in mathematical terms. This is because in mathematics there are solutions which do not relate to any physical condition or object. There also are expressions and terms in mathematics, like infinity, singularity and limits which are purely mathematical concepts not existing or occurring in Nature except in the sense of quantum uncertainty, infinite universe and saturated states of energy per unit volume (eg, singularities of BH Event Horizons and BH central spacetime energy or mass content) and such like theoretical extremes which we cannot directly access with our instruments.

So to the OP: My opinion is, maths does not exist in nature; it is a more refined logics system used to analyze and describe the behavior of a nature which existed and created its patterns and variability according to natural relationships determined by its fundamental states and potentials for those states, whether or not we humans existed to devise a mathematical branch of logics to model and convey that natural phenomena to each other, as with any other descriptive language but with more precise concepts and quantities being the main emphasis and goal of the meanings conveyed via our mathematics.

I hope my opinion does not offend anyone. It is only my opinion. Thanks.

 

IMO, you have this in reverse order.

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

or

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470551380.html

or

https://www.quora.com/What-is-the-difference-between-logic-and-mathematics

 

Thanks, Write4U. I read your references as supporting my opinion as to which has primacy, logics or mathematics. I note that the basics and tenets of logics are necessary to the further development of any mathematical system. That is precisely what I meant. All reasoning systems are logics. Mathematical reasoning system is a sub-set of logics, as your last reference puts into proper context in the last sentence. That is, the axioms and all other characteristics which make mathematics what it is as a system of reasoning, are dependent on the logics capabilities and methods to prove the train of reasoning is valid or not. Logics underlies all reasoning systems; mathematics is a strictly axiomatic system whose axioms are akin to starting premises in logics system. The logics premises set are generalized in nature; the mathematics axioms set are specific to a special mathematical sub-branch of that generalized logics system. That is why I have the opinion I have posted. I could be wrong in the opinion I hold; but I don't see your references proving me so. Have you any other counter arguments against my stated opinion?