Is Mathematics Alone a safe medium for exploring the frontiers of Science. Or should Observation and Hypothesis lead in front ?

[swansont]

The only times professional mathematicians do touch numbers and formulae are when they have to do something mundane such as balancing their bank account statement or paying a restaurant bill.

 

A mathematician colleague of mine remarked on several figure-the-restaurant-bill occasions that he was a mathematician, not an arithmatician.

[Mike Smith Cosmos]

It does, sometimes. You're asking for something that already takes place, but phrasing it as if it was something new. Like someone with button-fly jeans demanding that someone invent the zipper.

 

 

I invite you again to come up with an example of this happening.

 

The location of an irregular object within a container . No Maths will describe its location, at a particular time. [a dried pea in a bottle.]

 

 

The location of a bee within an atmospheric weather testing balloon . No maths will describe its location or can compute the time to reach a particular location.

 

 

The location of a mosquito in the Wembly Stadium in England with its all weather covering in place, at a time t , or the time it takes to reach a location.. ( x,y z )

 

 

I understand an electron in an atom is roughly the same ratio of a mosquito in the Wembly football stadium.

 

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~

 

The location of an electron in a particular energy band within the atom , at a particular time t or the time it takes for an electron to be at a specific location.

 

 

 

I believe the universe is full of gaps of not STRICTLY able to be mathematically calculated, Possibly statistically , but that is just a ruse to try and place it within the sphere of maths.

 

MATHS COMPUTE NO MATHS COMPUTE MATHS COMPUTE

 

 

Quantum physics is full of these mystery gaps , the natural environment is full of these gaps, the universe at large has many gaps .

 

In other words part of the universe can be modeled with Maths , Part of the universe can NOT be modeled effectively with Maths [ no good saying statistics is maths ,( that is just semantics ) ]

 

Now you guys have a dilema. You either say NO Maths NO PHYSICS . You are left with a lot of uncovered areas.

Or you say Yes there are gaps, and we are going to accept that BLUE SKY RESEARCH WITH CONCEPT/ HYPOTHESIS is going to have to lead the Way. ( even without effective maths. )

 

You are creating a false dichotomy here. Your diagrams, along with much that you have said in this thread, implies that "math boffs" are incapable of being creative thinkers. That in turn is motivated by your view that mathematics is a rigid world of numbers, canned formulae, and not much else. Neither one is the case.

 

The fact is that physics and mathematics have long been intertwined. Sometimes physics has pushed the boundaries of mathematics. Other times new mathematics have allowed physicists to push the boundaries of physics.

 

Your rigid view of mathematics as comprising numbers, canned formulae, and not much else is simply not the case. In fact, professional mathematicians can go for months, years, and entire career without using algebraic formulae. The only times professional mathematicians do touch numbers and formulae are when they have to do something mundane such as balancing their bank account statement or paying a restaurant bill.

 

There is plenty of room in the sciences for people who think calculus is hard mathematics. (It isn't. Calculus is what budding mathematicians and physicists learn when they first enter college, if not earlier.) Vast portions of the life sciences and social sciences are largely void of mathematics. Not in physics, however. There is no escaping the deep entanglement between physics and mathematics. If you aren't doing math you are doing physics.

 

There is a lot here, I do understand and agree with. Its just this particular Dogma ( No Maths Not Physics , Not Science ) that I am trying to say is dangerous for limiting Blue sky research. And because of this I am suggesting we do not put Only Maths as the guiding light into The Borders of the unknown.

Edited May 31, 2013 by Mike Smith Cosmos

[swansont]

The location of an irregular object within a container . No Maths will describe its location, at a particular time. [a dried pea in a bottle.]

 

 

 

The location of a bee within an atmospheric weather testing balloon . No maths will describe its location or can compute the time to reach a particular location.

 

 

 

The location of a mosquito in the Wembly Stadium in England with its all weather covering in place, at a time t , or the time it takes to reach a location.. ( x,y z )

 

 

 

I understand an electron in an atom is roughly the same ratio of a mosquito in the Wembly football stadium.

 

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~

 

The location of an electron in a particular energy band within the atom , at a particular time t or the time it takes for an electron to be at a specific location.

 

 

 

I believe the universe is full of gaps of not STRICTLY able to be mathematically calculated, Possibly statistically , but that is just a ruse to try and place it within the sphere of maths.

 

You forgot the second part of this: explain how these answers are arrived at without the use of math.

[Mike Smith Cosmos]

You forgot the second part of this: explain how these answers are arrived at without the use of math.

 

Well they are not yet . If ever ! There are no causal links that can be calculated in these instances.

 

That is it . We may well be living in a universe that is :

 

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

Non deterministic as a whole and thus the mold principle may be the only way when dealing with such matters.

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

 

[ CALCULATION NOT POSSIBLE IN THESE INSTANCES

only the remainder /most/ major /half/ minor are calculable with maths ]

 

 

EXCEPT CALCULATION NOT POSSIBLE IN THESE INSTANCES

 

 

 

 

EXCEPT CALCULATION NOT POSSIBLE IN THESE INSTANCES [ RED LINE]

 

 

 

CALCULATION NOT POSSIBLE IN THESE INSTANCES

 

 

MATHS can NOT cover ALL of Physics

 

 

~~~~~~~~~~~~~~~~~~~ QED ~~~~~~~~~~~~~~~~~~~~

Edited June 1, 2013 by Mike Smith Cosmos

[swansont]

Well they are not yet . If ever ! There are no causal links that can be calculated in these instances.

 

That is it . We may well be living in a universe that is :

 

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

Non deterministic as a whole and thus the mold principle may be the only way when dealing with such matters.

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

 

[ CALCULATION NOT POSSIBLE IN THESE INSTANCES

only the remainder /most/ major /half/ minor are calculable with maths ]

 

 

EXCEPT CALCULATION NOT POSSIBLE IN THESE INSTANCES

 

 

EXCEPT CALCULATION NOT POSSIBLE IN THESE INSTANCES [ RED LINE]

 

 

 

CALCULATION NOT POSSIBLE IN THESE INSTANCES

 

 

MATHS can NOT cover ALL of Physics

 

 

~~~~~~~~~~~~~~~~~~~ QED ~~~~~~~~~~~~~~~~~~~~

 

 

You've moved the goalposts. Nobody has put forth the claim that all problems are solvable.

 

You were supposed to give examples of "Concept followed by hypothesis followed by Experimental proof YET with NO maths yet found to support the Hypothesis and Experimental proof". Your location examples: how do you find the location without maths? Because if you haven't, each is simply a problem without a solution, not a problem with a math-free solution.

 

So let's have them: physics problems with math-free solutions

[Mike Smith Cosmos]

 

 

You've moved the goalposts. Nobody has put forth the claim that all problems are solvable.

 

You were supposed to give examples of "Concept followed by hypothesis followed by Experimental proof YET with NO maths yet found to support the Hypothesis and Experimental proof". Your location examples: how do you find the location without maths? Because if you haven't, each is simply a problem without a solution, not a problem with a math-free solution.

 

So let's have them: physics problems with math-free solutions

 

Well I will have a go. but ' i am caught between the devil and the deep blue sea '.

Because if I come up with what i feel is a reasonable solution, You will say , "Not Valid , No Maths, Not Physics, Not science , Dogs and Ducks, you can not be serious "

 

I am not saying I am going to come up with dogs and Ducks, But the universe is rather filled with Animals Soils Stars, water and all of natures lovely things , which only exist by Physics , quantum behavior, electron chemistry Tulips beautiful ..this That and the other. So I am likely to call on one of these as a Physics understanding of how things work. What I might well not be able to do is give you figures. Figures are numbers and numbers infer Maths.

 

 

 

oops!

 

WUFF I can count to ONE

 

One Bone !

 

One Cat!

 

 

I have it TWO DUCKS I can count to Two!

 

 

Hang about there is something wrong here. Itttsss Treee three ducks Eureka I am breaking new ground here !

 

 

 

 

Ok. The challenge is on :-

 

A Physics solution with as yet no maths, but based on Concept ,Hypothesis, observation , experiment proof and conclusion. .

So let's have them: physics problems with math-free solutions [ Swansont]

 

How about a Bottle of Italian Prosseco on this one ? That gives me 14 days .

. PHYSICS

 

 

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phys·ics noun plural but singular or plural in construction \ˈfi-ziks\

Definition of PHYSICS

1

: a science that deals with matter and energy and their interactions

2

a : the physical processes and phenomena of a particular system

b : the physical properties and composition of something

Origin of PHYSICS

Latin physica, plural, natural science, from Greek physika,from neuter plural of physikos of nature, from physis growth, nature, from phyein to bring forth — more at be

First Known Use: 1715

Other Physics Terms

amplitude, centrifugal, centripetal, convection, gradient,hysteresis, kinetic, lase, quantum

phys·ics noun plural but singular or plural in construction \ˈfiz-iks\ (Medical Dictionary)

Medical Definition of PHYSICS

: a science that deals with matter and energy and their interactions in the fields of mechanics, acoustics, optics, heat, electricity, magnetism, radiation, atomic structure, and nuclear phenomena

physics (Concise Encyclopedia)

Science that deals with the structure of matter and the interactions between the fundamental constituents of the observable universe. Long called natural philosophy (from the Greek physikos), physics is concerned with all aspects of nature, covering the behaviour of objects under the action of given forces and the nature and origin of gravitational, electromagnetic, and nuclear force fields. The goal of physics is to formulate comprehensive principles that bring together and explain all discernible phenomena. See also aerodynamics;astrophysics; atomic physics; biophysics; mechanics;nuclear physics; particle physics; quantum mechanics; solid-state physics; statistical mechanics.

 

 

 

LOOKS LIKE :- PHYSICS IS : about

 

 

Matter, Energy, Systems,

Properties, Composition

Growth, Being , Nature

 

 

methinks !

 

http://www.ago.net/assets/images/556/1029-594.jpg

 

 

 

Edited June 1, 2013 by Mike Smith Cosmos

[robinpike]

 

 

You've moved the goalposts. Nobody has put forth the claim that all problems are solvable.

 

You were supposed to give examples of "Concept followed by hypothesis followed by Experimental proof YET with NO maths yet found to support the Hypothesis and Experimental proof". Your location examples: how do you find the location without maths? Because if you haven't, each is simply a problem without a solution, not a problem with a math-free solution.

 

So let's have them: physics problems with math-free solutions

 

Mike, you will struggle with this because the above request has innocently assumed that proofs represented by maths can be shown to be absolute proofs. But no method of proof is absolute.

 

I would turn this around and argue that the proofs using maths are not proofs themselves either.

 

When it comes to fundamental physics, the mathematical theories that are taken as being absolute proofs, will contain assumptions that the proof relies on.

[swansont]

Mike, you will struggle with this because the above request has innocently assumed that proofs represented by maths can be shown to be absolute proofs. But no method of proof is absolute.

No.

 

I am not asking for "proofs represented by maths". I am asking for the promised science that contains no math.

 

robinpike, on 01 Jun 2013 - 10:02, said:

When it comes to fundamental physics, the mathematical theories that are taken as being absolute proofs, will contain assumptions that the proof relies on.

Which is tested when one compares the predictions with the result.

[robinpike]

 

No.

 

I am not asking for "proofs represented by maths". I am asking for the promised science that contains no math.

 

Which is tested when one compares the predictions with the result.

 

But there are lots of ways to obtain understanding in science without using maths.

 

Maths is just one form of reasoning, but there are others. For example, I am reasoning with you right now, but I am not using maths to do it.

 

In science, it is possible to understand something pictorially as well as mathematically.

[swansont]

But there are lots of ways to obtain understanding in science without using maths.

 

Maths is just one form of reasoning, but there are others. For example, I am reasoning with you right now, but I am not using maths to do it.

 

You aren't doing science, either, and the challenge was not "to obtain understanding." The hurdle is going to remain at the height at which it was originally placed.

 

In science, it is possible to understand something pictorially as well as mathematically.

 

Mapping and graphs are a subset of math.

[robinpike]

You aren't doing science, either, and the challenge was not "to obtain understanding." The hurdle is going to remain at the height at which it was originally placed.

 

Yes, but my point is that maths is no more valid a method of reasoning than other methods - and more to the point, maths is no more valid as absolute proof of a theory than other methods.

 

So, I believe that the suggestion is that maths is the only valid method of proving a scientific theory?

 

So as I suggested, in that case let's turn this around and use an example of a scientific mathematical theory that has been proven to be correct.

 

How about the behaviour of an electron near to a proton?

 

Is it the case that maths has been used to prove that the electron is an entity that, when near to a proton, exists only at any point in space as a probability?

 

Or if I have worded that badly, or indeed incorrectly, state what the mathematical theory of an electron near to a proton has proved to state, so that I may respond correctly.

Edited June 1, 2013 by robinpike

[swansont]

Yes, but my point is that maths is no more valid a method of reasoning than other methods - and more to the point, maths is no more valid as absolute proof of a theory than other methods.

 

So, I believe that the suggestion is that maths is the only valid method of proving a scientific theory?

No, I don't believe that to be the case. It has been suggested that math is a necessary part of formulating and demonstration the validity of a theory.

So as I suggested, in that case let's turn this around and use an example of a scientific mathematical theory that has been proven to be correct.

 

How about the behaviour of an electron near to a proton?

You mean like the QM solution of the hydrogen atom?

Is it the case that maths has been used to prove that the electron is an entity that, when near to a proton, exists only at any point in space as a probability?

You can't propose that an electron has a probability of existing which varies with position without math.

[Mike Smith Cosmos]

---------------------------Sono assente per 14 giorni -----------------------

senoir Ariva Derce

[ajb]

A mathematician colleague of mine remarked on several figure-the-restaurant-bill occasions that he was a mathematician, not an arithmatician.

My wife is far better at mental arithmatic that I am, she does the shopping and keeping track of our spending!

[Mike Smith Cosmos]

.

. The bottle of Prosecco is still on ice. And I am still thinking hard !

 

 

 

One thing that has become clear to me , is that the operation of the universe uses both techniques to maintain its functioning in the areas of :-

 

Matter, Energy, Systems,

Properties, Composition

Growth, Being , Nature

 

namely:-

 

areas of the above are clearly precise, predictable, ,can be defined by mathematical systems,

 

but other

 

areas are not based on deterministic principles,causality,formulated systems but rather " if it works, it prospers", "if it fails ,it declines" the universal mold ( the sum of everything that has gone before ) ,dictates the possible achievable goals..

 

 

Both systems seem to work in tandem to keep the Universe going in the way it does.

 

 

Perhaps this is why we have two different parts to our brain, two different sexes etc.

 

.

Edited June 22, 2013 by Mike Smith Cosmos

[studiot]

I think Mike has a valid point here that there is more to Science than mathematics, although I consider it extremely restrictive to exclude mathematics. It is a question of striking the right balance.

I also like the example of the drunken man and the lamp post.

In post#111 of another thread I offered the quick off the cuff example that IMHO has relevence here.

 

http://www.scienceforums.net/index.php?app=core&module=search&do=user_activity&mid=74263

 

 

Consider the mixing of concrete, without any mathematics at all.

Take some aggregate, sand, cement and water and mix them together. This will form concrete.

Or will it?

Only if you are lucky enough to arrive at reasonable proportions.

So to try again

Mix 4 parts by weight of aggregate with 2 parts by weight of sand and one part by weight of cement.

Add water and continue mixing, until the required consistency is achieved.

This will get you a respectable concrete.

Note that the instructions are part mathematical – for the dry ingredients

And part procedural for the water. This part cannot be mathematical.

But both types of analysis are required to get good concrete, you cannot exactly quantify the required water.

Note the emboldened part that offers a technical (scientific) issue that cannot be described by mathematics.

Edited June 22, 2013 by studiot

[swansont]

I think Mike has a valid point here that there is more to Science than mathematics

 

A point that I think nobody has disagreed with, but (as you say) you can't exclude math from it.

[studiot]

Reading back over this topic, I note someone identified diagrams as mathematic.

 

I disagree.

 

Diagrams are a discipline in themselves, which Mathematics, along with many other disciplines, makes good use of.

 

A point that I think nobody has disagreed with, but (as you say) you can't exclude math from it.

 

Indeed so.

 

However, looking at it from a fresh perspective, I would say you can't exclude Physics (and other sciences) from Mathematics.

Applications provide a whole point, motivation, raison d'etre or what you will for all but a few diehard purists.

[swansont]

However, looking at it from a fresh perspective, I would say you can't exclude Physics (and other sciences) from Mathematics.

Applications provide a whole point, motivation, raison d'etre or what you will for all but a few diehard purists.

 

I'm not so sure. I get the impression that quite a few mathematicians don't care if there is an application for the math they work on.

[studiot]

Would you consider a man who wants to exclude knowledge from all other disciplines in his work wise or foolish?

Edited June 23, 2013 by studiot

[Sato]

I don't understand what the fuss is; mathematics (formal or informal) is just logical and quantitative thinking. Mathematics is what you're using when you conduct any sort of thought experiment, especially in physics, and the greater the mathematical ability the greater the capacity to generate larger and more precise thought models and ideas. Of course, in order to express these models and ideas to other people you need a method of communication, that being formal mathematics such as algebra, trigonometry, calculus, linear algebra, etc. Sometimes the ideas are of such complex systems that complicated expressions must be used, otherwise there wouldn't be any way to accurately communicate the ideas, so you can't complain about there being "too much" mathematics in the theories unless you're only looking for a watered down and inaccurate understanding that you can use to fool yourself into thinking you have some sort of understanding of the actual phenomena.

[D H]

I'm not so sure. I get the impression that quite a few mathematicians don't care if there is an application for the math they work on.

 

I knew quite budding mathematicians who went into that field precisely because there was no practical application for the mathematics they planned to work on. They realized they had what it takes to major in / get a PhD in either mathematics or physics. Either way, whatever they worked on would eventually lead to better bullets, better bombs, better ways to kill people. The difference was that if they went with physics those nastier applications of their work would see fruit in their lifetime. With mathematics, they could die in peace because those nastier applications would only take place after they had died.

 

(That, plus the fact that math (to them) was easier than physics. Physics majors tended to be homework animals. Math majors: Party animals. A corollary is that obtaining a math PhD takes two to three years less time than does obtaining a physics PhD.)

[ajb]

However, looking at it from a fresh perspective, I would say you can't exclude Physics (and other sciences) from Mathematics.

Applications provide a whole point, motivation, raison d'etre or what you will for all but a few diehard purists.

This is a very good question.

 

It seems that most of the very important things in mathematics either have their roots clearly in physics or have found applications very quickly. Why this is so I have no idea, but it is clear that having good motivation and applications in mind helps stimulate the mathematical research.

 

The extream "limit" of this is Tegmark's mathematical universe hypothesis. It states that "Our external physical reality is a mathematical structure". More than this, it is often interepreted as saying that all mathematical structures will find a physical application.

I'm not so sure. I get the impression that quite a few mathematicians don't care if there is an application for the math they work on.

Right, though there are plenty that find it facinating that their abstract ideas can have anything to do with physics. One just has to wonder about Tegmark's idea.

 

I knew quite budding mathematicians who went into that field precisely because there was no practical application for the mathematics they planned to work on.

I see it now quite a lot with fellow postdoc and PhD students in mathematics. They have very little idea where some of the ideas originate nor the general applications. To me this is like having dinner without the dessert; you maybe full and contented, but you miss the big suprise at the end. Edited June 24, 2013 by ajb

[D H]

It seems that most of the very important things in mathematics either have their roots clearly in physics or have found applications very quickly. Why this is so I have no idea, but it is clear that having good motivation and applications in mind helps stimulate the mathematical research.

 

The extream "limit" of this is Tegmark's mathematical universe hypothesis. It states that "Our external physical reality is a mathematical structure". More than this, it is often interepreted as saying that all mathematical structures will find a physical application.

Right, though there are plenty that find it facinating that their abstract ideas can have anything to do with physics. One just has to wonder about Tegmark's idea.

There are a number of variations on this theme. Roland Omnès' physism, V. I. Arnold's notion that Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. I suspect that Arnold would have vehemently disagreed with Tegemark. Arnold most certainly decried the non-physical mathematics that was becoming vogue at the time he wrote his remarks.

 

It's also good to note that Eugene Wigner's "unreasonable effectiveness of mathematics in the natural sciences" does not apply to all of the sciences. I. M. Gelfand's counter to Wigner's unreasonable effectiveness was that Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.

[Mike Smith Cosmos]

I have thought long and hard about this 'dance' of Physics and Maths .

 

maths is based on number , number infers discrete items, Physics IN PART ONLY ( Particle Physics Only )

 

How these numbers relate and dance is the outworking of Mathematics.

 

It has been said that the physical ( hence Physics), World, is the outworking of Mathematics , which is, among others, Mike Tegmarks' ideas.

 

However that might have some weight, if THAT is all, that makes up the Cosmos. Even then Maths is by no means yet a completely mapped discipline . ie there could be much more maths yet to be developed or discovered )

 

BUT, the Cosmos contains much more than Particles, and their interplay.

 

Through discussion, argument , observation , experiment and otherwise , I have come to the conclusion that the Cosmos contains much more than Particles that dance the way of mathematics.

 

As well as particles there are whole things [not divided into numbers or arrangements of particles ] , Fields, probabilities based phenomenon , non causal based events, biological development, emergent phenomenon , and the list can go on. And although maths can attempt a shadow of fields, probabilities ,etc it [maths] is by then, no longer absolute , proof giving, a predictive driving, shaping force. No . !

 

Mike

Edited August 13, 2013 by Mike Smith Cosmos