Need some evidences from other disciplines about >3D space

[blue89]

in pure mathematics we commonly use >3D spaces. there will be many many types which are formulated. but I do not know whether we use any of them as an actual usage in life of science.

I see at this document https://en.wikipedia.org/wiki/Hilbert_space hilbert spaces are being used at physics discipline and/or electric electronic engineering.

I request anyone to provide any sample of direct usage of >3D space(s) as evidence if there exists or how its usage is.

(note only formulizations are not acceptable, usage is required.)

Edited September 6, 2016 by blue89

[kisai]

 

 

I request anyone to provide any sample of direct usage of >3D space(s) as evidence if there exists or how its usage is.

 

I have captured some 3D space inside my coffee cup. Sometimes it is inhabited by air and sometimes by coffee. I find it much more interesting when the space contains coffee.

Edited September 6, 2016 by kisai

[ajb]

Phase spaces in classical mechanics (assuming autonomous) are 6 dimensional - 3 positions and 3 momenta. So classical mechanics and control theory applied to engineering often uses spaces (usually smooth manifolds) of dimension greater than 3.

 

In physics 4 dimensional manifolds are to be found in relativity theory.

 

Infinite dimensional spaces are often found in functional analysis as applied to engineering and physics - you already stated Hilbert spaces and quantum mechanics. But other spaces such as Banach and Fréchet spaces also appear.

 

There are also more general notions of 'spaces' that appear in physics, I am not such if they appear in engineering.

[blue89]

THANKS for your reply!

could you provide pictures of usage. it should be effective.direct usage defines just this meaning at real.

for instance , Euclid space's 3D can be shown. (both formulization and picturing)

[ajb]

could you provide pictures of usage.

Pictures? Not really, but you can find textbooks and papers that use these notions.

[blue89]

Pictures? Not really, but you can find textbooks and papers that use these notions.

 

Dear ajb , we already know in mathematics there is numerous theories related this context.

but I could not see the picture / apperance which might prove it realistic.

Let remember/see what respective scientist :Stephen hawking says at my this thread http://www.scienceforums.net/topic/98054-a-query/

Edited September 6, 2016 by blue89

[ajb]

...but I could not see the picture / apperance which might prove it realistic.

What do you want a picture of?

 

Anyway, as you are interested in engineering, geometric mechanics with constraints and control theory has been applied to many things including space-craft, underwater craft etc. The methods are also being exploited in economic theory.

 

You can google more for details.

[Phi for All]

Let remember/see what respective scientist :Stephen hawking says at my this thread http://www.scienceforums.net/topic/98054-a-query/

 

!

Moderator Note

Please don't use one thread to advertise another. If necessary, simply repeat the relevant quote.

 

Don't respond to this note; just remember not to do this, please.

[studiot]

You should look up

 

Generalised Coordinates

Degrees of freedom

 

Which are used in many areas of science an engineering

 

Thermodynamics and statmech - Gibbs Formulation

Mechanics - Hamilton - Lagrange dynamics

[blue89]

 

"

 

Generalised Coordinates

Degrees of freedom

"

 

 

what is the actual meaning of this two sentences/phrases?

Edited September 6, 2016 by blue89

[ajb]

what is the actual meaning of this two sentences?

You can usually treat the collection of all possible values of the parameters that describe a rigid body or a collection of bodies or particles as coordinates on a smooth manifold.

[blue89]

You can usually treat the collection of all possible values of the parameters that describe a rigid body or a collection of bodies or particles as coordinates on a smooth manifold.

 

the second phrases please ,that one and the following phrases' (the second ones') meaning is alrady obvious in its first meaning.

I did not ask the first meaning I thought that he might tell something seems like a secret

this are well known in all languages as a method of also cryptology

I asked just this one whether it existed.

 

anyway ,if there is not any else maning ,ok it has already been understood.

 

is there any else meaning

 

Degrees of freedom

about this sentence?

/phrase?

Edited September 6, 2016 by blue89

[ajb]

Degrees of freedom are the parameters - basic examples from mechanics include position, velocity or momentum.

[blue89]

1)Phase spaces in classical mechanics (assuming autonomous) are 6 dimensional - 3 positions and 3 momenta. So classical mechanics and control theory applied to engineering often uses spaces (usually smooth manifolds) of dimension greater than 3.

 

2)In physics 4 dimensional manifolds are to be found in relativity theory.

 

 

 

ok. could you specify please the first one .

no necessity for the second one. really I do not think that my knowledge would be enough for physics on this stage to allege so advanced expressions which are all quite interdisciplinary.

my methods will not be traditional already.

 

I am using quite different methods or try to use it. but probably it would be enough logical to think the possibility of such different methods.

[ajb]

ok. could you specify please the first one .

The best thing is to pick up a book on classical mechanics - or just read wikipedia for now.

 

Look up Lagrangian, momentum and phase space.

[blue89]

The best thing is to pick up a book on classical mechanics - or just read wikipedia for now.

 

Look up Lagrangian, momentum and phase space.

 

unortunately I don't believe me to achieve such bright things at mechanics.

 

but I have strong belief at electricity & optics and/or related these contexts.

to succeed/reach bright results.

[ajb]

unortunately I don't believe me to achieve such bright things at mechanics.

Okay, but the basic ideas are not so hard and this is what you are asking about. Anyway, we regularly deal with spaces of dimension greater than three in classical mechanics, statistical physics, thermodynamics and so on. All areas of physics that have found direct applications in engineering and so on.

[blue89]

wait plase for around 5-10 minute, I am checkind some keywords.

we regularly deal with spaces of dimension greater than three in classical mechanics ✔, statistical physics✘ , thermodynamics ✔ and so on. All areas of physics that have found direct applications in engineering ✔ and so on.

 

actually ,I think all these will provide the logical reason for why such qualified journals are not publishing heavily theoritic materials/papers. and they seem right on this issue. otherwise of course this will not be correct to refuse the necessity or worth of theoritic studies. these are different.

 

we know that in this century engineering studies are more lucrative. my interests about physics (to use at creation for engineering product would be : magnetism , electric fields , optics (lens - eyes (usage) some new methods or approaches) - radioactivity. waves. ...etc.

 

but I meant I don't have enough ability for mechanism. I may learn or create something. by I observedd that it takes much more times in comparişson to the interest subjects given above.

 

and as an example ,some new methods will/might be related with the usage of fundamental riemann's integral theories..

(integral forms)

[ajb]

actually ,I think all these will provide the logical reason for why such qualified journals are not publishing heavily theoritic materials/papers. and they seem right on this issue. otherwise of course this will not be correct to refuse the necessity or worth of theoritic studies. these are different.

What are you talking about?

 

Many good journals publish works in the areas I have stated here.

[blue89]

What are you talking about?

 

Many good journals publish works in the areas I have stated here.

 

I thought that great journals would also care the benefits of literatures.

for instance , if we explore / invent a treatment of one well known catastrpphic disease or a piece of it , that great journal and regularly almost all people will care it.

but thin please , I don't believe that honest mathematicians were not hardworking. in contrary this , they are generally study hard.

but think also the reason why they are living troubles just like me and other ones , although believe that they study hard ,they have economic matters. this is quite unethic.

but I am not complaining so much , this was my own abuse to choose so theoritic department. I should have chosen engineering in order not to live economic matters.

, anyway I believe this is UNIVERSAL truths ,so I request someones not to feel negative my this last sentence if they feel.

I will ask a question. now in order not to miss the goal of thread

Many good journals publish works in the areas I have stated here.

 

note: I have no clear idea about this point. this might be true ,too. could you show me any journal which publishes mathematical paper and its IF > 20 ?

Edited September 6, 2016 by blue89

[ajb]

for instance , if we explore / invent a treatment of one well known catastrpphic disease or a piece of it , that great journal and regularly almost all people will care it.

Well, lots of scientists will not cite such a paper unless they are working on something similar.

 

note: I have no clear idea about this point. this might be true ,too. could you show me any journal which publish mathematical paper and its IF > 20 ?

You have made the great mistake of trying to compare impact factor across different disciplines. You clearly cannot do this, and so your request is just meaningless.

[blue89]

 

 

Phase spaces in classical mechanics (assuming autonomous) are 6 dimensional - 3 positions and 3 momenta. So classical mechanics and control theory applied to engineering often uses spaces (usually smooth manifolds) of dimension greater than 3.

the question was this one, could you write some clear and succint instructions which may persuade us that >3D is actively used.

for instance if we would use a 1D ,we may choose a tool (V and m is not important there)

if we would like to use 2D dimension ,we may choose a circle as in electric field to use.

but if we would like to use 3D ,it would be better to use calender

there are only simple analogy that might be acepted as to picture.

but what about >3D to give as eaxmple?

[ajb]

the question was this one, could you write some clear and succint instructions which may persuade us that >3D is actively used.

Just simple classical mechanics of particles or bodies we need position and then we need some information about how the system evolves. In particular, as we usually have first order differential equations we need to also consider the velocity ; also we are often interested in phase dynamics and so we need momentum.

Edited September 6, 2016 by ajb

[blue89]

1)Well, lots of scientists will not cite such a paper unless they are working on something similar.

 

 

2)You have made the great mistake of trying to compare impact factor across different disciplines. You clearly cannot do this, and so your request is just meaningless. ✓

 

1) this may not be truth at medicine I think. because for instance while some diseases are caused by viruses , most of them are caused by bacterias. but bacterias & viruses are difinitely difefrent descriptions.

for instance , AIDS is caused by a type of virus. but tetanus is caused by a type of bacteria. both of these two catastrophic ilness have no actual solution after infection.

but I am sure ,when any medical dotor invent the treatment for any of these , with extreme probability this will not be valid for the scond one.

 

2) I don't mean the IF may define the prominence. but it seems that it might define popularity.

also we are often interested in phase dynamics and so we need momentum.

 

but we may use also phase out of mechanics ,for instance ,waves have phase. probably we will be able to accept that some waves approxiamtely have no mass in compasion to other ones.

heyy ajb , really it is pleasure to take warning from such a careful scientist like you. I have never felt nervous/negative up to now.

what a relief personality belonginy you!

congratulations :-)

*** ONE TYPE OF ACTUAL ELEGANCE / WISDOM ***

Edited September 6, 2016 by blue89

[studiot]

Good Journals ?

 

Looking at my copy of

 

International Journal of Solids and Structures

Vol32 No1

January 1995

 

Which I keep for the article

 

Green's function for general disk-crack problems

 

Y. L. Xu

 

(side note this article may be relevant to your earlier threads about integration)

 

I see that in the list of references there is one from your own university

 

Delale & Xu Stress field in a circular disk containing an edge dislocation and its application to the solution of disk crack problems

 

Bulletin Istanbul Technical University. (1994)

 

Perhaps these guys are still there?

Edited September 6, 2016 by studiot