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

[ajb]

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

The real numbers with the standard ordering are dense. This means that for any x < y, there exists z such that x < z < y. In short this is a continuum.

 

Or you could put the discrete topolgy on the real line...

[Mike Smith Cosmos]

The real numbers with the standard ordering are dense. This means that for any x < y, there exists z such that x < z < y. In short this is a continuum.

 

Or you could put the discrete topolgy on the real line...

 

To me what you have said, sounds a bit like mathematical gobble-de-goop. I appreciate it is most likely not to a real mathematical person.

I presume it means all values of x,y, and z in a three dimensional space can be packed sufficiently densely as to be viewed solid. if necessary (maybe not ). Or all parts of 3 D space can be identified and described math wise. In what ever way maths is able to describe.

 

However I might be hopelessly off beam.

 

Perhaps you can put me right as to what it does mean ?

 

Mike

[swansont]

 

To me what you have said, sounds a bit like mathematical gobble-de-goop. I appreciate it is most likely not to a real mathematical person.

I presume it means all values of x,y, and z in a three dimensional space can be packed sufficiently densely as to be viewed solid. if necessary (maybe not ). Or all parts of 3 D space can be identified and described math wise. In what ever way maths is able to describe.

 

However I might be hopelessly off beam.

 

Perhaps you can put me right as to what it does mean ?

 

Mike

 

It means that your description of numbers as discrete steps is wrong. There are no gaps between numbers.

[Mike Smith Cosmos]

 

It means that your description of numbers as discrete steps is wrong. There are no gaps between numbers.

Are you suggesting that every point (x,y,z) in three dimensional space is covered by a maths coordinate,? And every possible state of that point is covered by maths. ? And every point continuous (x,y,z) can 'do' anything in any time. ?

 

Wow !

 

I find that hard to believe. ! Sort of wishful ( mathematical ) thinking. ! ?

 

Is this what this Manifold is ? [ that appears in all of ajb's papers ] ?

 

It sounds more freaky than anything I have ever mooted here !

Edited August 13, 2013 by Mike Smith Cosmos

[studiot]

No Mike, it's actually a game called the epsilon-delta game.

 

You offer the size of your smallest step from one number to the next and I will find a number that fits between them, no matter how small you make that step.

 

[Mike Smith Cosmos]

No Mike, it's actually a game called the epsilon-delta game.

 

You offer the size of your smallest step from one number to the next and I will find a number that fits between them, no matter how small you make that step.

 

 

Is this something you made up , or is it a great maths gem ? It sounds like the Frog jumping half way out of the center of a pond, over and over, and never getting out ever !

Edited August 13, 2013 by Mike Smith Cosmos

[Greg H.]

Are you suggesting that every point (x,y,z) in three dimensional space is covered by a maths coordinate,? And every possible state of that point is covered by maths. ? And every point continuous (x,y,z) can 'do' anything in any time. ?

 

Wow !

 

I find that hard to believe. ! Sort of wishful ( mathematical ) thinking. ! ?

 

Is this what this Manifold is ? [ that appears in all of ajb's papers ] ?

 

It sounds more freaky than anything I have ever mooted here !

 

It has nothing to do with coordinates, manifolds, or anything else but numbers.

 

It works like this:

 

Person A: Pick Two numbers and I will pick a number between them.

Person B: 1 and 5

A: 2

B: 1 and 2

A: 1.5

B: 0 and 1

A .5

B: 1/2 and 1/10

A: 1/3

 

Basically, for any two numbers you can think of (m and n), there will ALWAYS be a number (p) that falls between them. One easy way to see this is to simply average the two numbers. For example:

[math] Let\: m = 1 \:and\: n = 1.5,\: find\: p\: such\: that\: m < p < n[/math]

One such value for p can be found by:

[math] p = \frac{1 + 1.5}{2}[/math]

[math] p = 1.25[/math]

 

We can validate this by looking at the original inequality and seeing if our values hold true:

[math] m < p < n = 1 < 1.25 < 1.5[/math]

 

So what you see is that for every pair of numbers you can think of (m, n) there will always exist at least one number (p) between them. This is what we mean when we say that numbers are dense.

Edited August 14, 2013 by Greg H.

[studiot]

 

This is what we mean when we say that numbers are dense.

 

 

 

It's me that's dense.

 

Numbers are very very clever.

 

[ajb]

To me what you have said, sounds a bit like mathematical gobble-de-goop. I appreciate it is most likely not to a real mathematical person.

I said it partly in jest.

 

It means that for any pair of real numbers lets say a and b, with a < b,there always exists a real number c, such that a < c < b. There are always numbers sitting inbetween two given numbers.

[Mike Smith Cosmos]

I said it partly in jest.

 

It means that for any pair of real numbers lets say a and b, with a < b,there always exists a real number c, such that a < c < b. There are always numbers sitting inbetween two given numbers.

 

Then surely you would end up like physics with something like Plank's constant. Very very very small but still NOT continuous?

 

and then if you went out 3 dimensional ( x,y,z)

 

although the fragment would be minutely small , nonetheless it would still be " particular" if that is a word ?

 

Mike

 

Edited August 15, 2013 by Mike Smith Cosmos

[ajb]

Is this what this Manifold is ? [ that appears in all of ajb's papers ] ?

Informally, a manifold of dimension n is a (topological) space that locally (think of small peices) looks like [math]\mathbb{R}^{n}[/math].

 

Basically it means we can put local coordinates on it.

 

Upon some techinical stuff, it means we can do algebra and calculus on a manifold by using our knowedge of algebra and calculus on [math]\mathbb{R}^{n}[/math]. This seems very well suited for classical physics, which is why I am interested in such things.

No Mike, it's actually a game called the epsilon-delta game.

 

You offer the size of your smallest step from one number to the next and I will find a number that fits between them, no matter how small you make that step.

You will bring back my nightamres about analysis with talk like that!

[Mike Smith Cosmos]

Informally, a manifold of dimension n is a (topological) space that locally (think of small peices) looks like [math]\mathbb{R}^{n}[/math].

 

Basically it means we can put local coordinates on it.

 

Upon some techinical stuff, it means we can do algebra and calculus on a manifold by using our knowedge of algebra and calculus on [math]\mathbb{R}^{n}[/math]. This seems very well suited for classical physics, which is why I am interested in such things.

 

You will bring back my nightamres about analysis with talk like that!

 

 

What the heck is R [math]\mathbb{R}^{n}[/math]. is that R to the power n if so what is R

 

Mike

Edited August 15, 2013 by Mike Smith Cosmos

[swansont]

Then surely you would end up like physics with something like Plank's constant. Very very very small but still NOT continuous?

 

and then if you went out 3 dimensional ( x,y,z)

 

although the fragment would be minutely small , nonetheless it would still be " particular" if that is a word ?

 

Mike

Nope.

[Mike Smith Cosmos]

Nope.

 

Well if you propose ,that the universe can be entirely mapped at every coordinate point . But not just mapped described in every possible mathematical way by functions of every sort you are back to the philosophers like La Place, Decart, Berkley who went into the ideas of knowing and predicting everything that will happen.

 

This , I thought we had all moved on from , as being just nonsense ?

[swansont]

Well if you propose ,that the universe can be entirely mapped at every coordinate point . But not just mapped described in every possible mathematical way by functions of every sort you are back to the philosophers like La Place, Decart, Berkley who went into the ideas of knowing and predicting everything that will happen.

 

This , I thought we had all moved on from , as being just nonsense ?

That's not what you asked. You asked if math was discrete because space may be, and the answer to that is no. Math has no requirement to inherently describe anything physical.

[Mike Smith Cosmos]

That's not what you asked. You asked if math was discrete because space may be, and the answer to that is no. Math has no requirement to inherently describe anything physical.

O.K. fair enough.

I just think going down the route of thinking Maths is capable of describing everything, or even As Mike Tegmark proposes everything is maths., is a wrong turn. Pushing the power of maths Way too far. I was trying to suggest that one of its many shortfalls was its Mainly Based on Number, and number tends to be discrete, [ one number here and one over there ] no matter how small a distance over there can be.

 

I am lost in a fog of manifolds, R to the n , and x.>z>y 's now . I have been led up a maths alley and mugged !

 

Mike

Edited August 15, 2013 by Mike Smith Cosmos

[studiot]

 

I was trying to suggest that one of its many shortfalls was its Mainly Based on Number

 

Some of the most powerful mathematical ideas are non-numeric.

 

Symmetry, pattern, shape, congruence, equivalence, duality to name but a few.

[ajb]

For sure one should not think that mathematics is simply about numbers.

 

An old definition of mathematics was "the study of numbers and shape", but this is far to narrow for modern mathematics.

[Humblemun]

Recent comments by an Astronomy orientated Researcher Dr Paul J Abel (Patrick Moore Sky at Night Fame ) (see ajb blogg), has posed questions as to whether maths should be leading the resolution of the ( Quantum Gravity issue), which it is, in string theory and other maths orientated research., Yet ( he indicates ) what is really required is a New Einstein ! Observers, Thinkers , and Hypothesis, to lead the field and then the mathematicians can follow and tidy up the details. !

 

 

Post script. P.S.

 

. hypothesis : " a suggested explanation for a group of facts, accepted either as a basis for further verification or

. as likely to be true. [ Greek hupotithenai to propose, literally: to put under ]"

 

. hypothesize or hypothesise "to put forward an hypothesis "

 

.

. h .................. " a man/woman who puts forward an hypothesis is called an h................ ( not sure )

 

 

. hypothetical : " based on assumption rather than fact or reality "

 

.

The relatively new discipline of Simulation Modeling is also a better way forward than mathematical modeling imv. Only when we have a simulation model of the creation of structure itself, which then continues to produce a picture which closely resembles our view of the multltitude of galaxies, can we really begin to pat ourselves on the back. A simulation model of spiral galaxy rotation is beyond our capabilities at the moment.

Edited August 29, 2013 by Humblemun

[Mike Smith Cosmos]

The relatively new discipline of Simulation Modeling is also a better way forward than mathematical modeling imv. Only when we have a simulation model of the creation of structure itself, which then continues to produce a picture which closely resembles our view of the multltitude of galaxies, can we really begin to pat ourselves on the back. A simulation model of spiral galaxy rotation is beyond our capabilities at the moment.

 

What exactly is the Driver of these " Simulation Modeling "

 

Mike

 

Ps thanks for your comments !

[Humblemun]

 

What exactly is the Driver of these " Simulation Modeling "

 

Mike

 

Ps thanks for your comments !

It's an understanding of the system you are trying to represent. This hapens within the human mind and is then entered as computer code. The computer then represents the dynamics of the system on a monitor screen.

 

Here's a Wikipedia view on it:

 

Simulation modeling follows a process much like this:

1. Use a 2D or 3D CAD tool to develop a virtual model, also known as a digital prototype, to represent a design.
2. Generate a 2D or 3D mesh for analysis calculations. Automatic algorithms can create finite element meshes, or users can create structured meshes to maintain control over element quality.
3. Define finite element analysis data (loads, constraints, or materials) based on analysis type (thermal, structural, or fluid). Apply boundary conditions to the model to represent how the part will be restrained during use.
4. Perform finite element analysis, review results, and make engineering judgments based on results.

[Mike Smith Cosmos]

It's an understanding of the system you are trying to represent. This hapens within the human mind and is then entered as computer code. The computer then represents the dynamics of the system on a monitor screen.

 

Here's a Wikipedia view on it:

 

So the CAD produces a three dimensional model under the designers hand. The computer turning the design into underlaying Code one presumes. Then do you let it run within some boundaries , or using some initial conditions with incremental changes ?

 

I presume this is what generates these simulations of two Galaxies colliding ?

[Humblemun]

 

So the CAD produces a three dimensional model under the designers hand. The computer turning the design into underlaying Code one presumes. Then do you let it run within some boundaries , or using some initial conditions with incremental changes ?

 

I presume this is what generates these simulations of two Galaxies colliding ?

Yes, that's the general idea. I have a personal mind-model of the creation of structure. I've always wanted to simulate it, but it was beyond my capabilities. I'd be grateful of any positive feedback: Reality Was Born Analog But Will Digital Die?. NB I actually think these two initial opposing fractal helix structures could create an overall force of attraction via Archimedes screw particle emissions and cause an implosion rather travelling around a hypersphere to create a subsequent collision.

 

Edit: This anaysis has led to my prediction of the forthcoming Juno flyby on Oct 9th 2013: an large positive additional acceleration with a signature lateral deviation to the left. (Caused by an excess of left-hand spinning Archimedes screw gravitons).

 

P.S. I just checked your profile. I studied Simulation Modelling at Brunel University at MSc level whilst employed as a Scientific Officer at DERA Farnborough. Professor Ray Paul was an originator of this discipline I believe. I didn't complete the course, but left enlightened enough to leave my job (I have mild Aspergers), and travel the world with a friend, gathering information to solve the whole shebang when in middle age. That time has now arrived (lol)

 

Essay Abstract

 

An analysis based on the imagery of the creation of structure from the starting point of a void. A visual representation of spinning threads of energy which emerge and then grow into ‘spinning threads of spinning threads’. Two opposing mirror matter structures conserving laws of conservation of energy and momentum is envisaged. These analog structural energy trees then break free and traverse a wraparound universe to collide on the opposite side of a hypersphere. The Big Bang irregularities are thought to be due to a slight non-spherical aspect of this hypersphere, meaning the two trees don’t meet 100% head-on. The high energy collision breaks the spinning threads into discrete digital components. Some of the resultant forms are of long-lasting donut helices which are our familiar protons and neutrons.

Edited August 29, 2013 by Humblemun

[swansont]

The relatively new discipline of Simulation Modeling is also a better way forward than mathematical modeling imv.

In what way is a simulation model not a mathematical model?

[Humblemun]

In what way is a simulation model not a mathematical model?

My Professor of Simulation Modelling used to say that both were complementary. When he went for a contract, he could come out of the room and have a prototype working simulation model of the system described within 15 minutes and then show the potential clients. This factor would often give him the winning egde over the mathematical modellers. It suits people with very visual types of imagination, as opposed to natural mathematicians. I naturally prefer to imagine a mechanical system for understanding, whilst a mathematician doesn't, they can rely on the logic of the equations.

 

My professor said that the two methods were entirely different but would often come up with exactly the same answer/solution.

Edited August 29, 2013 by Humblemun