Re: [LINK] Numbers limit how accurately digital computers model chaos

[David]

On Thursday, 26 September 2019 09:35:45 AEST Bernard Robertson-Dunn wrote:
> IMHO, the issue is not mathematics or chaos, it's the state of what passes 
> for research today.

Bernard, would you like to explain that in more detail?

David L.





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Re: [LINK] Numbers limit how accurately digital computers model chaos

[Bernard Robertson-Dunn]

On 26/09/2019 12:18 am, antonybba...@gmail.com wrote:
>
>
> Antony Barry
> antonybbarry at me.com 
> Mob +61 433 652 400
>
> On 25 Sep 2019, at 6:51 pm, David  > wrote:
>
>> We could have a long debate about this!
>
> Been done.
>
> The Unreasonable Effectiveness of Mathematics in the Natural Sciences
> - Wikipedia
> https://en.m.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
>
Thanks Tony, good to see you again in this forum.

... "mathematical formulation of the physicist's often crude experience
leads in an uncanny number of cases to an amazingly accurate description
of a large class of phenomena".

Mathematical models can be used in two domains - one to describe and
explain in general, the other to predict behaviour in the specifc.

In the first, non-linearity hardly matters. In the second it is critical.

A classical example is the three body problem. A mathematical model can
be constructed that explains, at a conceptual and logical level, the
structure and relationships of three masses.

The equations are not solvable, analytically. When a specific example is
modeled numerically, the errors grow exponentially which make
predictions useless, beyond a certain limit.

Getting back to the original post, all this has been known for quite a
long time.

To quote from my first comment:

> Numbers limit how accurately digital computers model chaos
Gee, do these people not know how to research their subject.

IMHO, the issue is not mathematics or chaos, it's the state of what
passes for research today.

Bernard

-- 

Regards
brd

Bernard Robertson-Dunn
Canberra Australia
email: b...@iimetro.com.au

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Re: [LINK] Numbers limit how accurately digital computers model chaos

[David]

On Wednesday, 25 September 2019 16:36:10 AEST Bernard Robertson-Dunn wrote:

> As you state, mathematics is a language, a model, of the real world.  It may 
> exist on its own in the real world (you can get a degree in the subject), but 
> like any other language, its use is as a representation or reality, validated 
> by experiment.
> 
> And when you put numbers (data) in a model, it can become more than a 
> generalisation, it can become highly specific - Apollo 11 on its journey to 
> the moon and back.

We could have a long debate about this!

I suggest the axioms of any given system of mathematics are concepts derived 
from the real world.  And as Kurt Gödel showed, no formal system can be 
complete because some _true_ propositions therein cannot be proved.  This seems 
disappointing for something made in heaven.

But mathematics itself is not used to model the real world.  Such models are 
the province of physics, where they're known as "theories".  Mathematics is 
used to express and quantify these theories, but their substance is more like a 
fictional story with very special constraints; for example all observable 
aspects must accord with what we actually observe, and they must be consistent 
with other, established, stories.

Newtonian & Einsteinian gravitation constitute a classic example of two 
theories / stories which are wildly different in substance and in the 
mathematics used to express them.  That's physics.

Well IMHO anyway...

David L.




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Re: [LINK] Numbers limit how accurately digital computers model chaos

[Bernard Robertson-Dunn]

On 25/09/2019 3:11 pm, David wrote:
>> All mathematics involves intellectual models / mind-stuff.
>> Mathematics is not, and not of, the real world.
> Now that's a very brave assertion IMO.  It can also be argued the reason why 
> mathematics allows us to model the real-world so successfully is that it's a 
> generalisation derived from the world we see around us.  That's why the 
> number "zero" was late to be recognised, for example.

It may be brave, but IMO Roger's assertion is totally justifiable.

As you state, mathematics is a language, a model, of the real world. It
may exist on its own in the real world (you can get a degree in the
subject), but like any other language, its use is as a representation or
reality, validated by experiment.

And when you put numbers (data) in a model, it can become more than a
generalisation, it can become highly specific - Apollo 11 on its journey
to the moon and back.

-- 

Regards
brd

Bernard Robertson-Dunn
Canberra Australia
email: b...@iimetro.com.au

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