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Why Math Rocks

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  Why Math Rocks Sam Wormley <swormley1@gmail.com> - 2016-04-01 19:01 -0500
    Re: Why Math Rocks jimp@specsol.spam.sux.com - 2016-04-02 01:22 +0000
    Re: Why Math Rocks Fabian Russell <fb@zen.info> - 2016-04-02 06:14 +0000
      Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 08:23 +0200
        Re: Why Math Rocks Fabian Russell <fb@zen.info> - 2016-04-02 12:43 +0000
          Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 15:13 +0200
            Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 15:38 +0200
              Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 15:46 +0200
            Re: Why Math Rocks Fabian Russell <fb@zen.info> - 2016-04-02 18:48 +0000
              Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 21:12 +0200
                Re: Why Math Rocks Fabian Russell <fb@zen.info> - 2016-04-02 19:28 +0000
                  Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 22:27 +0200
                    Re: Why Math Rocks Fabian Russell <fb@zen.info> - 2016-04-04 10:55 +0000
                      Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-04 19:19 +0200
                        Re: Why Math Rocks Fabian Russell <fb@zen.info> - 2016-04-05 08:53 +0000
                          Re: Why Math Rocks Sergio <invalid@invalid.com> - 2016-04-05 10:44 -0500
                            Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-05 23:43 +0200
                              Re: Why Math Rocks Sergio <invalid@invalid.com> - 2016-04-05 17:25 -0500
                                Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-06 07:50 +0200
                          Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-05 23:16 +0200
                          Re: Why Math Rocks Odd Bodkin <bodkinodd@gmail.com> - 2016-04-05 17:10 -0500
                            Re: Why Math Rocks Fabian Russell <fb@zen.info> - 2016-04-10 18:44 +0000
                              Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-10 20:49 +0200
                                Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-10 20:58 +0200
          Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 16:23 +0200
      Re: Why Math Rocks Mahipal <mahipal7638@gmail.com> - 2016-04-02 08:02 -0700
        Re: Why Math Rocks benj <none@gmail.com> - 2016-04-02 12:26 -0400
    Why Math Rocks HVAC <mr.hvac@gmail.com> - 2016-04-02 06:18 -0700
      Re: Why Math Rocks benj <none@gmail.com> - 2016-04-02 12:14 -0400
        Re: Why Math Rocks Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-04-03 10:33 +0200
          Re: Why Math Rocks HVAC <mr.hvac@gmail.com> - 2016-04-03 04:31 -0700
            Re: Why Math Rocks Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-04-03 14:27 +0200
              Re: Why Math Rocks HVAC <mr.hvac@gmail.com> - 2016-04-03 07:29 -0700
                Re: Why Math Rocks benj <nobody@gmail.com> - 2016-04-04 00:49 -0400
                  Re: Why Math Rocks HVAC <mr.hvac@gmail.com> - 2016-04-04 04:46 -0700
                    Re: Why Math Rocks benj <none@gmail.com> - 2016-04-04 13:50 -0400
                Re: Why Math Rocks benj <none@gmail.com> - 2016-04-04 13:46 -0400
    Re: Why Math Rocks Sergio <invalid@invalid.com> - 2016-04-02 09:02 -0500
      Re: Why Math Rocks Poutnik <poutnik4nntp@gmail.com> - 2016-04-02 16:30 +0200
      Re: Why Math Rocks benj <none@gmail.com> - 2016-04-02 12:27 -0400

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#567340 — Why Math Rocks

Why Math Rocks
> http://www.npr.org/sections/13.7/2016/03/30/472405110/why-math-rocks


> The challenge with math is that if you don't look with the right
> eyes, you don't see how pervasive and all-encompassing it really is.
> We somehow detune ourselves from the myriad patterns that surround
> us, both outside and in. We don't count heartbeats (that would drive
> most people mad, as you can check in this amazing Radiolab program
> The Heartbeat. And we don't associate evergreens with cones or tend
> to analyze the symmetry in people's faces — at least consciously.
> Yet, all of our gadgets and machines depend on our understanding and
> ability to apply math to different materials.
>
> At a deeper level, much of the natural sciences are about identifying
> patterns in nature that we then call "laws." These laws usually have
> some form of mathematical expression, as in Newton's laws of motion
> and gravity, or the law of conservation of energy. In fact, such laws
> are so essential to our understanding of the universe that many
> scientists believe that math goes beyond human invention, being the
> fundamental language of nature.


-- 

sci.physics is an unmoderated newsgroup dedicated
to the discussion of physics, news from the physics
community, and physics-related social issues.

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#567345

Sam Wormley <swormley1@gmail.com> wrote:
> Why Math Rocks

Because it has its own group that isn't filled with lunatics and
spamming ass holes like you.


-- 
Jim Pennino

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#567395

On Fri, 01 Apr 2016 19:01:20 -0500, Sam Wormley wrote:

> Why Math Rocks
>

Mathematicians can set up clear, beautiful, and concise equations
that cannot be solved.

This "rocks?"

Indeed, the vast majority of practical scientific computation
is performed with crude "brute force" techniques.


>
> http://www.npr.org/
>

NPR?  How many women and minorities did they showcase?

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#567397

Dne 02/04/2016 v 08:14 Fabian Russell napsal(a):
> On Fri, 01 Apr 2016 19:01:20 -0500, Sam Wormley wrote:
> 
>> Why Math Rocks
>>
> 
> Mathematicians can set up clear, beautiful, and concise equations
> that cannot be solved.

Some cannot be solved, some can.
It is not flaw of math, but nature of problem.
> 
> This "rocks?"
> 
> Indeed, the vast majority of practical scientific computation
> is performed with crude "brute force" techniques.
> 

Numerical solution is not generally considered as brute force,
and often contains a lot of mathematical skills to set it.

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#567424

On Sat, 02 Apr 2016 08:23:33 +0200, Poutnik wrote:

> 
> Some cannot be solved, some can.
>

Let me fix this:

Most cannot be solved; very few can.

>
> It is not flaw of math,
>

It does indicate the sheer impotence of mathematics, however.

Mathematics is the VERY BEST that human beings can do, but
its true power is severely limited. 

> 
> Numerical solution is not generally considered as brute force,
> and often contains a lot of mathematical skills to set it.
>

ALL DE solvers ARE brute force -- no exceptions.

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#567433

Dne 02/04/2016 v 14:43 Fabian Russell napsal(a):
> On Sat, 02 Apr 2016 08:23:33 +0200, Poutnik wrote:
> 

>> Some cannot be solved, some can.

> 
> Let me fix this:
> Most cannot be solved; very few can.

Many can.
Many cannot be, but just analytically,
and it is seldom a real problem.

True power is not determined by existence of analytical solution,
but by ability of equation formulation
describing reality behaviour.

>>
>> It is not flaw of math,
> 
> It does indicate the sheer impotence of mathematics, however.
> 
> Mathematics is the VERY BEST that human beings can do, but
> its true power is severely limited. 

Aside of above, even if analytical solution existed,
it would often imply
complete knowledge of initial/border conditions as input data.

E.g. it does not matter
if differential equations for atmosphere evolution
have analytical solution or not,
if initial atmospherical data are so sparse.

>>
>> Numerical solution is not generally considered as brute force,
>> and often contains a lot of mathematical skills to set it.
> 
> ALL DE solvers ARE brute force -- no exceptions.
> 
Computation demanding is not synonymum for brute force.
BTW, analytical solution can be
even more computational demanding than numerical one.

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#567439

Dne 02/04/2016 v 15:13 Poutnik napsal(a):

> Computation demanding is not synonym for brute force.
> BTW, analytical solution can be
> even more computational demanding than numerical one.

BF solution approach
is checking all conditions for in discrete cases,
or as big density of all conditions as possible in continuous cases.

Examples are encryption breaking for the former,
Monte Carlo quantum chemistry computations for the latter
( like screensaver distributed searching for new medicaments ).

For weather forecast computation by brute force
the computation would not be finished
in cosmologically short time
with all the human computation power.

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#567443

Dne 02/04/2016 v 15:38 Poutnik napsal(a):
> Dne 02/04/2016 v 15:13 Poutnik napsal(a):
> 
>> Computation demanding is not synonym for brute force.
>> BTW, analytical solution can be
>> even more computational demanding than numerical one.
> 
> BF solution approach
> is checking all conditions for in discrete cases,
> or as big density of all conditions as possible in continuous cases.

I.e. BF is excluding ways to narrow search path,
going through all branches
and a posteriori exclude those that do not fit.

DE solvers definitely go along very narrow set of paths
to solution, no matter how computational demanding they are
( or they would even with analytical solution )

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#567532

On Sat, 02 Apr 2016 15:13:32 +0200, Poutnik wrote:

> 
> BTW, analytical solution can be
> even more computational demanding than numerical one.
>

That's because in most cases an "analytical" solution
is just a deliberate illusion.

Here is how a LOT of mathematics works:

An equation cannot be solved but we know that a solution
to the equation does exist.  Therefore, we just call this
unknown solution some name like F.  We may be able to determine
the basic properties of F, such as its additive or multiplicative
behavior, but we do not know its value.  But F can be approximated
using various "brute force" techniques.

So now we have F and we pat ourselves on the back.  Based
on this flimsy process, we believe that mathematics is a
wonderful and powerful tool.

Note: examples of F are sine, cosine, Bessel, log, erf, etc.

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#567538

Dne 02/04/2016 v 20:48 Fabian Russell napsal(a):
> On Sat, 02 Apr 2016 15:13:32 +0200, Poutnik wrote:
> 
>>
>> BTW, analytical solution can be
>> even more computational demanding than numerical one.
>>
> 
> That's because in most cases an "analytical" solution
> is just a deliberate illusion.

Not if one knows what it means.
> 
> Here is how a LOT of mathematics works:
> 
> An equation cannot be solved but we know that a solution
> to the equation does exist.  Therefore, we just call this
> unknown solution some name like F.  We may be able to determine
> the basic properties of F, such as its additive or multiplicative
> behavior, but we do not know its value.  But F can be approximated
> using various "brute force" techniques.

Functions are not computed by brute force techniques.

> So now we have F and we pat ourselves on the back.  Based
> on this flimsy process, we believe that mathematics is a
> wonderful and powerful tool.
> 
> Note: examples of F are sine, cosine, Bessel, log, erf, etc.
> 
You may confuse analytical functions
as finite combination of elementary functions and operators.

and computational representation of elementary functions.

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#567539

On Sat, 02 Apr 2016 21:12:30 +0200, Poutnik wrote:

> 
> Functions are not computed by brute force techniques.
> 

How is sin(x) computed?

How is bessel_0(x) computed?

Etc.

They are computed using brute-force methods such as power
series or other iterations.  The resulting values are
only approximations.

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#567545

Dne 02/04/2016 v 21:28 Fabian Russell napsal(a):
> On Sat, 02 Apr 2016 21:12:30 +0200, Poutnik wrote:
> 
>>
>> Functions are not computed by brute force techniques.
>>
> 
> How is sin(x) computed?
> 
> How is bessel_0(x) computed?
> 
> Etc.
> 
> They are computed using brute-force methods such as power
> series or other iterations.  The resulting values are
> only approximations.
> 

By Chebyshev orthogonal polynomial. They converge very fast.

Computer inplementation is not algebra.

And you do not know what brute force term means.


-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#567822

On Sat, 02 Apr 2016 22:27:53 +0200, Poutnik wrote:

> 
> And you do not know what brute force term means.
>

You are missing the main point of my post.

I do not dispute mathematics in general.  I simply
am against the idea that mathematics is some divine
and powerful development of the human intellect.

As anyone who does creative mathematical work is well aware,
mathematics is quite weak and ineffective.  We all wish
that it could be more potent, but, outside of a few special
cases, it is not.

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#567869

Dne 04/04/2016 v 12:55 Fabian Russell napsal(a):
> On Sat, 02 Apr 2016 22:27:53 +0200, Poutnik wrote:
> 
>>
>> And you do not know what brute force term means.
>>
> 
> You are missing the main point of my post.
> 
> I do not dispute mathematics in general.  I simply
> am against the idea that mathematics is some divine
> and powerful development of the human intellect.

I am as well against the idea of math
as divine and powerful development of the human intellect.

I am for the idea of math
as powerful tool developed by the human intellect.

> 
> As anyone who does creative mathematical work is well aware,
> mathematics is quite weak and ineffective.  We all wish
> that it could be more potent, but, outside of a few special
> cases, it is not.

Math as a language is not weak, but a powerful tool,
useful for ( but not limited to ) describing of relations
between observed quantities.

Try to develop QED, quantum chemistry or GR without math.

What may be weak is math interpretation and implementation.

And what definitely is weak is math implementation
by degradation to aritmetic over limited set of rational numbers
as that is what FPUs do.

In fact, FPUs do not know anything about non rational numbers
like sqrt(2) or trancendent ones as pi or e.

I put aside high level computer languages or SW
for symbolic operation over algebraic notations.

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#568011

On Mon, 04 Apr 2016 19:19:01 +0200, Poutnik wrote:

> 
> Math as a language is not weak, but a powerful tool,
> useful for ( but not limited to ) describing of relations
> between observed quantities.
> 

The main purpose of science is PREDICTION rather than DESCRIPTION,
and the inability to solve most equations analytically is a failure
in prediction, and hence our ability to control the world.






> Try to develop QED, quantum chemistry or GR without math.
> 
> What may be weak is math interpretation and implementation.
> 
> And what definitely is weak is math implementation
> by degradation to aritmetic over limited set of rational numbers
> as that is what FPUs do.
> 
> In fact, FPUs do not know anything about non rational numbers
> like sqrt(2) or trancendent ones as pi or e.
> 
> I put aside high level computer languages or SW
> for symbolic operation over algebraic notations.

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#568046

On 4/5/2016 3:53 AM, Fabian Russell wrote:
> On Mon, 04 Apr 2016 19:19:01 +0200, Poutnik wrote:
>
>>
>> Math as a language is not weak, but a powerful tool,
>> useful for ( but not limited to ) describing of relations
>> between observed quantities.
>>
>
> The main purpose of science is PREDICTION rather than DESCRIPTION,

no, main purpose is understanding the process, relationships, and 
modeling them.

> and the inability to solve most equations analytically is a failure
> in prediction,

I would not use the word "failure", I would say many processes are too 
complex to be solved by just math, take problems with more than 5 
degrees of freedom, like a robot with an arm with 10 joints that can 
each move in 6 ways.  They can learn a path of motion, but the # of 
equations and solutions from just a math point of view is too complex

and hence our ability to control the world.

use math to control Hillary Clinton when she ascends the throne...


so to sum up, math is a language and tool that helps solve complex 
problems, describe processes, relationships, modeling, but cannot solve 
very complex problems.

there are large areas where math works well, and as you get near the 
edge, it dosent work that well, and when past the edge there is no math 
that works.

one area is encryption, another area is statistics, you will see this 
fadeout of math applibility if you take advanced calculus

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#568120

Dne 05/04/2016 v 17:44 Sergio napsal(a):

> 
> one area is encryption, another area is statistics, ...

Why do you think mat is weak in these areas ?

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#568134

On 4/5/2016 4:43 PM, Poutnik wrote:
> Dne 05/04/2016 v 17:44 Sergio napsal(a):
>
>>
>> one area is encryption, another area is statistics, ...
>
> Why do you think mat is weak in these areas ?
>

one example;

in encryption, there are good math techniques that generate excellent 
codes, but the understanding of how to detect errors that occur to the 
encrypted part is usally varies from good to poor, to unknown. 
Calculation of the Probability of Undetected Error, PUE.  The encryption 
generation uses solid known math, but one cannot tell from that math if 
it can detect errors very well.  A few codes are fully known, most are 
unknown. The military has some codes run on special chips (by 
contractors) to find out by exaustive search this factor.

the encryption code generators are like a few good known threads in 
thousands of possabilities.  but the math is not there yet to show the 
other possabilities are good.




Statistics, - good book => the Black Swan where it was argued wallstreet 
was misusing the binomial distribution (book came out before the 2008 
crash).  (wall street was and still is)

in general, I think math applications has a hard time with 
multi-dimentional problems (or larger than 5 variables)


take a fastest route + minimize gasoline for Uber, over a 2 dimentional 
city, with streets and pickup times, and drop off time locations.
	for 1 car, 10 pickups(trips) during the day how does the computer 
determine the solution.
	for 271 cars, 4821 pickups,   etc...

this "bleeding edge" of math is what is being published in the 
professional journals today.  like going from the known, (math works 
fine) into the unknown (math starts to degenerate, solution sets vague...)

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#568205

Dne 06/04/2016 v 00:25 Sergio napsal(a):
> On 4/5/2016 4:43 PM, Poutnik wrote:
>> Dne 05/04/2016 v 17:44 Sergio napsal(a):
>>
>>>
>>> one area is encryption, another area is statistics, ...
>>
>> Why do you think mat is weak in these areas ?
>>
> 
> one example;
> 
> in encryption, there are good math techniques that generate excellent 
> codes, but the understanding of how to detect errors that occur to the 
> encrypted part is usally varies from good to poor, to unknown. 
> Calculation of the Probability of Undetected Error, PUE.  The encryption 
> generation uses solid known math, but one cannot tell from that math if 
> it can detect errors very well.  A few codes are fully known, most are 
> unknown. The military has some codes run on special chips (by 
> contractors) to find out by exaustive search this factor.
> 
> the encryption code generators are like a few good known threads in 
> thousands of possabilities.  but the math is not there yet to show the 
> other possabilities are good.
> 



> 
> Statistics, - good book => the Black Swan where it was argued wallstreet 
> was misusing the binomial distribution (book came out before the 2008 
> crash).  (wall street was and still is)
> 
> in general, I think math applications has a hard time with 
> multi-dimentional problems (or larger than 5 variables)

> 
> 
> take a fastest route + minimize gasoline for Uber, over a 2 dimentional 
> city, with streets and pickup times, and drop off time locations.
> 	for 1 car, 10 pickups(trips) during the day how does the computer 
> determine the solution.
> 	for 271 cars, 4821 pickups,   etc...


> 
> this "bleeding edge" of math is what is being published in the 
> professional journals today.  like going from the known, (math works 
> fine) into the unknown (math starts to degenerate, solution sets vague...)

That all may be a question of point of view.
Is math weak or is the problem difficult ?
Math is not a magic wand to say its magic is weak
if it cannot do this or that.

-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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#568117

Dne 05/04/2016 v 10:53 Fabian Russell napsal(a):
> 
> The main purpose of science is PREDICTION rather than DESCRIPTION,
> and the inability to solve most equations analytically is a failure
> in prediction, and hence our ability to control the world.
> 

Description and prediction are 2 sides of the same coin,
and both are important to science.

Definition of function is not limited to analytical nor closed formula.
Math expressions are superset of close-form and analytical expressions.

https://en.wikipedia.org/wiki/Closed-form_expression#Analytic_expression

Inability of analytical solution is not failure of prediction,
as the form of prediction is not limited.

it is just a failure of not reasonable idea
what prediction has to look like.

It has nothing to with control of the world.


-- 
Poutnik ( The Pilgrim, Der Wanderer )
Knowledge makes great men humble, but small men arrogant.

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