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Interesting article in August 2011 Scientific American
Message #1 Posted by Don Shepherd on 23 July 2011, 9:47 p.m.

It's called "Why Math Works" and it asks the question "Is math invented or discovered." The author is an astrophysicist and the discussion is a bit deep, but it is an interesting read for the layman, including those of us who push buttons on HP calculators.

      
Re: Interesting article in August 2011 Scientific American
Message #2 Posted by dbatiz on 24 July 2011, 2:39 a.m.,
in response to message #1 by Don Shepherd

Iím sure there are more profound thinkers out there that will take issue with my opinion. However in the spirit of discussion I offer the following: When either using linear regression to approximate values between data points, or using calculus to predict planetary movements; math seems to be validated by how well it can represent and predict situations in the real world. As such, all the interactions, cause/effect, variables and relationships already exist and are waiting patiently to be discovered by intellects capable of seeing beyond obvious, quantifying the subtle, and finding the connection between the apparently un-related.

Again, only my opinion, each discovery sheds light on the fantastic complexity, elegance and care of our creation.

Very respectfully,

David

      
Re: Interesting article in August 2011 Scientific American
Message #3 Posted by Thomas Radtke on 24 July 2011, 3:08 a.m.,
in response to message #1 by Don Shepherd

My view on this topic:

As math originated from natural philosophy, its foundation reflects our perception of the world. If a farmer owning n cows buys another cow and subsequently counts the herd, he will likely reckon n+1 cows.

Thousands of years later, observations in our nature still guiding the way math is being developed, e.g. Newtons calculus. Few hundered years ealier, Cavalieri failed to invent it. There had to be a question in physics to do it right ;-).

            
Re: Interesting article in August 2011 Scientific American
Message #4 Posted by Mark Hardman on 24 July 2011, 9:59 a.m.,
in response to message #3 by Thomas Radtke

Quote:
Thousands of years later, observations in our nature still guiding the way math is being developed, e.g. Newtons calculus. Few hundered years ealier, Cavalieri failed to invent it. There had to be a question in physics to do it right

Careful there Thomas. Walter will be all over you that it was indeed Leibniz that invented the calculus first and not Newton. For once I'd actually agree with him ;-) Furthermore, Leibniz's invention of the calculus stemmed from his pure mathematical studies into the "tangent problem."

                  
Re: Interesting article in August 2011 Scientific American
Message #5 Posted by Thomas Radtke on 24 July 2011, 10:22 a.m.,
in response to message #4 by Mark Hardman

Quote:
Careful there Thomas. Walter will be all over you that it was indeed Leibniz that invented the calculus first and not Newton. For once I'd actually agree with him ;-) Furthermore, Leibniz's invention of the calculus stemmed from his pure mathematical studies into the "tangent problem."
I don't want to discuss that in depth, especially not with Walter ;-). To me, Newtons way to solve the problem is much more obvious. It just looks like Leibniz had taken the idea from Newton to make a theory, where other mathmaticians had to fail.
                        
Re: Interesting article in August 2011 Scientific American
Message #6 Posted by John B. Smitherman on 24 July 2011, 11:05 a.m.,
in response to message #5 by Thomas Radtke

Not to throw fuel on the fire... here's an interesting article on the Newton vs Leibniz debate:

Link

Regards,

John

                              
Re: Interesting article in August 2011 Scientific American
Message #7 Posted by Thomas Radtke on 24 July 2011, 11:13 a.m.,
in response to message #6 by John B. Smitherman

Quote:
Not to throw fuel on the fire...
All the fuel has been burned long ago. No new insights here.
      
Re: Interesting article in August 2011 Scientific American
Message #8 Posted by John B. Smitherman on 24 July 2011, 8:49 a.m.,
in response to message #1 by Don Shepherd

Don, deep stuff and very interesting.

Here's a link to a book by the same author of the SA article - Mario Livio, "Is God a Mathematician"

Link

and another book by George Lakoff and Raphael Nunez, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being"

Link

Both are interesting reading.

Regards,

John

      
Re: Interesting article in August 2011 Scientific American
Message #9 Posted by David Hayden on 24 July 2011, 10:36 a.m.,
in response to message #1 by Don Shepherd

Math is a model of the physical world. The properties of the physical world are definitely discovered, not invented.

The model (math) is both invented and discovered. We invent pieces of it and then discover the various properties that follow from the pieces to keep it consistent. The value "i" is a perfect example. We invented i=SQRT(-1) and huge amount of math followed from this.

            
Re: Interesting article in August 2011 Scientific American
Message #10 Posted by Tommy on 24 July 2011, 11:16 a.m.,
in response to message #9 by David Hayden

I agree. An other beautiful example is the invention of zero as a placeholder. I think the Olmec people was first, but India often gets credit for this achievement.

            
Re: Interesting article in August 2011 Scientific American
Message #11 Posted by Mark Hardman on 24 July 2011, 1:16 p.m.,
in response to message #9 by David Hayden

And yet, if we were a species of infinitesimally small beings and lived in a quantum space where the laws of physics that govern the trajectories of cannonballs and planetary orbits no longer applied, I wonder what sort of mathematical framework we would have invented. It certainly would not have been the calculus of Newton and Leibniz.


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