The Story of Maths
 

Time Warner cable programming has been out here since Tuesday. Tired of reading and plinking on my guitar, for entertainment I downloaded an interesting series while at the office - The Story of Maths, with Marcus du Sautoy.
It is about the history of mathematical discoveries. I found it fascinating until the end of the third episode. Then it got depressing.
I used to think the beauty of math was that it was so ordered and universal and was exempt from the chaos of human experience. It was kind of a universal refuge for me. It was a place where the world made sense. There were immutable laws.
Apparently, the laws aren't immutable. du Sautoy showed Euler's demonstration that trigonometry only works in a 2 dimensional world. You start thinking about 3 dimensions and the shortest distance between two points is no longer a straight line, the angles of a triangle do not add up to 180. (you smart guys probably already know this. It was news to me.) When you get to 4 dimensions all heck breaks loose. Fifth dimension - forget about it. It's chaos.
There is no refuge, there is no order.

The Story of Maths - Top Documentary Films

I'm enjoying this series too. Curved space is odd for sure. But with the discovery of gravitational waves we are going to need an understanding of curvature if we are ever going to have warp drive. :)

As the # of dimensions goes up the rules just more complicated. It's not chaotic just more complex.

Some further good reads are 'Flatland' and 'Sphereland'

I agree with Bill Verburg. More complex, not immutable. As we develop greater abilities to measure, the complexity increases.

The evolution of our concept of 'time' is a monkey in the wrench for me. Time used to be a constant. Come to find out, it ain't!

Just received Flatland...looking forward to the read.

I suspect it all devolves to probability.
We can't know anything for sure.© 2016 by me, so remember you heard it here first

They were right:

http://forums.pelicanparts.com/uploa...1455307842.jpg

If we can understand the nature of the conductivity of the gel, I would think it would not be long before we are able to manipulate it.

Perhaps we can someday simply follow the shortest pathway from one area of the gel to another.

Wormholes never made sense to me. At first they were conduits to another universe, which is absurd by definition. Then they were described as places where gravity 'folds in on itself'.

Uh Huh.

Warping space makes much more sense to my mechanical thinking. Warping, however, requires the manipulation of space-time which is accomplished by extremely high velocities. My conductivity theory would require no manipulation. There must be areas in the the universe that are less affected by the various forces of gravity, time, etc. Less dense areas, so to speak. Dots in the universe with below average static.

You simply connext the dots.

"The Story of Maths" is available on Netflix Streaming too.

Hmm, I've read Flatland and loved it. I've never heard of Sphereland. There are also, two different Flatland movies. One is one youtube.

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curved space is something astronomers, surveyors and navigators have dealt w/ for ages

The sum of the interior angles of the triangle connecting any 3 points of the surface of Earths oceans will always add up to more than 180°, on Continental areas it can be more or less than 180° depending on whether the surface has net concavity or net convexity. For instance if the area surveyed in in a valley where there is net concavity the sum of the interior angles is > 180°, but if the area surveyed is on a mountain where net curvature is convex the sum of the interior angles will be <180°. The only place where the interior angles of a triangle add up to 180° is on a flat surface like a desk. In astronomy it was debated for years whether the observable Universe had intrinsic curvature separate from the curvature induced my local mass or energy. Measurement has shown it to be flat within a .4% margin of error.

the shortest distance between any 2 points on the Earths surface for a navigator is an arc. part of a so called great circle.

Yeah, you guys need to get out more...

I took 7 years of this stuff in college and engineering school... Math is just another tool, no different than a 10mm wrench or a 13mm socket...

Thank you, billy.

You have confirmed for me that 7 years' education on this stuff is an approximate equivelence to a lifetime of thinking about this stuff. Therefore, I saved alot of money.

Math is a tool to verify or refute expansive thinking. Math is teachable. Thinking is a gift.

Yeah, but it's the coolest tool that you won't find in a tool box.

Except that when I look at a wrench or socket I immediately know how to use it...math takes a bit more effort...for me at least.

The toolbox is your noodle. Use it and its contents wisely.

Maybe I'm jaded from having multi variable calculus drilled into my head for years.

For the 180 degree triangle, cut a slice through the earth creating a plane with the 3 vertices. Voila - your 3 angles add to 180 degrees again - where's the magic?

Here's the thing about that. A mathematician would look at some one these simple multi variable concepts and could solve them in their head. Hand the same guy a wrench or socket and he might think you've given him a hammer.

Take 3 folks, one builds a car from scratch, chassis, suspension, body, etc.... Number 2 is a mathematician that to most of the world could work magic with math (if they understood it at all), and then the third guy writes and plays his own beautiful music. They all have toolboxes overflowing with tools (albeit, completely different tools). The results of all three are fantastic and important. (OK, the car builder may do a little math if he's designing the suspension)

Everyone has a toolbox. Some people have a toolbox that's overflowing with tools. Some folks are doing pretty good to have the equivalent of a hammer and a screwdriver.

and as long as they all have an open mind and a reasonable vocabulary they may all share cocktails while engaging in interesting conversations. like this one!

BTW matrix algebra made me cry.