Local is Not Global

 

I’m Old Fashioned

I am not such a clever one
About the latest fads
I admit I was never one
Adored by local lads
Not that I ever try to be a saint
I'm the type that they classify as quaint

Maybe being adored by locals is not all it’s cracked up to be?

A phrase in the environmental movement is to “Think global, Act local.”  It acknowledges that our local actions  have a global impact. This has been true throughout history.  Recognizing that there is a difference between local and global has changed our way of thinking.

The Earth is flat.

It appears to be flat, Euclidean, to a local observer. The problem is that a local observer is very, very small compared to the size of the Earth. There was evidence that was inconsistent with a flat Earth. The shadow cast by a stick at noon became longer the father north you travelled. The mast of ships appeared over the horizon before the whole ship could be seen. The ocean did not fall off the edge of a flat earth, etc. These could all be addressed if it were recognized that the Earth was a sphere,  not flat. When you do large scale navigation you use non-Euclidean spherical  geometry to find the Great Circle Distance based on the surface as a sphere, where the sides of a triangle are very large compared to the radius of the Erath and the angles of a triangle do NOT sum to 180 degrees.

The Sun revolves around the earth.

To a local observer on Earth, it appears that the Moon and the Sun revolve around the Earth. But this geocentric model causes all sorts of problems requiring the “retrograde” movement of planets. All of these “retrograde” movements disappear if it is recognized that the Earth actually resolves around the Sun. Deep space voyages and astronomy rather than astrology are made possible by recognizing that we actually have a heliocentric earth.

My frame of refence is the correct and only frame of reference.

Is the local observer's the only valid frame of refence? Einstein showed that ALL frames of reference are possible and valid. Tying to reconcile an absolute, like the speed of light, with only one frame of reference resulted in trying to accommodate the aether though which light travelled. Einstein’s Theory of Relativity resolved this and many other seeming paradoxes such as the precession of Mercury, black holes, the apparent movement of stars during eclipses, and resulted in among things including atomic energy.

The universe is flat, Euclidean.

A local observer may assume that because his frame of refence is flat, Euclidean, that the universe is flat. However if the universe is Euclidean, then it requires dark matter and dark energy to resolve: cosmic inflation, the rotation of Galaxies, discontinuities, etc. that are either paradoxes or complications to try and resolve those paradoxes. If the universe is hyperbolic, has negative curvature as opposed to positive, spherical, curvature, these paradoxes may be resolved without the need for complications. It may also suggest that gravity is an apparent force, unlike the other three intrinsic forces. The movement that is observed in a Euclidean frame of refence might appear to be the force of gravity but it might actually be just particles minimizing their energy, which is equivalent to maximizing their entropy.

If you think globally and act locally, the Earth is spherical,  the sun resolves around the earth, and there is more than one frame of reference to an absolute. What else might recognizing that the universe might be locally flat and globally hyperbolic entail.