Friday, February 19, 2010

Thoughts about our Fractal Universe

My last post prompted some very thoughtful responses. Tesh was even kind enough to link to a terrific website called http://www.gigagalaxyzoom.org/ that has absolutely terrific zoom-able pictures of our own Milky Way galaxy.

When confronted with such immensity it is hard not to get a tad philosophical. How can a mere human mind cope with all this immensity?  Even if you do somehow come to terms with the awesome vastness of the Milky Way just cast you eyes back to the deep field picture and realise that every dot in that picture which itself is but but a tiny speck of the sky represents an entire galaxy. If those concepts are not enough to completely overwhelm your mind then consider that there is a parallel immensity at lower scale. Every pebble on the Earth is itself an entire universe of atoms and the atoms are comprised of a plethora of sub atomic particles. Every time we probe deeper we seem to discover yet another layer of structure beneath that which was already known.

My own personal reconciliation with all of this immensity is to try and accept that the universe we live is has a kind of fractal nature. Not fractal in the sense of self similarity but in the sense of having a complex structure at arbitrarily small and arbitrarily large scales. You can zoom in as far as you like or zoom out as far as you like and you will always find an immensity. Having come to that conclusion the next logical step is to accept that we live at a certain scale and to do our best to master the universe at that scale.

Being human though it is hard to be content with that. One of our great strengths as a thinking species is our ability and indeed our need to simplify complex problems by reducing them to simplified equivalences. I understand this very well because I am an engineer by training and it is a commandment of engineering science that arbitrarily large and complex systems can be reduced to first or second order equivalent models.  We understand first and second order systems very well. We can describe their behaviour and we can control it.

This urge to simplify complexity to a level we can comprehend is revealed at the very largest scale in cosmology and at the very smallest scale in the various attempts to come up with a "theory of everything". Both endeavours attempt to reduce the complexity by putting bounds upon it which are within the grasp of the human mind. Both endeavours are probably equally futile. The fractal nature of the universe thwarts all attempts at reduction.

PS: I know that I may be using the term fractal wrongly in the above post. Mathematical fractals have as I understand it a property of self similarity which means that they can be reduced to a simple recursive description. The universe on the other hand does not appear to have self similarity but does appear to have a complex structure at arbitrary levels of magnification. If there is a better word to describe such a system than fractal I don't know it.

5 comments:

Tipa said...

Fractals are geometric forms with a fractional dimension.

A curve or line is one-dimensional. But if you make that line really jagged, it can come to look more and more like a plane, until it comes as close as you like to a plane. A 1 dimensional figure has come close to being 2 dimensional -- it might have a fractal dimension of 1.1, or 1.99999 as it near plane-ness.

Take a plane and crumple it up so that it slowly begins to fill volume. Its fractal dimension is rising from 2 to 2.1, 2.2, 2.9999 as this infinite place comes to fill up all its space.

You can then think of recursive algorithms that generate plane-filling curves or space-filling planes, and determine their fractal dimension mathematically.

While the universe definitely clumps, I wonder if that clumping is necessarily fractal. In fact it seems almost anti-fractal, and the clumpiness would seem to prevent spacetime from filling higher-order dimensions.

mbp said...

The recursive algrorithm property certainly doesn't apply to the universe as we know it except to the very crudest approximation but the the suggestion of higher order dimensions emerging from never ending complexity complexity is tempting to my inner nerd.

Is the clumpiness really a problem? I know the universe viewed through our four dimensional lens is mainly emptiness but does a fractal actually have to physically fill an n+1 dimensional volume in order to approach n+1 dimension. This is way outside my area of expertise but it would seem to me that the local complexity would be just as important as the actual volume filled.

Anonymous said...

Some comments:

- There is no urge in us to reduce! That's an absurd idea. After all, nature is only doing what is natural - nature doesn't make decisions. Finding a simple answer is more an indication of having found the correct answer rather than any need for reduction as such.

- There is plenty of examples of obfuscation in our human world.

- You are being dumb if you don't run with a reduction that works.

- I believe quantum mechanics describes limits for the smallest sizes.

- If you are wanting some order at a galactic scale you've got some rather beautiful spiral shapes. I can guess there is order in the local clusters also - performing their slow dances.

- Large scales also means large lags. Bigger will always be slower. Yes our perceptions are at human speeds but that doesn't mean we can't record one speed and playback at another speed.

- I think at large scales time becomes an integral part of every function. To describe galactic sized volumes, or larger, time has to be included in it's shape. So, that's one added complexity that can't be reduced any further without over-simplifying.


Solbright

Dov Henis said...

From Scientism Worldview...
Fractal UniverseLifeHuman

http://themishmoshblog.blogspot.co.il/2013/05/50-human-body-mysteries.html
http://universe-life.com/2006/03/07/joshua-lederberg-in-tune-with-the-enemy/
http://www.sciencenews.org/view/generic/id/64286/description/More_than_a_chicken_fewer_than_a_grape


Cells in humans
Human’s bacterial symbionts : There are ten times more bacteria colonizing a human than the number of own human cells in its body (10^14 versus 10^13, respectively). Circa 900 taxa. The structures of their communities vary tremendously. The gut might be considered New York City, whereas the skin is perhaps more like Memphis

Organisms within the cells
Organisms WITHIN the cells are the genetic material in the cells, including in the mitochondria, i.e. the tens of thousands RNA nucleotides genes, the base life organisms, and the DNAs, the template organisms formed and continuously updated by the RNA genes.

Drive and purpose of life’s evolution
Life is like a Russian Babushka set of dolls, each of its chronological phase of evolution being essentially a repeat of the earlier phase on a grander scale.
The nature of life is expressed clearly even in its most basic patterns whereas the continuously added genetic expressions, effected by cultural developments, are variations on the basic theme. The basic theme is simply and plainly that the drive and purpose of life are nothing else but life itself. The drive and purpose of life are the creation and propagation of life’s base organisms, the RNA nucleotides genes. This is natural selection, natural selection of life, of the RNA nucleotides genes.

Drive and purpose of the evolution of the universe
The universe is a two-poles cyclic evolution of the state-of-gravitons, which are the universe’s base particles. The two poles are all-mass and all-energy, i.e. singularity and complete resolution of all compacted mass into energy, i.e. into gravitons in motion.
The drive of the universe evolution is gravity, the propensity of energy reconversion to mass, the propensity of the gravitons, the fundamental mass-energy particles, to cluster at lowest energy level, at the state of least motion.

Dov Henis (comments from 22nd century)
http://universe-life.com/
http://universe-life.com/2012/11/14/701/
-The 20yrs development, and comprehensive data-based scientism worldview, in a succinct format.
-The Genome is a base organism evolved, and continuously modified, by the genes of its higher organism as their functional template.
- Everything in the universe derives from mass-energy duality, from the universe cycle between the two poles all-mass-all energy.
- The Origin Of Gravitons is the ONLY thing unknown-unexplained in the Scientism Universe.




Dov Henis said...

On The Essence And Matrix Of The Universe-Life
The following three sentences are the shortest data-based TOE…seriously.

Natural Selection/ Self Replication/ Gravity

- Self-replication is the ultimate mode of natural selection is the essence and drive and purpose of the universe. Period.
- The pre-Big-Bang singularity is the ultimate self-replication of the cycling mass-energy universe. Period.
- Earth’s RNA nucleotides life is just one of the myriad modes of self-replication.

Dov Henis (comments from 22nd century)
http://universe-life.com/
http://universe-life.com/2012/11/14/701/
-The 20yrs development, and comprehensive data-based scientism worldview, in a succinct format.
-The Genome is a base organism evolved, and continuously modified, by the genes of its higher organism as their functional template.
- Everything in the universe derives from mass-energy duality, from the universe cycle between the two poles all-mass-all energy.
- The Origin Of Gravitons is the ONLY thing unknown-unexplained in the Scientism Universe.