September 25, 2012

# The Scale of the Universe: The Smallest, the Largest, and the most Complex.

### Size Differences

It is difficult for us to fathom the scale of the universe. The differences between the smallest structures and the largest are so enormous that linear scales are useless. We need exponential scales, which make the numbers appear to be easy, even when the geometry is simply incomprehensible. A simple example can demonstrate these size differences – there are more atoms in a glass of water than there are glasses of water in all the oceans combined. (If you don’t believe it, here is the math.)

On an exponential scale in meters, humans are located at the midpoint between the nanometer scale (1×10−9 m) (a strand of DNA is 3 nanometers thick) and  the scale of stars ( the sun is 1.4 ×109 m in diameter.) Reaching “down”, what we try to do in nanotechnology, is just as difficult as reaching “up,” exploring the solar system with our probes. But, the journey is only beginning.

This beautiful website demonstrates the scale differences of the universe very well: http://scaleofuniverse.com/

### Space and Time

If we compare space and time on a logarithmic scale that compares meters and seconds, we get the graph on the right.

(From Penrose, Roger: The Large, the Small, and the Human Mind. Canto 2000, p. 5)

Given the size of the human being, it should have a shorter lifespan.  In relation to the overall size and age of the universe, we live longer than we should, given our size. Or, we are more enduring in time, rather than in space.

### Complexity

The human brain has the weight of about 3 pounds; it consists of about 100 billion nerve cells (1011), and each nerve cell connects to multiple other nerve cells with an average of 1000 to 10,000 synaptic connections. This means that there are about 100 trillion synaptic connections, which is in exponential terms 1014. The brain is the most complex structure we can find (so far)  in the universe, and we don‘t know much about the structural rules of such complex objects.  Most importantly, they are us. Creating a detailed map of the brain is therefore a really daunting task.

The genome has about six billion bits of information, which is in the order of magnitude of 1010 bits. The genome is therefore substantially smaller, or less complex,  than the mature human brain. From the aspect of pure information content, it is estimated that  there is  about a billion (109) times more information in the brain than in the human genome.  The difference in information originates from the self-organization of the brain as it interacts with the person’s environment.

### Interesting Numbers

Source: http://www.wolframalpha.com/

Estimated number of galaxies in the observable universe: 1.7 x 1011

Estimated number of stars in the observable universe: 3 x 1023

Estimated number of atoms in the universe:  1080

Years since the beginning of the universe: 13.75 billion years.

Seconds since the beginning of the universe: 4.339 ×1017

Estimated number of cells in the human body: 1014

Estimated number of atoms in the human body: 7 x 1027

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### Category

Cosmology, Philosophy of Nature, Physics, Sciences