Scales of the Universe:
Small, Large, and Complex
It is difficult for us to fathom the true size of the universe. How do we grasp our place in this enormous vastness, filled with almost incomprehensible structures, like black holes, or super-heavy suns? How do we represent the universe itself? The differences between the smallest structures and the largest are so enormous that linear scales are useless. We need logarithmic (exponential) scales, which make the numbers appear to be easy, even when the geometry is simply incomprehensible. An 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, the math is in the footnotes.)
Human intuition is simply not capable to grasp the dimensions that surround us. We need sophisticated scales to visualize the vastness that surrounds us.
How do we represent the flow of time, the age of the universe, together with the idea that time can be considered the fourth dimension?
In cosmology, the age of the universe is the time elapsed since the Big Bang. The current measurement of the age of the universe is around 13.8 billion years. NASA scientists translated this relationship between space and time into an image, and here is the result:
The universe we inhabit is the vertical disk at the end of this expanding funnel. The image represents the reduction of a large-scale four-dimensional universe into something three-dimensional because it adds the idea of movement (time as history) to the picture.
Instead of representing the universe as a dimensional entity, can we think of it in terms of three different frontiers: the largest, the smallest, and the most complex? And where is the human being situated in this regard?
Space and Time
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. Well, our journey is only beginning.
If we compare space and time on a logarithmic scale that compares meters and seconds, we get the graph below. (From Penrose, Roger: The Large, the Small, and the Human Mind. Canto 2000, p. 5)
The result is somewhat surprising: We are located somewhere in the middle of the scale in terms of space (extension), but towards the high end in terms of time. Given the size of the human being, shouldn't it 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, to say it in another way: we are more enduring in time than in space.
Complexity: Brain and Genes
What about complexity? In this regard, humans rank at the very top end of universal scales.
The human brain has a 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 can be expressed in exponential terms as 1014.
As a network, the brain is the most complex structure we can find (so far) in the universe. We don't know much about the structural rules that govern extremely complex objects like our brains.
Even though the brain is integral to who I am, I am completely unaware of its operation. There is no material self-awareness in the physical object of my brain; there is only the consciousness that holds the information I am writing down right now. Modern science still knows very little about the brain and its interactions with the human mind as we experience it. There exists a real barrier, called the mind-body problem. Creating a detailed model and a deeper understanding of the brain is a truly daunting task, more difficult than mapping the physical universe.
What about the genome? It 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 content originates from the self-organization of the brain as it interacts with the person's environment over the course of a lifetime. Learning adds a lot of information to our minds, and the brain grows and networks itself as it matures throughout the lifespan.
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
This beautiful website demonstrates the scale differences of the universe very well: http://scaleofuniverse.com/
Atoms in a water cup:
Let us take “one cup” to be 250 ml or grams of water.
The molecular mass of water is: 18.01528 g/mol - Google
Avagadro’s number is: 6.0221409e ^23 - Google
So, one cup of water holds 8.3569904e ^24 molecules of water.
At 3 atoms per molecule, that is 2.5070971e ^25 atoms per cup of water.
All the water on, in, and above the Earth, would be about 332,500,000 cubic miles, or 5.54368183 × 10^21 cups of water on earth - Google
2.5 x 10^25 is much larger than 5.5 x 10^21. Therefore, there are far more atoms in a cup of water than there are cups of water on earth.
You would learn a lot more by doing the calculation yourself!