What a great video. Many thanks to Cristóbal.

About the year 1200, Fibonacci helped change Europe from Roman Numerals to the Arabic/Hindu numbers which most of us now use worldwide. Did you know the Romans even did double entry accounting in Roman Numerals?
Can you imagine doing your checkbook using Roman Numerals? Aaarghh !! Thank you. Thank you Thank you, Fibi. 

FIbi's famous numerical series seen above also leads to Nautilus shells and Sunflowers and … more later 

- Sometimes, when I found myself as a student in a particularly boring class, I doodled and drew Fib Spirals.
- More recently, I taught some school children to do the same. ...


Now, after Big Things - light years, galaxies, stars and planets,
let’s talk about tiny things much smaller than us -
the little picture:

At this level, things are so small they are invisible to normal vision - 

Matter is made of Invisible Machines

Our universe is an engine of creation. Gravity obviously gathers aggregations or lumps of matter like piles of dirt, planets, stars and galaxies but the universe also generates structures with parts that assemble, like blocks or bricks which lead to other structures - from elementary particles, which make up nuclei and atoms, to complex organic molecules that are the basis of life itself. Here we will explore these structures and the amazing outcome.

Nature does this, not by having a few parts but by having unimaginable, vast numbers of parts.
The scale is enormous. :
- all those strange sub particles - quarks, leptons, bosons - making elementary particles
- all those elementary particles - electrons, protons, neutrons - making atoms
- and all those atoms making molecules
- and all those molecules making more complex molecules, which make up us, you and me.

These numbers are far beyond huge! The combinations and structures are far beyond quantities like:
  - millions = 106, billions = 109, even trillions = 
1012 , even far beyond Avogadro's number = 1024
  - Probably many times greater than 1080 , the estimated number of protons or 
  100,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000,  000,000,000,000 


Remember when you were young, riding in the family car and the mileage counter in your speedometer   turned over to some larger round number? It was a big deal. Everybody watched and that was only a few thousands of miles - 3 to 6 digits. Here is a 400,000 mile rollover at right. 

Now imagine you were watching the number rollover and how long it would take for it to turn over not 3 or 6 or 10 or 20, 40, 60, but 80, eighty, digits! 

Every time one of these 1080 or more particles moves and they all move billions of times per second - it is a new universe of possibility. It becomes obvious that despite the complexity that we see, the universe has explored only a tiny fraction of the possibilities here in fourteen billion - 14,000,000,000 - years!

Current estimate is that the observable universe - the part we can see - weighs about 1054 kg. Using carbon as an example, where one pinch or mole weighs 14 grams, then:

At one per second or heartbeat, it would take you a million times the age of this universe to count the atoms in one pinch of carbon.

[atoms in one pinch of carbon = 1024;  age of this universe = 1018 seconds;    1024/1018 = 106 or one million]


When we say machine, many of us think of cars and lawnmowers, etc.  MIchael Collins, Apollo astronaut, was asked what he thought during blastoff of the Saturn V moon rocket. He said: "Well, you think about the fact that you are at the top of 6 million parts, all made by the lowest bidder!" 

Millions may seem like a lot of parts to us, but it is nothing compared to nature where even the period at the end of this sentence contains trillions of atoms. Nature builds structures not only consisting of trillions of atoms but also  billions of cells, each making millions of molecules - every second. How can this be done? Well, we think a factory is fast when it makes hundreds of products per day. But nature makes atoms into factories, producing molecules, trillions of them. And then those trillions of factories make parts such as proteins that our bodies use, by the billions - every second. 

The smaller the parts: the more there are, and the faster they go. !!!

That is how evolution works. All those trillions of trillions of trillions of parts probe everything and everywhere, every tiny crack of possibility, over and over again, billions of times every second - for billions of years - never stopping. Eventually we get some fault tolerant, self reproducing, metabolically driven molecules - our cells. SO:

Atoms, molecules and cells are too small for our eyes to see and so are invisible machines to us.

Countless invisible machines explore every possibility in our universe, trillions of times every second.

Amazing things are produced - Jellyfish and whales, flowers and birds - you and me.

In this century - the 21st - we will make structures the way nature does. We will grow them. ...

Next >>> Atoms & Molecules


Suggested reading:

“Some seminal works stand out like beacons in the history of science. Newton’s Philosophiae Naturalis Principia Mathematica and Watson and Crick’s A Structure for Deoxyribose Nucleic Acid come quickly to mind. In recent decades we can add Eric Drexler’s Engines of Creation, which established the revolutionary new field of nanotechnology. In the twenty years since this seminal work was published, its premises and analyses have been confirmed and we are starting to apply precise molecular assembly to a wide variety of early applications from blood cell sized devices that can target cancer cells to a new generation of efficient solar panels. We can now see clearly the roadmap over the next couple of decades to the full realization of Drexler’s concept of the inexpensive assembly of macroobjects constructed at the nanoscale controlled by massively parallel information processes, the fulfillment of which will enable us to solve problems — energy, environmental degradation, poverty, and disease to name a few — that have plagued humankind for eons.”

— Ray Kurzweil 

Here is a link to a a free PDF download:   "Engines of Creation" by Eric Drexler

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