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How to things that are so small and so limited in variety, such as quarks, protons, electrons, neutrons, and nucleotides, make up things that are so complicated and completely different, like elements and DNA?
Answer 1:

First I want to say this is a good question. It is really amazing that things can grow from small atoms to element or even more complex DNA or molecules. I think they can be understood in two key principles:

1) You have some varieties of basic elements
2) There are other degrees of freedom for upper level combination

To illustrate, one good related example is why do we have more than 100 different elements on earth while all of them are simply made of neutrons, protons and electrons. To apply the two above mentioned principles in this case: firstly we have neutrons, protons and electrons as the basic elements to form the atoms; secondly to make an atom, we have the freedom to choose different numbers of neutrons, protons and electrons. A different combination of those particles can make a different chemical element. Using only one proton and one electron we can make a Hydrogen atom. Using 8 protons, 8 neutrons and 8 electrons we can make an Oxygen atom. That's why we have more than 100 elements while all of them are simply made of three particles.

One step further, now we have more than 100 elements, a combination of different numbers of chemical elements would make millions of different chemicals in our daily life. It could be as simple as a water molecule (two H and one O), or as complex as a DNA. Here I want to emphasize, other than the numbers of elements we can choose, there is one more degree of freedom: how do we arrange them in space. Using the carbon atoms only, we can make carbon, diamond, graphene and more. The key is when we consider other degrees of freedom, things can get complex.

One more good example is that the English word that we are using. There are simply only 26 letters running from A to Z. By using a different combination of different numbers of letters and put them in different order (for instance: IP vs PI), we can have a infinite number of words in principle. Not all of them are meaningful to us, but still we have more than 1 million words in English (Maybe only 10 thousand in our daily life). One step further, by making a combination of words we can make a sentence. Even more, we can have paragraphs, chapters, articles, books etc., from words. That's how things are getting more and more complex if we add some other degrees of freedom.

Best,


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