What if you were to cut the computer or handheld device you are reading this on in half. Then cut those pieces in half, and those pieces in half, and so on. Would you ever get to a point where this was no longer possible? Is there a building block so fundamentally small that it cannot be divided into smaller pieces?
This question has been asked since ancient times, in fact the word atomos was first coined by Leucippus sometime between 400-500 BCE. Leucippus, like many in his time, was a philosopher and was trying to one-up another philosopher named Zeno. Zeno had come up with the rather mindblowing idea that all motion must be an illusion. He reasoned that in order to walk across a room you must first cross half that room. But in order to cross half the distance across the room, you must first cross half that distance too and so on. Because you can divide the distance between any two points into an unlimited number of halves, there must be an infinite number of points. Since crossing an infinite number of points is impossible, all motion must be an illusion.
Leucippus clearly didn't buy into Zeno's idea and proposed the following clever counterargument. It is impossible to divide a given distance into an infinite number of points because eventually you would reach some sort of fundamental building block that cannot be divided further. He called these building blocks "atomoi" meaning "indivisible". Leucippus passed his ideas onto his students and one of them named Democritus took it even further. Democrites claimed that atomoi each have different shapes which allow them to hook together an various ways. He said that the atomoi themselves never change, they simply recombine in different ways to make different materials.
The ideas of Leucippus and Democrites were surprisingly ahead of their time considering it wouldn't be until the year 1800 before the first atomic theory would be proposed by John Dalton. They were correct that atoms were the building blocks of matter and that the atoms themselves never change, they simply combine in different ways. A substance which is only made of a single type of atom is referred to as an element, and a substance made of two or more different types of atoms combined is called a compound. There are about 98 naturally occurring elements but upwards of 118 have been either already been synthesized in labs or probably will be in the near future.
You probably remember the periodic table from high school chemistry (or possibly from your nightmares depending on how much you like chemistry). This chart quite literally contains all the building blocks required to make everything around you including yourself. In fact there's a good chance that nearly all of the 98 naturally occuring elements are somewhere in your body right now, if only in trace amounts. Just like Democrites said, atoms can combine with other atoms to make compounds, however the atoms themselves never change.
Ironically, despite being correct about the existence of atoms and their ability to combine to form compounds, Leucippus and Democritus were actually wrong about the most important part of their arguement. Atoms, a.k.a "indivisibles", can actually be divided!
So was Zeno right? Are there really an infinite number of points between any distance? Should I post the moving green stick man picture again with a clever caption? As it turns out, the atom is made up of three smaller particles: positively charged protons, negatively charged electrons, and neutrally charged neutrons. The protons and neutrons bond together in the nucleus of the atom and the electrons stay around the outside forming a so-called "electron cloud". An atom can be identified by the number of protons in its nucleus (this is the number it is given on the periodic table). The number of protons will determine the number of electrons needed to make a neutrally charged atom. In other words you need 2 electrons to have a neutrally charged Helium atom since Helium has 2 protons. If the electrons and protons are not balanced, the atom has a charge and is called an ion.
The neutrons however are a different story, they play a role in allowing the nucleus to bond together. Changing the number protons would change the element, changing the number of neutrons however changes the isotope. Any given element can have several different isotopes, but not all isotopes are stable. Any time there isn't a proper balance between neutrons and protons, the nucleus will try to rearrange itself into a more stable configuration. This can result in neutrons becoming protons, protons becoming neutrons, or even in the atom splitting into two (known as nuclear fission).
So if the "indivisible" atom can actually be broken down into protons, neutrons, and electrons, can these particles be further broken down? As far as we can tell, electrons are truly fundamental particles. They cannot be further broken down and are part of a family of fundamental particles known as leptons. As for protons and neutrons, they are made up of even smaller particles called quarks. A proton is made of two Up quarks and one Down quark and a neutron is two Down quarks and one Up quark. Quarks, like electrons, are fundamental particles and cannot be further broken down.
And so we have finally arrived at the answer to our original question. If you were to cut the device you are holding now into progessively smaller and smaller pieces, you would eventually end up with quarks and leptons (in addition to a voided warrenty) which cannot be broken down further. Looks like Democrites and Leucippus have the last laugh on this one.