So, let’s say there are some people who have just found out atoms exist, but have absolutely no idea about how small they are. How might one get it across to them?
Well, an easy way of doing this is starting with something that someone probably already does know of and then comparing to that the thing they don’t know, and that you’re trying to make them know, in this case, how small atoms are. For example you could share the fact: ‘There are more atoms in a litre of water than there are litres of water in the world’. This works very effectively because people already know perfectly well the size, to a sufficient level of detail, of a litre, and all the world’s water as they have seen the sea, and even if they haven’t, I presume they have enough of an idea of the amount, and that means they also know how the rough scale of how many litres of water are in the world, no-one knows exactly, but we all know it’s a LOT, and that we’re familiar with. Then, after hearing what we’re familiar with, we are then told that there are EVEN MORE atoms in just a litre of water, which we know the size of, getting across the point of how small atoms must be, to fit more in a litre than litres in the world’s oceans.
Now, what if you use the example that even a TEASPOON of water has more atoms than the number of teaspoons worth of water in the world, this is still new information, and it actually further emphasises how small atoms are, because, as remember the audience doesn’t know the size of an atom, and we are just giving conditions that it fits to give them an idea of it, and since they are thus open-minded as to its size, after this new information, if let sink in well, the people should realise that since a teaspoon is much smaller than a litre, that for there to be still a higher number of atoms in a teaspoon, which has decreased from the number of atoms in a litre, than the number of teaspoons worth of water in the world, which has increased from the number of litres in the world, as a teaspoon is smaller than a litre, so there must be more of it, implies that an atom must have to be EVEN SMALLER to fit that many into an even smaller space, which is why if you think that ‘Saying there are more atoms in a litre of water than litres of water on Earth is the same thing, and suggests to no greater extent the smallness of an atom, than and as saying there are more atoms in a teaspoon of water than teaspoons worth of water on Earth’, then you have misunderstood what has happened.
However, unless you properly think about it like I have done, it is certainly NOT immediately easy to see just how obviously WRONG this viewpoint is, and indeed this is the case for a lot of math concepts that seem to require an ‘unfamiliar’ kind of thinking, but are really very straightforward. This can be done by taking this example to the EXTREME. Before I do so, I just want to make everyone know that a MOLECULE of water = 3 atoms
It might be easy to think that ‘Saying there are more atoms in a litre of water than litres of water on Earth is the same thing, and suggests to no greater extent the smallness of an atom, than and as saying there are more atoms in a teaspoon of water than teaspoons worth of water on Earth’ but saying that is like saying ‘Comparing the amount of atoms in an OCEAN of water to OCEANS of water on Earth is the same thing, and suggests to no greater extent the smallness of an atom, than and as comparing the amount of atoms in a MOLECULE of water to MOLECULES of water on Earth’
Now that I have scaled the difference up from between a litre and a teaspoon to between a WHOLE OCEAN and nothing but a MOLECULE, which is a hundred thousand times too small to see, it becomes so obvious and common-sensical that it is very much NOT the same thing at all, but rather the complete opposite. Also, I do admit that it was not the best of me to use molecules in my example because people don’t have any idea of that if they don’t already know the size of an atom, which would defeat the point of this, but the point was that it’s much more impressive, the smaller the object can be and still have more atoms in it that that object compared to something huge, like the Earth, because that would mean the atom must also be smaller to fit that condition and keep that statement true.