The Universe in Perspective


7: Pong World


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"You may think I'm small, but I have a universe inside my mind." - Yoko Ono



Stylized SunPong World: Small vs. tiny vs. miniscule vs. wow

We've investigated the size of the Earth in detail and you have a good idea just how big it actually is. Yeah, ok, it's a shrimp astronomically, but it's big to us.

We're now going to use the Earth as a magnifier as we seek to understand the very small.

I mean the really really small.

Consider the point of a needle. That, in everyday life, is pretty small. But even so it's dimensions are on the order of 10ths of a millimeter and it is see-able by human eyes. In fact, for most of us, this is about the limit the human eye can resolve.

But there is so much more to the Universe beyond the needle-point level.

You are familiar, I assume, with one of the central tenets of Biology: all living things are made of cells. Cell size, for the most part, is about the same over all living things. Cell sizes in a flea are the same as the cell sizes of Elephants and Blue Whales. They are the same in an onion and in a Giant Redwood tree. They are the same in an onion and a flea.

Yes, there are cell size variations but mostly for specialized cells. Animal cells run from about 50 µm to 10 µm (50 to 10 hundreths of a millimeter), while plant cells run from 100 µm to 10 µm (a tenth millimeter to one hundreth millimeter). There are exceptions, but they are rare: the human egg cell, for example, which is a tenth millimeter, and some amoeba species, etc.

Remember that the µm stands for micrometer (also called a micron) and is 1 × 10-6 m (a millionth of a meter), equivalent to a thousandth of a millimeter.

A fairly typical cell size, which we will use here, is 20 µm. This is a typical cell size shared by both plants and animals.

We will now take a selection of these cells, closely packed as if they were in place in a living thing, and this selection will be exactly the size of a Ping Pong ball.

We're going to assume the cells are cubical, but keep in mind that cells can be all kinds of shapes: sphereoidal, stringy, pancake-like, and more.

This Ping Pong ball-sized lump filled with 20 µm cubical cells would contain about 4 and a quarter billion cells.

Now we will inflate the Ping Pong ball-sized lump, and everything within it to scale, until it is the size of the Earth.

Now imagine yourself on the surface of the PingPong-Cell_Lump-Earth. You will find the tiny cell is now a gigantic cube 6,400 m on a side.

Each cell has a cell membrane holding in all the cell contents. Considering the cell's inflated massive volume we might expect a fortress-like wall holding back the injuries of a non-caring world. We expect a massive wall that could protect the cell from attackers, from physical injury, and prevent the loss of water and other precious fluids, while yet allowing it to take in nutrients and oxygen. Yet when we inspect the cell wall, which does perform all these functions and more, we find it to be, astonishingly, only about 2.25 m thick.

Plant cells contain a structure known as a chloroplast. This structure is THE basis of all life on Earth (there are only a handful of extremeophile exceptions), since it uses sunlight to convert carbon dioxide and water into sugars. These chloroplasts would be floating around in this titan cell and be about 1,500 meters long by maybe 400 or 500 m wide.


Cells from the plant Bryum capillare.

The green balls within the cells are chloroplasts.

Photo courtesy of WikiMedia Commons.



Bacteria, which literally cover everything you touch, would also be here stuck on the surface of our pong world. Escherichia coli (3 µm x 0.6 µm), for instance, would be an entire (primitive) cell about 1000 m long and 200 m wide. In the real world, bacteria are the smallest things light microscopes can resolve, and even then just look like dots or rods (the limit of light microscope resolution is about 1000x).


A pile of bacteria from the species Escherichia coli.

This is not a light microscope picture but was taken using the technology of Scanning Electron Microscopy (SEM). This technology only shows the surface of objects but at very great magnifications.

Photo courtesy of WikiMedia Commons, public domain from the USDA.



Viruses, like cold, flu, and HIV, are much smaller. A typical flu virus would be, here on PongWorld, 40 m in diameter and so would just fit into an Olympic sized pool.


A pile of viruses.

This photo was taken with yet another technology called Transmission Electron Microscopy (TEM). This technology shoots electrons through ultra-thin slices and so can show internal structure. This picture is about 100,000x.

Photo courtesy of WikiMedia Commons, public domain from the US CDC.



Now this has been a bit like a tour with me calling out: "...and over here we have the Eiffel Tower, while there you can see the Louvre", as if these structures and objects are just sitting there for you to see and admire.

But you wouldn't actually be able to recognize a thing (unless you are a chemist)!

Because here we have inflated our biological tissue to the atomic level. Each of these structures is made up of a conglomeration of atoms.

Atoms which, for our purposes, approximate spheres/balls. And so, for as far as you could see, would be mountains of balloon-animal-like conglomeration structures.

Take, for instance, water. Earth life requires water. The cell is made up predominantly of water and so this is what you would see the most. All the other cellular structures are floating around in this sea of water.

Quick introduction to atoms, we go into more detail in a later chapter. What you need to remember now is simply that atoms are, in general, electrically neutral.

While the outer portion of the atom is made of negatively charged electrons, the central nucleus of the atom contains the same number of positively charged protons. This cancels out any net electric charge.

The atom's structure can be considered as spherical for our purpose. The outer wall of this atom-ball is made up of the orbiting electrons whizzing around the central nucleus.

Almost none of what you see here on Pong-Earth are individual atoms floating about. They are combined in various ways with other atoms, and when two or more atoms are connected, or bonded, to each other the entire conglomeration is called a molecule.

The water molecule, chemically, looks like this:

Water Molecule

The water molecule in three views.

The first is standard chemical representation of atom connections. O stands for Oxygen, H for Hydrogen (pm stands for picometer).

The second is stick and ball representation. Oxygen is usually colored red, Hydrogen white.

The third is a 3D representation showing approximate size relationships. The structure of water is quite special for life and that is why the details are so important.

Photos courtesy of WikiMedia Commons.

water notation

water stick and ball

water 3D


Water is made up of 2 Hydrogens and 1 Oxygen (H2O). Note the water molecule increasingly resembles a "pixelated", stylized, balloon-animal approximation to Mickey Mouse with Oxygen being his head and the Hydrogens his ears.

On our Pong-World scale one of these water structures is about 9 cm big.

So, first off you would be seeing a lot of balloon-mickey-mouses tumbling and churning around. But within this ocean of balloon-waters are floating very complex molecules that make the cell the living thing that it is.

For instance I mentioned that plant cells can have chloroplasts, the literal food engine of this planet. The chloroplast contains many complex molecules but the main one responsible for using sunlight to produce food is the chlorophyll molecule pictured here:


An example of a complex life molecule, chlorophyll in two views.

The first is standard chemical representation of atom connections. H is Hydrogen, O is Oxygen, C is Carbon, N is Nitrogen, Mg is Magnesium.

The second is a 3D representation showing approximate size relationships. White is Hydrogen, black is Carbon, blue is Nitrogen, green is Magnesium, and red is Oxygen.

It really does look like a (complicated) balloon animal doesn't it?

Photos courtesy of WikiMedia Commons.


chlorophyll 3D


And so on our tour this is what you would be seeing and unless you've studied chemistry exhaustively you would be hard pressed to recognize anything, except maybe water.

Our tiny cell has turned into a gargantuan, mountain-sized cube filled with tiny engines of chemistry. But of course we're not yet done investigating the very small.

Each of these molecules are made up of many combinations of atoms. A dominant atom in a biological sample is Hydrogen, which is the simplest atom. It consists (usually) of a single electron in "orbit" whizzing around a single proton in the central nucleus.

Let's grab one of the many balloon-water molecules and yank off an "ear" (the white portion of the water molecule).

We are now holding a single hydrogen atom. It's radius depends on many things particularly how it is bonded to other atoms. So in one case it would be considered to be one size (using the Van der Waals radius), while in another case it would be another size (using the Bohr radius).

For our purposes we will consider a single, isolated hydrogen atom to have the Bohr radius and so, in our inflated pong-world, the hydrogen atom would be like holding a 3.3 cm diameter squishy balloon (smaller than a ping pong ball by about 20%).

But the crazy thing is, when you look inside this Hydrogen atom, you see...absolutely nothing. It's empty. Zilch. Zero. Nada.

I should mention here that we are looking at things so small that the concept of "radius" and "diameter" and "length" are all a bit mushy due to quantum mechanical effects. Particles this small have the dual property of being like small particles and at the same time being smeared out energy waves. But it is possible to get "effective" radii and sizes and we'll have to be happy with that because that is how Nature is.

So, anyway, our Hydrogen atom appears to be completely empty at this scale. And that is because the proton is really really really small. Its effective "diameter" is much smaller than the entire atom itself by around 10,000x.

So. We are going to take our 3.3 cm hydrogen atom and inflate that until it has an 800 m radius. As we now stand in the center of this hydrogen atom sphere, where the "wall" of the electron orbit is 800 m away in all directions, we would find our central proton to be the size of a Ping Pong ball.

At the proton level we really are at the smallest thing that can be called a "particle" and that can have a "radius". While there are "parts" to the proton (called quarks) they become better described through the realm of energy rather than measuring rods.


The Universe continues to make sense at these scales and continues to be understood by the equations used by physicists. But those equations do reach a limit where there can be nothing smaller. There is a theoretical minimum "length" in the Universe, it is called the Planck Length.

The Planck Length is the smallest measure where it still makes "sense" to talk about "length".

The Bohr radius of the Hydrogen atom is 5.3 × 10-11 m.

The radius of a proton is about 5 × 10-15 m

The Planck Length is, ahem, 5.16 × 10-27 m., about a trillion times smaller than a proton.

Let's get waCky kraZy and take a look at the scale of the Universe around the Planck Length. You will need to keep in mind all the comparisons we've made up to now, in particular the size and scale of the Observable Universe.

The following is a rough, but in the neighborhood, approximation:

If we inflate a Hydrogen atom until it is is the size of the Observable Universe:

The electrons would be orbiting all the way at the edge of the Universe.

The Proton would have a radius out to the Andromeda Galaxy.

And the Planck Length would be 40 m, about the size of an Olympic swimming pool.

You may have already realized it: we, people, animals, and plants of Earth, live just about in the middle of the hugest distances and tiniest lengths of the Universe. We think about things, on a daily basis, in the meter range, and the edge of our Universe is about 1026 m away while the smallest possible length is 10-27 m away. Eerie, and pretty cool.

It could be that the Universe is much bigger.

Remember we can only OBSERVE it out to a certain distance due to the constancy of the speed of light. But maybe, beyond the "edge", the Universee is 10 times bigger...

Or a 1000 times bigger...

Or a trillion times bigger...

We simply don't (can't?) know.

Its time to start considering the other two major components of our Universe: space and energy. But before we can really meaningfully do that we need to, in the next chapter, talk about chemistry in a bit more depth.


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