Size Matters: A lot more than we think!
If you think humans are insignificant against the vastness of the universe, then you do not know the half of it!
Spiders and Things
Outside of the National Art Gallery in Ottawa, Canada, is a very large steel spider sculpture named Maman. Like many works of art, when Maman was they first erected there was much debate about what it symbolized; why it was installed in that particular location; and whether it was worth the cost.
As would be expected with any profound work of art, many people had much praise for the sculpture, while others had other less heartfelt words for it. But the surprising part for me was that most people remained somewhat ambivalent about it — passing by it on a daily basis without taking much notice. It is when such a work of art does not provoke a reaction that puzzles me most.
The creator of Maman (Louis Bourgeois) says it is a dedication to her own mother, and motherhood in general, symbolizing nurturing and protection. It is an interesting idea, but when I first saw Maman, I had a different interpretation. My first impression was that it was a statement about the scale of nature; a kind of reciprocation of the spatial perspectives of our two species. Perhaps I’m showing my bias toward nature, but here is what I mean.
We are accustomed to thinking that the size of the average adult human, being about one and a half to two meters in height, is the benchmark from where we gauge the relative size of other life forms, and other things in general like mountains, rivers, or buildings. But there is so much more to reality beyond our normal sense of space relative to us humans. Every living species has its own way of situating itself relative to its environment, and it is reasonable to assume the spider sees its world on what we would refer to as a more microscopic level, relatively speaking. By contrast, one cannot help wonder what the spider thinks when it sees a human? I mean, if you think spiders give us the heebie-jeebies when we see them crawling across our basement floor, imagine something 1000 times bigger than you coming at you all of a sudden! I suspect spiders know a lot about heebie-jeebies as well!
So the experience of walking under a spider gives us a better appreciation for differences in scale in our respective worlds. I also suspected the statue was located where it is to encourage large numbers of the public to have this experience. And it has proven to be very effective. It is one thing to look at magnified photos of spiders or other tiny creatures, but it is quite another to experience walking under a gigantic replica of one.
Maman invites us to experience this change of perspective, wherein she plays the role of the big scary giant, and we take the role of the tiny vulnerable creature. At least to me, such experience invites us to re-think our relationship with nature and our place in it. As any ecologist will tell us, nature is full of diversity, and it takes species of all sizes in a complex web-of-life to keep life on Earth functioning as a whole. So perhaps Maman symbolizes motherhood in a different way than what her creator had intended, and our interpretations are not so different after all?
More Than Meets the Eye
This leads us to other questions about the perspective we humans take on other aspects of world around us. Take for example, our everyday perception of sunrise and sunset, or the cycles of the moon. We are accustomed to seeing the sun and moon as relatively the same size as seen from our perspective here on Earth. This is evidenced by a solar eclipse where, almost seemingly by design, the moon blocks the sun almost completely at 100%.
In reality, at approximately 1,300,000 km in diameter, the sun is about 100 times the size of the Earth (which is approximately 13,000 km in diameter), which in turn is about 4 times the size of the moon (which is approximately 3200 km in diameter). So while the Sun is about 400 times the size of the moon, they appear to be about the same size to us from our perspective here on Earth. The illusion in size is related to the large differences in distance they are from the Earth, which in itself, is difficult to truly appreciate.
Here’s the problem. When we learn about the solar system in school, we are often presented with pictures of the type shown below, where the sun is shown to be the large massive fireball that it is, and the planets are shown in some relative sizes as orbiting the sun and some arbitrary distance. But the actual contrast between the sizes and distances cannot be physically represented in a page size illustration to a proper proportional scale. So what we learn is actually a distortion of reality.
By contrast, consider a picture of Mercury relative to the Sun. With about a 5000 km diameter, Mercury is just a bit larger than our Moon, and only about 40% the size of Earth. So imagine a larger black dot of 2.5 times the size of Mercury just next to it, and you will have a better depiction of the relative size of the Earth, Moon and Sun if they were all closer together. Keep in mind that the distance between Mercury and the Sun is about 58 million kms! So in reality, it would appear merely as a speck of a black dot if it was actually immediately adjacent to the Sun than it is in the photo below — as would the Earth.
These differences in size are almost impossible for our human brains to truly comprehend simply because it is difficult, if not impossible, for us to experience them directly in their actual proportion. As with the experience we get from the spider Maman, it is only by walking under and around her that we begin to appreciate the reality over the illusion.
So while it is one thing to read about these things in textbooks using simple graphical or pictorial illustrations; it is quite another to experience them directly. But of course we cannot experience the actual distance between the Earth and Sun physically — it would not only take a very long time and a lot of money to fly there, it would also be fatal! We can, however, mimic the experience in other ways.
One way is to work with scaled models. In the case of the Sun, Earth and Moon, having such an experience is made possible using a few common items and a nice afternoon walk to a football field. All that is needed is a beach ball, a green pea, and a tiny sugar ball (like the kind used on wedding cakes). If the Sun were the size of a large beach ball (say about 1 meter diameter), then the Earth would be 100 times smaller at about 1 cm, which is about the size of a green pea. The moon is about 4 times smaller than the Earth, which is about 2.5 millimeters, which is about the size of the small sugar ball. Put those three objects together and you have a fair approximation of the differences in their relative sizes.
But what is more surprising (and this is the fun part), is to spread them apart at their actual scaled distances from each other! To do this, place the beach ball at one end of the football field, and walk all the way to the other end of the field with the pea and sugar ball. Now THAT will give you a much better appreciation for the real differences in size and distance between them!
Now imagine how much further away you would need to walk to get a sense of the distances of Saturn and Jupiter (which would be about the sizes of a golf ball or tennis ball respectively), or even Uranus, Neptune, and let’s not forget poor little Pluto! You would likely need to walk several blocks or outside your town limits for an accurate depiction. Mind-blowing, isn’t it?
It’s a Numbers Game
That type of exercise can help us appreciate how different our spatial reality is from our perception of it. In fact, it is so difficult with so many things, that our only way of dealing with them accurately is to use numbers. On the large scale, the distance between the Sun and Earth, at approximately 150,000,000 km, is used as a standard unit for measuring astronomical distances, known as an Astronomical Unit (AU). It is a convenient measure because it is easy to divide or multiply by 10. Our human brains have a very difficult time conceiving the vastness of astronomical distances and sizes of astronomical bodies, and so the best we have to work with are numerical notations to describe them.
The scientific notation we use is 10 raised to the power of how many times we need to multiply the number 10 to reach a very large number. We are easily familiar with smaller values such as 10² which is 10 x 10 = 100; or 10³= which is 10 x 10 x10 = 1000. So where 1 AU = 150,000,000 kms, the scientific notation would be 1.5 x 10⁸ km. And while it is difficult to wrap our heads around how large these distances actually are, it is even more difficult to describe in words or pictures.
There are a number of videos on YouTube  that provide visual depictions of the size of our universe relative to the Earth and Sun, and as good as they all are, they too have difficulty fitting it all into a screen display. But here is one that does a reasonably good job:
What I like most about this video is the ending when it mentions how “there are more galaxies in the universe than there are grains of sand on Earth; and that there are more atoms that make up one grain of sand than there are galaxies in the universe”!
Now ain’t that a kick in the pants! Not only are we dealing with things of incredible large sizes and distances, but to think that what everything is made of is as small as the universe is large is beyond mind-boggling. No amount of insomnia will enable our human brains to conceptualize it in any way (I know, I tried).
The distance between the Sun and Earth serves as a fair comparison of the distances we find between things on an atomic level; that is if we think of the Sun being the nucleus of an atom, and the Earth as an orbiting electron. Distances at that scale are measured in Angstroms, which are equivalent to 10-¹⁰ meters (where the exponent of -10 means 10 zeros after the decimal place; or how many times we need to divide by 10 to reach a very small number). And that is only at the atomic level. When we get down to sub-atomic and quantum levels, things get even murkier with scales reaching 0.00000000000000000001 meters (10-²⁰ m), and smaller! It’s enough to make your brain go bonkers!
All Things Big and Small
But here is what I really think is the most fascinating things about all this size stuff. From what we now know about the evolution of the universe (i.e. from the Big Bang until now), everything was built from the bottom up in that all of the largest things that occupy very large scales and distances are built from the very tiniest of things at the quantum level! I do not know about you, this is another thing that I just find mind-boggling, and I get dizzy if I even try to wrap my head around it. The best graphical depiction I can come up with is the following funnel type diagram.
I call this visual a STEM visual, where STEM is an acronym for Space, Time, Energy and Matter. The two axis are space along the bottom which go in both negative (micro scale) and positive (macro scale) directions, and the vertical axis which shows time in billions of years before present (BP). The STEM visual shows how the individual things on the left (on a micro level) make up their corresponding collective things on the right (on a macro level), along with their corresponding size scales. The vertical axis shows the approximate scale of time it has taken for each level to come into existence over the history of the universe. As with any other attempt to visually depict the immense size differences in both space and time, this visual does not do the reality any justice. But it helps to visualize a few important relationships that often escape our normal human sense of space and time.
Our human span of space-time awareness is confined to the very top of the STEM diagram between approximately a millimeter (10-³ meters) and several kilometers (10³ meters), and human time which goes back to about a 500,000 years ago. Because of vast scale differences, I had to truncate the top of the diagram where we place the emergence of our human ancestors at approximately 1,000,000 years , which in itself is only a sliver of time over the 4.6 billion years of the history of our planet. In fact, this diagram still does no justice to the differences in scales of our normal day-to-day span of awareness where we humans are predominantly preoccupied with stuff that happens only within our lifetimes and within several kilometers of where we live. At best, we may think of things on a microscopic level in terms of the nutrition we put in our bodies, or globally in terms of what is happening in other parts of the world, but that too is still just a sliver of the full scale of the reality that we are a part of. It is this bigger picture that can change our perspective and appreciation for who and what we are in this big mystery of a universe.
Perhaps one of the most bizarre things the STEM visual conveys is the interesting relationship between very smallest things and very biggest things that we have been able to observe so far. From what we understand of the origin and evolution of the universe, the relationship between the two presents a paradox of sorts. It is a paradoxical in that from the moment of the Big Bang the universe both blew apart and came together at the same time! It blew apart in the sense that both space and time, and the matter that formed within it has been expanding infinitely. It has come together in the sense that all the stuff created within the universe started building up in localized areas until we eventually have planets, including our own with life and civilization. The strangest aspect of the paradox is that the blowing apart would not have happened without the coming together; and nothing would come together without simultaneously blowing apart!
Now of course this is a very general depiction to which there much detail can be filled in. But its key message is that the universe and the reality in which we exist spans tremendous spatial and temporal scales, and that each thing we see (including ourselves) is actually made from the stuff that came before it. The stuff on the left is physically nested within each level successively from bottom to top, and the stuff on the right is spatially nested within each level from the top to the bottom. So our place in the universe is part of one big nesting operation that spans the infinitesimally small to the infinitesimally large.
We Are NOT Insignificant
There are many videos on YouTube that attempt to show how big the universe is, and how small we are in comparison to it, including the one shown above. From watching any of these videos, it is not uncommon for people to come way with the impression that it makes us humans seem like we are insignificant. But nothing could be further from the truth, and here is why I think that is.
Take a look back at the STEM visual. It is actually misleading to look at our place in the universe only in terms of the grand size of things on the right, because we are also made from the infinitesimally small stuff on the left! It is another one of those mind-boggling things that makes your head spin 360 degrees to think that the atoms that make up our bodies are as small as the whole universe is large! That is, to think there is as much space within us as there is outside of us is almost impossible to conceive.
But here’s another bizarre thought: we are what the Big Bang is still doing! How is that? Well, it is common to think of the Big Bang and the stuff that happened during the early stages of the universe as something that happened way out there and way back in time. But in reality, the Big Bang was just the beginning, and we are a continuation of the same movie that it started. It is all the stuff we are made of! So the universe is not only out there, it is also simultaneously within us; all the way down to the most infinitesimal level.
It also seems a bit strange that the space and time that we occupy is about half way between the two observable extremes of approximately 10^–25 meters to 10^+25 metres. We are neither at the very large and nor the very small end of the scale. It has taken the universe the equivalent of 14,000,000,000 years and an unthinkable amount of space and energy to put us here. We only seem incredibly small and insignificant relative to the external size of the universe, but we humans are incredibly large and complex relative to the internal size of the universe.
So no, we are not insignificant by any means. In fact, as mundane as life may seem on any Monday morning, life on Earth, with all of its glory and its turmoil, is the most significant thing this universe has created (that we know of). And we, along with every other living creature, are all a very intricate part of it.
No doubt, such contemplations can go much deeper into asking ultimate questions about what meaning it all has. But before we can get to those questions, we need to consider a few more things we’ve been learning. For example, we know that the further we look out in the universe, the further back in time are the things we see. And to make things even stranger, according to much of what physicists have to say these days, space and time itself goes all whacky. Neither space, nor time can exist without the other. It is not like there was space before the big bang, and the universe created within it, and that time is simply about how things change within a pre-given space. If only it were that simple!
If you find yourself asking how space can exist without space in the first place, you need not feel alone. We may have hit the ceiling in terms of what we can conceptualize about the true nature of the universe in comparison to our perceptions of it. It also leads us to wonder that if the universe is expanding, then what is it expanding into? If there is an outer limit to the universe, what lies beyond it if it is not more space? Mind-bogglers, I know. So let us leave those questions to the professionals, and have them get back to us when they find answers the rest of us can understand.
So What’s the Point?
This spacing out session is really about what we know from what we see and experience within our limited human capacities. It challenges us to think about our place in the world and universe in a different way. The spatial and temporal frame of reference we have on a human and Earth-based scale is already enough to inspire us to contemplate these fundamental aspects of our existence.
A take away in all this is to consider a scene we are easily familiar with that we so often take for granted; a gathering of friends around a fire against the backdrop of the night sky. At first glance it may seem that such a photo is nothing spectacular, but in reality, it is a snap shot that contains everything that we know this universe has to offer.
So, in contemplating how size matters, we can learn to take any ordinary perspective and make it extraordinary. The fact is, we are a privileged generation to have at our hand knowledge that no other generation has had before us. The invitation is there to at least occasionally think of what it is all made of, how it all got here, and even more significantly, how everything, both living and non-living, is a unique expression of its mystery.
And with that, the only cherry I feel worthy of being placed on this cake is a poem by Max Ehrmann. Happy camping!
 Ottawa spider sculpture ‘Maman’; including a description of its interpretive history: https://en.wikipedia.org/wiki/Maman_(sculpture)
 Some interesting visualizations of the magnitudes we are contending with are available at the following links:
- Solar System Model in Desert — https://www.youtube.com/watch?v=Kj4524AAZdE
- Big History — https://www.youtube.com/watch?v=yqc9zX04DXs
- Powers of 10 — https://www.youtube.com/watch?v=0fKBhvDjuy0
- Cosmic Eye: A more recent visualization of the Powers of 10 — https://www.youtube.com/watch?v=jfSNxVqprvM
© 2021 — Brian Gregory