Abstract Ideas
Like Infinity and God
Thinking of infinity leads to reflections on existence. Bear with me for a moment to see how, but what does it mean to exist? Can something exist if only in concept? Is something real if only an idea? Or does an idea need to manifest itself in some physical form in order to exist? In other words, is material existence the only reality in our universe?
A silly example – unicorns. Are unicorns real? They are a real idea, but does this make them real? Mention unicorns to children and they all describe a magical horse with a single horn. But a unicorn has yet to exist in reality, if we mean exist in our physical universe. This idea has yet to take on flesh. Unicorns exist in fantasy. They exist in stories and pictures and ideas. They exist in cartoons and paintings and movies. But does this type of existence make a unicorn real? Until now, unicorns are not a real animal, simply the creation of mankind taking bits and pieces of known animals to create a creature of fantasy. Unicorns are only a figment of our imagination, a thought, a whim perhaps. Is a unicorn real because some little girl can draw one when you ask her to? Or, is a unicorn not real because unicorns only exist in fantasies? What is your answer?
The reason unicorns are important is because we need something analogous to infinity. Some might rightly ask – how does a horse of fantasy relate to an idea about never-ending or always accumulating? How is a unicorn related to infinity? They are related because neither can be scientifically proven to exist in our universe. This is why reflections on infinity led me to thoughts on existence. If ideas are excluded from what is real, we run into some serious and curious problems.
Sure, mathematicians and engineers use the concept of infinity to solve all sorts of real-world problems. But infinity does not manifest itself in our world, except in faith, the faith of people, chief among them mathematicians and scientists, but it is faith that allows infinity to play a role in our lives. But in our universe, infinity exists as a concept and not a physical reality.
For example, we may call something infinitesimally small, but it’s not. There is nothing infinitesimally small in our universe. Very small things exist, so small they are difficult to measure, like atoms, which are unseen by the human eye, but even though atoms are small, they are not infinitesimally small. Similarly, but on the opposite side of the size spectrum, the universe may seem infinitely big, but it has a finite size. The universe may seem unlimited because of curved space, like a circle is unending, but our universe is not infinitely large. That’s right, the universe may be marvelously and unfathomably large, but it is not infinitely large. The universe is finite with respect to space and time.
So, we may use the concept of infinity, but in reality, infinity cannot be proven to exist through science experiments. We simply use this idea because it is helpful for us to understand reality. And mathematicians, scientists and engineers use the concept of infinity all the time! Infinity is an abstract concept used to understand concrete realities. Infinity cannot be measured, not because we have bad instruments, but because we do not have any instruments that measure beyond this world – and infinity is beyond this world.
So, from a scientific point of view, infinity only resides as a concept in our minds that helps us understand reality. And in this, sure, infinity is quite different from unicorns, for unicorns don’t help humanity understand our universe. But the principle regarding how infinity helps us make sense of reality is important. Whatever we believe about infinity’s existence, we definitely use infinity to make sense of reality. And while we use the concept of infinity to understand the world and solve problems, infinity is beyond science. Science uses infinity as a given but cannot prove infinity exists through experiments. Science assumes infinity. I’ll say it again, science assumes infinity exists.
So, a scientist may use the concept of infinity, like a poet may dream of everlasting, but scientists use the concept because of our ability to see with our mind’s eye, our ability to see logically in faith. Scientists do not see infinity with physical eyes; scientists do not prove infinity with scientific tests and experiments; scientists simply use the concept of infinity to better understand our world. We use the concept of infinity in faith. And this was an amazing realization, to see how much I took for granted as fact that was in fact me practicing faith. I treated infinity as a fact, when in reality, I was practicing faith by relying on infinity without material proof of its existence.
And infinity is just the tip of the iceberg for humanity’s use of abstract concepts in order to understand everyday life – concepts like zero, imaginary numbers, or even money, are simply a few of many abstract concepts that influence reality. These concepts have value in this world while not needing to have physical existence. Let’s consider zero.
We take zero for granted, but not long ago, zero was considered a mathematical invention. Zero had to be invented to describe the lack of something. And this invention led to other abstract inventions (like negative, complex, and imaginary numbers) which help us understand all sorts of real-world objects like computers, satellites, orbits, and accountants. These mathematical inventions help us understand the complex universe we live in.
Another example, imaginary numbers are often used in physics and electronics, whether to calculate orbits of planets or to make computers run, but the square root of negative numbers are called imaginary because mathematicians ‘imagine them’ to solve difficult equations. The square root of negative numbers does not exist in our physical world. We cannot see or touch them, but imaginary numbers are vital for physicists and computer scientists in their calculations and computer codes. Otherwise, we’d never be able to allow satellites to orbit our earth, pinging invisible signals to devices that we can touch and see and use to chat with friends half a world away. This is only one example of many, but the point is, humans often use abstract concepts which cannot be proven through scientific experiments. If anything, they are only proven in the sense that they help make sense of reality. They are proven in practice. We can apply these ideas, and in their application, we have a better understanding of reality. But we cannot create a scientific experiment to prove infinity. Again, there are certain ideas that cannot be proven through science.
This is not unlike creating fairy tales and comic book universes to communicate important ideals or truths. Though Superman or Santa Claus or God or unicorns might not exist in the flesh, they help teach adults and children important truths, like the importance of protecting people (Superman) and giving to others (Santa Claus) and imagination (God, unicorns). Who knows, maybe the hope that we will one day fly with reindeer or go faster than a speeding bullet or create a new breed of flying horse helps bring joy to someone and capture their imagination, and there is great value in that. Einstein’s theory of relativity was the seed of an idea he had as a child – what would it be like to ride a light beam? A boy’s idea forever changed the world when that boy became a man. When Einstein used his childlike thoughts and reasoned like a man, he forever changed how we understand our universe. Einstein’s scientific findings have gone beyond science and bled over into all sorts of other fields, including arts and entertainment. The proliferation of space and time travel stories from the 20th century onwards is a very simple example of how his theory has not only helped us understand reality, but also given us joy by creating new genres of stories that include ideas on space and time travel.
As a scientist, who did not believe in God, this pointed out a few issues in my worldview. One, I had to accept the idea of God, just like I accept infinity and unicorns and fairy tales. I could no longer negate God, for the idea about God may be helpful, like infinity or fairy tales are helpful. The issue becomes one of existence in a form that is higher than an idea. The question about God becomes more complicated. I could no longer negate the existence of God as a scientific impossibility, for science points beyond itself and if I wanted to be consistent, I’d have to negate infinity as well; something I couldn’t do. As a scientist, I would not dare negate infinity; I depended on the concept of infinity too much in my science and engineering. Too much was made possible because of infinity in the real world. I realized, abstract concepts like infinity were useful for reality, and I had to make space for other abstract concepts like God. And so, simply put, I had to grant that God exists, even if only as an idea.
My thoughts about God changed. The question now becomes does God exist in a higher form than only a concept or idea? Does the idea of God take on flesh? Does the idea of God make better sense of reality?
Unfortunately, though tools of science may help understand the idea of God, the approach to proving God has to be different than simply setting up an experiment. Otherwise, an experiment to prove God would be like an experiment to prove infinity – impossible! I have to approach God like I do infinity. I have to use the idea of God to see if this idea makes better sense of reality, like infinity does.
One interesting aspect of infinity is its hiddenness. It is an unseen dimension of reality. Many scientific findings of the last 500 years are because scientists look at the world and understand unseen or ‘disguised’ forces, like gravity and energy transfer, and yet ‘see’ them through the eyes of faith – the faith of scientists in search of answers. By seeing through the eyes of scientific faith, scientists help humanity understand reality differently than if we were to simply see through natural eyes. The eyes of scientific faith help us see things as they truly are, not as they appear to be. And so, we know when the sun appears to fly across the sky it is in fact the earth orbiting the sun. We see in faith, beyond the deceptive appearances registered by our natural mind and senses. I needed to reconsider all that I thought I knew, and I needed to start by seeing how science makes sense of the invisible. Yes, I needed to make sense of the unseen.