How Far Is Infinity

There is a short film made in 1977 called Powers of Ten. It takes us a trip into outer space, and then back into inner space according to an oder of magnitude based on a factor of ten.

A couple is enjoying a picnic near the lakeside in Chicago in a lazy afternoon. The view starts from just one meter away. Every ten seconds, we look from ten times farther away until the couple is lost to sight. In 100 meters wide, we see cars on the highway and boats lie at their docks. As the distance grow, we see the great city on the lake shore, the whole Lake Michigan. In 10^6 meters, the Earth shows as a solid sphere.

Then the Earth diminishes into the distance, we witness the neighbor planets: Venus, and Mars, then Mercury. At 10^14meters, the solar system shrinks to one bright point in the distance. At last we past unfamiliar stars, clouds of gas and the Milky Way galaxy. As we approach the limit, the galaxies feel like dust and full of emptiness. We stop there and start traveling back home, until we see the hand of the sleeping man at the picnic.

In a few seconds the view enters the skin, crossing layer after the layer, from the outermost dead cells into a tiny blood vessel. Inside the white cell, we see the wall of the cell nucleus appears, the nucleus within holds the genes in the coils of DNA.

At the atomic scale, we see a group of three hydrogen atoms bonded by electrical forces to a carbon atom. Four electrons appear in quantum motion as a swarm of shimmering points. At 10^(–10)meters, we find ourselves right among those outer electrons and entering upon a vast inner space.

As technology improved, physicists kept going deeper and deeper, only to find smaller and smaller particles. Everything that was considered indivisible ended up having smaller “particles” and lots of empty space inside. Ironically the word “atom” comes from the Greek word for “indivisible”. The continuous endeavor to discover the smallest particle is rooted in the belief that any complex system can be understood by the sum of its parts.

It’s called reductionism.

Reductionism is the basis of many classical and modern science. A good example is the difference between western and eastern medicine. The western approach sees the body as a machine. If something goes wrong, the defective component is isolated and fixed. In contrast, the east consider health as a balanced state with integrity. Imbalance is treated by strengthening the body’s ability to heal itself.

Come back to subatomic particles. The problem is that they don’t behave as they are supposed to. Electrons don’t follow the laws of physics invented by Isaac Newton. Otherwise, since negatively charged electrons are strongly attracted to positively charged nuclei, every electron would be swallowed by nucleus, and atoms would shrink in size and undergo horrible contraction.

Moreover, in Newtonian physics, the momentum and location of an object tell us where it is and where it is going. But double-slit experiment shows that an electron moves in jerky leaps from one place to another without going in between. No one can predict where it is going to be next. Every time it is observed, it leaps to another unpredicted location. When not being observed, it exists occupying no actual space, more like a cloud, a “wave of possibilities”, an infinite possibility of potential location, surrounding the atomic nucleus.

If quantum physics is correct, then infinities are real.

Infinity has been the subject of discussion among philosophers from Aristotle to Euclid in Ancient Greek. Mathematicians extended the old philosophical concept and invented the magic symbol, ∞ in 17th century.

Imagine drawing a line on paper. What’s the total number of points on the line? The answer is infinite. Because in mathematics, between any two numbers there can always be found a third number greater than the smaller of the two and less than the larger. There is always an in-between. A point takes up no space.

You might also know that there are as many even numbers as there are numbers. At first it feels a little counterintuitive. Because even numbers are only part of the whole numbers. All the odd numbers are left over. The truth is there are infinite numbers of both. Infinity is not a number. It’s an idea that can’t be measured.

∞ +1 = ∞

∞ + ∞ = ∞

For the same reason, there are as many natural numbers as there are real numbers. Even though when you look at it within finite boundaries, the real numbers are bigger than the natural number. But since both of them are infinite, two infinities are equally infinite.

In mathematics, when a function goes to infinity, the point that is not defined is called singularity. For example, in f(x) = 1/x the singularity is the point when x = 0, because f(0) is not defined.

In spacetime, gravitational singularity is a location where the gravitational forces become infinite. At a singularity, all physical quantities take on infinite values. The laws of normal spacetime go crazy. Nearly everything calculable or measurable grows to unmanageable size. Space and time become highly stretched. Singularity exists at the center of black holes.

General relativity predicts that an object collapsing beyond a certain point would form a black hole with infinite gravitational force, reaching singularity. The initial state of the universe is also predicted to have been a singularity. Infinity has taken us a journey from an invisible mathematical concept to answering the most mysterious questions in human history.

Infinity is probably one of the biggest challenge to human imagination. Because we can’t see it. We can’t count it. We can’t imagine a color we have never seen before.

We do see infinite reflection effect sometimes. If you stand in front of a mirror with another mirror on the opposite wall. You can see yourself in the first mirror. The other mirror also “see” the first mirror and your reflection. Now the first mirror reflect the image of the mage. You are reflected an infinite number of times, but each image grow smaller and smaller.

But it’s still hard to wrap your head around the idea that something physical is unlimited, endless, unbounded. We live in a world that keeps reminding us how limited our life is. Everything we see with our eyes is finite. People feel “not enough” all the time and complain about not having enough time, money, or energy to achieve their dreams.

They believe in “survival of the fittest”. It makes sense to try everything to win the survival competition. But someone else’s gain will become their loss. With such scarcity mindset, they will see only limitations instead of opportunities. The focus will become avoiding losses rather than achieving gains.

Daniel Kahneman explains the asymmetry between losses and gains in Thinking, Fast and Slow. “Bad is stronger than good.” When we focus on preventing loss, we are more likely to pay a hefty price to ensure certainty.

Because of the possibility effect, we tend to overweigh small risks and are willing to pay far more than expected value to eliminate them altogether. Overweighting of small probabilities increases the attractiveness of both gambles and insurance policies.

When we set our goals based on what’s reasonable and how to cut losses, we end up selling ourselves short.

Abundance is the opposite of scarcity. Instead of seeing life as a finite pie, you believe there is enough for everyone. It means believing in all of life’s possibilities. Limitations, fear and desperation disappear because you know there is more than one way to reach your goals. Abundance is a state of being.

Infinity is a universal constant that comes from within.