**“Ever Expanding Universe”**

Homily by Halcyon Domanski

February 6, 2022

When I heard that this month’s theme was “Widening the Circle” the first thing to come to my mind was projective geometry. And since Science is one of our sources and Math is the language of God, I decided to share with you why.

There are two moments in my life when math became so clear. The first was in the 4th grade when I learned that zero was not the beginning but the center of everything, that it was all and nothing. And that numbers where continuous and never ending in all directions. That -1 was not negative anything it was just going in the opposite direction. The second time was in college when I took projective geometry, which is the first-time math made complete sense to me.

In projective geometry we of course have a point. However, a point is not one dimensional, as it is in other math, but three Dimensional or more. There is a line, but it can never be finite and the same can be said about a plane. In projective geometry all things are least 3 dimensional and infinite. What we see is just a section of any given thing. The projective part of this geometry is when you interrupt one plane with another and thus change the trajectory of the lines on the first plane.

You see this every time you turn the lights on in your car. The light is interrupted by the plane of the road, and it changes the lights trajectory, spreading out on the new plane in a different direction.

Now there is also the “Real Number” which is denoted in an equation with a capitol R. A real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion). The real numbers include all the rational numbers, such as the integer 5 or −5 and the fraction 4/3, and all the irrational numbers, such as 1.41421356…, the square root of 2, Included within the irrationals are the real transcendental numbers, such as *π* (3.14159265…). In addition to measuring distance, real numbers can be used to measure quantities such as time, mass, energy, velocity, and many more.

The line that runs through the real numbers is called the Real Projective Line. I know obvious name. And all lines go to infinity, just like all numbers do. Real Projective Lines are represented as a K in equations. This means that two K lines on a plane going into infinity next to each other will meet.

There are no parallel lines. The math is there trust me.Also, the points at the end of a *K* line going into infinity eventually connects, creating a closed loop or topological circle. The math is there trust me.

This means that you can take any geometric equation and make a point in infinity and still solve the equation. In fact, you can make all the points in infinity and the equation will still work.

Now there is so much more to it than that. But it is the essence of it.

So back to me in this class. When we learned that the Real Projective Line goes to infinity and eventually meets itself, I ask if that meant all lines are curved. Which lead to other formulas, more teaching, and yes, the theory is that all lines are curved.

I thought about this and came back and asked, “Then does that not make the universe infinitely cervical.”

When I asked this question, My Teacher asked, “Then what is the radius and diameter of this sphere?”

I thought about it and came back and said, “Well, if the sphere is infinite then so too is the radius and the diameter.”

He then asked, “Then where is the center of the sphere?”

Well DAMN if everything is infinite where is the zero, the middle, the center?

Over the next month I drove everyone crazy because this was all I would talk about at dinner, well not all, but close. Then one night after dinner when everyone had left but one friend, I was at it again.

I looked at a glass of milk on the table and said, “This is driving me crazy,” to much groaning. “Let’s say this glass is the center of the universe and FROM it in every direction to infinity is the universe.”

“Uh huh.” said the friend.

“Then what happens if I move the damn glass to over here.”

Bright light bulb above the head,

Angels singing on high,

The earth shifted on its axis,

and I started laughing and could not stop.

“What is so Funny?” my friend asked.

“I am the center of the universe, I am the center of the universe, and so are you.”

To which I got a smile, a headshake and a “I have to go do my homework.” and she left.

The next class I explained my revelation. I am the center, and the universe radiates from me in every direction to infinity. And you are the center, and the universe radiates from you in every direction to infinity. And both things are true because it is infinite, ongoing, never ending. All Real Numbers along any given Real Projective Line can be and are zero because the line is infinite. I am the center of the universe and so is everything else.

My teacher said, “Good, very good, now prove it mathematically.”

To which I said, “Nope, it’s enough for me that I figured it out, I have no need to prove it.”

He chuckled and said, “O.K.”

So how does this affect our lives, well in essence, in projective geometry, in the language of the Gods, you are responsible for everything. Remember the car light. The road is responsible for changing the trajectory of the light. Everything you encounter, you change its trajectory. Which in turn changes the trajectory of every single other thing in the universe. Our lives are but a miniscule Section of that infinite line. We do not have the capacity to see all the changes we are making. But we ARE making them. The question is, “How do you want to affect the universe.?” In what new trajectory do you want things to move. Look how Hitler changed the trajectory of our planet. Look how Jesus changed it. Look at all the things that have happened in the last 13 years and how that has changed the trajectory of all our lives. Obama, Trump, Marriage rights, the impact of Covid

on the U.S. I could go on and on.

You have the power to create the universe, you are the center of it all. What is it you want to make with your actions?

It is up to all of us, the centers of the universe to change it for the better.