WEBVTT

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Hi. What a week. We've been exploring dimensions

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in mathematics. We've seen how changing dimensions

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changes what we can see. Equations become pictures.

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Imaginary numbers expanded reality. Circles gave

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birth to waves. Topology changed what mattered.

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Artificial intelligence revealed how relationships

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themselves can become geometry. Again and again,

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mathematics illustrates reality is far more connected,

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alive, and beautiful than it first appears. And

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perhaps that is part of what Eddie Wu means when

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he says that mathematics develops a new sense

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within us. We begin seeing patterns that were

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always there, connections hidden underneath the

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surface, a deeper geometry. woven into reality

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itself. But mathematics also reveals something

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equally interesting. Even while dimensions change,

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certain things remain constant. Take a circle.

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There is really only one number needed to define

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a circle. Its radius. Once we know the radius,

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we can determine the entire circle. So if we

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want to measure the distance around the circle,

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the circumference, we use 2 times pi times the

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radius. That is a one -dimensional measurement,

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distance around the edge. But if we increase

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the dimension and ask for the area inside the

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circle, the formula changes to pi times the radius

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squared. We square the radius because area is

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two -dimensional. And if we move from a circle

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to a sphere and ask for volume, we get four -thirds

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times pi times the radius cubed. Now the radius

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is raised to the third power because volume is

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three -dimensional. Notice what is happening

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is as dimensions change, space expands and the

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formulas transform. The power of the radius changes

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from one to two, to three. But one constant remains.

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Yes, pi. No matter how the dimensions change,

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pi doesn't. I find this story fascinating because

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it is interesting math. But to me, it also illustrates,

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or maybe paints me a picture, of how my life

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transforms as I travel from one life experience

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or one dimension to another. Over the years,

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many dimensions of my life have changed. One

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dimension is my marriage. Another is becoming

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a parent. Then losing a parent. Again and again,

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I find life expanded beyond the framework I once

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had. And I expect more transformations ahead,

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more questions, more growth, and more stretching.

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But through all those changing dimensions, there

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has been one constant in my life, my faith. For

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me, faith does not guarantee certainty about

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every outcome, nor does it fully explain why

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things happen. But it has provided a steady anchor.

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underneath the transformations. Maybe that is

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what motivates me to ask more questions, explore

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new ideas, and seek deeper dimensions. Because

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my faith is not threatened by growth. It grounds

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me while I grow. So the more I explore mathematics,

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the more I feel like I'm discovering patterns

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that were already there waiting to be seen. And

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these patterns are like branches, spreading in

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countless directions from a great tree, a tree

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that is deeply rooted.