Hi. What a week. We've been exploring dimensions
in mathematics. We've seen how changing dimensions
changes what we can see. Equations become pictures.
Imaginary numbers expanded reality. Circles gave
birth to waves. Topology changed what mattered.
Artificial intelligence revealed how relationships
themselves can become geometry. Again and again,
mathematics illustrates reality is far more connected,
alive, and beautiful than it first appears. And
perhaps that is part of what Eddie Wu means when
he says that mathematics develops a new sense
within us. We begin seeing patterns that were
always there, connections hidden underneath the
surface, a deeper geometry. woven into reality
itself. But mathematics also reveals something
equally interesting. Even while dimensions change,
certain things remain constant. Take a circle.
There is really only one number needed to define
a circle. Its radius. Once we know the radius,
we can determine the entire circle. So if we
want to measure the distance around the circle,
the circumference, we use 2 times pi times the
radius. That is a one -dimensional measurement,
distance around the edge. But if we increase
the dimension and ask for the area inside the
circle, the formula changes to pi times the radius
squared. We square the radius because area is
two -dimensional. And if we move from a circle
to a sphere and ask for volume, we get four -thirds
times pi times the radius cubed. Now the radius
is raised to the third power because volume is
three -dimensional. Notice what is happening
is as dimensions change, space expands and the
formulas transform. The power of the radius changes
from one to two, to three. But one constant remains.
Yes, pi. No matter how the dimensions change,
pi doesn't. I find this story fascinating because
it is interesting math. But to me, it also illustrates,
or maybe paints me a picture, of how my life
transforms as I travel from one life experience
or one dimension to another. Over the years,
many dimensions of my life have changed. One
dimension is my marriage. Another is becoming
a parent. Then losing a parent. Again and again,
I find life expanded beyond the framework I once
had. And I expect more transformations ahead,
more questions, more growth, and more stretching.
But through all those changing dimensions, there
has been one constant in my life, my faith. For
me, faith does not guarantee certainty about
every outcome, nor does it fully explain why
things happen. But it has provided a steady anchor.
underneath the transformations. Maybe that is
what motivates me to ask more questions, explore
new ideas, and seek deeper dimensions. Because
my faith is not threatened by growth. It grounds
me while I grow. So the more I explore mathematics,
the more I feel like I'm discovering patterns
that were already there waiting to be seen. And
these patterns are like branches, spreading in
countless directions from a great tree, a tree
that is deeply rooted.