This question lies at the heart of a fascinating
area of mathematics called topology. Topology
studies shapes, but it looks beyond their exact
measurements. The fascinating thing about topology
is we usually are not concerned with how long
an object is or how sharply it bends. or whether
it is perfectly round. Instead, topology asks
what properties remain when a shape is stretched,
twisted, bent, or compressed without cutting
it apart or attaching pieces that were previously
separate. The most famous example involves a
coffee mug and a donut. At first, they seem to
have completely different shapes. One holds coffee
and the other might be covered in chocolate frosting.
But imagine that both are made from soft clay.
You could gradually shrink the cup while thickening
and rounding its handle. And if you continued
reshaping the clay without tearing it or joining
separate parts, the coffee mug could eventually
be transformed into the shape of a donut. and
the donut are essentially the same shape. And
why? It's because each has exactly one hole.
Their appearances are different, but an important
part of their underlying structure is the same.
Topology teaches us that appearance and identity
are not always identical. A circle can be stretched
into an oval. It can be pulled into a long irregular
loop. It might no longer look much like the perfectly
round circle we started with, yet as long as
we do not cut it, open or connect different parts
together, its basic topological structure remains.
And this raises an interesting question beyond
mathematics. What makes us... Us. A pregnant
woman certainly sees her body shape change. You
are certainly not shaped exactly as you were
20 years ago. Your body has changed. Your knowledge
has changed. Your relationships, responsibilities,
and beliefs may have changed. Experiences have
stretched you. Disappointments may have bent
you. and unexpected events may have pushed your
life in directions that you never anticipated.
And yet, through all those transformations, you
remain you. Now, this does not mean that nothing
important changes. Some experiences truly do
reshape us. We grow, we learn, we heal, and sometimes
become people our younger selves would barely
recognize. But change is not necessarily the
loss of identity. Like the circle being stretched,
our outward shape may change while something
deeper continues through the transformation.
Perhaps it is our memories. Perhaps it's the
relationships that have formed us. Perhaps it
is a deeply held purpose. Perhaps our identity
is not something we must preserve by ourselves,
but something grounded and being known and loved
by God. Topology invites us to look beneath an
object's current appearance and search for the
structure that remains. Maybe. we can learn to
look at people in the same way. A person's circumstances
may have changed. Their abilities may have changed.
Their body or personality may have changed. But
their value cannot be measured only by their
present outward shape. I am reminded of that
every week when I visit my dad at his retirement
home. Mathematics teaches us that not every transformation
changes what something fundamentally is. So,
beneath all the changes that you have experienced,
what makes you still you?