Hi, hopefully you have authority figures in your
life who you admire and respect, such as your
parents. But despite that respect, you may see
something in a different way, a different perspective
than they do. They may feel strongly about their
perspective, and it's easy to step back and let
their view become the only view in the conversation.
And yet, something doesn't quite sit right. So
how do you enter into that kind of conversation?
I know I have been there. And in those moments,
I ask myself, where can I find the courage to
engage rather than be silent and just conform?
Can math give us a clue on how to move forward?
Yesterday, we talked about how different starting
points can lead to different conclusions. Math
teaches us that we are allowed to begin in different
places. Math literally is an invitation to start
at a different point. But it is not chaos, because
once we begin, we must follow the logic wherever
it leads. That means in difficult conversations,
we can ask, what if we start from a different
place? What would follow from that? For example,
rather than judging someone who is angry, how
about we understand where the anger is coming
from? Now, you may think math is just about numbers,
but it is an exercise in digging deeper and considering
new starting places. Digging deeper and finding
a different starting point requires courage.
But the history of math is full of people with
that kind of courage. Take geometry. In school,
we learned that the sum of the angles for a triangle
is 180 degrees. This truth travels all the way
back to Euclid over 2 ,000 years ago. Euclid
built this by assuming five postulates were true.
A starting point, if you will. But in 1854...
Bernard Riemann and others had the courage to
change the starting point by changing how parallel
lines were defined, which is one of the five
starting points. When that new starting point
was taken seriously, the math world and eventually
the entire world completely changed. Entirely
new geometries emerged. In a very real sense,
New mathematical worlds were built from a single
change in assumptions. And those ideas did not
stay abstract. They became essential to understanding
curved space, which is what allows systems like
GPS on our phones to work accurately. Incredible!
That's what having courage to start at a different
place makes possible. This courage creates space,
literally, to explore what we might otherwise
dismiss. Of course, courage is not just about
math. It shows up in conversations, in relationships,
in moments where it would be easier to stay silent
than to engage in a way that feels honest. Because
challenging certainty carries risk. Sure. You
might be wrong. You might be misunderstood. You
might create tension. But without that courage,
something else happens. We stop exploring. And
when we stop exploring, our understanding stays
smaller than it could be. So my question today
is, where might I need the courage to stay in
the conversation long enough to consider a different
starting point?