Lessons from my Father
What mathematics and logic can teach us about life.
My father is a humble, softly spoken man and brilliant mathematician. I’ve had the privilege of witnessing his quiet, unwavering dedication to a field that few truly understand and even fewer have been brave enough to challenge. His work has been pioneering; applying geometric and mathematical principles to the fundamental architecture of collision avoidance systems in aircraft.
I’ll never be able to fully comprehend the depth of his work, or the scale of his contribution to saving lives globally through improved aviation safety. What I do know is that his work has already protected countless lives and will continue to do so every time someone steps onto an aeroplane.
Dad, if you’re reading this, I am proud of you. Today, I want to honour you. Not just for your dedication in the face of adversity, or for standing firm against criticism from those blindly protecting the status quo, but for how your lessons continue to guide me in my life.
I love you Dad.
Lesson 1: When you’re struggling to find a solution, invert the problem.
My father’s work in aerospace safety stands in stark contrast to the widely adopted practice of running computationally intensive simulations to map out all the possible routes where two or more planes might avoid collisions. This industry-accepted approach relies heavily on computational power, guesswork, iteration, and trial and error.
But Dad wouldn’t accept that such a precarious and unreliable method was appropriate for safety-critical systems. So he dedicated his life to finding a better solution.
One of his breakthroughs came by inverting the problem. Instead of calculating every possible safe path, he used elegant, repeatable geometrical equations that required far less computational power, by several orders of magnitude, to identify the only place where a collision could occur.
This approach delivered greater efficiency and far greater exactness. His guiding belief was simple: once you know where you can’t be, it becomes much easier to figure out where you can be. Inverting the problem brought clarity and ultimately, safety.
I’ve drawn on this principle in my own career, using it to unlock novel solutions when I’ve been stuck. And now, I find myself applying it to my life. As I enter a new chapter, I still don’t know exactly where I want, or need, to be. But I do know one thing with certainty: I can’t stay where I am and I must be willing to take the brave step to change my course.
Lesson 2: Not all circles are infinite loops.
I remember being quite young when Dad first showed me how a straight line could be viewed as a circle with an infinite radius. It blew my mind and I thought to myself I had discovered a considerable schoolyard flex. But I quickly realised that such an abstract concept proved unimpressive to most.
My Dad knows a lot about circles. How much, I don’t know. But if I tried to explain it I think we’d just go round and round. Unless the circle had an infinite radius, in which case we’d just go straight on ahead…
I reckon one day Dad might have a circle named after him, like the ancient Greek geometer Apollonius’s whose definition of a circle Dad’s work is inspired by and builds upon in the context of multi-dimensional space.
Sadly, I don’t have a life lesson from Dad’s or Apollonious’ circles, but I do from a feature of another kind of special circle Dad once showed me that I was reminded of just the other week by
.
I still remember Dad’s delight when showing me how what appears to be a circle may in fact be a three-dimensional spiral if you don’t constrict yourself to only looking at it from a single plane.
That idea has stayed with me ever since.
In life, it can often feel like we’re going in circles. Repeating the same patterns, facing the same struggles, stuck in the same place. But Dad was encouraging me to challenge this belief. To remove myself from two dimensional thinking. What if we’re spiralling upward, moving through the same coordinates that feel like familiar territory… but now we’re passing through it on a higher and higher plane?
What encouragement we might find if we are willing to look at life this way. Don’t ask if this feels like I have been here before. Ask yourself whether you’re better equipped this time around.
Sometimes growth doesn’t look like a straight path. Sometimes it looks like returning to where you’ve been, with more perspective, more faith, and a wider view.
Lesson 3: You can take logical steps to an irrational solution if you start from the wrong foundation.
My father loves logic and reason and his lessons in this area have proven to have broad application—beyond mathematics or engineering. Recently, I experienced a deeply hurtful conversation. One where I felt blindsided and my intentions misunderstood. What struck me was how, despite considerable evidence to the contrary, this individual had arrived at such a hurtful and irrational conclusion. They had taken what seemed like logical steps to them, based on their past experiences and understanding of others’ behaviours and not the context in which this conversation was taking place.
While the situation was unfolding, I found myself thinking of something my father once taught me: You can take perfectly logical steps and still end up at the wrong answer, if you start from the wrong foundation.
In this case, that’s exactly what had happened. The individual had made critical errors in the base assumptions underpinning their perspective, and as a result, their conclusion didn’t reflect the reality of the situation.
In Eugenia Chen’s book The Art of Logic in an illogical world (thanks
for lending me the book) Chen argues that many conflicts, misunderstandings, and divisions stem from people following what feels like a logical path, without realising that the path itself began from flawed, biased, or simply different foundations. Logic alone isn’t enough if the starting point is not sound or agreed upon. When you find yourself in conflict, ask questions to clarify whether in fact your perspectives or opinions share the same foundation. If they don’t, start here.It’s a reminder to check our assumptions and allow curiosity to precede judgement. To pause before reacting. To ask for clarification before asserting our opinions, especially if they may be hurtful to others. We must be willing to challenge what seems “reasonable” to us, because it might only feel that way because of where we began.
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I am grateful to be a part of the Writing 4 Resilience team. We’re a writers who are striving to build resilience in our local community with the goal of making Canberra suicide free by 2033. I would encourage you to check out their newsletters!
This is beautiful Tim 💚 I especially love the spiral story.
Beautiful Tim! :)
I read a quote the other week that said, " We don't view things as they are, but as we are."
Our mindset, past experiences and our views of ourselves shape our view of the world.