The Art of Solving Problems
The other day two EXPLORERs shared a birthday.
The obvious reflex: ‘wow, what are the chances?’
If you’ve done a year of statistics you’d know that the chances are actually pretty high. For us — we have over 100 EXPLORERs — it’s ‘obvious’ that the probability is close to 1. In other words you can be almost certain in such a large group that two people share the same birthday.
Counter-intuitive but right.
Check out: https://en.wikipedia.org/wiki/Birthday_problem if you are interested in the math.
I then found that we have 9 distinct days where 2 EXPLORERs share a birthday.
The natural reflex: ‘wow, what are the chances?’
THE PROBLEM TO SOLVE
The generalised version of the problem above looks something like this: In a group of N employees what is the probably that on M distinct days m of them share that birthday.
where, let’s say the EXPLORE example has N=100, M=9, m=2.
After a few minutes and some research it is clear that this is a tricky question.
WHEN I WAS YOUNG
Twenty-five years ago when asked this question there would be only one route to solving it — sitting in your room with a cup of coffee, a pen, a pad of paper and a lot of gumption.
You would have needed a statistical under-graduate degree, a fair grasp of probability theory and a flair for problem solving.
It feels like quite a hard problem (I could not find it anywhere on the web) and I suspect only a few could do it — say 50,000 people in the world could have come up with an answer within a month back in 1995.
So let’s say 0,0005% of the population could have answered this question back then.
TODAY
Today is a different story. Today if asked this question there are a number of avenues open to you:
1/ Brute-force the answer. Write some simple code that runs a set of simulations to find the answer. You could do this quite easily on Excel with some simple VBA code. A few EXPLORERs did this overnight with answers converging on a probability of 11%-12%.
2/ Crowd-source the answer. Post the question on Quora and wait for an avid statistician to show you how it is done. This would cost you nothing — just 15 minutes writing the question up and checking for answers every now and then. Who knows — perhaps even Jordan Peterson may be the one who is able to answer the question.
3/ Pay someone to do it for you. Post the question on a range of freelancer platforms (eg: www.upwork.com) and, for say $100, get the answer within a few days.
4/ Google it. A few hours on Google and you’re bound to find an obscure Post-Grad paper that sets out the math that you can use to calculate the probability.
5/ (E-)mail a friend. You likely know a friend of a friend of a friend in Academia who is likely to able to do this. They will gladly spend a few hours to show off their skills.
6/ Sit in a room with coffee. You could sit in a room with a cup of coffee, pen and paper and figure out the math.
There are probably a handful of other ways to find the answer. The point is you have options.
I suspect that today 50M people could answer this question within 24 hours. Call that 0,5% of the population and 1000X more than 25 years ago.
That’s quite a change
WHY IS THIS INTERESTING?
This thing called ‘progress’ is driving us forwards at ever-increasing speed. As technology creates more nodes on our Human Operating System (1–5 above) Metcalfe’s Law kicks in — the ‘Power of Us’ grows exponentially.
More people can do more things quicker.
It is amazing where we have come from and where we are heading.
What is also interesting is how the shape of problem solving is rapidly changing. In the past to solve a difficult problem required a smart PhD in a room.
Now it is different.
Very different:
1/ There are many ways to solve a problem. Being creative up-front to understand the various routes is probably one of the most important skills there is.
2/ Solving problems now requires collaboration, team-work and asking for help (sometimes difficult for ‘smart’ people)
3/ Most of the time you’re not the expert — rather find the expert and quickly leverage their 10,000 hours
4/ The best way to solve a problem is ‘Working Backwards’ — start at the end and find the fastest way to answer it … then move on.
5/ Solving problems now requires a bunch of new, softer skills: humility, agility, flexibility (working across different systems, people and domains) and clear communication.
DUSTING OFF THE BOOTS
My job today is very different to what I studied at University. But, also, very similar. I still work in small teams to solve difficult problems — not with pen, paper and code but rather with people, systems and ideas.
Same principles.
I miss the pen, paper and code though. Sitting in a quiet room with nothing but your thoughts, a warm cup of coffee and the promise of a blank page.
Here is my take on how to solve the ‘Distinct Birthday Problem’ above:
And the EXPLORE instance:
SD
2021
