It's March MATH MADNESS!

Welcome to March Madness...

The MATH behind the MADNESS!

Students came in talking about the NCAA brackets and how that would be the focus for the week before spring break.  First things, first: What is a tournament and how are they set up?

I set up a mini-tournament in the classroom.  8 students were put head-to-head in a critical game of coin flipping.  I had students complete a bracket and discuss how many different ways this bracket could be filled out

There can be only one!

Students came up with many different theories: 2*8, 2*7, 8*7*6*5*4*3*2*1, 2^8, 8^2... It was a good check in for me since we already had covered calculating outcomes of independent events.

Finally students realized this is the same as flipping a coin 7 times and settled on 2^7, or 128 possible outcomes.

"So, Mr. Taylor, the probability of two of us filling it out the same is 1 in 128?"
That was a good eye-opening realization for many of them: in this small bracket of just 8 teams there were 128 different possible ways to complete this.

From there I introduce a region of the tournament. We review what the rankings mean as well as how the tournament runs.  Students were randomly assigned one of four regions.  Students were told there were 16 teams in each region and were asked to make predictions as to how many ways those could be arranged. Many, understandably, made the jump that if there are twice as many teams, there should be twice as many outcomes.  They quickly checked the math and realized how far off they were.

Instead of 256 outcomes, it actually explodes to 32,768 possible outcomes!

Their homework night one is to complete a regional bracket and think about why companies will put up $1 million as a prize for a perfect bracket.

Students come in the next day and discuss their picks - they meet in their region and discuss similarities and differences.  They notice while many picks are the same (everyone took my advice and picked the one over the 16 seed), nobody matches exactly.

On day two we talk about the whole tournament.  Students pick up the pattern that there is one fewer game than number of teams (an 8 team bracket had 7 games, a 16 team region had 15 games.)  They use Wolfram Alpha to calculate this value.

They discover that the number is big.  Like really big.  Good thing we have reviewed scientific notation.... because the answer is 9.22 x 10^18, or 9,220,000,000,000,000,000... over 9 quintillion.

The question the becomes how to QUANTIFY a number that big?  Many students talk about having that much money, but is that even possible?

How big is big?

First, let's look at space.  Space is really big.  That should be a good place to find 9 quintillion.  The distance from the Sun to Neptune is 2.8 billion miles.  Billion is too small, so lets figure out how many INCHES it is from the Sun to Neptune.  Will that reach 9 quintillion?

Not quite:

Tournament: 9,220,000,000,000,000,000

 Distance in inches: 176,400,000,000,000

(I make sure to line up the place values to emphasize the SIZE difference. In this case the tournament value is over 51,000 times bigger.)

In other words: if you picked a random inch between the sun and Neptune, and I picked a random inch between the sun and Neptune, we are 51,000 times more likely to pick the same inch as someone picking every game in the NCAA tournament correctly.

Let that sink in a moment or three..

Not big enough, Solar System!

OK. Let's try this.  The accepted scientific age of the universe is about 14 billion years.  How many SECONDS has the universe been in existence?  TO WOLFRAM ALPHA!

 Tournament: 9,220,000,000,000,000,000

Seconds of the universe: 441,500,000,000,000,000

Wait. So not even that is a big enough number?  Well how close are we talking? Let's figure out the part of the whole:

441,500,000,000,000,000 ÷ 9,220,000,000,000,000,000 = .047

.047? That is LESS THAN 5%?  DO YOU KNOW WHAT THIS MEANS? 

The students sure did...  

"So wait. That means if Jeremiah filled out one tournament since the universe started, he'd only be 5% done?"

Yes.  5%  This number, 5 quintillion, is so ASTRONOMICALLY HUGE, that if you had a large supply of pencils, blank tournaments sheets, came into existence the same moment as the universe, and filled one out tournament per second, every second, since the universe started... you would be 5% finished. 

I love the madness. And Math.

Washington D.C. Marathon Race recap

On Saturday, March 11th I completed the Washington D.C. Saint Jude Children's Hospital. This was my 3rd marathon and my 7th marathon-or-longer event. It was also the toughest road event I've attempted.

I have been training for this run for nearly 12 weeks. I put in the miles, did the speed work, ran the hills, bought the Gu. I was ready. Then I checked the weather. 12 degrees with winds of 15 miles an hour... ouch. It certainly wouldn't be the coldest race I've ever experienced, but it presented another challenge to an already challenging distance.

The day before the run I got an e-mail from the race organizers. It warned us of the cold weather and included this advice:

Manage your expectations. This may not be the race to run a PR. Slow down according to the conditions and consider switching down distances if you are not feeling prepared. 

Here is the deal: Running is an outdoor sport. There are no rain delays, no cancelled due to snow. I'm not letting 'weather' be an excuse for not hitting my goal.

Five top layers. Worked perfectly! 

The day started in my typical fashion: I got lost. Seriously. Bree was so amazing and agreed to drive me to the start line at 5:30 AM since the metro did not start up until 7 am. I programmed the start in my GPS and off we went. The only problem was that I programmed the FINISH LINE into the GPS. Luckily I realized my error and Bree was SUPER patient with me. I was dragging her all around a pre-dawn city that we'd never driven in before and she never did anything but reassure me. I am so thankful for her.

Eventually we got to the right location, she dropped me off, and I was off to the start line. I got myself ready, dropped off my bag with a change of clothes and some post-run food, and did a little light running to warm up. I also got to take a group picture with other St. Jude Heroes. The start was actually quite well done. Marathoners started at 7:00 and Half-marathoners didn't start until 8:30, which meant the start was (relatively) small.

It took me a few miles, but I managed to warm up and was feeling really good. The wind wasn't too bad and before I knew it I was at mile six: CRAZY HILL! Still, after running so many hills I knew how to approach it and felt good when I got to the top. A couple miles later I got to see Bree, Sam, and Alexa. A mile later I got to see Wendi and Jason as well! My pace through the first half of the marathon was 10:54 minutes per mile, right at my 11:00 minute pace goal.

The second half of the marathon started well. Bands were still playing, the course was smooth and fast, and the weather, while cold, was still not crazy cold or windy. There were fewer historical spaces to see, but I pressed on and crossed the 20-mile mark at a pace of 11:07 minutes per mile.

This is where things got rough. The wind really started to kick up and gusts were very noticeable. Some course volunteers said gusts were close to 30 miles per hour. Running began to be challenging, but I kept moving forward. Still the grind of 20 miles and the weather were starting to take its toll.

Then came mile 22. I had previewed the course and knew there was a bit of a climb at 22, but after four hours of running my body decided it needed a break and I had to do some considerable walking. About half way up the hill, the 5-hour pacer passed me. I forced my body to run, but couldn't keep pace with her.

 Four hours of running? Perfect time for a climb!

 I have been involved in sports nearly all my life. I can honestly say none of them have been as emotional or frustrating as distance running. You train for weeks and literally can watch your goal pass you by.

 I do so much reflecting after an event. What could I have done better? Did I give it my all? What did I miss? Here is what I know: All that training made me run my strongest road race of my life. I left nothing out there. Usually when I cross the finish line I collect my 'goodies', meet anyone that is at the finish, and hang out a bit. After this run, I crossed the line, had someone put a medal around my neck, and then sat down and couldn't move. My legs were cramping and in pain. My body was hurting badly and I was pretty emotionally devastated that I didn't finish under 5 hours.

As it turns out I did set a personal record (PR) for a marathon distance (26.2 miles), but I ended up running 26.6 miles total and crossed at 5:02:52, 40 seconds slower than the Columbus Full, but at a slightly faster overall pace.

If I did this event this time last year I would have finished in a much slower time. I would have given up running much earlier. Given the conditions there is a chance I may not have even finished. I've learned so much and look forward to busting that official 5 hour barrier in the future. I know it is in me.

Thank you to all of you for your support. I had so many people check in with me about how things were going with training and how the run went. I am so blessed to have so many people in my life that care about me.

To those of you that donated any amount to my run: I was proud to represent all of you! With your help we raised over $700 for the Children of Saint Jude.

To those of you that donated songs to my run through St. Jude Children's Hospital: I had great conversations with all of you. You will never know how much those help me get through the miles. It is funny how my player knows exactly what song to play when I need to hear it. Seriously, nobody's song came up before mile 7 (after that first climb) despite the fact I had it on random.

To my amazing family: Thank you SO MUCH for trekking all over D.C. and the metro, putting up with the stupid coldness of the day, and supporting me on my runs. This day would have been so much more difficult without you there. Sam and Alexa: your signs were great, and I LOVED seeing you on the jumbotron! Bree: you are amazing. Thank you for everything you do for me. I love you.

What's next? That's always the question. Currently I'm registered for a half-marathon in April and then two 50km (31 mile). I'm looking forward to getting back on trails! Outside of that, we'll see where the rabbit hole takes me!

Love you all,

Michael