# An Insight and An Equation

Over my Spring Break, there were a few moments where I felt enlightened. Both came during a physical activity during which I was listening to a podcast.

The first insight, I could not remember the reference.  It goes something like this:

Let’s take losing weight as an example.  Many people desire greatly to lose weight.  However, that is not these individual’s task at hand.  Losing weight is straight forward: exercise more and stick to a diet plan.

The task at hand is getting your entire being into a place in which those two things are part of your daily routine.  This is a monumental task for many.  It can include (but is certainly not limited to) the following:

• Accepting the fact that you need to change your habits and mindset.
• Taking steps to change your habits and mindset.
• Making changes in your lifestyle that promote your newly developing better habits and mindset.
• Manipulating your newly formed habits into something sustainable.

This game never ends. Even for those that already have the great habits and mindset. The clock goes off.  It is time for your run.

The task at hand is not going for a run.  It is convincing your body to put the workout clothes on, followed by the running shoes. Now you need to convince your body to get outside.

Only now is the task at hand going for a run.

This process never goes away, but it does get easier with practice.

## The Equation

The following equation is not mathematical! So, you don’t need any mathematical ability to understand it.  In fact, if you are mathematically inclined in any way, you may scoff at the following equation and think, “That isn’t an equation!”

This comes from Tim Ferriss’s podcast with Joe Gebbia, the co-founder of AirBnB.  It is a fantastic podcast that I recommend, as Joe tells some great stories.  One of my favorites is of a prank he pulled in high school involving playing some Pink Floyd over the PA system.

One of the things he mentioned was the following equation:

$(SW)^2 + WC = MO.$

He frames it in terms of entrepreneurs, but it can apply in so many other areas of life.  The equation is interpreted as follows. When you have an idea, in terms of who will embrace and love your idea…

Some Will, Some Won’t…  Who Cares?      Move On.

I’m not much of an entrepreneur, but I loved this equation.  I immediately thought of how it applied to simply living your life. Living life in a way of belonging and not begin accepted. Live your life the way you want.

Some will accept the way you are, some won’t.  Who cares about how that split happens?  Move on, and be the person that you want to be.

# No Hardware, No Problem

Today, I competed in my very first Brazilian Jiu-Jitsu tournament.  Grappling Industries put on a round robin format tournament in Kansas City. My white belt, 170lb, Gi division had 4 other competitors.

I went into this tournament with a clear goal in mind. I wanted to survive all of my matches. That is, I wanted to last the entire 5 minutes without being submitted (or until I was able to perform a submission).

My first match was against a very tough competitor, and I remember being trapped in the same position for at least a minute.  I could hear teammates and/or my coach reminding me to breathe.  This was good advice.  I concentrated on breathing a while.  The match was not a high scoring match.  When time was called, I remember thinking that I had met my goal!  I had survived.

Bonus: I won my first match by a few points!

I sat down to compose myself when the table called out my name and told me my 2nd match was up next.  Holy shit.

In hindsight, I could have requested that I be given a little more time to recuperate.  In practice, we are given only a minute to recuperate.  I was given over 5.  That’s going to have to be good enough, I told myself.

My second match was against the eventual winner (and winner of the Absolute Gi he had competed in at he beginning of the tournament).  I knew it would be difficult to survive.  After a little bit of parrying back and forth on our feet, I got in a deep double leg take down.  This is great if you’re in wrestling.  In BJJ, they are not all that great unless you have both legs to one side and you’re not in the middle of them with your head outside to be guillotined in under a minute.

I didn’t survive.  Shake it off and move on.

Before my 3rd match, I had a longer rest time.  This helped.

My 3rd match was much more active, as I was able to get take-downs, work a little side control, get a sweep after losing side control, and work on a submission (that did not come to fruition). Again, when time expired, I got excited.  I survived again!

Bonus: I won my second match.  This time by a wider margin of points.

During the fourth match, I got too excited.  I got a take down and side control, and was applying a lot of top pressure, but didn’t quite get room for a submission.  More action, which led to more points.  Perhaps this got to my head?  Perhaps I let my guard down?  I was ahead by a wide margin.  He grabbed my lapel from the bottom position and applied such an effective cross choke on me that I had to tap out.  Except… I guess I didn’t tap out.

It is quite bizarre coming to with the ref holding and shaking your feet in the air while staring your coach in the eyes.

“Did you solve all the world’s problems?”

“Maybe. I got a good start on it, at least.”

I didn’t survive.  Grappling Industries doesn’t allow naps in the middle of matches, surprise, surprise. The experience was a great one though.

When I checked the standings, the first place finisher had won all four matches, and three of us won 2 and lost 2.  Because the other two competitors had won one of their matches by submission, they were awarded 2nd and 3rd place.  So, no hardware for the points guy.

You know what… no problem.  I’m happy having the experience.  The camaraderie of having your teammates all around you is indescribable.

Many would come away from this thinking that they need to obviously work on submissions.  If they could have submitted one of their opponents, they could have been in the running for 2nd or 3rd place.  But I didn’t come away thinking this.

I came away thinking I need to keep training and focusing on surviving and not getting myself into positions where I can be submitted.  If I could have survived all 5 minutes of all of my matches, I definitely could have won 3.

I’m a white belt. I just need to survive. Submissions will come in due time.

# Rates of Change

Last week, I was busy studying for (and then taking) the MFE Exam through the Society of Actuaries.  I hope I passed.  That was the reason I did not post.

Next week, I plan on posting about my experiences truly taking advantage of a break when there is no travel planned.

Until then, I solve problems.

Consider the following two problems.

1. A vehicle travels 30 mph for 1 hour, and then 60 mph for an hour. What is the vehicle’s average speed?
2. While traveling an unknown distance, a car travels half the distance at 30 mph and the other half at 60 mph. What is the vehicles average speed?

While the first problem is pretty easy to solve, the second one can be a bit more challenging.

First, recognize that mph stands for miles per hour, or in mathematical speak, mi/hr.

We do this so that we can see that when we multiply the speed by the time, we get the distance:

$30 \text{mi}/\text{hr} \cdot 1 \text{hr} = 30 \text{mi}$

For problem 1, we traveled 30 miles in the first hour, and 60 miles in the second hour for a total of 90 miles in 2 hours.  This means our average speed was $90/2=45$ mph.  Like I said, that one was easy.

When we’re working with distances and speed, to get the time you need to take distance divided by speed.  To see this, remember dividing by a fraction is the same as multiplying by the reciprocal:

$\frac{\text{mi}}{\text{mi}/\text{hr}} = \text{mi}\cdot \frac{\text{hr}}{\text{mi}} = \text{hr}$

For problem 2, we don’t know the distance. But that is OK.  We don’t need to. It turns out, we could pick any distance we wanted to solve the problem.  To make it easier, we will do that.  Let’s pick 120 miles.

If the vehicle travels 30 mph for 60 miles (half of 120 miles), then it will take the vehicle $60/30=2$ hours to do so. If the vehicle travels 60 mph for the second 60 miles, it will only take the vehicle $60/60=1$ hour to do so. Thus, the total travel time is 3 hours.

If the vehicle traveled 120 miles in 3 hours, then this means the average speed is $120/3=40$ mph.

Now that you know the answer, see if you can follow along by exploring any distance, we’ll call it d.

If the vehicle travels 30 mph for d/2 miles, then it will take the vehicle $(d/2)/30=d/60$ hours to do so. If the vehicle travels 60 mph for the second d/2 miles, it will only take the vehicle $(d/2)/60=d/120$ hours to do so. Thus, the total travel time is $d/60+d/120$ hours.  Getting a common denominator to add these fractions, we get a total travel time of

$\frac{d}{60}+\frac{d}{120}=\frac{2d}{120}+\frac{d}{120}=\frac{3d}{120}=\frac{d}{40}.$

If the vehicle traveled d miles in d/40 hours, then this means the average speed is $d/(d/40)=d\cdot \frac{40}{d} = 40$ mph.

See, the distance doesn’t matter.

### Riddler Express on March 2, 2018

The problem as stated on FiveThirtyEight was a rate problem:

Andrea and Barry both exercise every day on their lunch hour on a path that runs alongside a parkway. Andrea walks north on the path at a steady 3 mph, while Barry bikes south on the path at a consistent 15 mph, and each travels in their original direction the whole time — they never turn around and go back the other way. The speed limit on the parkway is the same in both directions and vehicle traffic flows smoothly in both directions exactly at the speed limit.

In order to pass the time while they exercise, both Andrea and Barry count the number of cars that go past them in both directions and keep daily statistics. After several months of keeping such stats, they compare notes.

Andrea says: “The ratio of the number of cars that passed me driving south on the parkway to the number of cars that passed me driving north was 35-to-19.”

Barry retorts: “I think you’re way off. The ratio for me was 1-to-1 — the number of cars that passed me going south was the same as the number that passed me going north.”

Assuming Andrea and Barry are both very good at stats, what is the speed limit on the parkway?

Although this problem may be too difficult to solve for many of you, some of you may be able to follow how it is set up.

We eventually want to find the speed limit on the parkway. I’ll call that v, for velocity.

There are a few other unknowns in this problem.  We are not given the flow of traffic northbound and southbound.  I’ll call these values $R_N$ and $R_S$.  An example value might be 30 cars per hour.  In this case, you would know that a car is passing a stationary object once every 1/30th of an hour (or 2 minutes).

First, let’s focus on the southbound traffic.  From a stationary point, the flow is $R_S$ as stated above.  However, if you travel south at a velocity of v (the same speed as the cars), the flow at which you see cars pass you that are going southbound reduces to 0.  This is a linear relationship.  If y is the perceived flow, and x is the velocity at which you travel, then

$\displaystyle y= -\frac{R_S}{v}x+R_S$

is the equation that describes this relationship. For a stationary object, x=0, and $y=R_S$, which is what we expect.  If we travel south at speed v, we perceive traffic flowing by us at $y=-\frac{R_S}{v}(v)+R_S = -R_S+R_S=0$ cars per hour.

Relative to Andrea, who is traveling north along with the northbound traffic, the flow of traffic that is going northbound is reduced to $-\frac{R_N}{v}(3)+R_N$.  From the perspective of the southbound traffic, she is traveling at -3 mph!  This increases the flow from which she sees the southbound traffic pass her to $-\frac{R_S}{v}(-3)+R_S = \frac{3R_S}{v}+R_S$.

We are given that the ratio of the second equation to the first is 35:19.  This gives us the complicated mess

$\displaystyle \frac{3R_S/v+R_S}{-3R_N/v+R_N} = \frac{35}{19}$,

which is equivalent to

$\displaystyle 57R_S+19R_Sv = -105R_N+35R_Nv$

after a little algebra (first, cross multiplying, and then, multiplying by v on both sides).

Using a similar argument for Barry, the flow of the traffic going southbound reduces to $-\frac{R_S}{v}(15)+R_S$ and the flow of the traffic going northbound increases to $\frac{R_N}{v}(15)+R_N$.  Since he witnesses a 1:1 ratio, this gives us the complicated mess

$\displaystyle \frac{-15R_S/v+R_S}{15R_N/v+R_N} = 1$,

which simplifies to

$\displaystyle -15R_S+R_Sv = 15R_N+R_Nv$

after a little algebra (cross multiplying while thinking 1=1/1, and then multiplying both sides by v).

We’re in a dilemma right now as we have two equations and 3 unknowns.  In order to be able to solve for a number of different variables, we need to have the same number of equations as we do unknowns.

We can get around this issue since we do not really care about the values of $R_S$ and $R_N$.  What we will do, is divide both the equations above by $R_N$, to create one unknown $R = \frac{R_S}{R_N}$.

Now, the two equations become

$\displaystyle 57R+19Rv = -105+35v$

$\displaystyle -15R+Rv = 15+v .$

This seems like a headache to solve, so let’s use our friend WolframAlpha.  This computational engine really likes x’s and y’s, so let’s plug

$57x+19xy=-105+35y, -15x+xy=15+y$

into that website and see what we get.

It provides us with the two solutions $x = -\frac{21}{19}, y = \frac34$, and $x=\frac53, y = 60$.  The second solution is the only one that makes sense, which suggests that the cars are traveling at 60 miles per hour.

Less important, but we might as well address it, are the flow rates.  We’re only able to determine the ratio of the flow rate of the southbound traffic to the northbound traffic.  If the southbound traffic has about 5000 cars per hour, we know the northbound traffic has about 3000 cars per hour since $x=5/3$.

There is a story that Saulo Ribeiro tells in his book Jiu-Jitsu University about Helio Gracie at age 90. Helio told Saulo,

Son, you’re strong, you’re tough, you’re a world champion, but I don’t think you can beat me.

Although the 90 year Helio wasn’t about to beat Saulo, he simply stated that Saulo couldn’t beat him.  And Saulo couldn’t. Helio survived. Saulo could not impose his game on the 90 year old Helio.

This taught Saulo a very valuable lesson: the importance of survival and defense in the art of jiu-jitsu.

In turn, I hope that it also teaches all of us a valuable lesson as well.

### The Basics

When learning something new and exciting, it is very tempting to dive head first into the vast ocean of your endeavor. This leaves us thrashing about here and there, with no real direction, lost in a seemingly infinite sea.

Perhaps it might be better to first build a sturdy boathouse and dock, and make sure that it is well kept.  Without these basic building blocks, we have nothing to land on or come back to.

As a beginner, it is tempting to want to take on the ocean right away. But it is best to limit our focus on the basics.

In Robert Pirsig’s Zen and the Art of Motorcycle Maintenance, he describes a writing assignment that a student is assigned. She is supposed to write an essay about her home town, but can’t do it. When the teacher changed the assignment, and instructed her to write about a brick in the opera house on a small block in her home town, the words began to flow.

Josh Waitzkin used the above reference in his book The Art of Learning. He applies the idea of limiting focus to martial arts in the chapter “Making Smaller Circles” (this chapter name was the inspiration of the featured image for this post):

We watch completely unrealistic choreography, filmed with sophisticated aerial wires and raucous special effects, and some of us come away wanting to do that stuff to. This leads to the most common error in the learning of martial arts: to take on too much at once.

As a brand new student in jiu-jitsu, I try my best to limit my focus on surviving and defending. This takes quite a long time. I had to tap out several times during a class a few weeks ago. Surviving and defending is tough enough!

Coach Criqui emphasized this same sentiment during a recent class, describing the confused state that students get themselves in after watching 20 YouTube videos of moves they want to practice.  He, too, encouraged us to limit our focus.

### The Instructor’s Dilemma

There are several BJJ Academy instructors I’ve listened to on The Grappling Central Podcast.  Many of them share a common sentiment: the struggle to drill and teach what should be taught versus drilling and running the program in a way that keeps students coming back.

Drilling basics, defense and survival strategies may get students in the door, but unfortunately, most of us don’t have the mindset of limiting our focus. We come in wondering how we’re going to compete and beat the instructor before we’ve learned how to defend against getting choked. Better yet, how to avoid positions that will lead to getting choked.

We want to dance before we can walk. We want to navigate the vast sea without a boat or a dock.

Students see where they want to be. Instructor’s know and understand the path the student needs in order to get there.

The successful student will work hard, think hard, and put the necessary time in, allowing their instructor(s) to lead them along the path the instructor knows so well.  They limit their focus and stay on the designed path.

Students who look for and take shortcuts and alternative routes will inevitably get lost and not succeed in the way they had initially set out to.

Stay on path. Limit your focus.

# PshycoWyCo 2018

The PsychoWyCo is a trail run around Wyandotte County Lake, which gives runners the option of 1, 2, or 3 laps.  That is, 10-miles, 20-miles, or 30 miles (which sounds better if you call if 50 k).

My experience running 10 miles on the PsychoWyCo Trail Run will never be forgotten.

It was a muddy mess of a trail. For the first few miles it was miserable. First entering the trail, the mud was unavoidable. Yet instinctively, while wearing nice running shoes, we tried to avoid it.

But then… it continues.

And then… it doesn’t stop.

It is forever muddy and sloppy and disgusting. For those in the correct mindset, the circumstances become accepted. “This is my life now,” is what we say in our heads. Even if the path clears ahead for a while, it does not matter. The damage has been done. We are mud monsters. This is our life until the finish line is crossed.

Without fully embracing the situation, you only allow your misery to continue. By embracing the suck, you begin to laugh at the course. Out loud, in fact. You think it won’t get any worse, and then BOOM! You laugh out loud at a hill that is near impossible to ascend because of the slippery, friction-less mud. “Ha ha!” you laugh, because if you don’t, you won’t make it up the hill.

Oh, look! Some more mud. There was black mud, brown mud, clay mud, icy mud, peanut butter fudge mud, and peanut butter fudge mud with greenish horse poop smeared inside.

Then there was slippery mud, sticky mud, sloppy mud, and splattery mud.

Sometimes, you would slide 1-2 feet. Sometimes, the mud would threaten to steal your shoe from you. Mud would seep down into your socks and shoes. It somehow found its way into your bones, too.

And we would laugh.

The drums beat. “Am I nearing the end?” Maybe so, but first there is this huge hill. Good luck. Here are some men dressed in Braveheart clothing and war paint beating a drum for you, cheering you on to the finish line less than a mile away.

There it is. The finish line. It is beautiful. It makes us smile. Maybe you think we were stupid to come out and run such a long distance through mud. Maybe we are. But we did it. We faced a challenge on that day and conquered it.

We laughed.

We lived.

And we’re so much better off for having done it, that it cannot be expressed in words alone. Some beating drums, some poetry, and a score by John Williams might get close.