Not To Be Trusted With Knives

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Happy 4th condo-versary to me!

Hey remember that time I bought a condo? Would you believe that was FOUR years ago? Where does the time go?

My mortgage broker sent me an (automated, I’m sure) “happy anniversary of having bought your condo” email, which is what reminded me that tomorrow is 4 years since I took possession of my humble abode. So I looked at my trusty mortgage countdown spreadsheet (because of course I have a spreadsheet) and according to my calculations, I have paid off 53% of my mortgage principal in 4 years. Not too bad, if I do say so myself. Of course, I ridiculously lucked out when I bought this place – the price was very good1, plus I have a few different source of income in addition to my day job, so I have had the luxury of being able to make lump sum payments. Also, I’ve had very little in the way of additional expenses, as my unit has been very well taken care of and the strata does an excellent job of maintaining the building.

Given that the Greater Vancouver real estate market continued to rise at an insane rate since I bought, I’m actually in the position where I own an even bigger proportion of the place than I would otherwise. When I bought the place, I made a 25% downpayment, meaning the bank technically owned 75% of my place. If the price of the place had stayed the same over the past four years, I would now own 65% of my place and the bank would own 35%. But since the value of the place has gone up, I now own 77% of the place if we use the most recent assessed value (which is what the province assessed my place as being worth as of July 1, 2017). If we use the average amount that units in my building that are identical to mine have sold for in the past few months2 (assuming that I could sell my place for that price), I currently own a whopping 82% of my place and the bank owns a mere 18%. It’s a weird situation – I like to remind myself that the “value” of my place is really all just theoretical given that I’m not planning to sell anytime soon. But it does give me the opportunity to do some fun math! #nerdery

Anyway, my next hurdle is that I’ll have to renegotiate my mortgage next year, as my mortgage was a 5 year term. The interest rates are higher now than they were 4 years ago, so I’ll have to pay a higher interest rate. Boo-urns. I guess I have a year to figure out how all that works.

  1. In the context of the time and place in which I bought it. It was an absolutely insane price if you compare it to just about anywhere else in the world. []
  2. Which is almost double what I paid. []

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Running Math

So it’s just 7 days until my next half marathon and I’m really not sure if I’m going to be able to achieve my goal of a sub-2 hour finsih. I’ve been far more diligent in my training since… well, pretty much since the first half marathon I ever ran. I completed all my hill runs. I’m doing my interval training. I did the long Sunday runs with my running club1. I feel strong and I have improved my pace, but I just don’t know if I’ve improved it enough to reach my goal.

I’m hoping to see this (or better) when I cross that finish line next week:

Image Credit: Posted by Adam Fagen on Flickr.

The thing with races, you see, is that you always run way faster on race day than you do when you are doing a training run. You aren’t even really trying to do it – you are just full of adrenaline and the energy of the crowd takes you away and you start running and you don’t feel like you are running that fast but when you check your pace, you are. When I ran the Hollywood Half marathon I was convinced that the 2:15 pace bunny2 was screwing up, because Alicia and I were way ahead of her and I was thinking “there’s no way we are running faster than a 2:15!” And then it turned out that we were – we finished in 2:09:57!

But the question is, just how much faster do you run on a race than during training? For example, the longest distance that I do in training is 20 km and my 20 km training run this time was 14 minutes quicker than my 20 km training run last June for Scotiabank. My finish time for Scotiabank last year was 2:15:05. Which begs the question: will a 14 minute improvement in my 20 km training run translate into a 15 minute improve on race day?

To try to figure this out, I turn to my old friend, Math. As luck would have it3, I have records of my 20 km training times for my last 7 half marathons (plus the finish times for my last 7 half marathons, of course). Now, I once swore to my MBA stats prof that I would always graph my data, so here’s a graph of said data:

The times are shown in seconds per km (rather than minutes:seconds per km) because despite all the awesome things that MS Excel can do, handling time values is not one of them. As you can see, my pace for my 20 km training time is not a good predictor of my pace on race day. On the plus side, my race pace is *always* faster than my training pace, but it has ranged from a mighty 1:15 per km faster (Scotiabank 2011) to a meagre 0:08 per km faster (Edge to Edge Tofino half marathon, of the horrible hills and knee injury infamy). I run an average of 0:46 per km faster on my races than my 20 km training runs, but given the aforementioned wide spread of the data, I wouldn’t take that average to be a good predictor Moreover, I hope it isn’t, because if I run my race next Sunday at 45 seconds faster than my 20 km training run, I’ll finish the half marathon in 2:13, which is despairingly slow.

Just to be sure that the graph wasn’t misleading me, I ran a linear regression analysis and found there is not, in fact, a statistically significant linear relationship between my 20 km training time and my pace time4. I even tried calling the Edge to Edge Tofino half marathon an outlier, so I could remove it from the data set, but there’s still no statistically significant relationship.

So, in conclusion, apparently my 20 km training pace is not a good predictor of how I’ll do next week. There’s just too many other facts at play I guess – whether I was giving ‘er on my training run or not, conditions on race day, whether the race route is insanely hilly à la Edge to Edge or a beautiful net downhill like Scotiabank5.

Something that Daniel taught me that he does with his races is having not just one goal, but a staged series of goals. If you only set a goal that you know you can achieve, then you aren’t going to have to push yourself to achieve it. But if you only set a goal that is really, really hard to achieve, you run the risk of not being able to appreciate what you do achieve because you didn’t reach that single, really tough goal that you set for yourself6. So I’m going to go into this race with three staged goals:

  1. a sub-2 hour half marathon – This is my ultimate goal. As described above, I don’t know if I will achieve this, but I don’t think it’s totally out of the realm of possibility7.
  2. a new personal best. My current PB Is 2:07:23, so I don’t acheive a sub-2 hr but I do better than 2:07:23, I willl be happy.
  3. finish. Even if I don’t set a new PB, it will still be an accomplishment to finish a half marathon. And given that this is my 12th half, I think finishing an even dozen of these races will be an accomplishment to be proud of.

Footnotes:

  1. Except for a few weeks where I have something else going on on Sunday morning, in which case I completed my long runs on my own at another time. []
  2. i.e., the person who runs at the pace that will result in finishing the race in 2 hrs 15 mins. Races have people like this for all sorts of different paces, so if you want to achieve a specific finish time, you can run with the corresponding pace bunny. []
  3. Where by “luck”, I mean, my nerdy habit of keeping records of everything. []
  4. I was hoping, before I started this, that I’d find a statistically significant relationship and then I could use the equation of the line to predict my finish time! Math, you have dashed my hopes! []
  5. Happily, next Sunday’s race route is also net downhill! []
  6. I’ve seen this happen before where someone sets a stretch goal and though they didn’t quite reach it, they really improved over their last race, yet they are sad at the end of the race and can’t enjoy the fact that they set a new personal best or took at a good amount of time off their previous race. []
  7. Unlike the last few times where I started training with a sub-2 hour goal, but wasn’t really diligent in my training and knew by race day that I would not be anywhere near that. []

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Math It!

Quadratic solverMy managerial economics prof offered my class the option to have a math refresher evening to make sure we are up to speed on the math we need to understand to be able to do the work we need to do in managerial economics. So after spending the past three days at the health care priority setting conference, which was chalk full of health economics1, I spent two hours this evening going over solving systems of equations and taking partial derivatives.

Needless to say, my brain is fried. Very glad I went though, because I feel much better about my ability to do my managerial economics assignments. Starting tomorrow.

Image Credit: Posted by Irregular Shed on Flickr.

  1. And ethics. And a twist of patient engagement to boot. []

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How Did You Celebrate World Maths Day?

Day 253Me, doing the gang sign for “pi,” in honour of World Maths Day. You did know that today was World Maths Day, right? I knew about this important occasion because I downloaded the Nerdidays Calendar from Dr. Dan’s website. Because days like World Maths Day are just too important to miss!

So, what did you do to celebrate?

I did the following:

  • spent much of the day calculating descriptive statistics for a project at work. I even made a few bar graphs! w00t!
  • got a free coffee at McDonald’s. They gave me a cup of coffee and I gave them $0.00 – that’s pretty good math by my calculation!
  • had a massage. Because, really, getting a massage is a good way to celebrate any occasion.

And now I’m going to teach some statistics.

What a great World Maths Day!

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Congratulations, Dr. Dan!

Guelph, ON – Not To Be Trusted With Knives’ Official Statistician & Tattoo Consultant, Daniel J. Gillis achieved his most significant accomplishment since the publication of his groundbreaking work on The Count today.  Eye witnesses report that Daniel, formerly known as Soon-To-Be Dr. Dan, wowed the masses who attended his PhD defence at the University of Guelph today with his mathematical genius and dashing good looks.  The Flying Spaghetti Monster is reportedly pleased with the work of the young academic and intends to reward his with copious amounts of beer and curry.

Henceforth, Dan shall be known as Dr. Dan.

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Happy Pi Day 2010!

Many people celebrate Pi Day by eating pie. I prefer to celebrate it by being irrational.
-Dr. Beth

In honour of Pi Day, I have hounded demanded of nicely asked my Official Statistician & Tattoo Consultant for some wise words about pi to share with you, my lovely readers1  So here, my friends, is some info on the wonder that is pi, from the wonder that is Almost Dr. Dan:

Not only is Pi irrational (i.e., it cannot be expressed as the ration of two integers), it is also transcendental.  That is, it cannot be a zero (or root) of a polynomial equation with integer valued coefficients.  For example, while root 2 is irrational, it is the solution to the following polynomial: x^2=2.

Other interesting Pi tidbits:

Indiana once had a ‘pi bill’ up for legislative discussion.  Turns out an amateur mathematician thought he had proved how to square the circle.  Sadly for him, it had already been shown that this was an impossibility in 1882 by von Lindemann.  Strangely enough, people still to this day try to prove that you can square the circle.  But I digress.  The pi bill indirectly asserted that pi was in fact 3.2.  Check out http://en.wikipedia.org/wiki/Indiana_Pi_Bill for full details.

I’ve also heard of other laws (but couldn’t verify the info) that had pi set to 4 (yikes!).

One of my favourite representations for pi is this rather simple looking infinite sum.  It’s credited to Gregory and Leibniz.

latex-image-1

As well, in honour of Pi Day, I give you this photo of Dan’s pi tattoo:

Photo on 2010-03-14 at 14.41

  1. After all, it is his first anniversary as my Official Statistician & Tattoo Consultant! []

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Happy Pi Day!

Yup, pi.  As in ” the ratio of a circle’s area to the square of its radius” [Source: wikipedia].  As in 3.141592…. As in March 14 (3/14).  And, now that I think about it, we are only six years away from an even more precise  Pi Day: March 14, 2015 (3/14/15) !

This holiest of holy days was recently brought to my attention by my friend, Almost Dr. Dan, who is an Almost Dr. of Statistics and who has tattoos of the Greek letters sigma, psi, delta, gamma, xi, and, of course, pi, on various locations on his body.

According to the Pi Day website:

With the use of computers, Pi has been calculated to over 1 trillion digits past the decimal. Pi is an irrational number meaning it will continue infinitely without repeating. The symbol for pi was first used in 1706 by William Jones, but was popular after it was adopted by the Swiss mathematician Leonhard Euler in 1737.

Also, through the Pi Day website I discovered my new favourite song: Lose Yourself (In the Digits).

And now, a declaration:

In honour of Pi Day, I hereby declare Almost Dr. Dan to be the Official Statisitian and Tattoo Consultant for Not To Be Trusted With Knives.

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All math should be taught via foodstuffs


Not sure how to cite this one. It came from here.  Props to my friend Dan for posting this in Facebook.