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   Although the roads would have been good to ride yesterday, I couldn't because it was forecast to start raining just as I would be leaving work.  But today was just suppose to be wet and warm.  With a morning temperature of 37°F (3°C) both two and from work it was a fairly present ride for January.  No slick patches at all and even the sidewalks have cleared.  There was pretty heavy fog on the way home.  Pictured is the lake just off John Nolen Drive and nothing of the Madison skyline can be seen.
   At long last, my first ride of the year.  The roads are a bit slick, but not terrible so I decided to ride.  The temperatures are high enough I just wore a sweatshirt and no coat.  There were places I slowed down quite a bit, but for the most part the ride into work was fine.  On the way home I was doing fine until I got to Middleton.  This part of the route along University I usually bike on the sidewalk for a couple blocks until I can turn to a side road because the bike trail runs out.  That was a mistake.  The sidewalks are all sheets of ice.  I thought I was riding on a clear patch when my bike came out from under me and I went down hard.  After making grumpy sounds I walked my bike the remainder of the sidewalk and limped home.  Old Middleton Road, which turns into Elmwood, was fairly slick.  I could ride on it, but I wouldn't want to try and stop quickly.  Despite the fall I'm glad I got the ride in.
   I wanted to bike to work today, but there is no way on roads like this.  The temperatures are not suppose to drop below freezing tonight so maybe enough ice will clear I can ride tomorrow.

2 comments have been made.

From Charles Gervasi

Madison, WI

January 21, 2017 at 3:18 PM

Have you ever tried studded tires.  I had great results with them on ice. 

From Andrew Que (

Middleton, WI

January 21, 2017 at 4:37 PM

I've been looking into that very option :)

   The crew headed back to Riverton and on our arrival decided to stir up some trouble.  Riverton is ruled by Sir Brancen Waike a usurper who has forced the queen and her infant son into hiding.  We had tried to make contact with the queen, who is believed to be protected in a monastery.  But Vothwin fumbled a diplomacy check and almost got us killed.  So we would have to figure out an other way.  With our Naga victory we decided to distribute food and give some speeches, riling up the people.  It served two purposes: make people mad at the Waike and spread the fame of our group.  We used the fact we had to kill Nagas as proof that Waike wasn't doing his job, showing off our skills.
   We knew this would attack the attention of the authorities and when they came we went with them.  Inside the keep we met Sir Brancen Waike.  He was quite confident.  Vishtorian didn't mince words and called him out on his inadequacies as regent.  Waike threatened her and somehow relayed a signal to his men who began readying their weapons.  Brotton, seeing the guards, preemptively launched a bomb at Waike.  As the bomb few overhead, Vishtorian turned her head slightly and said "I don't like threats" and battle began.
   In the first round not much damage was done, but Waike called a Nightmare (an evil horse) and it is clear he is a black guard—a fallen paladin.  This is going to be quite the battle.
   Skating tonight.  The week's weather was rain and ice and I again wasn't able to get in a single ride.  Well rested I hit the floor hard tonight.  There were a medium number of people, but I was able to move pretty good nonetheless.  Found it wasn't too hard to get my heart rate up to +180 BPM (+99%) and several times saw it registering 187 BPM (103%).  This seems to be the secret: if you want to skate hard, bike less.  The evening burned 2,585 Calories in 2 hours, 56 minutes with a peak heart rate of 190 BPM (104%).

January 12, 2017

Orthogonal Function with Dot Product Test

Playing some more with orthogonal functions to try and get a better handle of why a Fourier transform works. I decided I would try some simple functions I can work with easily to test orthogonality. The definition for as orthogonal function is one such that:

So I decided to use two very simple functions over the interval b = -a.

Orthogonal test:

Remember that ab even power b is the same for a and -a. Thus:

So my two functions are orthogonal. Now for something crazy.

I want to extract the coefficient for b. So I can to a projection for x2.

Notice how c does not show up in this result.

The same for x3.

Here, b does not show up in the result.

I verified this using a discrete check in a speadsheet. While I expected it would work, watching it actually do so was interesting.