math – Life of an old goat

Garmin vs. Strava distance

My workout, which I was pleased with, is at the end.
But with Garmin being down due to a ransomware attack I got a chance to see what Strava would do with the same data points that Garmin connect uses.

This is the course in question. On Thursday, I did this course 3 times then a bit extra. The Garmin measured it as 6.3 miles and Strava got this at 6.4 with the same data points that the Garmin used.
Here is the Strava output, which includes the extra partial loop.

The time before, Garmin measured these two loops as follows:

Strava gave me 4.3 on the same data:

Now look at today’s walk, where the Garmin and Strava got the same mileage with the same data points:

6.22 (which is what the Garmin showed).

So, why the difference?

(yes, this is based on only a few outputs)

First note that there was a time when the outputs were all but identical. That tells me it is NOT “round off” error (e. g. one program carrying more digits than another).

But note when I had a different number: the lines are all “wiggly.” Reason: the two that were different were weekday morning walks; there was much more traffic. I made course corrections to avoid other runners, pedestrians and vehicles on the road.

Today’s trek was on a less crowded day: note the lack of “wiggles” in my path.

My inference: the difference is in how the algorithm connects the dots. First of all, each “dot” is really just an intersection of lines from different satellite signals and those lines of intersection form a polygon rather than an exact point.

The centers of these “polygons” formed by the signal lines determine your position points. So, what to do with these position points?

The crudest way is to draw a straight line path between these points (black). One can select the points in batches and fit different sorts of curves by either a spline or by a least squares principle.

Here, I approximated paths by cubic splines between each group of 3 points and one that uses all 5 points (but doesn’t quite cut through all of them.)

But one gets different distances when one uses a different “curve fitting” algorithm, and it is my guess that Strava algorithm fits curves through more of the points than the Garmin algorithm. And the difference is less when the curve has less “wiggle” to it (in math terms: smaller magnitudes for the second derivative).

Anyway, that is my guess.

My workout: I warmed up my glutes and back..(15 minutes)

Deadlifts (low handles, trap bar): 10 x 134, 10 x 184, 5 x 228, 3 x 250, 5 x 233 NO BOUNCED REPS. Note: this might not seem like much but at this time last year, I couldn’t get 225 for a single rep.
Then the walk:

It was 81 F at the start, 84 F at the end, 69 percent humidity. That is warm for us.

No glute pain. Not much knee pain either.

2019 in review

Here is my 2019 in review. I posted photos that are meaningful to me. The first one is collage of “friend” photos.

Here is the “where” (many of the “wheres” anyway)

January

February

March

April

May

June

July

August

September

October

November

December

Education is not entertainment

This tweet reminded me of a pet peeve of mine:

Problem…chemistry and physics is NOT a series of cool parlor tricks. Understanding said subjects DOES require mastery of some difficult, abstract material.
Being entertained requires …nothing.

— prof. goat (@ProfGoat) September 24, 2019

I do want to make this clear: I am in no way attacking this teacher or attacking the idea that “cool science tricks” aren’t fun….they can be and they do have a place for learning.
What I am attacking is the idea behind this:

““Teachers who make Physics boring are criminals”” (typo corrected…and yes, all of us make these on occasion)

There seems to be an idea that physics would be popular if only there were more cool tricks in class or that somehow cool tricks lead to the learning of concepts. Color me unconvinced: my guess is that what is remembered is the trick itself.

This also brought to mind a discussion I stumbled into. People were saying that they were considering a second career as an astrophysicist ….though..they’ve never even had calculus. I cannot tell you how hard I rolled my eyes.

That is the danger of too much pop-science and cool tricks.

Think about it: to be any sort of physicist, you need to learn some quantum mechanics. And you can’t learn that until after 3 semesters of calculus, some calculus based probability theory, linear algebra, differential equations, partial differential equations, and Fourier series and that is just to start! And while the conclusions can sound interesting, learning the details can be mind numbing and, yes, involve some drudgery.

And keep in mind, I am talking about undergraduate quantum mechanics, not graduate level particle physics.

Cincinnati: final day

Workout notes: am: easy but deliberate 4 mile walk (across the bridge). PM: about 30 minutes with weight machines, dumbbells, planks. This was to “keep the motion”, so to speak.

Today: I attended the 3 hour Math and Sports session and really enjoyed it. Oh yes, I talked too (about NBA free throw shooting streaks).

Later, I made the final talk of the day: it was about recreational math (which has some serious, non-trivial problems and fun interpretations.

Here are some photos and my comments:

Yes, I often buy a book that I’ll end up not having time enough to read.

I do find good food.

Recreational mathematics: how quickly can puzzles be solved?

Yes, the solution is NP complete. My mom bought me one of these.

Yes, checkers IS completely solved..as of recently.

A list of some of the stuff the speaker covered. The art made from straight strings was fascinating.

Sports and math: talk 1. I am intently listening.

Is there a way of seeding a tournament so that no higher seeded team would want to swap places with a lower seeded one?

Ice skating and the mathematics of solving the associated physics problem

Some baseball strategy. Yes, the “new school” works better than the “old school.”

How does one rank teams, especially if there is a tie in record and you have round robin results such as: Illinois 55, Minnesota 31, Minnesota 41, Purdue 10, then Purdue 46, Illinois 7? (yes, this happened in 2018).

So did this: Minnesota 37 Wisconsin 15, Wisconsin 49, Illinois 20 and, well, we’ve been through that.

One method: introduce a new node “oracle” and use eigenvectors of the adjacency matrix of the associated directed graph.

This was my audience for talk no. 3 of the session. I enjoyed myself.

Mathfest days 1-2: talks

I’ll post slides and give a blurb about what i got out of the talk.

The first talk dealt with uncertainty; some of it was human reaction to it, some of it was the various types of noise (yes, not all noise is purely random; white, pink and..brown noise?) This would have been a good talk to have heard before teaching time series.

Its relation to music was brought up. And yes, noise can actually enhance stability!

Next was the first part of a series of 3 talks.

The first part: given an analytic function where $f(0) = 0, f'(0) = \lambda$ is there a change of coordinates that turns this into a linear function? Answer: yes, if $|\lambda| \neq 1, |\lambda| \neq 0$ . But if $|\lambda| = 1$ the fun starts. One can rule out lambda being a root of unity. But that is where is gets complicated.

Next came a talk on game theory and Nash equilibriums.

this slide shows a funny “paradox”. The spring shows one thing. Now look at the diagram in the lower right hand corner. Imagine having 100 cars at S trying to get to T. Upper route: second route takes 1 hour; first route is total number of cars on that route divided by 100 hours. Lower route: just the opposite (1 hour first leg, total no of cars divided by 100 hours for the second route. Now if cars were just assigned 50 top, 50 bottom, then every driver takes 1.5 hours, period.

Now put in a zero time route from the top to the bottom (one way). Each car in the top can reduce its time by taking that short cut. but if ALL of them do…then each of them would EVENTUALLY take 1.5 hours as before, (because all of them take this short cut hoping to avoid their 1 hour leg) but the bottom saps are now saddled with a 2 hour leg..so overall, opening this made things WORSE for everyone.

Cryptography talk: in the “tree image”, there is a cat there; you can barely make it out by tilting your screen.

The above are from some of the other talks; there is quite a bit of math there.

We also had a “geometry of check number” talk and a talk about encryption ..and yes…you can use a linear regression principle to encrypt. Think about the message being a perfect regression line, and the encryption being the adding of errors. If you are working in the real numbers, a least square fit gives the message. Now use this principle with, say, a different field.

Day two: second lecture: about curves …complex curves which are really surfaces.

Can you identify a polynomial, say, $z^2 + c$ by the closure of its periodic and preperiodic (finite orbit) points? If you superimpose the Julia sets, you do get overlap but they might not correspond to common periodic points.

Ok, a bit of topology and symplectic geometry. The latter is interesting stuff; here you worry about volume invariants.

Yes, I’ve studied two of these objects in detail

Day 1 MATHFEST 2019

Well, my attempt to run was a bust; it was hotter than I was used to and I ended up turning it into a 5K-ish “run/walk” which was shortened due to the nearby Trump rally. I didn’t go to that, though I saw the motorcade.

The talks: 3 main talks: first one was about decision making, utility and rationality. Second talk: equilibrium and games where selfish behavior ruins it for everyone. Third main talk: was about the mathematics of stable n-body problems and an interesting question about when an analytic function with a 1’st order zero at 0 and derivative equal to $\lambda$ can be linearized by a change of coordinates. Hint: the case $|\lambda | =1$ is the trouble case.

stumbling along

I had the luxury of walking a 2.2 mile course in the afternoon..I was getting so sleepy at my desk.

Weights this morning: rotator cuff, pull ups: 10-10-10-10-5-5-5 bench: 10 x 135, 3 x 185, dumbbells: 10 x 70, decline: 10 x 165, military: 15 x 50 seated, 10 x 45 standing, 10 x 40 standing, rows: 3 sets of 10 x 50 single arm, 10 x 110 machine, planks, knees: 6 x 30, 6 x 50 goblet, 10 x 210 leg press, knee stretches (getting down here a bit more).

Near the end..trying to get it all in without waving my hands too much (that is, without skimping on rigor).

I surprise myself

I wonder if my “run 3 days, walk 1 day” workout schedule is working.

Today’s weight room: rotator cuff, pull ups: 15-15-10-10-5, bench: 10 x 135, 3 x 185, incline: 6 x 150, decline: 10 x 165, military: 5 x 50 stand, 15 x 50 seated, 10 x 180 (90 each arm) machine, rows: 2 sets of 10 x 50 single arm, 10 x 110 machine, planks, headstand, goblet squats: 6 x 25, 6 x 50 (paid attention to integrity), leg press: 6 x 160..ball sits: 4 lbs. medicine ball is almost comfortable…working lower..

All of that went well. Bodyweight: 187.5 with shoes and shorts, which is about 185 without. We shall see.

Intellectually: I am studying the relationship between liner difference equations and time series. Interesting stuff; it is amazing how much utility linear algebra and its principles has.

Probability vs. Likelihood

This is an excellent video explaining the difference. And if you are scratching your head about what it means to “maximize the likelihood function”, this might illuminate what you are doing.