Bob Dylan "Restless Farewell"

This song is a masterpiece. The sentimental tune, borrowed from The Parting Glass, amplifies the emotional power of the lyrics, which are pure poetry.

The song is about a life lived honestly and the life beyond this life that waits.  He's lived honestly and will leave this world without giving a damn.  It's only a "false" clock that ticks out his time -- just an annoyance to distract him.  The dirt and dust that covers his face (when he's buried) are merely "rumors" and "gossip," easily pierced by the arrow of the truth.  It's the darkness that dies when the curtains are drawn (death) and the dawn that follows.

Note:  The lyrics on Dylan's website have an error.  It says "The time aint' tall, yet on time you depend."  The lyric on the album "The time ain't tall, if on time you depend."  The "if" conveys the opposite meaning of "yet" and is consistent with the interpretation that it is a false clock that counts down our days.

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Avoid doing it automatically

Geoffrey Colvin in his book Talent is Overrated talks about the paradox of automaticity:
“Frequently, when we see great performers doing what they do, it strikes us that they’ve practiced for so long, and done it so many times, they can just do it automatically. But in fact, what they have achieved is the ability to avoid doing it automatically.  Great performers never allow themselves to reach the automatic, arrested development stage in their chosen field.  That is the effect of continuous deliberate practice — avoiding automaticity.” (Emphasis mine)

This is interesting.  It reminds me of Alberto Salzar's training of Galen Rupp and Mo Farah where they are constantly worried about form, including "minor" details like thumb position.  Supposedly your mind/body naturally finds its most efficient running form, but maybe not?  Maybe the more open to change you are, the less repetitions it takes to reach better form.

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negative numbers

Reading Turnbull The Great Mathematicians. 

Why did the idea of negative numbers confuse us as kids?  Because there's no such thing.   -2 is an order to subtract 2.  It's an operation.  -3 + 1 = -2 means subtracting 3 and adding 1 has the same effect as subtracting 2.

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generalized Hough

Generalized Hough is used for an arbitrary shape.  The shape is parameterized by the center point and the set of vectors leading from the boundary points to the center.  These displacement vectors are indexed by the orientation of the tangent of the shape boundary at that point.  For an edge point in a test image we calculate its orientation angle (gradient?) and look up the corresponding displacement vectors (might be more than one depending on how discretized).  Each vector votes for the shape's reference position.  Votes will accumulate at the actual position as with the Hough line transform.

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hough transform

A Hough transform is an algorithm used in computer vision (image processing) application.  A computer image is a 2D array of values.  To identify a particular object in an image, we see if it matches a model for the object.  If we have an explicit mathematical model for the object, then we can seek to find the parameters for that model.  In the most common case for Hough transforms, Hough lines, we're seeking to find the slope and intercept of a line from a binary (1s and 0s) image (generally generated from edge detection).

We could take every subset of pixels (1s) and try and fit a line and then check the goodness of fit versus some criteria, but this would be computationally prohibitive.  A Hough transform takes each pixel and finds all the parameters that are consistent with a point at that location (a "1" at that pixel coordinate).  If there's a "1" at pixel (x_0, y_0) then all (m, b) such that  y_0 = m x_0 + b or  b = -x_0 m + y_0 are consistent with a line through that point.

Note that b = -x_0 m + y_0 is a line.  The point (x_0, y_0) in image space becomes a line "Hough space."  The parameters m and b in image space become the axes in Hough space, so it's also called "parameter space."  Here we have used m and b because the object of interest is a line, but it could be a different set of parameters for a different object.  (There are also Hough circles for instance where the parameters are the center and the radius.)

Each point in the image space maps to a line in Hough space.  All the points on a line in image space will correspond to a family of lines in m-b space that intersect.  We can find these intersections by discretizing m-b space and added up the values in each bin.  Each point in image space "votes" for a line in Hough space.  When these votes accumulate for a particular (m, b) past a threshold, we declare that such a line exists.

In practice, we don't use m and b because they can't handle vertical lines so the polar representation of a line is used.  A point at (x_0, y_0) votes for d = x_0 \cos \theta - y_0 \sin \theta where d and  \theta are the polar coordinate of the line.   d-\theta space is discretized and an accumulator array filled with the "votes" to determine whether a line with those parameters exists.


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Meaning of Bob Dylan's "License to Kill"

It's hard to believe I'm 41 years old, count myself as a Bob Dylan fan, and have never heard this song.  Watch Mr. Dylan on David Letterman.  It's mesmerizing.

So, what does it mean?

Here's my interpretation:  At its base, License to Kill is describing the consequences of a Godless society.  Without God, who will take away man's license to kill?  We've killed God and now man "only believes his eyes."  Without a world beyond ours, we live in an echo chamber of our own creation and it's making us "ill."

The consequences have left us isolated and on the brink of destruction.  "The first step was touching the moon" evokes reaching for the stars (and not heaven) as well as the space race and arms race.  The "license to kill" could  also reflect the president's license to "push the button," but I think that's too narrow an interpretation.

The imagery creates a feeling in the reader that can work on many levels.  The lines

Now he worships at an altar
Of a stagnant pool
And when he sees his reflection, he's fulfilled

evokes the theory of evolution, man in the image of man rather than God. The pool is also stagnant, lifeless. He's looking into the abyss and seeing no life, only his narcissistic self.  The stagnant pool where he sees his reflection could even evokes the reflecting pool in Washington D.C.  I think Dylan often picks an image that evokes feeling in the readers that he wants.  He's not trying to send a precise coded message.  This isn't a puzzle.  He's trying to get you to "feel" what he saying rather than think it.

The woman appears to be a device external to "man," looking to God ("facin' the hill") or whatever has replaced Him.  She could be the man's mother, watching her son raised without God -- "groom him for life and set him on a path where he's bound to get ill" -- eventually seeing him killed by the war-filled society -- "buried in stars."  Stars also evokes the space theme.  He doesn't go to heaven, but he's buried in stars (cold and lifeless).

She's left in the cold in the current world.  Again, the language "cold chill" and "night grows still" ties in with the cold, dead vacuum of space man has created with "touching the moon."

It's remarkably well crafted.

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experience quality

My blood pressure goes down when I edit text in a text editor, write equations in LaTex, store arrays in HDF5, write numerical code in numerical python,  or any time I hit a nail with a hammer. truly experience quality one must both embrace and apply it as best fits the requirements of the situation. According to Pirsig, such an approach would avoid a great deal of frustration and dissatisfaction common to modern life.

-- Wikipedia article on Zen and the Art of Motorcycle Maintenance

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Brad Osgood's Fourier Transform Course

Stanford and many other universities have made videos of class lectures available for free via youtube and other outlets (such as iTunes U). Let's pause for a moment and appreciate that. Holy crap! You mean I can learn linear algebra from Gilbert Strang? Why, yes you can! I don't want to make too much of it. I suppose this information has been available since we've had public libraries, but it just seems like there are no excuses anymore.

I combined my love of learning with my love of running and hatred of heat and humidity by watching the 30 video lectures of Brad Osgood's Fourier Transform course while running on the treadmill. I picked the course because someone had sent out a link at work about 6 months ago that I saved and then I was working with our Fourier Transform IR and realized I didn't know as much as I'd like about Fourier transforms.

Here's my brief review: It is un-****ing-believable.

He's a mathematician at heart and he lets you know when he's cheating and introduces much more rigor then you'd expect in an engineering class, but he doesn't let it bog him down. He motivates the lectures with history and lets you in on where the big steps are, usually with a sarcastic, "What could be more obvious?" How many times have you heard a professor dryly recite a derivation that's one of the crown jewels of civilization as if it were obvious?

He also appreciates the applications and uses them as motivation. The use of the diffraction problem to introduce sampling and interpolation is really original.

Beyond that, he's just an excellent communicator. You always know where you are and where you're going. He outlines the steps beforehand, gives guideposts along the way, and summarizes with "Where did we start and where did we finish?" It's really just excellent stuff.

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