Approachability

Today is the birthday of Michel Rolle born 1652 in Ambert, Basse-Auvergne, France.  Rolle is known for Rolle's Theorem which states that in calculus, any differentiable function that attains equal output values at two distinct points must have a point between those two where the first derivative (the slope of the tangent line to the graph of the function) is zero.

Quote of the day: John Maynard Keynes, "I can't remember my telephone number, but I know it was in the high numbers."

In mathematics, a limit of a function at a input value (x-value) is the output value (y-value) that the function produces as the input value is approach from the right and left of the input value.  For the function to have a limit at that particular input value, the formed output value must be the same from both the left and right sides.

Functions that have asymptotes do not have numerical limits at the asymptote.  As input values approach the particular numerical value where the asymptote exists, the function may increase or decrease without bound.  The asymptote acts as an invisible boundary, a forcefield.

Two famous quips concerning asymptotes I have used in my class:  "You need to know the difference between your asymptote and a hole in the graph."  and "Holy shift!  Did you see the asymptote on that mother function."

Recently, I have had a parent call me and state that I am unapproachable.  I guess the parent was stating the I was asymptotic.  I have thought about that comment since that phone call.  I can be unapproachable.  The part of my personality is my Achilles' Heel.  I have made a conscious effort to be more approachable.  That particular characteristic does not come naturally to me.  I work closely with a colleague and he is warm and welcoming.  I, on the other hand, have to work at it.  I need . . . I require full concentration from myself and from my students when I teach.  I believe that my focus can be alarming and frightening to students.  Often, when I am focused on a problem, I can be gruff and too quick to the point.  I also have a well-defined bubble that surrounds me.  I am not a very "touchy, feely" kind of a guy.  I really work at giving my best instruction to my students.  I just need to create an approachable limit.

Helter Skelter, Life, and Differentiation

Today is the birthday of Charles Tinseau born 1748 in Besançon, France.  Tinseau researched and wrote on the theory of surfaces.

Quotes For Today

Johannes Kepler: "The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics."

Saint Albertus Magnus: "Do there exist many worlds, or is there but a single world?  This is one of the most noble and exalted questions in the study of Nature."

Charles S. Pierce: "Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility."

"Helter Skelter"

When I get to the bottom I go back to the top of the slide
Where I stop and I turn and I go for a ride
Till I get to the bottom and I see you again
Yeah yeah yeah hey

Do you, don't you want me to love you
I'm coming down fast but I'm miles above you
Tell me tell me tell me come on tell me the answer
Well you may be a lover but you ain't no dancer

Now helter skelter helter skelter
Helter skelter yeah
Ooh!

Will you, won't you want me to make you
I'm coming down fast but don't let me break you
Tell me tell me tell me the answer
You may be a lover but you ain't no dancer

Look out helter skelter helter skelter
Helter skelter ooh

Look out, cos here she comes

When I get to the bottom I go back to the top of the slide
And I stop and I turn and I go for a ride
And I get to the bottom and I see you again
Yeah yeah yeah

Well do you, don't you want me to make you
I'm coming down fast but don't let me break you
Tell me tell me tell me the answer
You may be a lover but you ain't no dancer

Look out helter skelter helter skelter
Helter skelter

Look out helter skelter
She's coming down fast
Yes she is
Yes she is coming down fast

(My head is spinning, ooh...

Ha ha ha, ha ha ha, alright!

I got blisters on my fingers!)

                                                         by Lennon, McCartney

"Roller coaster of emotions; some days good, some days bad", as quoted by a listener on MPR in a conversation about the emotional stress of the passing of his dog.

"Good days, bad days, and then there are terrible days . . . I never know when.  On terrible days, I feel so alone and am in so much pain", as quoted by a friend whose son passed away less than a year ago.

I have taken a considerable amount of time in composing this blog.  In a recent conversation with Sam, he noted this by remarking that I "may soon lose my audience".  I have noticed the closer the topics of my blog are to my heart, the more difficult they are to write.

Differentiability addresses slopes of tangent lines.  

The blue function is differentiable and red and green lines are tangent lines on the function.  The red line has a slope of 4 and the green line has a slope of 0.

 

The blue function is not differentiable at x = 1 because at that value a vertical tangent line is formed.

I have ridden some roller coasters but refuse to ride "The Wild Thing".  This ride seems to approach a vertical tangent which raises my fear to the level of panic.  I have never liked rides.  When I was very young, I rode on a ferris wheel with my mother.  As we reached the absolute height the wheel was from the ground, I was joyful.  I believe I could see all of Rochester, Minnesota in front of me but as we passed that apex and started our journey down, my panic set in.  I screamed that I wanted to stop.  As time passed, I revisited my ride.  I have ridden many ferris wheels since.  Although I panicked, I knew my mother was there and I eventually realized that the ride would end.  I view this experience as a differentiable function.  I experienced highs and lows but those moments were brief, a gradual rise and fall.  "The Wild Thing" causes a fear for me that is beyond rational.  I do not see the fun.  I experience the absence of safety or hope.  I view this experience as a function that has a moment which is not differentiable.

I tell my students that on graphs that come to sharp points that at that location the function is not differentiable.  I tell them that if they could run a finger along the graph, points that are not differentiable would cause a prick of pain and perhaps a loss of blood.

My dad is 93 years old.  I know his transition is inevitable and soon.  He can be described as a robust and highly cognitive elderly man but I know his time is short.  I view this transition as a function that gradually reaches a peak or valley and then gradually eases.  Contrast my future experience with that of friends that lost their son suddenly.  This transitional function radically painfully peaks, with no sight of an end.  This sharp, stabbing sorrow is combined with confusion, emptiness, and loneliness.

My question is how do I comfort my friends?  How do we all move on?

"Good days, bad days, and then there are terrible days . . . I never know when.  On terrible days, I feel so alone and am in so much pain."