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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."
"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.
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!)
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.
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."
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."
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