David Custis Kimball - blog

You: Why Dave; why now?
Me: Well, I've two talented kids; the younger mentioned my stopping with the lectures. Then enthusiastically asked, 'Dad, can I help you set up a blog?' Moments later, Me: 'OK, that's a great idea, thinkin' they might just read it someday.

me ---> 'Gaarr of Blog' <---

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Just use 'Search' for the topic of choice or Waldo, perhaps.

Matters of Import & Timely Expertise
repressing gossip and hate-speech.

An Unmapped Ponderocity:
To say: '"He is a man of truth," is to say nothing; to say: "He is a man of of," is to state an elementary truth of logic.'
Winston Davids, 1969 - Trinity College Valedictorian - 1970; known endeavor: actuarial contributions to The Donald; since has contacted me and sadly is quite ill. Ask prayers for recovery; thanks for his brilliance and music.

Feb 12, 2012 10:11am
Mathematics, Humor, History The difference of &#8216;who you are&#8217; and &#8216;what your best friend thinks of you&#8217; is a vastly important and not easily appreciated or acquired distinction, dare I say &#8216;distribution&#8217;. Without reading this book, I&#8217;m in tuned to its significance.  After all, from Paul Dirac&#8217;s mouth I heard &#8216;Show it mathematically and it will be so.&#8217; And it is not that I wish to guide or push someone in a favored direction which I do not believe in or feel is true, but to express something with the given facts in such a way as to make it as precise as is possible to the current &#8216;State of Affairs&#8217; (Wittgenstein) is a memory-worthy endeavor. I added &#8216;Humor&#8217; as part of this because humor seems to be the greatest facilitator of ambiguous certainty.  Bazinga isomorphismes: Leonardo da Vinci’s ability to embrace uncertainty, ambiguity, and paradox was a critical characteristic of his genius. —J Michael Gelb Say you want to use a mathematical metaphor, but you don’t want to be really precise. Here are some ways to do that: Tack a +ε onto the end of an equation. Use bounds (“I expect to make less than a trillion dollars over my lifetime and more than $0.”) Speak about a general class without specifying which member of the class you’re talking about. (The members all share some property like, being feminists, without necessarily having other properties like, being women or being angry.) Use fuzzy logic (the ∈ membership relation gets a percent attached to it: “I 30%-belong-to the class of feminists | vegetarians | successful people.”). Use a specific probability distribution like Gaussian, Cauchy, Weibull. Use a tempered distribution a.k.a. a Schwartz function. Tempered distributions are my favourite way of thinking mathematically imprecisely. Tempered distributions have exact upper and lower bounds but an inexact mean and variance. T.D.’s also shoot down very fast (like exp{−x²} the gaussian) which makes them tractable. For example I can talk about the temperature in the room (there is not just one temperature since there are several moles of air molecules in the room), the position of a quantum particle, my fuzzy inclusion in the set of vegetarians, my confidence level in a business forecast, ….. with a definite, imprecise meaning. Classroom mathematics usually involves precise formulas but the level of generality achieved by 20th century mathematicians allows us to talk about a cobordism between two things without knowing everything precisely about them. It’s funny; the more advanced and general the mathematics, the more casual it can become. Like stingy stickler things that build up to a chummy, whatever-it’s-all-good.   Our knowledge of the world is not only piecemeal, but also vague and imprecise. To link mathematics to our conceptions of the real world, therefore, requires imprecision. I want the option of thinking about my life, commerce, the natural world, art, and ideas using manifolds, metrics, functors, topological connections, lattices, orthogonality, linear spans, categories, geometry, and any other metaphor, if I wish.

Mathematics, Humor, History

The difference of ‘who you are’ and ‘what your best friend thinks of you’ is a vastly important and not easily appreciated or acquired distinction, dare I say ‘distribution’.

Without reading this book, I’m in tuned to its significance.  After all, from Paul Dirac’s mouth I heard ‘Show it mathematically and it will be so.’ And it is not that I wish to guide or push someone in a favored direction which I do not believe in or feel is true, but to express something with the given facts in such a way as to make it as precise as is possible to the current ‘State of Affairs’ (Wittgenstein) is a memory-worthy endeavor.

I added ‘Humor’ as part of this because humor seems to be the greatest facilitator of ambiguous certainty.  Bazinga

isomorphismes:

Leonardo da Vinci’s ability to embrace uncertainty, ambiguity, and paradox was a critical characteristic of his genius. —J Michael Gelb

Say you want to use a mathematical metaphor, but you don’t want to be really precise. Here are some ways to do that:

  • Tack a +ε onto the end of an equation.
  • Use bounds (“I expect to make less than a trillion dollars over my lifetime and more than $0.”)
  • Speak about a general class without specifying which member of the class you’re talking about. (The members all share some property like, being feminists, without necessarily having other properties like, being women or being angry.)
  • Use fuzzy logic (the ∈ membership relation gets a percent attached to it: “I 30%-belong-to the class of feminists | vegetarians | successful people.”).
  • Use a specific probability distribution like Gaussian, Cauchy, Weibull.
  • Use a tempered distribution a.k.a. a Schwartz function.

Tempered distributions are my favourite way of thinking mathematically imprecisely.

Tempered distributions have exact upper and lower bounds but an inexact mean and variance. T.D.’s also shoot down very fast (like exp{−x²} the gaussian) which makes them tractable.

For example I can talk about the temperature in the room (there is not just one temperature since there are several moles of air molecules in the room), the position of a quantum particle, my fuzzy inclusion in the set of vegetarians, my confidence level in a business forecast, ….. with a definite, imprecise meaning.

Classroom mathematics usually involves precise formulas but the level of generality achieved by 20th century mathematicians allows us to talk about a cobordism between two things without knowing everything precisely about them.

It’s funny; the more advanced and general the mathematics, the more casual it can become. Like stingy stickler things that build up to a chummy, whatever-it’s-all-good.

 

Our knowledge of the world is not only piecemeal, but also vague and imprecise. To link mathematics to our conceptions of the real world, therefore, requires imprecision.

I want the option of thinking about my life, commerce, the natural world, art, and ideas using manifolds, metrics, functors, topological connections, lattices, orthogonality, linear spans, categories, geometry, and any other metaphor, if I wish.
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