Tuesday, August 28, 2007
Sunday, August 26, 2007
Sunday, August 19, 2007
Thursday, August 16, 2007
Wednesday, August 15, 2007
Tuesday, August 14, 2007
Monday, August 13, 2007
"The formula I am using is Ohm’s Law and mainly its relationship to power and potential, not so much the concept of resistance and flow (which to me are acting more like the glue to the whole thing)
I = V/R
Power = voltage multiplied by current
P = V*I
P = (V*V)/R
P = R * (I*I)
V = P/I
So I just found synonyms of the different variables, sometimes a couple of layers deep, and just started playing with the word combinations and formulas to see what “stuck to the wall” so to say.
“Resistance and Current are acting as opposing ideas”
R = Resistance: opposition, blocking, defiance, protecting, refusal, struggle, antagonism, animosity, antipathy, hatred, hostility, rancor, rivalry, avoidance, abstention, prevention, recession, recoil, restraint, retreat, interruption, indecision, delay, hindrance, procrastination.
I = Current: flow, effusion, emanation, flood, flux, gush, juice, plenty, plethora, river, stream, tide, appear, begin, commence, crop up, derive, emanate, emerge, ensue, follow, happen, head, issue, occur, originate, proceed, result, rise, set in, spring, start, stem, creation
“Power is the realization of the Voltage”
V = Voltage: potential, energy, conceivable, imaginable, doable, plausible, possible, quiescent, thinkable, ability, aptitude, capability, capacity, vitality
P = Power: dynamism, effectiveness, faculty, function, influence, skill, force, locomotion, motility, propulsion, authority, will, decision, longing, passion, pleasure, purpose, resolve, yearning, love, adoration, affection, ardor, desire, excitement, lust.
The word equations (concepts) seem to work better and make more sense to me when defined in terms of Power and Voltage rather than Current and Resistance."
Sunday, August 12, 2007
The Paradigm Poem
Unlike a simple mathematical structure as in the “Similar Triangles Poem”, the “Paradigm Poem” is a mathematical poetry technique that borrows its structure from an existing equation of scientific or cultural significance. The “Paradigm Poem has many sub-categories which are as numerous as there are categories for applied mathematics. Examples that we could consider would be: “Physics Paradigm Poem”, “Chemistry Paradigm Poem”, “Business Accounting Paradigm Poem”, “ Psychophysical Paradigm Poem” etc.
If we think in terms of metaphor using the cognitive scientific language of George Lakoff then we would classify the language of the variables “inside the equation structure” as the ‘target domain’ and the context or traditional meaning of the equation as the “source domain’
Let me show an example of a “Physics Paradigm Poem” using Newton’s second law. For this example I am going to use an excerpt from my essay on “Polyaesthetics and Mathematical Poetry” Journal of Mathematics and the Arts, Volume 1, Issue 1 March 2007 , pages 35 - 40 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954
“My personal view is that almost all mathematic applications rely on using equations with the intent similar to simile. The variables in the equation are compared explicitly with the result for uses in denotation. For example, in the case of an application of
Newton’s second law F = ma, or Force equals Mass times Acceleration, we are comparing the variables m (Mass) and a (Acceleration) explicitly to F (Force).
I can now make a mathematical poem based on the latter example by expressing the Force of ‘yesterday’s freedom’ as being equal to ‘a lush clover patch’
multiplied by ‘the swelling sweet summer breeze traversing the morning’. We can then put this in the form of a mathematical equation as; Yesterday’s freedom = (a lush clover patch) (the swelling sweet summer breeze traversing the morning). In other words, I set the Force to ‘Yesterday’s freedom’, the mass to ‘a lush clover patch’, and I accelerated the mass by ‘the swelling sweet summer breeze traversing the morning’. All of these
phrases relate back to the original equation from physics F = ma. I want to emphasize that I was very careful when I made my choice for acceleration so that the phrase is evocative of the mathematical description of acceleration as defined by physics. Acceleration is the
change in velocity of an object per unit of elapsed time during that acceleration. Here, the change in velocity is implied by ‘swelling’ and the change in time is implied by ‘traversing’.”
In the above example we are using the words “Yesterday’s freedom; a lush clover patch; the swelling sweet summer breeze traversing the morning” as the variables of the equations which supply us with the target domain and then we are using the equation from physics F = ma, its scientific meaning and historical significance as the source domain.
The bottom line concerning the ‘paradigm poem’ is that we borrow an equation from the past which inherently contains historical significance and serves as an paradigm or mathematical model that seems almost “a vessel” to carry the mathematical poem. The paradigm poem always borrows an existing mathematical structure to serve as a source domain in our metaphor.