Re: CCL:Alternant hydrocarbons and the film "My Fair Lady"

Hello Dr Pang:
 To answer your question:
 >1.Have you any material, which explains "alternant" in plain
 English ...
    The word "alternant" shows up in matrix algebra.  The
 "alternant" may
 be defined as the determinant of a Vandermonde matrix.  The 3x3 Vandermonde
 matrices have this form:
  1    a    a^2
  1    b    b^2
  1    c    c^2
 The determinant of this matrix, the ALTERNANT, is equal to
 (a-b)(b-c)(c-a) = (b-a)(c-b)(c-a)
 4x4 Vandermonde matrices have this form:
  1    a    a^2    a^3
  1    b    b^2    b^3
  1    c    c^2    c^3
  1    d    d^2    d^3
 The alternant for this matrix is the product
 (b-a)(c-a)(d-a)(c-b)(d-b)(d-c)
 etc...
 More generally, the product of all differences of a set of n numbers
 y_1, y_2, y_3, ... y_n is equal to the determinant of the corresponding
 n x n Vandermonde matrix (alternant) having elements y_1, y_2, y_3,
 ... y_n on the 2nd column.  So for the general n x n case, the alternant is
 Product_for_all_pairs_i,j_(0<i<j<n+1)_of_(y_j-y_i)
 See formula 14.311 in I S Gradshteyn and I M Ryzhik "Table of
 integrals, series, and products", corrected and enlarged edition
 prepared by Alan Jeffery (Academic Press, 1980, New York).
 I guess one could, by extension, define "alternant" as follows:
 the alternant associated with an ordered set of numbers is the product
 of all the ordered differences that can be formed from these numbers.
 It may not sound like plain English, but working out examples helps.
 Here's some sets of numbers and the alternants associated with them:
 {7, 4, 5}     the alternant is (4-7)*(5-7)*(5-4)= 6
 {7, 5, 4}     the alternant is (5-7)*(4-7)*(4-5)=-6
 {7, 5, 4, 1}  the alternant is (5-7)*(4-7)*(4-5)*(1-7)*(1-5)*(1-4)= 432
 {7, 5, 1, 4}  the alternant is (5-7)*(4-7)*(4-5)*(1-7)*(1-5)*(4-1)=-432
 {7, 1, 5, 4}  the alternant is (5-7)*(4-7)*(4-5)*(1-7)*(5-1)*(4-1)= 432
 Rene Fournier.
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 On Thu, 13 Sep 2001, Henry Pang wrote:
 > Hi CCL
 >
 > I am interested to find out if my impression CC is a super reductionist
 > field is reasonable. The word "alternant" is found in CC books.
 Ira Levine
 > (1983), Quantum Chemistry says, "An alternant hydrocarbon is a planar
 > conjugated hydrocarbon in which the carbon atoms can be divided into a
 > starred set and an unstarred set."
 >
 > My several general chemistry books do not mention alternant. I do not find
 > any entry for "alternant hydrocarbon" in the Cambridge
 International
 > Dictionary of English, Academic Press Dictionary of Science and Technology,
 > but the Concise Oxford Dictionary says, "alternant is alternating, of
 > alternating layers". I do not find any mention in books of cosmology,
 > astronomy, physics, archaeology, anthropology, history, language,
 > linguistics, law, medicine, surgery, politics, metal work, or mass media
 for
 > example.
 >
 > I do have some idea; alternant is interesting in molecules such as
 > cyclobutadiene, naphthalene, benzyl radical, azulene, cyclopentadienyl
 > radical. I am looking for any discussion regarding what the word
 "alternant"
 > means in plain English, which other people in the university and community
 > might appreciate as human beings, even though not expert in CC.
 >
 > Please understand I am not being disrespectful or even facetious. Do you
 > recall the award film "My Fair Lady"? Common flower girl Eliza
 Doolittle
 > asks phonetics expert Professor Higgins to teach her to speak like a lady.
 > Eliza becomes the belle of British society and the Prince takes her hand to
 > lead her to the dance floor at the great Ball. Higgins takes all the
 credit.
 > As he says, "I knew I could do it." He tells Eliza, but she
 replies in total
 > defiance, "I do not understand anything you are saying to me. I am too
 > ignorant!"
 >
 > I am not CC, but just an Australian medical doctor. I am just curious about
 > CCL. Forgive me, but CCL seems like an intense activity looking the
 computer
 > measurements and bond strengths of the Lego blocks put together by my
 > children into interesting creations. CCL day in and day out, seems about
 > finding better ways of computing the minute details of my children's Lego
 > blocks?
 >
 > Questions -
 > 1.Have you any material, which explains "alternant" in plain
 English for my
 > children, so they might really understand what the animal is in real terms?
 > 2.Have you ever heard of another word "Holism"? Could holism be
 of any
 > interest to the super reductionist field of CC? Does it really matter to
 the
 > world or our Universe in any case?
 >
 > (I am disgusted and very sad about New York and the Pentagon)
 >
 > Regards
 > Dr Henry Pang (medical)
 > Australia
 >
 >
 >
 >
 >
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