I wanted to drop you a note to let you know I had a chance to read your book while on vacation in Key West this February. I enjoyed it very much. I have always enjoyed history, particularly the Civil War. Most of my reading has been related to the military aspects. Your book gave me a better understanding of Lincoln as a person, and will stimulate me to read more in that regard. Although I don't often spend time reading appendices in books, I very much enjoyed the speeches and letters presented. They were particularly interesting with the Euclidean approach to their breakdown. I haven't studied geometry since the 10th grade, but I can still remember doing proofs.

As the book was written, I also came away with a much better appreciation of the legal system, though I am not yet ready to change professions.

   -Dr. Carl Hays

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I found Abraham Lincoln and the Structure of Reason to be an enlightening and enjoyable study.  I've shared it with my two high school children who found relevance with their mathematics and English. Now I'm finding Euclidean parallels in everything :-)

     - Larry Kollasch

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Another reader:

1.    “Lincoln before Euclid – As you point out in your book, Lincoln was an amazing man, an eloquent speaker, and an adroit trial lawyer.  So, naturally, the question arises:  how logical and how compelling were Lincoln’s speeches before he read Euclid?  It would be nice to see some speeches before 1849, as a basis of comparison.  Were they also logical and well-reasoned, though in a more primitive kind of way?  Did Lincoln, in the old days, rush to make arguments early, rather than waiting patiently until he had all his ducks in a row?  Which Euclidean elements, if any, were missing?”

2.    “Lincoln’s Fidelity to Euclid – In all the speeches you’ve analyzed (and in some letters too), you find sections that seem to fit all six of Euclid’s elements.  It is possible that others would have reached somewhat different conclusions:  specifically, they might have found a specification section missing in speech #1, a proof section followed by a construction section followed by more proof in speech #2, etc. Was Lincoln so devoted to Euclid that he couldn’t write a good speech without adhering slavishly to the Euclidean template?  Your notes from the Columbus speech suggest that Lincoln’s use of Euclid’s six elements may have been loose in some instances, tight in others.” 

3.    "“The Power of Euclid – Lincoln’s speeches had so much going for them  great topic, iron logic, a generous spirit, winged words, and a Euclidean structure – that it’s difficult to disentangle the relative importance of each.  If any politician were to master Euclid’s six elements and apply them systematically to every one of his or her speeches, would the speeches suddenly be judged brilliant and compelling?  I think not.  With Lincoln, I suspect, Euclid’s logic was so attractive because he himself was already a deeply thoughtful and logical man.  So, to paraphrase your cake metaphor, towards the end of your book, it may be that Lincoln was the cake and Euclid the icing.  Which is not to downplay the importance of the icing (my favorite part of any cake, anyway).  The take-away lesson, for ordinary mortals who aspire to be better speakers, may be:  Euclid can help you to organize your thoughts better, but in the final analysis, much also depends on whether you have something to say.”

4.  A reader, who is an attorney, emails: "At this point in time I have read the preface, foreword and introduction to your book. I have one question. Perhaps it is answered in the book, if it is, just tell me, it’s answered in the book. Did Abraham Lincoln consciously apply the elements of a geometric proposition to his writings and speeches or did it just happen subconsciously because of his study of Euclid? It is interesting to me that I never did truly grasp algebra, but I did grasp geometry."

Response: There is a significant difference between geometry (not including analytical geometry) and algebra. Euclidean geometry is based on language. Algebra is based on equations. In Euclidean geometry you see the big picture. In algebra you see tiny steps. Your question (about whether Lincoln consciously used the elements of a proposition -- or whether it was subconscious) is pretty much answered in the book. If, after reading the book, you don't think so, ask again.

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Please e-mail your questions and observations to either of the authors.