Comments on: Descartes, Algebra, and Alienation

By: Mark Shiffman

Mark Shiffman — Mon, 30 Nov 2009 17:18:34 +0000

Just in case anyone else comes across this post, I’ll respond to O Watson:

Not sure what you mean by “real mathematics”, but if 4 years studying history of mathematics from primary sources in college and 4 years as a teaching assistant in mathematics courses at the University of Chicago counts, then I suppose I must have picked up some knowledge of it along the way.

Also not sure what you are trying to say with your “arrows” metaphor. Geometry developed for a couple thousand years without algebra, and algebra for a few hundred without being applied to geometry. Some people in the 16th and 17th centuries decided that the two could serve as representational equivalents, and I have raised the question whether important things are lost in the results of that decision.

Now I would ask whether you have made the intellectual experiment, as I have, of thinking through ancient geometry (Euclid and Apollonius in particular) with your thoughts as insulated as possible from the conceptual filter of Cartesian algebraic geometry. That would be a first step to what I would call “understanding real mathematics,” and it would be great if they taught that in graduate math programs.

By: Euclid vs. Descartes « PHI 270: History of Modern Philosophy

Euclid vs. Descartes « PHI 270: History of Modern Philosophy — Wed, 16 Sep 2009 18:40:15 +0000

[...] http://www.frontporchrepublic.com/?p=4097 « First Precis [...]

By: Septeus7

Septeus7 — Mon, 29 Jun 2009 21:57:55 +0000

I would prefer it if rather than looking to Euclid’s method of deductive proof for geometry as an alternative to Descartes and to move into anti-Euclidean geometry of Gauss and Riemann.

However, since the main subject here is Descartes I don’t think any discussion of Descartes would be complete without talking about his main detractor Leibniz.

When scientist stop trying make the constructs of Descartes and Newton congruent with the discoveries of Einstein and Planck and instead just accept the fact that Leibniz was right all along perhaps we have a bit progress and the so-called Enlightenment’s hostility toward Christianity will pass from our culture and we will get Western civilization back.

By: Owen Jones

Owen Jones — Fri, 26 Jun 2009 15:21:37 +0000

Just a word about Voegelin and gnosticism. Voegelin was interested in the symbol of The Beginning. Not just as the first cause, and certainly not just as a beginning in time, but as a symbol for a kind of starting point of existence, which is why in his later work he focused on an analysis of the structure of consciousness. Gnosticism therefore is an example of derailment or deformation of consciousness, but just looking at examples of deformation is not a sufficient way of looking at and understanding the structure of consciousness. As a practical matter, problems such as gnosticism are the starting point of philosophy. Voegelin philosophized because he was reacting to the political situation, the fact that people and governments would kill masses of people, particularly their own people, for no good reason. But why? It is not just a problem with motivation, or even a problem of orientation, although this is getting closer.

So in his last published volume (unfinished) he works on the question of the structure of consciousness, and there is a significant emphasis on the problem of the in-between nature of reality, working off of the beginning phrase of Genesis 1, “In the beginning…

So while there is always an astounding treatment of individual thinkers and historical “movements” in Voegelin, and a wealth of historiographic materials, the essential Voegelin, shall we say, is concerned about the structure of the in-between nature of consciousness and of reality as a whole, and what is it about the structure of consciousness that pushes beyond its structure.

So he never, in his later work, asserts that all of these cultural problems we are experiencing can be traced back to one thinker, or one historical period. That would be a gnostic interpretation of history. But it is a common problem among (we) conservatives, looking for some period of history, or one thinker that caused everything to go wrong with the idea that we can somehow get behind or go before that thinker and make everything right again.

By: Postmodern Conservative — A First Things Blog

Postmodern Conservative — A First Things Blog — Fri, 26 Jun 2009 05:39:07 +0000

[...] the diagonals of the inscribed parallelogram; you might just find your way to Mark Shiffman’s condemnation of coordinate geometry at FPR. I’ve many a gripe against Descartes, but did not consider his mathematical work to be [...]

By: Bob Cheeks

Bob Cheeks — Mon, 22 Jun 2009 23:35:13 +0000

D.W.’s back, all is well with my….!

Boy, from now on you let us know! This is a bunch of crap, you coulda been wrapped around a telephone pole on a deserted stretch of highway just a-moulderin’!

I thought someone aggravated you, but on second thought I knew that was unlikely…you being the aggravator!

Shiffman’s going all the way with gnosticism, this is cutting edge, new materials, the analysis….somewhere in the bosom of Eternal Being Voegelin smiles! By the time we’re done, we’ll need a good priest and a rabbi to get you right with the Lord!

My best to the wife, shalom, and congrats on the youngest’s graduation!

By: D.W. Sabin

D.W. Sabin — Mon, 22 Jun 2009 23:09:10 +0000

Cheeks,
Though never fully “Well”, I am not unwell…… just off on a Y axis to yorn X axis for a spell. The youngest graduated from Univ. of Oregon and one cannot go all the way to Crunchy Eugene from Tight-arsed New England without both enjoying Portland’s restaurants or the remote beaches of Oregon where cell phones have yet to trill. The Geometry of the Willamette Pinot Noir Vineyards also much to commend them whilst the Concept and middle daughter are inside at a tasting rail pretending to understand as the vin master expounds upon that lovely concept of terroir. Posts 21′ on center, vines about 5′-6″ o.c and the rows around 5′ apart, all descending the hill rather than traversing it…..a scene with equal parts nature and mathematics conspiring to create an indisputable proof that the culture begins in a marriage of plant and the soil consecrated by the Farmer as Justice of the Peace.

I am a non-imbibing Terroirista but fortunately, that little bit of fanaticism aint yet on the No Fly List.

As to Algebra, my eternal gratitude is extended to the good Doktor Shiffman for finally clearing up for me why I could never fully trust algebra. And all these years I thought I was simply dense. There was always something a tad shifty to me about Algebra with its overtly hypothetical relations of x to y and its simultaneous dance with the finite and infinite. I felt more at home in geometry….always demanding the right to actually clutch or inhabit form with my mind to confirm it is really there. Talk about knee-jerk skepticism. Not seeing the real places of the little geometric boxes in algebra, I gave up on it early but know that without it, the map of our mind is less than complete.

Patrick’s reference to Christopher Alexander is spot on. We respond well to a narrative architecture of compression and tensile expressions with relationships between windows and doors based upon human scale because we are conversant with the fundamentals of this architectural dialogue. It is not alien. Approach the modern deracinated and omni-place strip mall and the scene is devoid of dialogue and human scale because it holds no relationship beyond the merely transactional. It’s scale is with the automobile and speed. The breadth of a stride is irrelevant because the turning radius of a delivery truck is all that really matters.

Had I been aware that mathematics can be a social science, I might have tried harder at penetrating my barriers against the arid axis of algebra.

Lastly, with this site’s steerage of my reading list toward Augustine and Voegelin , you have bucketed me but good damn ye.

By: Clare Krishan

Clare Krishan — Mon, 22 Jun 2009 15:37:58 +0000

Good of John Medaille to ponder ‘relationship’ – may I offer by way of clarification: Square’s dream in Abbot’s Flatland,

http://www.youtube.com/watch?v=INgA1uiYRS0

where the King of Lineland knows no “relationship” of right or left, only forwards or backwards (aka that much vaunted “progress” we’re all supposed to be cheering for in Iran right? Or would that be left? Heck in Islam, does anyone care which way is up or down so long as its green, assertive, and raucously voiced?)

An ethical voice (a moral if you will) presumes a point of departure which Mark criticizes Descartes for rendering as arbitrary, am I correct? The fault of liberal modernism is it assumes majority/superior quantity as a valid legitimator of “relationship” (or a function of agency, ie how many degrees of freedom an agent is permitted to exercise logically) Consider in chemistry the function of chirality, carbon’s 4-fold valency permits “quantities” of atoms to combine in right-handed or left-handed fashion on the tetrahedron, in forms healthy or lethal to nature, molecules that metabolize or metastasize, life-giving or toxic.

Right relationship is key to our understanding of liberty in community. In economics a theory of value predicated on Cartesian mathematics (a ‘pris fixe’ definition of justice) will always be usurious, in that it usurps from the actor that degree of freedom to imagine the best (moral) use of the resources to be householded in the place and time of the circumstances he or she finds herself in, an obligation to sustain self (and ones dependents) in place that precedes any exchange of values to be anticipated from outcomes as yet indeterminate. Historicism collapses respect for the common good of a number of unique persons in magnitude of family bounded by a patrimony, into a concern for maximum good of the multitude of defined citizens of the state bounded by their gross national debt. The creative potential of the imagination instead of being the engine of human flourishing is denigrated to the rank of worker-bee/eunuch for the “soul of the hive” no?

By: Mark Shiffman

Mark Shiffman — Sun, 21 Jun 2009 21:28:43 +0000

I’ll second H.C.’s recommendation. You can start with the appendix, “The Origins of Geometry”, which briefly gives an idea of Husserl’s analysis of loss of meaning over time through what he calls “sedimentation”. This actually is a seminal text in the whole post-modern conversation (Derrida’s first book was a commentary on it), and it’s a good introduction to Jacob Klein’s very important book mentioned in my earlier comment. Husserl sees the symbols gradually and continually losing concrete reference to the original experiences that gave them meaning, whereas Klein points out a qualitative difference brought about by Viete, Stevin and Descartes in early modernity. Klein’s correction is a very important response to both Husserl and Heidegger, and is what initially convinced Leo Strauss of the radical rift between ancients and moderns.

By: H.C. Johns

H.C. Johns — Sun, 21 Jun 2009 18:00:40 +0000

Great comments, great piece. I’d just throw out that one of the very best books on this subject was never completed, but is still worth looking at: Husserl’s The Crisis of The European Science’s is both a very interesting development of his own phenomenology and a reversal of the modern understanding of mathematical meaning. It’s a tough read but its one of the most convincing refutations of the Cartesian-Kantian schema I’ve ever read. Its a real shame he never finished it. Sigh.

By: Bob Cheeks

Bob Cheeks — Sat, 20 Jun 2009 14:06:02 +0000

Caleb, congrats on getting Walsh’s new one, I’ve read excepts and it’s very interesting. Somewhere along the line I’m going to have to beg it off the publisher. I’m glad to have your opinion of “The Growth of the Liberal Soul.” YOu might want to review that on FPR, I’d love to read it!
I just got Gooch’s bio of the beloved Flannery for review.
RCC

By: John Médaille

John Médaille — Sat, 20 Jun 2009 13:01:17 +0000

Mark, on the question of form, I have only questions, at least from the “physical” standpoint. Physics seems incapable of accounting even for physical forms, much less those “coordinated and sustained capacities for the life-activities.” We know a great deal of the chemistry of life, but cannot produce life from chemistry. But even for inanimate things, their form exceeds their chemistry. I think it possible that even form arises from relationship; what else could “coordinated capacities” mean? “Coordination” is a relationship. I am trying to keep relationship primary because I don’t want anything prior to it when speaking of the Trinity.

By: Caleb Stegall

Caleb Stegall — Sat, 20 Jun 2009 12:35:20 +0000

Bob, delighted to know you are hooked up with Fritz. I have know Fritz for many years and I believe I am supposed to be reviewing the Walsh book you reference for his new publication, though I haven’t actually received the volume yet. I was very disappointed by Walsh’s book Growth of the Liberal Soul, however, I hear tremendous things about his latest. -cs

By: Bob Cheeks

Bob Cheeks — Sat, 20 Jun 2009 11:04:57 +0000

Caleb, delightful and insightful comments on the beloved EV. He maintained the principle that ‘governed’ his work in the first three volumes of the seminal work, Order and History. But on Vol. four, The Ecumenic Age, a jaw-dropper as you know, he “revises his understanding of how the history of order must me analyzed and he altered his conception of history based on this revised analysis.” A note of interest: I’ve developed a fondness of FWC Schelling in reading a book (The Modern Philosophical Revolution)by a student of EV’s, Dr. David Walsh of CUA. EV would be proud of Walsh and his work is just breathtaking.
In any event, I was reading in Vol. 33, EV’s discussion re: his writing of Order and History and he altered his thinking in writing this work, prior to the above. He was, as you know, not a rigid academic, his work always depended on the materials and on the truth. So Order and History is the product of a noetic epiphany brought about by EV’s reading of Schelling’s History of Myth. Here he abandoned the idea that ‘idea’ was anything but nonsense, rather there is only the history of experience-Schelling was THE father of Existentialim-and consequently EV’s work centered on the analysis of experience.
I’m a contributor to Fritz Wagner’s Voegelin View website. Please check it out and I’m sure Fritz, who has amassed tons of EV material and makes it available to the faithful, would be delighted with your input, I know I would. Also, Fritz was a student of EV’s at ND! And, yes the exploration of EV’s thought is most promising, as is Drs. Shiffman and Peters analysis of the gnostic phenomenon, which is very important, seminial, work being published on your site!
Best Wishes

By: Kevin J Jones

Kevin J Jones — Sat, 20 Jun 2009 02:16:12 +0000

I would have benefited from a more detailed treatment of the classical idea of magnitude.

“There is a marvelous beauty to the way the relations of figures are revealed when Euclid proves that the area of the square on the hypotenuse of the right triangle is the sum of the areas of the squares drawn on the other two legs. This beauty is entirely missing in the formula “c squared equals a squared plus b squared,”"

This reminds me of someone who only has a reading knowledge of a language. He understands a passage only by translating it into his native tongue rather than understanding it in its own terms and in its own “life.”

Only in the case of math, our native tongue is Cartesian.

Isn’t “translation error” a major distortion in modernity?

By: Mark Shiffman

Mark Shiffman — Sat, 20 Jun 2009 01:49:16 +0000

Clare: Of course Galileo is important in the way motion and nature get redefined mathematically. There are a number of key players in this story. But Descartes is, in a way, the most complete player. But I appreciate your use of Schindler as a corrective to my account, since that is how I have the good fortune to be able to use him often. I’ll have to mention that you invoked him when he’s over for dinner Monday.