Infinity: Qualitative and Quantitative

Came across this passage from a letter Franz Rosenzweig sent to Hans Ehrenberg in 1918:

What does the irrational number mean in relation to the rational?  For rational numbers, infinity is an always unattainable limit, a forever improbable magnitude, even if it is of the order of certainty, of permanent truth.  With irrational numbers, on the contrary, at each of its points that limit comes up against rational numbers, almost physically, with the presence specific to numbers, thus liberating it from its abstract, linear and one-dimensional nature (from which its hypothetical status also proceeds), to confer a “spatial” totality and an obvious reality on it.  In the form of the infinitesimal number, infinity is the secret spring, forever invisible, of the rational number and its visible reality.  On the other hand, through the irrational number, infiinty is manifested, becomes visible, while forever remaining an alein reality: a number that is not a number, or so to speak a “non-number.”

What an interesting (and oddly clear) passage.  It’s a rather succint statement of  Rosenzweig’s conception of redemption (and critique of Hegel) and sheds a some light on how Rosenzweig approaches some of the problems  towards the end of the Star, e.g. progress, messianism, election and history.  Anyway, at long last I have gotten a hold of Stephane Moses’ recently translated The Angel of History: Rosenzweig, Benjamin, Scholem.  Time permitting, I’m hoping to throw together some thoughts about Moses’ text and more broadly, Rosenzweig sometime soon.

21 thoughts on “Infinity: Qualitative and Quantitative

  1. Have you read Eric Jacobson’s Metaphysics of the Profane: The Political Theology of Benjamin and Scholem? It’s pretty interesting, I’ve been reading it on and off for some months now…

  2. Mikhail,

    What an interesting passage. It strongly reminds me of similiar things that Spinoza was trying to express (or at least seemed to be trying to express) as he talked about kinds, or magnitudes of infinity, infinities that happen between limits, and the limits of which can allow us to say that one infinity is larger or smaller than another.

    For Spinoza this was an indication that mathematics was not the path or ground for understanding God, and thereby not Nature either. I have not thought the issue through in the last few days due to travel, but he seems to imply that the division that mathematics makes, the limits it imposes, only demarcate recessive real, concrete infinities on either side, magnitudes within magnitudes (or something like that).

    • Ah, you are very right! I meant Shahar (I very often miss the little green font of the author’s name on your blog). Sorry Sharhar. All these thoughts directed towards you and your original post.

      • Except I always put more socks in my crotch area to indicate a much larger academic potential and was sharply distinguished by my superior tone and dismissive comments about others.

      • First, it was the ‘my reading list is longer than yours,’ then it was ‘my publication list is longer,’ accompanied by the moral authority these lengths breed. But Mikhail you’ve outdone us all by getting right to the point. Well done.

        BTW, how is the metaphysics of the profane book. It’s been on my radar for a while now, but I haven’t got around to picking it up. Is there a formulated phrase you could provide that gives us the gist?

      • Alexei, it’s pretty decent and I think were I specializing in Benjamin or Scholem or Rosenzweig, I would certainly pick it up (a bit too pricey for me, so I have a library copy). It has some smaller pieces on justice [Gerechtigkeit] by Benjamin translated (with German accompanying) and analyzed in the nice chapter on “Prophetic Justice” and some great analysis of violence and politics of “pure means” (which was the main reason I got it), but reading around I find a lot of interesting biographical info about Scholem – Benjamin and since I’m yet to read Scholem’s A Story of a Friendship, it’s all new and exciting stuff to me.

        I find the discussion of “pure means” very intriguing, I think Peter Fenves has a cool essay about it and I generally like the idea of what Benjamin does in “Critique of Violence” vis-a-vis “pure means” and “culture of the heart”…

      • sounds like i should really take a look at it then. Nuts, another book to read. The list is so long already….

      • It’s “sandwich bags,” please, I’m developing a set of precise conceptualizations here – are you mocking my project? It’s likely because you have no project of your own or/and you are jealous of my success in ontoknowlogy

      • I demand you write a post differentiating between sandwich bags and plastic bags! Also, in this same post be sure to dismiss my energy draining category mistake as a repetition of an essentialized type whose short hand descriptor is some mythologized creature and/or animal.

      • That’s what my next book is about, I will post in much detail on the process of its awesome creation and transformation from a series of napkin sketches I made while waiting to pick up my Chinese food into large elaborate graphs I drew on the walls of the local bar’s restroom (once they take me off the banned list) into a book – you should know all the details, including how many times I visit the bathroom while writing my opus plasticum – now you have something to look forward to, don’t you?

  3. I recently bought and tried to read the Star of Redemption (perhaps it was even at Shahar’s recommendation, I can’t remember the influence), and found it a bit interminable. Actually, rather interminable, never getting to the grist. The guy should have written a 30 page essay instead of an enormous book. It would have been fascinating.

      • Shahar,

        But it is still 233 pages! I mean, 233 pages in the hands of a concise, razored-edge thinker can be brilliant and invigorating, but this guy’s style (and maybe you love him) is incredibly repetitive, ad nausium. And it isn’t because he doesn’t know what he is doing. Its because he thinks that repetition in some way performs his point of history. I kept waiting for the “messiah” to come and redeem the endless, if spiraling, circles of his book, and there was no redemption…sigh.

        I say this with respect to your own enjoyment of his work, as it seems that you have solved or appreciate his style, but I could take 30 pages of it, not another 200.

        I had great hopes for the book when I bought it, as you might tell. I liked the thing about Jews and identify found in the blood and not the earth, but all else left me cold and a bit bored.

      • Now that would be interesting! If only I had access to a fruitful library I would certainly read it.

        [If ever of course you awake in the middle of the night with a mad compulsion to type up the essay until the wee morning light…]


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