## objet a in place of Phi

### April 24, 2008

Here is a link on Wikipedia about the Golden Ratio, as well as continued fractions. It’s interesting that the golden ratio is generally represented by phi (the phallus), but lacan replaces is the the *a…*

The important bit seems to be this (from the continued fractions page):

## A property of the golden ratio φ

An interesting result, stemming from the fact that the continued fraction expansion for φ doesn’t use any integers greater than 1, is that φ is one of the most “difficult” real numbers to approximate with rational numbers. One theorem

^{[1]}states that any real numberkcan be approximated by rationalm/nwith

While virtually all real numbers

kwill eventually have infinitely many convergentsm/nwhose distance fromkis significantly smaller than this limit, the convergents for φ (i.e., the numbers 5/3, 8/5, 13/8, 21/13, etc.)consistently “toe the boundary”, keeping a distance of almost exactly away from φ…

Now, this doesn’t make much sense to me, but it seems that perhaps Lacan is using this equation to show that reaching what’s behind the phi-as-phallus (i.e. the *a*) is impossible. There is nothing behind it.

I don’t have my texts in front of me, but I recall thinking that the 1/1+1 etc was a demonstation of a ‘there is no metaposition’ thesis. IE, the determined form of every iteration of the calculation finds its place within the immediate result of that particular calculation.

Z says that as you move along a set of results, you’ll eventually find at least one, immediate, not-previously-sublated element that embodies the entire form of your very effort at generating that set of results.

In plainer language: ‘You are in your own picture.’

I kinda thought that’s what Lacan meant when he compared the Cogito to the continued fraction – you keep thinking in a loop, one that stays a constant distance from the thing that would bring the loop to the end (i.e. the emptiness of the subject…).

Is that what you’re shootin’ at?

I’m shooting at shadows, ghosts… the shots I take loop around & come heading back to me. The trick is no longer to have a need to dodge the bullets.