This therefore stood out at me in what you wrote above: “The slight problem I have, however, is that this notion of a movement that attempts to re-invigorate philosophical first-order arguments under the banner of ’speculative philosophy’ seems aimed specifically at philosophy. The content, of course, still comes forward as first order arguments, but the structure or dynamic of the movement looks on this account to be second-order (a kind of ‘metaphilosophical’ movement). That may or may not be a positive thing, I’m not sure, although I’m certainly uncertain. What is clear, however, is that a new fashion is on the rise and at the centre of it is a brand name rather than a ‘proper name’.”

Something that is intriguing me, and which I have been writing about for the past few months (as a way of summing up a general direction for myself in philosophy), is Deleuze’s wish for a ‘pop philosophy’. Do you think that there is an almost standard deficiency today in the way that philosophers/academics/theorists seem to conceive their role, for the simple fact that they have this desire to cash their ideas out practically? (Or, at least, know that they cannot maintain consistently enough these days the ‘purity’ of their position as knowers, since this has to mean some sort of social derivation, and not an essential link between knowledge and status like a century or so ago.) With Deleuze, in brief, I think the idea of pop philosophy tends to attract the most vain prejudices of commentators, and their belief in their role as ‘explainers’ seems to go hand in hand with a kind of ‘cojolling-of-the-masses to behave like a bourgeois’ procedure. Yes, single mothers + penchant for neat analysis = happiness. Apparently. What do you think?

‘diamond time’ is a concept in construction I suppose, or perhaps idle whimsy, or perhaps poetic license. speculation for production.

the sharpening of the soul…yes, it suggests a kind of normativity, that somehow we need to correct our vision and that is problematic. more interestingly I’m drawn to the idea that the soul (let’s continue to talk about this soul thing) is itself a kind of sharpening, a dynamic towards a point, a strange attractor dynamic no doubt but a dynamic nonetheless. ah, curious speculations of course.

One thing I think that is odd, however, is Rucker’s claim that ‘Matter isn’t dumb’. Whilst this is a claim I cleave towards at the moment and one I’m kind of trying to develop in my own way - or something similiar - it does smack of a strange kind of activity - quite how is matter ‘intelligent’? Presumably in the same way that ‘crowds’ are taken to be intelligent, that is, that they express solutions to problems. I’m not sure this is enough for intelligence since it seems to lack what we would usually want to think of as fairly central to intelligence, which is understanding.

Many thanks for the interesting link and comment.

“Although it’s a cute idea, I think computronium is a fundamentally spurious concept, an unnecessary detour. Matter, just as it is, carries out outlandishly complex chaotic quantum computations just by sitting around. Matter isn’t dumb. Every particle everywhere everywhen is computing at the maximum possible rate. I think we tend to very seriously undervalue quotidian reality … This is because there are no shortcuts for nature’s computations. Due to a property of the natural world that I call the ‘principle of natural unpredictability’, fully simulating a bunch of particles for a certain period of time requires a system using about the same number of particles for about the same length of time. Naturally occurring systems don’t allow for drastic shortcuts”.
http://boingboing.net/2008/03/04/rudy-rucker-versus-t.html

I don’t know Leibniz well enough to know if this might be compatible, but it’s a fairly unusual position, since most radicals these days believe everything is contingent. COMPUTRONIUM is an idea, partly due to SF author Charlie Stross, that the cosmos can be converted to ‘computronium’ and reality will then be computed or simulated. This seems similar to many militant notions of utopia… Mark

as to the lens polishers, yes, I think the Ethics is exactly that, ‘a polishing device, meant to sharpen the soul to clarity’ - the curious fact that the efficacy of the lens depends on the precision of the distortion it provides never seeming to impinge on Spinoza at all. inadvertently he seems to acknowledge that the soul needs this sharpening, but for what…

http://www.absoluteastronomy.com/topics/Inflection_point
http://www.absoluteastronomy.com/topics/Inflection_point
http://mathsfirst.massey.ac.nz/Calculus/SignsOfDer/POI.htm (this one is good)

Please scrap parts of my above definition, I would like to elaborate and clarify. I made a mistake between the inflection point and the intersection point. They are very much different but more often than not they do relate, given the function.

Now I don’t know how higher-level Maths or other corners of Maths use the notion of the inflection point, but the one that I learned in college was best seen as this:

The point of inflection is the point where the direction of the line alters and seems to come back on itself such that if a tangent is drawn then it will cut through the line. It is the change in element (or sign, neg/pos) of a line. Think of a river that meanders such that it comes back to face itself but will not touch itself, instead it changes trajectory, it only views itself from a distance and continues on in another direction. In some definitions it is seen as the point where the curve alters its concavity from either upwards or downward (when viewed as a movement from left to right). This may be significant to the Leibnizian monad.

It is categorized as the point where there is a transition in the overall trajectory of the graph from one sign to the next. Usually these points are indicated by x or y being equal to zero, but it is not necessarily so. The way they find inflection points is through 1st or 2nd derivatives, depending on the function, but usually the first suffices. The maximum or minimum extremity of the first derivative is usually where the inflection point of the function is found.

These are just little particularities though, that are not so significant. The one thing to take is the relationship between the change of element and the inflection point.

In answer to your first question: yes, a function can have many inflection points e.g. a sin graph. However, it is only the coordinates of the inflection point in the sin graph that change, and usually they descend by a constant or rise by a constant e.g. if inflection in sin graph is at 0,0, next one will be ([-]6,0), the one after ([-]12,0)… ([-]18,0) etc. Other graphs may be different, but if the function is constant I am pretty sure the relationship between inflection points will likewise remain constant. Or some functions may have no inflection point, even though they change direction, but do not change sign, i.e. x^2.

I think to answer your final question is a little difficult, as I am not entirely clear myself regarding the necessity and relationship of either of these two definitions:

-a) The tangent that crosses the graph.
-b) The point where it begins to change sign.

I would take b) as more essential, because one can draw a tangent and cross the graph, but not be at an inflection point. As such, I think its best if we take definition b) as necessary and sufficient, but a) as only necessary.

The key component of the inflection point is that it changes a sign. Also if we draw a tangent somewhere on the graph and that tangent crosses the graph itself, then you have an imminent inflection point. I hope this helps a little more. Also, I found the little diagram on inflection point on wikipedia quite useful for visualization. Alternatively you can draw your own graphs by downloading this brilliant little program:

http://www.padowan.dk/graph/Download.php

I would recommend the first download due to derivatives.

I’m settling back into the notes again and will post some more soon - at the moment the ’shortest’ and not too useful response to the connection between an ‘essence’ (in the new form, ie: as an event) that Deleuze is developing in the Leibinz book and the inflection point would seem to be a kind of analogy between the monad within the best possible world as a point on a curve of variability. The inflection point would on this reading be an inflection point within a particular possible world, offering the option for the same curve to have another inflection point within another possible world. That would seem to be where the analogy might break down, hence why I would want to explore further the concept of inflection point.

For example, does each formula have one and only one inflection point? Would it be possible, for example, to generate a variation of inflection points on the same curve, each of which formed on the basis of the ‘grid-ing’ that enframed the curve?