If you're wondering why all the Heidegger, I've been doing a pretty concentrated study of Being and Time for the past while, so it's been on my mind. Taking that into account, welcome back to the world of survival ontology:
It can be that, or at can, equivalently, be viewed as an indicator as to how volume transforms when side-lengths are uniformly scaled. I don't mean to say that one is more fundamental than the other, but they are both notionally different and, in my experience, of similar importance.
Yeah, I'm sort of generalizing its mathematical significance to get the job done, but it isn't particularly pertinent to the argument in general (see below).
This could be said about pretty much any mathematical entity, couldn't it? (maybe that's what you indicate in what you write afterwards). On the other hand, the notion of dimension (or various particular mathematical characterisations) is a relatively free-standing one, one that does not exist to achieve a specific purpose, or was not used to. It doesn't do anything; in some instances where it arises it might solve problems, but sometimes I just calculate the dimension of things with no particular purpose in mind.
Yes, it could, and actually I think mathematical tools can still have readiness to hand as tools which are used skillfully by someone to some end. In this particular case, however, I am talking about applied math used to solve a particular physical problem like the one from which string theory emerges and from which we have ten dimensions, etc., and I am talking about it in the context of how it relates ontically to the universe, as that is sort of the focus of the discussion and why I brought ontology back: the question "Does the space we inhabit have ten dimensions and what, exactly, does it mean to say that?"
As a point of note (this isn't related to the original argument), though, I think mathematical tools, when they are employed skillfully, can have a use or a purpose, in that they can be part of the referential totality of equipment. They have a 'towards-which,' (das Wozu, in terms of serviceability) which could be to solve a particular problem, a 'for-which' (das Wofür, in terms of usability), which could be for the sake of research or to better understand a concept and a 'for the sake of which' (das Worumwillen, in terms of ultimate goal) which goes back to how the operations relate to your stand on your existence: doing math is what a mathematician does. You are not a mathematician if you sit at home and eat ice cream all day instead of doing math. You have to, you know, get out there and do some math.
And these things are relatively transparent as long as they are inconspicuous, that is as long as they are not unready-to-hand for some reason. It's when you try to solve a new problem or try to do work in an unknown field that they become conspicuous.
When the idea of 'purpose' becomes difficult or ambiguous is normally when we use purpose in the cultural sense in our stance primarily as consumers. When people say pure math has no purpose, they mean it doesn't necessarily produce things which generate money or products, which is generally how most people in our society approach what it means to be a person living today in the capitalist first world. If you do math at home by yourself and no one pays you, you are wasting your time in idleness; if you are employed to do math but it doesn't really appear to contribute to the GNP, that is a little better; but if you are using mathematical tools as an engineer to create a new product to sell in the market, that is really the best because it relates directly to the economy and is 'productive'. However, I don't agree with that and it certainly isn't a useful definition of 'purpose' for the purposes of doing ontology, as it relies very heavily on the interpretation of meaning for one subset of our local population.
(I'm not familiar with the term 'towards-which'... do you know what it is auf Deutsch?)
Das Wozu, apparently.
It does imply many things about space. It's probably a matter of convention whether one regards space as being present at hand though...
Whether space
itself is present at hand (at least in the Cartesian sense of being an object with properties) has been a huge debate, but it really amounts to whether it is disclosed as having properties, and I think GR actually settles that pretty well.
One of the central ideas of Heidegger's ontology which is really glossed over in his writings, unfortunately, is the idea of unreadiness to hand as being the means by which entities are disclosed as present at hand. You can look at it as being an advancement of Wittgenstein, really, in as much as we have this enormous, holistic mess (the referential totality) which we simply take up and use in our concernful dealings as equipment (Zeug), and it is from that which objects become distinguished as atomistic things with properties only when it is necessary to distinguish them as such.
This is why I don't identify the middle third of the standing lamp next to me or an arbitrary two foot square section of floor as being intelligible objects with properties. There is no inherent 'objectness' to the entire lamp that is not possessed by the middle third of the lamp, it is distinguished only by my need to distinguish it and recognize that some subset of the means by which it is employed as equipment can be distinguished from its relations with other things: i.e., it stands on the floor and plugs into the wall and draws power, which are aspects it can have only in relation to other things, but if I had to develop a model of the lamp I could represent its state of being on or off as being a property belonging solely to the lamp itself and not to the lamp in reference to other things.
In this sense, of course, it is a matter to convention whether
anything is present at hand, and that is really the point Heidegger makes. Space is treated in physics as present at hand because, thanks to GR, we know it has properties like curvature which can be separated from the things around it.
Player
