November 20th, 2010 / 1:02 pm

Snippets

Snippets

Christopher Higgs—

If you desire braincandy/eyefood, check out Kristin Cerda’s excerpt from “{measurable angle [is to (meaning as periphery) is to] tide}” found in the new issue of *Out of Nothing*.

tell em y u mad doggie

seems like an interesting form. i would like it better if the words didn’t seem as computer-generated or you know, as mechanical or formal or something, as the digits they’re placed in

i’m interested to know how out of nothing runs on all yalls browsers, just the home page really — does it take a long time or it is pretty smooth. Im running firefox.

Firefox here, too – pretty smooth, pretty quick. You’re having a problem?

(On the page(s?) where there’s a up-and-down-slideable box inside a larger up-and-down-slideable box, the larger (or outside) box can’t be slid up and down directly; the cursor has to be clicked over the up or down arrows at the top and bottom, respectively, of the slider’s column. Hope that’s not too, um, technical.)

The square root of 2

isa “rational number”, if one takes geometric objects to be somehow real – as ‘real’ as numbers are. The square root of two is theratioof a diagonal to a side ofeverysquare.The “rationality” of the square root of 2 is, in my reading, a vital element in

The Menoof Plato. Plato’s Socrates is rescuing, for Meno (and for us), the kernel of Pythagorus’s wisdom from the husk of Pythagorean mysticism, by showing that the square of a diagonal is twice the area of that diagonal’s square. (This demonstration indicates that the square root of 2 is theratioof a diagonal to a side of its square.)I don’t think this cool-sounding phrasing is accurate. Gravity doesn’t ‘modify’ spacetime, it accounts for that geometry – it

isthe bending of spacetime. Considered in this way, “bodies” – entities of or exhibiting or engaged in ‘mass’ – don’t ‘disturb’ spacetime; the “depressions” aren’t inhabited by them, but rather,are“bodies”. Spacetime isn’t a trampoline with feet here and there pushing it more or less down; spacetime is the pushing-down where ‘feet’ are, and ‘feet’ actually are the pushing-down itself.Well that’s just fucking unreadable.

What’s fucking unreadable,

Dave? Chris’s snippet, Kristin’s excerpted text, the new issue ofOut of Nothing, one or more of the comments on the thread, something else on the page that you commented on, or something not on your computer screen at all?bro…

the square root of two is not a rational number

a proof of its irrationality is even contained in that excerpt

a rational number is a number that can be expressed as “a/b” where “a” and “b” are integers and b is nonzero

no such “a” and “b” exist such that “a/b” equals the square root of two

that’s all that is being said

you are right that the ratio of the length of the hypotenuse of a square to the length of its side is the square root of two

the thing is that if the length of the side of a square is rational, then the length of the hypotenuse is irrational, and if the length of the hypotenuse is rational, then the length of the side is irrational, and the quotient of a nonzero rational number and an irrational number is irrational

bro…

it has nothing to do with “geometric objects” not being considered “real”

math says nothing about “ontology”

we’re talking about the lengths between points that are denoted by a number…

bro…

i have a math degree and shit…

tell em y u mad doggie

damn

Wouldn’t math say something about ontology insofar as it serves to describe some thing(s), much in the same way that any other language would?

no

marshall, look again at how I qualified the claim of the square root of 2 being mathematically “rational”:Without this qualification: yes, “rational numbers” are numbers that can be represented by – that is: are equal to – the ratio of two integers (or: one integer divided by another without remainder). [The divisor, as you say, can’t be 0.]

With the qualification: the reality of mathematical objects

isthe – or rather: an – issue, both in Cerda’s excerpt (explicitly) and in what I’m saying (also explicitly).The reality of numbers and of geometric shapes was also absolutely an issue for the Pythagoreans, marshall. The legend that Cerda refers to: Pythagorus killed (or had killed) Hippasus not because his math was wrong or trivial, but rather, precisely because it yielded a result that violated a Pythagorean precept about

reality.So, rather than reading the word “rational” dogmatically, in the given way as though that’s the

onlyway, let’s think – still in the math-degreebox but outside of the math-teacherbox – of “rational” as referring to ‘ratio of mathematical objects’, and [QUALIFICATION] let’s assume that objects like squares are ‘real’ like objects like numbers are ‘real’ objects. (Perhaps not empirically real, not perceptible, but conceptually real – manipulated with logical consistency so as to yield true results, given true premises.Mathematicallyreal, no?)The square root of 2, while

notbeing the result of one integer divided by another,isthe numerical value of the division of the diagonal of a square by one of its sides. In the second case, whilenottalking about theratioof two integers, wearetalking about theratiobetween– denoted, in the latter case by numbers

notboth integers.Do you see? Your ‘correction’ is entailed in the thing you’ve ‘corrected’, while a justification for the qualification – that the reality of geometric and arithmetical objects be considered equal – was left as your responsibility.

Perhaps your training in mathematics orients you away from flexibility in considerations such as these.

But I’m gambling and shit, marshall, from your comments at this site, that you privilege logically consistent flexibility of thought about things like

rationality, even precisely definedmathematical“rationality”, and can see how the square root of two could be considered to be a “mathematically rational” number, despitenotbeing an arithmetically “rational” number.Here’s a picture of what Cerda’s talking about:

http://ogremkv.files.wordpress.com/2007/10/grwarp.gif

The gravitational object is pictured as a ball resting on a net-like surface, which sags downward as a result of the weight of the ball – much like a person’s heels depress the surface of a trampoline.

But, with respect to the surface being a picture of spacetime, there

isno ball on the surface, no planet or star or particle. Rather, the curving of the surfaceisthe presence of mass, of a ‘ball’ of some mass.Gravity does

not“modify the geometric structure of spacetime itself, making slow deep depressions in the fabric”. The “depressions” or “disturbance[s]” in spacetime – as pictured –are“bodies” – adding the ‘ball’ at the bottom of the depression is a misleading heuristic device.no problems, im just designing a website right now and figuring out how far i can push certain things without making the user all frustrated. i noticed the sidebar thing too, which is weird because i didnt know media languages affected how your keyboard interacts with the sidebar. kinda mind blowing really, even if it is a mistake.

<< math says nothing about "ontology" >>

Alain Badiou disagrees.

Alain Badiou is a Maoist dolt who ought to stop commenting on mathematics.

Ok, the square root of 2 is a “rational number” when you change the definition of “rational number”. The square root of 2 is also an “elephant” when I change the definition of “elephant”. What’s the point.

These “change[s in] definition” are not comparable in the way you set them alongside each other.

Did you read Cerda’s excerpt, linked to in Higgs’s snippet?

That excerpt was the provocation for the conversation you’ve entered – that is, ‘entered’, if your analysis and question are to be taken seriously.

The question is whether ‘rationality’ in mathematics is – and if so: how it is – connected to realities which are not obviously purely mathematical, like empirically determinate ‘experience’. Pythagoras made a strong claim about numbers, namely that they’re

allequal to the division of two integers without remainder, which ‘ratio’ leads directly to our expression “rationalnumber”. He/His direct followers were, the story goes, mortally offended to be shown the fact of what we call “irrational numbers”. The Pythagorean sense of a formally and finally (and perhaps efficiently) causal entwinement of reality and “rationality” is a major current in the self-understanding of Western civ; it has a history roughly concurrent with the other histories of Western civ. It’s my opinion that Plato’s dialogueThe Menocontains a response to Pythagoras’s (legendary?) distress: “irrational” numbers are, in the reality of geometric objects, the fixed ‘ratios’ of known quantities (notintegers), like the ‘ratio’ of the diagonal to the side of a square. I think Plato, inThe Meno, is saying that realityis“rational” –mathematically“rational” – , just not in the way Pythagoras had expected it to be.That’s the point,

letters.damn, this is sweet, also way digging up the comments here, who’da thought that intense math shit would inspire htmlgiant readers so much? i’m jealous.

It is playful, I suppose.

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