I/O cc______________________“Cecelia”

Making love in the afternoon with Cecilia

Up in my bedroom (making love)

I got up to wash my face

When I come back to bed

Someone’s taken my place

Chronicle SU The Internet Chronicle — Documenting What’s Left.

(A) Those Might It Dawn On ‘Em

So ya — I filed a lawsuit. Soykice eye, blue and assign-

ed (crimp) amoral uses’ details. Hoh, boy.

Theory, scientific 23, critical phenomenon,

ergodicity, critical exponent____Marsha____phase transition, ima-

ges I sing (… extension of the function (f*)…”filling in time”), j-invariant,

elliptic integtal, Weierstrass of those.

Happencestanton Esperry Et

OCT BLUE

SUN OINK

should look at those eyes,

those 4-eyed ducted piddle

dremorma tile spell elite

E E T T H G

H I R T Y A

E O S T C O

N I T U T A

H _ N N __ S

there is nothing that you can’t set_______________Hello

even if I’m a van I’m a dear boy

I fall on the floor laughing

jubilation gravy tray yay us

we just trained________________________I’m a deaf person I’m saving these cards

___________________proof of the read

__________________ we got the gab

and if we tell ya the name of the game, boy

SEB I’m down, correct?

SEB You’re taut.

working ham

legal theories are boots on the ground in astated subjective. Dialed-in on a time dividing all time grows significant. The object however excluded, must be area with area.

Why’d you ask?

I wonder –ed topologically you don’t “densify”, excuse me, “fuck you”, densities. Chin-up bar, any chinny you could chin, of that nature. You are.

Quantify SUBJECTIVE things like a reason to get out of bed COMPACTIFIED

airy result

airy resolve

Objections

your pants off

how’s that

with flowers

how is that

it’s a pun

I demonstrated

a girl.

Know we’re dead?

Just up from the bottom right is no *no*where.

a heavy black jaywalker S1

we bury them

John, whatever, a ghost’s shift’s in, he can’t, and,

## R =18

## G = 7

so against the wall

GR Shredder Sl

Main article: Causal structure

Vectors are classified according to the sign of η(v,v). When the standard signature (−,+,+,+) is used, a vector v is:

Timelike if η(v,v) < 0 Spacelike if η(v,v) > 0

Null (or lightlike) if η(v,v) = 0

This terminology comes from the use of Minkowski space in the theory of relativity. The set of all null vectors at an event of Minkowski space constitutes the light cone of that event. Note that all these notions are independent of the frame of reference. Given a timelike vector v, there is a worldline of constant velocity associated with it. The set {w : η(w,v) = 0 } corresponds to the simultaneous hyperplane at the origin of this worldline. Minkowski space exhibits relativity of simultaneity since this hyperplane depends on v. In the plane spanned by v and such a w in the hyperplane, the relation of w to v is hyperbolic-orthogonal.

Once a direction of time is chosen, timelike and null vectors can be further decomposed into various classes. For timelike vectors we have

1.future directed timelike vectors whose first component is positive, and

2.past directed timelike vectors whose first component is negative.

Null vectors fall into three classes:

1.the zero vector, whose components in any basis are (0,0,0,0),

2.future directed null vectors whose first component is positive, and

3.past directed null vectors whose first component is negative.

Together with spacelike vectors there are 6 classes in all.

An orthonormal basis for Minkowski space necessarily consists of one timelike and three spacelike unit vectors. If one wishes to work with non-orthonormal bases it is possible to have other combinations of vectors. For example, one can easily construct a (non-orthonormal) basis consisting entirely of null vectors, called a null basis. Over the reals, if two null vectors are orthogonal (zero inner product), then they must be proportional. However, allowing complex numbers, one can obtain a null tetrad which is a basis consisting of null vectors, some of which are orthogonal to each other.

Vector fields are called timelike, spacelike or null if the associated vectors are timelike, spacelike or null at each point where the field is defined.

* get outta here __

There are various equivalent ways of defining the tangent spaces of a manifold. While the definition via velocities of curves is quite straightforward given the above intuition, it is also the most cumbersome to work with. More elegant and abstract approaches are described below.

*

The exponential map is also useful in relating the abstract definition of curvature to the more concrete realization of it originally conceived by Riemann himself—the sectional curvature is intuitively defined as the Gaussian curvature of some surface (i.e., a slicing of the manifold by a 2-dimensional submanifold) through the point p in consideration. Via the exponential map, it now can be precisely defined as the Gaussian curvature of a surface through p determined by the image under exPp of a 2-dimensional subspace of TpM.

## Leave a Reply