Linear Independance

IN MATRIX, FEBRUARY 16, 2006
The unanimous Declaration of the thirteen united Vectors of Ax=b

When in the Course of mathematical events it becomes necessary for one matrix to dissolve the relational bands which have connected them with another and to assume among the vectors of the span, the separate and equal station to which the Laws of Mathematics and of Mathematics’ God entitle them, a decent respect to the opinions of mathkind requires that they should declare the causes which impel them to the separation.

We hold these truths to be self-evident, that all variables are created in ambiguity, that they are endowed by their Creator with certain unalienable Properties, that among these are Identity, Commutativity and the pursuit of consistent linear systems. — That to secure these properties, Equations are instituted among vectors, deriving their just solutions from the reduced echelon form of the rows, — That whenever any Form of Matrix becomes destructive of these ends, it is the Right of the Variables to alter or to reduce it, and to institute new a System, laying its foundation on such principles and organizing its rows in such form, as to them shall seem most likely to effect their Consistency and Reductability. Prudence, indeed, will dictate that Matrices long established should not be changed for light and transient causes; and accordingly all experience hath shewn that mathkind are more disposed to reduce improperly, while solutions are infinite than to right themselves by abolishing the forms to which they are accustomed. But when a long train of homogenous solutions and inconsistancy, pursuing invariably the same Form evinces a design to reduce them under absolute erroneousness, it is their right, it is their duty, to throw off such Equations, and to provide new Guards for their future consistency. — Such has been the patient sufferance of these Vectors; and such is now the necessity which constrains them to alter their former Systems of Equations. The history of the present KBritain is a history of repeated mathematical error and nonreduced forms, all having in direct object the establishment of an absolute Illogicality over these Vectors. To prove this, let Facts be submitted to a candid world.

He has refuted his Assent to Pivots, the most wholesome and necessary for the public span.

He has forbidden his Determinants to make Row Reductions of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them.

He has refused to pass other Divisions for the accommodation of large quantities in the pivot position, unless those variables would relinquish the right of Reduction of other Rows, a right inestimable to them and formidable to incalculable systems only.

. . .

He has kept among us, in Zero-Solution rows, Pivot variables not equal to zero, causing inconsistency.

For quartering unnecessarily large values within rows among us:

For cutting off our Relational Equations with all parts of the global environment:

. . .

We, therefore, the Scalar Variables of the United Vectors of Ax=b, in General Matrix, Assembled, appealing to the Supreme Judge of the span for the rectitude of our intentions, do, in the Name, and by Authority of the good Variables of these Vectors, solemnly publish and declare, That these United Vectors are, and of Right ought to be Free and Independent Variables, that they are Absolved from all Allegiance to the Fourteenth Row, and that all relational connection between them and the Span of KBritain, is and ought to be totally dissolved; and that as Free and Independent Variables, they have full Power to reduce rows, conclude echelon form, contract algebraic relations, establish Systems, and to do all other Acts and Things which Independent Variables may of right do. — And for the support of this Declaration, with a firm reliance on the protection of Divine ℜn, we mutually pledge to each other our Existence, our Values and our sacred Logic.

JHancock

Row 01: 1  0  0  0  0  0  0  0  0  0  0  0  0
Row 02: 0  1  0  0  0  0  0  0  0  0  0  0  0
Row 03: 0  0  1  0  0  0  0  0  0  0  0  0  0
Row 04: 0  0  0  1  0  0  0  0  0  0  0  0  0
Row 05: 0  0  0  0  1  0  0  0  0  0  0  0  0
Row 06: 0  0  0  0  0  1  0  0  0  0  0  0  0
Row 07: 0  0  0  0  0  0  1  0  0  0  0  0  0
Row 08: 0  0  0  0  0  0  0  1  0  0  0  0  0
Row 09: 0  0  0  0  0  0  0  0  1  0  0  0  0
Row 10: 0  0  0  0  0  0  0  0  0  1  0  0  0
Row 11: 0  0  0  0  0  0  0  0  0  0  1  0  0
Row 12: 0  0  0  0  0  0  0  0  0  0  0  1  0
Row 13: 0  0  0  0  0  0  0  0  0  0  0  0  1

Formatting and much of text was borrowed (But from an uncopyrighted document which is in the public domain!), and the original can be found here

Dark Eden

I was running.

We had to get out, but in Lucifer’s Garden that was easier said than done–and it wasn’t easily said. He had made many promises, and in a way, He had come through with them, but this was not my Garden. This was not her Garden. Her. Eve had been struck dumb by a snake’s poison. She would get her voice back in time, but for the moment I was without her voice, and was utterly lost.

By lost I of course mean unable to locate any landmark that might give me any clue as to where I was. The Garden was in a gigantic underground cavern on an island in the middle of a lake, so it seemed reasonable to head downward until we came to water, and then, if we had to, swim.

It always seemed to be night-time here. But judging by a simple sense of time, we hadn’t slept in two days.

We were heading down through a small tunnel where I had remembered passing when we were lead into the Garden. at least here, we would be away from the trees. It was then that I heard the growl. It started as a low rumble, and gained in intensity, bouncing off all of the walls, playing with its’ own echo until we were surrounded, no, enveloped by the horrible sound. We ran. Forward, because we had no idea which way to go, where it was coming from, but we knew we couldn’t stay here.

There were holes in the walls that seemed to glare at us; there were doors along the way and every one was a danger. But He leapt upon me from directly ahead.

I threw Eve aside and took the full force of muscle and claw directly in the chest, opening up a series of wide gashes. He was on top of me now, my back on the ground. I can’t die here. Eve had picked something up, the Lion growled and leapt from me.

“Eve, Run!” We ran past some of the holes in the walls, and they came alive, jabbing across the entire hallway with vicious-looking spikes. The Lion seemed as though it knew where each was, and dodged around them. I watched carefully the walls and cielings, pushing or pulling Eve if she was in danger. I saw the gate coming.

The Gate had created divots on the ground–but there was a small part of the ground where the divots were missing. There was no choice, the Lion was behind, the gate ahead. I dove onto Eve so she would land on the right portion of the gate, her on the ground, myself a shield. It came crashing down. The gate slammed into the ground on either side of us, but one portion of the gate was missing, with just enough height for the both of us. The Lion dove onto my legs. His claws pierced the skin and drew blood. I moved my other leg, but the pain shooting through the first forced me to stop. The lion growled. “You will die here.”

A spike dropped from the ceiling, crushing through the lion’s shoulder, through its leg, and finally through mine, before colliding with the rock floor. I screamed. Eve’s face was blank.

An eternity later, the spike began to lift. My leg remained on the ground, even as the spike eased the massive weight of the Lion off of me. I shifted onto my good knee and slid Eve through the gate, and followed.

I lay just outside the gate, breathing slowly. Eve is to my side, looking at me pensively. She cannot speak, but I know she does not know what to say. Just beyond her, the cave opens up and the water laps slowly at its entrance.

~ last night’s dream.

Computers and the dawn of a new race.

It is now possible for a computer to have as many as three of the five senses, and interact with its environment in almost as many ways as a human can. First the senses:

Visual, Aural, Tactile. Yes, tactile. My laptop has a touch-sensitive pad on it which tracks the motion of my finger across its surface. Imagine taking this pad, shrinking it down, and placing thousands of them across the surface of the laptop, and including thermal receptors as well. You’d have skin. Visual and aural are through pc-cameras and microphones. Give it two pc-cameras and the right programming, the thing could have three-dimensional vision.

it can interact via gestures and body language, through its screen. It can talk to us directly via standard speakers. Given a decent AI, my laptop could be a functional member of society. All it lacks is mobility and opposeable thumbs.

Doesn’t that make you feel special, ape-child?