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the random thought thread

In order to elucidate this concept with a simple example lets have a look at a 1D-"quasicrystal" in form of a Fibonacci chain, which is a quasiperiodic sequence of short and long segments. We embed this 1D-"quasicrystal" in a 2D-"higher dimensional space" which in this case has the form of a simple square lattice. One unit cell of the higher-dimensional space is filled yellow. The axes show the orientation of the two orthonormal subspaces Ve, Vi. The slope of Ve with respect to the 2D-lattice has to be an irrational one. In this case it is tau=1.618... The left image demonstrates the projection method, where we have a strip of projection with finite width. All points of the 2D-lattice inside this strip are projected onto the external space Ve, thus giving the quasiperiodic sequence (red,green..). The right image shows the section method in which a hyperplane (here a 1D-line) that is parallel to Ve cuts the higher-dimensional space. The occupation domains that are attached to each of the lattice points (here: bars) intersect with the hyperplane (here: line) thus producing the same quasiperiodic sequence as in the left picture. These occupation domains (here: bars) extend parallel to the internal space Vi. We can generalize this to nD cases with n=5,6,.. In that case the internal space would be (n-3)-dimensional and the occupation domains would be two-dimensional (eg.polygons) or three-dimensional (eg. polyhedra).
 

skibunny24

Enthusiastic Receiver of Reputation
Jun 16, 2010
3,281
585
Renton, WA

JayBear

Monkey
Working 55 hours a week at something Im into, Is a hell of alot easier then 30 hours a week watching the clock..

sidenote: If you do lots of research on the intrawebs, you will believe it is either impossible or un profitable to stray from the herd..Dont believe the hype..
 
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$tinkle

Expert on blowing
Feb 12, 2003
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can't use snipping tool to capture how to find snipping tool from winkey/cmd

#rainonyourweddingday
 

lovebunny

can i lick your balls?
Dec 14, 2003
7,317
245
San Diego, California, United States
1994's Most Bizarre Suicide
Don Harper Mills

At the 1994 annual awards dinner given by the American Association for Forensic Sciences, AAFS President Don Harper Mills astounded his audience in San Diego with the legal complications of a bizarre death. Here is the story...

On March 23 the medical examiner viewed the body of Ronald Opus and concluded that he died from a gunshot wound of the head caused by a shotgun. Investigation to that point had revealed that the decedent had jumped from the top of a ten story building with the intent to commit suicide. (He left a note indicating his despondency.) As he passed the 9th floor on the way down, his life was interrupted by a shotgun blast through a window, killing him instantly. Neither the shooter nor the decedent was aware that a safety net had been erected at the 8th floor level to protect some window washers, and that the decedent would not have been able to complete his intent to commit suicide because of this...

Ordinarily a person who starts into motion the events with a suicide intent ultimately commits suicide even though the mechanism might be not what he intended. That he was shot on the way to certain death nine stories below probably would not change his mode of death from suicide to homicide, but the fact that his suicide intent would not have been achieved under any circumstance caused the medical examiner to feel that he had homicide on his hands...

Further investigation led to the discovery that the room on the 9th floor from whence the shotgun blast emanated was occupied by an elderly man and his wife. He was threatening her with the shotgun because of an interspousal spat and became so upset that he could not hold the shotgun straight. Therefore, when he pulled the trigger, he completely missed his wife, and the pellets went through the window, striking the decedent.

When one intends to kill subject A, but kills subject B in the attempt, one is guilty of the murder of subject B. The old man was confronted with this conclusion, but both he and his wife were adamant in stating that neither knew that the shotgun was loaded. It was the longtime habit of the old man to threaten his wife with an unloaded shotgun. He had no intent to murder her; therefore, the killing of the decedent appeared then to be accident. That is, the gun had been accidentally loaded...

But further investigation turned up a witness that their son was seen loading the shotgun approximately six weeks prior to the fatal accident. That investigation showed that the mother (the old lady) had cut off her son's financial support, and her son, knowing the propensity of his father to use the shotgun threateningly, loaded the gun with the expectation that the father would shoot his mother. The case now becomes one of murder on the part of the son for the death of Ronald Opus...

Further investigation revealed that the son became increasingly despondent over the failure of his attempt to get his mother murdered. This led him to jump off the ten story building on March 23, only to be killed by a shotgun blast through a 9th story window.

The medical examiner closed the case as a suicide.