the pane in the way

By Henryk Szubinski

youre out driving at night and suddenly you smash through a glass pane in the middel of the road

what are the chances that this would not be real or that it would define a chance accident which would be concurrant only with a similar or subsequent sequence of events to which the basic answer is= no or yes

as defines the values of the basis of a vechicle input into a road and the amount of angles it can make as it turns would define the chance of the basic laws of vectorisations as being in the forwards vector responses of the central nervous system and the ability of a vechicle to be prone by the vector ahead, making the chances of a angfle field 90 degrees to the left or 90 degrees to the right

black hole effect

= the displacement of the vechicle by a basic limitations of its value to which the volume of vechicle and the area or volume of the glass pane would

= the same values as are defined on the values of switching the visual visability field and the displacement of the vechicle

as a uncertainty:

the 180 degrees / A = displacement x volume

meaning that 2 zones of optional steering /volume as a 270 degree 3 value dimensional plane

2/3 =displacement as 1 field of view x 4

2/3 x 1/4 of the unified field theory defining the error or uncertainty as:

0.416 % as relates to a unified value =1 or a singularity where gravity is active so that

1/0.416=2.4

error = +/- 0.416 L.Y to -2, 2.4 Vol to -3

this would define the chances that a vechicle would deccellerate at such rate that the sudden displacement without any evidence would lead to the non collision of ,lets say a photon…even s such the chances are very low. The theory must rely on the usage of a indicator which would observe the glass pane by some irregularity in the way..Even as such the deccellerations must be computed to a very high rate of deccelleration and the glass pane being in contac with the vechicle at very low displacement and velocity so that the shatter effect is a part of a subsequently very low chance of the shatter effect being observable by a time displacement in slow motion…Taking in all of the values ,the chance or the uncertainty has quadrippled into: a error for

3.32 for the light year value to -2

and

19.2 for the volume to -3

at such a value , the possibility of the vechicle reversing back in time to observe the shatter effect as a time problem based on the sequence of events as the definitions of a sequence of uncertainties

3.32/19.2———————-1.664/9.6——————0.832/4.8———0.416/2.4

this then is the values for time reversal

0.1729—————————0.1733—————-0.1733———————-0.1733

as a basis for the common value, the reversal of time could be possible by the similarity of reversal at a stable end value that has altered by 0.004 as the amount of faseing in a faster than light situation with some basic warping which at the universal parameters of light year values

the resultance for a 15 billion l.y universe =26 x 10 to 9

and its stable state value =6 x 10 to 7

.

.

The concept of **shattering** of a set of points plays an important role in Vapnik–Chervonenkis theory, also known as VC-theory. Shattering and VC-theory are used in the study of empirical processes as well as in statistical computational learning theory.

## Definition

Suppose we have a class *C* of sets and a given set *A*. *C* is said to *shatter* *A* if, for each subset *T* of *A*, there is some element *U* of *C* such that

Equivalently, *C* shatters *A* when the power set *P*(*A*) is the set { *U* ∩ *A* | *U* ∈ *C* }.

For example, the class *C* of all discs in the plane (two-dimensional space) cannot shatter every set *A* of four points, yet the class of all convex sets in the plane shatters every finite set on the (unit) circle. (For the collection of all convex sets, connect the dots!)

We employ the letter *C* to refer to a “class” or “collection” of sets, as in a Vapnik–Chervonenkis class (VC-class). The set *A* is often assumed to be finite because, in empirical processes, we are interested in the shattering of finite sets of data points.

## [edit]Shatter coefficient

To quantify the richness of a collection *C* of sets, we use the concept of *shattering coefficients* (also known as *shatter coefficients* or the *growth function*). For a collection *C* of sets Ω, Ω being any space, often a probability space, we define the *n*^{th} *shattering coefficient* of *C* as

where “card” denotes the cardinality, that is the number of elements of a set.

*S*_{C}(*n*) is equal to the largest number of subsets of any set *A* of *n* points that can be formed by intersecting *A* with the sets in collection *C*.

It is obvious that

- 1. for all
*n*. - 2. If
*S*_{C}(*n*) = 2^{n}, that means there is a set of cardinality*n*, which can be shattered by*C*. - 3. If
*S*_{C}(*N*) < 2^{N}for some*N*> 1 then*S*_{C}(*n*) < 2^{n}for all .

The third property means that if *C* cannot shatter any set of cardinality *N* then it cannot shatter sets of larger cardinalities.

## [edit]Vapnik–Chervonenkis class

The VC dimension of a class *C* is defined as

or, alternatively, as

Note that *V**C*(*C*) = *V**C*_{0}(*C*) + 1.

If for any *n* there is a set of cardinality *n* which can be shattered by *C*, then *S*_{C}(*n*) = 2^{n} for all *n* and the VC dimension of this class *C* is infinite.

A class with finite VC dimension is called a *Vapnik–Chervonenkis class* or *VC class*. A class *C* is uniformly Glivenko–Cantelli if and only if it is a VC class.

research data courtesy of Wikipedia