If the fourth dimension is a physical concept and not purely metaphysical, through what medium does it extend??

In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension.

Being to Hobbes ( and the other empiricists ) is the physical universe: The world, ( I mean ... the Universe, that is, the whole masse of all things that are ) is corporeall, that is to say, Body ; and hath the dimension of magnitude, namely, Length, Bredth and Depth: also every part of Body, is likewise Body ... and consequently every part of the Universe is Body, and that which is not Body, is no part of the Universe: and because the Universe is all, that which is no part of it is nothing ; and consequently no where.

In physical terms, dimension refers to the constituent structure of all space ( cf.

The concept of dimension is not restricted to physical objects.

For mathematical purposes, elementary particles are normally treated as point particles, although some particle theories such as string theory posit a physical dimension.

Their physical and emotional rapport was very strong from the start, and the age difference and different acting experience also created the additional dimension of a mentor-student relationship.

The notion of physical dimension of a physical quantity was introduced by Joseph Fourier in 1822.

By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension.

In Islam, purification has a spiritual dimension and a physical one.

In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension.

* Even though a dimensionless quantity has no physical dimension associated with it, it can still have dimensionless units.

“ It is auditory in the physical dimension but equally powerful as a visual force in the psychological dimension .”

In theory, a system of fundamental quantities ( or sometimes fundamental dimensions ) would be such that every other physical quantity ( or dimension of physical quantity ) can be generated from them.

According to Gurdjieff, only one dimension of the three dimensions of the person — namely, either the emotions, or the physical body or the mind — tends to develop in such schools and sects, and generally at the expense of the other faculties or centers, as Gurdjieff called them.

Unpleasantness, another synonym of suffering or pain in the broad sense, is used in physical pain science to refer to the basic affective dimension of pain ( its suffering aspect ), usually in contrast with the sensory dimension, as for instance in this sentence from Professor Donald Price: “ Pain-unpleasantness is often, though not always, closely linked to both the intensity and unique qualities of the painful sensation .” Words that are roughly synonymous with suffering, in addition to pain and unpleasantness, include distress, sorrow, unhappiness, misery, affliction, woe, ill, discomfort, displeasure, disagreeableness.

Besides the lack of an adequate ethical dimension to the Governor's case, one can ask seriously whether our lead over the Russians in quality and quantity of nuclear weapons is so slight as to make the tests absolutely necessary.

The quantity may also be given as a ratio of two different units that have the same dimension ( for instance, light years over meters ).

The number l ( D ) is the quantity that is of primary interest: the dimension ( over C ) of the vector space of meromorphic functions h on the surface, such that all the coefficients of ( h ) + D are non-negative.

I make a kind of chromatic versification and for syllables I use strokes which, variable in quantity, cannot differ in dimension without modifying the rhythm of a pictorial phraseology destined to translate the diverse emotions aroused by nature.

Returning to one dimension for simplicity, when a is the infinitesimal quantity ε, the Gaussian initial condition, rescaled so that its integral is one:

Thus, until seventeenth century, lines were defined like this: " The line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...] will leave from its imaginary moving some vestige in length, exempt of any width.

Here the trace of the identity operator is the dimension of the vector space, i. e. the dimension of the space of modular forms of a given type: a quantity traditionally calculated by means of the Riemann-Roch theorem.

In SI, a separate base unit ( the ampere ) is associated with electrical phenomena, with the consequence that something like electrical charge ( 1 coulomb = 1 ampere × 1 second ) is a unique dimension of physical quantity and is not expressed purely in terms of the mechanical units ( kilogram, metre, second ).

where ε < sub > 0 </ sub > is the vacuum permitivity, a quantity with dimension, namely charge < sup > 2 </ sup > time < sup > 2 </ sup > mass < sup >− 1 </ sup > length < sup >− 3 </ sup >.

It is thus a vector quantity with dimension length / time².

* The dimension of a physical quantity, as used in dimensional analysis

The moment of inertia ( technically, second moment of area ) of the hull section is calculated by finding the neutral or central axis of the beam and then totaling up the quantity for each section of plate or girder making up the hull, with being the moment of inertia of that section of material, being the width ( horizontal dimension ) of the section, being the height of the section ( vertical dimension ), being the area of the section and being the vertical distance of the center of that section from the neutral axis.

Hemingway's fiction is supported by a `` moral '' backbone and in its search for ultimate meaning hints at a religious dimension.

The inventory of tones is much smaller, and commonly the contrasts range along one single dimension, pitch level.

A `` mental image '' subconsciously impressing us from beneath its language symbols in wakeful thought, or consciously in light sleep, is actually not an image at all but is comprised of realities, viewed not in the concurrent sensory stream, but within the depths of the fourth dimension.

but when the sounds of the two speakers are allowed to mix, there is excellent depth and dimension to the music.

What was lacking was a real sense of phrase, the kind of legato singing that would have added a dimension of smoothness to what is, after all, a very oily character.

against multiple comparisons in one dimension, it is not conservative

In C ++ ( 1983 ), class templates exist for multi-dimensional arrays whose dimension is fixed at runtime as well as for runtime-flexible arrays.

The number of indices needed to specify an element is called the dimension, dimensionality, or rank of the array.

A one-dimensional array ( or single dimension array ) is a type of linear array.

The addressing formula is completely defined by the dimension d, the base address B, and the increments c < sub > 1 </ sub >, c < sub > 2 </ sub >, …, c < sub > k </ sub >.

This point of view is useful in abstract algebraic dimension theory due to Gabriel and Rentschler.

Coronals have another dimension, grooved, that is used to make sibilants in combination with the orientations above.

The number of possible aggregations is determined by every possible combination of dimension granularities.

Also every finite dimensional vector space admits a basis, whose number of elements is equal to the dimension, and every element of the vector space can be uniquely expressed as linear combination of basis vectors.

Color images are typically represented as a combination of images in three primary colors, so that the signal is vector-valued with dimension three.

The combination of both aspects means they simulate a quiet open-space of infinite dimension, which is useful when exterior influences would otherwise give false results.

To the cynicism typical of the genre, Nietzsche brings a new dimension by his combination of nihilistic energy with historical consciousness.

In linear algebra, a basis for a vector space of dimension n is a sequence of n vectors α < sub > 1 </ sub >, ..., α < sub > n </ sub > with the property that every vector in the space can be expressed uniquely as a linear combination of the basis vectors.

In modern times, most commonly, a painted marking of a consistent shape or shapes ( often rectangular ), dimension and colour or combination of colours is used along the trail route.

of dimension n can be defined as a combination of Hodge numbers, namely