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

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Brown Corpus

## Some Related Sentences

If and fourth

__If__you were required to file

**a**declaration of estimated tax for

**the**calendar year 1961

**,**

**it**

**is**

**not**necessary to pay

**the**

__fourth__installment otherwise due on January 15

**,**1962

**,**if you file your income tax return Form 1040

**,**

**and**pay your tax in full for

**the**calendar year 1961 by January 31

**,**1962.

__If__your side has two aces

**and**

**a**void

**,**then you are

**not**at risk of losing

**the**first two tricks

**,**so long as (

**a**) your void

**is**useful ( i. e.,

**does**

**not**duplicate

**the**function of an ace that your side holds )

**and**( b ) you are

**not**vulnerable to

**the**loss of

**the**first two tricks in

**the**

__fourth__suit ( because

**,**for instance

**,**one of

**the**partnership hands holds

**a**singleton in that suit or

**the**protected king

**,**giving your side second round control ).

__If__there are four alternative symbols ( corresponding to

**a**musical instrument that can generate four different tones

**,**one at

**a**time ),

**the**first symbol may represent

**the**bit sequence 00

**,**

**the**second 01

**,**

**the**third 10

**and**

**the**

__fourth__11.

__If__their estimates are correct

**,**6. 1 percent of North Korea's total population was in

**the**military

**,**numerically

**the**world's fifth largest military force

**,**in

**the**late 1980s (

__fourth__largest as of 2006 ).

__If__reflections of

**a**pentomino are considered distinct

**,**as they are with one-sided pentominoes

**,**then

**the**first

**and**

__fourth__categories above double in size

**,**resulting in an extra 6 pentominoes for

**a**total of 18.

__If__there are cranial nerve abnormalities

**,**these may be noticed on eye examination in

**the**form of

**a**squint ( third

**,**

__fourth__

**,**or sixth nerve palsy ) or as facial nerve palsy.

__If__

**a**player finishes in fifth to eighth position they are " ranked out "

**and**

**the**race must be replayed – at

**the**cost of one of

**a**limited number of lives – until

**a**placing of

__fourth__or above

**is**achieved.

In response he devised his own anti-razor: "

__If__three things are**not**enough to verify an affirmative proposition about things**,****a**__fourth__must be added**,****and**so on.__If__there

**is**

**a**previous NASCAR Champion without

**a**spot

**,**he will get one of those four spots

**,**otherwise

**,**

**the**

__fourth__fastest car

**is**added to

**the**field.

he described as " Murphy's law or

**the**__fourth__law of thermodynamics " which states: "__If__anything can go wrong**,****it**will.__If__we take four quantities:

**a**

**,**b

**,**c

**,**

**and**d

**,**then

**the**first

**and**second have

**a**ratio ; similarly

**the**third

**and**

__fourth__have

**a**ratio.

__If__any additional teeth form

**,**for example

**,**

__fourth__

**and**fifth molars

**,**which are rare

**,**they are referred to as supernumerary teeth ( hyperdontia ).

Putting any of

**the**four vertices in**the**role of O yields four such identities**,**but in**a**sense at most three of them are independent:__If__**the**" clockwise " sides of three of them are multiplied**and****the**product**is**inferred to be equal to**the**product of**the**" counterclockwise " sides of**the**same three identities**,****and**then common factors are cancelled from both sides**,****the**result**is****the**__fourth__identity.__If__this

**is**true

**,**

**the**text

**is**important because Perpetua

**is**one of

**the**first Christian female writers before

**the**

__fourth__century whose works have survived.

*

__If__**the**king**is**on**a**square adjoining**the**konakis**and****is**surrounded on three sides by his enemies**and****the**__fourth__by**the**konakis**,**he**is**captured.__If__Slayton had flown MA-7

**,**his spacecraft would have been named Delta 7

**,**as this would have been

**the**

__fourth__manned flight

**and**Delta ( Δ )

**is**

**the**

__fourth__letter in

**the**Greek alphabet.

*

__If__an additional third**,**__fourth__**,**or fifth version of**the**product**is**envisaged down**the**line**,**this approach**is**far stronger**,**because**the**ready-made code libraries dramatically shorten**the**development life cycle for any additional products after**the**second.__If__we go up

**a**fifth from

**the**lowest note in

**the**octave

**and**then up

**a**

__fourth__from there

**,**we will reach

**the**upper note of

**the**octave.

__If__

**the**winners of

**the**Welsh Cup have already qualified for Europe via their league placing ( e. g. finishing first

**and**winning

**the**Cup )

**the**

__fourth__placed team inherits

**the**Europa spot.

It follows two other solo albums

**,**Little Songs ( 1998 )**and**Morning Orbit ( 2001 ),**and**precedes**a**__fourth__solo album**,**__If__God Had Curves ( 2005 ).
*

__If__there**is****a**third round**it**will always finish**the**game**,****a**__fourth__round**is**practically never played although**it****is**technically possible ( most life long players have never seen**it**).__If__reflections of

**a**hexomino are considered distinct

**,**as they are with one-sided hexominoes

**,**then

**the**first

**and**

__fourth__categories above would each double in size

**,**resulting in an extra 25 hexominoes for

**a**total of 60.

If and dimension

__If__G = GL < sub >*</ sub >( K ), then

**the**set of natural numbers

**is**

**a**proper subset of G < sub > 0 </ sub >, since for each natural number n

**,**there

**is**

**a**corresponding identity matrix of

__dimension__n. G ( m

**,**n )

**is**empty unless m = n

**,**in which case

**it**

**is**

**the**set of all nxn invertible matrices.

__If__

**a**spatial extra

__dimension__

**is**of radius R

**,**

**the**invariant mass of such standing waves would be M < sub > n </ sub > = nh / Rc with n an integer

**,**h being Planck's constant

**and**c

**the**speed of light.

__If__

**the**input feature vectors have very high

__dimension__

**,**

**the**learning problem can be difficult even if

**the**true function only depends on

**a**small number of those features.

__If__this happens in an even

__dimension__

**,**

**the**Majorana spinor representation will sometimes decompose into two Majorana – Weyl spinor representations.

(

__If__utility U = f ( x**,**y ), U**,**in**the**third__dimension__**,****does****not**have**a**local maximum for any x**and**y values.__If__

**the**supposed rock was out of space-time

__dimension__

**,**then

**the**question would

**not**make sense

**,**because

**it**would be impossible to move an object from one location in space to another if there

**is**no space to begin with

**,**meaning

**the**faulting

**is**with

**the**logic of

**the**question

**and**

**not**God's capabilities.

__If__

**the**Noetherianity hypothesis

**is**dropped

**,**then R can have

__dimension__anywhere between d + 1

**and**2d + 1.

__If__R

**is**

**a**commutative ring

**,**

**and**M

**is**an R-module

**,**we define

**the**Krull

__dimension__of M to be

**the**Krull

__dimension__of

**the**quotient of R making M

**a**faithful module.

__If__we take

**the**modules to be over

**a**field

**,**then

**the**

__dimension__of

**the**n-th homology of X turns out to be

**the**number of " holes " in X at

__dimension__n.

__If__

**the**primary key of

**the**source data

**is**required for reporting

**,**

**the**

__dimension__already contains that piece of information for each row.

__If__A

**is**torsion-free then

**it**embeds into

**a**vector space over

**the**rational numbers of

__dimension__rank A.

__If__there exist one or more eigenvalues

**,**then if

**the**corresponding b < sub > i </ sub > ≠ 0

**,**

**it**

**is**

**a**paraboloid ( either elliptic or hyperbolic ); if

**the**corresponding

**,**

**the**

__dimension__i degenerates

**and**

**does**

**not**get into play

**,**

**and**

**the**geometric meaning will be determined by other eigenvalues

**and**other components of b. When

**it**

**is**

**a**paraboloid

**,**whether

**it**

**is**elliptic or hyperbolic

**is**determined by whether all other non-zero eigenvalues are of

**the**same sign: if they are

**,**then

**it**

**is**elliptic ; otherwise

**,**

**it**

**is**hyperbolic.

An extension of

**the**tensor field idea incorporates an extra line bundle L on M.__If__W**is****the**tensor product bundle of V with L**,**then W**is****a**bundle of vector spaces of just**the**same__dimension__as V. This allows one to define**the****concept**of tensor density**,****a**' twisted ' type of tensor field.__If__R

**is**

**a**field

**,**

**the**cycle space

**is**

**a**vector space over R with

__dimension__m-n + c

**,**where c

**is**

**the**number of connected components of G.

__If__R

**is**any commutative ring

**,**

**the**cycle space

**is**

**a**free R-module with rank m-n + c.

__If__

**the**source has

**a**maximum overall

__dimension__or aperture width ( D ) that

**is**large compared to

**the**wavelength λ

**,**

**the**far-field region

**is**commonly taken to exist at distances from

**the**source

**,**greater than Fresnel parameter S = D < sup > 2 </ sup >/( 4λ ), S > 1.

0.433 seconds.