But that’s just part of the story: the easy part. The difficult part is this. Jesus loves those terrorists. He loved them when they slit the throats of unarmed passengers, and He even loved them when they flew those planes into balls of fire causing thousands of His children to die in flames and blood and agony. And He continues to love them still as they roast in eternal hell and damnation.
On September 11, 2001, the world fractured. It's beyond my skill as a writer to capture that day, and the days that would follow — the planes, like specters, vanishing into steel and glass; the slow-motion cascade of the towers crumbling into themselves; the ash-covered figures wandering the streets; the anguish and the fear. Nor do I pretend to understand the stark nihilism that drove the terrorists that day and that drives their brethren still. My powers of empathy, my ability to reach into another's heart, cannot penetrate the blank stares of those who would murder innocents with abstract, serene satisfaction.
This is an especially good time for you vacationers who plan to fly, because the Reagan administration, as part of the same policy under which it recently sold Yellowstone National Park to Wayne Newton, has "deregulated" the airline industry. What this means for you, the consumer, is that the airlines are no longer required to follow any rules whatsoever. They can show snuff movies. They can charge for oxygen. They can hire pilots right out of Vending Machine Refill Person School. They can conserve fuel by ejecting husky passengers over water. They can ram competing planes in mid-air. These innovations have resulted in tremendous cost savings which have been passed along to you, the consumer, in the form of flights with amazingly low fares, such as $29. Of course, certain restrictions do apply, the main one being that all these flights take you to Newark, and you must pay thousands of dollars if you want to fly back out. -- Dave Barry, "Iowa -- Land of Secure Vacations"
Wings of OS/400: The airline has bought ancient DC-3s, arguably the best and safest planes</p> that ever flew, and painted "747" on their tails to make them look as if they are fast. The flight attendants, of course, attend to your every need, though the drinks cost $15 a pop. Stupid questions cost $230 per hour, unless you have SupportLine, which requires a first class ticket and membership in the frequent flyer club. Then they cost $500, but your accounting department can call it overhead.
OS/2 Skyways: The terminal is almost empty, with only a few prospective passengers milling about. The announcer says that their flight has just departed, wishes them a good flight, though there are no planes on the runway. Airline personnel walk around, apologising profusely to customers in hushed voices, pointing from time to time to the sleek, powerful jets outside the terminal on the field. They tell each passenger how good the real flight will be on these new jets and how much safer it will be than Windows Airlines, but that they will have to wait a little longer for the technicians to finish the flight systems. Maybe until mid-1995. Maybe longer.
A Mexican newspaper reports that bored Royal Air Force pilots stationed on the Falkland Islands have devised what they consider a marvelous new game. Noting that the local penguins are fascinated by airplanes, the pilots search out a beach where the birds are gathered and fly slowly along it at the water's edge. Perhaps ten thousand penguins turn their heads in unison watching the planes go by, and when the pilots turn around and fly back, the birds turn their heads in the opposite direction, like spectators at a slow-motion tennis match. Then, the paper reports "The pilots fly out to sea and directly to the penguin colony and overfly it. Heads go up, up, up, and ten thousand penguins fall over gently onto their backs. -- Audobon Society Magazine
MVS Air Lines: The passengers all gather in the hangar, watching hundreds of technicians check the flight systems on this immense, luxury aircraft. This plane has at least 10 engines and seats over 1,000 passengers; bigger models in the fleet can have more engines than anyone can count and fly even more passengers than there are on Earth. It is claimed to cost less per passenger mile to operate these humungous planes than any other aircraft ever built, unless you personally have to pay for the ticket. All the passengers scramble aboard, as do the 200 technicians needed to keep it from crashing. The pilot takes his place up in the glass cockpit. He guns the engines, only to realise that the plane is too big to get through the hangar doors.
Well, don't worry about it... It's nothing. -- Lieutenant Kermit Tyler (Duty Officer of Shafter Information Center, Hawaii), upon being informed that Private Joseph Lockard had picked up a radar signal of what appeared to be at least 50 planes soaring toward Oahu at almost 180 miles per hour, December 7, 1941.
With that exception, Paris is amiable. It accepts everything royally; it is not too particular about its Venus; its Callipyge is Hottentot; provided that it is made to laugh, it condones; ugliness cheers it, deformity provokes it to laughter, vice diverts it; be eccentric and you may be an eccentric; even hypocrisy, that supreme cynicism, does not disgust it; it is so literary that it does not hold its nose before Basile, and is no more scandalized by the prayer of Tartuffe than Horace was repelled by the "hiccup" of Priapus. No trait of the universal face is lacking in the profile of Paris. The bal Mabile is not the polymnia dance of the Janiculum, but the dealer in ladies' wearing apparel there devours the lorette with her eyes, exactly as the procuress Staphyla lay in wait for the virgin Planesium. The Barriere du Combat is not the Coliseum, but people are as ferocious there as though Caesar were looking on. The Syrian hostess has more grace than Mother Saguet, but, if Virgil haunted the Roman wine-shop, David d'Angers, Balzac and Charlet have sat at the tables of Parisian taverns. Paris reigns. Geniuses flash forth there, the red tails prosper there. Adonai passes on his chariot with its twelve wheels of thunder and lightning; Silenus makes his entry there on his ass. For Silenus read Ramponneau.
Pere Pamphile had seen Dantes pass not ten minutes before; and assured that he was at the Catalans, they sat down under the budding foliage of the planes and sycamores, in the branches of which the birds were singing their welcome to one of the first days of spring.
HORIZON (Gr. [Greek: horizôn], dividing), the apparent circle around which the sky and earth seem to meet. At sea this circle is well defined, the line being called the sea horizon, which divides the visible surface of the ocean from the sky. In astronomy the horizon is that great circle of the sphere the plane of which is at right angles to the direction of the plumb line. Sometimes a distinction is made between the rational and the apparent horizon, the former being the horizon as determined by a plane through the centre of the earth, parallel to that through the station of an observer. But on the celestial sphere the great circles of these two planes are coincident, so that this distinction is not necessary (see ASTRONOMY: _Spherical_). The _Dip_ of the horizon at sea is the angular depression of the apparent sea horizon, or circle bounding the visible ocean, below the apparent celestial horizon as above defined. It is due to the rotundity of the earth, and the height of the observer's eye above the water. The dip of the horizon and its distance in sea-miles when the height of the observer's eye above the sea-level is h feet, are approximately given by the formulae: Dip = 0´.97 [root]h; Distance = 1
_Associated Projective and Descriptive Spaces._--A region of a projective space, such that one, and only one, of the two supplementary segments between any pair of points within it lies entirely within it, satisfies the above axioms (1-10) of descriptive geometry, where the points of the region are the descriptive points, and the portions of straight lines within the region are the descriptive lines. If the excluded part of the original projective space is a single plane, the Euclidean parallel axiom also holds, otherwise it does not hold for the descriptive space of the limited region. Again, conversely, starting from an original descriptive space an associated projective space can be constructed by means of the concept of _ideal points_.[42] These are also called _projective points_, where it is understood that the simple points are the points of the original descriptive space. An _ideal point_ is the class of straight lines which is composed of two coplanar lines a and b, together with the lines of intersection of all pairs of intersecting planes which respectively contain a and b, together with the lines of intersection with the plane ab of all planes containing any one of the lines (other than a or b) already specified as belonging to the ideal point. It is evident that, if the two original lines a and b intersect, the corresponding ideal point is nothing else than the whole class of lines which are concurrent at the point ab. But the essence of the definition is that an ideal point has an existence when the lines a and b do not intersect, so long as they are coplanar. An ideal point is termed _proper_, if the lines composing it intersect; otherwise it is _improper_. Entry: 10
Through any point there always pass three planes, at right angles to each other, across which there is no tangential traction. These planes are called the "principal planes of stress," and the (normal) tractions across them the "principal stresses." Lines, usually curved, which have at every point the direction of a principal stress at the point, are called "lines of stress." Entry: A
Let a, b, c be the given lines, and p, q, r ... lines cutting them in the points A, A', A" ...; B, B', B" ...; C, C', C" ... respectively; then the planes through a containing p, q, r, and the planes through b containing the same lines, may be taken as corresponding planes in two axial pencils which are projective, because both pencils cut the line c in the same row, C, C', C" ...; the surface can therefore be generated by projective axial pencils. Entry: 90
The capacity of two parallel planes can be calculated at once if we neglect the distribution of the lines of force near the edges of the plates, and assume that the only field is the uniform field between the plates. Let V1 and V2 be the potentials of the plates, and let a charge Q be given to one of them. If S is the surface of each plate, and d their distance, then the electric force E in the space between them is E = (V1-V2)/d. But if [sigma] is the surface density, E = 4[pi][sigma], and [sigma] = Q/S. Hence we have Entry: V
These planes only have a real angle of inclination if they possess a line of intersection within the actual space, i.e. if they intersect. Planes which do not intersect possess a shortest distance along a line which is perpendicular to both of them. If this shortest distance is [delta]12, we have Entry: VI
15. _Theories of Correspondence._--We have several recent theories which depend on the notion of _correspondence_: two points whether in the same plane or in different planes, or on the same curve or in different curves, may determine each other in such wise that to any given position of the first point there correspond [alpha]´ positions of the second point, and to any given position of the second point a positions of the first point; the two points have then an ([alpha], [alpha]) correspondence; and if [alpha], [alpha] are each = 1, then the two points have a (1, 1) or rational correspondence. Connecting with each theory the author's name, the theories in question are G. F. B. Riemann, the rational transformation of a plane curve; Luigi Cremona, the rational transformation of a plane; and Chasles, correspondence of points on the same curve, and united points. The theory first referred to, with the resulting notion of "Geschlecht," or _deficiency_, is more than the other two an essential part of the theory of curves, but they will all be considered. Entry: 15
(5) _On the Equilibrium of Planes or Centres of Gravity of Planes_ ([Greek: Peri hepipedon isorropion ae kentra baron hepipedon]). This consists of two books, and may be called the foundation of theoretical mechanics, for the previous contributions of Aristotle were comparatively vague and unscientific. In the first book there are fifteen propositions, with seven postulates; and demonstrations are given, much the same as those still employed, of the centres of gravity (1) of any two weights, (2) of any parallelogram, (3) of any triangle, (4) of any trapezium. The second book in ten propositions is devoted to the finding the centres of gravity (1) of a parabolic segment, (2) of the area included between any two parallel chords and the portions of the curve intercepted by them. Entry: 5
The form {010} perpendicular to the axis of symmetry consists of a single plane or pedion; the parallel face is dissimilar in character and belongs to the pedion {01´0}. The pinacoids {100}, {001}, {hol} and {h´ol} parallel to the axis of symmetry are geometrically the same in this class as in the holosymmetric class. The remaining forms consist each of only two planes on the same side of the axial plane XOZ and equally inclined to the dyad axis (e.g. in fig. 62 the two planes XYZ and X´YZ´); such a wedge-shaped form is sometimes called a sphenoid. Entry: HEMIMORPHIC
If we remember that a line is perpendicular to a plane that is perpendicular to every line in the plane if only it is perpendicular to any two intersecting lines in the plane, we see that the axis which is perpendicular both to AA1 and to AA2 is also perpendicular to A1A0 and to A2A0 because these four lines are all in the same plane. Hence, if the plane [pi]2 be turned about the axis till it coincides with the plane [pi]1, then A2A0 will be the continuation of A1A0. This position of the planes is represented in fig. 38, in which the line A1A2 is perpendicular to the axis x. Entry: 1
ANHYDRITE, a mineral, differing chemically from the more commonly occurring gypsum in containing no water of crystallization, being anhydrous calcium sulphate, CaSO_{4}. It crystallizes in the orthorhombic system, and has three directions of perfect cleavage parallel to the three planes of symmetry. It is not isomorphous with the orthorhombic barium and strontium sulphates, as might be expected from the chemical formulae. Distinctly developed crystals are somewhat rare, the mineral usually presenting the form of cleavage masses. The hardness is 3-1/2 and the specific gravity 2.9. The colour is white, sometimes greyish, bluish or reddish. On the best developed of the three cleavages the lustre is pearly, on other surfaces it is of the ordinary vitreous type. Entry: ANHYDRITE
If two projective axial pencils are placed in such a position that a plane in the one coincides with its corresponding plane, then the two pencils are perspective, that is, corresponding planes meet in lines which lie in a plane. Entry: 33
Crystals of blende belong to that subclass of the cubic system in which there are six planes of symmetry parallel to the faces of the rhombic dodecahedron and none parallel to the cubic faces; in other words, the crystals are cubic with inclined hemihedrism, and have no centre of symmetry. The fundamental form is the tetrahedron. Fig. 1 shows a combination of two tetrahedra, in which the four faces of one tetrahedron are larger than the four faces of the other: further, the two sets of faces differ in surface characters, those of one set being dull and striated, whilst those of the other set are bright and smooth. A common form, shown in fig. 2, is a combination of the rhombic dodecahedron with a three-faced tetrahedron y (311); the six faces meeting in each triad axis are often rounded together into low conical forms. The crystals are frequently twinned, the twin-axis coinciding with a triad axis; a rhombic dodecahedron so twinned (fig. 3) has no re-entrant angles. An important character of blende is the perfect dodecahedral cleavage, there being six directions of cleavage parallel to the faces of the rhombic dodecahedron, and angles between which are 60°. Entry: BLENDE
Corundum crystallizes in the hexagonal system. In fig. 1, which is a form of ruby, the prism a is combined with a hexagonal pyramid n, a rhombohedron R, and the basal pinacoid C. In fig. 2, which represents a typical crystal of sapphire, the prism s is associated with the acute pyramids b, r, and a rhombohedron a. Other crystals show a tabular habit, consisting usually of the basal pinacoid with a rhombohedron, and it is notable that this habit is said to be characteristic of corundum which has consolidated from a fused magma. Corundum has no true cleavage, but presents parting planes due to the structure of the crystal, which have been studied by Prof. J. W. Judd. Entry: CORUNDUM
CUBE (Gr. [Greek: kubos], a cube), in geometry, a solid bounded by six equal squares, so placed that the angle between any pair of adjacent faces is a right angle. This solid played an all-important part in the geometry and cosmology of the Greeks. Plato (_Timaeus_) described the figure in the following terms:--"The isosceles triangle which has its vertical angle a right angle ... combined in sets of four, with the right angles meeting at the centre, form a single square. Six of these squares joined together formed eight solid angles, each produced by three plane right angles: and the shape of the body thus formed was cubical, having six square planes for its surfaces." In his cosmology Plato assigned this solid to "earth," for "'earth' is the least mobile of the four (elements--'fire,' 'water,' 'air' and 'earth') and most plastic of bodies: and that substance must possess this nature in the highest degree which has its bases most stable." The mensuration of the cube, and its relations to other geometrical solids are treated in the article POLYHEDRON; in the same article are treated the Archimedean solids, the truncated and snub-cube; reference should be made to the article CRYSTALLOGRAPHY for its significance as a crystal form. Entry: CUBE
In two pencils we may either make planes correspond to planes and lines to lines, or else planes to lines and lines to planes. If hereby the condition be satisfied that to a flat, or axial, pencil corresponds in the first case a projective flat, or axial, pencil, and in the second a projective axial, or flat, pencil, the pencils are said to be _projective_ in the first case and _reciprocal_ in the second. Entry: 92
Diamond possesses a brilliant "adamantine" lustre, but this tends to be greasy on the surface of the natural stones and gives the rounded crystals somewhat the appearance of drops of gum. Absolutely colourless stones are not so common as cloudy and faintly coloured specimens; the usual tints are grey, brown, yellow or white; and as rarities, red, green, blue and black stones have been found. The colour can sometimes be removed or changed at a high temperature, but generally returns on cooling. It is therefore more probably due to metallic oxides than to hydrocarbons. Sir William Crookes has, however, changed a pale yellow diamond to a bluish-green colour by keeping it embedded in radium bromide for eleven weeks. The black coloration upon the surface produced by this process, as also by the electric bombardment in a vacuum tube, appears to be due to a conversion of the surface film into graphite. Diamond may break with a conchoidal fracture, but the crystals always cleave readily along planes parallel to the octahedron faces: of this property the diamond cutters avail themselves when reducing the stone to the most convenient form for cutting; a sawing process, has, however, now been introduced, which is preferable to that of cleavage. It is the hardest known substance (though tantalum, or an alloy of tantalum now competes with it) and is chosen as 10 in the mineralogist's scale of hardness; but the difference in hardness between diamond (10) and corundum (9) is really greater than that between corundum (9) and talc (1); there is a difference in the hardness of the different faces; the Borneo stones are also said to be harder than those of Australia, and the Australian harder than the African, but this is by no means certain. The specific gravity ranges from 3.56 to 3.50, generally about 3.52. The coefficient of expansion increases very rapidly above 750°, and diminishes very rapidly at low temperatures; the maximum density is attained about -42° C. Entry: DIAMOND
The ray-surface (represented in fig. 99 by its sections in the three principal planes) is derived from the indicatrix in the following manner. A ray of light entering the crystal and travelling in the direction OA is resolved into polarized rays vibrating parallel to OB and OC, and therefore propagated with the velocities 1/ß and 1/[gamma] respectively: distances Ob and Oc (fig. 99) proportional to these velocities are marked off in the direction OA. Similarly, rays travelling along OC have the velocities 1/[alpha] and 1/ß, and those along OB the velocities 1/[alpha] and 1/[gamma]. In the two directions Op1 and Op2 (fig. 98), perpendicular to the two circular sections P1P1 and P2P2 of the indicatrix, the two rays will be transmitted with the same velocity 1/ß. These two directions are called the optic axes ("primary optic axis"), though they have not all the properties which are associated with the optic axis of a uniaxial crystal. They have very nearly the same direction as the lines Os1 and Os2 in fig. 99, which are distinguished as the "secondary optic axes." In most crystals the primary and secondary optic axes are inclined to each other at not more than a few minutes, so that for practical purposes there is no distinction between them. Entry: 5
Since the circulation round any triangular area of given aspect is the sum of the circulation round the projections of the area on the coordinate planes, the composition of the components of spin, [xi], [eta], [zeta], is according to the vector law. Hence in any infinitesimal part of the fluid the circulation is zero round every small plane curve passing through the vortex line; and consequently the circulation round any curve drawn on the surface of a vortex filament is zero. Entry: 37
"Foundation" also means the base (natural or artificial) on which any erection is built up; generally made below the level of the ground (see FOUNDATIONS below). A foundation-stone is one of the stones at the base of a building, generally a corner-stone, frequently laid with a public ceremony to celebrate the commencement of the building. The term is also applied to the ground-work of any structure, such as, in dress-making, the underskirt over which the real skirt is hung, any material used for stiffening purposes, as "foundation muslin or net." In knitting or crochet the first stitches onto which all the rest are worked are called the "foundation chain." In gem-cutting the "foundation-square" is the first of eight squares round the edges of a brilliant made in bevel planes and from which the angles are all removed to form three-corner facets. Entry: FOUNDATION
In the general motion of the top the vector OH of resultant angular momentum is no longer compelled to lie in the vertical plane COC´ (fig. 4), but since the axis Oh of the gravity couple is always horizontal, H will describe a curve in a fixed horizontal plane through C. The vector OC´ of angular momentum about the axis will be constant in length, but vary in direction; and OK will be the component angular momentum in the vertical plane COC´, if the planes through C and C´ perpendicular to the lines OC and OC´ intersect in the line KH; and if KH is the component angular momentum perpendicular to the plane COC´, the resultant angular momentum OH has the three components OC´, C´K, KH, represented in Euler's angles by Entry: 8