It is often stated that Copernican astronomy is ' simpler ' than Ptolemaic.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Analogously, anyone who argues that Einstein's theory of gravitation is simpler than Newton's, must say rather more to explain how it is that the latter is mastered by student-physicists, while the former can be managed ( with difficulty ) only by accomplished experts.

In a sense, Einstein's theory is simpler than Newton's, and there is a corresponding sense in which Copernicus' theory is simpler than Ptolemy's.

Its life history is much simpler than that of the truly colonial bumblebees and can serve as an example of the life cycle of many other species.

Basically, this means that simpler processing equipment ( the mixture has good flowing characteristics ) and less external heat ( the foaming reaction is exothermic and develops internal heat ) are required in one-shot foaming, although, at the same time, the problems of controlling the conditions of one-shot foaming are critical ones.

In this model the electron cloud of a multi-electron atom may be seen as being built up ( in approximation ) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals.

Yet a simpler alternative interpretation of the conflict between these two figures is that the Historia Brittonum is preserving traditions hostile to the purported descendants of Vortigern, who at this time were a ruling house in Powys.

( Another simpler system, called ladder bracing, where the braces are all placed across the width of the instrument, is used on all types of flat-top guitars on the back.

* The 400 / 800's 10 KB operating system was replaced with a simpler 2 KB BIOS, of which 1 KB is the built-in character set.

The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood.

However, some modern scholars have argued that the demons and temptations that Anthony is reported to have faced may have been related to Athanasius by some of the simpler pilgrims who had visited him, who may have been conveying what they had been told in a manner more dramatic than it had been conveyed to them.

There is no simpler intermediary between being and non-being that explains and classifies being.

* economical: bioleaching is in general simpler and, therefore, cheaper to operate and maintain than traditional processes, since fewer specialists are needed to operate complex chemical plants.

If the large-scale Universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred ( or special ) observer or vantage point.

Respiration is the oxidation of carbon whereby it is broken down into simpler structures ; essentially the opposite of photosynthesis.

It is Eromonga -- look hard, you can see with your naked eye the wooden scaffolding on the cliff ''.

It is hard to see how the situation could be otherwise.

Work is under way to see whether new restraining devices should be installed on all nuclear weapons.

It is the gait of the human who must run to live: arms dangling, legs barely swinging over the ground, head hung down and only occasionally swinging up to see the target, a loose motion that is just short of stumbling and yet is wonderfully graceful.

But more important, and the thing which the casual traveler and the blind sojourner often do not see, is that these places and activities are often the settings in which Persians exercise their extraordinary aesthetic sensibilities.

Obviously, such a Northern tourist's purpose is somewhat akin to a child's experience with Disneyland: he wants to see a world of make-believe.

I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.

So great a man could not but understand, too, that the thing that moves men to sacrifice their lives is not the error of their thought, which their opponents see and attack, but the truth which the latter do not see -- any more than they see the error which mars the truth they themselves defend.

It is much less difficult now than in Lincoln's day to see that on both sides sovereign Americans had given their lives in the Civil War to maintain the balance between the powers they had delegated to the States and to their Union.

Lucretius has remarked: `` The reason why all Mortals are so gripped by fear is that they see all sorts of things happening in the earth and sky with no discernable cause, and these they attribute to the will of God ''.

The only chance of renovation is to open our eyes and see the mess.

So we see that a specialist is a man who knows more and more about less and less as he develops, as contrasted to the generalist, who knows less and less about more and more.

What I am here to do is to report on the gyrations of the struggle -- a struggle that amounts to self-redefinition -- to see if we can predict its future course.

One way to determine whether we have so dangerous a technology would be to check the strength of our society's organs to see if their functioning is as healthy as before.

Hence the prime issue, as I see it, is whether a democratic or free society can master technology for the benefit of mankind, or whether technology will rule and develop its own society compatible with its own needs as a force of nature.

Actually, you could wish for some passion, now and then, but when you look around the world and see the little volcanos of current history which partisan social passions have wrought, you are glad that in these pamphlets there is at least some civilized calm.

One who invites such trials of character is either foolhardy, overconfident or too simple and childlike in faith in mankind to see the danger.

But I can see from this latest trick of memory how much more arbitrary and influential it is than the will.

Moreover, if the critic instructs his audience in what to see in a work, he is contributing to this pseudo-thinking ; ;

There is every reason to recognize that in the very last years of his life, as we shall see, Thompson did take the drug in carefully rationed doses to ease the pains of his illness, but the exact date at which this began has never been determined.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Other notational traditions do exist ; Italian solo music is typically written at the sounding pitch, and the " old " German method sounded an octave below where notation except in the treble clef, where the music was written at pitch.

During the Mediaeval period, the foundation was laid for the notational and theoretical practices that would shape western music into what it is today.

The most obvious of these is the development of a comprehensive notational system ; however the theoretical advances, particularly in regard to rhythm and polyphony, are equally important to the development of western music.

A notational symbol that represents a number is called a numeral.

In particular the Shiva Sutras, an auxiliary text to the Ashtadhyayi, introduces what can be considered a list of the phonemes of the Sanskrit language, with a notational system for them that is used throughout the main text, which deals with matters of morphology, syntax and semantics.

Because a preorder is a binary relation, the symbol ≤ can be used as the notational device for the relation.

This alternate notational scheme is used primarily in verbal discussions or where a linear representation is desirable in print, but may also be permissible as during-game transcription by either or both players.

where R < sub > i </ sub >< sup > j </ sup > is a matrix and in the second expression the summation sign was suppressed ( a notational convenience introduced by Einstein that will be used throughout this article ).

An advantage of decimal notational systems is that they are infinitely extensible, and when new subdivisions are introduced, they need not disturb the existing allocation of numbers.

; Capabilities of UML and implementation language mismatch: Typical of other notational systems, UML is able to represent some systems more concisely or efficiently than others.

A semantic feature is a notational method which can be used to express the existence or non-existence of pre-established semantic properties by using plus and minus signs.

Such notation does not indicate the presence of physical dimensions, and is purely a notational convention.

In his posthumously published book, ' Rhythmic Proportions in Early Medieval Ecclesiastical Chant ' ( Brill, 1958 ), where the term ' semiotic ' is used, tables are presented of neumes of different notational styles once used in various parts of Europe ( e. g., Nonantola, Laon, Brittany, Aquitaine, Switzerland ).

The system of neumes used in most of the earliest notational styles is rhythmically complex and sophisticated, particularly the styles of Laon and Einsiedeln Abbey.

The problem with the point and the comma as either decimal mark or digit group separator is that, internationally, they have both often been used for both meanings, and their meaning is context-dependent ( one must know which notational system is being used in order to interpret them ).

He perhaps is most famous in music history for declaring that it was not possible to notate sounds — an assertion which reveals his ignorance of the notational system of ancient Greece, so that knowledge had been lost by the time he was writing.

Even if Sitchin is referring to written rather than to spoken language, it is unlikely that his contention can be persuasively defended, since Sumerian ideograms were preceded by the Azilian and Tartarian signaries of Europe as well as by a variety of script-like notational systems between the Nile and Indus rivers.

The IPA ’ s major contribution to phonetics is the International Phonetic Alphabet — a notational standard for the phonetic representation of all languages.