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.

The Axioms required to make the theoretical machinery operate are set out tersely and powerfully, so that all permissible operations within the theory can be traced rigorously back to these axioms, rules, and primitive notions.

The point is that an ethical critic, with an assist from Freud, can seize on this theory to argue that tragedy provides us with a harmless outlet for our hostile urges.

This can only be for one of two reasons: either the two are quite different and will require totally different theory ( and hence techniques ), or our existing theories are insufficiently general.

Philosophy can prevent the working scientist from becoming slothful and self-content by noting the assumptions and level at which a hypothesis or theory is framed.

In the second-order theory, one of the normal stress differences can be calculated from the first-order stress relaxation function.

But then this theory confesses that it is completely at a loss as to how the image can possibly be received by the brain.

Unless one takes refuge in the theory -- however disguised -- that Negroes are, somehow, different from white people, I do not see how one can escape the conclusion that the Negro's status in this country is not only a cruel injustice but a grave national liability.

The exact number and placement of Endosymbiotic theory | endosymbiotic events is currently unknown, so this diagram can be taken only as a general guide It represents the most parsimonious way of explaining the three types of endosymbiotic origins of plastids.

Brønsted-Lowry theory can also be used to describe molecular compounds, whereas Arrhenius acids must be ionic compounds.

The second reaction can be described using either theory.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.

Sometimes slightly stronger theories such as Morse-Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe are used, but in fact most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.

Of course, the current state of technology at any given time can put limitations on what can be achieved experimentally and theoretically so it may take considerable time for theory to be refined.

The and convention for amino acid configuration refers not to the optical activity of the amino acid itself, but rather to the optical activity of the isomer of glyceraldehyde from which that amino acid can, in theory, be synthesized (- glyceraldehyde is dextrorotary ;-glyceraldehyde is levorotatory ).

In quantum field theory, this process is allowed only as an intermediate quantum state for times short enough that the violation of energy conservation can be accommodated by the uncertainty principle.

The more ambitious theory of Wilhelm Nitsche, which assigned to Anaximenes a larger part of the Demosthenic corpus ( speeches 10-13 and 25, letters 1-4, proems ), can be rejected.

From about 1955 he started to work on sheaf theory and homological algebra, producing the influential " Tôhoku paper " ( Sur quelques points d ' algèbre homologique, published in 1957 ) where he introduced Abelian categories and applied their theory to show that sheaf cohomology can be defined as certain derived functors in this context.

Thus, while altruistic persons may under some circumstances be outcompeted by less altruistic persons at the individual level, according to group selection theory the opposite may occur at the group level where groups consisting of the more altruistic persons may outcompete groups consisting of the less altruistic persons.

Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.

The earliest and most direct kinds of observational evidence are the Hubble-type expansion seen in the redshifts of galaxies, the detailed measurements of the cosmic microwave background, the relative abundances of light elements produced by Big Bang nucleosynthesis, and today also the large scale distribution and apparent evolution of galaxies predicted to occur due to gravitational growth of structure in the standard theory.

The cell theory, first developed in 1839 by Matthias Jakob Schleiden and Theodor Schwann, states that all organisms are composed of one or more cells, that all cells come from preexisting cells, that vital functions of an organism occur within cells, and that all cells contain the hereditary information necessary for regulating cell functions and for transmitting information to the next generation of cells.

The theory was based on how heat-treating metal works ( the temperatures are lowered to room temperature from a high degree causing certain strength increases in the molecular structure to occur ) and supposed that continuing the descent would allow for further strength increases.

Apart from the commonly cited example of water turning to steam with increased temperature, Gould and Eldredge noted another analogy in information theory, " with its jargon of equilibrium, steady state, and homeostasis maintained by negative feedback ," and " extremely rapid transitions that occur with positive feedback.

The theory is usually contrasted with a theory that talks about events occurring in the fullness of time, or when an overwhelming wave of smaller events causes certain developments to occur.

Leamer emphasized that Leontief did not interpret H-O theory properly and claimed that with a right interpretation, the paradox did not occur.

According to the theory of evolution, genetic variations occur without specific design or intent.

A monoid for which the operation is commutative for some, but not all elements is a trace monoid ; trace monoids commonly occur in the theory of concurrent computation.

But just like string theory, in order for the theory to satisfy causality, the theory must be local, and so the topology changing must occur at a single point.

According to psychohistory theory, each of the six psychoclasses co-exists in the modern world today, and, regardless of the changes in the environment, it is only when changes in childhood occur that societies begin to progress.

The Everett many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a multiverse composed of mostly independent parallel universes.

Historian Alan Berger reports that Holocaust deniers argue in support of a preconceived theory — that the Holocaust either did not occur or was mostly a hoax — by ignoring extensive historical evidence to the contrary.

Many surfaces of this type occur in the theory of fractals.

Eventually a competing theory involving the gradual accumulation of mutations was shown to occur in nature so often that geneticists largely dismissed the moving gene hypothesis.

William Crookes proposed a " brain wave " theory in which he claimed telepathy might occur due to high frequency vibrations of the ether.

In simultaneous equilibrium systems, phenomena that are in apparent contradiction to Le Chatelier principle can occur ; these can be resolved by the theory of response reactions.

In probability theory, a probability space or a probability triple is a mathematical construct that models a real-world process ( or " experiment ") consisting of states that occur randomly.

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of Bernoulli trials before a specified ( non-random ) number of failures ( denoted r ) occur.

This theory also assumes that causality must be constant: i. e. that nothing can occur in the absence of cause, whereas some theories hold that an event may remain constant even if its initial cause was subsequently eliminated.

A state, the highest form of human organization in fact and theory, could be subjected to Law only by a manifestation of self-will, or consent.

It appeared that the theory could be saved in one way only.

The social exchange theory postulates that altruism only exists when benefits outweigh costs.

Also, as we now know, bosons also have antiparticles, but since bosons do not obey the Pauli exclusion principle ( only fermions do ), hole theory does not work for them.

But this extremely ingenious theory would at most explain only the mystic word Abracadabra, whose connection with Abrasax is by no means certain.

The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis ( the symmetrical axis of the system ) are infinitely small, i. e. with infinitesimal objects, images and lenses ; in practice these conditions are not realized, and the images projected by uncorrected systems are, in general, ill defined and often completely blurred, if the aperture or field of view exceeds certain limits.

Consequently the Gaussian theory only supplies a convenient method of approximating to reality ; and no constructor would attempt to realize this unattainable ideal.

Bundle theory, originated by the 18th century Scottish philosopher David Hume, is the ontological theory about objecthood in which an object consists only of a collection ( bundle ) of properties, relations or tropes.

However, the argument concludes that the conceptual challenge of bare particulars leaves a bundle of properties and nothing more as the only possible conception of an object, thus justifying bundle theory.

The choice between the two definitions usually matters only in very formal contexts, like category theory.

Remaining issues, such as the cuspy halo problem and the dwarf galaxy problem of cold dark matter, are not fatal to the dark matter explanation as solutions to such problems exist which involve only further refinements of the theory.

The BCS theory, however, requires only that the potential be attractive, regardless of its origin.

According to this theory, the cycle of philosophical upheavals that in part drove the diversification of Buddhism into its many schools and sects only began once Buddhists began attempting to make explicit the implicit philosophy of the Buddha and the early suttas.

In complexity theory, the satisfiability problem ( SAT ) is a decision problem, whose instance is a Boolean expression written using only AND, OR, NOT, variables, and parentheses.

Paracelsus ( 1493 – 1541 ), for example, rejected the 4-elemental theory, and with only a vague understanding of his chemicals and medicines formed a hybrid of alchemy and science in what was to be called iatrochemistry.

Claude Shannon proved, using information theory considerations, that any theoretically unbreakable cipher must have keys which are at least as long as the plaintext, and used only once: one-time pad.

Charles Darwin proposed the theory of universal common descent through an evolutionary process in On the Origin of Species, twice stating the hypothesis that there was only one progenitor for all life forms and ending with " There is a grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one ".

Chomsky argued that in order to explain language, we needed a theory like generative grammar, which not only attributed internal representations but characterized their underlying order.