Fredkin's field was physics, but he became involved with computers in 1956 when he was sent by the Air Force, where he had trained as a jet pilot, to the MIT Lincoln Laboratory.

However, physicists find some vagueness, problems with Bell theorem compatibility, and lack of empirical falsifiability in Fredkin's expression of his ideas.

# If Fredkin's first fundamental law of information is correct then Einstein's theory of general relativity theory is not entirely correct, because the theory does not rely upon digital information.

The 6-phase clock described in Fredkin's " Digital Mechanics " might be a counting mechanism for the 6-dimensional directional-measuring device that measures the curvature and torsion of information flow.

However, careful consideration might reveal considerable merit underlying Fredkin's metaphors.

This book discusses Edward Fredkin's work.

Fredkin's career and achievements have much of their motivation in " Digital Philosophy ", a particular type of pancomputationalism described in Fredkin's papers: Introduction to Digital Philosophy, On the Soul, Finite Nature, A New Cosmogony, and Digital Mechanics.

Fredkin's digital philosophy contains several fundamental ideas: Everything in physics and physical reality must have a digital informational representation.

# If Fredkin's second fundamental law is correct then the Copenhagen interpretation of quantum mechanics is not entirely correct, because quantum randomness lacks a digitally deterministic explanation.

Straightforward interpretations of Fredkin's ideas seem to violate Bell's inequalities.

* Dr. Edward Fredkin's Digital Philosophy site.

When the concept of the DC multiverse began to take hold, Luthor's red-haired incarnation was rewritten as Alexei Luthor, Lex's counterpart from the Earth-Two parallel universe.

For them, objections to the multiverse as a concept are unimportant.

This idea was eventually expanded into the concept of a multiverse, including such worlds as Earth-Three, which was an " opposite " world where heroes were villains and historical events happened in reverse of how they occurred in real life ( e. g., President John Wilkes Booth being assassinated by an actor named Abraham Lincoln ), and Earth Prime, which was ostensibly the " real world " and used to explain how real-life DC staffers ( such as Julius Schwartz ) could occasionally appear in comics stories, and so forth.

Swiftly spun off into their own title in Oct / Nov 1960, the Justice League would become the backbone of the DC Universe, and thanks to the concept of the multiverse, regularly engage in annual " team-up " s with their 1940s counter-parts, the Justice Society in tales written by Fox.

The two publishers have used the multiverse concept to fix problems arising from integrating characters from other publishers into their own canon, and from having major serial protagonists having continuous histories lasting, as in the case of Superman, over 70 years.

Ellis also introduced the concept of a multiverse to the series, drawing upon the mathematical concept known as the Monster group for inspiration.

* The Flash # 123-the " Flash of Two Worlds " story introduces Earth-Two, and more generally the concept of the multiverse, to DC Comics.

The title refers to the fact that the story takes place in two parallel universes, a concept loosely based on multiverse theory.

At the time of its release, the concept of a massive multiverse was supposed to have been dropped following Crisis on Infinite Earths, with a single Earth ( Earth-1 ).

Since then, however, DC has brought back the concept of a multiverse.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

The concept of being relatively prime can also be extended to any finite set of integers S =

The related concept of " standard " numbers, which can only be defined within a finite time and space, is used to motivate axiomatic internal set theory, and provide a workable formulation for illimited and infinitesimal number.

The third was an important one in number theory, in which the concept of a finite field was first articulated.

He also introduced the concept of a finite field ( also known as a Galois field in his honor ), in essentially the same form as it is understood today.

He used this concept to define finite and infinite sets, subdividing the latter into denumerable ( or countably infinite ) sets and uncountable sets ( nondenumerable infinite sets ).

There is a notion of ind-finite group, which is the concept dual to profinite groups ; i. e. a group G is ind-finite if it is the direct limit of an inductive system of finite groups.

Limiting results are not statements about finite samples, and indeed are irrelevant to finite samples .< ref > Kolmogorov ( 1963a ) ( Page 369 ): " The frequency concept,

Although physical modelling was not a new concept in acoustics and synthesis, having been implemented using finite difference approximations of the wave equation by Hiller and Ruiz in 1971, it was not until the development of the Karplus-Strong algorithm, the subsequent refinement and generalization of the algorithm into the extremely efficient digital waveguide synthesis by Julius O. Smith III and others, and the increase in DSP power in the late 1980s that commercial implementations became feasible.

The original concept of Reed – Solomon coding describes encoding of k message symbols by viewing them as coefficients of a polynomial p ( x ) of maximum degree k − 1 over a finite field of order N, and evaluating the polynomial at n > k distinct input points.

Note that this concept of boundedness has nothing to do with finite size, and that a subset S of a bounded poset P with as order the restriction of the order on P is not necessarily a bounded poset.

As part of the development of Lebesgue integration, Lebesgue invented the concept of measure, which extends the idea of length from intervals to a very large class of sets, called measurable sets ( so, more precisely, simple functions are functions that take a finite number of values, and each value is taken on a measurable set ).

The concept of bounded rationality revises this assumption to account for the fact that perfectly rational decisions are often not feasible in practice because of the finite computational resources available for making them.

In addition, several capitalist states have emulated the concept of central planning, though in the context of a market economy, by setting integrated economic goals for a finite period of time.

The ultimate in large numbers was, until recently, the concept of infinity, a number defined by being greater than any finite number, and used in the mathematical theory of limits.

However, since the 19th century, mathematicians have studied transfinite numbers, numbers which are not only greater than any finite number, but also, from the viewpoint of set theory, larger than the traditional concept of infinity.

In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians developed the concept of the universe having a finite past with a beginning.

In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians developed the concept of the universe having a finite past with a beginning.

According to this concept, there is a finite amount of wealth and goods in the universe, and any goods taken from one part of the " river " must be appropriately replaced or paid for by other methods.

It is a computer implementation of the mathematical concept of a finite set.

Amongst his most original contributions were: his " Conjecture II " ( still open ) on Galois cohomology ; his use of group actions on Trees ( with H. Bass ); the Borel-Serre compactification ; results on the number of points of curves over finite fields ; Galois representations in ℓ-adic cohomology and the proof that these representations have often a " large " image ; the concept of p-adic modular form ; and the Serre conjecture ( now a theorem ) on mod-p representations that made Fermat's last theorem a connected part of mainstream arithmetic geometry.

An instance of a list is a computer representation of the mathematical concept of a finite sequence.

The concept of state is formalized in an abstract mathematical model of computation called a finite state machine, used to design both sequential digital circuits and computer programs.

The concept of plane duality readily extends to space duality and beyond that to duality in any finite dimensional projective geometry.