# INFORMATION IN THE STRUCTURE OF THE UNIVERSE

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INFORMATION IN THE STRUCTURE

OF THE UNIVERSE

Vladimir Nesterov

Concept of “information” is widely used in modern

science; Latin “informatio” literally means “data” or

“message”.

No scientist who dealt with basic studies of information

could discover physical essence of this concept.

Appearance of information theory was induced

by development of technical communication systems

which had to ensure information exchange. I’d like to

emphasize – technical systems, operation principles of

which are determined by physics laws, i.e. laws of material

world. Optimization of such systems operation

required first of all dealing with amount of information

which can be transmitted via communication channels.

That is why it is natural that first steps in this field

were fulfilled by employees of Bell Telephone Companie

– Н. Nyquist, R. Hartley and C. Shannon. Later

on results of these works formed a basis for Shannon’s

calculation of communication channels data throughput,

improving of messages coding and decoding methods

and solving of other questions related to optimization

of technical communication systems operation.

Collection of these notions, called by Shannon “mathematical

theory of communication”, became a basis

of classic Information theory. However in Shannon’s

works explanation of information physics was missing;

substitution of “information” and “amount of information”

concepts happened. Shannon’s Information

theory did not answer to “What is information?” question;

it only answered to “What amount of information

may be transmitted in time unit using a set certain

signals?” question. It should be understood clearly that

without revealing of “information” concept’s physical

essence and at the same time naming frequency characteristic

of code letters by “amount of information”

term, Shannon created a possibility for identification

of two absolutely different in their nature phenomena:

information as a physical category and information as

frequency of a certain message happening.

Norbert Wiener – father of cybernetics or “science

of control and communication in the animal and the maIn

the beginning was the Word.

Gospel of John

V.I. NesterovPhysical basics of informational interaction

-5-

chine” – also had no clear idea about physical essence of

information. “Information is information, not matter or

energy, it is something else”, – he wrote.

French physicist L. Brillouin noticed that Shannon’s

formula for information amount calculation

is similar in its structure to formula offered by Boltzmann,

which is used for entropy amount calculation.

Concept of messages entropy allowed Brillouin to postulate

“omnipresence” of information and assume that

measure of information amount, related to a certain

object, may be a complexity of its internal structure.

Abovementioned postulates and their consequences are

given by L. Brillouin in his studies in details. Brillouin

took the following value as the universal measure of information

amount:

I = k ∙ ln p, where

p – a “complexity” of a certain object’s structure; k – a

constant depending on chosen system of measure units;

ln – a natural logarithm.

This formula resembles Boltzmann’s formula for

entropy amount calculation:

S = k ∙ ln W, where

S – entropy, k – Boltzmann constant, W – thermodynamic

probability.

Hence appears one important circumstance: when

we lose information we increase entropy of a system, in

other words – we decrease level of its internal structural

organization.

Thereby,

I + S = const

as a consequence of the second law of thermodynamics

– entropy of a closed system is a constant value and

it cannot decrease with time.

In the 60’s of the last century thanks to L.

Brillouin “negentropy principle of information” appeared

and became widely known. Differing from

entropy, regarded as irregularity measure of a certain

system, negentropy usually means measure of order

or structural “complexity” of surrounding system related

to various entropic processes in physical world.

Brillouin offered to express information I and entropy

S in the same units – informational (bits) or entropic

(erg/degree).

B. Kadomtsev notes that values I and S are formally

equal because I corresponds to information of one single

state of many possible states, S is defined by multitude

of all states.

In modified in accordance with modern ideas

Information theory information is regarded from the

point of view of physical statistics as a certain mathematical

abstraction, a measure of algorithmic state of

chaos. Information theory describes principal laws of

information exchange, but it does not reveal its physics.

Quantum-entropic logic theory became a theory

regarding information as a material category revealing

physical essence of entropic-information interactions

and describing interaction of mass, energy and information

within a system.

Quantum-entropic logic theory postulates:

1. Information is a material category, just like energy

and mass of a system.

2. Due to the fact that information is material it follows

the conservation law. Information cannot disappear

without a trace or appear from nowhere. Total amount

of information in a closed system (a system which does

not exchange mass, energy and information with environment)

– is a constant value.

It should be noted that Quantum-entropic logic

theory deals with negentropic properties of information

only. Object of this branch of learning is something

poorly resembling what we call information in everyday

life. Indeed, in everyday life semantic, intensional aspect

of information prevails, but Quantum-entropic logic

theory does not consider semantics of information at all.

In 1923 duke Louis de Broglie, a young French

nobleman, assumed that wave properties are typical not

only for light but for matter also. His arguments were

that Einstein’s equation

E = mc2

(с – speed of light in vacuum) links mass with energy,

but on the other hand Einstein and Planck linked energy

and wave frequency. Combining these two principles

one may conclude that mass should have wave

incarnation also.

Quantum-entropic logic theory expands de Broglie

conclusions to all material mediums, including information.

It shows that all matter display wave properties.

Quantum-entropic logic theory offered a formula

for information wave radiation quantum which links in

with energy of a system through Planck constant.

Formula:

I =

(h – Planck constant) links energy of any material

system with level of its complexity, in other words,

with level of its structural organization. Level of complexity

(structural organization) is the same essential

quality of any material system as mass and energy

of this system. Information has even more universal

character than mass, because a number of fundamen–6-

tal particles, such as photon, have no mass at all. But

all material objects, with no exceptions, have more or

less complex structure, that is why we probably should

speak not about quantum-wave dualism (where

“wave” term means force fields only), but about triunity

in description of material world, when information

is included into equation together with mass and

energy as a full member.

Electron interference phenomenon discovered

by Davisson and Germer demonstrated in reality that

electrons are similar to waves. Austrian physicist Erwin

Schrödinger assumed that these waves are electrons

“spread” along space. But this concept was too

inaccurate. How can “spread” electron be in several

places at the same time? It complicated interpretation

of what “spread” electron really is.

In 1926 German physicist Max Born suggested his

own interpretation of electronic wave. Born’s theory

relates to one of the most strange and incomprehensible,

from the point of view of human logic, property

of quantum theory. Nevertheless it is proven by great

amount of experimental data. According to this theory

electronic wave must be interpreted from the point

of view of statistical probability. But rightful question

arises: “How can probability function, a certain

mathematical abstraction govern electron behavior,

as if it is real physical field?” Here lies obvious logic

disagreement. Statistical probability, from the classic

physics standpoint, is non-material category and it

cannot be related to implementation of fundamental

laws of physics. As Einstein said about it: “He (God)

does not play dice”. Any physical theory, even if it is

mathematically flawless, must have internal noncontradictory

logical structure. Supporters of quantum

mechanics, in their try to fix logical disagreement,

say that probability in quantum-mechanical calculation

have higher fundamentality than roulette has.

But it is still unclear what this higher fundamentality

consist of? Probably wave function would get even

higher fundamentality in one case only: if it could be

regarded as a physical field. What is probability according

to Information theory – it corresponds to information

(I) of one state out of many possible states.

Hereby terms “probalbility” and “information” may

be unified in this context. From the point of view of

Quantum-entropic logic theory information is a material

substance, a physical field directly linked to energy

and mass of an object.

Thus application of Quantum-entropic logic theory

postulates may eliminate severe logical contradictions

existing in quantum mechanics.

One of properties of information fields, which

follows from quantum mechanics postulates, is that

information fields must be transferred by some class of

microparticles, just like electromagnetic forces, at the

level of fundamental particles, are transferred by photons.

In physics there is a tradition to call interaction

fields particles with names with “-on” endings, such

as “photon”, “gluon”, etc. that is why fundamental

particle of information-entropy exchange was also

called “informon”. So infomons are the most fundamental

quantum beam of information. Although infomons

are still to be experimentally proven (if it is even

possible someday), one can say with certainty that infomons

must have the following properties: they must

have no mass; they must have negligibly and vanishingly

small, but not zero, interaction energy and have

spin 2.

What is spin of a particle? Spin is a quantum-mechanical

term corresponding to moment of momentum

in classic mechanics. Fundamental particles have

“inherent” number of spin, equal to integral or halfintegral

number (in Planck constant units), which

never changes.

All known particles in the Universe may be divided

into several groups: particles with spin 1/2, which

form matter of the Universe; particles with spin 1,

which create forces acting between particles of matter

– photons, weak gauge bosons and gluons. Infomon

must have double spin of photons, gauge bosons

or gluons, i.e. spin 2, in order to transfer informationentropic

interaction.

Superstring theory starts with suggestion about

what is the lesser indivisible component of matter.

For many decades generally accepted answer was that

matter consists of particles – electrons and quarks –

which are positioned as point which cannot be divided

and have no size and internal structure. Conventional

theory stated and experiments proved that

these particles are connected by various means, forming

protons, neutrons and vast variety of atoms and

molecules, forming everything around us.

Superstring theory offers another picture. It does

not deny principal role of electrons, quarks and other

particles, but it states that these particles are not

points.

For the first time Superstring theory was formulated

in 1968 by Gabriele Veneziano, young Italian

physicist who worked in CERN and studied strong

nuclear interactions. Leonard Susskind of Stanford

University, Holger Nielsen of Niels Bohr Institute and

Yoichiro Nambu of Chicago University have offered

physical justification of Veneziano’s discovery. These

scientists have shown that interaction between particles

happens due to smallest, extremely thin, almost

rubber-like fibers of energy, few hundreds billions

times thinner than separate atoms of nucleus. These

small elastic fibers were called strings. And just like

guitar strings vibrate in various ways, each of which

creates different chords, superstrings may also oscillate

in various ways. But these oscillations do not

produce various music notes; Superstring theory says Physical basics of informational interaction

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that they produce various properties of particles. Tiny

string vibrating in a certain way will have mass and

electron charge. In accordance with the theory such

vibrating string is something we use to call electron.

String vibrating in other way will have all required

properties to identify it as quark, neutrino or any other

kind of particles.

All families of particles are unified in Superstring

theory, because each of them appear from various vibrating

states (mods) done by one and the same basic

object – superstring.

Information fields’ properties analysis allowed

making a conclusion that in spite of the fact that Superstring

theory was discovered in attempt to understand

strong interactions, it is actually may be resolution

of another problem also. It may be quantummechanical

theory of information-entropy interaction.

Such conclusion is possible because in strings

oscillation spectrum John Schwarz and Joel Scherk

have found a mod corresponding to zero-mass particle

with interaction energy value about a zero and

spin 2. Presumably these characteristics are distinctive

features of informon. Thus string theory equation

contains quantum-mechanical description of information

fields.

The only parameter necessary for strings calibration

is their tension. How to define this tension? If we

could touch a superstring we would know its hardness

and would define tension just like we do it with guitar

or another string instrument. But because fundamental

strings are so small we cannot use this method and

we face a necessity to develop an indirect method.

Schwarz and Scherk have developed an indirect

method of strings tension defining used in Superstring

theory in 1974. Their calculation showed that intensity

of interaction transferred by string oscillation in

accordance to fundamental particle is inversely proportional

to a string tension. And as soon as informon

transfers vanishingly small interaction, obtained value

of tension must be enormous, about 1039 tons – value

of so-called Planck tension.

When guitar strings are fastened, which guarantees

constancy of their length, superstrings have

no such fastening limiting their length. Instead of it,

enormous tension of informon string will force loops,

which are examined by strings theory, squeeze to submicroscopic

size. Under Planck tension, with participating

sub-Planck fluctuations, informon string may

be squeezed to a size lesser than Planck length, i.e.

lesser than 10-33 cm. Thanks to such great tension

energy of informon string oscillating loop becomes

truly gigantic in comparison with usual scale of fundamental

particles physics, millions and millions times

higher than electron string energy.

According to modern conception of quantum

mechanics, there is no such thing as distance shorter

than Planck length and time span lesser than Planck

time (10-43 seconds). If concept of informon fields is

correct it means that existing concepts of space and

time – system in which quantum mechanics operates,

turns out to be incomplete and applicable in particular

cases only. Involvement of informons fields theory

consists in the following: space and time do not lose

their meaning in extremely small scales, lesser than

Procrustean bed of Planck length, instead of that they

modify into another, more fundamental concepts.

Decreasing below Planck scale becomes possible because

concepts of space and time continue in form of

other and more universal notions.

If we look at distances scale within Planck length

we will see that quantum-mechanical fluctuations of

transforming informon field are so substantial and

may cause so strong and uneven inflation of space

that it can turn into foamed, turbulent and swollen

form. John Wheeler offered term “quantum foam” to

designate a state discovered during studies of ultramicroscopic

space and time in scales lesser than Planck

length. In this “quantum foam” terms of classic physics

such as “farther” and “closer”, “in front” and

“behind” (even “before” and “after”) become fuzzy

and vague.

Basic principles of general theory of relativity and

quantum mechanics allow defining of approximate

scale of distances, passing to which turns off laws of

existing physics and turns on other quantum-entropic

logics. Smallness of Planck constant and vanishingly

small value of information-entropy interaction force

has negligibly small size, about 10-33 cm. Here is an

example to illustrate this size: if we scale up size of

atom to a size of the Universe, Planck length in this

case will be equal to height of two-storied building.

There is a concept of phase states in physics. In

general case phase relates to possible descriptions

of physical system at changing of its parameters on

which this system depends (for example, temperature,

string tie constant, type of space, time, etc.).

In respect to a matter phase state means one of

possible states of the matter: solid, liquid and gaseous.

We take ice as an example. If you increase its temperature

above 0 degrees Celsius, solid ice will melt

down and eventually turn into water. Ice is a rock-solid

state, water is viscous liquid. Simple observations

show no evident signs that their molecular composition

is identical – H2O. If you continue to heat up

water, in some period of time, when temperature of

water reaches 100 degrees Celsius, another transformation

will happen: liquid water starts to boil and

turn into steam, which in its turn does not resemble

water and ice in appearance at all. Although of course

all three substances have the same molecular composition.

Changes from solid to liquid and from liquid to

gaseous are known as phase transitions. -8-

So many words about ice, water and steam and

their phase transitions – how can it be related to matter

and information? Quantum-entropic logic theory

states that not only a substance may be subjected to

phase transition, but all matter also may. There are

grounds to be sure that when matter goes through

specific critical states, similar to 100 degrees Celsius

for steam and 0 degrees Celsius for water, it is also

subjected to radical extensive transformation.

Substance may be conventionally represented

as “frozen part” of matter. When a particle of a substance

reaches speed close to speed of light in vacuum

(300 thousand kilometers per hour) it starts to “melt”

and turns into energy. Therefore force fields may be

rendered as “liquid” part of matter. When size and energy

of a particle decreases down to Planck values energy

starts to “boil” and transform into information.

Thus information field may be represented as “gaseous”

part of matter.

Big bang theory is the basic theory of space origin.

This theory describes evolution of space from

split second after something had happened to the existence

of the Universe, but it does not say a word

about time zero. Big bang theory does not cover the

bang itself. It says nothing about what had exploded,

why it had exploded, how exactly it had exploded

and, frankly speaking, had there been an explosion

at all? The Big bang is a totally mysterious phenomenon.

What could be that outside directed force which

started the expansion of the Universe? Certain types

of strong repulsive forces must have played a crucial

role in the bang, but what natural forces could

it be? For many decades this most important of all

cosmological questions remains unanswered. And

only in 2000s was made a suggestion that this force

could be transforming informon field. During time

span, in comparison with which nanosecond might

seem eternal, early Universe provided a scene where

information displayed its repulsive properties, dragging

one region of space from another with inexorable

force. Repulsive effect of transforming informon

field was so strong that it not only engaged the bang,

but revealed something which forces the Universe

to expand for already 14 billion years until the present

day. In theory, which operates information field,

early Universe expanded with overwhelming gigantic

coefficient, in comparison with standard Big bang

theory, thus enlarging our cosmological perspective

to the degree when we understand that our galaxy is

the one among hundreds of billions galaxies.

The “Information bang” theory offers the most

important modifications of standard Big bang theory

propositions, gives an idea about events which happened

at point zero and in the earliest moments of

the Universe existence. This theory gives answers to

key questions lying beyond standard model of the Big

bang theory, makes a number of predictions which

find experimental proofs.

These questions which could not be answered by

standard Big bang theory:

1) Where all this mass and energy filling the Universe

came from?

2) What causes inflation of space and matter?

were successfully redirected to Theory of extensive

transformation of information into substance and

energy.

But even in this situation some fundamental basics

remain unclear:

– Was there a time before the Information bang

and if yes, what was it like?

– What caused informon field to initiate the Information

bang?

These questions remain unanswered and still wait

for their discoverers. They are part of urgent scientific

matters that move forward cosmological studies and

remind us about many tangled knots, which we have

to untangle before we say that we completely understand

structure of the Universe.

Some brand new aspects in understanding of

space expansion from the point of view of informon

field’s universal effect in any scales of matter structural

organization are worthy of mentioning separately.

Until the present days the Universe expansion

is regarded by many scientists only in mechanistic

way, as recession of galaxies, without involvement

of other astronomical and physical objects of lesser

sizes. Theory of extensive transformation of information

into substance and energy regards the Universe

expansion as global and universal process, involving

The Big Bang space with all contained in it material objects at any Physical basics of informational interaction

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distances from the Universe down to separate quantum

of matter.

From this point of view, if space expands it

should mean that in addition to recession of galaxies,

inflating space within a certain galaxy will move

all its stars away from each other, in its turn inflating

space inside every star or planet or inside us or inside

anything will move all constituent atoms away from

each other, and inside atoms – electrons, protons and

neutrons and deeper and deeper down to the smallest

components of matter. So because all tissue of space

expands, all basic physical constants will expand proportionally.

Space will force every thing, including

our measuring bars, increase its size and that is why

it is impossible in the essence to recognize that some

expansion really happens.

Relying on special theory of relativity Einstein

proclaimed that gravitation and acceleration are absolutely

identical. Accelerated observer, according to

Einstein, warps space just like gravitation does. Moreover

Einstein proved that in general gravitation and

acceleration are indistinguishable.

There is scientific methodological principle,

named after philosopher-nominalist William of Ockham,

saying in simplified way: “Entities must not be

multiplied beyond necessity”.

Following this principle, if all problems related

to time-space warping may be solved from acceleration

standpoint only, it means that absolutely similar

and identical to them effects related to gravitation, in

the final analysis may be brought to accelerated movement,

not involving such category as gravitation. In

other words gravitation may be “cancelled” due to

uselessness.

There is no doubt that gravitation is the basic

physical category underlying modern physics including

general and special theories of relativity. Any attempt

to discard it will be interpreted as madness

rather than manifestation of scientific courage. But is

this idea crazy enough to be true?

All abovementioned requires more detailed explanation

and we will try to present it.

Theory of extensive transformation of information

into substance and energy says that space expansion

provides extension of any physical body included

in tissue of space. Thus Sun, Earth and other astronomic

objects, usually considered to be as stationary

ones, in fact extend, inflating from inside as balloons.

If we could prove that astronomical objects, including

stars and planets, not only extend, but extend with

acceleration, in this case using principle of acceleration

and gravitation equivalence, gravity effect may

be brought to accelerating extension of astronomical

body. I.e. accelerating extension may completely imitate

gravitational attraction.

Thus whole question, in general, is to define if

Universe extends with or without acceleration now?

Two groups of astronomers – one under guidance

of Saul Perlmutter in Lawrence Berkeley National

Laboratory, another under guidance of Brian

P. Schmidt in Australian National University – have

proved fact of accelerating expansion of the Universe

by measuring of remote supernovas speed in the 90’s

of the last century. Thanks to innovative technology

of simultaneous observation of thousands of galaxies

via wide-angle telescope, these teams were able to

find about four dozens of supernovas at various distances

from Earth. After careful calculation of distance

and velocity of recession both groups came to

unequivocal conclusion: speed of the Universe extension

increases, i.e. space expands with acceleration.

Researchers of supernovas concluded that observed

accelerated expanding requires directed outside repulsion

of cosmological constant, function of which

may be fulfilled by transforming informon field. Informon

field may play role of a force imitating gravitation

at phenomenon of astronomical objects accelerated

expansion.

Thus when you drop a glass, it is not gravitation

field that attracts it to Earth, but expanding Earth

bumps into the glass.

Paraphrasing well known Einstein’s quote we

may say that Quantum-entropic logic theory is too elegant

to be wrong. It is characterized by inner logical

consistence; it does not contain inner logical absurdity.

It is the case when beauty and elegancy of one or

another physical theory corresponds to beauty and elegancy

of surrounding world.

Of course there is no assurance that such considerations

will lead us to the truth. Nevertheless all

Receding galaxies-10-

About the author:

Nesterov Vladimir Igorevich – physician, biophysicist, full member of Academy of Medical and Technical

Sciences. Chairman of the Institute of Practical Psychophysics directorate; President of International Academy

of non-linear diagnostic systems.

the time, especially now as we enter an era when our

theories describe fields which cannot be experimentally

studied, physicists will count on such aesthetic

consideration that may help to avoid dead ends. Until

now such approach demonstrated its strength and

forecasting power many times.

Quantum-entropic logic theory is not a modest

theory. Its objectives and promises are great and it is

exciting and praiseworthy, because if a theory claims

to be a theory of the Universe, it must be equal to the

real world not only in approximate draft, but in every

small detail also.

Author would like to thank Dr. Brian Greene for his

help with this article. References

1. Claude E. Shannon, Warren Weaver. The Mathematical Theory of

Communication. UnivofIllinoisPress, 1963. ISBN 0-252-72548-4

2. C. Shannon, Papers in theory of information and cybernetics. — Moscow: Publishing house of

foreign literature, 1963. — 830 p.

3. H. Nyquist, “Regeneration theory”, Bell System Technical Journal, vol. 11, pp. 126-147, 1932

4. Hartley R.V.L. Transmission of information — Bell System Technical Journal – 7. — 1928. —

С. 535-63.

5. Norbert Wiener Cybernetics: Or Control and Communication in the Animal and the

Machine. — 1948. — Paris, (Hermann &Cie) &Camb. Mass. (MIT Press) ISBN

9780262730099;

6. Léon Brillouin La science et la théorie de l’information (Masson, 1959)

7. Brillouin L. Scientific indeterminacy and information. – Moscow: Mir, 1966.

8. Kadomtsev, Boris Borisovich. Dynamics and information. — Moscow: Publishing house

«Advances of physics», 1999, ISBN 5-85504-010-3

9. L. de Broglie. Ondeset quanta // Comptesrendus de l’Académie des sciences. — 1923. —

Vol. 177. — P. 507—510.

10. C. Davisson, L.H. Germer (1927). “Diffraction of electrons by a crystal of nickel”. Physical

Review 30 (6): 705–740.

11. Schrödinger, Erwin (December 1926). “An Undulatory Theory of the Mechanics of Atoms and

Molecules”.

12. M. Born. Problems of Atomic Dynamics — MIT Press, 1926.

13. Letter from A. Einstein to M. Born dated 12 December 1926 [Max Born,Physics in my

generation, Springer-Verlag, New York (1969), p. 113]. Also: “…Even the great initial success

of the quantum theory does not make me believe in the fundamental dice-game…” — Albert

Einstein, 7 September 1944 (p. 149). The Correspondence between Albert Einstein and Max

and Hedwig Born 1916-1955 with commentaries by Max Born, ISBN 0-8027-0326-7

14. Veneziano G., NuovoCim., 1968, 57A, 190 (also unpublished manuscript by Suzuki M., 1968)

15. L. Susskind, “Harmonic Oscillator Analogy for the Veneziano Amplitude,” Phys. Rev. Lett. 23,

545 (1969).

16. L. Susskind, “Dual-Symmetric Theory of Hadrons I,” IlNuovoCim. 69A, 457 (1970).

17. H. B. Nielsen, “An Almost Physical Interpretation of the N-Point VenezianoModel,”submitted

to Proc. of the XV Int. Conf. on High Energy Physics (Kiev, 1970), unpublished.

18. Y. Nambu, “Quark Model and the Factorization of the Veneziano Model,” p. 269 in Proc.

Intern. Conf. on Symmetries and Quark Models, ed. R. Chand, Wayne State Univ., 1969

(Gordon and Breach, NY 1970) .

19. Y. Nambu, “Duality and Hadrodynamics” Notes prepared for the Copenhagen High Energy

Symposium (1970).

20. Scherk und Schwarz. Dual Model for Non Hadrons. In: Nuclear Physics B. Band 81, 1974

21. Scherk und Schwarz. Dual models and the Geometry of Spacetime. In:Physics Letters B. Band

52, 1974

22. John Archibald Wheeler, Kenneth William Ford. Geons, Black Holes, and Quantum Foam: A

Life in Physics (1998). NewYork: W.W. Norton&Co, ISBN 0-393-04642-7

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