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This course  deals with the general aspects of a transmission system, which consist of the source of information, the transmitter, the channel, the receiver, and the final destination of the message. The definition of information and a quantitative measure of information are given. The statistical properties of the source, its entropy, and the rate at which information is produced by the source are discussed. The transmission of primary signal functions into secondary signal functions at the transmitter, the capacity of the channel to transmit the secondary signal function in the presence of channel noise, and the possibilities of recovering the primary signal function at the receiver are studied.
The over-all performance of transmission is discussed as to fidelity considerations and the effective rate of transmission.
These principles are applied [End Page ] to pulse-code modulation as an example of modern transmission of information. Central to designing a transmission system to communicate information efficiently is the concept of entropy as developed in information theory, especially by Claude Shannon.
A four-thousand-level course would have been reserved for advanced students, and Pynchon switched majors from engineering physics to literature after his first year. His own omnivorous curiosity and reading, as well as his sense of play in using recondite concepts, doubtless provided ample stimulation for the exploration of entropy in the various guises discernible in his texts.
One of the new sciences born of the rich research funding of the war was cybernetics, a discipline heralded by Norbert Wiener who recoined the name to designate a field soon in turn to split into a myriad of new applications and specialties in the postwar science boom. Unlike some other major ideas in modern science, understanding entropy is not made easy by using physical models. Like many other concepts from engineering physics and cybernetics, entropy is an abstraction based on mathematical analysis of the activity of indeterminate microstates comprehended only in terms of the probabilities associated with large ensembles of separate constituents molecules in thermodynamics, bits of information in communications.
Some grounding in the mathematical concepts of statistical thermodynamics is doubtless required in order to feel secure in understanding entropy. Since I wrote this story I have kept trying to understand entropy, but my grasp becomes less sure the more I read. But the qualities and quantities will not come together to form a united notion in my head. As formulated by the second law of thermodynamics, in any interaction exchanging energy, the amount of thermal energy convertible to mechanical energy is diminished.
In such interactions, entropy—a measure of un usable energy—increases. Thus in any interaction exchanging heat, thermodynamic entropy increases, and the energy available to do mechanical work to serve human purposes decreases.
From this inevitable degradation of usable energy comes the late-nineteenth-century melancholia of a heat-death awaiting the universe, as all the available useful energy levels out into a cosmic stasis of inert equilibration. So inescapable did this frigid end of the cosmos appear that the chemist-turned-novelist H. Wells depicted the oblivion of all thermodynamic motion in the revised conclusion to The Time Machine as a universal cessation of physical activity.
Thus, in its historical discussion, the OED notes that the earliest English users of the term, Peter Guthrie Tait and Maxwell, domesticated it to signify a positive state that reversed what Clausius intended, using entropy as a measure of the energy available for work.
As a measure of the energy escaping into forms of heat unusable for mechanical purposes, entropy proved to be a powerful concept for developing modern thermodynamics. My argument here, however, is that as an author Pynchon is less interested in entropy in its thermodynamic manifestation, than in the form developed in twentieth-century information theory.
One having to do with heat-engines, the other to do with communication. It was a coincidence. Nefastis to the contrary, the connection between entropy in thermodynamics and in communications theory is more than a coincidence. Hartley in the s through the culminating genius, Claude Shannon, in the s and s, employed mathematical theorems resembling some of the basic equations of Boltzmann to establish modern communications theory.
This differentiation can be used to perform work, as in the system of a steam boiler and condenser where the heated steam expands, drives a piston, and then cools down. However, in information theory, entropy does not signify thermal motion directed toward running steam engines. The entities subjected to statistical study in information entropy are not molecules but whatever units figure in the communications system.
But both for molecules and for units of information, entropy concerns the statistical behavior of very large numbers of separate entities. Entropy characterizes the extent to which these large numbers of units display basically similar or different behaviors, and thus it measures what degree of certainty we can attain about the likely history of a single given molecule or bit of information.
The larger the number of different information units—and the more equal the probability of encountering any one unit relative to the others—the less certainty we can have about receiving any one specific unit. Thus, as with heat engines in thermodynamics, entropy in information theory counterintuitively quantifies and thus confers value upon the randomness—not the order—of the closed system.
Entropy signifies and prizes our lack of knowledge about any specific unit. Shannon and his colleagues went one step further in explicitly denying that information was by definition meaningful. The word information, in this theory, is used in a special sense that must not be confused with its ordinary usage. In particular, information must not be confused with meaning. The greater the entropy, the greater the freedom of choice and the greater the overall information that may be communicated.
But it follows that greater [End Page ] freedom to choose among the various units conveying information presupposes greater uncertainty at the receiving end of which units may in fact be selected for transmission. The greater this freedom of choice, and hence the greater the information, the greater is the uncertainty that the message actually selected is some particular one. Thus greater freedom of choice, greater uncertainty and greater information all go hand in hand.
At high entropy, then, the possible message units that can bear information are as close to being equally likely of occurrence as possible. And the higher the possible number of choices among initial messages—the fewer restrictions imposed on choice—the less likely it is that any one message will receive preference over another. We have less knowledge about any specific message being favored over any other.
Such a system, with many possible messages, provides the potential for high information flow. High entropy accompanies this greater freedom of choice and greater uncertainty.
Information theory, then, is concerned with the consequences in communications of increasing or decreasing the ensemble of different message units of known probability available for transmission as well as with encoding and decoding those units to minimize the effect from noise. The units in themselves may be arbitrary and may mean nothing at all: the measure of success in an information system has nothing to do with the subjective value of the messages communicated to a human audience.
For example, consider an imaginary message system made up of a single sentence, of any length or degree of complexity you like. In [End Page ] this information system the only choice is whether or not to communicate the sentence.
The degree of freedom is minimal: either the sentence is sent, or it is not. Differentiation, choice, and entropy are low. Then consider an information system constituted of all the words in the sentence, which can be arranged in any fashion, language, or code. And of course if we make the basic units the letters of the words rather than the words themselves, the freedom, uncertainty, and information increase again. Correspondingly, the demands on the reader to sort out the information—to filter the intended message from the unintended noise however introduced —is all the greater.
Vineland is an interesting counterexample to this thesis, as argued below. In Pynchon, and in other energetic information systems, the reader literally must be prepared for anything. In such high-entropy information environments, the equal probabilities for a large number of messages means that the uncertainty of what comes next is maximal.
Thermodynamic entropy always either remains the same or increases in an interaction; high thermodynamic entropy is associated with equilibrium and stasis. In contrast, high information entropy connotes maximum freedom to choose from among many different units of information. In both cases, larger numerical values for entropy indicate greater uncertainty about the microstates of the constituents of the macrostate, but the consequences are different: for thermodynamics, higher values suggests stasis and inactivity, while for information, higher values promise greater potential for information transmission.
In their insulated apartment, Callisto dictates his memoirs registering his despair over the universal heat-death ordained by the second law, while the neurasthenic Aubade minds her feeble energy. So successful are they at preserving their isolation and forming a closed system that they exchange no energy—Callisto cannot save the dying bird he cradles because he cannot give of his own warmth to save its life.
They literally do no work, having no available energy to expend. Callisto and Aubade communicate little, and are approaching emotional as well as physical death. The three factors that Weaver cites as signs of high information entropy—freedom, uncertainty, and information—all register low. Thus, in terms of information, their source entropy is low.
In terms of information entropy, this ensemble is at a high level: the microstates defining the individuals are numerous and unpredictable. They have available the potential to party, to communicate, and, for Mulligan himself, to reflect on the randomness he has created and how he might best serve himself and the others by making some use of it.
Thus they have the capacity to do work, because they are far distant from stasis or equilibrium. Despite—or one might argue because of—his chaos, Mulligan thus is able to perform useful work, and in the third-to-last paragraph of the story he appears like a deus ex machina to do so:.
So he decided to try and keep his lease-breaking party from deteriorating into total chaos: he gave wine to the sailors and separated the morra players; he introduced the fat government girl to Sandor Rojas, who would keep her out of trouble; he helped the girl in the shower to dry off and get into bed; he had another talk with Saul; he called the repairman for the refrigerator, which someone had discovered was on the blink.
This is what he did until nightfall, when most of the revellers had passed out and the party trembled on the threshold of its third day. One visitor is Saul, apparently an engineer familiar with information theory. The end of their communication is sadly predictable. Irrelevance, even. All this is noise. Noise screws up your signal, makes for disorganization in the circuit. You never run at top efficiency, usually all you have is a minimum basis for a workable thing. Words have given way to violence; fists and flung books become bits of information lacking all meaning.
We last see Saul grasping for the monster tequila sour that Meatball has just mixed. Soon his world will be nothing but meaningless noise. Weaving such a fabric together by allusions to thermodynamic and information entropy is at best an exercise in metaphysical wit. But in the end, the theories from science serve merely as clever intellectual allusions.
Eliot that in his Introduction to Slow Learner he laments having injected into other early stories. Vineland presents a low-entropy environment inhabited by people very like each other. They are little differentiated in their energy levels, and thus have little that is novel or arresting to say or do.
Willingly they submerge their differences in a TV-dominated culture in which their mental energies sink to a lowest common denominator of sitcom reruns. In Vineland , even the crucial energy distinction between life and death is reduced to the point where whole colonies of the living-dead the Thanatoids spring up around the countryside. If mediated lives, he figured, why not mediated deaths? Brock Vond, the high-energy manipulator of the novel, uses his insight into the unconscious desire of self-declared rebels to lose their differentiation to manipulate all around him:.
To Mondaugen the question is the source and meaning of these sferics, a riddle in terms of the totality of a communications system.
The essential parts of such a system were formulated by Claude Shannon [End Page ] as a relationship between transmitter, channel, and receiver his structure became a model for later texts, including Cornell course The information source selects a desired message out of a set of possible messages. The transmitter changes this message into a signal which is actually sent over the communication channel from the transmitter to the receiver.
The receiver is a sort of inverse transmitter, changing the transmitted signal back into a message, and handing this message on to the destination.
In the process of transmitting the signal, it is unfortunately characteristic that certain things are added to the signal which were not intended by the information source.
Read “Entropy,” a short story by Thomas Pynchon
This course  deals with the general aspects of a transmission system, which consist of the source of information, the transmitter, the channel, the receiver, and the final destination of the message. The definition of information and a quantitative measure of information are given. The statistical properties of the source, its entropy, and the rate at which information is produced by the source are discussed. The transmission of primary signal functions into secondary signal functions at the transmitter, the capacity of the channel to transmit the secondary signal function in the presence of channel noise, and the possibilities of recovering the primary signal function at the receiver are studied. The over-all performance of transmission is discussed as to fidelity considerations and the effective rate of transmission.
Thomas Pynchon, Newton’s Second Law and Entropy
This page of the essay has words. Download the full version above. Introduction Pynchon deals in his work with a complex concept of entropy and reveals how certain trends in our contemporary culture marked by massive consumerism, have a tendency that is similar to that of an entropy. The two main scientific types of entropy, thermodynamic and that of information theory, are deeply explored by Pynchon in his early short story Entropy.
"ENTROPY" by Thomas Pynchon
In the bootleg edition, Pynchon went even further. Meatball Mulligan restores order and momentum to his lease-breaking party, which had reached its third day and was running down. However, this popular sense that entropy and force are opposites, that entropy suggests something negative and passive, while force is positive or active, is technically not correct. As Pynchon notes in his Slow Learner introduction, the idea of entropy was first developed by the 19th century physicist Rudolf Clausius, who built on earlier ideas of the French engineer Sadi Carnot. Carnot and Clausius were both trying to understand how heat energy is transformed into useful work, such as when steam drives a piston in an engine.