Mumford: The Road Through Magic (Technics and Civilization, 1934)

The Fountain of Youth
The Fountain of Youth

Between fantasy and science is magic. Magicians were necessary to reach science, as they were the first to both believe in marvels as well as seek to “work them”. It’s difficult to define precisely where magic ends and science begins, but two unscientific qualities of magic are: “secrets and mystifications” and “a certain impatience for results.” Regarding the latter, fraudulent acts of magic were commonplace amongst alchemists of the 1500s, (as is sometimes the case amongst scientists today) for the sake of achieving immediate results. But, what the alchemists and magicians could be thanked for is working with their hands, in their laboratories, with real tools and real substances, and most of all, on demonstration. The alchemists, magicians, and early scientists lacked systems. “As children’s play anticipates crudely adult life, so did magic anticipate modern science and technology: it was chiefly a lack of direction that was fantastic: the difficulty was not in using the instruments but in finding a field where it could be applied and finding the right system for applying it.”

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Von Neumann: The Brain: The Problem of Memory within the Nervous System (The Computer and the Brain, 1958)

firebrainMost likely, the nervous system contains one or more memory organs. We don’t know what or where they are any more so than did the Greeks, who believed it was in the diaphragm. We just know that if it exists, then it must have a great capacity.

In a computing machine, memory size can be quantified. It has a maximum capacity, which can be expressed in bits. A memory that can hold a thousand letters has a capacity of 6,450 bits, for example.

How much? How much!?!?!?! Assuming a 60 year human lifespan, a bunch of neurons, each able to receive 14 distinct digital impressions per second, and that we never truly forget things—we just focus away from them–lands us at around 35 million terabytes of data stored in the brain (aka 2.9 billion iPhones).

What is the physical embodiment of memory? One proposal is that it’s the variability of stimulation criteria—that is, the threshold of stimulation changes depending on frequency of the cell’s use. Another proposal is based on distribution of axons connecting cells—in disuse, an axon becomes ineffective over time, while in frequent use, a stimulation is facilitated by a lower threshold over a given path. Another proposal is genetic memory—chromosomes and their genes have memory elements, so perhaps this is the case in an expanded sense. There are many other suggestions also.

“Systems of nerve cells, which stimulate each other in various possible cyclical ways, also constitute memories”—this would go hand-in-hand with the “strange loops” of Gödel, Escher Bach. Likewise, vacuums-tube machines can do the same via “flip-flops”.

But we have good reason to believe that the active organs do not function also as the memory organs. That’s how early computers (the ENIAC) began, with small memory components, and with time memory components have become larger and “technologically entirely different” than active organs.

Mumford: The Obstacle of Animism (Technics and Civilization, 1934)

Cloaca: A Mechanical Pooping Machine
Cloaca: A Mechanical Pooping Machine

While the natural world came as a great inspiration for technology (hornets nests: paper; rolling logs: wheels; lungs: bellows), technological development could only proceed slowly until the machine could be dissociated from living things. Airplanes were unsuccessful so long as they were designed to have bird (Leonardo da Vinci) or bat (Clement Ader) wings, bodies, and motion; Giovanni Branca’s human-shaped steam-engine was a nonstarter. In the meantime, circular motion, which we find infinitely useful, is only rarely seen in nature—perhaps most often by humans dancing. Dissociating life from actions resulted in the arm becoming a crane, firelight becoming electric light, human and animal work becoming mechanical work.

God, as clockmaker, had created and set an orderly world. If the world was nothing but God’s creation, wrapped in symbolism, and the Church the only path to the absolute, then there was no place for mechanical understanding or development unless Earth and Heavens could be divided. In the 17th and 18th centuries, that division became clear—there, the Heavens and the soul of man, and here, the earth. But even the monastery may be considered mechanical: its sterile environment, separate from the earthly world, temptations removed, strict rules and minimized irregularity as the self is replaced by the collective. A machine. And like a machine, it was “incapable of self-perpetuation except by renewal from without.” Hence, a great number of scientific discoveries came from monks. Further, Christianity’s teachings that the body is sinful, vile, and corrupt, to be mortified and subdued, meant that rather than celebrate the body, as pagans once did (gigantic symbols of fertility, etc.), it would be reasonable to move away from the body and toward the machine. Even as the Church would declare machines the work of the Devil, it “was creating the Devil’s disciples.”
The machine came about most quickly wherever the body was destroyed: monasteries, mines, and battlefields. It came about more slowly in places that gave life: agriculture.

Von Neumann: The Brain: Stimulation Criteria (The Computer and the Brain, 1958)

This is just a picture of some cows. Has nothing to do with this post.
This is just a picture of some cows. Has nothing to do with this post.

Neurons function as basic logical organs, and basically digital organs: if a neuron requires only one incoming pulse (stimulator) to produce a response, then it is an OR organ; if it requires two incoming pulses, then it is an AND organ. These two, along with simulating “no” can be combined in various ways into any complex logical operation.

It’s not simple as this, though: a neuron may have hundreds of synapses connecting it to other cells, perhaps even to one other cell, receiving an enormous number of pulse combinations, and to further complicate things, pulses may be characterized not only by frequency, but also by spatial relations to one another.
Therefore, while there is a stimulation requirement, that is, a threshold, it may be simple, or it may be very complicated. And in the case of receptors, being neurons that respond to stimuli, there may be more than a simple threshold. Further: “if the nerve cell is activated by the stimulation of certain combinations of synapses on its body and not by others, then the significant count of basic active organs must presumably be a count of synapses rather than of nerve cells.”

Mumford: From Fable to Fact (Technics and Civilization, 1934)

fact-checking“‘In the Middle Ages,’ as Emile Male said, ‘the idea of a thing which a man formed for himself was always more real than the actual thing itself, and we see why these mystical centuries had no conception of what men now call science. The study of things for their own sake held no meaning for the thoughtful man. . . . The task for the student of nature was to discern the eternal truth that God would have each thing express.’”
“How far could the mind go in [science] as long as the mystic numbers three and four and seven and nine and twelve filled every relation with an allegorical significance.”
“Unfortunately, the medieval habit of separating the soul of man from the life of the material world persisted, though the theology that supported it was weakened; for as soon as the procedure of exploration was definitely outlined in the philosophy and mechanics of the seventeenth century man himself was excluded from the picture. Technics perhaps temporarily profited by this exclusion; but in the long run the result was to prove unfortunate. In attempting to seize power man tended to reduce himself to an abstraction, or, what comes to almost the same thing, to eliminate every part of himself except that which was bent on seizing power.”

Von Neumann: The Brain: The Nature of Nerve Impulses (The Computer and the Brain, 1958)

GalvanifroescheStimulation of nerve cell is similar to two digital markers: 0 in the absence, 1 in the presence, of electrical impulse. This is a high level description of the more conspicuous aspects of nerve impulses—with nuance, the digital qualities are less clear.
“Natural componentry favors automata with more, but slower, organs, while the artificial one favors the reverse arrangement of fewer, but faster organs.” Thus “the human nervous system will pick up many logical or informational items, and process them simultaneously,” while a computer “will be more likely to do things successively. . . or at any rate not so many things at a time.” The nervous system is parallel, while computers are serial. But the two cannot always be substituted for one another—some calculations must be done serially, the next step must follow the one previous to it, while other calculations done parallel, to be done serially require immense memory requirements.

Mumford: The Influence of Capitalism (Technics and Civilization, 1934)

monopolyThe “romanticism of numbers” directly led to the rise of capitalism, already well-structured by the 1300s, and modern (double-entry bookkeeping, bills of exchange, letters of credit, speculation in ‘futures’) by the 1500s. The result: abstraction and calculation became part of the everyday lives of city people. Business became more abstract, concerned with non-commodities, imaginary futures, and hypothetical gains. Marx: “money does not disclose what has been transformed into it”–everything can be bought and sold. Money is the only thing one can acquire without limit. Money both grew out of a need through trade, as well as promoted increased trade. The continual and fast-paced development of machines can be attributed to the lure of commercial profit.

Von Neumann: The Computer: Characteristics of Modern Digital Machines (The Computer and the Brain, 1958)

computerbrainComprises “active” and “memory” organs (he’s including “input” and “output” as part of “memory).

Active organs: perform basic logical actions, sense coincidences and anticoincidences, and combine stimuli, regenerate pulses to maintain pulse shapes and timing via amplification of the signals.

These functions were performed by (in historical succession): relays, tubes, crystal diodes, ferromagnetic cores, transistors, or by combinations of those.

A modern machine will contain 3,000-30,000 active organs, of which 300-2,000 are dedicated to arithmetic, and 200-2,000 to memory. Memory organs require further organs to service and administer them—the memory parts of the machine being around 50% of the whole machine.

Memory organs are classed by their “access time”—the time to store a number, removing the number previously stored, and the time to ‘repeat’ the number upon ‘questioning’ (that is, write/read times, respectively). To classify the speed, you could either take the larger of those two times, or the average of them. If the access time doesn’t depend on the memory address, it is called “random access” (RAM).

Memory registers can be built of active organs—which, while fastest, are also most expensive (i.e,. built out of vacuum tubes). Thus, for large-memory operations, it’s cost-prohibitive. Previously, relays were used as the active organs, and relay registers were used as the main form of memory.

It is possible, however, to reduce the required memory to solve a problem by considering not the total numbers needed in memory, but the minimum needed in memory at any given time. And if that can be determined, numbers can be distributed between faster memory, and slower memory, based on when they are needed—that is, perhaps all the numbers can be stored on the slower memory, while the necessary numbers of the moment are stored on the faster memory. I assume this is how computers now function—everything is stored on the hard drive, while the absolutely necessary things to the current operations are stored in the RAM.

Magnetic drums and tapes are currently (1950s) in use, while magnetic discs are being explored (and now, 2015, becoming obsolete in favor of SSDs).

Inputs are punched cards or paper tapes, outputs are printed or punched paper—that is, means for the machine to communicate with the outside world.

Words are saved directly to named numerical addresses within the memory of the machine—the address is never ambiguous.

Mumford: Space, Distance, Movement (Technics and Civilization, 1934)

hereford_mapCultures can be differentiated by their unique conceptions of space and time. Europe in the Middle Ages understood space and time in terms of arbitrary, religion-based symbolism. For instance, medieval cartography presents land masses and water as arbitrary shapes (see the Hereford Map), related to each other allegorically. Further, time was understood as something fluid, where in storytelling the past is happening now, so that it’s realistic to the medievel mind to transport a story from a thousand years ago into the present, or as in Botticelli’s The Three Miracles of St. Zenobius, where three different times are presented at once. The result of this was the ability to understand what we presently only understand using science–ship’s drop off the horizon, demons drop down chimneys. Things in the world come and go in the same way as adults come and go in the eyes of children–things are all either mysteries or miracles. All things make sense through religion–“the true order of space was Heaven, even as the true order of time was Eternity.”

boticelliBetween the 14th and 17th centuries, space “as a hierachy of values” was replaced by “space as a system of magnitudes.” In painting, horizons, vanishing points, and visual relationships between things replaced symbolic relationships between things. Size no longer corresponded to divine proportions, but to distance, objects in relationship to one another. This meant a need to understand the world accurately. Space would now be measured in the same way time was measured with a clock. To understand something would be to place it, and to time it–how long to get there? By placing things geographically, there was now an incentive to explore and discover the world. And by graphing out the world, even while incomplete or inaccurate, there was now a basis of expectations, rather than the navigationally useless maps of the Middle Ages. Explorers did not need to hug the shoreline, as in the old maps, but could now launch into the open seas and return to roughly where they began. Eden and Heaven were no longer to be found on maps. The concepts of space and time require us to begin, arbitrarily, with here and now–their conquest is through measurement, and through their conquest, scientific advancement. And in conquering space and time, the importance of numbers and counting grew.