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.”
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.
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.
“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.
The “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.
Comprises “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.
Cultures 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.”
Between 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.