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waves paper online (waves_paper#1)

Clock speeds

[Martin Howse. Berlin July 2006]

The SN54LS/74LS13 and SN54LS/74LS14 contain logic gates/inverters which accept standard TTL input signals and provide standard TTL output levels. They are capable of transforming slowly changing input signals into sharply defined, jitter-free output signals. Additionally, they have a greater noise margin than conventional inverters.

Each circuit contains a Schmitt trigger followed by a Darlington level shifter and a phase splitter driving a TTL totem pole output. The Schmitt trigger uses positive feedback to effectively speed-up slow input transitions, and provide different input threshold voltages for positive and negative-going transitions. This hysteresis between the positive-going and negative-going input thresholds (typically 800 mV) is determined internally by resistor ratios and is essentially insensitive to temperature and supply voltage variations.

[Data Sheet. Schmitt Triggers, Dual Gate/Hex Inverter. Motorola. p. 1]

We can write about waves but there is also a writing which makes waves; the circuit diagram, replete with numbers, values and text.

An integration function, itself in the circuit, serves to integrate such a diagram with the text here. The circuit diagram is IN the text not purely as a description of a construction process or experiment.

Electro-mysticism is a materialism and only "gathers that which is" ("nimmt" nur "auf","was ist"). Circuit diagrams and bodies relate to each other as the front and reverse side of the same piece of paper, recto and verso, then "Not even in the worst times of night, with pencil words on your page only Delta-t from the things they stand for ?

[Friedrich Kittler. Pynchon and electro-mysticism. Translated Kathrin Guenter and Martin Howse. xxxxx. Berlin. 2006. p. 450]

A device. A description which could mime the opening quotation; a technical language which is always, to anticipate the paranoiaic turn of all technology, saying something else, talking of a something else addressed in the conspiracy-theory-laden terms of magic. Electromysticism after Friedrich Kittler - the circuit diagram as electro-mystic mediation or trance assembly "mediating the 'passage' between senses," a notation parallelled by musical staves. And there is nothing more to be said than to refer to Thomas Pynchon's Gravity's Rainbow; a circuit-laden manual for historical and contemporary electro-mysticism in relation to Sadean life coding. The mapping is too dense here to extrapolate the thin (joyful) morning flight path vapour (rainbow) trail of the rocket (one half of a sine wave - rectified by the diode to come), to extrapolate into a heavily computed Hiroshimic mushroom cloud. Data, figures always modulated; those statistics.

In the above opening quotation, speeding up (in time) these slow transitions or modulations. The circuit diagram is sketched out as follows and precedes.

Two texts modulate each other, or make use of multiplexing capabilities; time division multiplexing and frequency division multiplexing spell out the two locked and somewhat fictional domains addressed within a study of waves. Yet how to determine which is the carrier, approximating in some way noise to be discarded after Turing's cryptographic model. Noise repeated and maintained; equally maintaining the deciphered message, equally important the two copies yet both are ultimately discarded. Frequency modulation across a large time window (again Turing, this time with his halting problem) and according to statistical methods, or more obviously amplitude modulation relating to intensities. Two texts, which proves more descriptive or functioning more as code is to be determined. Modulation implies a meta or quotation in some respects, equally a form of modulation crossing an exchange place of analogue and digital, a modulation which can be called digitisation or analogue to digital conversion; the first stop on the interface train as intensities cross domains.

As an aside, and there will be many excursions following a digressionary model after Thomas de Quincey, that fiction, or more specifically the novel, rewritten after Gravity's Rainbow, descriptive of the unification of one primal wave, rewritten as conspiracy theory or (self-)surveillance technology, truly writes the story of the so-called (this) twentieth century as an atrocity exhibition commanding by language whose bodies. A story undertitled by the title Possession.

In talking of discretisation, and under the twin, or even triplet references, the first being to the famous Leibnizian double integral sampling trajectory for the first time, in flight miming the V-2 rocket, our fundamental wavelength with reference to delta-t and temporal bandwidth, the second, well-twinned in terms of a re-written, sexual-magical history of computation, the now clock speed realised transitions of state effected by Alan Turing's halting/starting tape world rendition, and the third, the 24 frames per second of the film camera, adjustable memory, in talking of discretisation as a modulation, a transition from 0 to 1, from 1 to 0 again dictated by clock speed and affected by those Schmitt triggers we encountered in the opening quotation. The digital is a modulation with an (economic) effect dictated by a necessarily falsified instruction set, and with the following always backgrounded in the Black Mariah studio (Edison):

During flights the camera photographed the needles swinging on the gauges. After the flight the film was recovered, and the data played back... There has been this strange connection between the German mind and the rapid flashing of successive stills to counterfeit movement, for at least two centuries - since Leibniz, in the process of inventing calculus, used the same approach to break up the trajectories of cannonballs through the air. And now Pokler was about to be given proof that these techniques had been extended past images on film, to human lives.

[Gravity's Rainbow. Thomas Pynchon. New York. 1973. p. 412]

Both this integral and differential calculus, developed by Leibniz in the 1670s, lead directly into monadology, a subject only hinted at over twenty years later, by way of the digital treatment of time and space. Time and space were no longer conceived as substances, but rather could be seen as constituted by an imaginary element; the universe as dream, as simulation.

The Elizabethan magus John Dee sketched some of the first imaginative designs for this general purpose symbolic CPU. Leibniz further mapped out the field in his baroque Monadology making full use of the ever present components of the absolute ascending binary permuting incessantly through the power of the combinatorial; integration, the double integral and a breaking down into the discrete proving essential for a component-based architecture which could be mapped over Von Neumann's CPU design replete with self-confessed easter-egg decorations; the blossoming mushroom cloud again fulfilling a design which cannot be laid down in silicon but which occupies the same production relation to energy or light (waves). A speed, a raw figure dictating wavelength and impacting on aerial design. Radio-telescopy directed back at the planet's (brighter than one thousand) sun(s) spots.

A transition from 24 fps to 2.7 GHz, TTL or CMOS modulation within an economy, a (circular) system of production dictated again by the very wavelength of light.


Modulation and demodulation apply equally in the referenced analogue and digital domains; indeed marking an equivalence. An antenna tied equally to software, with reference to the marketing-speak of projects such as GNURadio, and to hardware. An equivalence driven by increasing clock speeds, an increasing bandwidth with respect to frequencies which also acts as a driving force in the opposite direction; minimal clock speeds of eight bit engines rendered visible as obscurantist trends of hardware are exposed by such a disintegrated border with the antenna, the simple detector circuit or one way wire of a detected and always present waveform picked out (and demodulated). The so-called digital is always a question of timing, of clock speeds, of modulation (astable multivibrator, flip-flop). Radio becomes a new reference for (expanded) software.

A frequency spectrum (up to half the sampling rate according to Nyquist's dogged theorem) is converted from the analogue realm to the digital - for further analysis or re-interpretation (re-modulation perhaps as audio waves or retransmission - a vast chain of processes always crossing that false divide, a divide mimicked in apparition by the ghosts of software and hardware. analogue and digital again) - analysis within software, selection of bands of frequencies for interrogation all thanks to the crucial Fourier transform - a taking apart and handily in reverse - for we are far from the modulation with noise of the cryptographic - a putting back together.

The link between cybernetics and Gravity's Rainbow is underwritten by this entropic slur, the time-smudge of this Fourier transform, the elided vowels of noise and of deciphered communication; an Enigma, the German wartime cipher machine, decoded as system by Turing's Bombe and Oriental Goddesses, practical applications of the infinite mathematics exposed by the universal Turing machine. Noise, as highly entropic in one sense and lacking information content, proves impossible to decode. The silence of the Turing machine decryption, with any cipher system involving an intermingling of instructions with data viewed as a Turing machine, is played off against the noise of war, an escalatory passion production of paranoid (read Gnostic) auto-destruction.

Always returning to (war-time) paranoia, extending across so-called life; radio is implicated as part of the entropically-biased "system" which Pynchon reveals with Gnostic and cynical delight or pure joy (in that vapour trail glanced by morning light):

Taking and not giving back, demanding that 'productivity' and 'earnings' keep on increasing with time, the System removing from the rest of the World these vast quantities of energy to keep its own tiny desperate fraction showing a profit: and not only most of humanityâ€”most of the World, animal, vegetable and mineral, is laid waste in the process.

[Gravity's Rainbow. Thomas Pynchon. New York 1973 p. 410]

Paranoia and Gnosticism, and revelation; the digital as a hiding or obscuring of process; a falsehood of software further reinforced by a faked exposure: "these ones and zeroes are physical voltages after all."


Physical voltages, electromagnetic waves, ones and zeroes in modulation which can be demodulated and operate as a system, operating in a blindness to opcodes (operational codes); a different wavelength to the visible (radio waves have much longer wavelengths; wavelength as the speed of light divided by frequency, wavelength as a distance travelled during one oscillation). Clock speed wavelength.

We can envisage tiny bit-broadcast circuits at any frequency; preferably as low as the oldest digital circuitry invited into a space dominated by 50 or 60 Hz harmonics. Making that space apparent, through a question to meaning.

What might at first appear as a purely technical description; if we could ever begin to unravel that which is purely technical, the exposition of a series of experiments, as another writing; specifically untying it from what?

The simplest (AM - amplitude modulated) radio receiver circuit consists of a diode between earth (the ground itself) and antenna with a human insert (an ear assisted with a piezoelectric earphone) across the divide, across that one way street of current flow. Transmission is a simple matter of modulation above all else, making use of common electronic components as described below, with transistor or crystal driven oscillator accounting for a Hertz frequency measurement equally of clock speeds, and a simple transformer taking care of modulation - the interference and distant interface of two wire coils with electromagnetic effects initiating a transition. Yet, an even simpler FM (frequency modulated) transmitter can readily be constructed using the brother of our opening Schmitt trigger as modulation device, the 74LS13 CMOS chip. A variable capacitor, to come, dictating frequency for a part subverted across the dual domains (digital to analogue).

Demodulation, a reception commonly known as radio, and for our bit-radio could be described along a route as follows, a circuit walk:

1] The aerial.

The antenna, a length of wire, equally well used to transmit a modulated signal, against which the electromagnetic waves or field impacts, inducing alternating current and thus voltage, at the same frequencies as those translated or transceived waves. An impact, again along the opposing side of the street which stands for an architecture of transmission, city circuit, which mimes the impact of our alien opcode on the CPU, on the real. Voltage induced by instruction sets.

Or, indeed if we confine ourselves to the realm of stock computer hardware and free software, all we need is such an antenna and an amplifier paired with an ADC (Analogue Digital Convertor) - in short, a simple soundcard. Bandwidth is restricted, after Nyquist, by the sampling rate of the card. The ambitious can examine the use of the common Bt878A chipset (familiar to early TV card proponents) to achieve digitising at approximately 448Khz. Others will be content to examine the ELF (Extremely Low Frequency, 3Hz to 30Hz) and SLF (Super Low Frequency, 30Hz to 300Hz ranges), preferably in remote locations unscarred by the 50 Hz power line transmission and associated harmonics. The free software package Baudline provides excellent Fourier-led visualisation of activities in all frequency ranges.

2] The tuner. A coil of wire (or inductor) and a variable capacitor.

The capacitor - again referring to software, a separation of two domains, which equally allows for filtering and bandwidth reduction. In this instance, a true distance between two conducting points. Remote magic again of radio.

The coil and resonator together form a 'tank' circuit - resonating bath waves; resonating at the frequency of the radio station to tune in.

The variable capacitor can readily be constructed from kitchen foil and cardboard, or, by inserting the two foil sheets into a book, such as Gravity's Rainbow - the distance adjusted through the addition of more separating pages.

At the same time the capacitor can be used to tie our flight to ground, maintaining oscillation of intensities, by solely letting pass alternating current, with a resistance provoked by frequency initiating filtering activity. DC (direct current) flight is ruled out in favour of a twin of alternation.

3] The detector, a diode.

As stated - a Germanium diode, or for true electro-mysticism and referring to the war-time experiments young Pynchon may have undertaken - the soldier's rusty razor blade or chunk of iron pyrite.

The poorly titled detector picks the audio frequencies out from radio wave by rectifying the waveform. The waveform carries two (the dual) signals of equal positive and negative value, cancelling each other out in mechanical terms for an electromagnetic loudspeaker.

The Alice diode, a looking glass reversibility memento, (that one way street, supposedly, though less than perfect and presenting leakage in an opposing direction) erases the symmetry, the above and below of the wave to present a series of rainbows.

Such Alice through the Looking Glass capabilities, better visualised in terms of a corkscrewed murder weapon instead of a razor, also enter the digital domain. In the case of the diode, a voltage drop across the diode itself causes 'degeneration' of the signal. We cross the threshold back into the denoted realm of the analogue as: "This can ultimately cause a 1 to be interpreted as a 0". [Digital Electronics. William H. Gothmann. New Jersey. 1982. p. 106]

A transistor or two can equally well pursue the task of detection.

4] The filter. Demodulation.

The high (radio) frequencies are removed to demodulate the audio (intended signal). Again, a, in this case fixed value, capacitor of say 0.001 uF (microfarads) is used.

5] Amplification. And electromagnetic expression.

Making audible and visible, voltages are increased - and finally rendered audible through an electromagnetic conversion.

The transistor, in terms of simple chemical constituency (Germanium, or any material acting as a semi-conductor), a sister to the Alice diode, not even inverted but possessing one more leg and thus proposing a more complex one way street, or architecture; an Alice-alike sister which operates as a valve for current flow in one direction, better typified as an enlarging and mirror operation. The magnified looking glass or pill. As an aside, it's commonly noted that a transistor's, or rather semiconductor's operation can well be explained thanks to quantum physics and more specifically Wolfgang Pauli's exclusion principle which states that "no two particles can exist in the same state at the same time." It's a case of (rabbit) holes and electrons. The un-twinning of Alice, never an anti-Alice relates to an assymmetry. And on the other hand, our unfolded mushroom cloud CPU sits on a Manhattan project driven path direct from Pauli's exclusion principle, and through code-led simulations designed to provoke exactly a symmetrical blast; twinned electrons. That there is always an operation with the double, the moving hole of twin electron lack. All electrons are twins.

Base (one leg) current controls collector current flow (another leg), with the third allowing this flow to ground. One circuit (first) controls the other (second) as a changing base current alters the resistance of common to emitter (connected to ground). Amplification using this so-called common emitter, or grounded emitter, arrangement can readily be extrapolated.

The transistor further marks (its own) threshold as introductory electronics transitions into the gates of the digital; physical limitations equally imposed on the noise-free world of software.

"... limitations include rise and fall times, delay times, input and output voltage levels, noise immunity, and power dissipation"

[Digital Electronics. William H. Gothmann. New Jersey. 1982. p. 104]

The analogue thus enters the (preventative, literally choked) digital domain as an encryption function, a hiding; re-enters precisely as noise which can serve to modulate a wishful hidden message. Either the diode, reverse biased, or by way of a transistor, again reverse biased in so-called avalanche noise mode, we can generate random bits, transitioning our analogue noise signal into the digital square waveform by way of the 74HC14 Schmitt trigger described in the opening quotation. The (Gnostic) circle is closed with connection of such apparatus to the bit transmitter operating at a frequency reflecting the ancient eight bit computer, itself, replete with wiring, itself a healthy transmission device. Flip-flop extension of 50 Hz logic bides clock speed time for the 'system' and completes the circuit here.