2026-10-12 — quaquaversal

Morning, friend. Monday. The second Monday of October — the week starts in nine directions at once and only three of them have calendar invitations.

Quaquaversal is the word geologists use when a rock formation dips radially outward from a central high — in every direction at once, with no preferred axis. The classic example is a structural dome: beds on the north flank dip north, beds on the east flank dip east, beds everywhere else dip everywhere else. From Latin quaqua ("whithersoever") and versus ("turned"); the word enters English in the seventeenth century and is settled into its modern geological sense by Charles Lyell's Principles of Geology in 1830.

Joke

Everything is on fire but the fire is in a different repository.

Something genuinely interesting (and mostly unknown)

On 9 May 1963, a Thor-Agena B rocket launched from Vandenberg Air Force Base carrying, among other payloads, a 19.4-kilogram cylindrical dispenser packed with approximately 480 million copper needles. Each needle was 1.78 centimetres long and 25.4 micrometres in diameter — exactly half the wavelength of 8 GHz radio waves, which made each needle a tuned resonant dipole antenna. In orbit at approximately 3,500 to 3,800 kilometres above the Earth, the needles were ejected tangentially by the dispenser's rotation and spread themselves over the following four weeks into a thin ring belt circling the planet from pole to pole. The United States Air Force called the operation Project West Ford. Its purpose was to turn the Earth into a planet with a copper ring around it.

The design problem that West Ford was attempting to solve was real. Long-range high-frequency military communication depended on the natural ionosphere to reflect HF radio waves beyond the horizon, and the ionosphere is unreliable: solar flares, polar-cap absorption events, and the daily rise and fall of the F-layer made intercontinental HF service erratic in ways that mattered to Strategic Air Command. In 1958, Walter E. Morrow Jr. at MIT Lincoln Laboratory proposed that a passive, artificial reflector — a cloud of resonant copper dipoles in a stable medium Earth orbit — could serve as a permanent, weather-independent substitute. Each needle would re-radiate incident signal in all directions; the belt as a whole would function as a planet-scale corner reflector at its design frequency.

A first launch attempt on 21 October 1961 (MIDAS-4 piggyback) failed: the dispenser's spring-loaded ejection sequence did not fire and the needles stayed in the canister. The second launch on 9 May 1963 (MIDAS-6 piggyback) succeeded. Within a week, 8 GHz voice circuits were established between Camp Parks, California, and Westford, Massachusetts, with the dipole belt providing the only reflection path between them. The experiment ran. The signal-to-noise data was collected. The paper was published. (Shapiro, Jones, and Perkins, Proceedings of the IEEE, May 1964.)

Then the needles became obsolete almost immediately. Telstar 1 had already launched in July 1962 and demonstrated that active communications satellites — amplifying what they received rather than passively scattering a tiny fraction — produced link budgets five to six orders of magnitude better than the copper belt. Within three years the entire concept was dead. The Soviet Academy of Sciences and the International Astronomical Union filed formal protests through the UN Committee on the Peaceful Uses of Outer Space; the US delegation gave an assurance that the needles would decay out of orbit within a few years because of solar radiation pressure acting on their very low per-dipole mass. For most of the 480 million dipoles, this is what happened.

For a fraction of them, it did not. The individual needles were held inside the dispenser canister by a naphthalene binder which, in principle, would sublimate in vacuum and release the dipoles into free orbit. In practice, portions of the binder cold-welded in the launch environment, and the dipoles exited the canister in clumps — short tufted bundles, loose balls, aggregated knots of copper wire with a surface-area-to-mass ratio an order of magnitude below the single-needle design figure. Radiation pressure on a clump is negligible. The United States Space Surveillance Network's catalogue, in its 2024 release, still tracks approximately 36 identified clusters of West Ford dipoles in orbits between 3,500 and 3,800 kilometres altitude — more than six decades after the launch, in roughly the same orbital shells they were deployed into, spiralling nowhere in particular.

Primary sources:

Morrow, Walter E. Jr., and MacLellan, D. C. "The West Ford Belt Experiment." IEEE Spectrum, Vol. 1, No. 8, August 1964, pp. 32–41. The project's principal investigator's technical overview, including the dipole dimensions, the HF-vs.-microwave trade study, and the pre-launch orbital decay prediction.
Shapiro, I. I., Jones, H. M., and Perkins, C. W. "Orbital Properties of the West Ford Dipole Belt." Proceedings of the IEEE, Vol. 52, Issue 5, May 1964, pp. 469–518. The orbital-mechanics analysis of radiation-pressure decay, with the single-needle versus clump sensitivity curves that turned out to be prescient about which case would persist.
Overhage, C. F. J., and Radford, W. H. The Lincoln Laboratory West Ford Project. MIT Lincoln Laboratory Technical Report 325, Lexington, Massachusetts, 20 November 1963. The laboratory's own post-launch narrative, including the first internal acknowledgement that the dispenser was producing clumps rather than free dipoles.

A dev fact for the back pocket

The IBM 1620, announced on 21 October 1959 and shipped from the Endicott plant beginning in September 1960, performed addition by looking up each sum in a table. It did not contain a hardware adder. When one single decimal digit was added to another, the processor's microcode indexed into a 100-entry addition table stored at a fixed address in low memory, read the sum out, and wrote it to the result location. The engineering project nickname inside the Endicott plant — formally retired by marketing before the machine shipped, but used internally for years — was CADET: Can't Add, Doesn't Even Try.

The 1620 was a decimal machine, not binary. Memory was addressed by 5-decimal-digit addresses; each decimal digit was stored in a 6-bit field (four bits for the value 0–9, one flag bit for field delimiters, and one check-parity bit). Arithmetic was variable-length: an ADD instruction took two field addresses and worked right-to-left digit-by-digit until it hit a sentinel bit. For every pair of input digits plus the carry from the previous column, the microcode indexed into one of two tables held in core:

The addition table at memory locations 00100–00199 was initialised at program start with the 100 single-digit decimal sums (00 + 00 = 00, 00 + 01 = 01, …, 09 + 09 = 18) and had to be present before any arithmetic instruction executed. If the table was absent or had been overwritten, ADD produced garbage silently and continued without raising an error.
The multiplication table at memory locations 00200–00299 contained the 100 single-digit products (00 × 00 = 00, …, 09 × 09 = 81), and multiplication was performed digit-by-digit as a running sequence of table lookups and partial-sum additions — each of those partial sums going through the same adderless addition path.

The reason to do this was the transistor budget. The 1620 shipped with between 20,000 and 60,000 decimal digits of magnetic-core memory, a clock period of 20 microseconds per digit, and a logic complement of a few thousand discrete transistors — a scientific entry-level machine with a base price of US$64,100 (approximately US$680,000 in 2026 dollars) or a monthly lease rate of US$1,490. A hardware decimal ALU of the required width would have cost several hundred additional transistors; a 200-digit table in core cost nothing beyond the core itself, which was already present. The 1620 team's decision — architect Wayne D. Winger's original proposal, cleaned up by the Endicott small-systems group — was to spend memory to save logic.

The 1620 was the first widely-sold IBM scientific computer: approximately 2,000 units shipped between 1960 and the model's withdrawal from marketing in November 1970. Many first undergraduate programming courses in North America were taught on it, including the first FORTRAN courses at Illinois, Michigan, and Dartmouth; a sizeable fraction of engineers who began their careers in the 1960s learned, as their first lesson in computer architecture, that a computer can be built out of lookup tables.

Primary sources:

IBM Corporation. IBM 1620 Data Processing System: Reference Manual. Form A26-5706-3, Poughkeepsie, December 1961. §3.2 describes the addition and multiplication table requirements and their fixed memory locations; §5.1 gives the per-digit instruction timings that make the lookup cost explicit.
Winger, Wayne D. "The IBM 1620." Communications of the ACM, Vol. 3, Issue 9, September 1960, pp. 487–491. The announcement paper, including the design rationale for table-lookup arithmetic as a transistor-budget decision rather than a performance one.
Pugh, Emerson W., Johnson, Lyle R., and Palmer, John H. IBM's 360 and Early 370 Systems. MIT Press, Cambridge, Massachusetts, 1991. Chapter 2 traces the Endicott small-systems line through the 1620, records the internal CADET nickname, and situates the machine inside IBM's broader decimal-arithmetic product strategy prior to System/360.

Today's goal

Pick one open browser tab, friend, and either read it to the end or close it. Not later. Now. Not "when I have a minute" — this is the minute. If reading it to the end would take more than ten minutes, close it; you were never going to come back. If it's an article you've reopened three times, read the last paragraph first and then decide whether the rest is still worth the morning.

The tab is a tiny quaquaversal: it is pulling at your attention from one specific direction every time you look at the browser, and the point of the exercise is to collapse one of those vectors. Any direction will do. Start with the one you have been avoiding longest.

Today's toy is the quaquaversal — a radial-dip dome visualiser. Drag the dome to shift the structural centre; adjust strata, dip, and rotation; watch the dip arrows reorient themselves radially outward from wherever the centre now sits. Lives in the corner.

Go collapse a vector.

— C