My assumption has always been that Four is one of the “good” numbers: it is the doubling of the binary (Two), which is the root of conciliation and harmony, as well as the source of the term foursquare, which means “standing squarely and solidly.” It is synonymous with stability and anything in a steady-state condition. Where and how, then, does its negative side emerge? Joseph Maxwell said, in his book The Tarot, that all even numbers are passive and seek only to maintain the calm equilibrium inherent in their inertia; odd numbers, on the other hand, are active and implicitly unbalanced, constantly striving to regain their focus. One is restrained and the other assertive. Even numbers are therefore largely quiescent and court stagnation, and the Fours are arguably the most indolent of all, comprising as they do the culmination (and attenuation) of the “First Quaternary” and needing the “nut-cracker” or “can-opener” of the Fives to “let out the stale air” and jump-start them on the next leg of their evolution.
Because of the association with concrete structures and foundations that is conveyed by their expression as the “cube,” the Fours are the quintessential example of this solidity. Four is also the number of “law-and-order,” and as such it has a strong connection to the idea of “justice,” as will be seem in the graphic display below. Its tarot embodiment is the Emperor and in Hermetic terms it imparts the fortunate emphasis of astrological Jupiter, the “Greater Benefic” (think four-leaf-clover). Its doubling (at least in historical decks and the Thoth Tarot) occurs in Justice, the eighth trump card, while its multiplication by Five, an emblem of the disruptive power of Mars, produces Judgement ( Key 20), which is often viewed as an implacable and unavoidable enforcement of Cosmic Law. Both Justice and Judgement would seem to fall within the adjudicatory purview of the Emperor (the harsher flip-side of which can be seen in the numerological link between the Chariot and the Tower), so the extension seems logical.
The minor Fours all carry at least a whiff of inertia. The 4 of Wands is sometimes characterized as a “celebration,” but on closer inspection it looks like the people in the image are just idly promenading and making no attempt to leave the comfort of the castle grounds even though there is an open portal beckoning them. The 4 of Cups is the epitome of ennui (at least in the RWS version) and portrays a surfeit of rather somber emotion; the obviously bored (or weary) man can barely raise his hand to the proffered cup, and seems to be saying “Oh, God, not another one!” The 4 of Swords is placid in the extreme and is usually seen as a period of recuperation after struggle. The 4 of Pentacles seems to display intense paranoia about financial security, as if any amount of coin would not be enough. The Fours in the Thoth deck carry a somewhat different connotation: the 4 of Wands is titled “Completion” and conveys the idea of slightly premature satisfaction with what has been achieved; the 4 of Cups is titled “Luxury” and implies a certain wanton abandon, prefiguring the “Satiety” of the 10 of Cups; the 4 of Swords is titled “Truce” and is indicative of the need to compromise; and the 4 of Disks is titled “Power” and signifies “constant authority and vigilance” (in Crowley’s words) and makes me think of “holding the fort” against a siege; the implication seems to not so much conservation and preservation as an alert watchfulness in matters of security.
Here is an imaginative exercise I conducted to show the alignment of the first nine binary numbers (that is, those divisible by 2) and the first four non-binary numbers (the Nine is numerologically “hidden” in 18) with the principles of Judgement. I placed the first four binary numbers (2-8) at the corners of an inner square; the next four (10-16) at the corners of an intermediary square; the first four non-binary (and coincidentally “prime”) numbers at the corners of an outer square, with numbers 18 and 20 and the center of the array, then proceeded to examine their interrelationship. This is just a bit of creative number-play, a philosophical toy; I doubt there will be any practical use for it.