The numbers from one to twelve in the second book

The second book of the De occulta philosophia opens with praise of mathematics. Without it, Agrippa argues, none of the magical arts can be understood, because the celestial world is ordered according to number, weight and measure. He recalls the biblical Book of Wisdom, which says of God: «omnia in mensura et numero et pondere disposuisti», thou hast ordered all things in measure, number and weight. On this basis unfolds a long series of chapters, one for each number from one to twelve, which form the arithmological heart of the work.

The Pythagorean inheritance

The idea that numbers have a qualitative as well as a quantitative meaning goes back to the Pythagoreans, who saw in numerical ratios the foundation of the harmony of the cosmos. Plato, in the Timaeus, had built the soul of the world out of arithmetical proportions. In late antiquity this tradition had developed into arithmology, reflection on the symbolic properties of numbers, found in authors such as Nicomachus of Gerasa and in the Theologumena arithmeticae attributed to Iamblichus.

Christianity took up this inheritance. Augustine, Boethius and many medieval commentators on the Bible read hidden meanings into the numbers of Scripture, from the six days of creation to the twelve apostles. Agrippa unites the two currents, pagan and Christian, and adds a third source, Jewish Kabbalah, which he knew through Pico and Reuchlin.

From unity to four

One, for Agrippa, is not properly a number but the principle of all numbers, the image of God, who is unique and from whom everything proceeds. Two is the first true number and has an ambivalent character: it represents union, as in marriage, but also division. An ancient tradition, which Agrippa reports, regarded it as ill-omened, because in the Genesis account the second day is not called good.

Three is the perfect number par excellence, having beginning, middle and end, and it points to the Christian Trinity. Four is the number of stability: four are the elements, the seasons, the cardinal points, the rivers of the earthly paradise and the evangelists. Agrippa recalls that the Pythagoreans swore by the tetraktys, the figure of the first four numbers whose sum is ten, and that the Hebrew name of God, the Tetragrammaton, is made of four letters.

From five to twelve

Five, placed in the middle of the decade, corresponds to the quintessence and to the five senses. Six is a perfect number in the mathematical sense too, because it equals the sum of its divisors, and for this reason, according to Augustine, God created the world in six days. Seven has a special dignity: seven are the planets, the days of the week, the gifts of the Holy Spirit. Eight points to the beatitudes, nine to the Muses and the angelic choirs.

Ten closes the cycle of simple numbers and is the number of completeness: ten commandments, ten sefirot of the Kabbalah. Eleven, which goes beyond ten without reaching twelve, was considered the number of transgression. Twelve, finally, is the number of cosmic and sacred fullness, with the signs of the zodiac, the months of the year, the tribes of Israel and the apostles.

These chapters are a compendium of centuries of numerical speculation, gathered with learning and ordered with patience. Their historical value lies precisely in the synthesis: they show how, at the beginning of the modern age, mathematics was still inseparable from theology and symbolism, before Galileo reduced it to the language of measurable nature.