This explanation is a bit complicated. We may, though, reach 666 by a pure dialectical understanding which is quite simple. The principle is that the number 3 is the number of form, while the number 4 is the number of substance (this will be explained). The evolution of the number 3 is given by the series 3 - 6 - 21, while the evolution of the number 4 is given by the series 4 - 10 - 55. The number 6 indicates the dialectic of two forms of 3, for example he and her, as illustrated by the Star of David, but where the two of them assume the guise of respectively form and substance.
The reason why will become evident by the following explanation. It will be a bit complicated. First, let med introduce the second calculation.
The number 1 is the starting point, and the recognition an individual can not create anything by himself. A thing, be it an idea, a value, a matter of truth, can only be the basis for development and growth if there is an answering to the phenomenon. So Heaven needs earth. God needs man.
God stands alone if God punishes. Rage requires no fertile ground. But for something to grow, seed must go into the soil, dying, and what grows will be the offspring of the earth.
Thus, the number 1 can not stand alone if something should appear. Together with the number 2, however, a unit is made which by a development is given. The growth is given by the number 3, by which the figures 1 and 2 work together.
1 + 2 = 3
The development does not stop with the number 3. The next step is the significance of the number 3, and significance the number 3 gets by the number 4. As image, it is natural to use corn which in the spring is sown (the number 1), which in the summer blooms (the number 2), which in the autumn is harvested (the number 3) and which in the winter turns to cakes and bread (the number 4). The dial is what we will use as a picture recognizing the fact the unit of two forms a union of four. If we let 1 and 2 intersect, in that 1 runs horizontally and 2 goes vertically, we get four realities, and the dial indicates a trend.
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
The sum of 1 and 2 and 3 are 6. The number 6 is the number of the idea, that is of the form.
The sum of the numbers 1 and 2 and 3 and 4 is 10. The number 10 is the number of perfection. The number indicates what is being. The number 10 is the number of matter, that is the substance.
Thus, the number 6 is the figure for the union of 1 and 2 as the association ends in 3. The three of them provide six. And the number 10 is the number for the final creature when the three have gained importance, stated by the figure 4. The three of them together with four provide ten.
1 + 2 + 3 + 4 + 5 + 6 = 21
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
The quality of 3, therefore, is thought of as being 6, and the quality of 4 is thought of as being 10. But when the qualities are objectified, the qualities themselves are recognized as having qualities. And the quality of 6 is 21, since the sum of the numbers leading to 6 is 21, and the quality of 10 is 55, since the sum of the numbers leading to 10 is 55. Thus, the number 21 is the figure for the quality of the quality of the idea, or form, while the number 55 is the figure for the quality of the quality of matter, or substance. By the numbers 3 - 6 - 21 the evolution of the form given. And by the numbers 4 - 10 - 55 the evolution of the substance is given. Although the number 4 is the basic number, the development of the substance is given by three steps since the fourth step is foreign to the thing being formed. The child is formed in three stages, for nine months, and then it is born. And winter is foreign to the grain being sown in the spring, blooming in summer and harvested in the autumn.
The number 6 symbolizes ideal perfection, and the number 10 symbolizes material perfection. By the number 6, the form is established, and by the number 10, the substance is established. We arrive at the number 666 by first letting the figure 6 be multiplied by the quality of the number 6, namely 21. This renders the direct inset of idea into matter. In this case, the substance has a function. Then we let the figure 6 be multiplied by the quality of the number 10, namely 55. This renders how the substance turns over form in the way of the substance. In this case, the substance exerts a role. Then we let perfection 10 be multiplied by the quality of the number 6, namely 21. This renders the real love, considered to be so, in that matter, given by the number 10, here not resolves the idea, given by the number 6, but lets the form be the opinion of the substance, the idea be opinion of the matter. In this case, the substance works in a calling. The sum of these three ways is the number of the beast, which is 666.
These three approaches regarding the exchange between idea and matter are thought to be embodied in matter by concrete manifestations. There is made distinctions between necessity, utility and beauty. The direct lowering of the form into the substance is thought of as necessity. The way in which the substance conforms to the form in its own way is thought of as utility. And the way in which the substance lets the form govern the way of the substance by being idolized, is thought of as beauty. The picture we will use to illustrate is that of the tree. Necessity is given by the root of the tree, utility is given by the the trunk of the tree, and beauty is given by the foliage of the tree. But in the society, these three ways of exchange between idea and matter are enshrined in the sciences. We distinguish between psychology, built on necessity, sociology, built on utility, and theology, built on beauty. We distinguish between nature, culture and spirit.