This essay is a draft and will expand/change over time.

The basis for the doctrine of signatures and the tables of correspondence is the idea of interconnectedness.

Pythagoras, the Ionian Greek philosopher, believed in the microcosm and macrocosm, a vision of the world in which the part (microcosm) reflects the whole (macrocosm), and vice versa.  About 100 years later, Plato expressed the same idea in his Organicism, where the Universe and all of its parts are an organic whole.

The idea of interrelation between the celestial, magical or divine and the natural or mundane is a concept that is a feature of most esoteric philosophies, explained best in Faivre’s Access to Western Esotericism:  

Symbolic and real correspondences… are said to exist among all parts of the universe, both seen and unseen. (“As above, so below.”) We find here again the ancient idea of microcosm and macrocosm or, if preferred, the principle of universal interdependence. These correspondences, considered more or less veiled at first sight, are, therefore, intended to be read and deciphered.

….those that exist in nature, seen and unseen, e.g. between the seven metals and the seven planets, between the planets and the parts of the human body or character (of society). This is the basis of astrology – correspondence between the natural world and the invisible departments of the celestial and supercelestial world, etc.

Faivre, Antoine. Access to Western Esotericism. Albany: State University of New York Press, 1994.

In Hermeticism, we use the aphorism “as above, so below” to express this interconnectedness. The full work from which that phrase is taken informs us that the connection works in the other direction as well – what’s below is connected to what’s above.  

The Emerald Tablet, which is usually incorrectly attributed to Hermes Trismegistus, was written in Arabic between the 6 C.E. and 8 C.E. The text was translated into Latin in 12 C.E., and the earliest printed Latin text is from 1541. The relevant passage is as follows:

Quod est inferius est sicut quod est superius, et quod est superius est sicut quod est inferius, ad perpetranda miracula rei unius.

Et sicut res omnes fuerunt ab uno, meditatione unius, sic omnes res natae ab hac una re, adaptatione.

Polydorus, Chrysogonus. In Hoc Volumine De Alchemia Continentur Haec. Norimbergae: Apud Ioh. Petreium, 1541.
Image of “Tabula Smaragdina,” or “The Emerald Tablet.”

This has been translated in a variety of different ways, some more poetic than others. One of the best known translations is by Isaac Newton:

That which is below is like that which is above & that which is above is like that which is below to do the miracles of one only thing

And as all things have been & arose from one by the mediation of one: so all things have their birth from this one thing by adaptation.

“Keynes MS. 28, King’s College Library, Cambridge University.” Chymistry of Isaac Newton : Diplomatic Manuscript. Accessed April 9, 2020.

A more poetic version:

As above, so below, as within, so without, as the universe, so the soul.

The Kybalion: a Study of the Hermetic Philosophy of Ancient Egypt and Greece, by Three Initiates. Kila: Kessinger Pub. LLC, 1998.

“As above, so below” is easy to remember, sounds impressive, and cuts off most of the important parts of the idea.

Expecting two different planes of existence to work the same way will only lead to frustration. It’s important to remember that below and above – microcosm and macrocosm – correspond. Not match, not resemble, not become equivalent.

The celestial, unseen, divine, whatever we want to call that plane of existence, is entirely different from our own. No one truly believes that lighting a candle on the material plane will result in the same candle being lit on another plane, but we persist in catchphrases like “as above, so below.” It would be more accurate to say there’s a connection and an effect. What we do on the material plane affects the unseen, and vice versa. Even if it’s not seen, or heard, or felt by the person performing the action, something happens.
This is the place where hermeticism overlaps chaos theory. The butterfly flaps its wings in New Mexico and across the world, there’s eventually a hurricane. If the butterfly hadn’t flapped its wings in exactly that place in exactly that moment, the hurricane wouldn’t have happened. A hurricane and the flap of a butterfly wing are in no way equivalent, but they correspond.

This is why we talk about “tables of correspondence” rather than “tables of equivalency.”