Through Wisdom is a house built;
and by Understanding is it established;
And by Knowledge shall the chambers be filled with all pleasant and precious riches.
Wisdom (Chakhmah) , Understanding (Binah), and Knowledge (Da’at) are three concepts that lay at the foundation of Kabbalistic thought. The ability to manipulate the powers of creation – understood by Kabbalists as the letters and digits of the Tree- require mastery of these three principles by the initiate. However, while Chakhmah and Binah are identified as two of the three supernal sefirot (along with Keter), Knowledge (Da’at) itself is never considered a true sefirah. Few commentaries deny its importance and even fewer posit explanations as to where Da’at fits into the traditional paradigm of 10 sefirot. This is because at base level the sefirot of the Kabbalah compose a decimal system and there are only 10 digits and not 11.
Ten Sefirot of Nothingness
ten and not nine
ten and not eleven
Sefer Yetzirah 1:2
Not being one of the 10 sefirot emanated, Da’at cannot be considered a true sefirah for the same reason that the numeral 11 cannot be considered a digit. Despite this, Da’at is a pivotal and transcendent principle in Kabbalistic literature. The word Da’at literally translates to “Knowledge”, but also carries connotations of joining and intercourse as in the verse “Adam knew his wife Eve”(Genesis 4:1). As such, in Kabbalistic philosophy Da’at represents the same knowledge principle as the gnosis of the classical Philosophers – not relating to epistemological knowledge but rather to experiential Knowledge through union with the object in question… To experience God, is to Know God.
Kabbalah philosophy explains Da’at as the point of union between Wisdom(Chakhmah) and Understanding(Binah) and as a proto-sefirah that acts as the unifying principle for the entire Tree. Where the sefirot can be considered “vessels” for the Light, Da’at is the closest approximation of that Light – in fact, the Zohar identifies Da’at as the “Light of Chakhmah”. 
This traditional notion of Da’at along with the geometric paradigm of the Ari Tree is now prevalent amongst the various western magical currents that adopted Kabbalistic pathworking into their practice. Most students of western magic today will quickly identify Da’at as that non- sefirah that fills the void (both philosophically and geometrically) between the Supernal triad of Keter, Binah, and Chakhmah and the lower seven sefirot of the Tree. While this ethos resonates well with the Ari Tree (geometrically speaking), it does not apply to the Gra version of the Tree where the absence of a void does not impart a hidden or lost sefirah (See The Trees). Gra Kabbalists instead focus on Da’at as the unifying principle underlying the workings of the entire Tree. It is not localized as a point, but is instead employed through the balance and unity exemplified by the Middle Pillar as the harmony between the paths of the left and the right.
When we examine the Trees side by side, we find that the non-sephirah Da’at of the Ari corresponds to the placement of Tiferet in the Gra version. Indeed, when Da’at is taken as an underlying principle indicating Knowledge and union of all the sefirot, we find that in the Gra diagram Tiferet is the Da’at between Binah and Chakhmah, as Yesod is Da’at between Gevurah and Chesed, and Malkut is Da’at between Hod and Netzach. Looking at the Ari Tree, we are left to contemplate what is the Da’at of Chakhmah and Binah if not Da’at itself.
The spatial correspondence between the Ari non-sephirah Da’at and the Gra Tiferet is an interesting concept to work with; particularly for those who employ the vibration of divine names in their practice. In western magical currents the divine name attributed to Tiferet is YHVH ALVH V DA’AT (“YHVH is Deity and Knowledge”) bequeathing a link between Tiferet and the proto-sefirot Da’at. We also find a similar connection between Da’at and Tiferet in the Zohar, where Da’at is described as the child of the partzuf of Binah(IMA) and the partzuf of Chakhmah(ABA), yet this same “child” role is also assigned to the Microprosopus (Zeir Anpin) symbolized by Tiferet as the sefirah that reflects the common attributes of the lower six.  This interchangeable role between Da’at and Tiferet (representing harmony, love, and elevated consciousness) is something to keep in mind as we move forward in the discussion.
It is also interesting to consider that some schools of thought that employ both geometries of the Tree (Work of the Chariot, for example) see in these two diagrams an analogy to the Biblical Fall of Man – the geometry of the Ari Tree pertains to Man in his fallen state without direct access to the supernal triad, while the geometry of the Gra Tree displays pre-fall or resurrected Man with unobstructed access to all levels of truth. The state of “fallen” or “resurrected” describes the position of the Middle Pillar in each geometric paradigm – note that it is simply the sliding down of this central column of the Gra Tree that reveals the void found in the Ari Tree.
We may continue this analogy and parallel the two versions of the Tree with the two Trees of the Garden; the Tree of Knowledge and that of Life (see Concerning the Trees). Immortality, or the fruit of the Tree of Life, is hidden from us because Da’at, the fruit of the Tree of Knowledge, was consumed leaving us in a world of acting duality and separation (i.e. the void present in the Ari diagram). So the question becomes – How can we replant this lost “fruit” of Knowledge so that we may once again have access to the Tree of Life?
The answer may lie in practice as the venue through which Knowledge is experienced. One common technique in meditative Kabbalah is to map the sefirot to the subtle centers of the human body – visualizing the initiate as a veritable microcosm of the Tree. Through this practice we find that the non-sefirah Da’at (Tiferet in the Gra Tree) corresponds to the region of the throat. It is in this subtle center where sound (as vibration) and light (as the astral imprint of vibration) are united as One. While the throat may be the source of unity between light and sound as it is the point from which the divine names are spoken and vibrated, this unity between vibration and light happens within each subtle center. For example, the divine name for Yesod vibrates audibly from the Da’at center of the throat, but the imprint of that vibration happens in the Yesod center of the groin. Therefore, in practice, Da’at indeed manifests as the source of unity throughout all levels of the Tree. We may note the parallels to the doctrine of logos (“word”, “ratio”, “harmony”) in traditional Philosophy as the means through which gnosis is imparted to the initiate (see Gnosis and Logos). In particular, we are brought to the notion of Da’at as the metaphorical and literal “word of God”.
The doctrine of Da’at may have always been part of the teachings of the Tree and the 10 Sefirot of Nothingness, but its image was perhaps intentionally hidden from profane eyes only to be revealed to worthy initiates. The “profane” geometries of the Tree containing only the 10 Sefirot reflective of our own 10 digits (the 5 fingers of the left and right hands) and Da’at, the “hidden” 11th digit as the key by which the initiate could unify and transcends their polarity.
 A rather in depth discussion on the triad of Wisdom, Understanding, and Knowledge in Kabbalistic doctrine through the ages can be found in Aryeh Kaplan. Sefer Yetzirah (Boston, MA:Weiser Books, 1997).
 As the 11th non-sefirah there are some worthwhile correspondences to examine alongside the numeral 11. In traditional Pythagorean number philosophy – an undisputed influence on Kabbalistic thought – where there are only 10 digits, the integer 11 has merit on its own. It is the first of the double” numbers encompassing the unity of the ten digits (as the union of the first and last digits, 1 + 10)and is interpreted as the reflection of unity (1) upon itself – which fits perfectly into the traditional Kabbalistic interpretation of Da’at as that principle of unity and that point of reflection for the supernals to act upon and manifest the lower seven. Furthermore, through Pythagorean reduction 11 gives us the dyad(1+1=2) – yielding duality and articulating Da’at as the point of separation and, of course, unification between the supernal principles of the Godhead and the manifestation of those principles in the dimensional universe.
 Aryeh Kaplan(tran.). Sefer Yetzirah (Boston, MA:Weiser Books, 1997).
 Michael Laitman(translator). The Zohar (NY:New York, Laitman Kabbalah Publishers, 2007).
 Though of course, through careful observation and reflection of the Gra Tree into three-dimensional space we indeed find evidence of at least two more potential “hidden” sefirah (i.e the Tree as an isometric projection of a double cube). In particular, see Leonara Leet. The Secret Docterine of the Kabbalah(Rochester, VT: Inner Traditions Press, 1999).
 Aryeh Kaplan(tran.). Sefer Yetzirah (Boston, MA:Weiser Books, 1997).
 “Hesed, Gevura, Tifferet, Netzah, Hod, and Yesod combine into one Sefira, called Zeir Anpin (ZA). ZA itself is sometimes referred to as Tifferet, for this Sefira reflects the common attributes of all of its six Sefirot”. From Michael Laitman. The Zohar (NY:New York, Laitman Kabbalah Publishers, 2007). pp. 43.