The math problem comes in Finnegans Wake II.2 occurs right after Shem/Dolph shows his brother how to draw the two interlocking circles that I discussed in my last post. This post explores the math problem itself.

The passage begins as follows:

For, let it be taken that her littlenist is of no magnetude or again let it be granted that Doll the laziest can be dissimulant with all respects from Doll the fiercst, thence must any whatyoulike in the power of empthood be either greater THaN or less THaN the unitate we have in one or hence shall the vectorious readyeyes of evertwo circumflicksrent searclhers never film in the elipsities of their gyribouts those fickers which are returnally reprodictive of themselves. Which is unpassible. 

On my first read of the text, I couldn’t make hide nor hair of this, but on my third read through the text at the end of 2020, something clicked.

The key phrase to me is “in the power of empthood.” And the opening idea that ALP is “of no magnetude.”

That is, ALP is represented by the number 0 — much as her chapter, I.8, starts with the letter O — something here is being *raised* to the power of 0, an exponent.

It is the two brothers (the two Dolls) who are “dissimulant with all respects” from each other.  

The passage seems to be describing an equation that could be written like this:

(Shem + Shaun)^0

That is, it represents the action of the mother (0) on them. There are two possibilities:

Shem and Shaun could be in conflict with each other and represent different number values, which would produce some integer, and then it would be some integer raised to zero, which would equal 1.

(Shem + Shaun)^0= 1

That is, the action of the mother reconciles them, takes their conflict and makes them into one (HCE, the Father, ready to start the cycle again). [1 is HCE/the Father’s number because, by the number’s shape, it represents the penis — also, as the dreamer, he is the one that this book is all about (see the Wake‘s opening sentence to see how the way of the river “brings us…back” to HCE])].

But there’s another possibility. The brothers could be in balance and harmony. Say, Shaun = 5 and Shem = -5. If the brothers were balanced, then they would cancel out and produce 0. At this point, their zero would be raised to the zero of ALP, and 0^0 is undefined. It equals some unknown number. Here, the action of the mother takes their reconciliation and produces conflict.

To clarify what I’m saying, I will break the quotation above into two parts, each showing a different possibility:

Possibility 1:

thence must any whatyoulike in the power of empthood [that is, (S+S)^0] be either greater THaN or less THaN the unitate we have in one [that is, it must be some undefined number, if S and S balance out]

Possibility 2:

or hence shall the vectorious readyeyes of evertwo circumflicksrent searclhers never film in the elipsities of their gyribouts those fickers which are returnally reprodictive of themselves.

Or, if they are uneven, then the two battling brothers will never see for themselves the 1 and the 0 that exist on the “other side” of the equation (beyond the parentheses and beyond the equal sign). Locked in their brother battle, they will never notice the figures — 1 and 0 — that are reproducing themselves in the brother conflict. [fickers = figures, but also fuckers…also fingers, because we have ten fingers…1-0]

The passage goes on to discuss how 1 and 0 reproduce themselves as the brother conflict. But before I discuss this later part of the passage, a note:

The equal sign makes these equations something more complex than a linear pattern in which conflict turns into harmony and then harmony turns back into conflict. The two are equated with each other. The brothers’ harmony would equal an undefined number (which I take to represent the fallen world), while their disharmony (which I take to represent the fallen world) would equal 1 (which I take to be harmony and redemption).

In the usual way I think about the Wake, the Fall of HCE (the descent of one into many) corresponds to the combat of the brothers (the brawl at Finnegan’s Wake), while the brothers’ reconciliation corresponds to the resurrection of HCE (their merging back into one). That’s certainly one way to think of it, and we can imagine it as a cyclical process of falling and rising, just like Vico’s conception of history.

But this passage suggests that even that complex arrangement is too simple. The Fall and the Redemption are identified fully with each other here. The combat of the brothers is underlied by the unity of HCE [(S+S)^0=1] and is in fact the only way that unity can ever be expressed in the phenomenal world. Proper reconciliation, too, depends on the fallen world, and it doesn’t end the fallenness — it just starts the cycle all over again.

There is no stasis. To Fall is to Rise, and to Rise is to Fall. Unity only exists through division; division is the expression of unity. To feel and fall is the only way No-Thing-Ness can be. To attain enlightenment is to turn the cycle of the unenlightened world again to begin anew. There is no enlightenment apart from this; there is no unity apart from division. There is no sense in denying anything: life demands a Yes to it all, like the Yes that ends Ulysses, like the Great Affirmation of Nietzsche’s Amor Fati.

I said something very similar to this in discussing the Shem chapter. Breaking apart and putting back together happen at the same time, “one present tense integument.”

Hopefully, these ramblings make a kind of sense.

Okay, so how do those “fickers” — the 1 and 0, the father and mother — reproduce themselves?

 Quarrellary. The logos of somewome to that base anything, when most characteristically mantissa minus, comes to nullum in the endth

The querulous corollary is that there’s some equation that will end in 0. I looked up how to calculate the exponent of an equation, and wouldn’t you know it, you need to take the logarithm (here, logos/word…as in, “In the beginning, there was the word”).

The log of 1, in any base, is always zero.

Similarly, the log of 0, in any base, is always undefined.

It’s just a different way of writing the equations above.

So through the logos — through the Word, through language — the zero can become the many, and the one can turn the many into zero.

In this way, the 1 and 0 — the cosmic Father and Mother — produce the many, the conflict that is the only possible way that harmony can ever be expressed and understood.

It’s of a piece with the Zen idea that Enlightenment is here and now, not in some future, harmonious, ideal state. In the end, all of it cancels out to zero anyway. [Issy’s footnote on “endth” reads, “Neither a soul to be saved nor a body to be kicked.” Nothingness]

1 and 0 are, of course, the digits that comprise 10, and there’s something to be said about the Hebrew Qabalah being based on ten (there are ten sephiroth, or emanations from God that issue forth into the material world, which is the final sephira).

For the sake of completeness, here’s how Joyce describes the movement from 0 back to many:

orso, here is nowet badder than the sin of Aha with his cosin Lil, verswaysed on coverswised, and all that’s consecants and cotangincies till Perperp stops repippinghim since her redtangles are all abscissan for limitsing this tendency of our Frivulteeny Sexuagesima to expense herselfs as sphere as possible, paradismic perimutter, in all directions on the bend of the unbridalled, the infinisissimalls of her facets becoming manier and manier as the calicolum of her umdescribables (one has thoughts of that eternal Rome) shrinks from schurtiness to scherts.

This is a version of the fall (the sin of Adam and Lilith, Aha and Lil), and there’s a bunch of stuff in here about sines and cosines and tangents that I still need to figure out, but the gist of it, I think, is that calculating the values of those triangles inside the circles (from the diagram) shows the limits of the circles — which corresponds to the limitation of the infinite possibilities of Nothingness, which is like a cosmic version of the Fall.

Thus, infinity, the Eternal mother becomes manier — becomes many, but also becomes men…the brothers — and her unmentionables go from something flirty to something basic and common. Also, Schurze is German for apron, while shert means “joke.” 

The idea of joke puts me in mind of the laughing Buddha, and the idea that the flip side of “all is sorrow” is “all is a joke.” The absurdity of manifest existence (aptly embodied in Joyce’s absurd book). I am also reminded of the line from I.1 that the fall of Finnegan will leave “iggs for the brekkers,” where “brek” is Icelandic for “practical jokes” (but also Czech for “crying”). Manifest existence is, at once, sorrow and joy.

It only took fifteen years for all of this to click for me.