What does Louise write on the barrier with Abbott?

Question

In the movie Arrival, Abbott starts tapping on the barrier so Louise will write on it. She tells Ian that she can't do it with both hands, which prompts Abbott to help her.

What do they write together on the barrier?

Answer 1

An exact translation is probably not meant to be known:

The scene

To get a better idea of what that scene insinuates, first let's have a look at the script. This is from the final shooting draft (and differs slightly from the dialogue in the film). The scene you are referring to starts at page 79:

Louise and Ian arrive to find Abbott already here, advancing for the glass barrier. Abbott's movement suggest an urgency.

Abbott writes on the barrier, and prompts Louise to solve the logogram on the barrier.

The wall becomes more and more transparent, revealing Abbott more intimately than ever before.
The alien gestures at her.
Louise tentatively puts up two hands, then lowers one.

IAN: What?
LOUISE: I can't. I can't draw both ends at the same time.

She holds her right hand against the glass. It reacts by forming ink on Abbott's side.
As she does, Abbott holds up one hand against the glass on his end, to the left of her position.
Louise regards him curiously. Then she takes a breath, and begins to draw one end of this elegant, complicated circle.
As she does, Abbott draws on his end. Working in the opposite arc toward Louise's starting point.

IAN: What is he doing?

Louise's eyes widen as she realizes...

LOUISE: He's being my other arm. He's finishing my sentence.

The two co-authors finish simultaneously, connecting the arcs of their logograms into a circle.

Louise then has a sudden 'flashback':

Baby Hannah reaches up from her cradle, her little infant hand outstretched like Abbott's. Louise reaching down to let Hannah grip mom's pointer finger.

Louise snaps out of that quick vision. She takes a step back.
LOUISE: That's... That's it.
Looking at it head-on, the logogram is complete.

So, based on the epiphany at the end of this transcript, we can assume that the meaning of the logogram has to do with Louise realizing either the true character of her apparent flashbacks, or that in general time is non-linear.

The fact that she acknowledges she is physically and/or mentally unable to write the logogram with two hands (not opting to start at one end and draw in a circle), suggests she knows about the character of the language: the act of simultaneity is paramount to the writing (it could also indicate she's still inclined to linear temporality).
In this particular instance, the collaboration is telling as well.

I think the urge and determinacy with which Abbott communicates with Louise here - sacrificing himself in the process - is also of great importance: this message is not only relevant to Louise personally, but to the future of both races.

Based on these observations, I'd say this is the point at which Louise learns about the true nature of time - about its circularity.

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The symbol

The alien symbols are circular combinations of different parts, as can be guessed from the analyses in the film.

New signs can be formed by combining elements. All symbols consists of twelve distinct components:

This answer on the Fantasy & Science Fiction SE delves deeper into the construction of the symbols.

The online repository on GitHub of the 38 signs used in the film, does not contain the symbol from this particular scene in the film - with the distinct open top and forking ends, and one calm and one disorderly side:

                                                                                                                                                         ^source

Even those distinct components by themselves can't be seen in the other logograms, which leads me to believe it was deliberately left out.

From the appearance, some inferences can be made, however:

• the logogram is not completely circular, illustrating an interruption in time;

• the forking obvious on the one end could be symbolic for having a binary option (an illusion of choice?) - either at the end or at the beginning of the interruption;

• there is a disorderly and a calm half - is this about the relationship between humankind and the heptapods?

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The sequitur

Based on those premises - of what I think Louise realized, and the omission of the literal translation of the logogram - I'd say this scene shows us how Louise learns about the true nature of time by writing a symbol that is not meant to be able to be read by the audience.