Watching the new video demonstrating Cortana, I found it very interesting to see how Microsoft designed Cortana's visual representation. It's a little different from what I expected it to be based on prior leaks (I thought it was going to be some sort of animated traditional emoticon), it's very different from Siri's animations (although there are some similarities), and it's definitely not what some Halo gamers wished for ;)

So before we analyse it, let's summarize what we can see in the video (if it's tl;dr, feel free to jump to the conclusions below!)

Cortana's visual representation consists of a brighter circle and a less bright circle sitting close to each other. All the animations are based on that design.

Whenever the user is busy reading or entering information, the brighter circle pulsates slowly while the darker circle slowly rotates around it.

While Cortana is waiting for an initial command from the user, the brighter circle turns into a big dot and the darker one gets thicker, both pulsating calmly.

While Cortana is "absorbing the internet", the circles spin around their vertical axis, with the darker circle inside of the brighter one.

As Cortana thanks the user for entering useful information during the setup process, the circles pulsate vividly with the outer brighter one rotating at high speed.

As Cortana apologizes for an inconvenience, the brighter inner circle moves outside the darker one while spinning, and flattens out horizontally (resembling a bow or closing of the eyes). The same animation can be seen as Cortana stops listening because the user didn't say anything.

As Cortana greets the user, the circles are reduced to a single curved line, which is not static but fluctuating in length (resembling a smile).

There's an animated Cortana live tile that animates in the same way as it does when it's waiting (Maybe the animation is different when there are notifications from Cortana?...)

So what can we conclude from these findings?

From what is shown in the video, it seems obvious that the main purpose of the animations is to communicate with the user on an emotional level, rather than providing information about Cortana's activity status. The two most subtle animations are the "waiting" and the "searching" animations. Those two states of activity don't involve any emotional dynamics, so they basically just indicate that Cortana is there. Those animations that really attract the user's attention are the "greeting", "thankful", "apologizing" and "ready for commands" animations. It's interesting to notice that those are situations that are not associated with technical processes but with human interaction. And what's even more interesting is that there seems to be a focus on humble, polite forms of interaction. Cortana greets you with a big smile, she apologizes by gathering herself and making a low bow, she thanks you by jumping and spinning in excitement, and she focuses with her eye wide open waiting for her master's command. So as far as one can tell from this video, Microsoft seems to use the animations to make Cortana feel like the perfect servant: polite, focused, humble and submissive. Those characteristics may appear old fashioned and inappropriate for what is meant to be a personal assistant, but they happen to be the same qualities that customer service employees in Japan are known for - and if there's one thing that the Japanese way of working is praised for, it's effectiveness. And that's what I think Microsoft is going for - an effective, frictionless, seamless user experience.