So she wrenched her gaze away from the window—an antiquated thing, that—and brought up a display on her tablet showing the disposition of every vessel in the Cloud Ark. It was an app called Parambulator. It was not a literal rendering of what the cloud looked like, though you could make it show you that if you clicked the right menus. Parambulator was a tour de force of data visualization that would only make sense to people like Ivy, Doob, and most of the Arkies, who had spent a lot of time learning about orbital mechanics. Starting with empirical observations from Lina Ferreira and other mathematically sophisticated biologists, mathematicians like Zhong Hu had extrapolated swarm algorithms from three to six dimensions and physicists like Ivy had figured out how to make these algorithms work under the special constraints of orbital mechanics. In general, every vessel in the cloud was shown as a dot on a three-dimensional scatter plot showing information about its orbit. Six numbers—the orbital parameters, or, as everyone up here had begun to call them, the params—were required to convey everything about an orbit. Only three could be visualized in any given plot. So that was where the user-interface legerdemain came into play, and where someone like Ivy had to pay attention and engage all available brain cells. But the gist of it was that each arklet was a projectile that could strike Izzy, or another arklet, if its params were wrong. In a hypothetical, extremely simple Cloud Ark consisting of only two arklets, only one calculation needed to be performed: namely, the calculation that answered the question "Will Arklet 1 bang into Arklet 2 if both stay on their current courses?" In a three-arklet cloud, it was also necessary to figure out whether Arklet 1 would collide with Arklet 3, and whether 2 and 3 were going to collide. So, that was a total of three calculations. If the cloud expanded to four arklets, six calculations were needed, and so on. In mathematical terms these were known as triangular numbers, a kind of binomial coefficient, but the bottom line was that the number of calculations went up rapidly with the number of arklets in the cloud. For a hundred-arklet cloud it was 4,950 calculations, for a thousand-arklet cloud, about half a million. It would have flummoxed the simple computers of Apollo days but was nothing by modern standards—provided that accurate information could be had about each arklet’s orbit. An old-school, centralized approach would have been for all the arklets to report their params to a computer on Izzy, which would then do all the calculations and report the results. The reliability of that process could be improved if Izzy’s radars, observing the arklets and plotting their movements, filled in gaps in the data. And indeed something like that was happening all the time, not just on one computer on Izzy but on several. But this, again, was Ship thinking. Cloud thinking dictated that each arklet make those observations and do those calculations separately. The computer on a single arklet—call it Arklet X— might not have all the information needed to track every single one of the other arklets in the cloud, but it could identify the ones most likely to be a danger and focus on those. Others, as well as the central processors on Izzy, could assist it by sending messages to the effect of "You might not be aware of it, but you are possibly in danger from Arklet Y and might want to move it to the top of your list of things to keep an eye on." To which it might reply "Thank you, but I’m not getting good params for Arklet Y because Izzy is blocking my view on the radar." The cloud would then respond by in some sense becoming aware that Arklets X and Y needed to know more about each other’s params and giving a higher priority to making that happen.