How large a number of items can you visualize?

[Lagmonster]

I was challenged this morning to try to see how large a number of items I could visualize. The idea is to take a common distinct item you're familiar with, such as coins or apples or some such, and try to visualize increasingly large numbers of those items, starting with one.

The catch is that you're not permitted to group them together (so you cannot visualize eight pennies as two sets of four, or four sets of two). You're also not permitted to first memorize what a set number looks like by actually looking at a physical example and then trying to recall the image.

I realized, to my surprise, that I couldn't easily visualize a group of just about anything higher than five items without falling into the trap of grouping by threes and twos. And none of us could visualize a pile of eleven anything unless we pictured two rows of five and a one.

We have some engineering and mathematics-oriented types here; I'm wondering if perhaps they would be able to perform better at mentally visualizing physical examples of larger numbers of identical items, or if there's just a limit to human mental processing at work here.

[Ahriman238]

Grouping is a lot more convenient for most purposes, and takes literally no effort.

I tried imagining pennies in a sort of loose spiral shape, but the 24th completed the pattern, which I'm assuming counts for these purposes.

[Formless]

This seems to related to something called "Subitizing" where people can instantly identify (not count! This is exponentially faster, and even babies can do it) groups of items at a glance and tell you how many of them are there... but apparently being able to identify groups larger than four at once is pretty rare and difficult even with practice. I've done it, but it just feels easier to identify the group of three and the group of two, and that's so fast already that its hard not to do that. And trying to get a group of six at once just seems like too much without grouping them into subgroups.

I dunno if it has anything to do with the limits of human visualization ability, but that would be an interesting hypothesis for study.

[Wing Commander MAD]

Along with what Formless mentioned, it sounds like its related to "The Magical Number Seven, Plus or Minus Two" and working memory capacity.

[Wild Zontargs]

Is forming an array "grouping"? If I form a mental row of things, then stretch it out to a 2d array, then to a 3d array, with each individual object still individually "visible", I can manage 512-1000 (8^3 is easy, 10^3 gets a bit fuzzy when rotated).

[madd0ct0r]

I used to experiment with this back in the steel widget factory.

My boss could 'recognize not count' up to 5, while I never really got above 3. Sets of ten were 3 sets of 3 + 1 loose. Three of those was thirty. I tended to use 4 by 5 layouts of blocks of ten for 100s, but that wasn't counting, just recognising the aspect ratios of the resultant rectangle.

[lance]

At least 4, but not 6

[Zeropoint]

Five is the limit for me, at least when it comes to "recognizing, not counting" objects in an irregular pattern.