Are we missing an important lesson about visualization? Visualization is almost becoming a topic like a porn,(dictionary.com: television shows, articles, photographs, etc., thought to create or satisfy an excessive desire for something, especially something luxurious) for a good reason especially recently, enabled by the need to summarize the big data where data dross can be a problem.
The following discussion is useful as a generic topic to justify students to learn algebra and equations than just relying on geometrical explanations, though I have to tell you that I loved geometry as a kid and visualization definitely has a role in simplifying complex communication in simple easy to understand conclusions.
So the topic is not about whether visualization has benefits or not. It is about using it in a meaningfully useful ways.
I explain this using the following 7 dimensional visual representation.
A segmentation scheme typically involves many variables to condense the whole population into say any where from 4 to 10 homogeneous groups, and even 10 is a lot if we have to create distinctive marketing programs. For example, I know of segmentation schemes that are any where from 40 to 80 groups because you can explain more variation; however, the direct applicability of those large segmentation schemes require further grouping based on some additional data.
So in the end it will result anywhere from 4 to 10 segments for developing and applying marketing plans.
So let us say we have a seven class segmentation scheme, based on probably 15 generic (foundational) variables that are commonly available.
or much simpler 4 dimension Venn diagram.
The Second picture shows clearly how the intersecting sets are represented and it is simpler to work with compared to the seven dimension venn diagram. For example set A interaction with set D is the bottom most set.
The purpose of a Venn diagram is to show geometrically the number of units that belongs to intersection of sets or non-intersecting sets (which is a union of pure intersecting sets). Note that the full set which results in these subset representations and their intersections is called the ‘Omega’ set. In the second example it is set 16+all the numbers in the mutually exclusive sets created by the various intersecting sets out of four primary sets. The primary sets are A, B, C, D in the above 4 dimension (second picture) Venn diagram. Intersecting region means the elements in that region are members of the intersecting sets.
Can you see how quickly the conversational meaning of interpreting the intersecting or non-intersecting factors become complicated as the number of dimensions increase as you go from 4 dimensions to seven dimensions. However, when you draw the picture, it is not easy to see the various intersecting regions. The 4 dimensions provides a possibility of 2^4 possible distinct sets, which is 16 distinct sets. For 5 dimensions it is 32, 6 dimensions it is 64 and for 7 dimensions it is 128 distinct intersecting sets. These 128 distinct sets are supposed to be captured by the top picture. The bottom picture shows 15 bounded regions and the one outside of the union of all those bounded sets.
Imagine the 128 sets representation of 7 dimensional representation.
The only accomplishment of the above tabulation is to show you how to achieve the systematic symbolism of getting all possible intersections and what sets contribute to what representative intersecting sets on the left. A better representation could be actual counts in those places where there are ones. The important point is that in this representation, you won’t go round and round to figure out which representative intersecting cell has how many counts. Note that in practical life, the conversational sets (a combination of these intersecting sets which could be rewritten as and/or/not/nor conditions) could be much higher than this.