[tsimionescu]

No, you do not need to, and will not generally be able to, describe everything that a graph conveys in text. Graphs can give you an intuitive understanding of the data that text would not be able to, simply by virtue of using other parts of the brain and requiring less short term memory. If a graph can be replaced with 5 pages of text, that doesn't mean that you get the same information from both - you're likely much more able to keep one image in your short term memory than 5 pages of text.

[godelski]

A word is worth a thousand images. Wait...

[inciampati]

But a graph, which provides a view at a certain level of resolution, can often be described in a few consise statements. That's why we make them, to get a view we can condense.

[tsimionescu]

No, if we can condense something in a few short statements, we don't generally bother making a graph. We exactly make graphs when something is not easily explained in words, but instead requires visualization.

Of course, not all graphs are equally information dense, and some are only used for decorative purposes more than actually conveying information. But in the general case, and especially when used well, graphs convey much more information at a glance than a short text description could.

[smj-edison]

I feel like it's more that we have statements that are "pointers" to the graph. "According to Figure 1, we see that temperature rises do to pressure." So we can summarise with words, but the intuition and proof comes from the visual medium.

[PopAlongKid]

Many years ago, in college, I used to volunteer for Recording For The Blind, reading various math texts aloud. I had to verbally describe every illustration in the textbook, including graphs, using a few concise statements. Not perfect, but possible.

[tsimionescu]

You can describe any graph to some low level of detail, sure. But does it actually help anyone? Do people with complete blindness, for example, gain anything from hearing a description of the graph of f(x) = x as "a straight line at a 45° angle crossing the graph at 0", compared to what seeing people gain from viewing that graph?