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Comment by Chris_Newton

11 years ago

There are plenty of advantages to text formats, to be sure. Others have mentioned many already, so I won’t repeat them. But let’s also consider both the disadvantages and how many of the advantages are “accidental” rather than inherent benefits of using a textual format.

One disadvantage of text is its lack of expressive power. Try reading the equation shown in the article aloud. Now try giving a one hour lecture on advanced quantum mechanics without the aid of mathematical notation. We can often represent information far more concisely and accurately with a good notation than with text alone, particularly when there is some inherent underlying structure that goes beyond what we can conveniently represent with some linear sequence of a tiny set of symbols. Computers are good at that kind of thing, but we don’t read Shakespeare in binary, and we certainly don’t draw the Twitter icon from the article using nothing but 1s and 0s.

Another disadvantage of text is how much it relies on everyone to use the same conventions, even though in the real world they don’t. Go just about anywhere in the world and you can recognise what the little pictures of a man and a women on the two doors in the restaurant mean. Replace them with ‘M’ and ‘F’ and you’ll see people who don’t speak English waiting outside to see who comes out of which door. We use different languages. We use different alphabets. In technology, we use different encodings for glyphs and invent all kinds of other concepts in an attempt to standardise how we represent written text, and we still create numerous bugs and portability issues and lost-in-translation problems. We’ve been using computers for half a century and change, and we still haven’t standardised what the end of a line looks like. Or was it the end of a paragraph?

Now, certainly the simplicity of a text format has big advantages today in terms of things like searching for data and programmatic manipulation. But how much of that is just convention and historical accident? Right now, I’m typing this using an input device heavily optimised for text, because that’s what my computer comes with. If I want to input some graphical notation, say an equation, my choices are probably limited to using some awkward purely textual representation (TeX notation, etc.) or some even more awkward half-text, half-mouse graphical user interface. Neither is an appealing choice, which is why it takes those of us working in mathematical disciplines forever to type up a simple note or paper today.

Technology does exist that can interpret a much wider range of symbols drawn with a stylus or other pointing device as an alternative means of input, but usually as a niche tool or a demonstration of a concept. Until we routinely build user interfaces that parse freeform input and readily turn it into whatever graphical notation was intended, a lot of us are still going to reach for a pencil and paper whenever we want to draw some quick diagram to explain an idea. But I bet a lot of us still do draw that diagram instead of speaking for another five minutes to try to explain it.

Personally, I’m looking forward to the day when source control doesn’t show me a bunch of crude text-based edits to my code, but instead a concise, accurate representation of what I actually changed from a semantic point of view. But to do that sort of thing, we have to have more semantic information available in the first place, instead of relying on simplistic and sometimes error-prone textual approximations.

Technology does exist that can interpret a much wider range of symbols drawn with a stylus or other pointing device as an alternative means of input, but usually as a niche tool.

Handwriting math equations is built into Windows 7 and 8. Over half a billion computers potentially have access to it.

http://windows.microsoft.com/en-us/windows7/use-math-input-p...

  • That’s a great example of what I mean. The intent is laudable. For now, the tool is far too limited/flawed for professional work, but one day maybe our input/output devices will be kinder to this kind of interaction and our software will routinely support alternative forms of input to work with data that isn’t purely textual.

    I think a more polished example that is available today is the use of stylus and graphics tablet with drawing software. That is a relatively mature field where the use of alternative input methods to keyboard+mouse is well established, and skilled users already do some amazing things.

Mathematical notation is text. Speech isn't.

  • Mathematical notation is text.

    That’s a stretch, no? Mathematical notation is textual in the same way that, say, a flow diagram, an org chart or the structural formula for a chemical compound are textual. That is, there are textual glyphs in the visual representation, but the positioning and the other symbols are important to the meaning as well.

    Can you type a mathematical equation on a keyboard, represent it unambiguously in a standardised character set, put it under version control, diff it, merge your edits with those of a colleague, still have something you can display reliably at the end, and then go back a decade later and search your archive for a specific equation? Not with any tool set I’ve ever seen. It’s still difficult enough just representing non-trivial mathematics on a web page so that everyone can read it.

    Speech isn't.

    No, but one of the advantages of textual representations that has been offered in this discussion is that textual formats can be used as inputs to screen readers and the like for improved accessibility. So again, I think this points to the inadequacy of purely textual notations as a way of representing complex information.

    • > That's a stretch, no?

      No.

      > That is, there are textual glyphs in the visual representation, but the positioning and the other symbols are important to the meaning as well.

      The positioning of symbols is important in plaintext too! There is a distinction between the space separating words, versus the space separating paragraphs.

      Similarly, all those non-letter symbols are important to the meaning. (Like the parentheses indicating that this is a side comment.)

      I'm not sure I understand your argument here -- do you think mathematics would be text if it didn't have superscripts and subscripts?

      To some extent you seem to be arguing that because tools for working with mathematical text are currently woefully in adequate, mathematics is not text. But this view seems backwards to me -- surely other languages that are not based on the latin character set had proper tooling developed later?

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