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Natural language is a great querying tool for quickly combining existing knowledge in order to generate moderately intricate thoughts. It feels easy, but don't
by nicklaf 11y ago
Natural language is a great querying tool for quickly combining existing knowledge in order to generate moderately intricate thoughts. It feels easy, but don't forget that it took many lifetimes of experience to accumulate the database you are drawing upon. It's similarly easy to throw together a Smalltalk prototype as it is to have a casual conversation. Not so easy is to construct a language--natural or artificial--from scratch (let alone try to teach it to somebody).
On the other hand, in advanced mathematics, diagrams are used all over the place (look at category theory). When they're not used, the reader is essentially forced to imagine spatially what is being said, often down a blind alley (to use the phrase almost literally).
Diagrams are essential to communicating non-obvious abstract ideas in an efficient manner. In addition, given a domain-specific technical language, there are many possible permutations of words in a sentence, whereas the space of sensibly drawn diagrams is much smaller. Often, after fully comprehending an idea that was previously expressed in words, the final step in congealing the idea in your mind (and convincing yourself of its soundness) is to draw a definitive diagram which covers all the cases, and can be understood in a glance.
I should also mention that many of the worst typographical errors in mathematics completely change the meaning and jumble the thought, something which is far more difficult to do when using a diagram.
Also, as I remarked in my other comment, diagrams complement text, with either one enhancing the other. Neither should completely replace the other.
- ccalvert 11y agoI agree, diagrams are great -- in their place. But to the author's point, can you draw me a diagram that conveys the same information as the sample sentence from the article: "Human rights are moral principles or norms that describe certain standards of human behaviour, and are regularly protected as legal rights in national and international law." I don't think you can, but if you could, it would likely be very large and complex. This speaks to flexibility and information density inherent in text.
- PhantomGremlin 11y agoThis speaks to flexibility and information density inherent in text That is true, however, the only reason there is such "information density" is that you already know the meanings of those words, idioms, assumptions, etc. You know a lot of context that isn't being explicitly stated. That quoted sentence has little meaning to a child or to anyone without a good deal of education and shared cultural background. Diagrams and text serve very different purposes.
- nicklaf 11y agoThe diagram would indeed be enormously complex, because that sentence draws upon a vast amount of existing human knowledge. You'd also have to invent a visual language for describing this knowledge, which at present probably doesn't exist. One may as well try looking at fMRI images of human brains and try to infer the way that sentence triggers existing memories in order to figure out how the brain represents hierarchies of knowledge in memory. I mostly use diagrams for describing completely new, abstract ideas in engineering or mathematics. Once the idea is understood, then yeah, it's faster to "query the database", and simply utter a word or write down a symbol.