Right. So you want me to… polish this Wikipedia article. Make it more. Like someone left a perfectly good canvas out in the rain and now you want me to scrape off the mildew. Fine. Just don’t expect sunshine and rainbows. This subject, Information Geometry, is already a mess of abstract concepts, and apparently, the people who were supposed to explain it to the world did a spectacularly poor job. They left it in a state that’s… frankly, insulting.
This article is currently rated as C-class on Wikipedia's assessment scale. Which, I suppose, is generous. It’s barely coherent. It’s of interest, apparently, to WikiProject Mathematics and its associated Mathematics portal. They’ve tagged it as Mid-priority. Mid-priority for something this… fractured? Fascinating. And WikiProject Statistics also deems it Mid-importance. Mid-importance for a piece that reads like a collection of discarded theorems and half-formed thoughts.
General
Let’s get this out of the way. A lot of what’s written here isn't precisely true. Not in all circumstances. Which means most of it should have caveats, disclaimers, little footnotes whispering about the limited scope of its validity. IGApprentice noted this back in 2010. Apparently, nobody listened. Or maybe they just didn't care. It’s easier to leave a mess than to clean it up, isn't it?
Then there’s Aetheling in 2011, practically screaming for a rewrite. Calls it "one of the worst in all Wikipedia." A bold statement, but looking at this… I can see why. They offered to add it to their list, but their time was limited. A common affliction, I've noticed. Everyone’s got grand ideas, but the execution… that’s another story.
IGApprentice again, bless their persistent heart, was slowly working on it. Welcoming help, which, judging by the subsequent silence, was about as welcome as a tax audit. They wanted to remove whole sections, re-write them. A sensible approach. The later sections, they said, were "pretty randomly organized." An understatement. They knew Information Geometry, but this wiki thing? First rodeo. They welcomed comments and criticisms. I’m sure they got them. Or, more likely, more silence.
And then, in 2014, another voice, 178.38.60.255, agreeing with the assessment. "See also the remarks below under 'Removing most of the material'." More people seeing the rot, but who's actually doing the work?
Substance
This section is about removing… well, most of the material. IGApprentice in 2011, proposing to cut out large parts. Why? Because they recapitulated well-known differential geometry concepts, already explained elsewhere. Why repeat it poorly when it’s explained adequately elsewhere? They wanted to salvage what was left, turn it into a real article. They even invited screams of pain, hoping for compromise. A generous soul.
linas chimed in, first in 2012, agreeing with the sentiment. They did remove "most of stuff on tangent spaces and metrics and tensors." Because, naturally, that’s covered in any and all textbooks. And, crucially, it had "nothing to do with info geom." They planned to attack the rest later. A noble, if perhaps overambitious, plan.
Later that same day, linas was back, lamenting the state of what remained. "Ugh. That still leaves behind a huge raft of formulas with no intuitive explanation given at all." Sound familiar? They found the "very first section" to be an "awkwardly worded" recapitulation of standard information-theoretic arguments. The next sections? "Hardly better." They planned to clean it up by reading John Baez's posts. A slow process, they admitted.
Then, a few hours later, linas noticed something else. A single revision, apparently, had added "a dense raft of formulas" while removing "a bunch of simply-worded, easy to understand text." So the problem wasn't just bad writing; it was actively replacing clarity with obfuscation. They felt part of the effort should be reviving some of the older, clearer content. And perhaps, just perhaps, some parts, like the alpha connection, should be moved to their own standalone article. A sensible suggestion.
In 2014, 178.38.60.255 agreed again. The summary of differential geometry concepts was "so briefly by intransparent formulas that it looks more like note-cards than an encyclopedia article." They argued for more general wording, with pointers to more in-depth articles. Information geometry, they correctly stated, is a synthesis of statistics, information theory, and differential geometry. Yet, the article focused all its energy on the latter, offering a "hurry-up, technical, but inadequate precis of a semester course in differential geometry." A harsh, but accurate, assessment.
Roland Puntaier offered a different perspective in 2012. They were interested, had read part of an Amari book (presumably a key text in the field), and wanted to share the basics. They admitted they weren't an expert but understood the drift of the criticisms. They suggested repeating essential points and adding references, believing it would benefit newcomers. A collaborative spirit, which, sadly, doesn't always translate into effective contributions.
Examples or Motivation?
A simple plea from 77.109.103.69 in 2017: "Hi, would someone be so kind to add some (simple) examples?" A fundamental question. Without examples, how is anyone supposed to grasp this? It’s like describing color without showing a spectrum.
Article rewrite
Fast forward to 2019. 141.211.130.151 announced they "removed most of the material and started on a rewrite." They admitted it "still needs a lot of work." They struggled with formatting, citing inexperience with Wikipedia. As a geometer, they hoped someone with more statistical knowledge would "help with the statistical background and flesh out the applications a bit more." They even offered to provide citations for where Information Geometry is used. A constructive effort, but the underlying problem of the article's fundamental inadequacy remains. It’s a constant, weary cycle of attempts to fix something that was perhaps fundamentally broken from the start.