(This page demonstrates new explanation-based features in Arbital. Please don't post this page to Hacker News or other large sites, since Arbital's features are still very much under development, and we're not sure Arbital can handle large amounts of traffic. Commenting or editing on Arbital currently requires a special invite code and is not generally available. If you are a superprogrammer interested in working for Arbital or you are an accredited investor interested in Arbital, you can contact Alexei Andreev at alexei@arbital.com. (This is not an offer to sell securities nor a solicitation to buy securities. This is merely a solicitation of interest to begin a discussion with the Company’s officers. Any offer to buy or sell securities will be made by formal documents and be made to accredited investors only, in accordance with Title II of the JOBS Act.))
According to its advocates, Bayesian reasoning is a way of seeing the world, and our beliefs about the world, in the light of probability theory, in particular Bayes's Theorem or Bayes's Rule. This probability-theoretic way of seeing the world can apply to scientific issues, to tasks in machine learning, and to everyday life.
This explanation of Bayesian reasoning is hosted on Arbital, a startup and website still under development. It demonstrates the use of several new Arbital features to make complicated explanations easier to write, and steer every user to the text that fits them best. Rather than different pages on Bayes being pitched to different technical levels and different interests, Arbital tries to have a single page where all of your friends can send all of their friends, without everyone needing to find a slightly different URL.
One of these Arbital features is smart links. If you hover your mouse over green text, you'll see a popup with a summary of the page behind the link. These summaries are intended to explain, or remind you of the explanation, quite briefly; so if they're still confusing, click on through. A popup may also contain multiple tabs with summaries of different technical levels, like "Brief", "Summary", and "Technical" tabs. Similarly, whole pages may also have different tabs, which you can click on to see explanations targeted at different audiences.
Let's start with a key question for deciding which page versions and summaries you'll see by default. You'll always be able to click through to other page tabs, so nothing will be hidden from you.
[multiple-choice: What's the highest level of math you can read easily? a: I'm bad at math. !knows: Math 0 b: I'm not bad at math, but I'm not especially good at it either. knows: Math 0 c: I can have fun with math, and I won't be anxious if I see a word problem I don't already know how to solve. knows: Math 0, Math 1 d: I am a programmer, physical engineer, or some other profession that calls on me to sometimes think in algebra. knows: Math 0, Math 1, Math 2, Ability to read algebra f: I do research-level math. Hit me with the LaTeX formulas. knows: Math 0, Math 1, Math 2, Math 3, Ability to read algebra ]
[!knows-requisite(Math3): [knows-requisite(Math2): [multiple-choice: Cool! Do you read calculus too? a: Yep, I grok integral signs. knows: Ability to read calculus b: Nope, sorry. ] ] ]
[knows-requisite(Math1):
[multiple-choice: Are there any aspects of Bayesian reasoning that especially interest you? (This will cause you to be shown additional details in the text.) a: I'd like fewer diversions, at least on my first read-through; I'd rather not be distracted or have the explanation slowed down. b: Maybe... ] ]
[knows-requisite(Bayes_maybe_details):
[multiple-choice: Are you especially interested in using Bayesian reasoning as an everyday life skill, and in the exercises and homework needed to learn how to parse real-life situations into Bayesian concepts? a: Yes b: No ]
[multiple-choice: Are you especially interested in philosophical justifications for Bayesian reasoning, or in Bayesian justifications for philosophy? a: Yes b: No ]
[multiple-choice: Are you especially interested in hearing contrasts or justifications from the perspective of other statistical viewpoints, such as significance-testing and frequentism? a: Yes b: No ]
[multiple-choice: Are you especially interested in mathematical foundations, axiomatizations, and proofs? a: Yes b: No ]
]