Filter This week

## [Link] S-risks: Why they are the worst existential risks, and how to prevent them

16 20 June 2017 12:34PM

## Instrumental Rationality 1: Starting Advice

12 18 June 2017 06:43PM

## [Link] Putanumonit: What statistical power means, and why I'm terrified about psychology

11 21 June 2017 06:29PM

## Bi-Weekly Rational Feed

8 24 June 2017 12:07AM

===Highly Recommended Articles:

Introducing The Ea Involvement Guide by The Center for Effective Altruism (EA forum) - A huge list of concrete actions you can take to get involved. Every action has a brief description and a link to an article. Each article rates the action on time commitment, duration, familiarity and occupation. Very well put together.

Deep Reinforcement Learning from Human Preferences - An algorithm learns to backflip with 900 bits of feedback from the human evaluator. "One step towards building safe AI systems is to remove the need for humans to write goal functions, since using a simple proxy for a complex goal, or getting the complex goal a bit wrong, can lead to undesirable and even dangerous behavior. In collaboration with DeepMind’s safety team, we’ve developed an algorithm which can infer what humans want by being told which of two proposed behaviors is better."

Build Baby Build by Bryan Caplan - Quote from a paper estimating the high costs of housing restrictions. We should blame the government, especially local government. The top alternate theory is wrong. Which regulations are doing the damage? It's complicated. Functionalists are wrong. State government is our best hope.

The Use And Abuse Of Witchdoctors For Life by Lou (sam[]zdat) - Anti-bullet magic and collective self-defense. Cultural evolution. People don't directly believe in anti-bullet magic, they believe in elders and witch doctors. Seeing like a State. Individual psychology is the foundation. Many psychologically important customs couldn't adapt to the marketplace.

S-risks: Why They Are The Worst Existential Risks by Kaj Sojata (lesswrong) - “S-risk – One where an adverse outcome would bring about severe suffering on a cosmic scale, vastly exceeding all suffering that has existed on Earth so far.” Why we should focus on S-risk. Probability: Artificial sentience, Lack of communication, badly aligned Ai and competitive pressures. Tractability: Relationship with x-risk. Going meta, cooperation. Neglectedness: little attention, people conflate x-risk = s-risk.

Projects Id Like To See by William MacAskill (EA forum) - CEA is giving out £100K grants. General types of applications. EA outreach and Community, Anti-Debates, Prediction Tournaments, Shark Tank Discussions, Research Groups, Specific Skill Building, New Organizations, Writing.

The Battle For Psychology by Jacob Falkovich (Put A Number On It!) - An explanation of 'power' in statistics and why its always good. Low power means that positive results are mostly due to chance. Extremely bad incentives and research practices in psychology. Studying imaginary effects. Several good images.

Identifying Sources Of Cost Disease by Kurt Spindler - Where is the money going: Administration, Increased Utilization, Decreased Risk Tolerance. What market failures are in effect: Unbounded Domains, Signaling and Competitive Pressure (ex: military spending), R&D doesn't cut costs it creates new ways to spend money, individuals don't pay. Some practical strategies to reduce cost disease.

===Scott:

To Understand Polarization Understand The Extent Of Republican Failure by Scott Alexander - Conservative voters voted for “smaller government”, “fewer regulations”, and “less welfare state”. Their reps control most branches of the government. They got more of all three (probably thanks to cost disease).

Against Murderism by Scott Alexander - Three definitions of racism. Why 'Racism as motivation' fits best. The futility of blaming the murder rate in the USA on 'murderism'. Why its often best to focus on motivations other than racism.

Open Thread Comment by John Nerst (SSC) - Bi-weekly public open thread. I am linking to a very interesting comment. The author made a list of the most statistically over-represented words in the SSC comment section.

Some Unsong Guys by Scott Alexander (Scratchpad) - Pictures of Unsong Fan Art.

What is Depression Anyway: The Synapse Hypothesis - Six seemingly distinct treatments for depression. How at least six can be explained by considering synapse generation rates. Skepticism that this method can be used to explain anything since the body is so inter-connected. Six points that confuse Scott and deserve more research. Very technical.

===Rationalist:

Idea For Lesswrong Video Tutoring by adamzerner (lesswrong) - Community Video Tutoring. Sign up to either give or receive tutoring. Teaching others is a good way to learn and lots of people enjoy teaching. Hopefully enough people want to learn similar things. This could be a great community project and I recommend taking a look.

Regulatory Arbitrage For Medical Research What I Know So Far by Sarah Constantin (Otium) - Economics of avoiding the USA/FDA. Lots of research is already conducted in other countries. The USA is too large of a market not to sell to. Investors aren't interested in cheap preliminary trials. Other options: supplements, medical tourism, clinic ships, cryptocurrency.

Responses To Folk Ontologies by Ferocious Truth - Folk ontology: Concepts and categories held by ordinary people with regard to an idea. Especially pre-scientific or unreflective ones. Responses: Transform/Rescue, Deny or Restrict/Recognize. Rescuing free will and failing to rescue personal identity. Rejecting objective morality. Restricting personal identity and moral language. When to use each approach.

The Battle For Psychology by Jacob Falkovich (Put A Number On It!) - An explanation of 'power' in statistics and why its always good. Low power means that positive results are mostly due to chance. Extremely bad incentives and research practices in psychology. Studying imaginary effects. Several good images.

A Tangled Task Future by Robin Hanson - We need to untangle the economy to automate it. What tasks are heavily tangled and which are not. Ems and the human brain as a legacy system. Human brains are well-integrated and good at tangled tasks.

Epistemic Spot Check Update by Aceso Under Glass - Reviewing self-help books. Properties of a good self-help model: As simple as possible but not more so, explained well, testable on a reasonable timescale, seriously handles the fact the techniques might now work, useful. The author would appreciate feedback.

Skin In The Game by Elo (BearLamp) - Armchair activism and philosophy. Questions to ask yourself about your life. Actually do the five minute exercise at the end.

Momentum Reflectiveness Peace by Sarah Constantin (Otium) - Rationality requires a reflective mindset; a willingness to change course and consider how things could be very different. Momentum, keeping things as they are except more so, is the opposite of reflectivity. Cultivating reflectiveness: rest, contentment, considering ideas lightly and abstractly. “Turn — slowly.”

The Fallacy Fork Why Its Time To Get Rid Of by theFriendlyDoomer (r/SSC) - "The main thesis of our paper is that each and every fallacy in the traditional list runs afoul of the Fallacy Fork. Either you construe the fallacy in a clear-cut and deductive fashion, which means that your definition has normative bite, but also that you hardly find any instances in real life; or you relax your formal definition, making it defeasible and adding contextual qualifications, but then your definition loses its teeth. Your “fallacy” is no longer a fallacy."

Instrumental Rationality 1 Starting Advice by lifelonglerner (lesswrong) - "This is the first post in the Instrumental Rationality Sequence. This is a collection of four concepts that I think are central to instrumental rationality-caring about the obvious, looking for practical things, practicing in pieces, and realistic expectations."

Concrete Ways You Can Help Make The Community Better by deluks917 (lesswrong) - Write more comments on blog posts and non-controversial posts on lw and r/SSC. Especially consider commenting on posts you agree with. People are more likely to comment if other people are posting high quality comments. Projects: Gaming Server, aggregate tumblr effort-posts, improve lesswrong wiki, leadership in local rationalist group

Daring Greatly by Bayesian Investor - Fairly positive book review, some chapters were valuable and it was an easy read. How to overcome shame and how it differs from guilt. Perfectionism vs healthy striving. If you stop caring about what others think you lose your capacity for connection

A Call To Adventure by Robin Hanson - Meaning in life can be found by joining or starting a grand project. Two possible adventures: Promoting and implementing futarchy (decision making via prediction markets). Getting a real understanding of human motivation.

Thought Experiment Coarsegrained Vr Utopia by cousin_it (lesswrong) - Assume an AI is running a Vr simulation that is hooked up to actual human brains. This means that the AI only has to simulate nature at a coarse grained level. How hard would it be to make that virtual reality a utopia?

[The Rationalist-sphere and the Lesswrong Wiki]](http://lesswrong.com/r/discussion/lw/p4y/the_rationalistsphere_and_the_less_wrong_wiki/) - What's next for the Lesswrong wiki. A distillation of Lesswrong. Fully indexing the diaspora. A list of communities. Spreading rationalist ideas. Rationalist Research.

Deep Reinforcement Learning from Human Preferences - An algorithm learns to backflip with 900 bits of feedback from the human evaluator. "One step towards building safe AI systems is to remove the need for humans to write goal functions, since using a simple proxy for a complex goal, or getting the complex goal a bit wrong, can lead to undesirable and even dangerous behavior. In collaboration with DeepMind’s safety team, we’ve developed an algorithm which can infer what humans want by being told which of two proposed behaviors is better."

Where Do Hypotheses Come From by c0rw1n (lesswrong) - Link to a 25 page article. "Why are human inferences sometimes remarkably close to the Bayesian ideal and other times systematically biased? In particular, why do humans make near-rational inferences in some natural domains where the candidate hypotheses are explicitly available, whereas tasks in similar domains requiring the self-generation of hypotheses produce systematic deviations from rational inference. We propose that these deviations arise from algorithmic processes approximating Bayes’ rule."

The Precept Of Universalism by H i v e w i r e d - "Universality, the idea that all humans experience life in roughly the same way. Do not put things or ideas above people. Honor and protect all peoples." Eight points expanding on how to put people first and honor everyone.

We Are The Athenians Not The Spartans by wubbles (lesswrong) - "Our values should be Athenian: individualistic, open, trusting, enamored of beauty. When we build social technology, it should not aim to cultivate values that stand against these. High trust, open, societies are the societies where human lives are most improved."

===EA:

Updating My Risk Estimate of Geomagnetic Big One by Open Philosophy - Risk from magnetic storms caused by the sun. "I have raised my best estimate of the chance of a really big storm, like the storied one of 1859, from 0.33% to 0.70% per decade. And I have expanded my 95% confidence interval for this estimate from 0.0–4.0% to 0.0–11.6% per decade."

Links by GiveDirectly - Eight Media articles on Cash Transfers, Basic Income and Effective Altruism.

Are Givewells Top Charities The Best Option For Every Donor by The GiveWell Blog - Why GiveWell recommend charities are a good option for most donors. Which donors have better options: Donors with lots of time, high trust in a particular institution or values different from GiveWell's.

A New President of GWWC by Giving What We Can - Julia Wise is the New president of Giving What We Can.

Angst Ennui And Guilt In Effective Altruism by Gordon (Map and Territory) - Learning about existential risk can cause psychological harm. Guilt about being unable to help solve X-risk. Akrasia. Reasons to not be guilty: comparative advantage, ability is unequally distributed.

S-risks: Why They Are The Worst Existential Risks by Kaj Sojata (lesswrong) - “S-risk – One where an adverse outcome would bring about severe suffering on a cosmic scale, vastly exceeding all suffering that has existed on Earth so far.” Why we should focus on S-risk. Probability: Artificial sentience, Lack of communication, badly aligned Ai and competitive pressures. Tractability: Relationship with x-risk. Going meta, cooperation. Neglectedness: little attention, people conflate x-risk = s-risk.

Update On Sepsis Donations Probably Unnecessary by Sarah Constantin (Otium) - Sarah C had asked people to crowdfund a sepsis RCT. The trial will probably get funded by charitable foundations. Diminishing returns. Finding good giving opportunities is hard and talking to people in the know is a good way to find things out.

What Is Valuable About Effective Altruism by Owen_Cotton-Barratt (EA forum) - Why should people join EA? The impersonal and personal perspectives. Tensions and synergies between the two perspectives. Bullet point conclusions for researchers, community leaders and normal members.

QALYs/$Are More Intuitive Than$/QALYs by ThomasSittler (EA forum) - QALYs/$are preferable to$/QALYs. visual representations on graphs. Avoiding Small numbers and re-normalizing to QUALs/10K\$.

Introducing The Ea Involvement Guide by The Center for Effective Altruism (EA forum) - A huge list of concrete actions you can take to get involved. Every action has a brief description and a link to an article. Each article rates the action on time commitment, duration, familiarity and occupation. Very well put together.

Cash is King by GiveDirectly - Eight media articles about Effective Altruism and Cash transfers.

Separating GiveWell and the Open Philanthropy Project by The GiveWell Blog - The GiveWell perspective. Context for the sale. Effect on donors who rely on GiveWell. Organization changes at GiveWell. Steps taken to sell Open Phil assets. The new relationship between GiveWell and Open Phil.

Open Philanthropy Project is Now an Independent Organization by Open Philosophy - The evolution of Open Phil. Why should Open Phil split from GiveWell. LLC structure.

Projects Id Like To See by William MacAskill (EA forum) - CEA is giving out £100K grants. General types of applications. EA outreach and Community, Anti-Debates, Prediction Tournaments, Shark Tank Discussions, Research Groups, Specific Skill Building, New Organizations, Writing.

===Politics and Economics:

No Us School Funding Is Actually Somewhat Progressive by Random Critical Analysis - Many people think that wealthy public school districts spend more per pupil. This information is outdated. Within most states spending is higher on disadvantaged students. This is despite the fact that school funding is mostly local. Extremely thorough with loads of graphs.

Build Baby Build by Bryan Caplan - Quote from a paper estimating the high costs of housing restrictions. We should blame the government, especially local government. The top alternate theory is wrong. Which regulations are doing the damage? It's complicated. Functionalists are wrong. State government is our best hope.

Identifying Sources Of Cost Disease by Kurt Spindler - Where is the money going: Administration, Increased Utilization, Decreased Risk Tolerance. What market failures are in effect: Unbounded Domains, Signaling and Competitive Pressure (ex: military spending), R&D doesn't cut costs it creates new ways to spend money, individuals don't pay. Some practical strategies to reduce cost disease.

The Use And Abuse Of Witchdoctors For Life by Lou (sam[]zdat) - Anti-bullet magic and collective self-defense. Cultural evolution. People don't directly believe in anti-bullet magic, they believe in elders and witch doctors. Seeing like a State. Individual psychology is the foundation. Many psychologically important customs couldn't adapt to the marketplace.

Greece Gdp Forecasting by João Eira (Lettuce be Cereal) - Transforming the Data. Evaluating the Model with Exponential Smoothing, Bagged ETS and ARIMA. The regression results and forecast.

Links 9 by Artir (Nintil) - Economics, Psychology, Artificial Intelligence, Philosophy and other links.

Amazon Buying Whole Foods by Tyler Cowen - Quotes from Matt Yglesias, Alex Tabarrock, Ross Douthat and Tyler. “Dow opens down 10 points. Amazon jumps 3% after deal to buy Whole Foods. Walmart slumps 7%, Kroger plunges 16%”

Historical Returns Market Portfolio by Tyler Cowen - From 1960 to 2015 the global market portfolio realized a compounded real return of 4.38% with a std of 11.6%. Investors beat savers by 3.24%. Link to the original paper.

Trust And Diver by Bryan Caplan - Robert Putnam's work is often cited as showing the costs of diversity. However Putnam's work shows the negative effect of diversity on trust is rather modest. On the other hand Putnam found multiple variables that are much more correlated with trust (such as home ownership).

Why Optimism is More Rational than Pessimism by TheMoneyIllusion - Splitting 1900-2017 into Good and Bad periods. We learn something from our mistakes. Huge areas where things have improved long term. Top 25 movies of the 21st Century. Artforms in decline.

Is Economics Science by Noah Smith - No one knows what a Science is. Thoeries that work (4 examples). The empirical and credibility revolutions. Why we still need structural models. Ways economics could be more scientific. Data needs to kill bad theories. Slides from Noah's talk are included and worth playing but assume familiarity with the economics profession.

===Misc:

Clojure Concurrency And Blocking With Coreasync by Eli Bendersky - Concurrent applications and blocking operations using core.async. Most of the article compares threads and go-blocks. Lots of code and well presented test results.

Optopt by Ben Kuhn - Startup options are surprisingly valuable once you factor in that you can quit of the startup does badly. A mathematical model of the value of startup options and the optimal time to quit. The ability to quit rose the option value by over 50%. The sensitivity of the analysis with respect to parameters (opportunity cost, volatility, etc).

Epistemic Spot Check: The Demon Under The Microscope by Aceso Under Glass - Biography of the man who invented sulfa drugs, the early anti-bacteria treatments which were replaced by penicillin. Interesting fact checks of various claims.

Sequential Conversion Rates by Chris Stucchio - Estimating success rates when you have noisy reporting. The article is a sketch of how the author handled such a problem in practice.

Set Theory Problem by protokol2020 - Bring down ZFC. Aleph-zero spheres and Aleph-one circles.

Connectome Specific Harmonic Waves On Lsd by Qualia Computing - Transcript and video of a talk on neuroimaging the brain on LSD. "Today thanks to the recent developments in structural neuroimaging techniques such as diffusion tensor imaging, we can trace the long-distance white matter connections in the brain. These long-distance white matter fibers (as you see in the image) connect distant parts of the brain, distant parts of the cortex."

Approval Maximizing Representations by Paul Christiano - Representing images. Manipulation representations. Iterative and compound encodings. Compressed representations. Putting it all together and bootstrapping reinforcement learning.

Travel by Ben Kuhn - Advice for traveling frequently. Sleeping on the plane and taking redeyes. Be robust. Bring extra clothes, medicine, backup chargers and things to read when delayed. Minimize stress. Buy good luggage and travel bags.

Learning To Cooperate, Compete And Communicate by Open Ai - Competitive multi-agent models are a step towards AGI. An algorithm for centralized learning and decentralized execution in multi-agent environment. Initial Research. Next Steps. Lots of visuals demonstrating the algorithm in practice.

Openai Baselines Dqn by Open Ai - "We’re open-sourcing OpenAI Baselines, our internal effort to reproduce reinforcement learning algorithms with performance on par with published results." Best practices we use for correct RL algorithm implementations. First release: DQN and three of its variants, algorithms developed by DeepMind.

Corrigibility by Paul Christiano - Paul defines the sort of AI he wants to build, he refers to such systems as "corrigible". Paul argues that a sufficiently corrigible agent will become more corrigible over time. This implies that friendly AI is not a narrow target but a broad basin of attraction. Corrigible agents prefer to build other agents that share the overseers preferences, not their own. Predicting that the overseer wants me to turn off when he hits the off-button is not complicated relative to being deceitful. Comparison with Eliezer's views.

G Reliant Skills Seem Most Susceptible To Automation by Freddie deBoer - Computers already outperform humans in g-loaded domains such as Go and Chess. Many g-loaded jobs might get automated. Jobs involving soft or people skills are resilient to automation.

Persona 5: Spoiler Free Review - Persona games are long but deeply worthwhile if you enjoy the gameplay and the story. Persona 5 is much more polished but Persona 3 has a more meaningful story and more interesting decisions. Tips for Maximum Enjoyment of Persona 5. Very few spoilers.

Sea Problem by protokol2020 - A fun problem. Measuring sea level rise.

===Podcast:

83 The Politics Of Emergency by Waking Up with Sam Harris - Fareed Zakaria. "His career as a journalist, Samuel Huntington's "clash of civilizations," political partisanship, Trump, the health of the news media, the connection between Islam and intolerance"

On Risk, Statistics, And Improving The Public Understanding Of Science by 80,000 Hours - A lifetime of communicating science. Early career advice. Getting people to intuitively understand hazards and their effect on life expectancy.

Ed Luce by Tyler Cowen - The Retreat of Western Liberalism "What a future liberalism will look like, to what extent current populism is an Anglo-American phenomenon, Modi’s India, whether Kubrick, Hitchcock, and John Lennon are overrated or underrated, and what it is like to be a speechwriter for Larry Summers."

Thomas Ricks by EconTalk - Thomas Ricks book Churchill and Orwell. Overlapping lives and the fight to preserve individual liberty.

The End Of The World According To Isis by Waking Up with Sam Harris - Graeme Wood. His experience reporting on ISIS, the myth of online recruitment, the theology of ISIS, the quality of their propaganda, the most important American recruit to the organization, the roles of Jesus and the Anti-Christ in Islamic prophecy, free speech and the ongoing threat of jihadism.

Jason Khalipa by Tim Ferriss - "8-time CrossFit Games competitor, a 3-time Team USA CrossFit member, and — among other athletic feats — he has deadlifted 550 pounds, squatted 450 pounds, and performed 64 pullups at a bodyweight of 210 pounds."

Dario Amodei, Paul Christiano & Alex Ray. - 80K hours released a detailed guide to careers in AI policy. " We discuss the main career paths; what to study; where to apply; how to get started; what topics are most in need of research; and what progress has been made in the field so far." Transcript included.

Don Bourdreaux Emergent Order by EconTalk - "Why is it that people in large cities like Paris or New York City people sleep peacefully, unworried about whether there will be enough bread or other necessities available for purchase the next morning? No one is in charge--no bread czar. No flour czar."

Tania Lombrozo On Why We Evolved The Urge To Explain by Rational Speaking - "Research on what purpose explanation serves -- i.e., why it helps us more than our brains just running prediction algorithms. Tania and Julia also discuss whether simple explanations are more likely to be true, and why we're drawn to teleological explanations"

## Idea for LessWrong: Video Tutoring

8 23 June 2017 09:40PM

Idea: we coordinate to teach each other things via video chat.

• We (mostly) all like learning. Whether it be for fun, curiosity, a stepping stone towards our goals.
• My intuition is that there's a lot of us who also enjoy teaching. I do, personally.
• Enjoyment aside, teaching is a good way of solidifying ones knowledge.
• Perhaps there would be positive unintended consequences. Eg. socially.
• Why video? a) I assume that medium is better for education than simply text. b) Social and motivational benefits, maybe. A downside to video is that some may find it intimidating.
• It may be nice to evolve this into a group project where we iteratively figure out how to do a really good job teaching certain topics.
• I see the main value in personalization, as opposed to passive lectures/seminars. Those already exist, and are plentiful for most topics. What isn't easily accessible is personalization. With that said, I figure it'd make sense to have about 5 learners per teacher.

So, this seems like something that would be mutually beneficial. To get started, we'd need:

1. A place to do this. No problem: there's Hangouts, Skype, https://talky.io/, etc.
2. To coordinate topics and times.

Personally, I'm not sure how much I can offer as far as doing the teaching. I worked as a web developer for 1.5 years and have been teaching myself computer science. I could be helpful to those unfamiliar with those fields, but probably not too much help for those already in the field and looking to grow. But I'm interested in learning about lots of things!

Perhaps a good place to start would be to record in some spreadsheet, a) people who want to teach, b) what topics, and c) who is interested in being a Learner. Getting more specific about who wants to learn what may be overkill, as we all seem to have roughly similar interests. Or maybe it isn't.

## [Link] Three Responses to Incorrect Folk Ontologies

8 21 June 2017 02:26PM

## [Link] Angst, Ennui, and Guilt in Effective Altruism

2 19 June 2017 08:38PM

## [Link] The evolution of superstitious and superstition-like behaviour

1 23 June 2017 04:14PM

## Priors Are Useless

1 21 June 2017 11:42AM

## NOTE.

This post contains Latex. Please install Tex the World for Chromium or other similar Tex typesetting extensions to view this post properly.

# Priors are Useless.

Priors are irrelevant. Given two different prior probabilities $Pr_{i_1}$, and $Pr_{i_2}$ for some hypothesis $H_i$.
Let their respective posterior probabilities be $Pr_{i_{z1}}$ and $Pr_{i_{z2}$.
After sufficient number of experiments, the posterior probability $Pr_{i_{z1}} \approx [;Pr_{i_{z2}$.
Or More formally:
$\lim_{n \to \infty} \frac{ Pr_{i_{z1}}}{Pr_{i_{z2}}} = 1$.
Where $n$ is the number of experiments.
Therefore, priors are useless.
The above is true, because as we carry out subsequent experiments, the posterior probability $Pr_{i_{z1_j}}$ gets closer and closer to the true probability of the hypothesis $Pr_i$. The same holds true for $Pr_{i_{z2_j}}$. As such, if you have access to a sufficient number of experiments the initial prior hypothesis you assigned the experiment is irrelevant.

To demonstrate.
http://i.prntscr.com/hj56iDxlQSW2x9Jpt4Sxhg.png
This is the graph of the above table:
http://i.prntscr.com/pcXHKqDAS\_C2aInqzqblnA.png

In the example above, the true probability of Hypothesis $H_i$ $(P_i)$ is $0.5$ and as we see, after sufficient number of trials, the different $Pr_{i_{z1_j}}$s get closer to $0.5$.

To generalize from my above argument:

If you have enough information, your initial beliefs are irrelevant—you will arrive at the same final beliefs.

Because I can’t resist, a corollary to Aumann’s agreement theorem.
Given sufficient information, two rationalists will always arrive at the same final beliefs irrespective of their initial beliefs.

The above can be generalized to what I call the “Universal Agreement Theorem”:

Given sufficient evidence, all rationalists will arrive at the same set of beliefs regarding a phenomenon irrespective of their initial set of beliefs regarding said phenomenon.

Prove $\lim_{n \to \infty} \frac{ Pr_{i_{z1}}}{Pr_{i_{z2}}} = 1$.

## Open thread, June. 19 - June. 25, 2017

1 18 June 2017 11:10PM
##### If it's worth saying, but not worth its own post, then it goes here.

Notes for future OT posters: