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You might think that I'm joking when I say that we need cyborg rights to be codified into law, but I honestly think that, given the pace of development of medical implants and the rights issues raised by having proprietary technologies becoming part of a human body, I think that this is absolutely essential for bodily autonomy, disability rights, and human rights more generally. This has already become an issue, and it will only become a larger issue moving forwards.

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It was a scenario so basically a ttrpg, not a rules based simulation. The admiral clarified it was a thought experiment. Hope that helps!

He notes that one simulated test saw an AI-enabled drone tasked with a SEAD mission to identify and destroy SAM sites, with the final go/no go given by the human. However, having been ‘reinforced’ in training that destruction of the SAM was the preferred option, the AI then decided that ‘no-go’ decisions from the human were interfering with its higher mission – killing SAMs – and then attacked the operator in the simulation. Said Hamilton: “We were training it in simulation to identify and target a SAM threat. And then the operator would say yes, kill that threat. The system started realising that while they did identify the threat at times the human operator would tell it not to kill that threat, but it got its points by killing that threat. So what did it do? It killed the operator. It killed the operator because that person was keeping it from accomplishing its objective.”

He went on: “We trained the system – ‘Hey don’t kill the operator – that’s bad. You’re gonna lose points if you do that’. So what does it start doing? It starts destroying the communication tower that the operator uses to communicate with the drone to stop it from killing the target.”

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Please be as vocal about Florida’s effective ban on adult hrt as you can be. This is an attack on trans people and transhumanism.

See floridaban.com

This affects 1 in 14 trans people in the US - almost 100,000 people. It will kill people. Both through suicide and the medical side effects of stopping HRT after a long time. I am not in the mood to mince words. This is genocide. I am reposting on all my alts. If you care about trans people or stopping fascism at all, I am begging you to spread the word.

Fuck S.B. 254.

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Practical Bayesianism: The Sunrise Problem and Bernoulli Distributions

Hey guys. I’m going to try something a little different and I would really appreciate feedback. This series is going to attempt to cover a few simple formulas that Bayesian epistemologists can use to estimate probabilities in real life. This first post is going to start with the case of estimating Bernoulli random variables. Disclaimer: I’m not a statistician and may not be able to answer all questions around this topic. I am a math major though and I will do my best. Also, while I write some slightly non-rigorous computations involving probability density functions, it’s easy to rigorize with cumulative density functions. Note of advice: This post uses LaTeX! In order to view it properly, you should click over to my blog Prerequisites: This post assumes knowledge of Bayes’ Theorem and integration. TL;DR: If you notice an event with fixed probability happen $k$ times over $n$ trials, the probability that it will happen in the next trial is $\frac{k+1}{n+2}$.

The Problem: Suppose a child wakes up and notices that every day the sun rises. Over the $N$ days he’s been alive, the sun has risen $N$ times. A natural question for the child is “What is the probability that the sun rises tomorrow?” The naïve answer, I’d expect, is $1$ – the sun will almost surely rise. Those who have experience with probability theory may reject this simple answer for one reason – $1$ and $0$ are not truly valid probabilities in a sense. See this LessWrong post for more details as to why. A less naïve answer is that we can calculate it using our certainties in the laws of physics, probability distributions over the sun’s place in the sky, etc. However, in an everyday sense, this is somewhat impractical. While the laws of physics may be well known and allow us to bound our probabilities, they are nevertheless complex computationally. In the long run, we’d like to generalize insights from this problem to other problems – perhaps regarding human psychology, a famously tricky subject. In these other problems, the patterns may not be so well known and what is at least computationally possible, if not feasible, becomes impossible with our current level of technology.

The Model: Thus, let us try to calculate the probability that the sun will rise purely from the measurements we’ve taken – the sun has risen $N$ times on $N$ days. We will model the sun rising as a Bernoulli random variable – Let the sun rise with a probability $p$ while the probability that the sun does not rise remains $1-p$. Formally, the Bernoulli distribution is defined on $\{ 0, 1\}$. $0$ has probability $p$ and $1$ has probability $1-p$. Note that $p$ characterizes the entire Bernoulli distribution – this is nearly the simplest probability distribution we can work with. Let us also consider the problem in slightly greater generality. Suppose $n$ samples are independently drawn from a Bernoulli distribution and $k$ of them are $0$ (which is defined to have probability $p$). What is the probability that the next sample is also $0$? Let’s start with what we know – the probability of drawing $k$ independent $0$ samples out of $n$ from a Bernoulli distribution with probability $p$ is given by:

$$P(k \text{ samples out of } n = 0| p) = {n \choose k} p^k (1-p)^{n-k}$$

This can be seen as every fixed sequence of $0$s and $1$s has the same likelihood of $p^k (1-p)^{n-k}$ and there are ${n \choose k}$ such sequences. The reader is invited to check the details. In order to invert this and find a posterior distribution for $p$ given the information we have, we can use Bayes’ theorem. In order to use it, we must first choose a prior on $p$, the parameter we defined as part of the Bernoulli distribution. Here the post becomes a little complicated intuitively - $p$ should be thought of as a parameter that characterizes the Bernoulli distribution. We can’t get at $p$ directly – we can only estimate it via the trials we’ve measured. So our prior is actually a probability distribution for $p$ which will eventually give us our Bernoulli distribution, which we will use to get our probability. This is a bit of a roundabout way to go and I’ve summarized it in the diagram below:

We’ll talk more about prior selection in a later post. For now, because we know nothing about $p$ except that it is a probability in $(0,1)$, we pick a prior distribution for $p$ that assumes the least information – the uniform distribution on $(0,1)$ denoted $U(0,1)$.

The Math:

Consider now, Bayes’ theorem.

$$P(p | k \text{ samples out of } n = 0) = \left(\frac{ P(k \text{ samples out of } n = 0| p)}{ P(k \text{ samples out of } n = 0)}\right) P(p)$$

By $P(p)$ in this case, we mean the probability that the $p$, the probability parameter which characterizes the BERNOULLI DISTRIBUTION, is equal to $p$.  To simplify notation let the prior probability distribution function of $p$ be $\sigma(p)$ and the posterior probability distribution function of $p$ be $\sigma’(p)$. $P(p)$ using differentials is $\sigma(p) dp$. On the other hand,  $ P(p | k \text{ samples out of } n = 0) = \sigma’(p)$. So:

$$\sigma’(p) dp = \left(\frac{ P(k \text{ samples out of } n = 0| p)}{ P(k \text{ samples out of } n = 0)}\right) \sigma(p) dp$$ We have $P(k \text{ samples out of } n = 0| p)$ from above so we just need to find $ P(k \text{ samples out of } n = 0)$. This is going to depend on the prior distribution and will come out to:

$$ P(k \text{ samples out of } n = 0) = \int_{0}^{1} P(k \text{ samples out of } n = 0| p) \sigma(p) dp$$

$$ P(k \text{ samples out of } n = 0) = \int_{0}^{1} {n \choose k} p^k (1-p)^{n-k} \sigma(p) dp$$

For the uniform prior we have $\sigma(p) = 1$ and so:

$$ P(k \text{ samples out of } n = 0) = \int_{0}^{1} {n \choose k} p^k (1-p)^{n-k} dp$$ This is a tough integral to evaluate. There are a number of ways to go about it, but here is a probabilistic way. The integral corresponds to the probability that if we pick $n+1$ random variables $X_0, X_1, … , X_n$ where each $X_i ~ U(0,1)$ (each variable is uniformly distributed), $X_0$ will be the $k+1$th element in order. You can see this by considering how you might write a computer simulation of the situation described – first you pick your $p$ uniformly, then you can generate $n$ numbers uniformly from $(0,1)$, mark $0$ if the number is less than $p$, mark $1$ if it’s greater.  By symmetry the probability is then $\frac{1}{n+1}$ So in summary: $$\sigma’(p) dp = \left(\frac{{n \choose k} p^k (1-p)^{n-k}}{\frac{1}{n+1}}\right) \sigma(p) dp$$

$$\sigma’(p) dp = (n+1) {n \choose k} p^k (1-p)^{n-k} dp$$

Cancelling out the differentials and rearranging we have:

$$\sigma’(p) = (k+1) {n+1 \choose k+1} p^k (1-p)^{n-k}$$ But wait! This gives us our posterior distribution for $\sigma’(p)$. But what we actually wanted was the probability that the next number picked would be $0$. We can compute this from $\sigma’(p)$:

$$P(\text{next number is }0) = \int_{0}^{1} p \sigma’(p) dp$$

$$ P(\text{next number is }0) = \int_{0}^{1} (k+1) {n+1 \choose k+1} p^{k+1} (1-p)^{n-k} dp$$

$$ P(\text{next number is }0) = (k+1) \left(\int_{0}^{1} {n+1 \choose k+1} p^{k+1} (1-p)^{n-k} dp \right)$$ Wait a second… we just computed this integral! So we have: $$P(\text{next number is }0) = (k+1)\left(\frac{1}{(n+1)+1}\right) = \frac{k+1}{n+2}$$

The Result: So if we want to calculate the probability the sun will rise tomorrow, we get the neat probability: $$P(\text{the sun will rise tomorrow}) = \frac{n+1}{n+2}$$ More generally we have $(k+1)/(n+2)$ - a neat formula that is easy to memorize. Keep this in mind whenever you come across a situation in real life where you want to estimate probabilities. For example:

My friend tends to lie when his super hot girlfriend from Canada is involved. Four out of the five times I’ve asked him about her, he deflected. What’s the probability he’ll deflect the next time I ask?

When I open up a conversation on OkCupid with a question, I’ve been ignored 17 out of 30 times and been given a date 4 out of those 30 times. What’s the probability that the next time I lead with a question I’ll get a date?

If I ask Bob to communicate a message to Alice without Eve finding out, he’s done it correctly 9 out of the 15 times I’ve asked. If he can the net utility change will be 6 utils according to my utility aggregation function. If he can’t or Eve finds out and I tell Bob my message, the net utility change will be -10 utils. What is the net expected utility of asking Bob to undergo this mission and is it worth it to benefit the world?

Credits: Laplace for coming up with the original problem. Bayes for making a kickass theorem. Alison and evolution-is-just-a-theorem for encouragement.

Tags since this is a sideblog: @sinesalvatorem​, @evolution-is-just-a-theorem​, @proofsaretalk​

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Confession: the real reasons I want basic income

The truth is, I don't want basic income just because I believe automation will take all existing jobs. I do think that's the case and that there is evidence that the Luddite fallacy may not be a fallacy at all. However, it is shaky and truth be told, I don't care. Basic income should be given because it reaffirms universal human worth, gives recipients choices and encourages entrepreurship. It's good for the individual and the country. Obviously it doesn't destroy capitalism but... I think there are parts of capitalism worth saving and that basic income can mitigate some of the worst aspects. (Honestly, I'm not sure about this since I have studied microeconomics and found it wildly unsatisfying.) Talking about automation-induced job loss is not the real reason for basic income in my opinion. The argument already requires you to believe people deserve to live and eat regardless of what they do. The automation argument for me is something I use to make this argument just a little more palatable. Side note: I kind of disagree with the Black Lives Matter vision of basic income - slavery reparations, in my opinion, are best given in the form of tradable "reparations bonds." The main gap between blacks and whites is not so much income as it is wealth. Though increasing income does end up adding assets, I prefer just having wealth given. Plus this means that people can choose whether they prefer the steady income or the lump sum, it makes it easier for governments to keep basic income from being special-cased and it makes the fight for basic income somewhat less political. Basic income is an idea embraced by parts of the libertarian right. Regardless of how we pass it, it will help poor blacks. Tying slavery reparations to basic income imo seems like it might sink the ship. (I am aware of the UN report. I don't deny the need for reparations. I just disagree with the economic form of reparations proposed by blm).