Epictetus

Karma: 956

Epictetus 22 Dec 2014 12:19 UTC
17 points
on: Welcome to Less Wrong! (7th thread, December 2014)
Hello. My name is Tom. I’m 27 and currently working an a PhD in mathematics. I came to this site by following a chain of links that started with TVTropes of all things.

I have been a fan of rational thinking as long as I can remember. I’d always had the habit of asking questions and trying to see things from every point of view. I devoured all sorts of books growing up and shifted my viewpoints often enough that I became willing to accept the notion that everything I currently believe is wrong. That’s what pushed me to constantly question my own beliefs. I have read enough of this site to satisfy myself that it would be worthwhile to make an account and perhaps participate in the community that built it.

Epictetus 23 Dec 2014 5:20 UTC
0 points
on: 0 And 1 Are Not Probabilities
If I roll a die, then one of the events that can happen will happen. That’s just saying that if S is my sample space, then P(S) = 1. Similarly, P(~S) = 0, which is just saying that impossible things won’t happen. The former statement is an axiom in the standard mathematical treatments of the subject. These statements may be trivial, but I distrust any mathematics that can’t handle trivial cases.

Rejecting 1 as a probability would be catastrophic when you’re dealing with discrete spaces. If you’re the sort to reject infinity, then it would follow that all probability spaces are discrete. At that point probability loses its rigor. Preference for odds or log odds just means that you have to live with using the extended reals with special conventions for the infinities.

Epictetus 23 Dec 2014 11:37 UTC
0 points
in reply to: ike’s comment on: 0 And 1 Are Not Probabilities
Real life is complex enough that there is merit to the philosophical position that one should refrain from assigning probabilities of 0 or 1 to nontrivial events. Categorically denying that any event can have probability 0 or 1 is an extreme position (which, applied to itself, would really mean that a given event would have a high probability of not occurring with probability 0 or 1).

From the purely mathematical standpoint, removing 0 and 1 from the set of possible probabilities breaks the current foundations of the theory. The existence of a sample space containing all possibilities does not depend on whether we humans can comprehend them all. If the sample space of all possibilities exists and P(S) < 1, then a lot of theorems break down. That’s where you live with idealizations like absolute certainty (or almost certainty in the infinite case) or else find something other than probability to use to model the real world.

Epictetus 23 Dec 2014 18:40 UTC
0 points
in reply to: ike’s comment on: 0 And 1 Are Not Probabilities
When I say that the possibilities can be listed in principle, what I mean is that there some set S that contains them and make no reference to any practical problems with describing or storing its elements. Like the points and lines of geometry, it’s a Platonic idealization.

There was a suggested fix to your problem in the post, why isn’t that good enough for you?

Because talk of magical symbols is a good sign that the passage was meant to ridicule the use of infinity. The very next paragraph seeks to expunge such “magical symbols” from probability theory.

Epictetus 26 Dec 2014 3:35 UTC
1 point
on: Rationality Quotes December 2014

At this point it should become apparent that I do not think that theorems are really proved. As G. H. Hardy said long ago, we emit some symbols, another person reads them, and they are either convinced or not by them. To simple people who believe whatever they read and do not question things for themselves, a proof is a proof is a proof, but to others a proof merely supplies a way of thinking about the theorem, and it is up to the individual to form an opinion. Formal proofs, where there is deliberately no meaning, can convince only formalists, and of the results obtained they themselves seem to deny any meaning. Is that to be the mathematics we are to use in understanding the world we live in?

-Richard Hamming, Mathematics on a Distant Planet

Epictetus 26 Dec 2014 4:16 UTC
1 point
in reply to: ike’s comment on: Rationality Quotes December 2014
Thanks! I’ve made the change.

Epictetus 28 Dec 2014 8:00 UTC
3 points
in reply to: gjm’s comment on: Rationality Quotes December 2014
I would say that atheism is a religion in the sense that it addresses the big questions that our familiar religions do. A religion that answers “Does God exist?” in the affirmative will have to address the follow-up questions like “What is the nature of God?”, “What is the relationship between God and man?”, and “How can I get God to stop smiting me?”. These follow-up questions are where traditional religions hit their stride and build an apparatus for communicating with God, educating people about the answers to these questions, etc. Atheism denies the existence of God (broadly speaking) and doesn’t have to answer the sorts of follow-up questions that theists do.

I think the issue gets complicated by the fact that our world is a lot different from the one that spawned the major religions. In olden days, priests were the learned class. They were philosophers, healers, historians and thinkers as well as spiritual leaders. Religion was inextricably tied to culture. You got philosophy, jurisprudence, history, and cultural norms along with the spiritual stuff. For example, think of how much of Jewish culture is tied up in Judaism.

Nowadays we have access to accurate information on many different beliefs and theories on any topic imaginable. It’s an intellectual buffet. Atheism grew in an environment where it wasn’t so closely tied to these cultural norms or that philosophy. Atheism is restricted to spiritual matters alone. So, I suppose the question of whether atheism is a religion depends on whether you think religion should provide a comprehensive guide to living.

Epictetus 1 Jan 2015 19:23 UTC
13 points
on: Rationality Quotes January 2015

To the superficial observer, scientific truth is unassailable, the logic of science is infallible; and if scientific men sometimes make mistakes, it is because they have not understood the rules of the game. Mathematical truths are derived from a few self-evident propositions, by a chain of flawless reasonings; they are imposed not only on us, but also on nature itself. By them the Creator is fettered, as it were, and His choice is limited to a relatively small number of solutions. A few experiments, therefore, will be sufficient to enable us to determine what choice He has made. From each experiment a number of consequences will follow by a series of mathematical deductions...This, to the minds of most people...is the origin of certainty in science.

But upon more mature reflection the position held by hypothesis was seen; it was recognized that it is as necessary to the experimenter as to the mathematician. And then the doubt arose if all these constructions are built on solid foundations. The conclusion was drawn that a breath would bring them to the ground. This sceptical attitude does not escape the charge of superficiality. To doubt everything or to believe everything is two equally convenient solutions; both dispense with the necessity of reflection.

-Henri Poincare, Science and Hypothesis

Epictetus 2 Jan 2015 21:05 UTC
0 points
on: Treating anthropic selfish preferences as an extension of TDT

One might then make an argument about the decision question that goes like this: Before I swore this oath, my probability of going to a tropical island was very low. After, it was very high. Since I really like tropical islands, this is a great idea. In a nutshell, I have increased my expected utility by making this oath.

If it is indeed in your power to swear and execute such an oath, then “I will make an oath to simulate this event and make such-and-such changes” is a legitimate event that would impact any probability calculation. Before swearing the oath, there was still the probability of you swearing it in the future and executing it.

The probability of going to a tropical island given that the oath was made is likely higher than it was before the oath was made, but the only way it would be significantly higher is if there was a very low probability of the oath being made in the first place.

Epictetus 3 Jan 2015 2:20 UTC
0 points
on: Understanding Who You Really Are

The answer was that these questions, when posed as philosophical dilemmas, were bullshit.

I’ve always interpreted them as prompts to introspection. The sages of old gave advice along the lines of “Know thyself”, which naturally leads one to ask, “Who am I?” I can say, “I am a mathematician”, which is fine when I need to list my profession but that line of questioning seeks to get past such superficial details. The purpose of the advice is to strip away the facades we put up to interact with others and to unearth the lies we tell ourselves. You can find the similar sentiments dressed up in the language of psychology and cognitive science on this very website. The questions are vague because you’re compressing a lot of information into a simple, easy-to-remember form.

As you’ve pointed out, in everyday usage context will dictate the appropriate response. The serious sages wouldn’t expect you to articulate a response because what they really want is to prompt some serious reflection. That leaves us with:

So when a young philosopher follows up your response with, “no really, who are you?”, you should respond with asking, “what in particular would you like to know?”

If you want to disengage from that conversation, the old “I am I” works. Or you can be graceful and say, “I’m still trying to figure that out.” The sort of young philosopher who asks these questions is unlikely to actually want or expect a “proper” answer.

Epictetus 4 Jan 2015 11:49 UTC
3 points
on: The Superstar Effect

However, the fact remains that investment decisions are all about expected value. Risk vs. reward. Risk isn’t inherently bad, it just needs to be balanced by the reward. An in the case of superstar industries, the potential reward is huge.

There are pitfalls to expected value. Volatility is a killer. A lot of risk management is devoted to reducing the impact of volatility on your position. Even Kelly bets, which maximize long-term expected return, are subject to wide swings. It’s okay to take on a few long shots with a high reward, but the longer the shot the smaller the fraction of your bankroll you want to bet (note that by the Kelly criterion, this holds true even if the potential returns are huge).

People seem to view large ventures like starting startups as a roll of the dice. They say things like, “9 out of 10 startups fail”. I don’t see things that way. I don’t see it as “a roll of the dice”. I see it as a deterministic puzzle that can be solved.

Any solution you can implement, a competitor can potentially implement as well. You can’t deterministically beat such a competitor.

Epictetus 5 Jan 2015 20:55 UTC
−1 points
on: How much does consumption affect production?
The practical part of me says that one single chicken will be absorbed into fluctuations in breeding, premature chicken deaths on the farm, and a supermarket’s expected excess chicken that gets donated or thrown into the garbage. Dealing with live animals and perishable products brings uncertainty and inefficiency.

Americans eat ~8 billion chickens a year. The uncertainty and inefficiency present in the market may well prevent the loss of a single chicken from ever being noticed. Those elasticity estimates are made by working with some fraction of total consumption and then extrapolating the results to individual chickens. The change you get from having 1% of the population turn vegetarian is different from having 50% go vegetarian. Go high enough and production starts getting cut faster than the fall in demand. Restrict supply, market chicken as a luxury item, and gouge the hell out of the price.

The conclusion is that an individual’s change in consumption will have practically zero impact, that the change of a nontrivial minority will run into elasticity, that change of large swaths of the population will reach the 1:1 ratio, and that change in a large majority may well go past the 1:1 ratio.

Epictetus 6 Jan 2015 4:19 UTC
−1 points
in reply to: gjm’s comment on: How much does consumption affect production?

On average I would expect that if my chicken consumption goes down by 1/year, the production of chickens for eating will go down by about 1/year, for the sorts of reasons that erratim gives.

My issue is that there’s a fair amount of waste built in. The chicken you don’t buy is probably just going straight to the rubbish heap. A large supermarket is already throwing away hundreds of pounds of meat each year. For example, British chain Tesco said that in the first six months of 2012, some 28,500 metric tons of their food was wasted. With just under 6,800 stores, that’s over 8 metric tons per store, per year.

To get the retailer to buy less chicken, you’d have to cut consumption enough to exceed their threshold for allowable waste.

I think that “practically zero” means “practically zero as a fraction of the whole, which is true but not directly relevant. (In the same way, donating to a charity that feeds starving people has “practically zero” effect on the problem of starvation, curing someone of cancer has “practically zero” effect on the problem of cancer, etc.)

I meant in absolute terms. If you donate to a charity, that money’s going to help someone. Curing someone of cancer drops the cancer population by one. With chickens, there’s the aforementioned waste problem where you may have to meet certain thresholds before you see any change.

Epictetus 6 Jan 2015 4:43 UTC
−1 points
in reply to: Timothy Telleen-Lawton’s comment on: How much does consumption affect production?
I mostly brought that up as something to keep in the back of your mind when working with a simplified linear model. You could see bifurcations and nonlinear behavior in real life.

Epictetus 7 Jan 2015 21:47 UTC
2 points
on: Circular Altruism
Let’s turn the argument on its head: if you could abolish torture at the cost of everybody getting a speck of dust in their eye, would you do it?

Next question: If you could stop the Holocaust at the cost of N people getting dust specks in their eye, what’s the maximum value you’d permit for N? That is, is there a number N with the property that if N people get dust specks in their eye, you prevent the Holocaust, but if N+1 people get dust specks in their eye, then the Holocaust proceeds on schedule?

Arguments that begin with something benign and proceed by degree to silly conclusions have been around since ancient times. Dressing them up in the language of mathematics doesn’t change their nature. The kind of utilitarian model presented here is not an accurate reflection of the real world. Locally you can get reasonable results if you decide to treat similar things on a linear scale, but for disparate things the linear approximation breaks down. You can still plug numbers into the model, but the answer is meaningless.

Epictetus 11 Jan 2015 21:25 UTC
8 points
in reply to: robot-dreams’s comment on: Rationality Quotes January 2015
This reminds me of Socrates’ quip:

How can you wonder your travels do you no good, when you carry yourself around with you?

Epictetus 11 Jan 2015 22:27 UTC
2 points
on: Existential Risk and Existential Hope: Definitions

Definition (iii): An existential catastrophe is an event which causes the loss of most expected value.

A good place to start, but I don’t know about the heavy emphasis on expectation. The problems due to skewed distributions are ever-present. An event with small probability but high value will skew expected value. If a second event were to occur that rendered this impossible, we’d lose a lot of expected value. I’m not sure I’d call that a catastrophe, though.

Epictetus 13 Jan 2015 21:43 UTC
20 points
on: Rationality Quotes January 2015

We have blind, one-eyed, cross-eyed, and squinting people, and visions long, short, clear, confused, weak, or indefatigable. All this is a faithful image of our understanding; but we know scarcely any false vision. There are not many men who always mistake a rooster for a horse, or a chamber pot for a house. How is it that we often meet with minds, otherwise judicious, that are absolutely wrong in some things of importance? How is it that the same Siamese man who can never be fooled when he is supposed to receive three rupees, firmly believes in the metamorphoses of Sammonocodom...

If these besotted beings are shown a little geometry, they learn it easily enough; but, strange to say, this does not set them right. They perceive the truths of geometry; but it does not teach them to weigh probabilities: they have taken their bent; they will reason falsely all their lives; and I am sorry for them.

-Voltaire, Philosophical Dictionary

Epictetus 23 Jan 2015 14:15 UTC
0 points
in reply to: Richard_Kennaway’s comment on: Respond to what they probably meant

And among these, there is the smallest undefinable number.

There isn’t. The collection of positive, undefinable numbers is bounded below by zero, but doesn’t actually have a smallest element (due to the reals not being well-ordered).

Epictetus 31 Jan 2015 23:42 UTC
2 points
on: The Value Learning Problem
I am uncertain about the notion of using simulation or extrapolation to deduce the system operator’s intentions (as brought up in Section 5). Pitfall one is that the operator is human and subject to the usual passions and prejudices. Presumably there would be some mechanism in place to prevent the AI from carrying out the wishes of a human mad with power.

Pitfall two is a mathematical issue. Models of nonlinear phenomena can be very sensitive to initial conditions. In a complex model, it can be difficult to get a good error bounds. So, I’d ask just how complex a model one would need to get useful information and whether a model that complex is tractable. It seems to be taken for granted that one could accurately simulate someone else’s brain, but I’m not convinced.

Otherwise, it’s an interesting look at the difficulties inherent in divining human intentions. We have enough trouble getting our intentions and values across to other people. I figure that before we get a superintellgent AI, we’ll go through a number of stupid ones followed by mediocre ones. Hopefully the experience will grant some further insight into these problems and suggest a good approach.