It's striking how much value there is in academia that I didn't notice, and that a base-level rational person would've noticed if they'd asked "what are the main blind spots of the rationality community, and how can I steelman the opposing positions?". Not a good sign about me, certainly.
Also, is that your actual email address?
I'm not convinced that "free at point of use" is a useful concept - it's more useful to figure out when and where costs are snuck in, and then decide if the price is worth it and if the right people are paying for it.
Go ahead and object that "nothing is really free", but "free at point of use", once we're being specific, is useful. It means, "This service is accessible without paying up-front, because the costs are being paid elsewhere." Of course there are still costs to be paid, but there are a couple of whole fields of study devoted to finding the most socially desirable ways of paying them.
So for instance, we have reason to believe that if, on top of the existing journal-subscription-and-paywall system, we added additional up-front fees for reading academic research papers, this would raise the costs of scientific research, in terms of dollars and labor-hours spent to obtain the outputs we care about.
Also, please, not every LW comment necessitates conceptual nitpicking. If I start with "academia publishes a lot of useful research which can be obtained and read for free by people who know how to do literature searches", please do not respond with, "Well what is free anyway? Shouldn't we digress into the entire field of welfare economics?"
I have some questions about step 1 (find a flexible program):
My understanding is that there are two sources of inflexibility for PhD programs: A. Requirements for your funding source (e.g. TA-ing) and B. Vague requirements of the program (e.g. publish X papers). I'm excluding Quals, since you just have to pass a test and then you're done.
Elsewhere in the comments, someone wrote:
..."Grad school is free. At most good PhD programs in the US, if you get in then they will offer you funding which covers tuition and pays you a stipend on the order of $25K
PhD programs in mathematics, statistics, philosophy, and theoretical computer science tend to give you a great deal of free time and flexibility, provided you can pass the various qualifying exams without too much studying.
Bolding the parts to which I object.
I have never seen anyone in a rigorous postgraduate program who had a lot of free time and could pass their quals without large amounts of studying.
Of course, I could just be, like magic, on the lower part of the intelligence curve for graduate school, but given that my actual measured IQ numbers ar...
I am of the opinion that if you do grad school and you don't attach yourself to a powerful and wise mentor in the form of your academic adviser, you're doing it wrong. Mentorship is a highly underrated phenomenon among rationalists.
I mean, if you're ~22, you really don't know what the hell you're doing. That's why you're going to grad school, basically. To get some further direction in how to cultivate your professional career.
If you happen to have access to an adviser who won a Nobel or whose adviser won a Nobel, they would make a good choice. The implici...
I think there'd be value in just listing graduate programs in philosophy, economics, etc., by how relevant the research already being done there is to x-risk, AI safety, or rationality. Or by whether or not they contain faculty interested in those topics.
For example, if I were looking to enter a philosophy graduate program it might take me quite some time to realize that Carnegie Melon probably has the best program for people interested in LW-style reasoning about something like epistemology.
email me (lastname@thisdomain.com)
That makes good sense over on your own domain whence this is cross-posted, but not here on LW. Here you might either want to describe your email address differently, or encourage people to PM you using the LW message system instead of emailing you.
PhD programs in mathematics, statistics, philosophy, and theoretical computer science tend to give you a great deal of free time and flexibility, provided you can pass the various qualifying exams without too much studying.
Economics also has good opinion among the EA/rationality crowd:
Is there any way to do these things without paying a large pricetag? Could you just lurk around campus or something? Only half-joking here.
be sure to first consider the most useful version of grad that you could reliably make for yourself... and then decide whether or not to do it.
Planning fallacy is going to eat you alive if you use this technique.
Teach classes.
Yeah, this was much more valuable than I realized at the time. I think it's a better way to learn to speak than most, because you have something to communicate, and you get to measure later on how well you communicated it. You don't have time to worry about being nervous.
If I remember my Lakoff & Núñez correctly, they were arguing that even the most abstract and un-physical-seeming of maths is constructed on foundations that derive from the way we perceive the physical world.
Let me pick up the book again... ah, right. They define two kinds of conceptual metaphor:
- Grounding metaphors yield basic, directly grounded ideas. Examples: addition as adding objects to a collection, subtraction as taking objects away from a collection, sets as containers, members of a set as objects in a container. These usually require little instruction.
- Linking metaphors yield sophisticated ideas, sometimes called abstract ideas. Examples: numbers as points on a line, geometrical figures as algebraic equations, operations on classes as algebraic operations. These require a significant amount of explicit instruction.
Their argument is that for any kind of abstract mathematics, if you trace back its origin for long enough, you finally end up at some grounding and linking metaphors that have originally been derived from our understanding of physical reality.
As an example of the technique, they discuss the laws of arithmetic as having been derived from four grounding metaphors: Object Collection (if you put one and one physical objects together, you have a collection of two objects), Object Construction (physical objects are made up of smaller physical objects; used for understanding expressions like "five is made up of two plus three" or "you can factor 28 into 7 times 4"), Measuring Stick (physical distances correspond to numbers; gave birth to irrational numbers, when the Pythagorean theorem was used to prove their existence by assuming that there's a number that corresponds to the length of the hypotenuse), and Motion Along A Path (used in the sixteenth century to invent the concept of the number line, and the notion of a number as lying between two other numbers).
Now, they argue that these grounding metaphors, each by themselves, are not sufficient to define the laws of arithmetic for negative numbers. Rather you need to combine them into a new metaphor that uses parts of each, and then define your new laws in terms of that newly-constructed metaphor.
Defining negative numbers is straightforward using these metaphors: if you have the concept of a number line, you can define negative numbers as "point-locations on the path on the side opposite the origin from positive numbers", so e.g. -5 is the point five steps to the left of the origin point, symmetrical to +5 which is five steps to right of the origin point.
Next we can use Motion Along A Path to define addition and subtraction: adding positive numbers is moving towards the right, addition of negative numbers is moving towards the left, subtraction of positive numbers is moving towards the left, and subtraction of negative numbers is moving towards the right. Multiplication by a positive number is also straightforward: if you are multiplying something by n times, you just perform the movement action n times.
But multiplication by a negative number has no meaning in the source domain of motion. You can't "do something a negative number of times". A new metaphor must be found, constrained by the fact that it needs to fit the fact that we've found 5 (-2) = -10 and that, by the law of commutation (also straightforwardly derivable from the grounding metaphors), (-2) 5 = -10.
Now:
The symmetry between positive and negative numbers motivates a straightforward metaphor for multiplication by –n: First, do multiplication by the positive number n and then move (or “rotate” via a mental rotation) to the symmetrical point—the point on the other side of the line at the same distance from the origin. This meets all the requirements imposed by all the laws. Thus, (–2) · 5 = –10, because 2 · 5 = 10 and the symmetrical point of 10 is –10. Similarly, (–2) · (–5) = 10, because 2 · (–5) = –10 and the symmetrical point of –10 is 10. Moreover, (–1) · (–1) = 1, because 1 · (–1) = –1 and the symmetrical point of –1 is 1.
The process we have just described is, from a cognitive perspective, another metaphorical blend. Given the metaphor for multiplication by positive numbers, and given the metaphors for negative numbers and for addition, we form a blend in which we have both positive and negative numbers, addition for both, and multiplication for only positive numbers. To this conceptual blend we add the new metaphor for multiplication by negative numbers, which is formulated in terms of the blend! That is, to state the new metaphor, we must use
- negative numbers as point-locations to the left of the origin,
- addition for positive and negative numbers in terms of movement, and
- multiplication by positive numbers in terms of repeated addition a positive number of times, which results in a point-location.
Only then can we formulate the new metaphor for multiplication by negative numbers using the concept of moving (or rotating) to the symmetrical point-location.
So in other words, we have taken some grounding metaphors and built a new metaphor that blends elements of them, and after having constructed that new metaphor, we use the terms of that combined metaphor to define a new metaphor on top of that.
While this example was in the context of an obviously physically applicable part of maths, their argument is that all of maths is built in this way, starting from physically grounded metaphors which are then extended and linked to build increasingly abstract forms of mathematics... but all of which are still, in the end, constrained by the physical regularities they were originally based on:
The metaphors given so far are called grounding metaphors because they directly link a domain of sensory-motor experience to a mathematical domain. But as we shall see in the chapters to come, abstract mathematics goes beyond direct grounding. The most basic forms of mathematics are directly grounded. Mathematics then uses other conceptual metaphors and conceptual blends to link one branch of mathematics to another. By means of linking metaphors, branches of mathematics that have direct grounding are extended to branches that have only indirect grounding. The more indirect the grounding in experience, the more “abstract” the mathematics is. Yet ultimately the entire edifice of mathematics does appear to have a bodily grounding, and the mechanisms linking abstract mathematics to that experiential grounding are conceptual metaphor and conceptual blending.
To take a step back. the discussion is about mathematical Platonism, a theory of mathematical truth which is apparently motivated by the Correspondence theory of truth. That is being rivaled by another theory, also motivated by CToT, wherein the truth-makers of mathematical statements are physical facts, not some special realm of immaterial entities. The relevance of my claim that there are unphysical mathematical truths is that is an argument against the second claim.
Lakoff and Nunez give an account of the origins and nature of mathematical thought that...
Among my friends interested in rationality, effective altruism, and existential risk reduction, I often hear: "If you want to have a real positive impact on the world, grad school is a waste of time. It's better to use deliberate practice to learn whatever you need instead of working within the confines of an institution."
While I'd agree that grad school will not make you do good for the world, if you're a self-driven person who can spend time in a PhD program deliberately acquiring skills and connections for making a positive difference, I think you can make grad school a highly productive path, perhaps more so than many alternatives. In this post, I want to share some advice that I've been repeating a lot lately for how to do this:
That's all I have for now. The main sentiment behind most of this, I think, is that you have to be deliberate to get the most out of a PhD program, rather than passively expecting it to make you into anything in particular. Grad school still isn't for everyone, and far from it. But if you were seriously considering it at some point, and "do something more useful" felt like a compelling reason not to go, be sure to first consider the most useful version of grad that you could reliably make for yourself... and then decide whether or not to do it.
Please email me (lastname@thisdomain.com) if you have more ideas for getting the most out of grad school!