I'm a physics dilettante... a little undergrad 101 stuff and some exposure to pop sci. I was mulling over the explanation of gravity as being warped space rather than a force, such that an orbiting body for example is not being held in orbit by the gravitational force exerted between it and the object it's orbiting but is merely traveling inertially in a straight line in a space that has been warped by a big mass in the midst of it.
Okay, thought I, I can picture that.
But then I tried to apply it to another scenario: hole drilled through the middle of the earth (or some simpler, non-rotating, isolated mass... weight dropped into hole. I imagine the weight oscillating back and forth, speeding up as it approaches the center, slowing down as it approaches the surface, then repeating in the other direction. I can't seem to grok a curved space that's so curved that an object can go in what appears to be opposite directions along the same path within it without a force being applied to it to make it do so. Yet I understand that from the POV of the oscillating mass, no force is felt. What am I missing?
What you might be missing is time. Things don't really "sit still" in spacetime - everything is always moving through time, but things that are moving fast through space are moving slower through time - it's like you have just one speed, but you can point it "out of time" and "into space."
When you travel through a curved spacetime, "sitting still" still means moving forward in the time direction. It's not like the curvature due to gravity creates a potential well that you "fall down." It's more like you're one of those stunt motorcyclists driving around the inside of a steel cage, constantly whizzing forward in a locally straight line, but changing what direction you're pointing due to the curvature of space.
This seems like a great question to me and I'm bummed I can't answer it. But here's a toy model that might help a bit.
Take a 2-dimensional spacetime shaped like the surface of a vertical cylinder, with space being the 1-dimensional equatorial circles, and time going vertically. Some of the straight lines in this space are slanted lines just going around and around the cylinder forever, and objects following those as world lines would sort of appear to oscillate around a point traveling along an exact vertical world line.
Anyway that model's only 2-dimensional, and the bigger problem is it's not the right type of geometry (it's Riemannian not Lorentzian). Also the cylinder is flat, not curved. But maybe it still helps.
There is a paper here which does something like this, and draws pretty pictures. The metric has been "absolutized" by replacing the negative coeffecients with their absolute values, so it becomes Riemannian instead of Lorentizian, but the diagram is then annotated with a bunch of yellow triangles showing "the direction of time", and together these two things apparently contain all the information of the original spacetime. For the spacetime around an ordinary planet all the triangles point in the same direction, so this Riemannian version seems like a valid representation, I guess.
Anyway, the red line in Figure 5 in the pdf shows something like what OP was asking about: a ball is thrown straight up, turns around, and falls down along the same path again.
I think maybe the key point is that although the ball is retracing its path in space, in spacetime it's just a long line which never loops back on itself, so it may be easier to believe that it's going "straight ahead".
The geodesics aren't lines in space, but in space-time. For the ball to fall through the Earth and back to its starting point takes about 5000 seconds, during which time light goes about 1.5 billion km. So a graph in space-time will be a sine wave whose period is 1.5 billion km and whose amplitude is 6400 km, a ratio of about 250000 to 1. The graph has very low curvature everywhere.
It is the same for the Earth's orbit round the Sun. It is not the spatial path of the orbit that is a geodesic, but the helical path it traces out in space-time. In one revolution it travels one year into the future, equivalent to a distance of a light-year. As a handy way of visualising this, the ratio of a light-year to an AU (astronomical unit, the radius of the Earth's orbit) is about the same as a mile to an inch. So in space-time the orbit can be visualised as a helix formed by wrapping a piece of string around a cylinder two inches thick and a mile long, which makes just a single turn over that distance. The curvature of this path is much lower than the spatial curvature of the orbital path.
Imagine a 2D plane where x is space and y is time. Let's say the Earth is stationary at x=0, so its trajectory is the y axis, and the metric of spacetime is "curved" near it.
We can represent the metric visually by sprinkling a bunch of sand near the y axis. Then lines of inertial movement ("geodesics") can be understood in two ways:
Given a pair of points, a geodesic is the line between them with the least sand (this represents the line being shortest according to the metric).
Given a starting point and velocity vector, keep moving so as to keep equal amounts of sand on your nearby left vs. nearby right - in other words, curve toward more sand.
Surprisingly, these two views are equivalent! For example, consider the geodesic from (1,0) to (1,1). It will bulge slightly away from the y axis, to avoid sand, and so at each point it will be curving toward more sand.
Now we can answer your original question. Place an object at (1,0) with velocity vector (0,1) (zero spatial velocity) and let it go. It will keep moving in the positive y direction, but curve toward the y axis where there's more sand, and eventually cross it at an angle. Then it will curve back by symmetry, and so on, oscillating back and forth in the x coordinate while moving forward in time.
Can that really be a shortest line between two points? Why not. Say the object makes one full oscillation, traveling from (1,0) to (-1,1) to (1,2). If you try to "straighten" the line by pulling on the endpoints, the midpoint will be pulled toward the y axis and catch more sand. So it might well be a local minimum.
Are there any resources that amount to "80,000 Hours for (hopefully reformed) underachievers"? I've been weighing the possibility of going back to school in the hopes of getting into a higher-impact field, but my academic resume from my bachelor's is pretty lackluster, leaving me unsure where to start reconstruction. My mental health and general level of conscientiousness are both considerably improved from my younger years so I'm optimistic I can exceed my past self.
So, I value having coherent and internally consistent beliefs. Are there any good tools or methods for helping train or test myself on that?
Like, prediction scoring can be helpful for calibrating individual probability estimates over time, but it'd be great to have some tool that would let me put in some probability estimates, then prod me with questions to check for mutually incompatible estimates, like by asking me to also estimate enough conditional combinations to make some inferences for me to sanity check against.
I am the same as you, and unfortunately I have yet to find an efficient method for that. Still, what I'm doing is having a friend whose ideas are (or rather whose ideology is) against mines so that it forces me to ponder over my own beliefs. The fiercer the debate, the more contradictions that arise.
Why do we not become a political party and build a rational world government. Or a less wrong world government ?
One would have to compete with the existing parties, which in e.g. the US is basically hopeless. There are countries where smaller parties have more of a chance, but even there it's a huge amount of work, and LW types are generally not the kind who would enjoy or excel at politics. Also LW users have a variety of political positions rather than having any unified ideology.
If one does want to have political influence, supporting or joining an existing party lets you leverage their existing resources while allowing you to specialize in the politics-things that you are good at, without needing to recreate everything from scratch.
This question has a weird implication of mutuality. What I think you mean to ask is "should some LW members support other LW members financially?".
My answer is "yes, if the donors think that's a good use of their financial resources."
Related questions you didn't ask, but should have:
After reading your followup, I have a few other rephrasings to propose:
It would help to be more specific about what you mean. There are many different kinds of financial support and there are different things you could mean with "should".
Both CFAR and MIRI get supported by donations that partly come from LW members.
My question was really stupid, actually I was thinking "I would like to spend at least 200 hours on this project, but it seems I won't get any money from it, maybe I could ask LW members if they want to support it financially".
A better question is "Can I ask you money to help me to build a software that may help you?", or "it is inappropriate to ask for money on LW, the platform discourages this".
Disclaimer: I am still not sure if this is the correct question. Anyway, I am developing some helper tools, and although I won't monetize them directly, it would be good to get some money from it, because I am not the guy who has enough money to not need any money from the community anymore.
Fundraising requests have been in the past posted on LessWrong: Berkeley REACH would be one example, the Grants & Fundraising Opportunities tag has plenty of other examples. If you want to ask for money I would recommend that you read through a bunch of the existing fundraising posts. They will likely both show you how to format a request and what kind of projects this community values.
In general you will likely come to the conclusion that while people are willing to fund promising projects, it needs more then just "helping a fellow community member" but a belief that the project is good value for money compared to other donation targets. And most people who donate significant amounts of money do it through an EA lense.
Why would they? Considering that LW readers are mostly rich Americans, they don't seem particularly needy.
Why would they?
Sometimes non needy people want to help other people in need. If you were looking to maximize happiness points across the world, for example, you would gain more points helping those members in need.
Considering that LW readers are mostly rich Americans
There are non-zero members suffering financially, that's why I asked that. It would be too easy for some people here to make this number go to zero.
>If you were looking to maximize happiness points across the world, for example, you would gain more points helping those members in need.
Wouldn't that only be true if we thought LW readers are the most needy across the world, or perhaps most easily helped?
I don't think so. For example, follow these instructions:
Now you can see, although most LW readers are not like this guy, this guy is among LW readers. My point is that we should financially support this guy, independently if he belongs to LW or not. I would say it is easy to help him and we have a reason to support him, and the fact he reads LW doesn't change the facts on his life. Again, although not common, we should be prepared to detect and solve this kind of unfortunate situation. At least this is something I would do if I had enough resources to help.
My point is that we should financially support this guy, independently if he belongs to LW or not. I would say it is easy to help him and we have a reason to support him, and the fact he reads LW doesn't change the facts on his life.
There's plenty of EA thought about how to donate to help the global poor. The question here is about whether you believe that the donation to one individual is more or less impactful then a donation to a GiveWell recommended charity.
How do people read LessWrong? I subscribe to the RSS feed of the front page, but that tends to be suboptimal, as some posts aren't that well-aligned with my interests or are questions/discussion starters as opposed to being mid/longform reads that I'd mostly want to read LW for.
Me too. I check it one or two times a day, with longer gaps up to a week or two when I'm busy on other things. I generally look at the last few days' titles, read the ones I want and ignore the rest. Those that I've read and have new comments show the comment count in green, so it's easy to note followups to things I'm interested in.
I do miss out on comments made more than a few days after the article is posted, as the post will have scrolled down far enough that I don't notice. They sometimes come to my attention (if a comment of mine gets a reply or a karma change), but often not.
I was subscribed to the RSS feed of all posts, but that was a bit overwhelming; so I'm now subscribed to the feed of "posts with 30 or more karma" that they provide, but I'm now finding that LW is much less interesting or useful to me - which I could have predicted, given that I'd already noticed that the karma of a post often turned out a bad indicator of how useful/interesting it would be to me. The posts I found to be the best were most often in the 5-15 karma range - but alas, there's no feed for that.
Now I'm thinking about just unsubscribing from the RSS feed and setting LW as my homepage.
Given that exponential technological progress is likely, or at least plausible, how is life expectancy only around 80 years?
The term "life expectancy" usually refers to something that's not a prediction. It's constructed from the past year's results of many age groups. See https://www.britannica.com/science/life-expectancy.
Oh, wow! So are there approaches that try to predict how long someone will live, taking into account that the future is likely to be (very) different from the past? And if so, what results do they typically get?
There's no observed exponential technological progress if you measure our ability to increase life expectancy.
Whether technology will actually increase or decrease life expectancy depends a lot on the assumptions that you put into your models.
The stupid questions thread was one of the regular threads on LessWrong 1.0. It's a place where no question is to stupid to be asked and anybody who answers is encouraged to be kind.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.