Lately I've been wondering about telescope resolving power, and physical limits on the size of features we can see at interstellar distances.
I know about the diffraction limit, which (by my quick and dirty math) seems to imply a telescope on the order of a kilometer in size could resolve objects several meters across, but I imagine it's actually more complicated than that. Does anyone know a good source of information on the topic?
There seems to be a pretty sharp lower bound on how cheap a living situation (e.g. rent on an apartment) can be in the parts of the United States I'm familiar with. I would have thought that there would be demand for cheap-but-bad housing on the part of people with low income. Here are some hypotheses I've come up with for explaining this, and I'd appreciate anyone who has relevant knowledge commenting if I'm on track:
What do you mean by "bad" housing?
One possible reason is that many of the relevant aspects of good or bad housing are governed by building codes (plumbing, HVAC, bathrooms, room size, etc.) which put a (often high) lower bound on how cheap a building can be built. In addition, the organization of the construction industry (many specialized subcontractors) means there's a fairly high fixed cost for any new construction. While this mostly applies to new construction, it can apply to existing buildings as well.
My tumblr of LWish topics:
http://coarsegrained.tumblr.com/
Will probably hold my own writing too when I have the free time to do it again.
Is anyone familiar with any statistical or machine-learning based evaluations of the "Poverty of Stimulus" argument for language innateness (the hypothesis that language must be an innate ability because children aren't exposed to enough language data to learn it properly in the time they do).
I'm interested in hearing what actually is and isn't impossible to learn from someone in a position to actually know (ie: not a linguist).
Here are some initial thoughts. I haven't finished working through it, so more to come:
Perhaps you should specify if the probability of detecting another player is an overall probability or on a per undetected player basis (so when there is only one player they haven't detected yet, when they detect a player it will always be that player they haven't detected)
in the definition of L_K, why is P(K survives turn i) outside the summation? What does i refer to then? Is P(K survives turn i) a constant ? Wont it in general depend on the current state of play?
Thanks for looking at it.
Probability is on a per player basis (ie: each turn, a player has a chance p for detecting each undetected player). I'll edit this so it's more clear.
For LK (as well as LR and L_P), the term outside the summation is essentially (probability the player survives the whole game) * (game length). It's necessary since the game is of fixed length, and the summation is adding (probability of dying on turn x) * (turn x). Consider if the probability of detection is zero, and players will never die - without the term outside the summation, the expected lifetime calculation will return zero.
If this sort of help is still available, I have some math I'm working through for a post that I'd love to have checked - a page and a half of fairly basic statistics.
It can be found here (pdf): http://dl.dropbox.com/u/430270/lwalienprisoners.pdf
Thanks!
Nice. Oscar Bonilla's visualization still gives me a better grasp, I feel. Maybe you could add a graph in Oscar's style - especially his last graph?
Euler-style diagrams may give a better conceptual representation. but unfortunately they are fairly useless for intuiting about actual quantities - people are simply aren't very good at comparing relative sizes of areas, and are much more accurate when comparing lengths.
I agree that the method I've chosen could be more enlightening, I'm just not sure how to do it while retaining the ability to make comparisons about the actual values.
For more on this, see http://lilt.ilstu.edu/gmklass/pos138/datadisplay/badchart.htm
From my buddy, a research psychologist:
"Oh yeah, those are a big issue. They're a big problem for medical shit and business shit. Less so for university stuff, for obvious reasons. Even the most basic recruitment agency knows about 'em. "
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The book "Avogadro Corp", which is otherwise not worth reading, has a plausible seeming mechanism for this. The AI, which can originally only send email, acquires resources simply by sending emails posing as other people (company presidents to developers requesting software to be written, to contractors for data centers to be built, etc.).
It probably wouldn't even be necessary for it to pose as other people, if it had access to financial assets, and the right databases to create a convincing fictional person to pose as.
If you seem human, it's not hard to get things done without ever meeting face to face.