As of January 2025, I have signed no contracts or agreements whose existence I cannot mention.
French, but because my teacher tried to teach all of the days of the week at the same time, they still give me trouble.
They're named as the planets: Sun-day, Moon-day, Mars-day, Mercury-day, Jupiter-day, Venus-day, and Saturn-day.
It's easy to remember when you realize that the English names are just the equivalent Norse gods: Saturday, Sunday and Monday are obvious. Tyr's-day (god of combat, like Mars), Odin's-day (eloquent traveler god, like Mercury), Thor's-day (god of thunder and lightning, like Jupiter), and Freyja's-day (goddess of love, like Venus) are how we get the names Tuesday, Wednesday, Thursday, and Friday.
Why is Google the biggest search engine even though it wasn't the first? It's because Google has a better signal-to-noise ratio than most search engines. PageRank cut through all the affiliate cruft when other search engines couldn't, and they've only continued to refine their algorithms.
But still, haven't you noticed that when Wikipedia comes up in a Google search, you click that first? Even when it's not the top result? I do. Sometimes it's not even the article I'm after, but its external links. And then I think to myself, "Why didn't I just search Wikipedia in the first place?". Why do we do that? Because we expect to find what we're looking for there. We've learned from experience that Wikipedia has a better signal-to-noise ratio than a Google search.
If LessWrong and Wikipedia came up in the first page of a Google search, I'd click LessWrong first. Wouldn't you? Not from any sense of community obligation (I'm a lurker), but because I expect a higher probability of good information here. LessWrong has a better signal-to-noise ratio than Wikipedia.
LessWrong doesn't specialize in recipes or maps. Likewise, there's a lot you can find through Google that's not on Wikipedia (and good luck finding it if Google can't!), but we still choose Wikipedia over Google's top hit when available. What is on LessWrong is insightful, especially in normally noisy areas of inquiry.
See the paper I linked in my other comment.
Eight years later, but we're finally approaching the technical capability to perform my proposed experiment to elicit tetrachromacy in a human trichromat through eye tracking and targeting a subset of retinal cells: https://www.science.org/doi/10.1126/sciadv.adu1052#sec-3
See the DISCUSSION section proposing further experiments.
Update: Claude made it to Cerulean City today, after wandering the Mt. Moon area for 69 hours.
See https://pauseai.info. They think lobbying efforts have been more successful than expected, but politicians are reluctant to act on it before they hear about it from their constituents. Individuals sending emails also helps more than expected. The more we can create common knowledge of the situation, the more likely the government acts.
It's also available on Android.
Finitism doesn't reject the existence of any given natural number (although ultrafinitism might), nor the validity of the successor function (counting), nor even the notion of a "potential" infinity (like time), just the idea of a completed one being an object in its own right (which can be put into a set). The Axiom of Infinity doesn't let you escape the notion of classes which can't themselves be an element of a set. Set theory runs into paradoxes if we allow it. Is it such an invalid move to disallow the class of Naturals as an element of a set, when even ZFC must disallow the Surreals for similar reasons?
Before Cantor, all mathematicians were finitists. It's not a weird position historically.
We do model physics with "real" numbers, but that doesn't mean the underlying reality is infinite or even infinitely divisible. My finitism is motivated by my understanding of physics and cosmology, not the other way around. Nature seems to cut us off from any access to any completed infinity, and it's not clear that even potential infinities are allowed (hence my sympathy with ultrafinitism). I have no need of that axiom.
Quantum Field Theory, though traditionally modeled using continuous mathematics, implies the Bekenstein bound: a finite region of space contains a finite amount of information. There are no "infinite bits" available to build the real numbers with. However densely you store information, eventually, at some point, your media collapses into a black hole, and packing in more must take up more space.
Physical space can't be a continuum like the "reals". It's not infinitely divisible. Measuring distance with increasing precision requires higher frequency waves, and thus higher energies, which eventually has enough effective mass to gravitationally distort the very space you are measuring, eventually collapsing into a black hole.
Below a certain limit, distance isn't physically meaningful. If you assume an electron is a point particle with "infinitesimal" size and you zoom in enough, you should be able to get arbitrarily high electric field strength. But at some point, high enough field strength results in vacuum polarization: virtual electron/positron pairs get pushed around and finally one of the positrons annihilates whatever you thought the real electron was, and then one of the virtual electrons doesn't have anything to pair with and becomes the real one. It's as if the electron is jumping around. You can't nail it down. It doesn't physically have a position down below a certain scale in time and space. There are no infinite bits. All the fundamental particle types are like this. There are no infinitesimal point particles. They're just waves.
There's also a cosmological horizon limiting how much of the Universe we can see. There's also a (related) past temporal horizon at the Big Bang. We can't see a completed past-temporal or spacial infinity, in any direction. We're not sure of the Ultimate Fate of the Universe, but it looks like Heat Death is probably it, given our current understanding of physics. So there's a future limit as well. The other likely candidate Fates are finite in time as well.
But even supposing finite information content in a finite region seems to be enough to make potential-infinite time not really meaningful. There's a finite number of states possible, so eventually all reachable states are reached. If physics is deterministic (it seems to be), then we get into a cycle. So time is better modeled as a finite circle, rather than an infinite line. And if it's not deterministic? Then we still saturate all reachable states, the order just gets shuffled around a bit. There's no phycial way to tell the difference.
Potential-infinite space is the same way. Any accessible region has a finite number of states, so at least some of them must repeat exactly in other regions. If there's some determinism to the pattern, then it's maybe better modeled as some curled-up finite space (although aperiodic tilings are also possible). If it's random, then we still saturate all reachable states, the order just gets shuffled around a bit. There's no physical way to tell the difference. Once all reachable states have been saturated, why does it matter if they appear only once or a googol or infinity times?
I feel like this has come up before, but I'm not finding the post. You don't need the stick-on mirrors to eliminate the blind spot. I don't know why pointing side mirrors straight back is still so popular, but that's not the only way it's taught. I have since learned to set mine much wider.
This article explains the technique. (See the video.)
In a nutshell, while in the diver's seat, tilt your head to the left until it's almost touching your window, then from that perspective point it straight back so you can just see the side of your car. (You might need a similar adjustment for the passenger's side, but those are often already wide-angle.) Now from normal position, you can see your former "blind spot". When you need to see straight back in your side mirror (like when backing out), just tilt your head again. Remember that you also have a center mirror. You should be able to see passing cars in your center mirror, and then in your side mirror, then in your peripheral vision without ever turning your head or completely losing sight of them.