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Thing I would do if I had enough money for $200 to be inconsequential: buy 2 pairs of identical bluetooth headphones—one permanently paired to my laptop and one permanently paired to my phone. This would save me lots of annoyance whenever I switch between the two. Bluetooth seems to just suck
Summarized, this post seems to be saying “Learning <thing> is most effective if you get the most effective teacher. The most effective teachers of <thing> aren’t necessarily the most skilled (“the best”) people—they are people who are marginally more skilled in <thing> than you (“the same”).”
The first sentence seems very true. The second sentence is often true, but as johnswentworth pointed out, there are exceptions. I’ll restate his exception and add two of my own.
(from johnswentworth’s comment) If the skill is niche, you may have no choice but to learn from the best. In particular, the best may be the best since they know something everybody else doesn’t.
It can be valuable to gain a “30000 foot overview” of a topic if you want to learn how experts in a field think. Such an overview is best given by “the best” in that field, not people who are “same”. For example, a graduate student in one field might attend a seminar in a different, only slightly related field, hoping to ignore the details and take away a broad bigger picture of the field.
Masterclasses exist. For example, a student musician may gain a lot from a single lesson with a world-class musician.
For examples 2 and 3, the shared attribute here is that it can be beneficial to learn the “compressed” knowledge the “best” expert has, rather than less compressed knowledge from a “same” teacher. Even if the student can’t “uncompress” this knowledge, there is still value in learning the general shape of a body of knowledge.
Problem: I compulsively pick at scabs. Often I do it even though I don’t want to pick at it because I know I’ll be worse off. (Scab will bleed, it’ll just reform anyway, and I’ll have to deal with the unhealed skin for longer.) Telling myself “don’t pick” doesn’t work, I get very distracted by the presence of the scab and HAVE TO pick.
Solution: put a band-aid over the scab. Blocking the scab makes picking more difficult. More crucially, the adhesive of the bandaid gives me a mildly ticklish sensation which masks the sensation that a pickable scab is present.
Caveat: this has been most helpful for face scabs, but face bandaids are awkward. This has worked fine for me because I tend to pick when I’m alone, so I can just apply bandaids when alone and take them off when people will see me. But if you spend most of your time around people this may not work for you.
That’ll teach me to post without thinking! Yes, you’re right that is the better way to deal with variance here. (Or honestly, the method from the above comment is the slickest way.)
I had been thinking of a similar kind of situation, where you have a fixed and varying sample sizes . Then, the smaller gives more extreme outcomes than larger . Of course, this isn’t applicable here.
Thanks for describing your data! I was hoping to hear stuff exactly like this.
In particular I can confirm experiencing these states
This is the best time for boring but important work
Cognitively I’m sharpest during this time (I can think the fastest but can’t focus that well)
at different times of the month (and I think it correlates with my cycle) but haven’t noticed patterns this granular. I’ve started collecting data (and am trying to not let my knowledge of where I am in my cycle bias my perceived measurements) so maybe in several months I’ll be able to confirm similar patterns.
The intuitive way to think about this is the heuristic “small numbers produce more extreme outcomes”. Both choices have the same expected number of deaths. But the 50% option is higher variance than the 5% option. Our goal is to maximize the likelihood of getting the “0 deaths” outcome, which is an extreme outcome relative to the mean. So we can conclude the 50% option is better without doing any math.
Perhaps a better way to describe this set is ‘all you can build in finitely many steps using addition, inverse, and multiplication, starting from only elements with finite support’.
Ah, now I see what you are after.
But if you use addition on one of them, things may go wrong.
This is exactly right, here’s an illustration:
Here is a construction of : We have that is the inverse of Moreover, is the inverse of . If we want this thing to be closed under inverses and addition, then this implies that
can be constructed.
But this is actually bad news if you want your multiplicative inverses to be unique. Since is the inverse of , we have that is the inverse of . So then you get
so
On the one hand, this is a relief, because it explains the strange property that this thing stays the same when multiplied by . On the other hand, it means that it is no longer the case that the coordinate representation is well-defined—we can do operations which, by the rules, should produce equal outputs, but they produce different coordinates.
In fact, for any polynomial (such as ), you can find one inverse which uses arbitrarily high positive powers of and another inverse which uses arbitrarily low negative powers of . The easiest way to see this is by looking at another example, let’s say .
One way you can find the inverse of is to get the out of the term and keep correcting: first you have , then you have , then you have , and so on.
Another way you can find the inverse of is to write its terms in opposite order. So you have and you do the same correcting process, starting with , then , and continuing in the same way.
Then subtract these two infinite series and you have a bidirectional sum of integer powers of which is equal to .
My hunch is that any bidirectional sum of integer powers of which we can actually construct is “artificially complicated” and it can be rewritten as a one-directional sum of integer powers of . So, this would mean that your number system is what you get when you take the union of Laurent series going in the positive and negative directions, where bidirectional coordinate representations are far from unique. Would be delighted to hear a justification of this or a counterexample.
If I’m correctly understanding your construction, it isn’t actually using any properties of . You’re just looking at a formal power series (with negative exponents) and writing powers of instead of . Identifying with “” gives exactly what you motivated— and (which are and when interpreted) are two different things.
The structure you describe (where we want elements and their inverses to have finite support) turns out to be quite small. Specifically, this field consists precisely of all monomials in . Certainly all monomials work; the inverse of is for any and .
To show that nothing else works, let and be any two nonzero sums of finitely many integer powers of (so like ). Then, the leading term (product of the highest power terms of and ) will be some nonzero thing. But also, the smallest term (product of the lower power terms of and ) will be some nonzero thing. Moreover, we can’t get either of these to cancel out. So, the product can never be equal to . (Unless both are monomials.)
For an example, think about multiplying . The leading term is the highest power term and is the lowest power term. We can get all the inner stuff to cancel but never these two outside terms.
A larger structure to take would be formal Laurent series in . These are sums of finitely many negative powers of and arbitrarily many positive powers of . This set is closed under multiplicative inverses.
Equivalently, you can take the set of rational functions in . You can recover the formal Laurent series from a rational function by doing long division / taking the Taylor expansion.
(If the object extends infinitely in the negative direction and is bounded in the positive direction, it’s just a formal Laurent series in .)
If it extends infinitely in both directions, that’s an interesting structure I don’t know how to think about. For example, stays the same when multiplied by . This means what we have isn’t a field. I bet there’s a fancy algebra word for this object but I’m not aware of it.
Wow the long and heavy periods sound insane and exhausting. Yeah I have asked doctors about ways to mitigate period pain—seems like “4 hours of pretty bad cramps” was not enough for them to recommend anything beyond going on the pill.
I have not been explicitly collecting data on productivity vs period. I do track my cycle and (when I remember) my symptoms throughout the month. I have a few reasons to believe that my menstrual cycle greatly influences my productivity:
The obvious fact that I can’t do anything productive during the first 4 hours of my period.
For me, minor physical symptoms like stomach ache, headache, bloating happen during certain points of my cycle. These symptoms make me slightly worse at concentrating / socializing, which decreases my productivity.
Sometimes there are days where I am unusually productive. They never happen during or right before my period.
I think the conversations here have inspired me to track more data more reliably!
Lucky you!
(Even if it doesn’t affect productivity, do you at all notice fluctuations in energy level?)
I’ve spoken to two doctors. Both seemed to think this was within normal range and advocated for the pill as a tool to reduce painful period symptoms. My impression is that my period symptoms are maybe in the top half of severity, but not the top quartile?
Ah, I actually also have experience with the first bullet point. From what I remember, these “long cycle” periods were less problematic than my periods are off the pill. But, the particular pill I was on had negative side effects so I eventually stopped.
Increasing cycle length would definitely improve my situation (assuming I can find a pill with no negative side effects). I think it’s good to consider but not exclusively focus on that option because:
The selection of pills that are compatible with long cycles seems to be relatively small (at least my doctor says so)
On a 1 month cycle one might be able to manufacture more “highs” than on a 3 month cycle
Interesting! It’s good to hear that your energy levels off the pill roughly match mine.
Your experiences on the pill are also interesting to hear. I suppose to figure out what effects all of these hormones have on me I would have to sample different combinations for long enough time frames to notice effects (as you have been doing).
Do you think you are unusually prone to panic attacks / depression? I wonder whether the pill brings out specific fixed traits in people (like depression) or whether it exacerbates characteristics they were already unusually prone to.
I wonder this because in hindsight, maybe some of my previous issues were caused by the pill. I’ve been on two different pills (annoyingly it was long ago enough that I’m not sure which kinds of pill).
(Issue: I am prone to disordered eating) The first time was to kickstart my period after I stopped menstruating for 6 months due to rapid weight loss. On the pill I binge ate a lot and gained a lot of weight. No doubt some bingeing was due to my eating disorder but maybe the pill exacerbated things.
(Issue: I am prone to low libido) The second time was because I wanted to control PMS symptoms. It tanked my libido so I stopped after several months.
So for me, maybe the things I am prone to are “eating disorder behavior” and “low libido”, so those are the main things I should expect the pill to noticeably influence. (In particular, I have never shown many signs of depression / anxiety so maybe I shouldn’t expect a pill to cause those symptoms.) This feels somewhat related to the recent SSC (ACT?) posts about taxonometrics and dynamical systems.
The external link “A write-up of the proof of Aumann’s agreement theorem (pdf) by Tyrrell McAllister” seems to be broken. At least, I get a 404 Error. I am not sure how to best fix this but I thought I may as well point this out.
Question about people who do calorie restriction (CR) in humans with the goal of anti-aging. Do they experience “brain fog” i.e. decreased cognitive performance? Intuitively that seems like a major drawback of CR but perhaps brain fog can be eliminated with a healthier diet / getting used to consistent CR over time? Curious to hear evidence of/against this.
The case against a inbox with lots of items. This is certainly not a hot or unusual take but I am writing it anyway. I describe how I transitioned my TODO list setup from “big pile of email notifications” to something slightly more efficient (but still low tech overhead).
I used to use my email inbox as a generic TODO list, with items ranging from “reply to this person” to “remember to go to this calendar event” but also “fill out the application for this program”, “read this blog post”, and so on.
I think email inbox is still the best place to put reminders of the form “write an email to this person”. However for all the other stuff I find using email inbox quite inefficient.
Every time I scan through an email inbox with lots of items, I have to re-”compute” what that TODO item was supposed to be again. For example: “hmm, this is just a link, (I click the link), oh, it’s that blog post Person X told me about that I’ve been meaning to read”. Doing this for many items is kind of computationally expensive, no matter how clearly phrased the reminders are.
Instead, here is where I put reminders which used to be items in my inbox:
For reminders of the form “read this thing”, I have bookmark folders based on different topics. (I used to have a big bookmark folder called “To Read”, but it was too computationally expensive to figure out what was what.) The topics are relatively broad; things like “Career advice”, “Fun”, “Math”, “ML”. The idea is that usually I’m in the mood for a specific topic, so I can go to the appropriate folder and knock off some todo items.
For reminders of the form “go to this calendar event” I have been consistently using Google Calendar. The key is to really deliberately get in the habit of actually checking my calendar (I used to not do this so email was a failsafe way to remind myself to go to important things).
For reminders of the form “fill out this form / application” I make that a “this week” or “this month” TODO item in my longer term planning system (which is just a google doc since that’s been working out fine).
This system has been great since I spend way less time scanning through emails that don’t need my attention (it had really been adding up) and because it’s low-tech so it barely requires additional effort.
Ah, that is a big timesaver. Thanks!
Summary: this post is mostly for self reflection. I my first impressions (likes/dislikes) after using Roam, a note-taking app with good “linking” features. I also use this post to think about some Roam-related decisions (should I look into competitor apps, should I upgrade to Roam’s lump sum “Believer” plan).
I’m trying out Roam and liking it so far. I started using it when I started working on a research project in order to reap the full benefits.Before I list pros and cons, I should clarify that I am a novice at Roam. I know I am not using Roam close to optimally, and probably some of the disadvantages I’ve listed are due to my lack of knowledge rather than problems with Roam. (Feel free to tell me where I am Being Wrong on the Internet because then I will learn more about Roam!)
Advantages of roam:
Organization system makes it easy to want to write. There are “daily” pages which you I can tab to at any time by pressing Alt+D. Or, I can create “topic” pages for a book I’m working through, a concept, whatever. So when I open Roam to work I know I’m either learning something and taking notes in Roam, or maybe writing my miscellaneous ideas in my daily page.
It feels fast. Better than google docs or Overleaf. Difference between offline environment barely noticeable (meaning occasionally I get a big lag spike because of an internet problem on my end, rather than a constant amount of noticeable latency).
Search results are fast and relevant. If you’ve written those words before, they’re easy to find. Admittedly my graph is small since I’m new so I’ll have to wait and see whether Roam scales.
“Page links” are useful. I thought it would be annoying to get in the habit of linking [[Some Concept]] every time I say it but it actually isn’t. Worst case I can write first and link later. I think it’s genuinely useful to be able to click [[Some Concept]] and see all places I’ve mentioned it—this is helpful if I want to refresh my understanding of a concept for example.
“Block links” are even more useful. Roam notes are a bunch of nested bullet points and a block is a single bullet point. Each block has a reference code. If you paste that reference code elsewhere, the same block appears (but underlined and “linked” to its source). I find this super super useful because often my brain is writing and thinks “wait this is just X thing I’ve seen / written before”. With block references I can just paste that block in (or a link to it). It’s so much faster than my previous workflow, which was scrolling up through my ideas document, or even browsing different files, looking for where I’d written that thing before.
TODO list. There is an easy shortcut (Ctrl+Enter) to add a block to my TODO list. So it’s easy to go and look at all my TODO items on different pages. This is great if I am writing something and want to make a note to come back to a point without breaking out of flow.
Disadvantages of roam:
LaTeX needs two dollar signs. Also Roam’s LaTeX is clunky. If you write two dollar signs, it autocompletes the next two, but you can’t advance through those by pressing dollar sign—you have to use the right arrow key instead. I wish there was a setting to use Overleaf-style input instead.
Some features which seem like they should be intuitive are not intuitive. Most notably I still am not comfortable with moving blocks and the side panel.
Limited offline functionality (I think?). I thought Roam was only supposed to work if you were connected to the internet. However it actually seems to work fine if I am temporarily disconnected from the internet, which is great! TODO (I’d be pressing Ctrl+Enter if I was in Roam☺) is experiment with this and see how offline I can go.
Works fine but not great on mobile. It’s decent but just slightly clunky in browser. I think I would be more likely to reference my graph if there was a smooth mobile app than if I had to open my phone’s browser and get to the appropriate page every time.
Some shortcuts are counterintuitive. It’s hard for me to remember all the Shifts, Tabs, and Ctrls. And then Ctrl+Shift+o is how you open links for some reason? This is kind of unfair criticism since every feature-heavy platform takes time to adjust to but it’s a current bottleneck of mine for sure.
Some stuff seems to require using the mouse. For an app with so many shortcuts you’d think there’d be shortcuts for thinks like “paste current blocks’ reference into clipboard”. It’s hard to reliably right-click the tiny bullet point (necessary for grabbing the block reference) so this is a bit of a time waster.
Something I am uncertain about is whether I should switch to a cheaper competitor app. I have money but not that much money. $15/month is worth it to me since Roam seems to be increasing my productivity, but also maybe a free competitor app with Roam’s linking capabilities would also increase my productivity by the same amount.
Something else I am uncertain about is how to make the decision of whether to stay on the monthly plan ($15/month) or switch to the Believer plan ($500 for the next 5 years). In order to make this decision I feel like I need to both quantify how much Roam will actually improve my productivity and whether cheaper competitor apps will improve my productivity by the same amount. It’s worth mentioning that the Believer plan comes with extra features (including “offline mode”)—but it’s hard to know how much I will like this without actually purchasing the Believer plan.
I feel like in order to compare which of two apps is better I need to spend a long time (say 6 months) getting fairly good at each app. Otherwise, I will just be comparing how shallow the learning curve is for beginners.
So, my current plan is to go all in on Roam for the next 6 months and give it a fair shot. Then after that I will explore/exploit competitor apps, spending an amount of time on them proportional to how likely I think they are to beat Roam.
This is an interesting way to think about it. For me, I’m not sure whether it’s as much of a pressure differential as much as it is a pressure threshold. The latter meaning, if I exceed a certain level of excitement about a topic, then I feel a compulsion to communicate (and it feels effortless). By contrast, if I have not hit that level, it becomes much harder to write or think about that topic. I wonder whether developing more motivation based on the “sink” would in turn make me a more effective communicator...
Yes, that’s exactly what I was thinking of!
Yes, I completely agree with this point. I hope I made it clear that I like thinking about data like this exclusively for personal “outside view”-y reflection. So things like, “Oh I haven’t gotten anything done this morning, maybe it’s because of (x cycle variable), so maybe I can do (y intervention) to fix things”. And then, generalizing to other women only in the sense that they might find it helpful to think similar thoughts.
They didn’t mention sex drive, but the binary variable “had sex” did come up in the study. However individual fluctuations cancelled out any patterns beyond “more sex on weekends” and “less sex during periods”.