boerseth
If OpenAI had never made a push to get good at maths, we might still have a sizeable group of peopne stuck at that first line. I say that because I still hear in discussions the naive rebuttal "But we'll still need _someone_ to {one-step-up-in-hierarchy}" . Although you have to be curious now how long that sentiment can last.
The good news for those doing abstract maths might be that, now that OpenAI have proven that their AI can do the job in principle, there's probably not much left in it for them to keep going. Mathematicians should know better than anyone the lack of a direct profit motive in doing the work that they do.
(Edited for clarity)
But if the art instead beems with intention and effort, chances are that it will be interesting. And in order for anyone to create something so brimming with signs of effort, they must have cared about the piece, the message, the artform, or something along the process. This post talks about effort and attention, but you could phrase it as a question of reciprocal "caring". If you want me to care, show me that you even care yourself.
It is getting harder and harder to suss out what is genuine though.
While the connections are interesting, I would be as interested in the disconnects, as there's a bunch of cases where our human intuitions can fail us in subtle ways. This is actually one of the lessons I treasure from mathematics: it has helped me grow a healthy set of alarm bells for those unintuitive cases. Especially for probability and statistics.
No. That is quite literally exponential growth, basically by definition. If x(t) is a growing value, then x'(t) is it's growth, and x''(t) its acceleration. If x influences x'' , say by a linear relation
x''(t) = x(t)
You get exponentials out as the solutions. Not hyperbolic.
I always thought of the exponential as the pole of the function "amount of work that can be done per unit time per human being", where the pole comes about from the fact that humans cease to be the limiting factor, so an infinity pops out.
There is no infinity in practice, of course, because even though humans should be made independent of the quantity of extractable work, you'll run into other boundaries instead, like hardware or resources like energy.
After skimming over all of them, it seems like most "simple" operations take on the order of 20ns. I will leave with that rule of thumb in mind.
That's not true. From the little time I've spent trying to read and write some simple programs in BF, I recall good examples being pretty legible.
In fact, because the language only relies on those few characters, anything else you type becomes a comment. Linebreaks, whitespace, alphanumeric characters and so on, they just get ignored by the interpreter.
Have a look at this, as an example: https://brainfuck.org/chessboard.b
For me, it seems so much simpler to keep the two separate. You won't be forced to wash the heating element every time you wash the cup. Can't heat a different cup while the other is in the dishwasher, unless all your cups are self-heating. Normally, the only way for a cup to break is if it shatters, but with an inbuilt heater there's electronics that can break too. And should the cup shatter, now the heater is unusable too, or vice versa.
An intuitive argument against the claim could be made from the observation that people "jinx" eachother IRL every day, despite reality being vast, if you get what I mean.
Rather, every day whenever other more important chores or duties loomed, I'd notice one of my guitars laying around, in my couch or my bed or leaning next to my desk. And most times, I'd give in. There's always a new skill, technique, lick, or song that I'm working on, or something I've recently mastered that gives me joy to play.
If anything I think discipline would have hurt my guitar skills over the years.
As for the meantime: I still did have my bank's ID chip with me as a backup, so I could have used online banking to make a transfer to myself with something like Western Union, and crossed my fingers that my bank wouldn't require verification by phone for this suspicious transfer. That would have gotten me some cash at least within the course of the next day, but my friend helped me out, so it didn't come to that.
Without friends around, though, and one or two more unfortunate circumstances piled on, I really don't know. It's unsettling to realize how little it takes to be forced to sleep in the streets.
These "cascades of misfortune" I've run into happen largely because of how we've placed certain institutions at the center of our lives and our society, or perhaps more precisely because of the "convenient" solutions of theirs that we've all been coralled into adopting.
I'm thinking of social media networks, smartphone companies and their app stores, banks and their electronic payments, etc. Everyone's opted in, and we don't realise how much we've given up as a result, with all these "convenient" alternatives, now made mandatory to replace the old and inconvenient solution.
We don't realize, that is, until you're standing at the bank teller in a city away from home, passport in hand but otherwise robbed of phone and wallet, hoping to withdraw some cash to keep you alive while you sort this mess out - only to learn that the bank is no longer able to do that for you. You can't just get your own money. You could withdraw at the ATM, but with a card of course, and that for a fee with a pretty low upper limit. But banks don't serve that purpose anymore. They're now software institutions that we are forced to have a relationship with and operate through in order to make monetary transactions.
Suddenly society has shut down. You can't log into anything without your phone and 2FA, so you're stuck without access to your favorite online services until you get a new SIM card and a fresh device. But even then, there's no riding public transit, because you don't have access to the apps they all operate through. Not that you'd be able to pay in those apps anyway, after cancelling your payment cards. And besides, you don't have anywhere you'd like to go anyway, because, aside from having basically no money to spend on food or events, there's no way to learn what's happening in this city without access to Facebook and all the company pages and events published there.
I forget now all the myriad ways that life grinds to a halt, but I do vividly remember feeling like nothing was possible. And that only because I lost one or two things which should be entirely optional in life! You shouldn't be required as a human, nor even as a member of society, to have a Facebook account, or a smartphone, or even a bank account (that last one is perhaps my most extreme take, but I stand by it).
Later I became obsessed with Argentine tango. Unfortunately, I thought, "comprehensible input" won't work with dancing, especially not a couple's dance. Nevertheless, unable to dance every day due to my local scene being quite small, I instead consumed a boatload of YouTube videos during my spare time. Instructional content, performances, class summaries, and what have you. And I progressed super quickly.
First off, as a leader, it is good to have seen competent dancers with good musicality and how they choose their steps to fit with phrases of songs. That much fits in parallel with input-based language acquisition techniques. But I also think I gained a good amound of intuition about how to move my own body. Not perfect intuition, but more than nothing, which was very much my starting point.
I have done some backpacking these past two years, and it is worrying how easy it is to get into big trouble if you lose your phone or payment cards.
As an example, my debit card got eaten by an ATM on my way to Argentina, and after my 6 month travel, the backup credit card I had brought was about to expire.
Despite my card working as a means of payment, I was starting to feel the effects of this corner case in every aspect of modern life. I could not use our equivalent of cashapp, I assume because my card was about to expire. I could not ride public transit, or trains, or do things like book a yoga class with my friends, all because all these institutions basically only let you interact with their service through their apps, where I had no way to pay.
I spent some time visiting friends in the capitol on my way home, and tried to sort the situation out with my bank. They thankfully were able to order some new cards to their office, rather than to my home address. But immediately after my talk with them I found that my one remaining card had been cancelled.
Then I tried bringing my passport to withdraw some cash, but the bank teller almost laughed at me, before explaining that you can't just do that anymore. The bank isn't even allowed to let you get your money in cash and leave. You can get bits of it in bills at the ATM for a fee the price of a coffee, but also that requires a card, of course.
Electronic payment solutions are so convenient, for the public and for institutions, for law enforcement and control, that we've forgotten how much we need to give up in order to use them, and now they're being made mandatory as we trudge along into a cashless society.
Now I couldn't even get food or shelter, if not for my friends. I remember half stumbling out of the bank with my passport in my hand, half dizzy with shock and anger. This, along with lots of other small mishaps like losing my phone and encountering trouble, kind of radicalized me on these topics.
However, researchers are able to say and find out a lot more about the way LLMs work and learn than they can about human brains. It might be to take the metaphor too far, but I sometimes like to think about how and whether at all these sorts of findings about AIs can apply in any way to us.
This particular case makes me wonder if there is anything to the human instinct to dismiss and ignore people entirely once you learn they're not morally aligned with you on some core issue. In particular we might ignore entertainers and content creators that have views we strongly disagree with, even if they're well reviewed and highly popular, and even if they seem to stay off those sensitive topics in a specific episode/movie/podcast/stand-up-special. We don't want to risk subliminally learning their corrupted values.
Edit: Not to say it is wise to "cancel" and ignore people you don't agree with. Frankly I think it is bad if you value discourse and keeping your mind open to new and differing opinions. Rather, I'm arguing here that it makes sense that this instinct of ours came about at all as we evolved, since it is probably beneficial to stick to your values.
Alternatively, if we still want to cling on to this ritual of measuring the performance of students, you could give each and every one of them oral examinations with AI professors.
I never got into emacs. Is Org worth it?
## Read the reference
It is very difficult to dance from written instuctions, but I think one hugely underappreciated resource is watching very intently great instructors dance basic movements. I did this in my early days, because it is very enjoyable entertainment when you apreciate this dance, and it was I think a large part of why I progressed rather quickly.
I could go on about this point, but I think there is a similar thing going on with humans and our mirror neurons when we watch others do something, to how we acquire spoken languages, and the recent wave of input-based language learning movements.
Another way to interpret this point might be to know the history of the dance, of Argentina, the broader dance communities and movements across the world, and the culture in general. The main advantage to this I think is to contextualize a lot of what you learn, and that the dancer becomes more immersed in the activity.
## Know your tools really well
Dancing involves some tools external to the dancer, like clothing and shoes, the dance floor of course, perhaps talcum powder to reduce friction, and most importantly the music.
While there is considerable advantage to be gained from wearing an outfit suited for dancing, there's a quick and hard cutoff as to how much knowing more about these things improve your dance. The same applies to the floor surface and so on.
But of these "tools", I think the biggest gain is found in familiarizing oneself with the music. Both gaining intuition about the structure of songs, melodies, and rhythms, but also gaining deeper insight and access to the emotions at play. Dancing is an opportunity to interpret all of these aspects of the song, and being familiar with the music, the medium that connects one with ones partner and also the thing you are trying to represent through movement, goes hand in hand with being able to execute the movements of the dance at all.
All of the points of the article apply here: the history of the music inform you of what the tango is all about, and of the different sounds and movements that are available to us today; the present, in the sense of what music is currently popular, and played live; limitations, in the sense of what different styles of tango music work with what sorts of movements and feelings; finally, the ecosystem is like a summary of all of the above, and something that people discuss at length in every milonga, like which orchestra they prefer, or which contemporary groups they like.
However, one thing that I think qualifies as a tool, although somewhat subtly, is the dancer's own body. I have not pursued this avenue very far yet, and am thrilled to realize that this is something I really ought to do. I know only a little bit about human anatomy, after strength training years ago. And as for my own body specifically, perhaps something like yoga, pilates, or calisthenics would be valuable.
## Read the error message / Break down problems
While there are no error messages in dancing, you definitiely feel when something isn't quite working out. If you're in a class and are trying to learn a step, it is crucial to be able to be critical of your own performance, and look for faults or inconsistencies.
Maybe a step feels a little off, like there's something awkward going on between you and your partner.
One thing I have noticed is that, if you are trying to go over a sequence of steps A-B-C-D, and something isn't quite working out at point C of the sequence, the soure of the error is usually actually somewhere in either point B, or perhaps already at point A.
This might remind some of looking at a stack trace of an error, and trying to figure out at which turn things went sideways. The problem is frequently not located exactly at the point where the error was actually raised.
## Don't be afraid to get your hands dirty
One of the dangers for any learner is calcifying into bad habits that were adopted at an early stage of learning. In order to break out of these, you have to be willing to abandon old guardrails, be uncomfortable over again, and to learn something over. This might be analogous to refactoring some kind of broken legacy code.
Growth is also possible through experimentation, abandoning old patterns in search of something new and potentially interesting. This also requires courage, and feels a lot like getting ones hands dirty, and applies to both programming and dancing and probably many other things alike.
## Always help others / Write / Status doesn't matter / Build a reputation
Since dancing is a communal activity, it is not so vital to be writing in order to be heard. But I still think that communication in this space is hugely valuable.
From what I have seen, any healthy dance community has great communication between the more experienced dancers and the less experienced ones. Unhealthy ones are often referred to as snobbish, The alternative, where there is a strong divide and exclusion from the top downward, are often referred to as snobbish, and I would characterize that as unhealthy. That sort of a scene will gradually wane from the high barrier of entry, and will wither and die if not already sufficiently large.
## Never stop learning / Have patience
Any tango dancer will tell you, no matter how experienced or accomplished they may be, that one never stops learning this dance. Even decades into ones journey, it is extremely common to hear dancers say that they're still working on their walk - which also happens to be more or less the very first thing you learn in your very first class.
## Never blame the computer
In a dance that famously requires two people, it is very easy for a lot of people to blame one's partner when something goes wrong. I think it is much more valuable to take the opposite approach, and always look to what you can improve in your own dancing, whether you are a leader or a follower, long before attempting to throwing accusations and corrections at your partner.
There may of course eventually come a breaking point, at which you want to raise some questions and explore together for a solution. But to immediately correct your partner, before they've even had a chance to correct themselves, is never a good approach in my opinion.
## Don't guess
I think this one is hard to stick to rigidly when learning how to dance. If you want to be completely sure of a movement before you try it out, you'll forever remain paralyzed. We all have to do some guessing in the beginning, trusting that our muscles move us through space in about the right way as the dance is supposed to be performed.
However, these guesses that we make are frequently wrong, and result in incorrect technique and bad habits which must be weeded out and corrected before they calcify too much.
So while I think not guessing at all is impossible, I think we really should not underestimate the value of any means available to us for correcting incorrect guesses that we have made and accumulated. These include someone more experienced than us that we trust, or private lessons from tutors who know what they're talking about.
## Keep it simple
It is funny, but this exact piece of advice is also so very frequently heard in tango classes. As you progress and learn and acquire vocabulary in tango, speaking now mainly about leaders, it is very easy to want to use it all and throw every shiny new step and sequence you know at the poor follower that you've convinced to join you on the floor.
Many also are nervous and afraid of the silence that comes with not moving all the time, and keep leading step on every beat in order to never make it seem like they're running out of ideas.
But in actual fact, it can be wildly better to relax, and do simple steps well, with tasteful pauses aligned with the music, than to hurriedly toss around every step that you know.
## My own final thoughts
Despite the fact that code is run on computers, and dance is performed by humans, I think this analogy holds really well. If you think about it, dancers are just meat robots performing fuzzy instructions written to their brain by themselves and dance instructors, or whatever they've acquired by watching others dance. You could summarize as follows the mapping in this analogy:
Spec <-> The goal that the dance-student is aiming for
Code <-> Steps that have been acquired by a dancer (maybe imperfect)
Runtime <-> A night out on the dance floor
Error <-> Improper technique
Programming <-> Learning and improving as a dancer
Programmer <-> Learner/teacher
For any autodidacts out there, that last part is good motivation to reflect some more on the points of this blog post.
Not to say that dancing is not commodifiable. People make a living offering classes, outfits, shoes, and travels centered on specific dance genres. But as a participant, you can get pretty far for a lot less money than the price of the proverbial night on the town.
I admire the honesty, but will continue to phrase these "why not" comments as insincere TODOs.
The existence of an infinite continued fraction is also not sufficient - off the top of my head, the very rational φ can be expressed as
φ = 1 + 1/(1 + 1/(1 + ...))
Edit: Apologies, I forgot that φ is in fact very irrational... Oops!