In figure 1 bottom-right they show how the correct answers are being found later as the complexity goes higher.
In the description they even state that in false responses the LRM often focusses on a wrong answer early and then runs out of tokens before being able to self-correct.
This seems obvious and indicates that it’s simply a matter of scaling (bigger token budget would lead better abilities for complexer tasks). Am I missing something?
Given the title I was very surprised to not have decision fatigue mentionend even once.
Decision fatigue is the well studied and obvious answer to why we don't like to choose ALL THE TIME.
worth pointing out that there was significant controversy around decision fatigue as part of the psychology replication crisis a few years back. I'm not an expert so I don't know what the outcome of that was or where the field stands today on it, but it may be that that is why it wasn't mentioned
Not always but often, when faced with two paths, one hard and one
obviously harder, my "mindset" kicks in and I pick the harder. Because
fuck it.
On deeper reflection, when I'm making those kind of choices, out
mountain-biking or yomping, they happen very rapidly and come from a
more direct place. My soul is demanding challenge. There's no fatigue.
It's not carelessness, just caution taking a back seat and reading the
map while I drive.
On the other hand, stuck between the choices of which two fine drinks
to order.... comfort kills.
“The world, for years, had been waiting for a solution for the most difficult problem in mathematics. Termed as the millennium problem by the Clay Mathematical Institute, it challenged the world’s best brains.”
This is a bit overly dramatic since there are actually six more so called ‘millenium problems’ to solve.
Anyway I enjoyed the read and learned something new about this fabulous achievement.
> It may help to know that BioNTech were in fact the developers of the Pfizer vaccine
It may help to know that Pfizer directly helped with the development - not just the manufacturing & distribution - and deserves some credit as well (even if not as much as BioNTech).
From their March 27, 2020 co-development press release:
"Pfizer and BioNTech to Co-develop Potential COVID-19 Vaccine"
"Builds on 2018 agreement to jointly develop an mRNA-based influenza vaccine"
"The collaboration aims to accelerate development of BioNTech’s potential first-in-class COVID-19 mRNA vaccine program, BNT162, which is expected to enter clinical testing by the end of April 2020. The rapid advancement of this collaboration builds on the research and development collaboration into which Pfizer and BioNTech entered in 2018 to develop mRNA-based vaccines for prevention of influenza."
Pfizer surely did help monetarily (investments) and offers global distribution, but that doesn't mean they had any hand in developing the science and the product.
Any big pharmaceutical company, like Bayer, could have done the same, but randomly Pfizer got lucky this time.
I mean yeah, but it's still a large complicated task. I don't think executing major projects like this should be handwaved because there's alternative options.
This is equivalent to saying there's nothing special about biontech as any specialist in novel MRNA vaccines could have developed these. Which did happen, at moderna.
That’s discounting the difficulty of manufacturing these new vaccines, which only a few companies know how to do, and also required many subcontractors.
If it were easy, it wouldn’t have taken so long to scale up manufacturing, even by the largest pharmaceutical companies.
Sure, and they can be proud of it and make all that money, but if you are in the market to ramp up a vaccination programme, you talk to Pfizer and not to Biontech. Almost like you'd go to Apple and not to FHG IIS for buying an iPod.
(I'm pretty sure that this comparison is a wild exaggeration of what actually happened and that Biontech representatives were very much involved in all the talks, but I assume more in an expert advisor role than as someone with actual influence on the outcome)
Absolutly amazed to see this article on Hacker News.
This guy (the author) is the real deal. I once had the pleasure to visit his workshop and he had me test a bass drum he recently made. An amazing piece indeed. Just a gentle tap from the beater and it produced a rich and powerful but quiet sound!
I often hear famous and extraordinary drummers on Youtube state that playing quiet is a skill every drummer can acquire. Yes, but no: It really does depend on the instrument as well if that sounds good! And most drums just aren’t made for it.
I'm glad that the "loudness war" in general seems to be over, and people focus more on quality, mixing and mastering rather than making things sound as loud as possible, especially when it comes to electronic music. Similarly as what you said, you know when a mix is very well made when it sounds good when you're playing it on low volume, not when it sounds good on high volume.
Nitpick: the "loudness war" is about mastering / compressing a recording so that it sounds louder at any given volume, it doesn't really have anything to do with optimizing things so they sound better at high volumes or a preference for loud sounding instruments.
I don't know. I'd argue that if the production process is influenced by the loudness war, then it too becomes part of the loudness war.
For example, a technique of masking distortion (or clipping, rather) is adding something with rich harmonic content (a trumpet for example) to parts that are expected to be hitting the wall and otherwise distorting / clipping.
Would trumpets be there otherwise? I don't know, but I'm sure producers are aware of the limitations of digital audio and as such adapt the music to it.
I worked as a mastering engineer for a couple years back in the aughts, and I can confirm that to really max things out requires production techniques.
For example, analog tape naturally saturates high frequency sounds before low frequency sounds, which brings down the peak level of a close mic'd drum. Peak limiting a recording which already has analog-saturated drums produces fewer audible artifacts.
In the abstract, at mastering-time you can achieve any absolute level without hard-clipping by smushing down the peaks with peak limiting and multi-band compression, then dialing things back up with makeup gain. But when compared against the original recording in a level matched test, at some point the processed result becomes unacceptably degraded.
To my mind it's the other way around. A "loud" recording with little dynamics sounds OK at lower volume; the listening fatigue sets in when the volume is increased. A dynamic recording, on the other hand, often sounds great when you turn up the volume and can really hear the difference between soft and loud sounds.
The difference is the delivery medium. It has always been in the interest of producers for individual recordings to seem louder relative to other recordings in the same genre, and that is still true today. However, a level matched experience is better for the consumer, so apps like Spotify apply perceptual loudness metrics and turn down maxed recordings.
That kind of level matching didn't happen with consumer CD players or vinyl turntables. Producers have to use different techniques to stand out in an automatically level-matched environment.
I dropped out of my maths degree after struggling for six years (!) at university - I had fallen too far behind. I can't just blame my part-time jobs for that.
Especially early on I often dismissed problems and assignments that I felt I wouldn‘t be able to tackle in terms of time or intellect.
This wasn‘t what the successful students did. They took on every problem with determination and focus.
No matter how hopeless. Along the way of failing they quickly developed their skills whereas I was falling more and more behind.
I then applied this lesson on my second attempt at university. A CS degree. Again I struggled at the beginning, but I became competent much quicker and in the end the degree was a breeze.
I had this problem and noticed it among others too. I think part of the problem is that in High School (and many times in undergrad, at least the beginning) you could get away with not doing the homework/studying/etc. So while you have the intelligence for the material you never learned the work ethic associated with achieving at the higher levels (and studying didn't force the material into long term memory as well). Sometimes I wonder how things would be different if these people learned an (academic[0]) work ethic early on.
[0] I stress academic here because at least in my case I was working a lot during undergrad. 40+hrs/week while in JC and 30+ when I transferred to a uni. But succeeding in those areas aren't the same as academic work ethic and I do want to acknowledge people that just ran out of energy.
In all seriousness, I stopped going to lectures* and studied at my own pace. My learning isn’t linear, so there will be some topics that are easy that you can move quickly on. Other topics take more time. Sometimes you can take a detour and dive deeper kn interesting topics.
Going to lecture, sitting in lecture, waiting around, etc. provided very little information per unit time for me. I can’t learn math or anything quantitative from watching someone do it. By using lecture time as study time I was able to double the time spent learning the material.
When you get stuck, go to office hours. Or look for notes from similar courses for a different perspective.
At the start of the course look at the book and see what the prerequisite material is. Review that material during the first week when there is time.
* exceptions being courses that have a participation grade.
I tried my best to have profs that followed a textbook.
I found lectures to be valuable only if I had reviewed the material beforehand. This was mainly because otherwise I just wouldn't be able to keep up in lecture.
If I had reviewed the material beforehand lectures were often extremely valuable for gaining new intuitions about a subject at hand that could be gleaned by an instructor's choice of explanation. And being able to ask questions in real-time was also quite valuable.
I wish I had realized this while I was still a student. By the time I was in grad school, it was too late. Now I make sure that I at least skim the material a bit before the lecture so I can see the other perspective, but also ask the professor/teacher any questions I had from my own pre-reading.
I think I agree with you. For me lectures where mostly about trying to take notes while the teacher wrote on the blackboard. Completely useless in terms of learning. I stopped going to lectures after a while and just learned on my own.
You'll win a lot more social points with your profs if you show up to the lectures and work on your own problems in your notebook. As an added benefit, if the lecture offers something special beyond what you can gain from the book then you'll be there in person to receive it.
If you have other significant demands on your time then school is going to be hard no matter what strategy you choose and might just take a lot of years to finish (please vote for UBI to help change that status quo). Assuming you can commit to school full-time though, it's less of an issue:
- You can finish a typical bachelor's degree in 5y by devoting 48h/week to school (12h for classes, 36h for assigned work). That's more time than most teachers expect, and except for a few unlucky points in time where multiple large projects coexist you'll rarely have to actually spend that long studying.
- It's hard to express just how much of a difference it makes to start with a little easier content to ensure you have the requisite background; don't let your pride hold you back. E.g., if the university places you in math class X, start at class X-1. You'll spend less total time learning throughout your education, be far less stressed, get better grades, and understand the material better.
- If you just want the degree, a lot of the first 1-2yrs of college courses can be replaced with CLEP/AP/... tests. Anyone can take them (not just in high school), and it'll take a lot fewer hours and dollars to get a passing score on one of those than it will to get a good grade in an equivalent college course (at most universities such tests won't affect your GPA, so even a score of 40% on some of them still gets you a passing grade).
- It's quite a bit more efficient to take more courses at once, especially if they're closely related (e.g., topology, abstract algebra, real analysis, ...). If you have closer to 70-100h/w to spend in class and studying then consider finishing your degree in 2-3y instead of 4-5y. You'll still have plenty of time to do fun things over the summer and winter holidays, and I know I personally found it more motivating to have an end date in the near future.
I'm nearly completion of a Bach Comp Sci that I've spent ~20 hours per week over 6 years (by the time I finish). I've done this while working full time as a single father who studies part time.
The time aspect is brutal. I'm ready to have regular hobbies. I'm ready to have a serious girlfriend. I'm ready to have regular social events. 6 years is a long time to just stop having a fulfilling life.
EDIT: I'm 1 grade in 1 unit off a perfect GPA. I'm at the point where I'm willing to have my GPA drop in order to free up some time to actually not be consumed by uni for the remainder of the time.
> It's quite a bit more efficient to take more courses at once, especially if they're closely related (e.g., topology, abstract algebra, real analysis, ...).
I agree that the interplay between related topics helps me form a more robust of understanding of the material.
On the other hand, it might be worth considering proactive and retroactive interference, (the difficulty of storing similar, long-term memories).
The layman's takeaway is that it's generally better to learn a variety of non-related topics concurrently instead of similar ones in order to facilitate better long-term recall.
I actually graduated in math, but I did struggle with these things. I also graduated in France where we have many more hours of class and the math program is pretty intense (did a year in Canada and it was a piece of cake in comparison). There’s also the fact that at that time you’re discovering yourself, partying, dating, etc. which takes a lot of time...
How much class did you have? My first year at university had three hours of tutorials and ten hours of optional lectures per week. Subsequent years had less. There was plenty of time.
My engineering degree had six classes per term at 3 hours of class time per course. Two of those would be labs with a 3h lab each week. So 24 hours of in person time per week, with an expectation of 2-3 hours or outside work for every in class hour.
This was probably my biggest gripe with my mech eng degree. Every minute you spent grinding through a difficult topic until you understood it, was a minute that you needed to be studying for another exam or working on a project. In the end I came out with a pretty decent GPA, but a serious case of impostor syndrome as I never really felt like I had absorbed most of the material. Of course engineering is a demanding field, but I've often wondered if students would benefit from having five classes per term.
You are suggesting that these are quotes from the article. They are not.
Also in the linked interview one of the scientists leading the study openly admits these points: “We cannot simulate a world of UBI. [...] We will not find out anything about these economic consequences, not even about possible power shifts between employers and employees, the amount of net costs or the effects on migration.”
This study is meant to add data to the picture and improve the discourse.
Once when I was frustrated with my current Job at a large corporation, an experienced friend told me the secret.
He said, they'd value "predictability over excellence".
Meaning, talk about your goals, give an estimation and arrive exactly on point. It doesn't matter if it's your personal project or projects/processes where you take the lead.
Being faster than estimated, or finding a better way and switching while your doing it will not be appreciated.
This really unlocked a lot of success and explained many glass walls i've been running into before.
I joined a large company about 9 months ago, coming from startups, and while I knew things would be slower, your quote seems to make explicit something that I've observed in my time here.
I think I had the mentality of "putting out fires" that is always the case in startups, and so for a few months I was stressed that I wasn't doing enough, since my workload was lower than I'd experienced at startups.
But I've learned that the work that is value most is the work that helps others, and what helps others seems to be anything that is highly predictable. So, "showing up" and consistently being responsive and available during work hours. But also writing automations which are visible, reliable, and have a material impact on a team (or many teams).
Thanks for your insight, I think I'll keep that more front of mind in the coming weeks
Arithmetic existed long before its axiomatization. Arithmetic was useful and no one stumbled upon contradictions in it. So it was natural to suppose that it can be described by some axiomatic system. Peano found it.
It is a system for modeling concepts invented by man. Everything that falls out of such a system is a product of the invention. Numbers don't inherently exist. Everything derived from that concept can't be a "discovery".
This is an excellent point. When I took algebra as an undergraduate I was blown away by the fact that you can choose any axioms and then derive an algebra based on those axioms. I was blown away because prior to that course I just assumed that our “standard” axioms were immutable.
> If you only look at mathematics I think it's simply: - Axioms are invented - Conclusions are discovered
How would you revise this statement if we lived in a "Mathematical Universe", like Max Tegmark's hypothesis.
> The magic part for me is that some axioms have been chosen so well that their conclusions are confirmed in the real world.
It's actually hard to avoid Turing completeness, and once you have that, any recursively enumerable function is calculable. All you need is addition and multiplication on numbers.
Can you give some examples of axioms in pure math that run completely counter to our physical world? For example:
It is NOT possible to draw a straight line from any point to any other point.
It is NOT possible to extend a line segment continuously in both directions.
etc...
or
Things which are equal to the same thing are NOT equal to one another.
If equals are added to equals, the wholes are NOT equal.
The whole is LESS than the part.
Note that the original forms of the above axioms "make sense" to us because everything in our physical experience agrees with them. So when you said that the "physical counterpart ... is immaterial", I was curious to see an example of a "physically impossible" axiom.
You can invent and pick axioms in many ways that (probably) won't lead to inconsistencies.
But they won't all be powerful enough or relevant in the real world.
Well, then it sounds like your reasoning gets it backwards: the axioms that produce systems without significant consequences or connections outside of their own abstract realm end up being ignored.
Or in other words: the constraints on maths are imposed from outside of maths.
Doesn't this imply that, while you can invent all the axioms you like, you must discover which ones are consistent with each other and with experimental results.
