Human behavioral complexity peaks at age 25: study | Hacker News Reader

Human behavioral complexity peaks at age 25: study

journals.plos.org

196 pointsHooke80 comments

Did anyone even read the article. The study has nothing to do with complex behavior or "sophisticated" behavior. It's a study on your ability to generate random list of results, like "listing the hypothetical results of a series of 12 coin flips so that they would 'look random to somebody else'"

That strikes me as a poor measure of true randomness.

Why? Do you suspect that subjects were deliberately making their choices less random because they anticipated the poor performance of another person in assessing randomness? It seems like a good assumption that they knew they were trying to fool a sophisticated randomness test that they couldn't second-guess.

No, just humans are well known to be bad at actual randomness.

Considering that a random generator could generate 11111111111111111111111111 5 times in a row...it's a bit hard to claim someone's test results as a failure of randomness unless you claim you want a gaussian distribution or some other type of "character of randomness." Ie. running diehard tests on it and whatnot. A fixed number of trials is deceptive unless you can see the algorithm behind the numbers. And for a human being..you can't. So unless you have a giant sample size, and even when you do, there is a bit of a mischaracterization done depending on what tests you are going to use to determine how random the data is

In this context it's probably better measure of randomness than true randomness.

What 'appears random' is better measurement that matches what people try to do.

People are not good at recognizing randomness, they confuse it with homogeneity. True randomness generates more human recognizable patterns than people think. If you as people to generate random string of 1's and 0's, they avoid long strings of 0's or 1's too much.

I don't quite follow what you're attempting to say here, I mean to say that the study is flawed because "It's a study on your ability to generate random list of results", with the inference that supposedly those who generate the most random results and those who appear by human estimation to do so are the same people, because humans are actually bad at randomness, exactly as you yourself say here.

So what "appears random" is not at all a good measure of what is "actually random" to put it as simply as possible.

The goal is the ability to generate strings that match the "approximate sense of complexity" (ASC) of the subjects. To do so requires the ability to avoid any routine and inhibit prepotent responses.

Research goal was to measure cognitive ability and randomness is just measure stick. The actual mathematical complexity is correlated but there is human bias. The bias itself is irrelevant if it's constant. The relevant is how closely subjects can generate strings that appear random and complex (randomness with bias) for humans.

In other words

measure = statistical randomness + bias

Because the bias is almost universal (see the modulating factors in the article) it's not interfering with the thing they try to measure.

It's not supposed to be a measure of "true randomness" but a measure of the capacity to generate random-like results.

It's not supposed to be a measure of "true linguistic proficiency" but a measure of the capacity to generate linguistic-proficiency-like results.

So in each case what's the gap between actual linguistic proficiency / randomness, and the appearance thereof? And of what value is measuring these human perceptions rather than the actual facts in each instance (like taking all the results and putting them into a scatter output and seeing if there is actually a pattern in the pseudorandom data, or formally analysing the grammar and spelling in question and verifying that it is technically correct rather than just "english sounding" https://youtu.be/gU4w12oDjn8?t=2m)

Can we draw conclusions about that Italian gentleman's ability to make a song that sounds like English pop music "better" than an English pop music song that is actually technically grammatically correct, and use it to infer that he's got better English skills than the writer of the technically correct song?

And if not, why are we trying to make statements about the ability of some randomness souce not based on any actual measure of true randomness?

>So in each case what's the gap between actual linguistic proficiency / randomness, and the appearance thereof?

That there are no hard constraints/expectations like in measuring the quality of a e.g. software random number generator implementation.

They don't expect to find true randomness in the results, just to measure how much randomness (entropy if you will) those various age groups are capable of producing.

it appears to be a way to measure complex behaviors, and higher cognitive functions, however - so I don't think the commenters are that far off.

I'm sure it is an important factor in how the brain works, and that the research is insightful. I'm having some trouble with the idea of extrapolating complex behaviours from what essentially is a micro-benchmark of cognition. That sounds overly reductionist to me.

Although I guess it is impressive to find consistent results within said micro-benchmark, of course, since that hints at something fundamental about our biology (in the reddit AMA linked elsewhere in the comment the author claims to see no difference for gender, educational background, etc; suggesting age is the main factor. That seems significant).

I would call this test an analogue of IQ testing. Again, we see how mainstream thought places IQ on a pedestal. Mainstream thinking overvalues and overrates mental gymnastics, such as performance on IQ testing. But learned experience is in my opinion far more valuable and should be valued more by mainstream thought. At age 60, it is true that I cannot perform as well on IQ tests. But in my opinion my understanding of the world is much greater. I was like a child at age 25, even though I tested well on IQ tests. But I was just a child. Does mainstream scholarship explore this facet of human development? Not much....

Isn't the lower scores for older people just a result of the flynn effect? This doesn't mean a personal drop in "absolute" g, if it's really a thing

I'm interested by the path of reasoning from evo-psych. The underlying mechanism may manifest in higher-order features like motivation. How this motivation is mediated by culture (both economic and social) might lead us to draw interesting connections with both pathology and maximising productivity.

The question is whether the correlation stays strong, though. I can imagine this accurately measuring decline in complex functioning, but I can also imagine it being the correlation that weakens as you age. In the second case, it would just be a warning to compare same-age statistics when comparing between people.

yeah, but apparently barely declines untill say 60+. Speed suffers however.

"The adult years were remarkable in that complexity remained at a high level for a protracted period, in spite of a slow decrease of speed during the same period. This suggest that during the adult period, people tend to invest more and more computational time to achieve a stable level of output complexity. Later in life (>70), however, speed stabilizes, while complexity drops in a dramatic way."

and

"These speed-accuracy trade-offs were evident in the adult years, including the turn toward old age. During childhood, however, no similar pattern is discernible. This suggests that aging cannot simply be considered a “regression”, and that CT (completion time) and complexity provide different complementary information. This is again supported by the fact that in the 25–60 year range, where the effect of age is reduced, CT and complexity are uncorrelated (r = −.012, p = .53). These findings add to a rapidly growing literature that views RIG tasks as good measures of complex cognitive abilities [21, for a review]."

It almost sounds like people try harder and harder to keep up with societal expectations of continued "sharpness"... until they hit some age where cultural norms say they aren't expected to be sharp any more. And then they stop trying, which causes an outsized decline as their lowered expectations of their own capability, feeds into lowered capability, which feeds back into further-lowered expectations.

could be, I really don't know. I can imagine perfectly benign scenarios too; if our long-term memory grows with time, maybe there's just more possible connections/associations to filter out with time too, so that decision just becomes harder, with only the deeper old age being simply tissue decline, the exhaustion of cognitive reserves etc.

Somewhat relatedly, I think I heard on some old Skeptic's guide to the universe episode about an experiment with some nootropic, maybe it was a racetam though I think it was mondafinil, and this kind of reaction time to response accuracy tradeoff was observed, on young healthy adults. Those with less correct answers slowed down, presumably concentrated better and gave better answers, but those already good at whatever the task was simply were slower and yet no better.

Is it possible to get a link to that episode?

ah, I'm sorry but I really don't remember. this was some years back.

Maybe http://www.theskepticsguide.org/podcast/sgu/530

https://www.sgutranscripts.org/wiki/SGU_Episode_530

hey, that's not bad; didn't even expect SGU had such detailed transcripts.

But actually looking for it now, the particular study I had in mind seems to be from a science or fiction segment from this episode:

http://media.libsyn.com/media/skepticsguide/skepticast2014-1...

Interesting to see how Steve's assesment of modafinil evolved between the two episodes

Thank you so much for your time. I was really curious.

>And then they stop trying, which causes an outsized decline as their lowered expectations of their own capability

As if there are no physiological factors at play?

I mean, tons of studies have shown declining mental capacity, degenerative diseases increase with age, etc. Even in animals that have no, or much less, "societal expectations for sharpness".

Ok, comments on fig. 2.

The 95% confidence intervals are plotted, but clearly the distribution of their subjects seems to sample heavily near where they find their peak (~25 to 40 ish), and correspondingly, the drop offs are away from that area...

Seems fishy to me.

Also, if you look at the right side of figure 1 there are lines on the bottom of the complexity chart for each of the tasks, presumably representing people who essentially did not do the task (although they still seem to have spent a variable amount of time not doing the task). It looks like this skews older, and just by eyeballing the chart some of the 75+ would be upward trends if not for that bottom line. I skimmed the article and did not see a discussion of this.

Furthermore, the poor sampling near the edges of the plots leads me to suspect that the trend away from a flat line is due to Runge's phenomenon. The peak may be nothing other than the oscillations from this phenomenon leaking into the interior of their data set.

I am conducting a survey as a first attempt to see what's going on. If you would be so kind, please take it here:

https://j.mp/CoinFlippingSurvey

If I get about 100 more respondents, I will release the data and analysis at the same link.

i can't tell if i'm more humored or intrigued.

It's not easy to click to the left or to the right 128 times. Can't you just replace it with a textbox where users type T or H, or something like that ?

I agree. It is so much easier and quicker on a smartphone though.

The survey is intentionally dumbed down so non-technical users don't have to type much. You can almost say it is geared toward the general population, many of whom use smartphones.

I wonder how/if this relates to the fact that many mental illnesses fully manifest around 25 as well.

"Roughly half of all lifetime mental disorders in most studies start by the mid‐teens and three‐fourths by the mid‐20s." - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1925038/

From personal experience I'd say it can relate to mental illnesses caused by trauma, hostile environments, etc.

Getting over trauma and other emotional baggage has resulted in large improvements in sustained focus, lower inhibitions, and general cognitive improvements for me and I'm well past the age of 25.

Different roots here, but same results.

Gradually worsened up until ~25, though. Vastly improved after a couple of years, and seeing the tail ends ~30

The brain reaches its full maturity around this age so it's unsurprising any mental illnesses reach their own peak in somewhat of a parallel.

As a personal aside, it makes me question the sensibility of letting kids go off to war, vote, drink, or smoke before this age.

>The brain reaches its full maturity around this age so it's unsurprising any mental illnesses reach their own peak in somewhat of a parallel.

Why would that be "unsurprising"? It's not like mental illness is intuitively correlated with increases/improvements in brain functioning...

If anything, one would expect the inverse: for some mental illness the increase in brain functioning around mid-twenties would somewhat help reduce it.

A large part of this is that doctors are wary to diagnose mental disorders in children/teenagers, though. Often, symptoms of mental illness during development are just the brain doing the neurochemical equivalent of "one leg growing faster than the other"—it ends up balancing out.

There is still some element of truth to this, though, especially with bipolar disorder and psychosis. It puts me in mind of the fact that allergies can also manifest around 25... and makes me wonder if there's a connection there.

FWIW, I developed a rather severe allergy to many types of fish out of nowhere at 31.

Authors' Reddit AMA:

https://www.reddit.com/r/science/comments/6accnw/plos_scienc...

In high school, my math teacher once asked us to write down a random string of zeroes and ones, similar to what they did in the study to measure "cognitive functioning". He then asked us to count the number of times we alternated between 0 and 1. He told us that while most people try to have about a 50% split between 0 and 1, many alternate too often (0101101 instead of 0100011). Maybe there are other tests that one could learn to improve one's randomness, or at least write down a random string faster (they also measured speed).

In the introduction, they cite that "the complexity of a subject-produced pseudorandom sequence (…) is surprisingly resistant to practice effects". However, is it also resistant to teaching effects?

This is a great question. What are the speed requirements?

https://www.quora.com/Is-it-possible-for-a-human-to-generate...

You could probably come up with a reasonably good, fast mental PRNG algorithm, and practice that.

Pick a phrase (name, address, phone number would do), discard white space, and convert the upper two bits to binary.

Example: "Pick a phrase" would become

  00 01 11 11 01 00 00 10 01 11 01...

That's certainly not random, but unlikely to be detectable for shorter sequences.

(Edit: it probably is a fun exercise to write a program that decodes this code that reaches >75% (lossy) compression)

That would hurt you on speed. It's much faster to just pull numbers out of your head as fast as you can write them down. That should be protection against using an algorithm. Even if you do have a fast algorithm, it would still get slower as you age, so you could use it to compare yourself at different ages.

The test might also be scored using randomness tests that would pick up the repeated use of the same algorithm, like the one you described. Distribution of letters and their (ASCII?) bits won't be perfectly random. You could also hand code exceptions for known algorithms as you discover them.

That's what interests me. Monitoring your own cognitive ability as you age for early detection and tracking of neurodegenerative diseases. For this, you need a test that's resistant to practice.

"It's much faster to just pull numbers out of your head"

I don't doubt that, but the context was to generate reasonably good (in the sense of "looks like independent samples from a 50/50 distribution") sequences.

Humans are notoriously bad at that (example: in the first 9 bits, one would expect four consecutive zeroes or ones. Try finding someone who produces that when 'just pulling numbers out f their head as fast as you can write them down').

I think this will be significantly better (as indicated above: for shorter sequences), even though it lumps a, e, i, n and r to the bit pattern '01'. It also can be quite fast, even if you do it by memorizing the mapping from letter to 1..26 doing 'mod 4', and conversion to two binary digits.

There are a whole bunch of test for true white noise:

http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html

For those who don't want to visit the link, some of the more intuitive examples:

* Ratio of zeros to ones (and in subsets)

* Longest string of zeros/ longest string of ones (and in subsets)

* Frequency of ngrams (00, 01, 10, 11, 000, 001, ...)

* Maximum cumulative sum (treating it like +1 -1)

You can test and refine your randomness ability here: http://www.loper-os.org/bad-at-entropy/manmach.html

Perhaps this has something to do with completion of myelination to the frontal lobes.

FWIW, I've been discovered with MS exactly at 25.

Previous discussion : https://news.ycombinator.com/item?id=14131086

I completely believe this. I was far more sophisticated in my late 20's.

In my late 30's I learned to stop being such a douche... and I became far simpler.

We all see through the Matrix as we get older...

I'm 20 years old in my first year of university, and I'm probably going to fail the final exams next week. I don't think I'll be having the chance to take advantage of this peak.

Just because you don't make it in university doesn't mean you can't do some amazing things.

I failed my oral exams in the Math Ph. D. Instead of retaking them, I left with a Master's, made a lot of money and started my own company which now has over 4 million users.

Also, forget about the peak, if you build value for yourself, you'll have more every year. If you're building value for others and earning money, then invest it somewhere that makes a difference.

In fact, if money is what you're after you are probably better of getting the degree and then leaving academics, I don't know many people who stayed in the academic circuit and ended up being well off.

In academia, only those who get tenured professorships are sitting pretty. And they get to sit pretty for decades. Everyone else has to hustle to get their crumbs. I know people who are teaching adjuncts and they get paid crumbs ( $2 or $3K PER SEMESTER ). This is at a highly competitive university where tuition + board is $80K. I could not believe it.

3K per semester with an advanced degree? That's insane. You earn more being a graduate student. Is that a non-STEM field? A regular job would be a much better option.

Yes, it is insane.

Universities have become sweatshops. There are a handful of tenured foremen/women, but everyone else is busking it.

The students are psrt of the cash crop, investment income, donations from alumni, and grants make up the rest.

Original thinking and game-changing research have been deprecated.

What? What does you comment have to do with the topic?

It seems like you got offended by the title, which has nothing to do with what you wrote.

You seem to have a chip on your shoulder about being a failure at math ( or failing to get a PhD ).

You are wrong :)

Even if that really happens: there's plenty of ways you can spin this into an advantage, long term.

An event like this closes some doors, but will also open others.

In any case: good luck with the exams! You can do a lot of exam preparation in a week! Don't give up before it's over :-)

Thank you; the pass mark being only 40% has given me some hope. It's been a large step up in terms of volume of content from what I did to get in.

I would rather hope to fail than to slip by with 40%-60%. You'll waste 5 years of your life (because such slackers rarely get it done in 4) and come out not knowing much and forgetting that little bit too after a year or so. I can't really give a personal cautionary tale (I am a slacker, but of the courses I passed I tried to do well at least on the final and still remember a lot of details plus where to refresh memories) but I see it often enough in others. Some of them are fine with it, some of them regret it, some of them double down and find a new school / degree program. Take a close look at what you want from the university system -- little learning but socialization or just a simple piece of paper (they look a lot nicer in a frame) is entirely justifiable, just consider how you might judge your choices in hindsight once you're at the end (as well as have an idea of what you'll do at the end).

When I was in first year (a long time ago), the computer science department was quite new. This meant that courses were held in various different places -- engineering, science, math, etc. Unfortunately, this ultimately meant that I had to pass by the campus pub between every class, with predictable results (drinking age where I lived was 18).

Whether you pass or whether you fail will not have as big an impact as you think now. What is important is understanding how to improve. For me, I staked out a chair in the library with all the foreign students who seemed to live there. I got in to school at 7:30 am and I went home at 5:00 pm. I watched what all those foreign students were doing and copied them.

Later talking with them, I discovered that the reason they lived in the library was because their tuition and living expenses were covered by their extended family. You'd have 20 people sending money that they really couldn't afford just so that one person might get a foreign education and a high paying job to lift everyone out of poverty. If they failed their exams, people in their family would likely die of disease, etc as a result.

So I don't know anything about your situation, but probably it's not as bad as what my friends in the library had to endure. You've got a week. It might not be enough time to salvage first year (like I said, been there, done that). But use that time to understand what you need to do from here. Go to the library. Pick out a seat where you intend to live. Today is a good day to start to see what you can do.

Excellent advice.

At the end of my first semester at university, my Calc I professor pulled me aside after class for a chat. We talked about a bunch of things, but one piece of advice in particular stuck with me.

He said: "You are lucky to be so privileged - to study at a university for free, to have a supportive family, and to be such a smart and capable student - but you are also quite unlucky. Unlike other less privileged students around the world, you need to create your own drive. Without motivation, you'll have a tough time overcoming the inevitable difficulties you'll face in the future."

So that's what I ended up doing. Firstly, I started to imagine myself being from a much less fortunate background, and therefore treated my studies as a matter of utmost importance. And secondly, I put a target in my mind for what kind of person I want to be in the far future. I visualized this in quite a bit of detail, sometimes even imagining myself being interviewed! (weird, I know)

A little over 5 years later, I'm in a top 10 PhD program in my field. I'm still not certain this is what I want to do for the next 4 years, but I think I'm on top of it for now. Worst case scenario is I drop out with a MS and enter the workforce. Still, I'm immensely thankful that I have the option to think about this. Many people don't.

That's an interesting story, though I find that I oscillate between periods of perceived dread (though, as your Calc professor mentioned, I am privileged in this regard to not have it as much of an issue) and periods of a kind of laid back-ness in which I procrastinate and put things off as much as they possibly could be put off. This has been a recurring problem for me, possibly because the enjoyment of playing games or watching TV is an instant relief and pleasure.. the years of my life after university are distant and contingent.

On one hand I know that I need to work in order to get anywhere, on the other hand I pass it off by saying "you don't have to do this work to succeed". Couple this with the fact that whenever I want to start working there's a huge mass of things to choose from and I don't know where to start with it, or that I have very little willpower to stay with a question if I don't make progress.

It's hard, and I fear I may never learn. I tried to study in the library but alas no habit formed, even after a few weeks. I had diminishing returns by doing that.

One trick for breaking that is to get addicted to improving your craft. For me, it was originally starting an open source project, but there is something magical about a cup of coffee, a big stack of paper, and a math book that you have just the right prerequisite knowledge for.

My problem may be that I don't have much passion for the subject I'm studying (electronic and computer engineering), as I originally applied to do a different degree. Although I find some parts of the subject interesting (digital systems, perhaps some mathematics), others I find hopelessly hard (analogue electronics and physics). A bad part is that I don't even have a way to evaluate my knowledge against the standard which is expected of me; the course is new, and the past papers contain material which may or may not be relevant or taught before. Could I have an impostor syndrome, or do I really not know enough?

Motivation may be what I need, or perhaps it is discipline? I can't stick with things. I will relate an example without hyperbole; today I was trying to find three unknown variables in three equations (A), using matrices first by combining with the identity matrix (I), as (A|I), then forcing zeroes into the bottom left and top right corners of A, and dividing through to transform A into the identity matrix, what is left is A^(-1).

I repeatedly failed to get the correct answer, probably due to some silly arithmetic error. I gave up and started to watch old episodes of Simpsons and read HN.

I'm not a firm believer in what I consider the common definition of passion. You, and only you, have to make your passion. Personally nothing I've tried jumped out of me. Every career has it's enjoyable, intellectually engaging parts, and it's monotonous, weary parts.

If you want to stick with EE and CompE, sit down and list all of the things you enjoy, no matter how seemingly insignificant.

"For what it’s worth: it’s never too late to be whoever you want to be. I hope you live a life you’re proud of, and if you find you’re not, I hope you have the strength to start over again" - A butchered quote from The Curious Case of Benjamin Button

Do some reading on how to develop willpower. Although I'm not a fan of the rest of the site, I found the Art of Manliness did a decent 3-part on how to cultivate willpower and hone it into productive pursuits.

I had it super easy in school. I was gifted enough to coast through with no study whatsoever. It was basically just an organised social life for me. Same with first-year uni, because school had taught me enough to coast through that. Come second year, however, it was new material and it wasn't forced down my throat with the structure that school provided. I crashed and burned miserably, failing 1 subject and barely scraping through 2 others (i.e.: pass by 2-3%).

It took me until 4th year to teach myself how to teach myself, and how to develop that discipline and willpower necessary to stay focused on a goal. It also took that long to learn how I learn, that is whether I learn best through reading lecture notes, watching examples, doing problems, etc. You're never really taught any of that at school, but you're expected to know it by uni to do self-guided learning. It's a hard ability to pick up, too.

With your example, I'd encourage you to watch some Khan Academy lectures. Maybe listening to and watching exmaple problems works better for you than reading textbooks or lecture notes. Additionally, maths is in particular one of those things where tonnes of practice problems will help reinforce it until it just 'clicks'. In isolation the processes may seem simple as you watch them, but the practice is what helps you identify the underlying patterns and thus know which technique to choose when, and how to identify that you've executed the technique properly.

You might benefit from this Coursera course [1] "Learning how to Learn". It addresses many of the issues you've mentioned above. It provides a few helpful tricks to combat procrastination and it's straightforward.

https://goo.gl/brJ0qN

look. you'll never get good grades, because you don't like school. neither did i. i'd never, ever, ever go back to graduate school. getting C's and barely graduating is perfectly fine. that's a lot better than going crazy trying to excel at something you detest, and dropping out from mental anguish. (very common)

once you really understand this, it takes a tremendous burden off of your own mental state.

then, the trick is to just force yourself to do just enough work to finish with a degree, so that your money is not wasted. and doing that is not really hard. it really isn't.

your goal should be to get on with the rest of your life, not feel bad about the fact that you hate school.

Look, I think everyone procrastinates in one form or another. The key is to know when it's time to procrastinate on the procrastination (meta, huh?). In other words, you have to delay your procrastination to get the job done. It differs from person to person, so you need to find a way to do that effectively. I'm also guilty of procrastinating pretty frequently, but I've figured out how to manage it such that it doesn't affect my grades and/or work performance too much.

Regarding your comment on ECE, I also found that I enjoyed some courses more than others (I did enjoy most though). For example, I absolutely hated my power systems and power electronics courses. The latter was one of the only courses I got a B+ in, so I didn't do well in it either. As one of the other commenters mentioned, you need to get used to the fact that you won't enjoy everything in your field/job. The trick is to learn how to deal with it and get it over with, or try to work on it with someone who loves the topic you hate.

Have you tried drugs? Seriously, even something as basic as making sure you have a minimum amount of caffeine each day (pills are cheap and don't ruin your teeth) can make all the difference, much better than reading and trying to apply the latest in Motivational Techniques or Learning to Learn or plain inspirational writing/shows/music/games. Other drugs like modafinil (http://www.gwern.net/Modafinil) have their benefits too, or melatonin supplements if you need help getting to sleep. Talk to a psychiatrist to see if you need such things yadda yadda, I don't think you'd be all that receptive to "therapy" as a solution but could be wrong. I only mention drugs because your posts reminds me of myself as well as a former close friend. I won't say drugs like caffeine are solely why I'm in a cushy software job and he's doing dishwashing or something (last I got in touch he seemed to have found a happy place in life though) but when we were close we were both chronic procrastinators, I sacrificed a lot of sleep and just managed to finish more things and doing that has a way of compounding your ability to finish more things later (even if much slower than your 'ideal self' that is fully focused all the time).

Another strategy is to study with another person, in person. It can be hard to apply if you're relatively antisocial though, or worry too much about bruising your ego by exposing ignorance. If it helps study with a person you think is 'dumber', like you're doing them a favor, though really it's for yourself, and if nothing else you might be surprised they're not so dumb.

Last thing, learn shortcuts, embrace laziness (one of the Three Virtues of Programming), and automate. Learn some math software. In your example of solving three simultaneous equations, every time I had to do that I would do it with my TI-89 calculator. And not always the same way! But usually I used a slightly different (and imo simpler when not done by hand) matrix method. For 3 equations, get them all in the form of Ax+By+Cz=D, construct a 3x4 matrix with each row containing [Ai Bi Ci Di], and compute the row reduced echelon form to leave you with a diagonal of 1s in the first 3 columns telling you x/y/z correspond to the rows in the fourth column. With the calculator, it's as easy as typing rref([A1,B1,C1,D1; A2,B2,C2,D2; A3,B3,C3,D3]) Nowadays I'd probably just use Octave, which is the same syntax except without the commas. Similarly one course in my program had a section with lots of problems involving partial fractions expansion to help compute an inverse laplace transform. I'd just let my computers do the inverse transform directly, or at least do the partial fraction for me, since doing that crap by hand is tedious and of little value.

This is fantastic advice and very well written to boot. I think you could expand on this thought in a blog post or short story. I know I'd read it.

From the abstract: "Our main finding is that the developmental curve of the estimated algorithmic complexity of responses is similar to what may be expected of a measure of higher cognitive abilities, with a performance peak around 25 and a decline starting around 60"

Based on this and the points in the scatter plot, it looks to me like you have 40 years or so of mostly the same "behavioral complexity" you do now, in expectancy, but with the added benefit of accumulated knowledge. For most tasks, my bet is that the right accumulation of knowledge and learned intuition is a larger factor than any sort of base generative ability. So, rather than giving up, I'd start compounding that learning now, with an eye towards the long term...

"I'm probably going to fail the final exams next week."

You can improve on mental toughness to control emotion. It is not a fixed skill. Four skills needed to overcome ^fear^ and ^panic^ is through control of the limbic system: [0]

  - Positive self talk
  - Goal setting of tasks
  - Mental rehearsal of tasks 
  - Arousal control (breathing)

[0] "Mental Training" https://www.youtube.com/watch?v=AZ-24JtAFQw

Which is the most universal human characteristic - fear or laziness?

I've found that laziness is sometimes fear in disguise. I don't know how that contributes, but whatever I don't care to explain; I'll be downvoted anyways.

Poverty May Affect the Growth of Children's Brains https://science.slashdot.org/story/15/03/30/2159247/poverty-...

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