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Yes. Language acquisition follows a standard sequence with specific milestones universal to all languages. For example, the period around 6-12 months is critical for phonetic learning. Before 6 months, infants are able to discriminate between phonetic units present in any language, but after 12 months they are better at making distinctions that occur in their native language and worse at making distinctions that don't occur in their environment. For example, Japanese infants are just as good as American infants at distinguishing between r and l at birth, but lose some of this ability between 8-10 months.

(Chapter "Language", Principles of Neural Science, 5th ed.)

No deliberate puns required. As a computer algebraist, it bothers me that "Taylor shift" is un-Googleable.

I think serial PL designer Wouter van Oortmerssen started creating languages in his teens...

By the time we actually let people do that, we will have flying cars to commute with anyway.

Yep. Penrose's argument goes something like this (oversimplified): 1) Turing machines can't solve the halting problem. 2) Humans can solve the halting problem. 3) Therefore, humans can't be Turing machines.

There are two problems with this line of reasoning. The first problem is that 2) is unsubstantiated. A human can see immediately that 15 = 3 x 5, but this doesn't mean that we have a magical ability to factor integers instantly. By the frivolous theorem of arithmetic, almost all natural numbers are very, very, very large. We have some ability to analyze formal systems, but the systems we have managed to understand are very simple in the grand scheme of things. Almost all formal systems are very, very, very complex, and there is no evidence that we can understand them all and/or that our understanding process actually is correct (consistent) when extended indefinitely. Penrose's actual argument is of course more technical, and others have made more precise rebuttals.

The second problem is that the argument does not solve the problem of consciousness. Scott Aaronson put it nicely: "Even if we supposed the brain was solving a hard computational problem, it's not clear why that would bring us any closer to understanding consciousness. If it doesn't feel like anything to be a Turing machine, then why does it feel like something to be a Turing machine with an oracle for the halting problem?"

It's an interesting question, but many of the changes that occur with old age could simply be side effects of optimizing for performance before and during reproductive age and need not be evolutionarily advantageous per se.

This is not an accurate summary of what the study actually found. The article proposes a high-level explanation for how one aspect of learning changes with age.

The actual cause of this high-level change could be lower-level age-induced differences in neurotransmitter levels or in neuronal function and connectivity. As the article's summary points out, the actual biological basis needs to be investigated in further research.

It's also important to note that this study found a plausible explanation for changes in learning performance under specific circumstances. This is a very important qualification.

Learning in general is believed to involve many different interrelated mechanisms. It's well established that many different cognitive abilities (perhaps most importantly working memory) diminish with age, and some of this degradation is likely related to natural cerebral shrinkage (a healthy 75-year-old has a 15% smaller brain than a 25-year-old).

The brain has dedicated subsystems for different aspects of spatial and visual understanding.

Certain groups of cells (place cells, grid cells) are known to be involved specifically in the ability to track one's own location and movement within the external world. This ability is likely a very old and important evolutionary invention in the development of higher animals, thus very sophisticated and well integrated with other functions, particularly memory. Think of the method of loci, known already in Ancient Rome and Greece, or indeed how quickly one learns to navigate a new city (or a video game level, say). This probably explains the phenomenon the author describes.

That said, the relative importance of the various spatial-visual subsystems of the brain probably depends heavily on the task, and perhaps also varies between individuals.

Yes, I was of course nitpicking. The only reason I did so is that others in this thread already seemed to be commenting based on that interpretation of your post, and in the followup comments you all seemed to be talking past each other. I don't disagree with the content of your original post in general.

Pre-agricultural societies certainly had a clear division of labor between the genders, but could still have had a high degree of equality in the sense that both women and men had roughly equal power in the communal decision-making.

You claimed that "most ancient societies were blatantly misogynistic". I don't think the current evidence suggests this, unless by "ancient societies" you meant something like "ancient civilizations". I would define the term "ancient societies" as inclusive of pre-agricultural (hunter-gatherer) societies, and then one has to make a distinction. The established view is indeed that ancient hunter-gatherer societies were much more egalitarian than ancient agricultural societies. Exactly which features of agriculture led to the development of (more?) patriarchy is surely still being debated, though.

> However, the numerical value of K is notoriously difficult to calculate to high precision, so computation of more digits get increasingly slower.

It can be calculated to n digits in O~(n^2) time, which isn't really that bad. Something like Brun's constant or the area of the Mandelbrot set is probably a better example of a real number that is "notoriously difficult" to compute.

The submitted paper is well-written and appears to be correct, but it is far too short.

No reference is made to previous attempts to study Euler's conjecture or similar conjectures (there are surely a dozen other papers that ought to be cited in the introduction).

What led the authors to consider a computer search as opposed to any other approach? Does the method generalize?

It is indicated that the CDC 6600 was used. How was the programming done? How long time did the execution take? The instance is claimed to be "the smallest". In what norm? How can you be sure that the computer program did not skip any smaller examples?

The most serious problem with the paper, however, is that the only contribution is a purely computational statement which, though a counterexample to a conjecture, does not advance mathematical theory in any way.

Due to these shortcomings, my recommendation to the editor is to REJECT the submission.

On the other hand, 1/3 is still not the (exact) solution to 3*x=1...

I've been reading another textbook on the same topic recently, and find it endlessly fascinating. I can grok quantum mechanics intuitively on some level, because it's governed by simple mathematical laws, even if those laws are quite different from everyday experience of how physical objects work. Understanding how ordinary matter (atoms, molecules, then solids and fluids) forms out of fundamental interactions is, in principle, just a matter of solving for N variables, and you can use statistics when N gets large. But the complexity of how life exploits the precise interactions between thousands of different molecules to assemble complex machines, on scales from single proteins to whole organisms, involving thousands of interconnected feedback loops to sustain the process and counteract the large-N averaging effect of the second law of thermodynamics, is just mind-boggling.

If you're a programmer and think 10 million lines of code constitutes a complex system, reading about how cells work on a molecular level should be humbling.

The core of what makes C elegant is that basically everything that looks atomic is atomic, in the sense of taking O(1) space and memory (at least until C99 introduced its abominable variable-length arrays, and perhaps some other features I'm forgetting about).

Absent macro obfuscation, it is easy to reason about what a snippet of C does and how it translates down to machine code, even taken out of context. In C++, something as innocent as "i++;" could allocate heap memory and do file I/O.

The downside is that C code can become quite verbose, and to do anything useful, it takes a lot of ground work to basically set up your own DSL of utility functions and data structures. For certain applications, this is an acceptable tradeoff and gives a great deal of flexibility. I think teaching this bottom-up approach to programming can be quite useful - in a way, it mirrors the SICP approach, albeit from a rather different angle.

The question is, why are there not more languages that have the same paradigm, but also add basic memory safety, avoid spurious undefined behavior, provide namespaces, with a non-stupid standard library, etc.?

Quick: how would you implement for (i = n; i >= 0; i -= k) with unsigned integers?

I just use a signed pointer-size type for all sizes and counters, and stay happy...

I'd like to see a single-player bot that can do human-level speedruns and/or beat stuff like https://www.twitch.tv/blooditekrypto/v/30795033

Baby steps. Beating other bots in deathmatch is a good start. I love that they only use the rocket launcher, giving the careless bot an equal chance of blowing itself up.

Parsing what's on the screen in Doom is potentially a lot easier than in modern games: since there is no texture filtering or anti-aliasing, and due to the 2.5D perspective, most vertical runs of pixels on the screen map exactly to (linearly?) scaled columns in wall textures or sprites. I would not be surprised if you could come up with a fairly simple algorithm to determine the exact position and orientation of the player and the objects on screen within the map, without any real AI/learning involved.

It would be useful if it had a tool to convert MIDI files to source code (ideally with some sane automatic structuring). I've sequenced some 15 megabytes of MIDI files, and would love to have them in a form suited for version control.

Moreover, TeX has no serious competition (at least in the niche of typesetting mathematical documents). There are plenty of good text editors and IDEs to go around.

MathJax works reasonably well, but I can almost read the TeX source out loud faster than the browser renders it (together with PDF.js, this has been my go-to counterexample whenever someone claims that JavaScript is performant).

With formula-heavy text, I'm forced to split documents artificially into multiple short pages to make rendering reasonably fast.

KaTeX looks quite promising, but it was missing support for quite a bit of basic markup the last time I checked. Perhaps it's better now.

Clearly the next goal for AI is a program that can teach Go better than human teachers.

No need to speculate. Selective breeding for intelligence is how we got herding dogs (Border Collies, German Shepherds, etc.).

Off-topic: we (the human species) have built an AI that can master the game of Go, but we don't yet have the intelligence to publish charts correctly on the web. That blur of a JPG is half a megabyte!

I would take one study with a grain of salt too. Even if the conclusions are correct in the setting of the study (and since most research findings are false, they probably aren't), it doesn't mean that you can extrapolate to every other setting, particularly the specific case of being the CEO of IBM. Hence "Make of that what you will."

But there could be an element of truth to it, which might warrant further research. If CEOs really do have a much more limited influence than they are given credit (or blame) for, then incentives perhaps ought to be adjusted, not just in the interest of fairness but also in the interest of finding better ways to actually improve performance.

The paper: https://dx.doi.org/10.1002/smj.2192

The PR version: http://today.tamu.edu/2015/10/15/ceo-effect-on-firm-performa...

Well, there was some recently published research that claimed to find that most of the effect attributed to CEO performance actually can be explained by random fluctuations. Make of that what you will.

In my opinion, the first course on ODEs shouldn't be concerned with the transmission of information.

That is where the wave equation comes in, in the first course on PDEs.

I think GitHub should starting doing something this for issues and pull requests.

Instead of the nondescript

- Issue #2654: misplaced comma on page 3 of documentation

- Issue #2653: open() should accept relative file path

it should be

- Quetzalcoatl's Rage: misplaced comma on page 3 of documentation

- The Dying Curse of Buluc Chabtan: open() should accept relative file path

There is so much variation in the methods that have already been used to derive "nothing up my sleeve" numbers that you could easily come up with 2^10 equally plausible methods. The 24 chosen bits for "BADA55" might be overkill; depending on the circumstances, being able to pick "A55" might be enough.