No, it doesn't depend on how you define "children." People get continually better at learning second languages, up at least to age 16. For every aspect of language (except accent) that people have measured, older people learn faster. Forget your anecdotes and read the literature.

your body must maintain a faster metabolism in order to keep your temperature at equilibrium

It only takes 35 kilocalories to warm one litre of water from 2 °C to 37 °C.

(Repost of an old message I sent to SL4 in 2003.)

Usually, like everyone, I forget my dreams. When I'm suddenly woken up, for example, by an alarm clock or by my cellphone ringing, it seems - I'm not quite sure if this is what is happening, but it's the explanation that seems most likely - it seems as if the last fifteen seconds of mental imagery are still "in my loop" when I wake up, so I remember them too, just as if they were lucid.

So the memory I actually have is of waking up, and then five seconds or fifteen seconds later, the phone rings. With an experience like that, it's easy to see why anyone less than a dedicated rationalist would assume psychic powers; "Oh, look, I become lucid fifteen seconds before the phone rings, I must be psychic".

Sometimes I'll even apparently remember that I have a dream in which an alarm goes off in my dream, which wakes me up, and then five seconds later the alarm goes off.

One needs to have done quite a lot of reading in cognitive science before one looks at that and says, "Timing fault in memory formation - yes, the brain really is that fragile", and not "I had a precognitive dream."

This led me to ponder the problem of dream memories and personal continuity. I now remember having experiences that I would not remember if I had not been woken up by an alarm clock; I remember those apparently lucid dream experiences, and those "inserted" memories, as if they were part of my ordinary life continuity. What happens to the person who experiences the dreams I have and don't remember? Did I really experience the dream of the alarm going off, or was the memory manufactured and inserted without ever being experienced? Are all dreams manufactured and inserted without ever being experienced?

This is where we stand at the moment I had my anthropic dream.

My cellphone rang and woke me up. I apparently remembered becoming lucid in my dream a few seconds before the cellphone woke me. And my "inserted" dream experience leading up to the cellphone ringing was the thought:

"If I don't wake up now, this experience will not have existed in retrospect. Therefore, since I'm now having this experience, something will wake me up."

Now, what this feels like is this:

You're dreaming, and your dream turns lucid, and you think to yourself: "If I don't wake up now, this experience won't have existed in retrospect. Therefore, since I'm having this experience, something will wake me up."

And then, a moment later, the cellphone rings and wakes you up.

The illusion of a spooky anthropic effect was very strong.

We make it up as we go along :)

Basically my wife and I ask ourselves "What is the next thing to learn, or what do the kids need to review?" Our very broad curriculum for math is operations in order, from addition to exponents and logarithms, with learning and graphing functions that use that operation at the same time. So, when they learn addition they learn linear functions and line graphing, curves when they learn exponents, etc. Then fractions and decimals, because you need to understand fractions to understand the unit circle, which is the basis for angles and therefore geometry and trig. Reading is easiest: make them read and discuss harder books than they read last week. Writing is similarly straightforward, though there we reach rhetorical techniques when we do persuasive writing, meter when we write poetry, etc. History we are doing linearly, and trying emphasize the history of technological progression and cultural progression over dates and names. For example, kids should know what the difference between neolithic and paleolithic societies is, or what the limitations of bronze tooling are. We also do a lot of timelines, so the kids know about the different states of various societies at the same time in history.

Finally, the best thing about this approach is that you can get your teachers to suggest things that would work well in your curriculum, or related areas that should be taught together. If you ever get anxious about missing something you can look up your local curriculum standards, though most often these will just show you how ridiculously ahead of public school the kids are.

Do what Harry's dad in HPMOR does: hire local grad students to be homeschool tutors. I do this for my 6 year old and 9 year old, and it is awesome. We parents do very high-level curriculum, taking about half an hour each week, and the tutors and kids do the rest. Teach at the kids' pace, choose material and progressions that make sense to you (or make sense to him), and have constant contact with teachers. I've found $20/hour is an attractive wage for most PhD students, and their expertise means that the barrage of "why?" questions the kids ask can actually be answered, often with current research findings. We've found we can cover 2 to 4 times the material in public school curriculum, and school is from 9 to 2. Also, you can do reasonable things like teach radians before degrees, graphing and functions along with each operation, foreign languages with native speakers, and Greek and Roman roots starting in kindergarten.

Thanks! He doesn't attend the Davidson school, but is a member of the organization.

You know, this is the third time I've seen Harry shipped with McGonagall.

[W]hat other popular internet phenomena can be co-opted for this purpose.

The Internet is, of course, for porn, so... rationalist erotica?

He is in Davidson Academy and finished DragonBox. He is fine with either type of instruction.

There's the Davidson Academy.

If he hasn't learned algebra yet, get him DragonBox; I'd be curious to learn whether he prefers explicit instruction.