yaks_hairbrush

The angular momentum of a spinning bucket of water has approximately nothing to do with the intrinsic angular momentum of the particles, though. Statistically, we'd expect all of the intrinsic spins of the electrons and quarks to cancel out entirely.

Rather, the angular momentum is due to the fact that the straight-line motion of all the atoms on the left side of the bucket is opposite in direction to the straight-line motions of all the atoms on the right side of the bucket. (With respect to the reference frame of the center of gravity of the bucket, etc, etc.)

And this suggests a path for lowering the magic number. We can lower the number of bits needed by noting that the required outputs for 8 through 14 (mod 15) are the same as the outputs for 1 through 7 (mod 15), only reversed.

The interesting thing here is that he used only algebra. This model therefore occupies a sort of sweet spot, insofar as adding to the accuracy of the model requires machinery a level above what was used to get this model.

To wit: If you want to take into account eccentricity (which I think would be the biggest source of error), the steps needed are fairly involved. For one way to do it, see [0].

[0] https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_m...

Note the date: 2013. This isn't a response to the blog post at all. Seems to have been part of the initial conversation or shortly after.

Think of it like this: Someone in Sacramento can get to Milwaukee in 3 days (driving). Someone in Chicago can get to Milwaukee in 3 hours (or less). That's a 24x factor.

When any old randomly chosen person Sacramento gets to Chicago, they do not gain a 24x efficiency in traveling. Rather, they've covered most of the distance to Milwaukee already.

My advisor at the time was 60-ish, and had tenure for 30 years or so. The gap in capability was (to my eye) mostly due to his experience.

40x sounds pretty conservative to me. I did graduate school in math (did not get a Ph.D.) and my advisor indicated that he assigns problems assuming a 200x multiplier between his capability and the students'. That is, he'd assume that something he could see how to do and could execute inside of a week would be a good thesis problem to keep a Ph.D. student busy for two years.

As far as the 10x programmer stuff... Obviously there are 10x and probably even 100x programmers. They're the experts, and there are not many of them.

Other parts of the country don't need an Ellis Act type framework. Most places, you can evict tenants when their lease is up.

There's the Caesar & Pharaoh series which does something along those lines, albeit with ancient cities.

I likewise find the "harmony with nature" idea to be laughable, but for a very different reason. If "nature" has any meaning at all, then we are part of it. Other animals are perfectly happy to change their situation to their benefit. Beavers, for example, can create lakes by choking off rivers. Are they living "in harmony" with nature? That feels like a strange question to me, and so I wonder why it shouldn't feel like a strange question when the beavers are replaced by humans.

That's not a scary question. One could simultaneously believe that an employee's performance was coincidence, but still give that employee a bonus (why not reward luck, after all?).

Fruit Loops sound like they wouldn't be too bad. Instead, the Kellogg's product is called Froot Loops.

It's a bit fitting: a bastardization of the spelling which underscores the bastardization of nutrition going on with the product.

Yes, you did. It may not have been stated explicitly, but it was implied in a couple places:

1. Binomial theorem. Its statement does not conventionally include any caveats about the x^0 case.

2. D(x^n) = n x^(n-1). When n = 1 and x = 0, you get a 0^0 on the RHS. If 0^0 is taken to be 1, the derivative rule holds. Else, the statement gets messy: D(x^n) = n x^(n-1) if (x,n) != (0,1)

A word from Knuth on the matter (warning: PDF):

http://arxiv.org/pdf/math/9205211v1.pdf

See page 6.

There's this app...

http://www.ortisoft.de/en/accessmenubarapps/

Essentially, "knock" the top of the screen twice with the mouse, and it'll switch to this application which has no menus. "Knock" twice again and it'll go back to your app.

Evolution requires selection pressure, whether natural or otherwise.

And there's still selection pressure from so many sources. Partial list: Some people die before they reach breeding age, some people refuse to have children, some people are born unable to have children, some people have children with dead-beat spouses, some people are simply incapable of caring properly for kids, some people are prohibitively undesirable as mates, and so on.

No chance! MN and WI are so proactive about road maintenance that we get pretty good roads despite the extra hassles caused by cold weather. I've spent a bit of time in Los Angeles and Hawaii, and those roads are easily in worse condition than the roads of Minnesota and Wisconsin.

Absolutely, yes! I was and still am upset with PPACA because it reinforces the horrid employer-provided care model.

> The world is run by extraverts.

Sure is. Collaboration is the trait that made humanity advance to where we are today. And things are better today than they have ever been in the past for introverts: much more collaboration is done remotely.

> The problem with extraverts — not all of them, I grant you, but many, so many — is a lack of imagination.

This is "the" problem? I think it more accurate to say that the author's problem with extroverts (see below) is that they want to socialize with him. Socialization is mentally good for most people, including most introverts.

Honestly, the three paragraphs starting here make me wonder if he has something deeper than simple introversion. I mean, it's fine to prefer to be alone, but it's less fine to feel fear about standard social interactions. If he does the latter, that's kind of a problem to my mind.

(A problem, by the way, that I deal with. I force myself to go to get-togethers with more than about five people. I'll be upset about it as the get-together looms, but I almost always enjoy it once I'm there.)

> So, extraverts of the world, I invite you to make a New Year’s resolution: Refrain from organizing stuff.

Oof. He's asking the majority of the people of the world to change their (generally healthy) habits for his benefit.

Humans are built for socialization. Socialization is a mentally positive activity for most people, and most people crave it.

> extrovert is common but wrong, because extra- is the proper Latin prefix.

extra- being the proper Latin prefix does not imply "extrovert" is wrong. We're speaking English, not Latin.

Another way to look at it is that the important quantity is not temperature, but its reciprocal. Absolute zero becomes infinity under this transformation, hence unattainable. Heat energy will flow from lower 1/T to higher 1/T, and more heat energy added to a system lowers the 1/T quantity of that system.

Presuming you're just letting gravity do its work and not, say, firing engines to resist...

You'd be in free fall, and that's a perfectly nice reference frame. Within that frame, your gravitational sensors would observe certain doom in every direction. This sphere of doom would get smaller until you were ripped apart from the tidal stress.

No. Inside the event horizon, all paths lead to the singularity. If you had gravitational sensors on your spacecraft, they would show the singularity all around you.

> Why is it necessarily the case that "stars would compress into this material rather than into black holes"?

There's a good argument to be made that this isn't necessarily the case. I was thinking that all particles are interchangeable at sufficiently high temperatures (i.e. they can switch from one particle to another so long as energy is conserved). I overlooked the fact that stars don't get hot enough.

> Or why can't it be the case that the crushing process doesn't take matter through the infinitely strong configuration on the way to black hole configuration?

If the "infinitely strong" configuration got crushed into a black hole, it wasn't infinitely strong.

> For example, why can't it be the case that there are two kinds of matter, one that can be used to build infinitely strong wire, and one that can't, with stars being made of the latter?

How would the infinitely strong wire be held together? Electromagnetic force? Strong force? Weak force? Those forces (which are the only ones we know about apart from gravity) travel at c. If part of the wire is in, while part is out, we will necessarily break the bonds holding the material together if we attempt to pull the wire clear. If nothing else, this breaking will occur because those bonds rely on force carriers traveling at c, and so somewhere along the wire those force carriers will not see the items they are supposed to bind together.

Let us say we hold the wire so that a portion of it is past the event horizon. The bit of the wire at the event horizon, if held stationary, is traveling at c because light is also stationary there. Whatever bond existed at that point is no more; the force carriers can't make it to the particles they're supposed to bind together.

Inside an event horizon, orbiting implies traveling faster than c from your reference frame. No can do.

(Note: this applies to an electrically neutral non-rotating black hole.)

> Not all your brain would be the same distance from the singularity.

True, but you are not standing still. You are moving. Accelerating, in fact. No messages need to be sent away from the event horizon for the brain to work.

> Complete ignorant question: there is always the discussion of "falling" in to a black hole, but could it be possible to "hang" something from outside the event horizont?(given an infinitely strong and quite long wire).

It's a good question, because it exposes some subtle assumptions being made.

The string breaks, because you cannot have an infinitely strong wire in a universe that allows black holes. If we could have such a wire, black holes would not be formed, since the wire's material would be able to resist being crushed into a black hole. Therefore collapsing stars would compress into this material rather than into black holes, and there would be no black holes.

Once inside the event horizon, every path leads to the singularity. You cannot get further away from it, and you cannot orbit it (or otherwise keep distance constant).

I think (note: I am not a cutting-edge theoretical physicist) that the brain would work fine against both of these effects.

First, I'm not sure it's possible for the brain to be half-way across an event horizon. When an in-falling object nears the event horizon, the horizon "dimples" in response to the changing gravitational field caused by the object's mass.

Second, once inside the horizon, it is true that messages cannot be sent opposite the direction of the singularity. However, your entire brain is moving toward the singularity, and therefore neural communication does not require messages to be sent away from the singularity.

>Things past the event horizon should be able to travel in the direction of it, though they will always turn back before actually crossing it.

According to the best of my understanding, if you're inside the event horizon, every direction you look leads to singularity. There are no paths away from the singularity.

That about sums it up. It's made worse by professors who have been trained to teach things in an unmotivated fashion.

I had a graduate probability teacher who said (paraphrased) "one of the beautiful things about math is that you start with a definition, and you prove some very simple things with the definition... so simple that you feel you're just using circular reasoning. Then you find that your definition is equivalent to a useful property!"

Actually, what happened when the stuff was developed is that someone wanted the useful property, and managed to rationalize a definition which fit. (example: group theory was done for hundreds of years before we had a definition of group. Noether noticed that a lot of folks were writing the same sorts of things in different contexts, so she distilled it down to three axioms.)

For a really concrete example, consider ordered pairs. A person being coy about their intent would say that "we define an ordered pair (x,y) on a set S as a set of the form {{x},{x,y}}, where x and y are in S."

It's safe to say that no one thinks of an ordered pair in that fashion. The intent was to have two ordered pairs be equal if and only if each of the two coordinates are equal. You can prove this from the above definition, but it's far more helpful to tell the audience in advance that we really want a structure with this property.

There is some concept of scope in math. At a fairly early level, a student learns sums and integrals. The variable of integration/summation's scope is just within the integral/sum.

At a higher level, some things have scope equal to a subfield of mathematics. A gothic p, for example, represents a prime ideal in algebraic number theory. It represents a parabolic Lie algebra in Lie theory. (Actually this causes problems when you're doing Lie theory and number theory at the same time.)

Well, pg didn't found the company that made him a millionaire until he was thirty years old...