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Sadly, TiVo and its ultra-intuitive user interface is not available in Japan, but there are plenty of similar devices, called “DVR” here (Digital Video Recorder). We have a Sony BDZ-X90 unit that we bought a year or so ago. Its list of features and functions is huge, exceeded only by its ridiculously high pricetag.

Anyway, it worked just fine until five days after the warranty expired, when suddenly only the display worked (and only to show “System Error”). A call to Sony confirmed that it would have to be sent in for service, so I dropped it off at a place nearby that handles Sony repairs, and asked them to ask Sony to fix it for free, since it's just out of warranty.

Of course, I understood that Sony didn't have to do that (it was just out of warranty), but it didn't hurt to ask.

We got it back today. It turns out that the hard disk had crashed, so it was replaced. The bill came to ¥0, so thanks Sony.

I'd prefer that things don't break, but being generous like that on the warranty, after the fact when you didn't have to, is classy (and good business; there's a reason we have so much Sony stuff).

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Nikon D700 + Nikkor 24-70mm f/2.8 @ 70 mm — ¹/125 sec, f/5, ISO 1100 — map & image data — nearby photos
Island
Okinawa, Japan

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Okay, so yesterday's post about Japan's Cherry-Blossom Season Off to an Early Start was somewhat misleading. I normally write about things in Kyoto where I live, but Fumie and I took a short trip (just two nights) to Okinawa, a string of Japanese islands in the East China Sea, well beyond Amami (which we've visited twice, and I've blogged about many times), about half way between the Japanese mainland and Taiwan.

We returned yesterday, and I posted some cherry-blossoms that we discovered while exploring Okinawa. To be fair, though, I have to note that the locals told us they expected cherry blossoms toward the end of January, and were surprised when we mentioned that we'd already seen some, so “early start” is technically true :-).

Our trip was only two and a half days, but I came back with 1,000 photos, all of which I intend to eventually force upon you :-).

Here's one, of a small island 100 meters off the coast of Oujima, itself a tiny shopping-mall sized island just off the coast of the Okinawa mainland. It was darkly overcast, windy, and raining when I took this shot at dusk, facing a slight break in the clouds that made the east much brighter than the west.

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Nikon D700 + Nikkor 24-70mm f/2.8 @ 70 mm — ¹/125 sec, f/6.3, ISO 320 — map & image data — nearby photos
Cherry Blossoms in Japan
January 5, 2009

Japan's cherry-blossom season has arrived a bit early this year. During a drive in the mountains yesterday, we came across some cherry blossoms that were just starting to bloom.

There weren't many blooms yet, but already lots of buds....

Nikon D700 + Nikkor 24-70mm f/2.8 @ 70 mm — ¹/125 sec, f/5, ISO 220 — map & image data — nearby photos
Budding Spring
in January

I normally don't post new cherry-blossom pictures until mid-to-late March (last year's “It Has Begun: Cherry Blossoms in Kyoto” went up on March 25th), although new plum blossoms do come a month earlier, with 2007's first plum-blossom post arriving in mid February, and last year's “Plum Blossoms at the Kitano Tenmangu Shrine” just catching the tail end of the plum-blossom on March 24th.

In yesterday's drive, we came across several different types of cherry blossoms. I think the ones above are known as kan'hizakura, while another kind we came across are quite a bit more..... rumply.... than I've ever seen...

Nikon D700 + Nikkor 24-70mm f/2.8 @ 70 mm — ¹/125 sec, f/10, ISO 2000 — map & image data — nearby photos
Rumply Sakura
of some sort

These rumply sakura were either somewhat deep pink, or almost pure white, but not much in between. The two colors could co-exist on the same branch.

Nikon D700 + Nikkor 24-70mm f/2.8 @ 70 mm — ¹/125 sec, f/7.1, ISO 640 — map & image data — nearby photos
White. Pink.

Nikon D700 + Nikkor 24-70mm f/2.8 @ 70 mm — ¹/250 sec, f/2.8, ISO 200 — map & image data — nearby photos

Cherry blossoms in the first week of the year. In the mountains. In Japan. Who would'a thunk.

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It's amazing how many people can talk themselves into believing something that's obviously wrong.

The other day the following question was posted on a widely-read programming blog by Jeff Atwood:

It quickly got almost 1,000 comments with people arguing about what the correct answer is.

Common sense tells us that gender of an unknown person is a 50/50 proposition. You strike up a conversation with someone who says “yeah, I've got two kids....” and you know that there's a 50/50 chance as to the gender of each kid. The person continuing “... and that's my daughter on the swing” has not revealed anything about the gender of the other kid. Thus, there's a 50/50 chance that the other kid is a boy, and hence a 50/50 chance that “the person has a boy and a girl.” This seems straightforward and common-sensical. 50% either way.

Yet, there were a lot of comments arguing that the answer is 67%. Consider all four ways someone could end up with two kids:

• girl then boy
• girl then girl
• boy then girl
• boy then boy

...and eliminate the “boy then boy” possibility because the question tells us that at least one of the kids is a girl, you end up with three remaining pairings that are possible in this situation. Two of the three involve both genders, so the odds are 2/3... about 67%... that the person “has a boy and a girl.”

Well, that seems pretty solid, and we all know that math can sometimes be counter-intuitive, so.... it must be true?

It seems that a lot of people are willing to let themselves be swayed by what they feel is a mathematical explanation, even when it flies in the face of the most simple, basic common sense. Common sense tells us that revealing the gender of one kid does not indicate anything about the other, so where is the flaw in the logic that leads to the 67% answer that otherwise (except for common sense) seems solid?

The key point here is whether the revelation about the girl gives us information intrinsically about a single child, or intrinsically about the pair:

• If the information is about one single child, it tells us everything about one kid and nothing about the other kid.
• If the information is about the pair, we know nothing specific about either kid, only one new datapoint about the pair.

The difference manifests itself in what we include and exclude when calculating the odds based on the new information.

Let's look at the “information about the pair” situation first....

After finding out that they have two kids, if you specifically ask “is one of your kids a girl?” and get a yes answer, you know, every time, that at least one is a girl and that it's impossible for both to be boys. Likewise, if you get a “no” answer, you know every time that they have two boys. When the answer is yes and you move on to calculate the odds that the person “has a boy and a girl”, you specifically include every two-kid permutation that includes a girl:

The three equally-likely pairings we include are the same as highlighted near the top of this post. Two of the pairings include both genders, and so there's a 2/3 chance – about 67% – that they “have a boy and a girl” in this situation.

Now, on the other hand, if after finding out that the person has two children and one of the kids randomly happens to be on the nearby swing and has its gender revealed as a girl, this information is intrinsically only about that one kid and tells us nothing intrinsic about the pair. Yes, by finding out that the kid on the swing is a girl you can say “this pair of kids includes at least one girl” and so when moving on to calculate the odds, you can exclude all boy/boy pairings, but the part that most people have missed is not in what you can exclude, but in what you can include....

In this case, you can not turn around and include every two-kid permutation that includes a girl because if the gender revelation is random, then on average, half of the mixed-kid pairings will have a boy revealed. Since you're ignoring cases when a boy is revealed, you have to ignore them when calculating the odds:

The “Include/Exclude” column in both tables is really “times you'll be informed about a girl among the pair”. In this latter situation where the revelation of gender is random, “exclude half” reflects that, on average, half the times the kid whose gender is revealed is a boy.

So, looking at what is included, we see that the pairings that have a boy are ¼ and ¼ which sum up to ½, a 50-50 chance, just like common sense tells us.

The key to all this is to understand exactly what information we are given, and what information we derive. Let's go back to look at the words actually used in the question posed to us:

This is awkwardly worded... does the “told” apply to “had two children” only? Is “one of them is a girl” the result of the person telling you that exactly, or is it information summed up by the person posing the question?

Because the initial question is so poorly worded, we have no choice but to fall back to our real-world experience to try to parse its likely meaning. I can imagine it both ways:

1. Me: Hey, haven't seen you in ages!
   Parent: Yeah, I'm married and have two kids now... that's my daughter over there on the swing.
2. Me: Hey, haven't seen you in ages!
   Parent: Yeah, I'm married and have two kids now.
   Me: Cool, I've got one. My sister just had a little girl.
   Parent: Heh, that'll be fun, I know what it's like to have a girl.

The answer to the posed question is “50%” for the first case, and “67%” for the second.

But that second case seems extremely contrived. The context of our real-world experience tells us that most people would say “I've got a girl, too”, implying that the other is a boy, or “I've got a pair of girls”. It just seems unlikely.

The first case – conversation somehow revealing the gender of one of the kids – seems much more likely, so when faced with the question as written the most reasonable interpretation results in an answer of “50%”.

Still, if you explicitly decide to choose the other reading (that the parent told you “one of my kids is a girl”), I'd suggest your choice is the less reasonable of the two, but in the context of that choice, you're perfectly correct to answer “67%”. That's the reading that the initial question-asker, Jeff Atwood, took in his followup post that revealed his answer to be “67%”

What amazed me in reading the various reader comments on both posts is how many people insisted that the answer was 67% in every possible situation. “The math is right there, are you stupid!?” Common sense screams that something is off here, yet flash a little math in someone's face and odds are they'll blindly follow.

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Two years ago during our New Year's break we went to a ryokan on the Ise peninsula, after which I posed about the great quantities of great food we were served. From the seaside balcony of our room on that trip, I happened to catch a few frames of a bird of prey taking the easy route and going with a prepared meal (stealing from a crow) instead of catching one itself....

Nikon D200 + Nikkor 18-200mm f/3.5-5.6 VR @ 200 mm — ¹/160 sec, f/6.3, ISO 800 — map & image data — nearby photos
“Dinner Ready?”

Nikon D200 + Nikkor 18-200mm f/3.5-5.6 VR @ 200 mm — ¹/180 sec, f/7.1, ISO 800 — map & image data — nearby photos
“Because I Can. Why Do You Ask?”

Nikon D200 + Nikkor 18-200mm f/3.5-5.6 VR @ 200 mm — ¹/160 sec, f/6.3, ISO 800 — map & image data — nearby photos
“I Hate To Grab-n-Run, But...”

Nikon D200 + Nikkor 18-200mm f/3.5-5.6 VR @ 200 mm — ¹/160 sec, f/6.3, ISO 800 — map & image data — nearby photos
See Ya
when I'm hungry again

Nikon D200 + Nikkor 18-200mm f/3.5-5.6 VR @ 200 mm — ¹/250 sec, f/8, ISO 800 — map & image data — nearby photos
Daddy's Bringin' Home the Bacon

This was two years ago not only in terms of time, but in equipment and skill as well, so the shots aren't great, but I thought it was at least a bit interesting.