Tuesday, January 31, 2012

One a day!

And with this post, which is cheating a little bit, I have made 31 blog posts in January, an average of one post a day.  I will not be able to keep up this pace, but one of my new years resolutions was to start writing and communicating more frequently.

Whitecrossed Seed Bug

Here is another recent find.  A whitecrossed seed bug (Neacoryphus bicrucis) on a breadfruit leaf.



Here are some comparison pictures.  They are native to the southeastern US, but have also been spotted in Hawai'i.  They are in the "true bug" order Hemiptera, in the seed bug family Lygaeidae

One of its cousins in the Lygaeidae is the unusual Wekiu bug of Hawai'i.  They are flightless, live at the summit of Mauna Kea, have "antifreeze," and eat dead insects out of the snowmelt. 

Brown Anole Fight

There were two large male Brown Anoles in our backyard the other day.

Here is one displaying his throat patch.


Notice he has ridges on his back and more of a spotted pattern on his sides.  The big males sometimes get this way. 


Here are both of them together.  They mostly stared at each other and bobbed their heads up and down.  Eventually one bit the other on the head then they both ran away. 

Drive to Hawai'i Kai

This weekend we took a drive to a new part of the island.  We loaded up in the van and went to the eastward point called Hawai'i Kai. 


A shot back into the van, for fun T decided to wear his sheriff outfit. 


M with her hair braided. 

Here are some random (non-postcard quality) pictures through Honolulu and along the way to give you an idea of what it looks like.

Diamond Head in the background. 

Then on to the Hawai'i Kai.  It is a very rocky coast with lava cliffs. 


At this point we started having car trouble.  (The next thing to replace is the radiator.  It has a slow leak, but we keep water stocked in the car because of this and I topped it off before leaving.)  I didn't expect this and I thought we had the radiator under control.  We coasted into a scenic overlook parking lot; we gave some time for everything to cool off and settle so I could check on the water and oil, so I snapped some pictures while we were waiting. 





You can also see some other islands from here.  Here is a picture towards Maui and Moloka'i; they are faint in the distance. 


Also,  further out and a little more to the south you can see the big island of Hawai'i!  In the shot below I zoomed in.  I know it is faint but it is there on the horizon.  The peak is Mauna Kea, 13,796 ft, the 15th highest peak on earth.  However, it appear to be lower than Maui because it is farther away, 175 miles or 0.7% of the earth circumference.  I suspect this is why this area on Oahu is called Hawai'i Kai.  In my beginning understanding of Hawaiian, kai means salt water, sea, ocean.  So this is the Hawai'i (big island) Sea of Oahu. 


Also, T got out of the van with his outfit and hammed it up a bit. 



That is "sting" written on the side of the shotgun.  It is a reference to a sword named sting in "The Hobbit".  By the way, he sawed off the nerf gun himself, which resulted in the foam darts shooting much further than before. 



When I looked under the hood I realized I had made a mistake.  I was distracted when adding water before we left (I was holding F in one arm, talking to T, adding the water with the other) and forgot to fasten the cap to the radiator securely, so the water had boiled and vented out.  No more holding the baby and carrying on unrelated conversations while working on the car.  By now the engine had cooled and we added water, so we went back part of the way but it started making a strange sound it hadn't made before.  So we pulled off the road to let it cool and check it again.  We took the opportunity to grab some Chinese fast food for lunch.  We hadn't eaten out as a family in a long time and it doesn't help fix the van if we get upset and don't enjoy ourselves a little whenever possible.  (Like living in the moment in Ivan Franko's A Parable of Life, see also The Mahabharata 11:5, which the poem is based on.)


Then our luck started turning a little more for the worse.  The first sign was our fortune cookies.  They were both empty.  V took the kids window shopping while I checked the oil, it was fine but a little low, so I walked to a gas station and bought some oil to bring it up a bit.  I messed with the connection hoses on the radiator.  There was a place where the connection was loose and corroded, and that steam vented out of slowly when the engine is hot.  Usually I keep duct tape in the car but we had taken it out to use in one of our projects and left it at home...  I fastened everything as well as possible.

Then, while going to get V and the kids my camera fell out of its case onto the ground.  This has never happened with me before, and a camera should not be dropped like that.  I checked it and it seemed fine with just a scuff on the outside of the lens body.  Apparently the clip that holds the camera in the case wasn't secured all the way.

We walked around a costco a bit "window" shopping then it was time to head back.  I got back out on the road and we went for a few miles then the engine started making noise again and heating up.  I pulled off to the side of the road and checked again.  It was venting steam and the water reservoir was down again.

At this point a police truck pulls up behind us with lights going.  I tell him we are having radiator trouble and ask if he has any duct tape.  He doesn't but firmly tells us to get off the interstate.  I explained that we don't know the area around here and he says to pull off at the next exit and U-turn.  I top it off with more of our water and he escorts us with lights going.  We pull off and he pulls across the opposing lane to block traffic while we turn.  There is a shell station and a chevron ahead.  I get in the lane for the chevron but then he pulls up beside us and says to go to the shell station because it is a service station and the chevron is just a filling station.  This is a problem because I have boycotted shell for 16 years since the execution of Ken Saro-Wiwa.  (There are only a few companies I boycott and/or do not buy stock in, Shell, Caterpillar (see here and here), Dell (here), and the country of Israel (here)--some people make fun of me for this, but I decide where I spend and invest my money.)  However, I have a cop with lights going telling me to go to the Shell station, so I resolve not to spend any money.  I pull in and the police go away.

It happens that there is a free water dispenser so V gets started filling up.  I go to the service guys and ask for some duct tape.  At first they seem to ignore me, so I go back to the van, but then a few minutes later one of the guys brings me some duct tape.  We have the water topped off again, double check all the caps and connections, and head off, without spending a penny at shell!  We made it back home this time without having to stop again.

As soon as I have enough money, I'm going to get the corroded connections to the radiator fixed up.

------

Update:  I am a bit confused over place names.  Now it seems that Hawai'i Kai is a development to the west of the easternmost coast area.  I have heard this point referred to as "Lanai Lookout."

-----

Update:  I was really confused; actually my source was wrong.  The islands visible in the distance are from left to right; Molokai, Maui (behind Molokai) and Lanai (separated off to the right, now it makes sense this is "Lanai Lookout").  The Big Island is not visible.

Sunday, January 29, 2012

The Birthday Paradox

This is another post related to my wandering thoughts on my daily commute.  In my first couple of weeks here, I was behind a car with a personalized license plate.  It was hard to figure out the meaning, which helped me remember it when I was behind it again a few days later.  This happened again with a different car more recently, I saw the same car several days apart driving in different places.  Both of these times I was in the city on a crowded interstate (yes, Hawai'i has an interstate ... think about that for a moment); we were surrounded by a large number of cars.  It seems like the chance of seeing the same car twice should be very small, which got me to wondering just how many cars there are around me on a daily basis.  

Our numerical intuition tends to be linear.  We have trouble with anticipating processes that grow exponentially and/or lead to very large numbers.  One of these miss-intuitions leads to the Birthday Paradox.  There are 366 possible birthdays, so it seems like you would need a room full of a lot of people, say 183 or half this size, to have an even 50/50 chance of two people sharing the same birthday.  However, only 23 people are required.  In other words, in a room of 23 people, there is a 50% chance at least two people share the same birthday.

Why is this number so small?  The answer lies in the process of pairwise comparisons and how they grow.  If we have two objects there is only one comparison (A to B) to be made between them.  If we have three then there are three ways to compare them in pairs (A to B, A to C and B to C).  If we have four there are six ways to compare (AB, AC, AD, BC, BD, CD).  With five objects we have ten possible comparisons; with six, fifteen; and so on.  Each object we add to the list can be compared to every preceding object, so the numbers start to grow quickly.  With 10 people in the room we have 45 pairs of birthdays to compare.  With 23, the 50/50 chance of the same birthday, we have 253 birthday pairs; almost 70% of the total number of possible birthdays. 

Another way to visualize these pairwise comparisons is that they are the triangular numbers.  If you stack plastic cups upside down, these are the number of cups required to make triangles of various sizes. 


To get to a greater height of the triangle, the base has to be widened, which adds to the number in increasing amounts.  By the way, cup stacking is an organized sport.  Here is a video. 



The triangular numbers are also a diagonal on Pascal's triangle


The first diagonal is all ones; the second is the counting numbers (1,2,3,4..), and the third are the triangular numbers (1,3,6,10,...).  The fourth row are the tetrahedral numbers (1,4,10,...), or what you get if you stack cups in a three dimensional triangle (pyramid).  The fifth row would be the number of cups required to stack in a four dimensional triangle, except that we can't reach in that direction.  Going the other way, the counting numbers, second diagonal, are what you get if you stack in one dimension (one on top of the other) and the first diagonal, all ones, are stacking in zero dimensions.  Zero dimensions is just a point so there is nowhere to stack beyond the first cup. 

The number of pairwise comparisons (triangular numbers) is given by n(n-1)/2 if n is the number of objects to compare.  This is approximately n^2/2 (or n squared divided by two, which is a parabola).  Here is a graph showing how the number of pairwise comparisons (y-axis) grows with n (x-axis), the number of objects to compare. 


The curve grows at an increasingly steep angle so that with 1,000 objects to compare there are half a million possible pairwise comparisons.  The squares of numbers grows much faster than the numbers themselves. 

Flipping this around and going back to the birthday paradox, the number of individuals needed to get the first match does not grow as fast as the total number of matches possible.  Suppose we were comparing something else, like auto license plate numbers on an island, you only have to sample a small number of the total to get a match and this sample is a smaller and smaller fraction of the total as the total number grows.  Here is a graph to illustrate. 


The total number of cars is on the x-axis.  The number of randomly sampled cars needed for a 50/50 probability of sampling the same car twice is on the y-axis.  So if there were a million registered cars on the island, you would only have to sample 1,400 to have an even chance of getting the same one twice. 


This graph shows how the fraction sampled until the first match is a smaller and smaller proportion of the total as the total grows.  With 10,000 cars you only need to sample 1.4% of the total; at one million cars this is 0.14%. 

This property, of rapidly shrinking fractions required to work with large numbers of unknown identities, can be taken advantage of in various ways, one way is called the birthday attack in cryptography, where matching hash functions can be found between documents to transfer digital signatures.  Another way can be to estimate the total size of a population from a smaller sample. 

There are approximately 700,000 automobiles registered in Oahu.  However, we all have daily patterns and regions we tend to, or not to, be in; depending on this overlap I am more likely to encounter some of these cars than others.  How many?  In other words, effectively what is the number of cars I am usually around while driving?  Both to answer my original question and because I might want to know how many people are likely to see a bumper sticker or advertisement I put on the car. 

To test this out I surreptitiously took pictures of cars while V was driving, usually to the grocery store and back, but also along my regular commute route to work.  (Yes, I know this seems strange, but it is harmless I think.)  Over a couple week period I had pictures of 590 cars, that I entered each day into a database--it seems like a lot but you can collect plate numbers quickly with just a few minutes of entering.  And there was one match!  I took a picture of the same car twice, five days apart, in two places.  Here are the photos.  (I blocked out the plate number for privacy.  I don't think this is entirely necessary, but it doesn't hurt.) 


Turing this around, if I were randomly sampling from approximately 250,000 cars I would expect a 50% probability of a match in a sample of 590 photos.  This is about 1/3 of the island, more than I expected! 

This reminds me of a trip I made with some friends to New York City in 1993, we saw the same person, a perfect stranger, on the street in different places on different days.  There was a story then, that was repeated on the drive to the city: there are so many people in NYC that if you pass someone on the street 10 years would have to go by before passing them again.  This may (or may not) be true for a specific person, but not for all the people you pass on a given day. 

This also helps explain seemingly amazing coincidences, like the woman that won the New Jersey lottery twice in four months.

Say I am behind or adjacent to ~100 cars each day to and from work and the grocery store.  Then on the next day 100 more cars.  There are 100^2 or 10,000 possible matches between the two days.  On the third day there is 100 more cars.  Then there are 100^3 or one million possible matches between the days, but I am only around approximately a quarter of a million cars each day according to my results above, so I have been behind the same car twice in these three days (on average, according to these rough guesses, I am behind the same car every 2.7 days, (log(250,000)/log(100))). 

In case anyone is curious, there were a few out of state plates, people that shipped their cars to Hawai'i.  These were from Alaska, Arizona, California, Florida, Georgia, and Nevada.  Plus there were a few federal government plates. 

There were also quite a few personalized plates, which is what started me on this track in the first place.  In contrast to the serial plates these are meant to be advertised so I will list them here.  Some are puzzling to figure out and remain a complete mystery to me. 

1J-ACE
4-BENJI
AGAPE
AMR-C
BELA
BGOODE
BIGDDY
CHZLNG
DEL
DFS-1
DS24ME
E-SABIR
EASE-UP
ENDURE
FEARY2
GODLDY
GRNWNV
GRRR
H8MYEX
HEL-LMS
I 2SEW
IGUANA
INA
IVIMAR
JAZLVR
JULZ87
JZANO
KAFFEE
KAI-EA
KALAIS
LABETE
LIKE 9
LU-SAN
M LITE
MBPPRP
MINI U
MOVE-ON
NELAZ-1
PERFEK
PRED8R
RAD
RDRK
RILLOZ
RLVRIA
SCTTSH
SENIE
SHANDL
SKTDVL
SMEEN
SRCHNG
SSS-1
ST33L3
SURFZ
TWIN-GL
VELINA
ZAYNAH

Friday, January 27, 2012

NASA funding

I heard a discussion on the radio a few days ago about NASA's budget and how it would need to be trimmed and focused on fewer prioritized missions in a tough economy...

To put this into perspective, NASA receives $19 billion annually; this is less than 1% of the US budget. (link)  The defense department receives $689 billion; 20% of the US budget.  (link)

The international space station cost to NASA is less than $30 billion (excluding the space shuttle, $55 billion was spent on space shuttle missions to the ISS), so lets say a total of $85 billion.  (link)

The second Iraq war cost at least $750 billion in direct costs to the US and may be as high a $1 trillion.  (link)  (Obviously this is ignoring the costs of human life, etc.) 

Each state in the United States has benefited from NASA spending.  In 1971 a 33% discounted rate of return was estimated for NASA investment/stimulus in the US economy.  More recent reports easily show that NASA spending stimulates the economy and creates skilled jobs.  (link)  (This ignores the less tangible benefits arising from the US being a leader in science and technology development.) 

Now is not the time to decrease funding to NASA.  If anything it should be increased dramatically, and it doesn't take a lot of creativity to see where that money might come from without raising taxes.  Unarguably, NASA helps the US, both in direct economic terms and in many other ways.

We, as Americans, were world leaders in space, but we have lost our vision and drive to apathy and cynicism.  We build monuments on the US mall in Washington, D.C. to wars.  Where are the other monuments to some of the greatest positive accomplishments the US has done, like the Apollo program and moon landing? 

NASA should be doing what only governments can do.  40-50 years ago this was simply orbiting the earth, the moon landing and building a space station.  Now, private companies routinely send up satellites, and are on the verge of replacing the space shuttle heavy lifting and docking with the international space station.  Soon private companies, and other countries such as China, Russia and the EU will land on the moon.  We need to broaden our focus and be more ambitious in our vision.  NASA should be conducting manned exploration of the solar system (we need a moon base, Lagrange base, a martian space station, and a Ceres base, in that order, one of the biggest problems is radiation shielding so lets solve that problem) with more powerful non-chemical propulsion technologies, like the Orion project and VASIMR, that can accomplish manned missions to other planets in months rather than years. And we should be beginning serious unmanned exploration of interstellar space, like the Daedalus and Longshot projects, to pave the way for others to follow.

This expansion would build up a solar system wide infrastructure (and economy), so further exploration becomes easier (lower gravity wells, etc.).  There are many possible benefits for earth as well.  For example, we could start mining Helium-3 to solve the earth's coming energy crisis. 

We can do amazing things if we just decide to do them.  Let's get started!

Tuesday, January 24, 2012

Hawaiian elephant spider

A closeup of a rare elephant spider crawling on the front steps of our house!   

Actually this is a pink-spotted hawkmoth (Agrius cingulata).  The hawkmoth family (Sphingidae) includes some fascinating species such as the bee hummingbirds (and here) and the death-head moth from Dracula (I want to make a note about new media based on older media in a later post).  Also, look at this Oleander Hawkmoth

V was returning from the grocery store after dark so we left the porch light "burning" for her.  Then M noticed this large moth flying near the light.  When trying to identify it I got quite excited at one point and thought it might be the endangered Blackburn's Sphinx Moth, but it is a pink spotted hawkmoth instead.  They are found in Central and South America and are long distance migrants.  They occasionally show up in West Africa and Europe and are naturally found in Hawaii and the Galapagos.



Here it is parked next to a house gecko hanging around by the light, to give an idea of size.


Sunday, January 22, 2012

Reading

M reading a library book on a Saturday afternoon.

We do not have a TV set in the house, which is a situation I am quite happy with.  I feel that TV watching is addictive and unhealthy, especially for children.

Saturday, January 21, 2012