Friday, June 29, 2012

Ancient Navigators and the Demon Star

  I just read an article that shows that the Ancient Egyptians knew about the eclipsing binary star Algol back in the 13th Century BC.  It occurred to me immediately that this could have allowed ancient navigators to crudely measure longitude!

   Ancient navigators knew how to measure latitude fairly accurately.  All they needed to do was to figure out the apparent height of the North Star, measure the angle, and bingo, they had an estimate for latitude.  But what about longitude?  The easiest way to estimate that is to know that sunrise and sundown happen at different times depending on longitude (or, as we might think of it today,  what time zone you are in).  So if an ancient navigator knew sunrise was supposed to be a 6:55 AM in Oslo, and instead it happened at 7:55 AM, that would tell him that he was positioned 15 degrees West of the reference location, or out in the Norweigian Sea somewhere.  This can very easily be done today, what with electronic watches, but note that a sundial would not work to measure time, because it is based on the position of the sun, and automatically cancels out the effect that you want to see.  Other forms of ancient clocks were not very good.  It is generally assumed that the ancient navigators had no way to measure longitude until 1773, at which time John Harrison produced an accurate marine chronometer.  

    But wait a minute.  The Demon Star Algol (which actually consists of two stars which rotate around each other, Beta Persei A, which  regularly gets eclipsed by the dimmer Beta Persei B) dims by more than a factor of three for 10 hours at a time, dwindling easily seen with the naked eye.  This was recorded by the Ancient Egyptians according to an article that has just appeared in, by Charles Choi.  

   I frankly had no idea the effect was visible to the naked eye.    But according to Choi, Algol dims by more than a factor of three for 10 hours at a time, which is easily seen with the naked eye.  

     Jiminy Christmas, this is a huge effect, and I can't believe none of us apparently put two and two together before.  The clues are staring us in the face.   Algol, known as the Demon Star, represents the eye in Medusa's head!  Doesn't this suggest that ancients thought this star was a bit unusual??

    The period is 2.867 days now, but back in the 13th century BC it may have been closer to 2.85 days. The slowing is consistent with calculations of the change of mass of the binary as it spirals out.  
      The salient point is that if you know the period accurately, it becomes a universal clock that can be used from any point on the earth (as long as the weather is clear and if the eclipse occurs at night).  That allows the navigator to calibrate his hourglass and get a true calibration to measure longitude.  That could allow trans-Atlantic or trans-Pacific navigation.
     An observer could detect up to four events, depending on the sensitivity of the instrument (in this case, the human eye):  the beginning of the dimming phase; the end of dimming, the beginning of the brightening phase and the achievement of maximum brightness.  
    Over many cycles, it is possible to determine the period with great accuracy.  But how accurately can the magnitude or change in magnitude be estimated by the naked eye over a single cycle?  
   An upper bound exists from the ancient Greeks, who classified stars over six magnitudes.  Algol is normally magnitude 2.1, but decreases to about 3.3 and the back to magnitude 2.1 over 10 hours. The change rate is thus 1.2 magnitudes per 5 hours, or 0.24 magnitudes per hour. In recent times, naked-eye astronomer Alan MacRobert describes how to estimate magnitudes by eye to roughly within 0.1 magnitudes.  If so, a sunset-calibrated hourglass could be used to plausibly determine the minimum brightness of Algol within about 24 minutes, allowing a crude estimate of longitude, accurate to some 6 degrees, corresponding to 600 km at the equator.  At northern latitudes, this is roughly the difference between Dublin and London. 

Data from the Northern Houston Astronomy Club  indicate that it is possible to trace the light curve of Algol.  By extrapolating the shape of the curve and directly measuring the time of the minima, it is possible to estimate the time of minimum brightness to within about 0.01 to 0.02 periods, or plus or minus 20 to 40 minutes, or 5 to 10 degrees of longitude. If a highly skilled stargazer were able to improve upon the accuracy demonstrated by the North Houston Astronomy Club, better precision might be obtained. 

    Now, there is absolutely no evidence, as far as I am aware, that the ancients actually used this method to navigate.  The key would have been for ancient astronomers to realize that the brightness variations occur independent of longitudeBut if someone had made that connection, it is clear enough that longitude could have been crudely estimated in ancient times.

For Additional Reading

History of Longitude, Wikipedia,

Thursday, June 21, 2012

Why Are You Booing Your Children?

   Hey, you!  Why are you booing your children?  
This is what we want--a happy team getting some healthy exercise with friends.

   Yes, I'm talking to you, the parents of my 10 year old daughter's teammates in kiddie basketball and church league volleyball.  Now, most of the parents are very nice and support the children, and the programs are designed to promote sportsmanship and do a very good job of that.  The child players are really great.  But it seems that some of the parents are kind of weirded out by seeing their children play.

   Oh they don't literally yell, "Boo!  You stink!"  to their 10 year old.  However, some of them--especially Dads--seem compelled to yell more polite things that mean the same thing.  For instance....

    "Jane!  WHAT WAS THAT?"  (translation:  Your performance is unacceptable= you stink.)
    "Mary!  YOU DIDN'T CONCENTRATE!"  (Translation:  I would have made that play = you stink).

    "COME ON ALICE!  YOU GOTTA MAKE THOSE."  (Translation:  You have failed = you stink).

    Usually parents are supportive of other kids, thankfully, but with their own kids they show little mercy. The parents seem convinced that their kids can not function without their "gentle constructive" criticism. 

    Now Dads and Moms, I have some boos right back at you.  JUST WHAT DO YOU THINK YOU ARE DOING?  THINK ABOUT IT!  Growing up is hard enough without Daddy and Mommy making sarcastic and critical remarks for everyone else to hear. 
   These are not teenagers trying to get ready for a pro career, like the kids playing for Bobby Huggins in an effort to land a million dollar contract.  Little girls especially are very sensitive in their young teens, and they are all going through that awkward stage (they usually stay there until at least age 40, by the way).  And, Dad and Mom, you ain't no Bobby Huggins. 

"Oh no!  DId you see that?"

   I notice that the 10-14 year olds on my daughter's volleyball team become afraid to try to make plays when they are criticized.  They stand in one place, hoping that someone else will make a play and save them, rather than trying to make a play.  I suspect that they would rather be doing something else, but they play volleyball in order to try--unsuccessfully--to meet their parents' expectations.

   Dad and Mom, please believe that your daughter knows when she misses a shot.  She does not really benefit from your genius observations pointing out their failures.  And remember that the rest of the kids hear what you are shouting to your kid.  It's not a private conversation.   It ain't cool. 

   I probably did some  booing of my own as an inexperienced parent, but hopefully I have learned a little over the years.  I find that it's much better to use encouragement for young children.  

  "That's okay--you'll get the next one."
  "Good try!"
  "Good hustle!"

   If your child's Coach is on the ball, he or she will make a habit of coaching the NEXT play, and never the LAST one.  Little kids forget whether they are supposed to play defense or offense.  They don't really need you to point out that they missed a short or failed to get a rebound.  Instead, they need to be told to forget about the last play and concentrate on the next one.  

   Perhaps sports can be a training exercise for parenting.  It's an opportunity to show what is really important--not winning or losing or the proper form to shoot a layup--but that parents love their children and will support and encourage them, no matter what.  

   Yay kids!  Have some fun out there, eh?