Winter Holiday Puzzles

I.  The squirrels here love to eat the many fallen walnuts (as well as the roots of my freshly planted native plants!) even though the meat inside is protected by a very hard shell.


But the squirrel has sharp teeth and manages, with great effort, to chew right through.

Gnawed Nuts_5064The puzzler is the many perfectly split walnuts which were lying on the ground near the end of April.  The inside meat has all been eaten without a trace of tooth marks on the shell:

Split Nut 5063I’d never noticed these hemispheres before.  The plane of the north-south split is fairly flat, smooth and almost polished.  How it happens I have no idea.  I took some whole walnuts, soaked them and froze them, and hit them with a hammer –  all to no avail, they refused to be smoothly split.  There is some secret cleaving process at work, and I’m certain the squirrels would love to take advantage of it if they could?
II.  The younger looking of a pair of bald eagles
2Eagles_8602has been putting sticks against this tree on Garden Island out back for a year now without getting one of them to stay in place.  This clip (click the white triangle in the middle of the picture below to play the video)
YouTube Preview Image
shows the bird hard at work, but at the very end the stick sadly drops to the ground once again, wasting all the effort.

It would be so beautiful to have an eagle’s aerie right here but the problem for now is how do I get the process to start?  It is not an easy tree for climbing!

III.  This winter’s weather has been so mild that my bees were actually gathering pollen on December 23, when the temperature was 50 F (10 C), who knows where this one found the bright yellow food packed onto her legs?
Pollen_8702I’ve found nothing in bloom anywhere nearby.  Ever tried following the “bee line” as they leave the hive on their way to their hidden food source?  I could not make it work.

It was so unseasonably warm that the Sandhill Cranes, who we haven’t seen for 10 years since Inez was last here from Spain, stopped by for the week of Xmas on their very late migration south.
Cranes 8746This photo was taken through a closed back window yet we could still here their unique chattering, clacking bills: sounded like humans squabbling about climate change.

IV.  Einstein very neatly showed that something with enough mass can visibly bend a ray of light. (Without any math, he simply stated that we could not tell the difference between the force of gravitational attraction and the force of accelerating a mass with inertia. So when a nearly horizontal beam of light from one wall to the other of your room seems to droop, it means either the room is accelerating upwards, or the room is being pulled down by a gravity field, which is also pulling the light beam down).

The sun at a distance of about 550 AU (Astronomical Units – 1 AU is the distance from earth to the sun) is massive enough to act as a “Solar Telescope” to form an image, of what might lie far, far behind it.   The enlarged image of a bright spot behind the sun becomes an arc or a circle.  A Black Hole would have a similar effect as the sun. (Radio waves are similarly bent.  A good receiver at the focus spot could listen to the radio programs from another galaxy, if any planets there happened to be broadcasting!)

APOD (Nasa’s Astronomy Picture of the Day) often shows images magnified by gravitational lenses.

Einstein Rings:  In the image below the gravity of a close luminous red galaxy (LRG) has gravitationally distorted, into a ring, the light from a much more distant blue galaxy which was directly behind the red one.
Einstein RingsMy Puzzle is that I can’t understand how this works, in even the simplest terms:

An ordinary glass imaging lens (convex) works by bending light rays to come together to form a convergent image.
Convex LensMy problem with the gravitational lens is that the light rays are more deflected the closer they pass to the massive gravitational object.  This results in a fanning out or diverging series of light rays and not the convergence of the rays needed to make a visible image.  The rays shown below, from a star, apart from the red one which is swallowed by the BH, have an increasing bend or deflection the closer they pass to the BH.
Black Hole LensThus the massive object acts as a rather strange concave lens.  I know a regular concave lens looks like this:
Concave Lensbut its effect on a bundle of light rays should show a similar, non-imaging, divergence!

A simple point of light, in this case one quasar far beyond the focusing mass of a faint spiral galaxy, is often shown forming an “Einstein Cross” as 4 spots, rather than an arc or a circle.
Einstein CrossThat too I fail to understand!

Perhaps a clue lies in the gravitational images formed, not by a point mass, but by a cluster of galaxies:
Gallactic Cluster LensThe cluster CL2244-02 above is composed of many yellow galaxies and is lensing the image of a very distant blue-white background galaxy into a huge arc.
Here the rays of light from a bright spot far behind the cluster mass might come almost straight through the gravitational center of the cluster with little or no deflection.  The next adjacent rays would be somewhat deflected, and the next ones a little more so.   Thus the central area of the galaxy cluster could conceivably act as a converging lens, but further away from the center and outside the cluster, the rays will be deflected away from each other resulting in the concave lens effect sketched above.  So could there possibly be an imaging process, but only in the center of the cluster?


Any solutions to any of these puzzles will be gratefully acknowledged.


Happy Solstice, Winter Holiday, Xmas and New Year 2016 to all.

3 thoughts on “Winter Holiday Puzzles

  1. What have you done with our cranes? They didn’t look so black and white when they left here.

    The walnut problem I understand, but don’t have an answer for. The other questions are far beyond my comprehension.

    But I wonder if your diagram (very nicely done, by the way) “diverging lens–no image formed” is correct? It seems like the further away from the center of attraction the light passes, the more the force would be at an angle to the direction of the light, so the more it would be bent. Light approaching the center directly wouldn’t be bent at all, but just accelerated…(whatever that means.) I’m trying to envision lots of tiny steel balls flying past a magnet, rather than a lens.

    • Nat,
      Light passing near a massive object is more bent the closer it passes. Interestingly the bend is only inversely proportional to the distance between the light ray and the center of the mass, unlike gravity or magnetism where the attraction is inversely proportional to the square of the distance. This means the force between masses or magnets becomes a lot stronger at close distances – you know the suddenly big pull between two magnets as they almost touch each other.

  2. Sorry, can’t help with the botanical or astronomical problems. However, I will try to get you some photos of the red kites which inhabit our area. They were very nearly extinct in this country but re-introduced to the Chilterns , about 20 miles away, about 20 years ago and have been breeding very sucessfuly. They look and sound wonderful in flight, but are very seldom seen on the ground or in trees. I have counted up to 20 birds circling in search of food.
    It seems people are buying raw meat to leave out for them which is not recommended but must provide spectacular views of them.

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