Some Geometric Thoughts...Dots

Just wanted to put on "paper" an idea so I can go to sleep this cold January night (-5 C here).

The idea:

If you put dots in a row on paper by a pencil, you will have only two directions to move the pencil along to connect those dots no matter how many dots there will be. But if you place those dots irregular, you will soon have an enormous variety of dot paths to choose among. But is there a finite answer about how many different paths there will be, I wonder. So is there a pattern of those dots that optimize the total of dot paths? Thinking about that problem (I don't know if anybody has thought of the problem before me) I conclude that there will not be an irregular shape that will optimize the total of dot paths, but a shape that must be symmetric, I think, which must mean that nature itself seek symmetries (but perhaps not reach that goal because of time delays by force interruptions).

It's tempting to think that some sort of spiral outwards from the first dot you make on paper will be the answer. So two similar spiral layers are separated by one with dots where there's an opposite "hole" in those two spiral layers - and visaversa. And the one spiral layer will also pair up with a similar spiral layer with one of those two spiral layers between. Reduce the distance between layers and even dots to almost zero in the spirals, and it will be like making a spiral of same size coins from a fixed point, each coin of second layer etc resting on two others coins ridges.

Think of those layers of coins as positive or negative items (positive and negative attracts), every two times, then the pile is held together. If you mark the items with a plus or minus sign - every two times, you will notice that there will be three plusses grouped with one minus sign (and visaversa with the 4 type nabor group - considering three sprial layers).

With all "4-groups" there will not be possible to keep the same distance between each same layer pairs as between  two items outside the same layer pairs, because the first instance means attractive force and the second means repelling in that cross each 4-groups make. But that is seen isolated - there's an overlap of 4-groups that balance out, I think. So I guess nature will try to keep the same distance between every items if they have the equal amount of charge (negative or positive).
 

Where's The Food?

Remember'em birdies now in the Winter. The snow came here in the lowlands at last in the first days of January. The highlands have been covered by snow since the middle of December. Forcing some birds from the woods, like woodpeckers, to visit cityslickers' bird trays and feeders - like mine!
(The picture was painted by an arm disabled - amazing! From a calendar I bought to support the arm disabled and mouth or leg painters).

At The End Of Yool 2011...

The table is empty except for some nipses... the bluish pottery at the chair was made by me at school more than 40 years ago...

My mom's 1st pine from her own garden is left alone at a corner... on the wall hangs pictures of my sister, her husband and their seven children (when they were young, fresh rascals).

I'm Dreaming Of A ...Er...

Greenish Yool? Only frost here today north of Dröbak...:-((

Ho-Ho-Ho (Me)... Have you been nice this year?:-)) If so: Merry Yoool !!!

100 Years Ago (Part 2)

Brutalized system of bringing up children before 1911. Katzenjammer Kids  first appearing in my country in 1911 changed all that... it seems! Just two years later women were allowed to vote and soon children also got their rights! "Knoll og Tott 100 år i Norge" at sale here now at Tronsmo - get it before Yool!

What To Buy Yourself This Time Of The Year?

Why not probably the greatest beginners keyboard: Yamaha PSR E423. Remember to add a headphone set - then you won't disturb your neighbours that perhaps otherwise will think that The Third World War has begun, and besides you won't hear any bombs going off in your city. I bought mine in June at Norsk Musikk Instrument AS (Oslo) for only NOK 2495 (about just 400 dollars!) to celebrate 2 years with unemployment, no women to push me around, and of course: The Brightest Day of the year (Solistice).

Learn About Your Ancestry

Remember to buy Scientific American for this November. Add a Finlux LED-TV with recording to a USB memory stick or hard drive to your living room... to keep scanned pictures from the past and films from Discovery and National Geographic TV Channel... to pass on to your descendants (if your country is civillized enough to allow that!)

100 Years Ago (Part 1)

 The firm I worked for is now 100 years old... not quite that staff at the firm now, I think.

 But perhaps more like this happy bunch...?:-))

I was with the firm 25 years ago. Me the third person to the left - the guy with no black stripe over the eyes.. felt a bit outside the dinner party in honour of the firm's 75 years! No, actually, I just want to annominize the staff and firm back then in case they don't want to be assosiateted with me now. At the dinner party I remember I wasn't to happy to be served reindeer steak that year - especially because of the nuclear disaster at Tsjernobyl (in 1986) not too far away where the reindeers lived. But at least I was easily spotted by the car drivers later in the dark when I travelled home...!

The Space Elevator

My own version. Stacks of telescopic tubes or sylinders with rocket fuel and motors at the bottom of each to drive a ramp up from start aera at 400 - 500 meters over the ground. With two columns that have 300 tubes each measuring 400 meter this ramp should reach 120000 meters = 120 km, which is about 1/3 of the distance up to the level of ISS (International Space Station). From there the space capsule will use it's own rocket motors. Each stack's upper tube's rocket motor start first and will at it's bottom lock into the upper part of the tube right under to drag this one along - but at the same time this tube will fire it's own rocket motor at it's bottom. To be sure the stacks won't tip over, they are balanced with rockets at the ramp. The stacks of tubes are each supported by a sollid column that measure 400 - 500 meter.

Halloween...

The Cheesy Way!

My Second Big Tomatoe !

About the same size as the first one, but more ripe! Not bad, considering little light here far north!

Leben im Korallenriff

The title of this 5000 pieces puzzle I solved during August and September (puuuh!) I think it's motif is from The Red Sea (see the documentary "The Desert Seas" on National Geographic Channel).