Tuesday, June 20, 2017

Math Puzzle Time: surround three

So that's the puzzle.  I think this was mixed up in my mind with something called frustrated systems and maybe generally, can crystal growth come up with something arbitrarily complexity.  At first I found plenty of boring solutions:

Even radially symmetric ones




 
Even spirals!





but were there TRULY CREATIVE solutions possible?  Two weeks later, it came to me:

Now... can I write an algorithm to do that?  Better yet, a set of local cellular automata rules that force it?  Better yet... is there a mineral out there that does this?










Can anyone find other kinds of solutions?

Convincing Geologists That The Continents Move (part of history of science in 100 tweets)

CONTINENTAL DRIFT/PLATE TECTONICS

science works by exploring every possible thing with wildly different tools and approaches and find that it all interlocks

Columbus' first voyage into the unknown most certainly doomed to take more months than he had supplies, lucks out and discovers new continent

using the stars on a spherical sky as guide, we begin to map coastlines onto a globe, the coasts of Europe/Africa fit north/south America!

we find rock formations and fossils on both sides of the Atlantic that match each other.

we sound the entire floor of the Atlantic ocean and map its valleys and mountains, we find a ridge in the middle that matches both coastlines

this ridge is hot with fresh magma rising and cooling to basalt, forming new ocean floor

core samples all along the ocean floor, the bedrock is all basalt

the continental crust however is mostly granite with basalt inclusions and folded metamorphosed sediments it has a much more complex history

core samples along ocean floor have deeper and deeper layers of sediment on top as you get closer to the coasts, closer to the coasts is older?

when we discovered radioactive decay, we learned how to tell the age of REALLY OLD rocks. yup, the ocean bedrock is older towards the coasts.

but ocean bedrock is, over all, young, only a few hundred million years old, continents much older, some rock billions years old.


THE ROLLING OCEAN CRUST MAGNETIC TAPE RECORDER:

why not measure the magnetic orientation of rocks? it orients to the magnetic field of the earth when the rocks form from molten magma

in young bedrock, the magnetic field is oriented towards the poles, in older bedrock, not so, either the poles move or the bedrock moved!

map the magnetic fields across the ocean floor! on either side of the ridge, parallel matching stripes, flipping north, south, north, south...

the north and south poles were reversing orientation every few million years?

look at the magnetic orientations of older and older bedrock on continents, they all point to stationary poles if we MOVE the continents!

well? lets go and WATCH the continents, ARE they moving apart?  HELLS YEAH, umm... by half an inch per year.  this takes radio, or radar or satellites

but 1/2 inch a year is enough if you multiply it by the radio-dates of the oldest ocean crust, BINGO, you get the distance between the coasts!

can entire continents REALLY move? how many MORE INTERLOCKING measurements do you want before you are convinced?  this is how science works

half inch out of 3000 miles is like 1 part in 100 million.  to get these measurements to match we are measuring THAT accurately.  SCIENCE!


so, like soup in a pot, the entire earth is gyrating round and round in a series of interlinked convection cells, continents floating on top

theory of plate tectonics interweaves all the disparate phenomena of geology: continents, oceans, volcanoes, earthquakes, mountain building...

Friday, June 9, 2017

The CONTINENTS Move? How We SLOWLY Came To Be Certain Of This

THE PLATE TECTONICS THREAD

what was the discovery?  science isn't like that!  not A discovery! many accumulating!

0) apes learn to sail, by starlight, leaving view of the shore!  this is the wild prehistoric early threads supporting our eventual science way.  we are explorers.  CRAZY ASSED explorers!  It's so important to us we risk death for it!

1) before sailing totally around the earth, before flying over the earth, before seeing earthball from the moon... Eratosthenes imagining earth is a sphere and figuring the sun is REALLY far away, uses geometry and shadows in cities 1000 miles apart to measure the circumference of the earth.  Anyway, greek astronomers reasoning from data on which stars are visible where on the earth and watching the shadows the earth makes on the moon from different longitudes... reason that the earth is probably a sphere.

2) columbus imagines, what the hell, instead of traveling months overland west to the opposite coast of the eurasian continent, i'll sail east and get to it the other way.  now, the greeks already taught us how to measure the size of the globe by the sun's shadows, columbus... it is too bloody far to sail!  but he convinced the monarchs of Spain to fund such a foolhardy adventure, what were all the motives?  desire for wealth?  adventure? cruelty?  i mean, probly it would be dismal failure, sure send 3 huge vessels with 100s of people in them to their deaths!

exploration is not cheaply won!  is it safe to come out of the womb?  no, not really!  but then again... we can't stay there either!

columbus LUCKED OUT and discovered a new continent half way there, unknown to europe!  well.. columbus screwed up, but his insanity opened the door...  even insanity can do this sometimes!  we eventually did learn to sail clear round the globe and routinely sail back and forth across wide oceans months at a time.

1) we map the coastlines and place them on spherical earth using the stars at night for coordinates, the shapes begin to become clear: old and new world coastlines match!

2) we collect fossils and map strata, placing them in a timeline, and see that they match directly accross the ocean.


3) The Atlantic ocean is an unfathomable huge devouring beast.  It swallows whole ships full of people.  just what IS an ocean?  WHAT IS DOWN THERE?  how deep is it? you can't swim more than a couple hundred feet down.  you can lower weighted ropes...  who, when, was the first to try it and find out just HOW DEEP does the ocean get?  how deep can you get with ropes, cables?


4) so we eventually bloody well decide, lets sound the whole frikkin ocean floor and see what it's shaped like! well eventually we learn to use... what did we use at first? sonar or radar?  clever clever apes!  either way it requires electricity!  and we map the shape of the sunless ocean floor, deep under MILES of water.  And eventually a sinous shape forms... we find the Mid Atlantic Ridge, curiously matches the shape of the coastlines on either side of it!  almost as if they were pulled apart from the center!

3.5) and perpendicular to it various subtrenches, stretchmarks?

4) how did we discover fresh magma was coming up from this ridge?

5) we LOOK AT EVERYTHING! Was George the ONLY curious monkey? NO. look at magnetization of rocks.  why did we look at the magnetization of rocks?  because that's what scientists do. they try EVERYTHING! look at magnetic orientation of bedrocks!  minerals in freshly cooled igneous rock have magnetic fields aligned with the Earth's magnetic poles.  but older rocks... the poles either were in different places in the past (not likely?) or the rocks have moved far since they were formed.  MYSTERIOUS.

6) so what the hell, lets map the magnetic fields recorded over the whole ocean floor.  WHY?  WHO EVEN THOUGHT OF THAT?  And we are rewarded with a beautiful pattern of stripes of alternating magnetic fields parallel to the mid atlantic ridge and the coastlines, and they match on either side of the mid atlantic ridge  too!  symmetrical!

6.5 Now, we've measured that the magnetic poles actually do wander around over the years a tiny bit...  Look FURTHER back in the bedrock and note that the north and south poles actually shift places every now and then.  WHAT?  (we are working on models that explain that.  i mean... how does the earth produce a magnetic field in the first place?  another story! vibrations from earthquakes hint there is electrically conducting molten iron in the core...)

6.6) are the stripes on the ocean floor recording these flips like a magnetic tape recorder?

7) we brought up samples from the ocean floor?  Sure we did, we drilled out cores and hauled them overboard!  the bedrock is ALL BASALT, quickly cooled magma, unlike the continents, which are much more complex, mostly granite.

7.5) Near the center ridge there is very little sediment over the basalt ocean floor, it hasn't been collecting sediment very long, but as you go further towards the coasts, the sediment layers over the basalt are thicker and thicker.  the ocean floor is older and older closer to the continents?

9) meanwhile, we were discovering radioactivity and half lives and how to radiodate rocks, millions of years old rocks, 100s of millions of years old rocks, BILLIONS of years old rocks.  Darwin and his geologist friends were right about the age of the geological strata all along even though the 19th century physicists couldn't imagine how it could be. SCIENCE ROCKS!

10) so we radiodate the samples of ocean crust, its ALL young, none older than a few 100 million years (while there is bedrock on the continents billions of years old), and gets progressively younger towards the mid atlantic ridge (birthplace of ocean crust?).  the clues are building up!

11) well, lets WATCH the continents! DO they move? YES! They are moving apart! what technology allowed us to do this? it's VERY SLOW. 2cm per year.  1 cm/3000miles is 1 out of 3000x5280x12x2 = 1 part in 100 million.  did we use radio?  satellites? and to get good match with radiodate of basalts should get measurement to 1 part in a billion!  but these are the kinds of measurements physicists have learned to make. 

yes, the numbers match.  the radiodating says the oldest ocean crust near the coasts is 250million years old.  2cm/yr *250million years is pretty close to the distance from the mid atlantic ridge to the coasts!  YAY SCIENCE!

SLOOOWLY the story dawns on us.. the magma coming out in the center, the basalt laid down on the floor younger at the center older as you go out, sediments deeper as you go out also agreeing with the older age of the ocean floor as you go further to the coasts, the magnetization marks matching on each side, the continents ARE moving apart at 2cm/yr and if you extrapolate that to their current distance apart you agree pretty well with the radiodating of the oldest ocean floor at the coasts, not to mention some plates are moving lateral to each other, some approaching each other and a trench where they meet, with volcanos spewing hydrated minerals that gets subducted..

A WILD NEW IMAGE of the earth, a mantle heated by radioactive decay is warm below and cool above so it's gyrating in convection cells JUST LIKE the ones in the atmosphere above it and over these gyrations the plates are being born and colliding into each other, and the continental plates are lighter than the ocean plates so they keep floating and accumulating riffraf.  where plates pull apart its fresh ocean trenches, where they GRIND past each other it's earthquakes and where they ram into each other, one sinks below and melts and makes mountains and volcanos.

if earth could move ENTIRE CONTINENTS, then surely it could move people's minds to change from viewing earth as a giant static rock to one where continents could move!