Flying around the world isn’t correctly Euclidean

The Abel Prize – the “Nobel prize of mathematics” – was awarded this year to a man who proved that the shortest distance between two points isn’t always a straight line.  

Most of us were taught in geometry that it was.  Rather like 2+2 always equals 4, the straight line of Euclidean geometry had the hard immutability of always, irrevocably being self-evident fact.  One might even say, of always being true.

But what Mikhail Gromov proved is that the shortest distance between two points isn’t a straight line if you aren’t on a flat plane.  What pilots have known for a long time is that if the points are located on a round three-dimensional object like Earth, the shortest distance between two points is a curved line.  It’s why, if you are flying between London and San Francisco, the flight heads north from London before heading south.  It’s not to avoid other planes on a busy airline highway.  It’s because it’s the shortest way to go. 

If you have a globe of the Earth which is big enough, you can test for yourself whether this and various other Euclidean “facts” are actually valid in a curved geometry.  

This is an illustration of the relativity of facts in science.  All scientific facts exist in a context.  Sometimes it takes no more than weeks, sometimes it take centuries to discover a different context in which an “absolute” fact is actually relative.  It’s the facts that took centuries to limit their context that gave us the impression for so long that some scientific facts are absolute.

But we now know from Einstein’s theory of relativity, for instance, that Newton’s theory of gravity doesn’t apply equally throughout the universe, and that time and space are not absolute.  We now know from quantum mechanics that before and after, up and down, and even existence and non-existence don’t appear to operate on the particle level the way they do in the world in which most of us spend our lives.

If you still are not convinced that all scientific facts are facts only within a specified context, think of the following puzzle that was offered to me as an adolescent: 

How many examples can you think of when 1 + 1 do not equal 2?  There are many.

Mother nature’s weapons of mass destruction

This week several of nature’s most deadly attacks have reminded us that occasionally there is a high price for calling Earth our home.  It’s an amazing place, if only because it is the only place in the universe we know of at this point where people like us could survive.  But we don’t live here without cost.

The earthquake that struck L’Aquila in central Italy has killed at least several hundred people and left tens of thousands homeless.  This isn’t the first or worst earthquake Italy has experienced, and it will not be its last.

Like San Francisco and Tokyo, among many others, it is where several tectonic plates are pushing against each other.  As they float inexorably in opposite directions, pressure builds up, and earthquakes are what happens when something finally snaps.  

Tsunamis, volcanoes, and earthquakes are all the result of living on the surface of a dynamic planet.  If we didn’t have these deadly eruptions, the surface of Earth would gradually be worn smooth, and water would cover the entire surface.  There wouldn’t be any land not covered by water anywhere.

So the price of keeping our world habitable on the most basic level is sometimes lethal to hundreds of thousands of people in just a few minutes, the product of an unexpected gigantic upheaval from the bowels of the earth.

Finger-counting

When I was a child in school, we were taught that using our fingers to figure out the answer to an arthmetic problem was wrong.  Some kids even got their hands slapped for doing it.

But it looks as if in this case it was the teachers who were wrong.  Research is showing that using gestures while one is thinking about a math problem actually improves thinking.  This seems to apply whether we are trying to solve a problem, being taught how to solve it by someone else, or explaining how we solved it.

So hand shakes all around.  

There are several radio podcast on children’s gestures on line well as several books by the author who has studied this subject most extensively.

Neanderthal genes

On Darwin’s birthday last month,  Svante Paabo announced that his work at the Max Planck Institute for Evolutionary Anthropology in Leipzig had mapped 60% of the genetic code for Neanderthal man.  

Why is this so fantastic?  Because Neanderthal man, who became extinct about 30 thousand years ago, is the nearest relative of Homo sapiens.  Even the incomplete code answers some questions we’ve been asking ever since the first Neanderthal fossil was founder in the Neander Valley in Germany:

• When and where did the Neanderthals live?  In Europe and western Asia from beginning about 400,000 years ago.  Homo sapiens originated in Africa about 200,000 years ago, but did not arrive in Europe until about 40 thousand years ago – just before the Neanderthals died out.
• Did the Neanderthals interbreed with Homo sapiens, or do the two species have similar ancestors?  The genetic code suggests that very little interbreeding, if any occurred between the two human species.  But both descended from Homo erectus.
• Why did the Neanderthals die out when Homo sapiens didn’t?  We still don’t know.  Some anthropologists speculate that it was the arrival of Homo sapiens.  Perhaps Homo sapiens hunted them for food, or simply competed with the Neanderthals for a decreasing supply of wild food provided by hunting-gathering methods.

Or perhaps the ice age which also coincided with the Neanderthal demise changed the conditions in which the Neanderthals thrived, and they could not adapt.

• Did the Neanderthals talk to each other?  Not sure yet.  They did possess a gene which humans must have in order to talk, a gene which chimpanzees don’t have.  If they did talk, their mental abilities were unquestionably greater than the cartoon Neanderthal would suggest.

The chances are that the insult to intelligence as “Neanderthal” is misplaced.  They survived for at least 375 thousand years.  Thus far, Homo sapiens has survived for about 200 thousand.

Looking inside Earth from above

Europe has just launched a spaceship called Goce which can monitor tiny fluctuations in Earth’s gravity.  These fluctuations are caused by such things as changes in ocean currents, melting ice caps, underground lava flows, and the presence of underground stores of oil, water, and various minerals.

It will, therefore, be immensely helpful in predicting volcanoes in time for people to escape from danger, for monitoring climate change, and in locating oil and other mineral deposits beneath Earth’s surface.

Later this spring, the Europeans are also launching Herschel, the most powerful telescope ever put into space.  Unlike Hubble, Herschel detects infrared radiation.  What scientists are hope to find out is whether stars developed after the galaxies were formed, or whether stars came first, and then massed together into galaxies, each of which has several hundred billion stars.

Another small step for mankind into a very very big universe…

Thoughts about ET

The search for alien life beyond our planet, even beyond our own galaxy, has been in the news quite often of late:

• a scientist has seriously suggested at a recent meeting of world scientists that we should be looking for alien life on our own planet.  He believes that quite possibly life has landed here from outer space – possibly on the tale of a comet – more than once.  If so, it might still be pulsing away in some unexpected corners of and crevices of Earth.
• both water and methane have been found on Mars.  Water is an essential ingredient of any form of life as we know it;  methane is produced by many forms of life.  So there could be life on Mars even now.  http://news.bbc.co.uk/1/hi/sci/tech/7829315.stm
• scientists estimate that there may be as many as 100 billion Earth-like planets in our own Milky Way galaxy.  What would an Earth-like planet, capable of supporting life as we know it, be like?  First, it would be rocky, not gaseous.  It would have water, and be close enough to its sun that water doesn’t freeze, but far enough away that it doesn’t boil.  A moon would be helpful, because the moon creates tides and helps ruffle up the surface of the earth, mixing chemicals and organisms in the oceans’ waters, which encourages small organisms to grow and provides food for larger life forms.  http://news.bbc.co.uk/1/hi/sci/tech/7891132.stm
• earlier this month, Nasa launched the Kepler Space Telescope to look for Earth-like planets outside our galaxy.  http://news.bbc.co.uk/1/hi/sci/tech/7918497.stm
• and then there is the mysterious signal from outer space received in 1977 that  lasted 37 seconds and had the characteristics predicted for an alien signal.  No one has yet been able to explain it. http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/books/article5797028.ece?token=null&offset=12&page=2  

The question is, if we did find ExtraTerrestrial life, how would we respond?  Would we try to kill it?

Who owns the rain?

Scientists have been warning for at least a decade that eventually humans were going to start fighting over water.  Not fighting over water for golf courses, swimming pools, and lawns, but fighting to get enough water to drink, wash, and stay healthy.

Despite the long-term water shortages in western United States, especially in California, but I was  astounded to discover that there are states in America where the rain that falls onto a person’s private property is not theirs.  It is illegal to catch it in rain barrels and use it to grow vegetables or flush the toilet.  That’s because some states have passed laws saying that the rain belongs to farmers and water companies who have bought rights to it, and so homeowners have no right to collect it.

Harvesting rainwater is illegal in some parts of Africa.  I had no idea it was illegal in some parts of the United States of America.

Currently the law is being challenged in the Colorado courts.  Whatever the outcome, as global warming increases desertification and the sources of drinkable water decline, there is going to be a shortage of water to meet our basic needs.  This catastrophe won’t happen in a single overnight explosion, eruption, wave, or crash.  

But it would be a catastrophe of no mean proportions nonetheless.

http://www.truthout.org/031909EA

A laser ray of hope

Anyone who has been following the problems of global warming for very long at all is acquainted with a variety of schemes that we humans have thought up to give us energy without giving us pollution.  So far, the magic elixir hasn’t been found:  

bio-fuels are competing with our global food and water supplies;  oil-producing algae aren’t yet producing; wind and wave energy only work when where there are wind or waves; solar energy has been too expensive or unreliable;  cold fusion uses energy to produce than it produces itself, but scientists can’t make it work in in practical terms;  conservation and using less energy seems a better idea for other people than it does for ourselves.

But we humans are a creative, innovative species and we haven’t given up.  Scientists in California are beginning a series of experiments using laser beams with the power 1,000 times greater than the US national grid.  

They think they just might be able to replicate the process that takes place within the sun in which atoms of hydrogen fuse together, producing a greater burst of energy than it was required to produce the fusion.

If they can do it, this ignition could be the basis of the ultimate clean energy – a no carbon, no radio-active waste, limitless, safe and secure energy source.

Even if they succeed, however, it will probably be 25 years before power stations using the process are commercially viable.  So we best keep our options open for a while.  

Oh, and turn out the lights when you aren’t using them.

http://www.timesonline.co.uk/tol/news/uk/science/article5908490.ece

Bees on a fast-food diet

In his best selling book, The Omnivore’s Dilemma, Michael Pollan argues that too much of our food is raised as a single crop in vast fields, and that above all, corn constitutes way too much of our diet.  He says these concentrations by big agri-businesses are undermining our health, the welfare of our animals, and depleting our soil.

Now it looks as if it’s also one of the causes of bee colony collapse.  Bees, like people, need a diversified diet to be able to fight off disease.  We need the bees to pollinate the plants that produce the food we eat, so the world-wide collapse of bee colonies is a serious global worry.

That’s the bad news.  But the good news is that the bees’ demise is not being caused – as many feared – by global warming, by genetically-modified crops, or even by pesticides.  It’s being caused by the bees’ vulnerability to several virus strains that are attacking their colonies.  And a diversified diet for the bees greatly increases their ability to fight it off.

Some beekeepers have resorted to giving supplements to their colonies – much as many of us take vitamin supplements to augment the nutrition in our daily food intake.  It helps.  But it’s expensive.

It would get to the heart of the problem if instead crops were more diversified in the first place, so that bees did not have to subsist on the bee-equivalent of fast food.

http://www.economist.com/research/articlesBySubject/displaystory.cfm?subjectid=548064&story_id=13226733

We can relax: the world will still be there

Two independent teams of scientists – one in Japan, the other in Tokyo – have just announced research which offers strong support for the view that reality continues to exist even when no one is thinking about it.

Whew! I canus all saying.  What with worrying about the world financial crisis, and global warming, and the human carnage being wrecked in more places than I have finger, at least I can stop worrying about it all disappearing if I don’t keep my mind on it.

This does, though, represent a serious scientific question posed by quantum physics.  Quantum physicists demonstrated that we can observe particles of matter and anti-matter annihilating each other in a burst of energy when they meet.  But does this always happen?  might these particles behave differently when nobody is looking?  Well, if you can’t look, how will you ever know?

The researchers solved the problem by polarizing photons (that obey the same quantum laws as particles).  They repeated this process many times, each time observing just a smidgen of the interaction which in itself was insufficient to draw any conclusions.  By watching different smidgens, however, they were eventually able to draw a full picture of the entire interaction.

Are you still with me?  Even if you don’t understand, keep reading, because what they found even the researchers themselves call “preposterous.”  

They found that when the photons are being observed, they interact differently than when they are not being observed.

Just like living things.  Maybe what we think of as the inanimate world really is alive.  Maybe we just don’t recognize it.

This sounds far-fetched.  Or at least it does to me.  But most children believe that what we adults think of  inanimate is alive.  And many ancient cultures think this even as adults.  So we have Stonehenge, as one example.  

And if you think the possibility that everything is actually alive in some way is utter nonsense, read the results that Professor Yokota found in the New Journal of Physics, or the demonstration by Professors Lundeen and Steinberg in Physical Review of Letters two months ago.  Or for an easier read:

http://www.economist.com/science/displaystory.cfm?story_id=13226725

The world of hard science is as strange as anything I have ever imagined.