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.

What we see isn’t always there

One of the fundamentals of applying the scientific method is the principle that conclusions are based on empirical evidence.  Scientific proof, in other words, is supposed to be based on “facts” that we can, in some way, see, touch, feel, and ideally measure.

But it’s not that simple.  The basic problem is that what we think we see isn’t always actually what is there.  Recently, Bernie Bamford, an Englishman was studying the imaging system produced by Google Ocean and identified what looks like man-made structures at the bottom of the Atlantic Ocean  just off the coast of the Canary Islands.  

This is very near the Strait of Gibraltar, where Plato talked about “Atlantis,”  a legendary city which Plato wrote had disappeared with its ancient civilization about three thousand years ago.  No one has ever found it, but if it exists, most people think it probably was covered by sea in a series of earthquakes.  (Egyptian priests said it was the because the people had stopped believing in god.)

A lot of people were excited by Bamford’s discovery.  But alas, Google says it is unlikely to be Atlantis.  Google says that what looks like man-made structures on their ocean images are artifacts.  The lines reflect the path taken by the boat as it was collecting the data about the floor of the sea below.

Now hardly anybody thinks Bamford’s lines suggest he found Atlantis.

But Bamford’s lines do illustrate why science makes two important demands of evidence that it accepts as truly scientific. 

The first is that more than one person has to be able to see it.  We humans – even normal humans not suffering from mental illness or drug-induced hallucinations – experience things all the time that nobody else can experience with us.  A great idea, physical or psychological pain, or even the taste of hot pepper on our tongue might show our our face, but nobody else feels our experience directly.  Our dreams often seem terribly real at night but not in the day.  So none of these experiences are considered scientifically verifiable, because they are private.  If somebody else can’t gather the same evidence or do the same experiment, it doesn’t count as scientific. 

That doesn’t mean it isn’t real.  It just means it’s not scientific evidence.  That’s why people who claim they lived another life before this one, or that they were captured by aliens might sincerely believe what they are saying.  Who knows?  they might not even be right.  But it’s not science.

The second scientific principle Bamford’s lines illustrates is that we should accept the simplest explanation for any phenomenon.  The explanation that the lines are a result of the data collection process is simpler than that there is a city buried there.  If someone wants to convince us of the latter, some further evidence will have to be brought forth.  The most obviously convincing evidence would be from a deep sea dive.

But I think it unlikely that anyone will mount an under water expedition any time soon to find out if those Bamford lines are matched by walls on the ocean floor.

I don’t think they are.  Do you?

Life after death: is proof possible?

Until about 200 years ago, most human beings believed that some kind of life continued after death.  In fact, most people usually lived with a lively sense of the presence of the dead in their own lives.

Then a change took place in the thinking of many scientists.  Until then, scientists took the position that we could prove something scientifically only through empirical observations – in other words, in terms of what we can observe or analyze as a result of what we perceive through our senses.  

What they didn’t say was that everything that was true, everything that existed, everything that happened, could be understood through the scientific method.  But now, many scientists argue that what is not subject to scientific understanding is not real.  Or at least, cannot be known, and since we can’t know it, it is, at best, irrelevant if not actually dangerously false.

Not all scientists today take this position, but many do.

Attitudes toward near-death experiences illustrate this difference.  Near death experiences (NDE’s) are those experiences reported by people who get close to dying, perhaps through a heart attack, an accident, or some proximate danger, but who survive.  

The reports of NDE’s are often quite amazing and life-changing.  They are often out-of-body experiences, and people feel that they have been in contact with another world.  They may “float” around the room or building, and have sometimes learned things that they could not have known if they had remained trapped in their body.

So is this evidence that there is life after death?  that we can continue to be alive even when we are no longer inhabiting our bodies?

We don’t know.  But can we ever know?  For now, most NDE’s are anecdotal, and have not been subject to rigorous analysis.  Sceptics says NDE’s are simply the hallucinations of a dying brain.

But other scientists are not so fast to dismiss NDE’s.  Science, they say, has brought us face to face with mysteries, conundrums, and unsolved problems of the most profound kind.  In fact, some would say that science has made the world far more mysterious than before.

The findings of quantum physics is a prime example.  On the quantum level where things are almost infinitesimally small, particles do not obey the same laws as they do at the level in which we exist.  Particles can affect each other even when they are millions of miles apart, they move in and out of existence, and before and after, or inside and outside, or up and down, don’t operate in the quantum world as we expect them to.

Nobody can explain this at this point, although no scientists deny the evidence that this is so.

So if you think science has created a neat pat world full of facts and indisputably right answers, think again.   Actually, religion just as often argues that it is in possession of indisputably right answers, not science.

Science, true science, reveals a universe as mysterious as you can get.  My own suspicion is that is why it frightens some people.

For what it’s worth, my own guess is that science is never going to produce “evidence” that convinces most people that there is life after death.  But I am positive that it will never produce evidence that there isn’t either.

How will it end?

If we live long enough, almost everyone will have asked how it will all end.  This momentous question is unanswerable because, although we might make predictions, the Principle of Uncertainty pervades everything any of us might say about the future.

But before we even get to making predictions, we have to decide which “end” we are talking about.

• Most of us are intimately concerned about our own death and of those who are dearest to us.  
• Besides our personal death, there are the various catastrophes which could bring about millions of human deaths, or the extinction of thousands of species in a single horrifying event.  
• Then there is the more ultimate end of the Earth as a planet on which life like ours can flourish.  
• And finally there is the end not only of our solar system, our galaxy which we call The Milky Way, but of the entire universe.

Science has a lot to say about each of these endings, but not a single one can science predict with precise infallibility.  Even when death is a mere second away, it is impossible to predict it with exact certainty.  It happens all the time in unexpected accidents.

Nonetheless, science can provide us with some facts.  And we as humans can make informed, if not infallible, decisions.

The next postings will look at some of the potential “ends” that science suggests could face us.

What is the God Particle?

Scientists who recently switched on the multi-billion dollar Large Hadron Collider (LHC) are looking for what has been called “the God Particle.”  But what is the God Particle, and how did it earned its exalted name?

Right now scientists (let alone the rest of us) don’t understand how the Big Bang can possibly have happened or, for that matter, how the universe continues to hold itself together, although it clearly does.  With Newton, scientists originally thought the explanation was gravity, but it turns out that gravity isn’t nearly strong enough to be holding the whole universe together on its own.  There must be something else.  What could that something else be?

The theory is that there is a huge field in the universe of something resembling sticky syrup that slows some particles down.  Being slowed down is what “mass” really is.  The professor who first proposed that this field exists is Peter Higgs (he’s retired now but still living in Edinburgh, Scotland).  That’s why the field is called “the Higgs Field.”  The particle that he proposes gets slowed down by the sticky syrup – err, by the Higgs Field – is called “the Higgs Boson,”  If I understand correctly, the Higgs Boson controls other particles, slowing them down and giving them mass.  And mass is what makes it possible for us to experience them.  Mass, for that matter, is what we and everything we touch and feel and smell and see around us has.  It feels like everything has mass, but that’s only because we cannot experience anything that doesn’t have mass, so things without mass feel like they don’t exist.

The Higgs Boson was nick-named the “God Particle,” because if scientists can find it, they can explain why the universe has mass instead of racing around in wild unconnected bits and explain how the universe – not to mention a leisurely cup of morning coffee – can possibly exist as it does. 

So, depending on your theological stance, discovering the God Particle whirling around for a split second or two in the LHC could explain how God created the universe with a Big Bang.

Is there God?

People who believe in God and those who don’t often find each other incomprehensible.  Even worse, they tend to think the worst of each other.  The believers fear for the salvation of the unbelievers, while the non-believers often secretly – or not so secretly – suspect believers of superstition, insecurity, and fear.

There is no possible final irrefutable proof either that there is, or isn’t, a God.   How, then, do we reach the conclusions which so many of us hold with such convictions?  This post is an attempt to look at a rational justification for either conclusion.

A Believer’s Argument

Many people who believe in God do so because we are here.  However far back one pushes the chain of events, there is always the question:  What or who caused that first event to happen?  How did the universe come into existence in the first place?  Even if you say “the big bang caused it,” one still is faced with the question “what caused the big bang?”  or “where did that infintessimal dot of energy that exploded into our universe come from?”

David Hume argued that events have causes.  Carried to its logical end point, this position leads many people to the conclusion that there must be a First Cause.  For believers, that First Cause is God. 

This doesn’t seem to me to be a wildly fanatic or illogical, neurotic, fear-induced conclusion.  In fact, it seems quite rational.  If it is, why then are there so many equally rational people who do not believe in God?

A Non-believer’s Argument

Many non-believers think that answering questions to which we don’t yet have an answer with “it must be God” does not have an historically very good record.  All sort of events and phenomenon which have been inexplicable in the past and so held up as proof of God’s existence are well understood now as natural occurences that do not require the direct intervention by God.  Volcanoes and tsunamis, the rising and setting sun, the  complexity of the human eye, a win on the lottery, or a lucky escape from an accident or illness have for centuries been alternately blamed on God or been a reason to offer prayers of gratitude.  But for many these events seem perfectly natural, often based on coincidence or chance, but not on God.  

What, though, about that First Cause?  What started it all in the first place?  Non-believers don’t answer this question with a being they call God.  God, for the believer, is eternal, infinite, beyond complete human understanding.  Why not, asks the non-believer, simply say it is the universe which is eternal, potentially infinite, beyond complete human understanding?

As far as the rational arguments go, it seems to me we can’t sling the epithet of irrational at either position.  Certainty, for those who possess it, seems to come from a different source.

No we can’t! The celebration of Pi

Pi is the circumference of a circle divided by its diameter.  Roughly speaking, that’s always about 3.14.  In American-speak, that’s today.  So today (I’m writing this on March 14th) is Pi day.

What I like about pi is that it is an example of the absolutely insolvable.  Pi isn’t exactly 3.14.  It’s 3.14 followed by an infinite stream of numbers.  Literally infinite.  So we can’t ever know exactly what it is.  It’s a prime example of the state of human knowledge.  Probably the inevitable, inescapable state of human knowledge:  we know a lot about it and can always learn more by generating as many more numbers after .14 as we have time and energy.

But we can never know it absolutely.  We can only know it “up to a point.”  There will always be more we can learn, and we will never reach the final Absolute Perfect Truth.

The elephant and the truth

A great number of people in the world believe they know the truth.  Many believe it with such passion and conviction that they are willing not only to dedicate their own lives to the service of this truth, but to kill and to die for it.  They know they are right and anyone who disagrees with them are wrong.

When I was a fairly young child, I asked my father if a story I’d heard was “really true.”   “What makes something true is a very complicated question,” he said, ”that takes great wisdom to answer.”  Then he told me the story of the blind men standing around the elephant.

Six blind men stood  around an elephant trying to discover what it looked like. The first one felt the elephant’s leg and reported that it was like a tree trunk.  Another grabbed its ear and said it was like a big fan.  The third got hold of the tusk and said it was like a large curved spear.  The one feeling the elephant’s side concluded that it resembled a large wrinkled wall.  The man who grabbed the elephant’s tail said it was a kind of snake, while the man at the other end who had hold of the elephant’s trunk said that it was some kind of water shower.

The men then started to argue, at first amiably, but as each insisted that he was right and had first hand experience to prove it, the arguments became more heated.  Each insisted that the others who disagreed with him were wrong, and gradually each began to insist that the others were not only wrong but also stupid, and even blinded by sinfulness.

This story is thousands of years old and originated somewhere in the Far East.  Some scholars think it was Buddha who first told the story to illustrate his insight that none of us ever have the complete truth.  Truth exists, he believed, but most of us spend most of our lives like a blind man in front of the elephant – thinking that what we see is the whole truth, while we only see a small part of it.  

My father used to tell me stories like this when I was young, many of which I couldn’t really understand at the time.  The elephant story has remained with me all my life.  It has convinced me that whether it is science or my religion that is the source of what I believe, I have not yet reached that level of wisdom where I see the whole elephant – that is the whole truth.

So even when people disagree with me, and I can’t see how both of us can be right, it might just be that each of us is examining a different part of the elephant. 

It is an amazing world we live in, and all sorts of apparently opposite things can be true at the same time. 

Another reflection on the blind men and the elephant can be found at http://www.baus.org/baus/library/a_glimpse.html

Is Earth really at risk?

Scientists and activist groups are warning that Earth’s environment is rapidly becoming unsustainable.  Two weeks ago, a United Nations report compiled by leading scientists from around the world and confirmed by the governments of the UN countries issued the most dire warnings.

Are things really this bad?  If they are, why do so many people think that warnings about global warming and environmental destruction are just hype?  Are they right?  But if things really are as desperate as scientists say, what can we do about it?  Are governments doing enough?  Can what we do as individuals have a meaningful impact or does recycling our trash and insulating our houses merely increase our feel good factor? 

Each of these questions are so complex that I think I need to tackle them in parts.  Otherwise I will descend into fuzzy platitudes that we’ve all heard before.

The first question is whether warnings are based on sound scientific research or if they are motivated by governments, business, professors, and plain ordinary people (if there is such a thing) seeking to maximize their own gain. 

• George Bush says there isn’t much of a problem.  Is this because he and his friends are oil men?  because he believes that a world dependent on oil might be an opportunity for America, armed with Iraqi oil, to gain greater world-wide power? 
• Some businesses say there isn’t much of a problem, but an increasing number are saying there is.  Is this because they believe the researchers or do they think only that it’s a chance to make big money selling “green” products and services to a gullible, frightened world?
• Even scientists don’t agree with each other, and most are even changing their minds over the years.  Are they seeking career advancement by climbing on the “environment bandwagon,” or is their research truly convincing?  Whatever the reason, the majority of scientists around the world in fields as diverse as astronomy, geology, agriculture, paleontology, archaeology, forensics, economics, mathematics, and population say they believe the problems facing us are becoming dangerously challenging.  They all agree the questions are immensely complex, and by the time we understand them completely and know for sure who is right and who is wrong, it will be far too late to act.

Given the size of the risk involved, I think we have to assume that the scientists are generally right.  Assuming they are broadly talking about real problems, what are they?

There is a great deal more to worry about than the Earth getting warmer and thawing ice caps.  But rather than start out with the complexities of climate change, tomorrow I want to post some findings about our population growth and what it means for life here on Earth.

Can we calculate the probability of God?

In a book called “Dangerous Ideas,” an eminent scientist says that the probability that there is a God is very low.  As a scientist, I object.  How does one calculate the probability that there is or isn’t a God?

In scientific research, probability is calculated after one has gathered the data.  The conclusion that something has such and such a probability is shorthand for saying that there is an X chance (for example 1 out of 100 or 1 out of 2 ), that the results one has found in the sample used for the research can be extrapolated to a wider group.

For instance, if I pull ten pennies and five nickles out of a sack of a thousand coins, it is possible to calculate the chances (or probability) that the entire sack is filled with twice as many pennies as nickles, and that there are no dimes and quarters in the collection at all.  But what research data would a scientist analyze to determine the probability of God?  Science has no conceivable way of calculating the probability that there is or isn’t a God.  The question is simply outside the area of scientific competence. 

Some scientists believe in God and some don’t.  But scientists really should not try to use science to argue the case for or against the existence of God.  Any more than one should use religion to argue that the theories of quantum mechanics or gravity or relativity or evolution might be right – or wrong.  

I am quite convinced that any concept of God should be robust enough to survive the discovery that the universe is, for us humans, a shocking surprise.  Faith in God does not require that we deny evolution anymore than we need to deny that the earth revolves around the sun.