It took us 500 years?

Do you know what the Chinese were building in 1100 AD? A three story high gadget called a Cosmic Engine. It was a water driven, escapement type clock that kept track of various aspects of time.  It took for granted the fact that the sun sits at the center of our solar system.  Five Hundred years later, the Catholic Church was threatening to burn Galileo at the stake for saying the same thing, thus committing two unforgivable sins; refusing to change and threatening to burn someone over an idea (no idea is perfect enough to justify that action).

We have to thank the Catholic church for it's monumental efforts to keep us in the Dark Ages. Thank God we have taken that kind of power away from them.

Evolution in the lab

If anyone tells you that there is no real-life proof of evolution, you can tell them this little story about evolution in the lab. It goes something like this:
 
Biologists were trying to figure out what first caused one-celled creatures to group together and become multi-celled creatures, or, creatures with bodies. One theory was that the molecules that glue cells together first evolved as a way for cells to latch onto other cells in order to consume them and that at some point it became prudent to be bigger so cells just used this glue to bunch up.

So, a chap with the unfortunate name of Martin Borass took an alga that is normally single-celled and let it live in a tank for 1000 generations. It continued to be single-celled. Then, he introduced a predator, a single-celled creature with a flagellum that engulfs other microbes to ingest them. Within 200 generations, the alga responded by becoming a clump of hundreds of cells.

Over time the number of cells dropped to 8 in each clump. Eight turned out to be the optimum number because they were big enough not to be eaten and small enough so that each cell could pick up light to survive. (This all took several years).

Perhaps the most interesting thing was that when the predator was removed from the environment, the alga continued to reproduce and form individuals with 8 cells. Another interesting point is that, since it was so easy to go from one cell to multiple cells in the lab, why didn’t it happen earlier in nature? Well, it turns out that compounds like collagen (the glue) takes a lot of energy to produce, energy derived largely from oxygen. It wasn’t until about a billion years ago that oxygen levels started to rise significantly, and that’s when bodies (muti-celled creatures) began to show up.

Rules of Engagement

War is made "civilized" by rules of engagement. This is where two countries, who obviously have a serious difference of opinion, decide to get together around a table and work out the rules they will "play" by as they try to cripple each other by killing off as many of the opposing forces as possible, in an orderly manner, of course.

Consider your situation as Canadian soldier in Afghanastan, however. You are part of a renewed offensive against the Taliban, however, you must do all you can to avoid killing civilians, and rightly so; far too many have died already. So when you are faced with a threat, it is incumbent upon you to first ask the person whether he is Taliban or not before shooting him. That may be tungue in cheek, but it doesn't fall far from the truth.

Suppose, however, you are a Taliban fighter. He doesn't care whether he kills civilians or not, his attitude is "kill them all, Allah will know his own", (I wonder who he learned that from). He also doesn't wear a uniform, instead, he tries to look as much like an innocent civilian as he can, and will continue to do so until the soldier with the red maple leaf on his shoulder asking what he is gets close enough, where upon he will pull out his gun and shoot him. Doesn't seem quite fair does it.

Who did the software?

Do you suppose that Microsoft provided the software for Toyota? I wonder. Do you suppose they never heard of "fail-safe"? Probably not. Great to be driving a Honda though.

Lets all worship the goat

Civilized life begins with coffee. Some would say it begins with beer, but they’d be wrong. It begins with coffee and ends with beer. We must thank a Goatherd, some Monks, the Arabs, but, primarily, we must thank a goat, for civilization.
 
It began in 850 AD when an Ethiopian goat got frisky after eating coffee berries. The goat herder noticed this and brought some berries to the local monks, who, after tasting them, threw the bitter berries in the fire, whereupon, the pleasant aroma made them try them again. They soon considered them a gift from God since eating the roasted berries allowed them to stay awake longer and get more work done. Later, the Arabs got wind of this wonderful thing, and, since they were not allowed alcohol, poured hot water over the roasted, ground up berries to make coffee.

Now we could venerate the Goatherd but no one knows his name. We could venerate the Monks, but we already have wine to thank them for. We could venerate the Arabs, but we already thank them for the alphabet. So it’s only fitting that we worship the goat for bringing civilization to the world. So here is a short history of coffee and the early temples devoted to it’s worship.

850 An Ethiopian goat gets high on coffee berries. The monks get high on the roasted beans.

1100 The Arabs first make coffee. (It took 250 years to get from roasted beans to coffee?)

1475 A year we should celebrate... the first coffee shop (temple) opens in Constantinople

1654 The first coffee shop in Italy

1607 Capt John Smith brings it to Jamestown. Apparently, however, it arrived in Canada earlier than that.

1652 First coffee houses in England (it costs a penny a cup)

1672 First Parisian café dedicated to serving coffee

1683 First coffee house in Vienna

1721 First coffee house in Berlin

1727 Brazil starts growing coffee from plants smuggles out of Paris

1750 Café Greco opens in Rome 1822 The French invent the espresso machine

1938 Instant coffee is invented in the US by Nestle thereby bringing coffee to its lowest point until Starbucks opens in 1971

1964 The fist Tim Horton’s opens in Hamilton Ontario
                                                      -.-

Currently, over 400 billion cups of coffee are consumed yearly throughout the world. I do my part.

Sandwich security

Did you know that you can buy plastic sandwich bags with fake mould spots painted on the surface? And why? Of course, to keep you lunch safe from the sandwich thief at work.

A Brief history of Shrodinger's Unfortunate Cat

It all begins back in 1905 when a chap called Max Planck found a simple formula that predicted the actual energy loss curve of charged particles rather than what Newton said it should be. However, Max's formula required a fudge factor, thereafter known as Planck's constant (h), which caused the energy to reduce in little jumps,

In 1905 to say Newton was wrong was scientific blasphemy so no one paid the least attention to Max's little jumps.

Except Einstein, who, in the same year, used Max's little jumps to explain the photoelectric effect, calling the emitted energy; photons. No one took them seriously either, not for another 18 years anyhow, and then they apparently got it all wrong.

Soon after that Ernest Rutherford fired some alpha particles through gold foil and found that the atom is mostly empty space with a small, hard, positive core, orbited by electrons.

Nobody liked his atom either: too unstable.

It remained unstable until 1913 when Neils Bohr used Plank's neglected constant to stabilize the atom, thus enormously expanding the realm of the little quantum jumps. This explained a lot of things about light.

Nevertheless, no one took this seriously either, except Einstein. They called it “number juggling”.

Things began to change, however, in 1923 when an obscure American physicist named Arthur Compton, found that light changed frequency when he bounced it off an electron. Not the sort of behaviour anyone expected from a wave, ergo, the photon must be real and light must be a wave and a particle. (this was called the Compton Effect, by the way).

Everyone perked up and said “holy shit” or words to that effect. And thus began the era of quantum double-think.

Louis de Broglie, a French physicist, then applied the Compton Effect to the atom and came up with the wave behaviour of the electron, thus providing it too with a dual nature.

Still not everyone was happy. Like Einstein, for example, who was quoted in 1923 as saying “Every Tom, Dick, and Harry thinks they know what the photon is, but they're wrong”. (he always seemed to be on a different path than everyone else). Also not happy was a guy named Erwin Shrodinger, who wrote to Bohr “...the whole idea of quantum jumps must simply be nonsense.”

So in 1925 while on a mountain vacation with his girlfriend (his wife stayed home), he embarked on a gallant effort to rid the world of the little jumps. He used de Broglie's “matter waves” to prove that energy moves smoothly from one state to another, not in little jumps. The result, instead, was that he laid down the basis for modern quantum mechanics, where things do, in fact, move in little jumps.

Everyone cheered, even Einstein for once in agreement, calling it genius, Planck called it epoch making. Shrodinger himself was delighted to think that he had gotten rid of the quantum jumping thing. Reality would never be the same.

Later, when what now passed for reality dawned on him, Shrodinger was heard to say: “If we are still going to have to put up with these damn quantum jumps, I'm sorry that I ever had anything to do with quantum theory”. If ever there was a reluctant hero, it was Shrodinger. Apparently he never accepted it.

Reality had to be put in its place. So in 1927, physicists met in Brussels, Belgium to do so. There they worked out a way for scientists to apply Quantum Mechanics to the physical world while ignoring the consciousness implications. It became known as the Copenhagen Interpretation, and is still the major interpretation in use today. It gets its name from the fact that Neils Bohr, along with Werner Heisenberg, from Bohr's institute in Copenhagen were its major designers. 

While there apparently is no “official” Copenhagen Interpretation, every version of it does state that: an observation produces the property observed. But, Bohr safely confined this action to microscopic particles only, and to a large extent it has remained there for the last 84 years, despite the fact that quantum theory applies to all matter, not just the microscopic. But it allows physicists to ignore the embarrassing entanglement of physics and consciousness and get on with their calculations.

It rests on three principles:

1. The probability Interpretation of the wavefunction:

Quantum theory does not specify a particle existence in addition to the wavefunction. The particle is the wavefunction; until you observe it, whereupon it latches on to reality. It's actual position in reality is where probability comes in.

Note that particle (or cat) states can be referred to in various ways:

Quantum state: The cat exists as a wavefunction or in superposition
Wavefunction: The cat is spread out as an energy wave.

Superposition: In quantum state but occupying two states or locations at once.

i.e. the cat is both dead and alive.

Normal state: The cat is either dead or alive, but in either case, it is “real”.
Newtonian matter: Ditto
Decoherence: The act of the wavefunction collapsing into “normal” matter.

2. The Heisenberg Uncertainty Principle

Really this is just a mechanical limitation: any observation of atomic particles disturbs them enough to prevent the disproof of quantum theory. Really, that’s an actual definition. (sounds like something invented by the Harper government).

3. Complementarity.

A difficult one. It apparently means that you don't have to observe the atom to know where it is, or rather to cause it to be somewhere. Your acquisition of knowledge (information) of where it is, is sufficient to collapse the wavefunction. It was Bohr's way of allowing physicists to ignore the consciousness connection to the “measurement problem” and get down to work. (More and more I think that Bohr would have been very comfortable in Harper's government.) It apparently means that if you put a stethoscope to the box and hear the cat breathing, you will have collapsed its wavefunction. (Bear with me here. I guarantee that this will not make any more sense later, in fact you could, by hearing the cat breathing now, cause it to have died sometime previously).

Its worth noting that some physicists consider the wavefunction simply as information, whatever that is. This idea seems to pop up quite often, especially amongst those trying to build quantum computers.

Actually the Copenhagen Interpretation also admits that observation creates a present reality and provides it with a past appropriate to that reality. In effect, our later choice of observation creates an earlier history (of the particle or cat) – we produce something backward in time. (hence smelling a dead cat in the box will have caused to have died sometime earlier.)

In 1987 several physicists decided that they would disprove the backward in time thing and thus disprove Quantum theory. Unfortunately for them, quantum theory's prediction that the later choice of experiment determined what the photon did earlier was indeed confirmed. John Wheeler, who had initially proposed the experiment said later that “Somewhere, something incredible is waiting to happen”.

Which finally brings us to Shrodinger's unfortunate pussycat. Back in 1932, a chap called John von Newmann thought up a test using Geiger counters and pairs of boxes (a test called the “Von Newmann chain”) that would prove that you can never, ever, actually see a particle in superposition.

An atom, in quantum mode, is fired through a partially reflecting mirror thus sending ½ of it's waviness into each box. The atom is therefore in quantum superposition state, that is, existing in two places at once, until you open one of the boxes to observe it, whereupon the wavefunction collapses (decoheres) and the atom materializes in one of the boxes.

Instead of looking into one of the boxes, you could, instead, open a hole at the end of each box to let the particle in its quantum mode out of both boxes to create an interference pattern on a screen. The particle would be either in one box only or would have been in both, depending on which way you choose to “observe” it.

Shrodinger was still unhappy, so a couple of years later he inserted a cat into the experiment to show how ridiculous quantum theory was. Which brings to mind other science concepts that were popularized by ridicule, such as the Big Bang.

The experiment involved Von Newman’s two boxes. The cat, of course, is placed in one box, isolated from the world, along with a Geiger counter which, when it detects an atom pulls the cork out of a bottle of cyanide, killing the cat.

When you open either of the boxes to observe the cat, the electron wavefunction will collapse into a particle in one of the boxes. If in the cat box, the cat will be killed, if in the other, the cat will survive. Until you looked, however, the cat was in superposition, i.e. both dead and alive.

If you take the cat test a bit further and don't look in the box until several days after you put the cat in the box and fire in the atom, you will find either a very hungry (and angry) cat or a very dead smelly cat because upon looking in the box you not only collapsed the wavefunction, but also created a past appropriate to the random result of either a dead or living cat.

This is, of course completely ridiculous. For several reasons:

1. The cat (and everything else in the box) would have to be in superposition state until you looked into the box. This is not possible since you cannot sufficiently isolate the contents of the box from the real world. Every macroscopic object not in quantum mode (the box itself for example) “observes” the cat. Even the cat's “entanglement” via gravity with objects outside the box would apparently be enough to collapse it's wavefunction.

2. The atom's wavefunction, upon entering the “box” containing the cat and Geiger counter becomes “entangled” with the enormously complex wavefunction of the Geiger counter (not to mention the cat) and is thus “observed” (entanglement is equivalent to observation because of the information exchange that takes place).

3. Thirdly; just do the experiment. You will always get either a dead or a living cat, which proves..... what? (not recommended if the cat means a lot to you or someone important to you)

It's very interesting that while Physicists will apparently nearly always admit to the measurement enigma, most are not usually curious about it. Some seem hardly aware of it even though they use quantum theory daily. Some get violent at the mention of it (Hawking , for example, although in his case the physical violence is limited). Even those that write about the enigma will often admit that they have gone for decades in their careers before becoming interested in it.

The main reason seems to be that quantum mechanics is enormously successful. No aspect of it has ever been proved wrong, it’s predictions are always correct. It works, and is used daily. Fully 1/3 of our economy depends upon it. Its not just an interesting theory, its the foundation of all physics. Thus the “shut up and calculate” approach.

In fact, careers have been destroyed when too much concern over the “measurement problem” is expressed. Only those wearing the armour of great success have been able to ask questions and survive, like Einstein, or Murray Gell-Mann who said when accepting the 1976 Nobel Prize for Physics, that Neils Bohr had brainwashed generations of physicists into believing the problem had been solved.

Einstein and Bohr never saw eye to eye on quantum mechanics. Bohr was a staunch defender and Einstein never wavered in his belief that there was more to say than quantum theory told. Nevertheless they remained very close friends to the end.

In 1935 Einstein published a paper along with two young colleagues (Boris Podolsky & Nathan Rosen) which became famous as the “EPR test” paper (after the first letters of their last names). The paper didn't so much claim that quantum theory was wrong, only that it was incomplete. It tried to show that you could in fact know the property of an object without observing it and that therefore that property was not observer-created.

Bohr, however, shot him down, but Einstein never accepted the rebuttal. At one point he apparently proclaimed "God is subtle but he is not malicious". Toward the end of his life, however, he said to a colleague in a letter: “I have second thoughts. Maybe God is malicious”.

That’s the way things stood for a long time. Then, in 1964 John Stewart Bell, a brilliant Irish Physicist, took a sabbatical to contemplate the quantum enigma more closely and the momentous result was “Bell's theorem” which most people ignored. It laid out a way to test reality and separability, i.e., to test whether things are real without being observed and whether objects could be “entangled” in such a way that effects on one can show up instantaneously on another far away.

John Clauser at Columbia U. was intrigued, and figured out a way to actually do the test. His experiments proved that the properties of objects in our world do have an observation-created reality and that there exists a universal connectedness, Quantum theory had survived its most serious challenge. Unfortunately John Clauser didn't. Apparently you can blaspheme in the physics world. His career was derailed because he had the temerity to question quantum theory.

However, a decade later, (in an apparently more receptive time) another physicist, Alain Aspect, in Paris, duplicated the experiments with more sensitive equipment and was able to produce an even more convincing result. Had Bell not died soon after, it is thought that he, Clauser and Aspect would probably have been awarded the Nobel Prize.

But it hasn't ended there. Physicists will almost universally admit that every interpretation of quantum mechanics involves consciousness, but they don't like it one bit. Apparently its one thing for physics to encounter consciousness, it's quite another to have to have a relationship with it.

And so the “interpretations” continue.

First came Neils Bohr's Copenhagen interpretation:

Which enabled physicists to confine observer-created reality to the microscopic, and ignore the fate of the cat.

Then came a host of others (and they still come):

Extreme Copenhagen:

Proposed by Aage Bohr (son of Neils Bohr and also a Nobel laureate) who took his father's interpretation further by claiming that atomic-scale objects do not even exist, so that no particles enter the box and the clicking of the Geiger counter, if indeed it does click, is simply fortuitous. (I kid you not). In this interpretation the cat starves to death, but we wouldn't see it anyway because photons don't really exist.

Decoherence interpretation:

Which somehow states that it all happens too fast for there to ever have been a measurement problem, and so they don't know whether the cat is dead or alive.

Consistent Histories (or decoherence histories):

Developed by Gell-Mann and Hartle, this one applies the decoherence interpretation to the whole universe, where, until recently, there were no observers to cause the cat's demise/continuance.

Many Worlds interpretation:

Originated by Hugh Everett in 1957, it maintains that when you look into the box, reality splits and the cat continues to live in one reality but dies in the other. This one is apparently favoured by many physicists. If you put the cat in the box, you should hope that your consciousness continues to travel along with the live cat to avoid the unpleasant encounter with its owner taking place in the other reality.

The Transactional interpretation:

Allows the wavefunction to collapse backward in time, meaning that the cat was probably dead when you put it in the box.

The Bohm interpretation:

Proposed in 1952, this one by David Bohm, apparently a bit of a maverick, simply assumes that particles do what Shrodinger's equations say they will and generates a “quantum potential” (whatever that is) to make them do that. The result is that the cat does actually die, and also continues to live on somewhere else and will eventually return to haunt you.

The Ithica interpretation;

Developed in Ithica New York by David Mermin at Cornell U. who claimed that it is a matter of separating subjective and objective probabilities. He is not sure whether the cat is dead or alive, but as soon as someone builds a quantum computer he'll be able to calculate the probabilities. It's worth noting here that probability is a measure of ignorance.

Quantum Information:

Liked by those trying to build quantum computers, this one states that the quantum state is not an objective physical reality, it is only knowledge (information). Apparently its sort of a twist on the Ithica interpretation. They'll also know the fate of the cat as soon as they get the computer built.

Quantum Logic:

States that instead of attempting to predict the fate of the cat, just open the box then set the rules of logic to fit the observed facts. It may be the most logical interpretation but not the most popular one.

GRW

by Ghirardi, Rimini and Weber. These guys just modify the Shrodinger equations to make all wavefunctions collapse randomly every so often. For atoms this would be every hundred million years or so. Since there are a very many atoms in the cat, one of them is bound to collapse just as you open the box, triggering the collapse of the entire cat randomly to the living or dead state, which doesn't really resolve the fate of the cat but could alleviate a lot Physicist's anxiety.

The Roger Penrose interpretation:

Penrose and Stuart Hameroff (an anesthesiologist) came up with a function of the brain called “objective deduction” whereby the “AND” function that allows the cat to be both alive and dead is turned into an OR function. This is apparently accomplished by, what other physicists have called, “pixie dust in the synapses”. And the cat? Well, it exists just as you might find it, either dead or alive, but in either case, it's definitely your fault.

And finally, the Henry Stapp interpretation:

Henry, bless his twisted little brain, invokes something he calls the “quantum zeno effect” (named for a Zeno-like claim: a watched pot never boils). And that's about where my understanding of it ends. I have no idea what happens to the cat.

Believe it or not, all of the above have been published in respected journals by respected Physicists. Some of them even speculate that our brains themselves might be in a constant superposition state. At the end of the day, however, apparently every interpretation of quantum mechanics involves consciousness. And the big questions are still with us:

1. What is consciousness?

2. And how does it affect reality?

A third important question is: why does collapsing the wavefunction produce a random result? (i.e. is it truly random or does it really depend one you where you catch the “probability wave” ?)

As Bruce Rosenblum (prof of Physics at U of California) puts it:

“Consciousness and the quantum enigma are not just two mysteries, they are THE two mysteries: the first, the physical demonstration of the quantum enigma, faces us with a fundamental mystery of the objective world “out there;” the second, conscious awareness, faces us with the fundamental mystery of the subjective, mental world “in here.” Quantum mechanics appears to connect the two”

I have my own theories. They are as follows (I'll spare you the mathematics):

1. Testing for consciousness:

Determining what consciousness is and what creatures may have it is apparently a big problem. I have a simple solution: if you can kill a cat by opening a box and looking into it, you have achieved consciousness. One has to be careful, however, in the (not so unlikely) chance that the cat's consciousness is of greater magnitude than your own, it may not be the cat who dies.

Bruce Rosenblum tells of explaining to a physics class the Alan Turin test for computer consciousness, whereby, “if you can carry on a conversation with it via a keyboard for as long as you wish and not be sure whether you are talking to a computer or a person, then the computer is conscious”. (Or, it may be that you are not - my observation). Anyway, after he told this, a young woman in the class objected to the principle, explaining that “I've dated guys who couldn't pass a Turin test”.

2. The “consciousness particle:”

I find it very surprising that physicists haven't yet fallen back on their old standby: when the going gets tough, create a new particle.

Physicists almost universally accept that observation produces the property observed, yet, to believe that this can be brought about by a purely mechanical brain unable to reach in any way beyond its own borders is ludicrous. A “consciousness particle” emitted by the brain would solve the problem, and just think of all the other problems that it might explain. Believe me, this is no wilder than some of those listed above. And the potential....well, I leave it to your imagination.

3. Maybe our perceptions are too limited:

There may also be something to the observation that we can only perceive our world in two ways: position and time. All of our senses can be attributed to these two. Speed is just a combination of the two. Sight is a function of photons coming in contact with our retina, smells, just molecules touching our smell receptors, etc. Perhaps there are those “out there” who are actually able to perceive superposition quantum states and to whom there is no “measurement problem”. Maybe they even have cats.

And finally:

If indeed consciousness can collapse wavefunctions, and if, indeed this collapse can spread so easily to other matter around it instantaneously, then, forget about the cat, just consider what we may have done to the universe the moment we achieved consciousness.

In fact, Roger Penrose and others have gone even further. It goes something like this: If the original conditions of the universe were chosen randomly, there would be only one chance in 10¹²³ that the universe would allow life (that’s far far less than the chance of picking a particular atom out of all the atoms in the universe). So we can tentatively say that it wasn't random. There would then seem to be very few possibilities left:

1. God: (An answer that leaves too many unanswered questions)
2. Multi-verse: i.e. there are many parallel universes, only a very few of which can support life, (There must be on hell of a lot of dead universes out there)
3. The strong Anthropic Principle: Which goes something like this: we set the parameters of the universe ourselves by reaching backward in time with our consciousness. (Don’t dwell on it too long, it will make your head hurt)

I didn't think these three up, believe me, and faced with a choice of the three I can understand why some would be tempted to pick # 1, although I think I'll keep looking for other alternatives.

Very prominent physicists have pointed out that quantum theory doesn't just apply to the small, but applies in principle to everything, and they go on to suggest that we may have in fact created our own “reality”. Even Hawking has said that finding the elusive Theory of Everything won't answer all the questions. He said: “ the usual approach of science of constructing a mathematical model cannot answer the question why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?”

I personally find it ironic that in the end, the only tool that physicists can use to understand reality is the one thing that they really don't want contaminating their equations; the human brain.

Esse est percipi (to be is to be perceived)

Lee Paulson

On the origin of life

On the origin of Life:  
An interesting news item popped up this morning. A Professor Chandra Wickramasinghe, Director of the Cardiff Centre for Astrobiology, who first propounded the theory of panspermia with Sir Fred Hoyle, claims absolute proof that the first microbes were deposited on Earth 3,800m years ago.  

He's not the only one to hold this belief. The venerable Francis Crick also held the idea that life was seeded from "out there". You can check it out at: 

http://news.bbc.co.uk/2/hi/uk_news/wales/south_east/8491398.stm  
 
The idea is not so far out actually. Astronomers have confirmed that gas clouds out there do contain organic molecules, and biologists keep finding extremophiles here on earth all the time.  I find it very curious that virtually ALL life on earth is based on the one blueprint... DNA. You'd think that more than one mechanism would have evolved, but not so, on this world so full of diverse life, DNA is all there is. Of course, pushing the problem out into outer space doesn't really solve it. If the first DNA molecules came drifting down from some interstellar gas cloud, why wouldn't some other kind of "life molecules" drift down as well? or is there only one kind out there too? or is it such a rare event that it only happened once in our 4 billion year history? 

Since it did apparently happen 3.8 billion years ago, rather early in the earth's history, one would rather expect it to have happened again, or is it just coincidence that it happened early in our history? The Drake Equation would indicate that such an event is very rare (although it refers to intelligent life only, and is, at best, just a guess).


The Drake equation states that:

where:

N = the number of civilizations in our galaxy with which communication might be possible;

and

R^* = the average rate of star formation per year in our galaxy

f_p = the fraction of those stars that have planets

n_e = the average number of planets that can potentially support life per star that has planets

f_ℓ = the fraction of the above that actually go on to develop life at some point

f_i = the fraction of the above that actually go on to develop intelligent life

f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time such civilizations release detectable signals into space.

New Blog site

Hi Guys: I'm going to try out this blog site..... looks good and I will be able to put my ramblings here without bothering everyone with my e-mails every day.