Tvindy

Infinity

Well, this is the day of the week when I publish some old work of mine. Lately I seem to be scraping the bottom of the barrel. There's just not much material left in this category, but I have a metaphorical spatula, and there's still a little bit of crap way down at the bottom. After all, there's no sense throwing out a barrel until it's completely cleaned out.

A few years back during one of my futile attempts to get a degree in Computer Science, I took a class called Discrete Structures. (I never did find out what that term meant.) One of the assignments given to us was a workbook exercise that asked us to define a set with an infinite number of elements. Each element had to be a pair of values, and one of them (but only one) had to contain the same value for both elements. I did it wrong.

I defined the first element as containing zero and infinity, respectively, with each subsequent element incremented by +1 and -1, respectively. So the second element would be (1, (infinity-1)). I defined the final element to contain infinity and zero, respectively. Going backwards, it would be incremented by -1 and +1 respectively. Based on my logic, there would be an infinite number of elements in the set between the two endpoints, since that's how many it takes to get from 0 to infinity, counting by ones, and vice versa. At some theoretical midpoint between infinity and zero, the two values would be the same.

But as I said, this was wrong. The professor explained to me that you can subtract any finite value from infinity, and by definition you still have infinity. That makes sense, because otherwise the value could not have been infinite to begin with. But it makes equal sense that if one subtracts 1 from infinity an infinite number of times, one would get zero. After all, infinity minus infinity must equal zero.

I found this situation extremely interesting, because on the surface it would appear to be just another one of those insoluble philosophical conundrums, where you have two mutually exclusive answers, but neither can be excluded. (i.e. Could God make a rock so large he couldn't lift it?) But I also accept that the professor knew what he was talking about but couldn't explain it without getting into mathematics that were beyond me. I'm in awe of the fact that such things can be grasped by the human mind using higher mathematics, and before I die I will at least master Calculus. (Although it may take me 20 years.)

Response to Comments on Yesterday's Post about "The Origin of Consciousness in the Breakdown of the Bicameral Mind"

I got some really interesting and insightful comments on yesterday's post. Since they require a lot of thought, I'll just respond to them in today's entry.

To Geoff: One problem I had summarizing the book was its use of the term consciousness. The book goes into it in great detail and describes various theories about it, but I couldn't get into all that in a brief post. Consciousness has a lot of definitions and means different things to different people. To my mind, no modern humans possess a fully conscious mind in the sense that so much of what we do is instinctive and not thought out. My impression is that there is a lot of stuff going on behind the scenes in my head that is completely hidden from me. But that's probably not what you meant by the term. For me, the difference between the consciousness of people today and thousands of years ago is a matter of degree.

The author also brings up the point that there is a detectable difference in the physical structure of the brains of schizophrenics. He speculates that the brain is so plastic that a young child brought up in a bicameral society might actually have the anatomy of his brain develop a little differently physically. (And of course that brings up the point that if that is so, what other configurations might be possible?) The issue of consciousness aside, the idea of being guided by hallucinations is intriguing, especially since early religions tended to describe constant direct contact with gods and ancestors, and then later religions portrayed the gods as being more removed and obscure.

You raise a good point about the Greeks describing themselves in terms of their beliefs. After all, the Iliad and Odyssey were epic poems and not documentaries. But it is interesting how much of those works revolves around gods appearing to individuals (never to groups) and telling people what to do. The author also suggests that muses were not just a symbol for literary inspiration; writers actually heard them and wrote down what they said. I don't have much of a classical education, so I can't really judge how different they were, but I remember reading more than once in the writings of C. G. Jung the idea that the ancient Greeks were actually far stranger and more alien in their thinking than most scholars are aware.

To Crawford Kilian: Thanks for the book recommendation (The User Illusion: Cutting Consciousness Down to Size). I've never read it, but I have read Consciousness Explained by Daniel Dennett, which seems similar. Instead of the veto concept, it deals with the bubbling-up theory which says that the subconscious is always releasing a myriad of tiny bubbles. The strongest ones grow and make it to the top (consciousness).

To Widdershins: That is an interesting idea. Whether or not that's true literally, what I've always found interesting about mind-altering drugs is that they cause a person's thought processes to work a little differently. Whether we like to admit it or not, we are all in a mental rut, constantly filtering everything through tried-and-true thought processes that are familiar to us. Once when I was in Amsterdam I tried some mushrooms, and was amazed how differently my mind started working. My thinking didn't appear to be less coherent, but it was very different, as if I was thinking with someone else's brain. I don't really advocate drug use, but I have to say that the experience did help to broaden my thought process by forcing me to think differently for a short period.

To Michael: Thank you for sharing that. I've never had more than brief encounters with people who are schizophrenic. I don't doubt that life must be very hard for them. Most people tend not to associate with people they see as different or can't understand. And a lot of people are easily freaked out. I've heard that in some tribal societies schizophrenics are venerated as having spiritual powers.

Thanks to all who left comments. (I love getting comments.) I'm not sure I believe the whole bicameral theory, but I find it very appealing. One thing I am fairly certain of is that there was some really weird stuff going on with people thousands of years ago. If nothing else, this book provides further evidence of that fact.

The Origin of Consciousness in the Breakdown of the Bicameral Mind

It seems I've been writing a lot lately about interesting theories on human evolution. Here is another one. Several years ago I read a book entitled The Origin of Consciousness in the Breakdown of the Bicameral Mind. It's worth reading just to be able to brag about having read a book with such an impressive title.

The author, Julian Jaynes, has an interesting hypothesis on the origin of modern consciousness. He believes that soon after acquiring language, human beings began to hallucinate. Back then, most of our intelligent thought took place in the subconscious. It probably still does today in the sense that we can be guided by our dreams or by sudden insights that appear from nowhere. But early man had far less awareness of his thought processes. According to Jaynes, once language had been developed, the subconscious used this ability to communicate directly with the conscious mind. In other words, people experienced auditory hallucinations that guided them by compelling them to act in certain ways. Through the development of religion, these voices came to be regarded as messages from the gods and the dead. It is very interesting to go back and reread the Iliad or Odyssey from this perspective, seeing the constant visitations from the gods as a neurological phenomenon.

This theory sees schizophrenia as a kind of throwback to that earlier mental state. In both cases, people hear voices which are so compelling and full of authority that they often cannot resist, even if they are told to do something terrible. The problem with modern schizophrenia is that the voices are almost always hostile and destructive. This may be due to the fact that to a fully conscious modern person, it becomes a struggle for control. The author does mention, though, that in giving talks about his theory, he sometimes encounters ordinary people who admit to him that they often hear voices, and have no problem with this fact. One woman told him that every morning when she does the housework she converses with her dead mother. So apparently there are some closet voice-hearers out there.

It's a very interesting theory, and I'm not sure that my post really does the book justice. Despite the title and length, it really is an easy and fascinating read. While the evidence is far from supplying incontrovertible proof, it is nevertheless well researched, and if nothing else, demonstrates that there was likely some very interesting transition state between when humans were mentally chimplike and when we started thinking like modern humans.

The Songbird Theory of Language Evolution

According to the Songbird Theory of the evolution of language, early humans first learned to sing, and only once they had become skilled at music did they begin to acquire actual language. They functioned much like songbirds, using elaborately crafted songs to attract mates. The more elaborate and complex the song, the greater the level of intelligence demonstrated and the greater the likelihood of attracting a mate. Natural selection would therefore have favored those who could best master complex rules of structure. This is how our ancestors developed the ability to handle the enormous complexities of syntax required to converse in everyday language. After that, it would not have been difficult to start adding meaning to the complex linguistic framework already in place.

Although this theory lacks any real physical evidence, there are a number of things about it that appeal to me. Firstly, I have studied several languages (which seems to be about all I do), and the deeper I get into a language the more amazed I am by its structure. Languages really are amazingly complex, far more so than is necessary for high level communication. (Check out the case system in Latin if you still have doubts.) Linguists are always uncovering new layers of subtlety in language, and there is no real hope that a single language will ever be fully described in all its nuances. If you were to analyze fully any conversation, even by the most uneducated individuals, you could write volumes about the structures that they use. Yet many people blather on endlessly using this immensely complex syntax while actually communicating very little. It's as if the syntax-creating structures in our brains have had far more time to evolve than the parts that convey meaning.

Also, there seems to be a prevailing view among linguists today that language arose suddenly fully-formed with no intermediate stages. This has always seemed ludicrous to me. If that were so, then we should be able to teach chimpanzees to communicate with fully-developed language just like us, if not by speaking, then by typing or signing. (They may be capable of some amazing communication using these methods, but it is not full-blown language, like in Planet of the Apes.) Linguists point to the fact that of all the thousands of languages and dialects spoken throughout the world, ever single one is fully developed and no less expressive than any other language. (Of course each one is specific to its cultural and geographic context.) Well, . . . duh! Obviously full language skills represent such an advantage that humans without such linguistic abilities would have long ago died out or taught themselves to master language. Just because there are no semi-verbal societies in the world today proves nothing. There are also no people in the world today who use stone hand axes, even though they were once commonplace. (We don't even know for certain how they were used, or for what.) The Songbird Theory provides us with an imtermediate step in human language acquisition -- probably one of many.

There is also the fact that music and poetry are universal to all cultures everywhere, without exception. This is interesting, considering that none of the other great apes are at all musically inclined. Music, even that which is accompanied by lyrics, seems to function different neorologically from regular speech. Some people who have suffered a brain injury, as in the case of a stroke, that causes them to lose the power of speech, can still sing perfectly well. So clearly, music is much more than just ornate speech.

For more information on this theory, check out this Discover article, which touches on it. For a more technical paper, go here.

Most Boring Post So Far

As most everyone who reads this already knows, every Tuesday I put up some old college paper of mine, thereby putting it into the public domain in the hopes that someday someone may find a use for it. (That's why people tend to steer clear of my blog on Tuesdays.)

Earlier today I was going through a stack of old floppies, most of which are no longer readable, and I came across the bibliography for my paper on the French subjunctive, which I posted last month. I had feared it was lost forever. Oh happy day!

Anyway, if you want to check it out (and I can't imagine why you would), you can click below to see it. (Hm, tomorrow's pic-of-the-week day; maybe I can post a photo of the bibliography.)

Aquatic Ape Theory

I've long been a proponent of the Aquatic Ape Theory, and it surprises me that it has never really caught on. Even after reading several criticisms of it with a fairly open mind, it still seems obvious to me that it must be true. I've just finished reading Elaine Morgan's most recent work on the subject -- The Aquatic Ape Hypothesis. In it she details the core arguments of the theory and responds to criticisms of her previous works.

I've wanted to post on this subject for a long time; I was just waiting to acquire and read this book to refresh my memory. Listed below, in no particular order, are the arguments that I find to be the most compelling:

• We love water. People enjoy going to the beach or a lake. Many have swimming pools behind their houses. And all the finest hotels have a swimming pool. It's not just that we are able to swim. Just about any mammal can do that if it finds itself in deep water. We seem to enjoy it immensely. That would seem to be a very unnatural behavioral trait for a mammal that never had its recent evolution shaped by a dependence on water. Certainly none of the other great apes share this with us. This alone makes the theory plausible.
• We're blubbery and mostly hairless. All of the larger aquatic mammals have lost their hair, just like us. And I really find it hard to believe that all this hair loss occurred as a result of mastering the use of fire. Even mammals that live in very warm conditions still have their hair. As a modern human with a heated home and access to heated buildings, I still experience plenty of occasions where I become quite cold, and it would be to my advantage to have a thick coating of fur.
• Human babies are fat, and they rapidly get fatter during the first few months of life. The other ape babies are born scrawny. If a human baby is placed underwater, instead of panicking, it will make its way to the surface, helped by its buoyant fat, and instinctively float on its back with its mouth and nose just above the waterline.
• Humans dehydrate much faster than other land mammals, and they are unable to store as much reserve moisture in their tissues. That's why doctors are always telling us to drink two liters of water a day. It's as if our ancestors lived most of their lives in a very water-rich environment.
• There are a number of intriguing human facial features that are not shared by the other apes. Most significant is that our nose juts out with the nostrils pointing downward, so we can submerse our heads underwater without the water instantly pouring into our nasal passages. It works like a diving bell. Also, we can flare our nostrils and make them bigger. This may mean that our ancestors' noses were closed by default and were only opened when their noses were intentionally flared. This is the case with sea lions. And it makes sense that we would quickly have lost this adaptation as soon as we left the water, since it would hinder breathing. Furthermore, humans have much more expressive faces than the other apes, who rely much more on posture and body language. That would make sense if we spent a great deal of time in the water with our bodies submerged and dedicated to the task of staying afloat. In that case, early humans would have to rely much more on facial expression to convey feelings and information.
• This is not mentioned by Elaine Morgan, but I think it's significant. About a year ago on PBS there was a documentary by a genetic researcher tracing the migration paths of early modern humans. (Sorry, I no longer remember the name of the program.) According to his findings, the first modern humans to settle outside of Africa followed the coastline eastward across Asia and ended up doing a bit of island hopping to reach Australia and Tasmania. What amazed me was that according to the researcher's interpretation of his genetic data taken from modern populations, this migration never strayed far from the coast. These people traveled thousands of miles over thousands of years and only established inland populations in Australia and Tasmania. How and why would they have done that without some sort of previously acquired aquatic adaptations. I realize that these were modern humans, nearly identical to us, and that the aquatic phase occurred and came mostly to an end millions of years ago in the time of Lucy, but it says a lot that early Cromagnons were so dependent on the sea. I should also say that the researcher did not mention the Aquatic Ape Theory.

Of course there are several additional arguments and further data beyond those listed above, but those are the arguments that I find personally to be the most convincing. Coupled with the fact that I can't see anything farfetched or highly implausible about the theory, I find it strange that so few people take it seriously. Much of that may have to do with the fact that Elaine Morgan does not have much in the way of academic credentials, but shouldn't the theory be evaluated based on its own merits and shortcomings rather than who its proponents are?

Books to Read When Pondering the Future of Humanity

The following post is a modified version of a reading list I posted to Amazon some time ago. I found each of these books to be absolutely fantastic. If you're at all interested in pondering the future of humanity, I would highly recommend reading all of them in the order presented here.

A good starting point is The Age of Missing Information. In the early 1990s, author, Bill McKibbon, had an entire day's cable programming recorded. This included 24 hours of each channel, totalling over 1700 hours of broadcasting. Over the following months, he watched it all. This book contains his reflections on what kinds of information television provides us and what it lacks. He compares what we learn from TV to the kind of information he is exposed to on a day of camping in the woods. And he reflects on the differences in the types and quantity of knowledge available to pretelevision generations as opposed to contemporary people, providing a good reflection on where we are today.

Next read Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan. This book was first published in 1994 but is still very current, because sadly, very little has been done in space since it was written. Sagan is very thorough. He discusses everything that has been achieved thus far in terms of spacetravel and exploration. He speculates about what will be possible in the future and the sorts of technologies that need to be developed. He gives a complete inventory of the solar system, including planets, moons, asteroids, and the Oort Cloud and what they have to offer future space travelers, both in terms of practical uses as well as intriguing unanswered scietific questions. He discusses encountering extraterrestrial life, both intelligent and not as well as travel between the stars in the distant future. There are many interesting tidbits here that you won't find anywhere else.

The third book on this list will absolutely blow your mind. It's The Age of Spiritual Machines: When Computers Exceed Human Intelligence by Ray Kurzweil. It explores the consequences of Moore's law (the observation that computer processing power doubles every 18 months) for the 21st century. Kurzweil argues that not only will computer power continue to increase exponentially throughout the next 100 years, but the rate of increase itself will probably increase. By 2099 there will be no distinction between human and computer intelligences. The vast majority of humanity will inhabit a completely virtual world in which our mental processes are accelerated a millionfold, and everyone is essentially immortal. I know it sounds like another crackpot book, but check it out anyway; the arguments are quite sound, and Kurzweil is a recognized technologist.

The Clock of the Long Now: Time and Responsibility: The Ideas Behind the World's Slowest Computer by Stewart Brand takes a much longer view of the future than Kurzweil. Brand is involved in a project to construct the world's first 10,000 year clock, a timepiece that, with occasional maintenance, will keep time for the next 100 centuries. The rationale is that such a project will influence people to take a much less shortsighted view of the future and consider how actions taken today may impact the distant future. The point is made that the effort required to effect change is usually directly proportional to how far in advance a change is attempted. This is especially relevant to environmental issues.

Now conclude your reading with Reason for Hope: A Spiritual Journey by Jane Goodall. In her latest autobiographical book, Goodall writes that people are often surprised and even skeptical when she tells them that she is hopeful about the future. This book is her answer to them. She reflects on her life from early childhood to her work in Africa, first with Leaky and then on her own, studying and working with chimpanzees, to her current environmental and educational work. She draws on evidence from her life experiences to argue that despite the frightening and precarious state the world is now in, she believes that humanity will ultimately have a bright future. (Why is it that half my posts turn out to be ape-related?)

Also of note is The Transparent Society: Will Technology Force Us to Choose Between Privacy and Freedom? I haven't read it yet, but based on the fact that it's by David Brin and was well-reviewed on Amazon, it's definitely a contender for this list.

On the web you can check out David Brin's essays about the future and Ray Kurzweil's enormous site dedicated to future technologies.

Happy reading!

Incredible Breakthroughs and Discoveries That No One Knows About (part 3)

Anything into Oil:
This is one of those things that's just too good to be true but nevertheless is. Researchers at Changing World Technologies in Philadelphia have refined a process known as thermal depolymerization, which can convert virtually any waste product into "high-quality oil, clean-burning gas, and purified minerals". We could, in theory, produce 4 billion barrels of oil just from our annual (US) agricultural waste production at $8 to $12 a barrel, which would be sufficient to completely end US dependence on foreign oil, while at the same time completely solving our waste problems. The process has no toxic or unusable byproducts at all. Furthermore, since none of the oil and gas generated from this process are taken from belowground carbon deposits (coal and crude oil), the net amount of carbon in the atmosphere would not be increased, and therefore use of the resulting products would not contribute to global warming. (So why has the federal government only contributed $12 million for R&D?)

My favorite line from the article:

If a 175-pound man fell into one end, he would come out the other end as 38 pounds of oil, 7 pounds of gas, and 7 pounds of minerals, as well as 123 pounds of sterilized water.

Quantum Computers:
How they are supposed to work is a bit beyond me, since it is based on quantum physics. But they are coming, and from what I understand, once they're perfected, we can throw Moore's Law right out the window (defenestration). They'll make today's supercomputers look like the abacus. From what little I understand, a functioning quantum computer can not only solve problems that today's machines couldn't even begin to tackle, but they form the solutions to those problems instantly (literally no passage of time). Once a problem is inputed, the quantum state of the processor is unable to exist in our universe in a state other than the one which represents a solution. In other words, its processing speed is infinite. And there is some notion about it existing simultaneously in every other state possible in a multitude of alternate realities. I should stop at this point, since I fear I am beginning to blather incoherently about something of which I have no real understanding. All I really know is that these machines will change the world in ways we can't even begin to imagine.

If you have a larger brain than I and would like to tackle understanding how quantum computers work, check out these links. I've listed them in order of increasing complexity:

• Quantum Computing
  
• Quantum Computers
  
• The ultimate no-brainer
  
• An Introduction to Quantum Computing
  
• A Shortcut Through Time: The Path to a Quantum Computer -- Amazon.com booklink
  

Incredible Breakthroughs and Discoveries That No One Knows About (part 2)

Life on Neptune?
Okay, this is extremely speculative, but I think it merits some consideration. In 1994 Carl Sagan wrote the following about the blue coloration of Neptune and Uranus:

Conventional wisdom holds that the absorption by methane and the Rayleigh scattering of sunlight by the deep atmosphere together account for the blue colors on Uranus and Neptune. But analysis of Voyager data be Kevin Baines of JPL seems to show that these causes are insufficient. Apparently very deep--maybe in the vicinity of hypothesized clouds of hydrogen sulfide--there is an abundant blue substance. So far no one has been able to figure out what it might be. Blue materials are very rare in Nature.

(Pale Blue Dot: A Vision of the Human Future in Space)

Sagan is careful not to speculate any further, but I can't help wondering if the blue substance might be oxygen. Oxygen is an extremely rare substance in Nature. The only phenomenon we know of that can create large amounts of it is life, and it doesn't have to be complex multicellular life, either. Simple bacteria could get the job done, and they wouldn't even have to have arisen there. A large comet or asteroid striking the earth billions of years ago would have been capable of sending chunks of bacteria-laden rocks into space where they bacteria would lay dormant until an eventual impact with one of the gas giants. This is not so improbable; bacteria are highly adaptable. In 1969 the Apollo 12 crew recovered a camera left previously by the Surveyor 3 probe, containing living microbes that had "survived launch, space vacuum, 3 years of radiation exposure, deep-freeze at an average temperature of only 20 degrees above absolute zero, and no nutrient, water or energy source." So the discovery of an unexplained blue substance on Neptune certainly does beg the question, yet strangely, it is a question no one seems to be asking. I've checked around on the web, and everyone seems to be giving the same methane-related explanation for the planet's blue color, the one that Sagan specifically stated in the above quotation nearly a decade ago could not account for it. (Examples can be found here, here, and here.) Perhaps some form of Neptunian conspiracy is at work.

Theory of Evolution Confirmed:
Until recently, I was very skeptical of evolutionary theory, not for religious reasons, but rather because it simply sounded farfetched. There is no question that evolution has been occurring; the fossil record is irrefutable. Over millions of years, life adapts to its environment by undergoing changes that eventually give rise to new and, in general, more complex species. My problem was with the mechanism. The idea that the entire process is governed by a combination of chance mutations and the principle of survival-of-the-fittest seemed utterly unbelievable, and there is no way to observe the process directly (at least not until science has been around continuously for a few million years to document it). Furthermore, there is no other known process in the natural world that behaves similarly. In other words, we know it occurs, but the theory as to exactly how it occurs seemed little more than guesswork. Then I learned about genetic algorithms, which are common knowledge only to people involved with Computer Science.

Basically genetic (or Darwinian) algorithms are computer programs that mirror the evolutionary process, as we understand it, to produce the design for a product through generations of simulations or to produce a new computer program. The process begins with a population of simple randomized representations. Each one is tested, and the ones that come closest to whatever the objective is have their traits combined together randomly to form the individuals of the next generation, along with a few random mutations sprinkled in for variety. Then the process is repeated again and again over successive generations. Examples of this are creating programs that allow computer generated characters to move realistically without having all their movements choreographed in advance
and designing robots that can locomote efficiently in the real world. (You can even download the program yourself to evolve your own robots.)

What's so intriguing about genetic algorithms is how accurately they mirror the behavior of evolution as seen in the fossil record. For one thing, there is a huge gain in complexity over the course of many generations. (There is a wonderful demonstration of this phenomenon here.) Also, there is a tendency for periods of stagnation over many generations with very little change, and then suddenly one individual is produced with a mutation that is so advantageous that there is a sudden developmental spurt in the population where the rate of change of the population accelerates tremendously as the new trait is assimilated, improved upon, and combined with new traits. Finally, the end product (the individual of the final generation which most best fulfills the criteria set forth by the programmer) is often of a level of efficiency and elegance that no human programmer or engineer could possibly match, or in many cases, even comprehend. Yes, that's right; using genetic algorithms, it is not at all uncommon for computers today to design/evolve chips that work better than anything a human could design and whose workings are beyond human understanding -- the very same situation we face in the study of biology.

So . . . maybe it's time I rethought my skepticism. It seems as though natural selection and survival-of-the-fittest can, in fact, account for the increasing level of biological complexity observed on the earth over time.

Breaking Ape News

For a blog that's purportedly "about nearly everything", it seems that this is quickly becoming an ape blog. However, I just came across some new (and quite disappointing) information on that CNN story about the newly discovered mystery ape. According to this letter by one of the researchers, the information previously released to the press is "far fetched" and "outdated", and the apes are almost certainly a subspecies of chimpanzee.

On the same page are a couple of supplemental links relating to the story. Check out the National Geographic article from last April and the preliminary DNA testing results.

A completely unrelated possible mystery ape encounter that has always intrigued me is that of de Loy's ape. Even if it wasn't an ape, it was certainly something unusual.