Briefly, the "interplanetary superhighway" is a term used to describe the network oflow-energy trajectories connecting the planets and moons of the Solar System. The trajectories on this "highway" are used by natural objects like comets and near-Earth asteroids and can also be used to design fuel efficient spacecraft trajectories. A good recent article on this appeared in an April 2005 edition of Science News and can be found online. I have a depository of some articles, etc here.

Chaos theory is the mathematical field of study that attempts to explain the fact that complex and unpredictable results can and will occur in systems that are sensitive to their initial conditions. Such systems include weather patterns, the stock market, fractals, planetary physics, and the motion of some asteroids, comets, and even planets.

The classic paradigm of chaos theory is the Butterfly Effect -- a butterfly in China flutters its wings, which triggers a huge, complex series of events that results in a tornado in Texas. Chaos theory explores how a tiny aberration in initial conditions can drastically change the long-term behavior of a non-linear, dynamic system.

In mathematics, chaotic systems aren't random -- they're just very hard to predict. Chaos, understood this way, is not the absence of a pattern, but the presence of a very complicated pattern.

The reason is that chaotic systems evolve according to rules, thus they are deterministic -- meaning that the outcome depends on the initial conditions which evolve according to those rules. Let me explain further.

The idea embodied by deterministic chaos in a system (such as the motion of several planets about a sun, or the weather here on earth, or the stock market, etc.) is the following:

I suppose you, yes even you, are an example of a chaotic system. You're much more complicated than the weather! Someone might think they know your "state" (your initial condition) and they might even know the laws governing how your state (moods, thoughts, ambitions, etc.) changes with time. But any imprecision in the measurement of your state will lead to total unpredictability in a short amount of time. This is part of what makes interpersonal interaction so interesting - people are unpredictable and it's interesting to see what they'll do next. It's also why dropping balls on to the floor or throwing them up in the air is quite boring - the system is simple and not very chaotic so we know exactly what the ball will do.

For further reading on the subject, I suggest Matthew Trump's "What is Chaos? A five-part online course for everyone." Dr. Trump is a professor at the Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems at the University of Texas at Austin. Or try James Meiss's nonlinear science FAQ. Dr. Meiss is a professor of Applied Mathematics at the Univ. of Colorado at Boulder.

For those who are interested, I've also come across an interesting article regarding theological reflections on chaos theory.

You can think of a manifold as a curved surface that might be of any dimension. Click here to see a picture of a two dimensional manifold which twists around in a complicated way. Mathematicians like to use manifolds because you can compute useful things using them, like the force of gravity, the weather, and why cats always land feet first. Manifolds come up a lot in physics; enough to make one say, What isn't a manifold?

You can find out from my papers and movies.

Motivated by a question by Jenny Smith's brother, Joey Smith, I started to write some ideas about this question. This is a first attempt at an essay.

To echo the words of NASA administrator Sean O'Keefe, the space agency needs "not an either/or but a combination" of unmanned and manned flights. President Bush's new budget for NASA gives about $5.6 billion to space and Earth science (unmanned missions) and human space flight -- meaning the International Space Station and the shuttles -- gets $6.2 billion.

Unmanned missions have one crucial advantage over human space flights, one this is ever in our mind after the Columbia tragedy of two months ago: Failures are embarrassing but not fatal. Furthermore, robots don't need astronomically expensive safety systems, so the dollar loss is less when a spacecraft goes awry.

Some unmanned missions are important for purely scientific reasons, like the Hubble observatory. But others are seen as 'scouts,' which are paving the way for future human explorers. Several missions to the Moon, Mars, or more exotic places like asteroids and Jupiter's moon Europa, have as part of their plan a determination of places which would be best suitable for human presence.

But let's get to the crux of your question: 'Why should we even engage in manned space flight?'

Motivation. Like it or not, we live in a world where people are motivated by manned space flight. It's part of our desire to explore and adapt to exotic places where we (biologically) "don't belong". If we remove this motivation, less will be accomplished because people will be less motivated. It is difficult to measure the dollar-worth of motivation, but it is significant. Without manned space flight as a goal, I would expect NASA's budget to be cut by a large fraction.

Research. Unmanned space probes still have limitations. Humans can conduct valuable field studies far better than any probes. Manned space travel has offered a wealth of biological and medical information that can directly help humans on Earth. Although unmanned probes and satellites are very useful to space exploration, manned space missions are essential to developing a thorough understanding of a particular region or planet.

Field Studies. Astronauts are able to conduct field studies, which require observation in the field, the creation of a conceptual model, and the formulation and testing of hypotheses. Field study is not a simple matter of collecting data: it requires the guiding presence of human intelligence. Human intelligence is needed throughout a field study, as the requirements might call upon humans to change their course to fit their needs. For example the Mars Pathfinder discovered an unusual, silica-rich type of rock, but because of the probe's limitations, NASA could not determine whether this composition represents an igneous rock, an impact breccia or a sedimentary rock. Another example was the USSR's unmanned Luna missions, which brought back moon rocks during the 1970s. Although the Luna missions were much cheaper than the Apollo missions, the results were virtually incomprehensible because the Luna robots picked up rocks indiscriminately; the Apollo missions had the knowledge and insight of the geologically trained astronauts to decide which rocks were of scientific interest and which rocks were not. Fields studies, which require human presence, can be of great value to the scientific community.

Medicinal Research. Another benefit of manned space travel is the medicinal research that can be conducted. Manned space exploration offers valuable research into many medical fields, such as bone loss, cardiovascular alterations, sleep and human performance, and muscular atrophy. Outer space is a distinctly different environment compared to anywhere on Earth, and the effects of microgravity and days that last an hour and a half give researchers many opportunities to study how the human functions under these conditions. The research that is performed in outer space helps people on Earth with many different medical conditions, including osteoporosis, heart disease, sleep disorders, muscular atrophy, and numerous other related illnesses. Manned space exploration offers many benefits to the people of Earth through scientific research in medicine.

Applications. If manned space flight can be made routine, cheap, and easy, suborbital flights might become routine cheap and easy. How much would you pay for a ticket to Australia on a one hour flight? There is almost certainly a large market for suborbital flights, if we can make the cost and danger sufficiently minimal. Organizations such as the X-Prize Foundation have been actively promoting the development of manned space vehicles by private industry to be operated on a commercial basis. The X-Prize challenge is to construct a vehicle capable of sub-orbital flight with three passengers, with the constraint of only allowing 10% of the vehicle dry mass to be expendable, and a turn around of 14 days to re-launch. There is also the possibility of more space tourism. We've already seen two examples of multi-millionaires paying about $20 million for a visit to space about the ISS. In a recent survey, about 30% of Americans, Japanese, and Europeans said that they would be willing to spend a quarter of a year's salary for a trip into space. So if the price for a ticket to spae could be lowered, this market could have tremendous potential. (see spacetoday.net/tourism)

War. We have never had war in space, but if war comes, any space-faring nation or coalition of nations will desire the upper hand. One important question is: are humans helpful to war in space? The answer at the moment is possibly yes. Currently computers have a very limited ability to plan and cope with unforeseen events. They will cease functioning if they fall out of communication and they are possibly even prone to subversion. Humans are much more adept at coping with unforeseen and inimical conditions. (see spacewar.com)

Capability. There is some difficulty in assessing the value inherent in having a capability. The cability to send men into space is inherently valuable, just like any other capability. Some unforeseen problem might arise requiring men in space. While this value is difficult to assess, it should not be ignored.

Final Thought. Manned space travel has evolved considerably since Yuri Gagarin became the first man in space on 12 April 1961. In the past forty years, there were manned missions to orbit, to space stations, behind the moon, and even to the moon's surface. Manned space travel offers the opportunities for scientists to conduct valuable field studies, as well as helping medical professionals better understand the human body. Unmanned probes and space satellites can still be used for many functions such as preliminary reconnaissance missions to collect general data on a planet or region of space, but they cannot replace live humans who can use intelligence to conduct much more detailed and ambitious studies. It would be foolish to discount the uses of both unmanned space probes and manned space missions entirely. It is important for the scientists at NASA to consider the advantages and disadvantages of both manned and unmanned space missions to accomplish their desired goals.

I just do. Maybe it's because there's more stuff in space than on Earth. It stirs my imagination. And no, it isn't empty. You just can't see what's there.