http://www.wolframscience.com/summerschool

We are looking for highly motivated individuals who want to get involved with original research at the frontiers of science. Our participants come from many diverse backgrounds, but share a common passion to discover and explore cutting-edge ideas. Over the past 10 years, they have included graduate students, undergraduates, professors, industry professionals, artists and even a few exceptional high school students.

If accepted to the Summer School, you will work directly with others in the Wolfram Science community, including Stephen Wolfram and a staff of instructors who have made significant contributions to NKS and Wolfram|Alpha. You will develop your own original project that could become the foundation of published papers or your thesis.

Take a look at the lecture notes from previous years to get a sense of what topics will be covered:

http://www.wolframscience.com/summerschool/materials

If you’re serious about getting involved with innovative ideas at the core of Wolfram Science and NKS, you should consider applying as soon as possible.

Apply online at:

http://www.wolframscience.com/summe…application.cgi

Filed under: The NKS Summer School ]]>

The back of the calf’s a great place for this 2-state, 3-color Turing machine. And hey, if you’re taller you can get more steps in the evolution!

For more great Wolfram NKS tattoo ideas, check out the lovely images generated by the hundreds of NKS-themed Demonstrations. Here’s a favorite of mine for that old chestnut, the flame tattoo:

Filed under: Turing Machines, Visual Art ]]>

We get a diverse set of applicants every year from fields such as computer science, mathematics, physics, biology, economics, finance, philosophy, architecture, music, linguistics, and other disciplines. Our accepted applicants have been undergraduates, graduates, post-docs, academics, professionals, and others.

The school is based on Stephen Wolfram’s book *A New Kind of Science*. Applicants are expected to have read the book, and be interested in its concepts. Read the book online.

To see some of what we do at the school, check out the NKS category of the Wolfram Demonstrations Project, and past years of the summer school.

Have questions? Send them to nks-summerschool@wolfram.com

Some NKS-themed Demonstrations:

Filed under: The NKS Summer School ]]>

The ninth annual NKS Summer School begins in just a few months, and we’d like to invite you to apply. The three-week, tuition-free program–June 27 through July 15 in Boston, Massachusetts–is a unique opportunity to get involved with original research at the frontiers of science:

http://www.wolframscience.com/summerschool

We are looking for highly motivated individuals who want to advance their careers in an NKS direction. Our participants come from many diverse backgrounds, but share a common passion to discover and explore cutting-edge ideas. Over the past nine years, they have included graduate students, undergraduates, professors, industry professionals, artists, and even a few exceptional high-school students.

If accepted to the Summer School, you will work directly with others in the NKS community–including Stephen Wolfram and a staff of instructors who have made significant contributions to NKS–on your own original project that could develop into published papers or the foundation of your thesis. You may also be eligible for college course credit.

Take a look at the lecture notes from previous years to get a sense of what topics will be covered:

http://www.wolframscience.com/summerschool/materials

If you’re serious about getting involved with similarly innovative ideas at the core of NKS, you should consider applying as soon as possible.

Apply online at:

http://www.wolframscience.com/summe…application.cgi

Filed under: News, The NKS Summer School ]]>

Wolfram Media today announced the release of A New Kind of Science (NKS) for the iPad, making Stephen Wolfram’s groundbreaking bestseller more accessible and mobile than ever before. NKS for the iPad is available on the App Store today for only $9.99.

The original NKS text has been converted into a sleek, easy-to-use mobile experience that goes anywhere on your iPad, making it more accessible to new generations of students, scientists, and big thinkers.

You will now be able to view 973 NKS illustrations more vividly than ever before using NKS for the iPad, which brings Wolfram’s revolutionary discoveries to life.

For more information about NKS for the iPad, please visit Wolfram Media:

http://www.wolfram-media.com/products/nksipad.html

To read Stephen Wolfram’s blog post about NKS for the iPad, please visit:

http://blog.stephenwolfram.com/2010/09/a-new-kind-of-science-is-on-the-ipad

Here are some screenshots of how the app appears on the iPad:

Filed under: Media, News ]]>

Maybe the math behind string theory is overrated anyway

So, we’ve reached a point where math can’t answer many questions in biology, but the most promising path for advancing physics (string theory) remains trapped in the realm of pure math. Is this a cue for panic? Maybe not, as illustrated in an exchange between two panelists: “You’re not upset because you’re not a mathematician,” Chaitin told Livio, “you don’t care because you’re a physicist.”

“We know there’s problems with quantum mechanics, but has that stopped anything?” Livio countered.

It’s not just quantum mechanics. Biology may have resisted easy quantification, but it has hardly slowed the field down. If math turns out to be just a tool (and a tool with some substantial limits), that may disappoint mathematicians, but it won’t necessarily slow down our ability to understand and model the natural world. This may be my background as a scientist talking, but that seems like the most important consideration, and I’m willing to live with a community of disappointed mathematicians in order to get there.

Filed under: Conferences, Mathematics, News, Philosophy ]]>

Here’s to a great eight years, and a great many more!

Filed under: News ]]>

http://www.complex-systems.com/

Simply go to the Abstract Archives and search for abstracts. Next to the title will be a link to the PDF download.

http://www.complex-systems.com/Archive/

This is a great resource for all those who want to explore these articles but don’t have access to a library with a subscription.

Let us know if you have any questions, and happy reading!

*(crossposted to the NKS Forum)*

Filed under: Journal of Complex Systems, News ]]>

Read the whole chapter here.

One way of seeing how the evolution of simple programs might have something to say about natural systems is to compare the images of growth, patterns, etc in natural systems with certain steps in the evolutions of particular cellular automata. Doing this, we see some remarkable similarities, which seem to—

“…reflect a deep correspondence between simple programs and systems in nature.” [p. 298]

Just as simple programs with different rules can have similar behavior (think Wolfram classes), so do certain systems in nature which seem very different behave in similar ways. The connection between the two comes down to components: whether it is built of molecules or black and white cells, the same universal features should be present in the behavior of the system — in other words, the mechanisms are the same.

Apparent randomness is common in nature. This section endeavors to explain how this randomness could emerge, by thinking of a natural process as the evolution of a simple program.

The result is three basic mechanisms for randomness: randomness introduced by interaction with the environment, randomness introduced by initial conditions only (no interaction, no intrinsic), and intrinsic randomness produced by the rules (no interaction, largely independent of initial conditions).

The first two mechanisms are dependent on the environment for the apparent randomness in their evolution. The third is not. Wolfram posits this third mechanism is responsible for a large fraction (if not essentially all) the randomness present in the natural world.

Example: a boat bobbing up and down on a rough ocean. However, the true origin of the ocean’s randomness may itself have a different mechanism.

Example: Brownian motion, say, placing a grain of pollen in a liquid, then observing its motion. However, the origin for the pollen’s randomness (constant bombardment by molecules of liquid) may have a different mechanism.

Example: A radio receiver producing noise, which in most cases is a highly amplified version of the microscopic processes inside the receiver.

However, it has been discovered that output from miscroscopic physical processes doesn’t always produce the best possible randomness, and in fact, output from devices meant to generate randomness at this level show significant deviations from randomness. More in general, interaction with the environment for randomness generation is imperfectly random, since the previous state of a device can influence the next state, so that the device is not in the same state when it receives each piece of input. QM states it takes an infinite amount of time for systems to “relax” to normal states, so we should expect that randomness generation in this manner is intrinsically imperfect.

Most generally, the environment-interaction mechanism for generating randomness is superficial since the randomness isĀ caused by some other random process, about which we know nothing except that it is “random.”

Exampe: roll a ball along a rough surface. The rough surface is unchanging, hence one can see it as the initial conditions for the path of the ball on which to roll, including the initial speed of the ball.

Such systems rely on their final state to be very sensitive to initial conditions. Other examples are coin tossing, wheels of fortune, roulette wheels, etc.

Some systems are so sensitive to initial conditions that no machine with fixed tolerances could ever be expect to yield repeatable results. This is the basis of chaos theory. Indeed, in recent years the mathematics of chaos theory has assumed that in practice, random digit sequences in initial conditions are inevitable.

However, this mathematical idealization is simplistic, considering that, in the example of a kneading machine, if one starts out with two points one atom apart, after thirty steps these two points would be one meter apart. This implies that one cannot make arbitrarily small changes in position, since atoms have finite size.

“And indeed in any system, the amount of time over which the details of initial conditions can ever be considered the dominant source of randomness with inevitable be limited by the level of separation that exists between the large-scale features that one observes and small-scale features that one cannot readily control.” [p. 313]

Example: Three-body problem

Example: The rule 30 CA:

The center column of rule 30 is considered random by most definitions, though there are some definitions of randomness which exclude randomness that is generated from a simple procedure. Wolfram argues, however, that if this definition were to hold most natural processes would be inable to produce randomness, when we know they in fact do.

Instead of defining randomness in that way, it makes more sense to define it as whether or not, given a particular sequence, one can easily determine from the sequence what the rules of its generation are.

“…the fact that simple cellular automaton rules are sufficient to give rise to intrinsic randomness generation suggests that in reality it is rather easy for this mechanism to occur. And as a result, one can expect that the mechanism will be found often in nature.” [p.321]

Wolfram postulates that whenever a large amount of randomness is generated in a short time, intrinsic randomness generation is the likely culprit. Also, intrinsic randomness generation is the most efficient way of getting randomness, as environmental randomness progressively slows the system with the addition of each new component.

One can detect intrinsic randomness by looking at its repeatability: if such randomness can be reproduced, it is likely intrinsic, because environmentally induced randomness would make a repeat run impossible, since the environment will change in each subsequent run.

EXAMPLE: Calculate the digits of pi. While they are seemingly random, you get the same answer if you start the calculation over, if you calculate it from atop a mountain, if you calculate it from the bottom of the ocean or from the atmosphere of Titan (good luck with that one!), and so forth.

elements, taking the average may make the system look smooth and continuous. For example, air and water appear continuous only because they are composed of such a large number of small, discrete components. However, the “key ingredient” that makes discrete systems with large numbers of components of appear continuous is often randomness.

Compare and contrast crystals (no randomness, appear structured and non-smooth), and non-crystalline solids, which appear smooth.

Random walks start with a discrete particle and then at each step of the evolution moving the particle left or right. Random walks can take place in as many dimensions as you like, with “left or right” being replaced by the direction of the various axes. So in one dimension it can move left or right or rather positive or negative along the number line, in two dimensions it can move {positive, positive}, {positive, negative}, {negative, positive}, {negative, negative} where each pair represents the direction along each axis, and so on.

With enough particles, random walks start to look smooth.

Other systems that look smooth given enough components are aggregation models, which are built by starting with a single black cell on a grid and adding one new cell on each step. However, the randomness involved in these examples are inserted from the outside at each step of the evolution of the system.

In these examples, the intrinsic randomness generations in the systems is able to make the systems behave in seemingly continuous ways. [p. 333]

However, not every system that involves randomness will ultimately produce smooth patterns of growth. “As a rough guide,” continuous patterns of growth seem possible only when there’s enough time over the life of the evolution, and small-enough scale changes.

As in the last section, we realize that discrete systems can appear continuous. The vast majority of traditional mathematical models have been based on such continuity. But in nature one also sees discrete behavior, like skin/coat pigmentation. This would seem to suggest that continuous models can sometimes yield behavior that appears discrete. For example, the discrete transition between water and steam when the water boils.

One can investigate such discrete transitions with one-dimensional CAs, by making continuous changes in the initial density of black cells. What happens is that when the initial density of black cells is less than 50%, only white stripes survive. When it’s above 50%, the black stripes survive.

In contrast to the approach of traditional science, programs immediately provide explicit rules instead of just working with constraints that have to be satisfied.

The problem with satisfying constraints is that, in practice, working out which pattern of behavior satisfies a given constraint usually seems too difficult for it to be something that routinely happens in nature. [p. 342]

Programs come with rules that explicitly tell you how a system will be worked out. Constraints don’t tell you the procedure for working out the system that satisfies them, however. A process based on picking out patterns randomly is incredibly unlikely to yield results even close to satisfying the constraints. Iterative procedures do better, but it usually only yield an approximate result, and often those procedures ‘get stuck’ during the iterative process and do not yield the behavior we’re looking for.

“One can look at all sorts of other physical systems, but so far as I can tell the storiy is always more or less the same: whenever there is behavior of significant complexity its most plausible explanation tends to be some explicit process of evolution, not the implicit satisfaction of constraints.” [p. 351]

In the book we’ve found that some programs show highly complex behavior, and others rather simple behavior like uniformity, repetition, or nesting. And there doesn’t seem to be any direct correspondence between the complexities of the rules and the complexity of the resulting behavior.

Most of the time we can’t tell from the rules what kind of behavior a system will exhibit. But sometimes, like in the case of complete uniformity in the rules (all states going to one state), we can. Repetition is the next simplest form of behavior. This will tend to happen with cyclic rules, like {State1 -> State2 -> State1}. Also, sometimes the basic structure of a system will only allow a limited number of states. The next simplest form of behavior is nesting. This process can be described by every element branching into smaller and smaller elements. The rules for these systems are scale-invariant, so regardless of the physical size, the rules applied are the same. But also there is a discrete splitting/branching in which several distinct elements arise from an individual starting element. Nesting can also arise as larger elements are built up from smaller ones.

These mechanisms are in some sense genuinely different, yet all can be captured by simple programs.

Filed under: The Summer School Series ]]>

Just a reminder to everyone that there’s still time to apply to the 2010 NKS Summer School, being held at the University of Vermont in Burlington, VT from June 21 – July 9, 2010.

This will be the eighth Summer School, and we’re confident it will be as successful as the last seven years.

Filed under: The NKS Summer School ]]>