Missions to Mars through 2020

Mars Science Laboratory

This mission is scheduled to launch in late 2009 with a goal of adding to the knowledge regarding the current and past habitability of Mars, including a  search for organic compounds. After reaching Mars in 2010 and landing by a new Sky Crane method, it is projected to be operational for nearly two years. This mission is an important milestone in the exploration of Mars because it will:

• Land a large and heavy rover on Mars - a skill necessary to a future Mars Sample Return mission.
• Have the highest precision landing to-date.
• Travel a larger distance than any previous mission - up to 20 kilometers.

Phobos-Grunt

Scheduled to launch in October 2009, this lander will study one of Mars' two moons, Phobos, and return samples to Earth which should arrive in 2012. It will have the capability of executing a pre-programmed mission to collect and return samples even if communications with mission control is lost. Ten different types of microorganisms will be aboard for the round-trip from Earth to Mars in order to study the effects of long term space travel on them.

The Chinese probe Yinghuo-1 will accompany the lander for most of the trip to Mars. It will separate in August or September 2010 and enter a highly elliptical orbit around Mars. It will study Mars' external environment, including its magnetic field and ionosphere.

ExoMars

The European Space Agency (ESA) is currently working on its own rover, ExoMars, that is scheduled to launch in 2013 and land on Mars in 2014. This rover will have a drill that can dig deep into the Martian surface to look for water and organics.

Mars Sample Return

Support continues to gather for international cooperation, including NASA and ESA, on an unmanned mission to return samples from Mars around the 2020-2022 time frame.

Chris K. Haley, NestedUniverse.net. Subscribe here.

NASA Principal Investigator Says Perchlorate Is a Positive Discovery

The discovery on Mars of the perchlorate ion, ClO_4, "probably comes down as a positive rather than a negative" says principal investigator Peter Smith. However, other scientists were less optimistic about the potential. Michael Hect of NASA's Jet Propulsion Laboratory described the finding as "neither good nor bad for life".

Perchlorate ions form salts with elements such as sodium and magnesium, as well as the ammonium ion among others. Some perchlorate salts are in fact, not only compatible with life, but certain bacteria strains can use them as an energy source.

Chris K. Haley, NestedUniverse.net. Subscribe here.

White House advised of pending NASA announcement regarding "potential for life" on Mars

Update 8/5/2008: NASA has issued a press release which indicates the potential discovery of perchlorate on Mars, a chemical which may make Mars less habitable than previously thought. You can follow the Mars Phoenix team's twitter log here.

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Aviation Week is reporting that the Bush Administration's Presidential Science Advisor's office has been advised of information that NASA plans to release sometime between mid-August and September 2008 concerning the habitability of the Phoenix landing site and the potential for life on Mars. While not directly pointing to evidence of life currently or in the past on Mars, the information is apparently "far more provocative" than previous announcements confirming the presence of water.

Although the original mission was scheduled to end in late August, NASA recently announced that the Phoenix Mars Lander mission will be extended through September 30, 2008.

This information will be of concern to Oxford professor Nick Bostrom, because of his recent argument regarding the Fermi paradox and the implications that the discovery of extraterrestrial life would have for the human species.

Chris K. Haley, NestedUniverse.net

Upcoming Singularity and Artificial Intelligence Events of Interest

Update 8/4/2008: This list will be updated with new information going forward at the following location: http://nesteduniverse.net/events.html

Here are some events through the beginning of 2009 that are of interest to the Singularity, Artificial Intelligence, and Robotics communities:

Date	Location	Event
September 1-3, 2008	Palma de Mallorca, Spain	Artificial Intelligence and Soft Computing (ASC-08)
September 1-3, 2008	Tokyo, Japan	Eighth International Conference on Intelligent Virtual Agents (IVA 2008)
September 3-4, 2008	Hollywood, California	Virtual Worlds Hollywood
September 4-6, 2008	Bulgaria	13th International Conference on Artificial Intelligence: Methodology, Systems, Applications (AIMSA-08)
September 28 - October 1, 2008	Technische Universität, Dresden, Germany	11th European Conference on Logics in Artificial Intelligence (JELIA-2008)
October 2-4, 2008	Syros, Greece	5th Hellenic Conference on Artiifical Intelligence (SETN-08)
October 25, 2008	Montgomery Theater, 271 S. Market St, San Jose, CA 95113, USA	Singularity Summit 2008
October 26-30, 2008	Salvador, Bahia, Brazil	19th Brazilian Symposium on Artificial Intelligence (SBIA-08) 10th Brazilian Symposium on Artificial Neural Networks (SBRN-08) Brazilian Symposium on Intelligent Robotics (JRI-08)
November 3-5, 2008	Dayton, Ohio, USA	20th IEEE International Conference on Tools with Artificial Intelligence (ICTAI-08)
March 6-9, 2009	Arlington, Virginia	Second Conference on Artificial General Intelligence (AGI-09)

Chris K. Haley, NestedUniverse.net. Subscribe here.

Gödel's First Incompleteness Theorem and Gödel Numbering

My last post talked about Kurt Gödel's incompleteness theorems. Gödel used a technique called Gödel numbering to prove his first incompleteness theorem. This numbering system allows mathematical statements to talk about other mathematical statements - in other words, it is a meta-mathmatical system. Essentially, Gödel numbering can be thought of as a function that assigns a unique integer to every mathematical statement in a formal langauge.

For example, consider the arbitrary symbol mapping below. Note that symbol mappings do not have to be unique. In fact, an infinite number of these mappings can be created which still give unique Gödel numbers to all possible correctly formed formulas.

Symbol	Mapping
+	1
0	2
x0	3
^	4
1	5
x1	6
*	7
2	8
x2	9
=	10
3	11
x3	12
)	13
4	14
x4	15
(	16
...	...

In general,

#	3 * # - 2
x#	3 * (# + 1)
Symbol#	3 * # + 1

Note that multiple, infinite sequences of symbols can be mapped by interleaving them within the sequence.

For example, the formula

   (x₀ + 1) = x₀² + 2x₀ + 1

maps to the following sequence of integers:

   16, 3, 1, 5, 13, 10, 3, 4, 8, 1, 8, 7, 3, 1, 5

In order to encode this sequence, and therefore the original statement, as a unique Gödel number, the following function can be used

   GödelNumber(y₀,y₁,y₂,...) = 2^y₀ * 3^y₁ * 5^y₂ * 7^y₃ * 11^y₄ * ... * prime_n^x_n

with subsequent terms following the sequence of prime numbers. The fundamental theorem of arithmetic guarantees that any natural number greater than 1 can be written as a unique product of prime numbers. Therefore, the original sequence of integers can be recovered uniquely through factorization. Our example statement can be mapped to the number

   56629029375664829465377722129717491809291752044

   912537386056572882766616710654748547866653818880

Note that the number is broken into two parts for presentation only - it is in reality a single 95 digit number. Mathematical proofs can, in a similar manner, be represented by sequences of Gödel numbers called Gödel sentences. Now assume that all the Gödel sentences which represent proofs that are true can be listed in a sequence:

  a, b, c, d, ...

Encode the statement "this mathematical proof does not appear in the list of Gödel sentences" as a Gödel sentence. Can it be found in the list? Assume that it can. If so, it must be false, because it states that it is not in the list. Therefore, it must in fact never appear in the list. This means that it is fact a true proof, and since it does not appear in the list, our list of "all true mathematical proofs" is necessarily incomplete.

Chris K. Haley, NestedUniverse.net. Subscribe here.

Speculations on Gödel's Incompleteness Theorems, the Halting Problem, and The Simulation Argument

Kurt Gödel

Kurt Gödel was a mathematician whose 1931 seminal work was the proof that all formal mathematical systems of sufficient complexity are necessarily incomplete. In other words, there are mathematical statements within these systems that are true, but which can never be proven within the system itself. Gödel proved this by showing that statements can be created which state that they can never be proven within the formal system. While these statements are in fact true, they can't be proven so - if they could, by definition they would not be true!

An analogy is the sentence "This sentence is false". This sentence cannot be a true statement, because if it were, we would have to believe what it states - that it is false. Similarly, it cannot be a false statement, because if it were, it would be true.

Nick Bostrom

Nick Bostrom is the Director of the Future of Humanity Institute at Oxford who has authored a Simulation Argument. Essentially, it states that:

Unless one of the following statements is true,

• The human species goes extinct before reaching a posthuman stage.
• Humans never become capable of running (or desire to run) computer simulations of their history.

then we are most likely living in a simulation now.

Turing Machines and the Halting Problem

The halting problem is a question in computability theory which asks if an algorithm can be found that decides whether a program (a Turning machine) will finish, or run forever, once given a description of such a program and a finite amount of input. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. The ideas within Gödel's incompleteness theorems are quite similar to those presented by the halting problem.

Speculations

Suppose that the universe that we live in is in fact a simulation, and it is being simulated by the equivalent of a Turing Machine. What are the ramifications of the halting problem and Gödel's incompleteness theorems in this regard? The "Scientific and technological approaches" section of the Simulated Reality entry in Wikipedia has some interesting speculations on software glitches, Easter Eggs, limitations on processing power, and the Heisenberg uncertainty principle.

Chris K. Haley, NestedUniverse.net

Jill Bolte Taylor: Brain scientist studies her own stroke

Dr. Jill Bolte Taylor is a Harvard-trained neuroanatomist. At the 2008 TED conference in Monterey, she talked about an amazing experience of being able to observe changes in her own consciousness and perceptions as she was having a stroke. This experience forever changed her outlook on life in a positive way.

Welcome International Science Grid This Week Readers!

Welcome iSGTW readers - thanks for stopping by! If you are interested in subscribing by email or RSS, please click here.

Regular readers of Nested Universe may be interested in taking a look at the iSGTW site at www.isgtw.org. This weekly newsletter promotes grid computing and stories of grid-empowered science and scientific discoveries from around the world.

An article that I wrote, Distributed Computing and the Singularity appears in the March 19, 2008 edition.

Chris K. Haley, NestedUniverse.net

The Singularity Effect

The A.I. Effect describes a human cognitive bias to discount improvements made in the science of Artificial Intelligence. Problems that in the past that were seen as extremely difficult, or intractable, are now seen in retrospect as having obvious solutions which no longer need to be described in terms of artificial intelligence.

Similarly, I believe that a "Singularity Effect" describes the discounting of advances in other technology areas such robotics, genetics, nanotechnology, etc. Consider how some of these technologies would have appeared to an observer from even 50 years ago:

• A camera which can detect and focus on faces, wait for people to smile before taking a picture and (soon) associate individual faces with names for indexing and future searching.
• A neckband that translates silent vocalizations into speech. Although this device does not directly read human thoughts, two people using this device coupled with wireless capabilities would essentially appear to be telepathic - certainly to observers from decades past.
  
• A computer operating system which achieves continuous speech recognition at normal speech rates and with high accuracy. It continually improves its accuracy by training itself on the speaker.
• A neuroheadset which gives a computer a limited ability to read a game player's thoughts and emotions.
• A tool accessible from anywhere for free which can generally search the most important areas of human knowledge and translate it to and from the most widely used languages, all within seconds.
  

Welcome to the Singularity!

Chris K. Haley, NestedUniverse.net

Boltzmann Brains

Ludwig Eduard Boltzmann was an Austrian physicist who made important contributions to the area of statistical thermodynamics. He lived in the last half of the 19th century and proposed that the low-entropy (high order) universe that we live in is the result of a random fluctuation in a larger, higher entropy (lower order) metaverse.

Although Boltzmann's proposal was made in advance of quantum mechanics, his idea is similar to modern day theories that the universe arose from a quantum vacuum fluctuation. Quantum mechanics predicts that particles can spontaneously arise from the vacuum if they are short-lived. Even in a perfect vacuum, pairs of particles and anti-particles are constantly being created and destroyed. This is possible because the total energy of the particle anti-particle pairs is zero.

In fact, the total energy of the universe appears to be zero [Stephen Hawking, A Brief History of Time, chapter 8]. Particles have positive energy, and the negative energy represented by the gravitational field of the entire universe appears to be exactly enough to cancel out the positive energy of the particles.

This idea leads to a paradox. In a metaverse that is larger than ours, random fluctuations of the size to create a universe such as our own will happen. Due to the size and number of particles in such a universe, these fluctuations will be exceedingly rare. The anthropic principal - the fact universes will only be observed when they are hospitable to observers - makes the amount of time between such fluctuations meaningless. These fluctuations could be happening every quadrillion years, or once every googolplex number of years. Fluctuations of a much smaller magnitude that simply create one fully formed brain for a brief amount of time should be happening with enormously higher frequency than universe-creating fluctuations. Such brains would be the smallest possible creations that would give rise to a sentient observer and are called Boltzmann Brains. The fact that such brains do not appear to exist is called the Boltzmann Brain Paradox.

There are a number of ways out of this paradox. One of the base assumptions could be false. Perhaps there is no metaverse or such quantum fluctuations do not happen on large scales.

Or, it possible that the concept of the Boltzmann Brain is true and you are the only sentient observer in the universe right now, complete with false memories of a life which did not exist. False inputs to your brain only make it appear that there are other observers with you. If true, it's possible that you will cease to exist in just a ...

Chris K. Haley
NestedUniverse.net