Mathematical Artwork Thumbnails

The images below are thumbnails of mathematical artworks I had made. Click the image for greater resolution.

Intelligent Design Conjencture derived from Theory of Evolution

In order for the following Intelligent Design Conjencture to be true, several condition must be met :
- Theory of Evolution must be true.
- Evolution is Turing Complete.
- Evolution go faster in faster computational medium.
- Hard Artificial Intelligence are feasible.


A good scientific theory must be able to make prediction, which can be evaluated by observation.

The theory of evolution is a good scientific theory, its claim have been verified by observation of fossil records from the past. Theory of evolution predicts that some sentient beings given enough time is going to evolve intelligence, and human is but an example of such thing.

The time required for humanity from when they gain full-sapience to modern technology is roughly 200,000 year.

Evolution from sentience to partial-sapience or full-sapience require billions of years, and not all species succeed reaching it.

Given that a species capable of full-sapience, have good probability of existing and continue to develop their technology in the timeline required for sentient species to evolve sapience, it is highly probable that a species will observe powers possessing greater intelligence, by the time they reach sapience.

Which means that if we take a random sapient species evolving naturally from a universe-sized box, most of them are going to observe powers possessing greater intelligence, by the time they reach sapience.

A technological civilization of a sapient species may catalyze the evolution of other sapient species, either via natural intelligence catalization or artificial intelligence catalyzation.

This intelligence catalyzation process may be deliberate or non-deliberate.

Deliberate natural intelligence catalyzation happen if the technological species provolve, train or teach less developed sentient beings, to develop their technological capability.

Non-deliberate natural intelligence catalyzation happen if the less developed sentient beings watch and learn what already technological species does.

Deliberate artificial intelligence catalyzation happen if the technological species create artificially created intelligent agent having full-sapient capability.

Non-deliberate artificial intelligence catalyzation happen if the artificial intelligence results from unexpected result from an experiment conducted by technological species.

If a technological species happen to discover space travel, the extreme difference of condition between worlds may force them to deliberately catalyze the evolution of new intelligent species, for their economic or memetic purpose. Which means that a naturally evolved technological species, may catalyze the evolution of more than one sapient species.

Since evolution process go faster in faster computronium, most species are going to be the result derived from evolution inside faster computronium.

Naturally evolved brain is a faster computronium than natural chemical process and biological evolution of pre-sapient beings. The development of technology means increase in computation demand, which fuel the development of even faster and more effective computronium.

Which means that if we take a random species in this universe, there are higher probability that they are result of evolution in the ideosphere of a technologically advanced species, rather than purely the result of natural evolution.

Which means that if we take a random species in this universe, there are higher probability that they are created by a technologically advanced beings ( very far more advanced than the created species, bordering on godlike ), rather than the result of natural evolution.

Quadratic Equation Solver

Download a free Quadratic Solver here!!

Quadratic Equation Solver, is an educational program made to explain ways used to solve various problem related to quadratic equations.

The problems it capable of solving is the one, in the patterns like below :
-> x² + 4x + 6 = 0 , 2x² + 6x + 7 = 0
-> x² + 6x + 6 = 12 , 3x² + 1x + 1 = 25
-> x² + 2x = 30 , x² + 33 = -5x
-> x² = 25 , x² = -25
-> ( x - 3 )( x + 6 ) = 23 , ( x + 5 )( x +2 ) = 33
-> ( x - 3 )( x + 6 ) = 2x² + 25
-> etc

And from those equation, the program is capable of deriving the value of :
-> Determinant ( b² - 4ac ).
-> The roots ( x1 and x2 ) by using quadratic (abc) formula.
-> The roots ( x1 and x2 ) by using factorization.
-> Determining values like x1+x2 ( Sum of Roots ) , x1*x2 ( Product of Roots ) , x1-x2 (Difference between Roots), etc.

In order to understand about how Quadration Equation Solver works, just download the program and follow this tutorial.

After you open the program you will be presented several interesting mathematical applications and scientific topics. The URL can be clicked if you are interested about the article.

But if your primary goal is to solve a Quadratic Equation, you better continue to "Quadratic Solver" page.

Solving x² + 5x + 4 = 0 using factorization

There you will be presented several type of Quadratic equation, the program capable of solving. In the example above, I requested the program to solve x² + 5x + 4 = 0 ( watch, which radio button is on ), using factorization method ( watch, which check box is checked ). Then I click "Solve the Equation" button.

Factoring x² + 5x + 4 = 0

Unlike most Quadratic Solver, this program will tell you the ways required to get the answer, in detail.

So now, how can I ask for the value of Sum of Roots ( x1 + x2 ) and the value of Product of Roots ( x1x2 ), from equation like -x² + 3x + 4 = -2x²-2x ?

Just light up the second radio button to choose the form of equation you want to solve ( cyan ), and choose what you want to know from that equation ( red ). Then click "Solve the Equation" button.

And the program will tell you how to get the answer, like the example above.

If you happen to have some free time, re-visit my blog in the future to give some comment or advice about the program, by clicking the URL above inside the program.

You may also copy the program to your friends for free, but you may want to remind them to download the latest version directly from this blog.

Have fun using the program. :D

Provolution and Fongoli Chimps

Some animal lovers have known for a long time, that animals are not as stupid as people usually think of. It seems that this claim is not merely a hoax. The definition of a useful scientific theory, is that it must make a predictions, which can be verified by observation, and the theory of evolution, predicts that there are possibility that other sentient beings on Earth may someday become intelligent species, just like human.

When I was a 10 years old child, I made a comic series, which only I and my siblings read. The settings of the comic are about millions of years in the future, when human had perished, while arks filled with different species of animals was sent to the space. My comic was largely influenced by the polular anime and manga at that time, Doraemon (by Fujiko F Fujio) and Astro Boy (by Ozamu Tezuka). Even now, I still think that everybody, even adults, should watch the anime. There are some good memetic content in both manga, which later I recognize as transhumanism, when I come across a website, called Orion's Arm.

Kind of cartoon I draw when I was 10 years old.

Funny enough that in high school I grow to become a religious, there is a path that I feel must follow, which lead me to become a member of my high school's religious community. There, I met two of my best friends, who are still my best friends until now. At that time, I learned about Creationism, and even my first paper, I wrote in high school is about Creationism, opposing my previous evolutionary worldview. Creationism told that every living being in Earth was created to be perfect, during my study of programming, I learned that a perfect system, must be able to change and perfectly adapt to environmental change. So did I abandon Creationism ? Well, no, but I will tell more about that in later post.

So when I met a website called Orion's Arm, I was drawn to it by a concept called provolution, which basically means that you can make humanoid form of any animal and give them intelectual capability as well ( unplifting ). I suspect that this meme had infected me since fairy tales depicting talking animals was told to me.

Article about Fongoli Chimps from National Geographic website.

But this may not be just a fairy tale, since I read an article about Fongoli Chimpanzee ( Pan troglodytes verus ), written by an Assistant Professor of Antropology Jill Pruetz ( blog ), from Iowa State University.

In the article, it is said that Fongoli Chimps, had begin to hunt bush babies ( Galago senegalensis ) by using spears they made from the branches of local tree. What surprised me, is the fact that in the article, it is mentioned that the chimps sharpened their spear, before using them for hunting, which is a proof that they had invented tool making by themselves. The article is also present in Iowa State University news service and her paper. The spear the chimps used can be seen in her paper.

Funny enough that there are some difference between what happened with the chimps, and what mostly believed to be happened in human evolution. It is believed that in case of human, it is the male who hunt, while the female looks for vegetables, but in case of Fongoli Chimps, it is female who go and hunt. May be they haven't invented agriculture, yet. A more funny thing is the fact that the method of making spears seems to be more complicated, the younger the chimps are, which show that there are some ongoing technology development on the play.

The issue that I am currently interesting of is "what humanity, as their older full-sapient siblings should do ?". Should we let them develop their own technology at their pace, or should we teach them what we know ? Are we going to enter an age, where animals can talk and interact with us as equals ? Will our world become like how it be in the fairy tales ? Will one day we see chimpanzee and human, learning the same thing in the same school and classroom ?

I will be interested to know different reaction from different people, feel free to make an educated comment.

Characters from Utawarerumono, an anime depicting a world where animals have become humanoid sapient beings.

Cellular Automata

Several days ago, I read an entry about Cellular Automation in Wikipedia, which links to a page titled Conway's Game of Life. In that page I learned that there is a simple rule in Cellular Automation, capable of generating complex pattern. Since I had been interested in the concept for a long time, I made the program yesterday (April 1st 2008).

There are many rules, which can be used in a Cellular Automation program. A Cellular Automation's rule have to mention what neighborhood condition should be fulfilled, to make a cell born, unchanged, or dies. The image above for example, is generated using rule 1/1, which means that for each cell, having one neighbor is going to come to life, but will die of loneliness if it have no neighbor, or die of overcrowd if it have more than one neighbor.

You can see the lexicon of rules, and the possible outcome in this Index of Rule.

Gosper's Glider Gun (Rule 23/3)

One of the pattern in Cellular Automation that I'm fond of is Gosper's Glider Gun which use Rule 23/3. The Gun, continuously produce a glider, which is a pattern capable of traversing the map. Since the glider is going to leave away, as soon as its pattern emerged from the reaction in a Gosper's Glider Gun, the Gun appear to shoot, with a glider as its ammunition.

I used Gosper's Glider Gun, to make a pattern consisting of 16 Gosper's Glider Guns, to make a Collider above. The collision between glider are unpredictable. Sometimes they explosively annihilate, sometimes they calmly annihilate, depend on how they collide.

The Collider is not stable, it will slowly degenerate itself to become the pattern above. The pattern above consist of only p1-oscillator and still lives. ( For definition of p1-oscillator and still lives, see this
Lexicon Of Life ).

I had made the X-Collider above as well, using 16 Gosper's Glider Guns in 4 different phase. The X-Collider, will continue to make a lot of glider collisions, and exhibit chaotic behavior. Whether these will result in degeneration or oscillation, is yet unknown. I haven't tried to play it long enough.

By merging different pattern I found in this Lexicon Of Life, I made the Space station above from components such as gliders, glider duplicators, octagon IIs,
octagon IVs, non-monotonic spaceships, and sparky spaceships. ( See the definition of each component in the Lexicon Of Life )

Download Cellular Automata Installer here.

Credits

A Strange Mushroom ( Zombie Hand )

Some days ago, a strange plant grow itself in my garden. I know that Indonesia is a country rich in biodiversity, but most people, including me are ignorant about it. Anyway, Indonesia's biodiversity, never failed to make me wonder about how creative the nature is.

Because of the spongy structure of the strange plant, we decide that is is some kind of mushroom. The shape resemble a zombie hand, digging itself out from the its grave, which is the reason why I decide to give it it's current name, Zombie Hand. Another reason for it's current name we gave to it, is because we suspect, that the origin of this plant is its seed that had been dormant for years, inside the compost we purchased and place in that particular area of my garden.

The strange plant, attracted the attention of my whole family because it smell so bad, like dead fish or dead rat. Our curiousity however, doesn't let us to remove it, because it may turn out to grow into some interesting plant.

Some of my employees, told me that this plant have also grown in their home, but their version of the same plant is more colorful than the one grown in my garden. They also said that this kind plant, which grow in their home, also emit somehow unpleasant smell.

I would like someone to identify what is the scientific name for this strange plant, along with the name of their ordo, families, and genus. Everyone in my home is curious abot this particular plant.

What will happen if moon have its own moon ?

There was a question back in Yahoo!Answer, which catch my interest. The question was, what will happen if the Moon have a moon. Actually there can be more than one answer to this question, or may be there are unlimited number of answer to this question, since there are so many possibilities on the mass, the initial position vector and the initial velocity vector of the moon of the Moon.

For the sake of simplicity lets assume, that the name of the moon of Moon is Usagi( うさぎ , means rabbit, refering to old belief that there are rabbits in the moon ), which mass is 2.3221E20 kg, or about 3.88688E-5 Earth Mass. Then we can predict what is going to happen by using NCGS or PPNCGS Gravity Simulator

Stable moon of Moon

For Usagi to orbit Moon in stable orbit, it may not be too far from the Moon, or Earth gravity field is going to disrupt the orbit.

For example, if the distance of Usagi and Moon is about 24544 km, and the orbital velocity of Usagi is 447.559 m/s, the orbit of Usagi around Moon is going to be stable.

Geocentric orbit path

Lunacentric orbit path

Unstable moon of Moon (Newtonian Simulation)

1. Geocentric Trajectory

But if Usagi is too close to Earth, then Moon is not going to have its own moon for a long time, since the orbit of Usagi is not going to be stable.

For example, if the distance of Usagi and Moon is about 64544 km, and the orbital velocity of Usagi is 275.991595 m/s, the orbit of Usagi around Moon is going to be unstable.

Usagi is going to escape it's Lunacentric orbit right away, since earth have higher mass and thus, stronger gravity field. Between time 0 until month 8 day 22, Usagi will orbit Earth twice in not so eccentric orbit, and twice in highly eccentric orbit.

Then between month 8 day 22 to year 1 month 7 day 5, Usagi will orbit Earth several time, inside the Earth-Lunar space, then move to higher orbit, and orbiting earth 5 times.

During the period between year 1 month 7 day 5 to year 2 month 9 day 22, Usagi will continue to orbit earth chaotically, moving between orbits in Earth-Lunar space.

During the period between year 2 month 9 day 22 to year 3 month 5 day 20, Usagi will orbit earth, as high as the Moon itself.

2. Lunacentric Trajectory

In order to gain more understanding about what is happening, we should see it from different point of view, that is why we need to see the orbit of Usagi, from Moon's point of view.

As we could see, Usagi is going to be pulled right away by earth gravity, form its Lunacentric orbit. Notice that the path of Usagi is chaotic since the first time, up to month 2, until it escape to higher orbit, with higher eccentricity.

Since between month 2 and month 8, Usagi didn't orbit Moon anymore, but orbit Earth in highly eccentric orbit, while the Moon continue to orbit Earth as if nothing happened, the path of Usagi relative to Moon, show retrograde motions, just like the path of any bodies relative to other bodies in a celestial sisterhood.

The path of Usagi relative to Moon, during month 8 to month 12, take my interests, since the plot result of Usagi's motion, somehow draw a face in the space between moon and earth. Looks like the face of a cute dog to me.

Between month 12 and year 1 month 11, Usagi orbit earth in relatively stable orbit. In that period, the path of Usagi relative to Moon, show common retrograde motion.

Instability begin to occur in Usagi's path after year 1 month 11. During the period between year 1 month 11 and year 3 month 5, Usagi continue to exhibit chaotic movement, sometimes dangerously close to Moon.

Unstable moon of Moon (Post-Parameterized Newtonian Simulation)

After trying to simulate what is going to happen using NCGS, I am curious abuot what is going to happen if I use my other Gravity Simulator, the PPNCGS which take relativistic effect into account.

Just link the simulation result of NCGS, the PPNCGS simulation result also shows, that Usagi is going to "take off" to higher Geocentric orbit, in month 2.

But the simulation result after that predict different movement of Usagi. PPNCGS simulation result, predicts that Usagi is going to orbit Earth in highly eccentric orbit, for about 5 times, during the period of time between month 2 to year 1 month 3.

Then PPNCGS simulation result, predicts that Usagi is going to orbit Earth in close orbit, during the period of time between year 1 month 3 to year 1 month 7, Moon gravity field, throw Usagi away from its orbit.

Between year 1 month 7 and year 2 month 9, Usagi is going to occupy different orbit, around Earth, changing its path as it encounter Moon in close distance, and being thrown by Moon's gravity field.

After year 2 month 9, Usagi is going to orbit earth in close distance, until the 2.3221E20 kg object finally collide with Earth in year 3 month 3.