let's call this a nice morning

i open my eyes, flat white sky
yawn, a cat stretches its body nearby
open sill, greenery with spills of gold
with hummingbird, sight and sound, behold!

hello world! some device lit up on top of wood
i sat to write something, wishing i could
"nice mornin'", some simple sequence appeared
something more, but then nothing followed, and so i jeered

after the hinges folded, out of the enclosure, i bolted
with the sound of footsteps, as i look around, the waiting balcony came near
there! i think i saw, after persuading the trees, the cool breeze greeted
"nice mornin'", as the breeze passed by, but then I have no words to spare

the houses beamed as the street welcomes the day
some two-foot passed, and then a four-foot, as the street cheers
i just stared and dreamed, fleeting thoughts as the clouds swept away
yes, it's a nice mornin';  all i could utter after these years

behind me the steps ascended, while quiet ground lay ahead
rusty bars amidst crawling leaves, new horizon unveiled
rubber on rock, i met the street as the sun pat my head
nice mornin', i sighed, as i set off to the field

ordinary special morning isn't it?
day by day, nothing has actually changed
though everyday, i knew every morning's different i think
it's just that, it's just that... short for words, "nice mornin'" is all i can say


crude verse, 2014

an attempt to be more mathematical (a look into Gödel's first incompleteness theorem)

Gödel's first incompleteness theorem:

"To every ω-consistent recursive class κ of formulas, there correspond recursive class-signs r such that neither (_vGen_r) nor Neg(_vGen_r) belongs to Flg(κ), where v is the free variable of r" (Gödel 1931).

I don't have much to say on this one so let's take a look at a more understandable version found in Wikipedia, quoted from Kleene 1967, p. 250 (Stephen Cole Kleene, 1967, Mathematical Logic. Reprinted by Dover, 2002. ISBN 0-486-42533-9.):

"Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory."

Now, I will make an attempt to outline the proof in the perspective of a machine.

Assuming that there is a truth machine capable of determining the truth of every statement S recognizable by the machine.  Let tM be this truth machine, and let tM(S) denote the truth of a statement S given as an input to tM. In this case, tM(S) will return either "true" or "false".  It will return "true" if the statement is true, and "false" if the statement is false. Let L_tM denote the set of statements recognized by machine tM; in this case, S ∊ L_tM.

Now, what if we are given this statement:

G = "tM will never say G is true", G ∊ L_tM.

• If tM(G) = "true", then this means that statement G does not hold, and G is therefore false. In this case, tM has just returned the wrong answer.  
• In order for tM to be correct about G, tM should not return "true" for statement G.  It therefore follows that what is being stated in G is the truth that tM cannot return "true" for statement G.  This makes statement G true, but tM cannot say that it is true. 

The explanation above shows that there exists a true statement in which tM cannot say that it is true.  Relating this to the paraphrased version of the theorem above, tM represents the formal theory, and G corresponds to a true but not provable arithmetical statement in the theory.

This theorem has controversial philosophical consequences since it follows that not all true statements in a particular formal system are provable under that system.  Extend this to mathematics as a formal system, and you might realize that not all true mathematical statements are provable under mathematics.  Similarly, if you consider courtroom language as a formal system, then there exists true statements in the witness stand that are not provable using the courtroom language.  However, Gödel's first incompleteness theorem doesn't exactly mean that there are certain truths that are not provable, since essentially it only exposes limitations in the "proving power" of formal systems.  At least, one can see that in the attempt of proving everything that are considered true poses the risk of facing the infinite and confronting the limitations of the human mind (that is the case if you consider the human mind as a formal system).

If you think there is something wrong with the above's attempt, just ignore this article and check this reference instead:
Rudy Rucker, 2004, Infinity and the Mind: The Science and Philosophy of the Infinite (Princeton Science Library).

When Fermi Paradox Invades One's Imagination

What we know about the universe is that it is vast, old, and growing in size.  How old? One estimate is that it is about 14 billion light-years old (http://www.space.com/25325-fermi-paradox.html).  Take note; it is in "light years".  So, it's definitely way more than 14 billion Earth-years old given the speed of light, which is ridiculously fast.

So, the universe is very very old.  We have this postulate that there is life out there other than ours, and that way older civilizations exist.  These civilizations might be more advanced, and therefore, they might have developed very powerful space technology, probably enough to have reached the Solar System and the Earth.  Seems likely, right?  Along this line of thought, Enrico Fermi, an Italian physicist, was said to have stated assumptions informally (http://www.seti.org/seti-institute/project/details/fermi-paradox), which I have noted down into these statements:
a.  a civilization with modest rocket technology but with enough resources could rapidly conquer an entire galaxy
b.  an empire could have conquered star systems within ten million years, enough to rapidly colonize an entire galaxy

Given these assumptions, Fermi thought that civilizations way older than ours, given the age of a galaxy and the universe, had more than enough time to make their presence manifested, say within the Milky Way galaxy.  So, as Fermi put it, "where is everybody?"  This is the so-called "Fermi paradox".  Many solutions have been proposed to address this problem, and I think they were interesting, or rather, entertaining.  However, at the bottom-line, what are the odds that Fermi's assumptions are true.  This leads to the Drake Equation (http://www.seti.org/seti-institute/project/details/fermi-paradox):

N = R* • f_p • n_e • f_l • f_i • f_c • L, where

N = the number of civilizations in the Milky Way galaxy whose electromagnetic emissions are detectable;
R* = the rate of formation of stars suitable for the development of intelligent life;
f_p = the fraction of those stars with planetary systems;
n_e = the number of planets, per solar system, with an environment suitable for life;
f_l = the fraction of suitable planets on which life actually appears;
f_i = the fraction of life bearing planets on which intelligent life emerges;
f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space; and
L = The length of time such civilizations release detectable signals into space.

The estimates for the value of N are not reliable as of this moment given that we only have assumptions so far, and we have no strong empirical evidence that life exists in other planetary systems.  Life is indeed very challenging under this research area right now, and while we are still groping for empirical evidence, it seems fun to think about the solutions to the Fermi paradox.  But wait, how feasible the assumptions are?

One may think that it is not possible for a single alien to have a life span of a million years.  Then, there might not be enough fuel for an unmanned spacecraft to travel a massive distance, and perhaps by traveling for more than a million years, the spacecraft may have disintegrated.  The idea seems absurd given the current technology.  However, we are talking about millions of years of advanced technology, about the "what if's".  Perhaps, the obstacles posed by the theory of relativity have been conquered.  However, in the case of Fermi's reasoning, the spacecraft involved can be slow; there's no need to develop a spacecraft that is as fast as the speed of light.  If you are familiar with the Bracewell-von Neumann probes, a civilization should just develop these probes.  They need not be fast, but they should be autonomous and self-replicating.  In order to replicate, they need to find and retrieve the necessary materials from space, e.g. asteroids.  The number of probes can grow exponentially, and a galaxy can be explored in "just" less than 10 millions of years.  Compared to the age of a galaxy, which can be billions of years old, the exploration can be considered quick.  So, we are left with the question whether the Bracewell-von Neumann probes are easy to build.

In tackling a solution to the paradox, we should assume that building the probes is easy or possible.  The possible solutions, therefore fall into three categories (http://abyss.uoregon.edu/~js/cosmo/lectures/lec28.html): (1) "they are here", (2) "they exist but have not yet communicated", and (3) "they do not exist".  I have encountered many interesting solutions, and you might want to check a less boring take on the subject matter here: http://waitbutwhy.com/2014/05/fermi-paradox.html.  Among these solutions, what I consider to be one of the mind-boggling ones is that all of us have been subjected to a superbly sophisticated simulation by the aliens, which makes the state of our existence similar to that in the movie "The Matrix".

On Space Exploration

Just some points to think about...

Even though we dwell in a world that is tangibly finite, the human mind, and heart if I may add, recognizes something infinite.  There might be such a thing as "infinite curiosity" despite the finite nature of the human mind that "produces" it.  Probably, some of the manifestations that seem to justify that there is such a thing as "love for infinity" are mankind's constant exploration, experimentation, and proclivity to face new challenges.  These manifest despite the state of being adequate in terms of material necessities such as food, shelter, and clothing.  Why long for something more despite being satiated already by material adequacy?  Are we driven by greed?  Are we driven by love?  Are we driven by some unknown inadequacy?

One example is space exploration.  After we have conquered the waters and continents of the earth, we are now trying to "conquer" the vast "lands" of beyond in the Milky Way galaxy and the universe.  Mathematically, we know that the universe has its bounds, but what about the "lands" of "even more beyond" outside of the universe.  Despite the impressive achievements in space exploration, the reasons behind doing the exploration provide a venue for some contemplation.  We have formulated many questions concerning the universe even though we still have a lot of questions to answer within the earth itself.  Perhaps, the answers to the questions that we have here on earth can be found by answering the questions about the universe.  However, it seems that the bottom line question is: "Are we alone in the universe?"  We have this curiosity about the existence of extraterrestrial life.  So, it seems that the curiosity is mainly about life and existence after all.  Life is finite, but there seems to be something infinite about it, and that something infinite is worth "fighting" for.