This past week I finished my reading of Mandelbrot’s most recent book The (Mis)Behavior of Markets. I actually didn’t like it that much. I found the book to be especially light on details; for a mathematical empiricist Mandelbrot didn’t actually explain, in unambiguous terms, the patterns that he sees in market data. He did a good job of showing that price charts appear roughly the same independent of company and time-interval. (That is, if you forget to label your axes then a chart covering a few years doesn’t look appreciably different from a chart covering only a few seconds.) But the details of how he knows about the multi-fractal patterns, and how to measure such patterns, or even the basic mathematical characteristics of mult-fractals went entirely ignored. Some of these details were given in a reference appendix for each chapter, but not nearly enough to satisfy my avid mind. The editor also did a poor job of citing Mandelbrot’s references to peer-reviewed papers throughout the text; you had to simply follow along in the appendix simultaneously while reading the main text (an annoying usability bug). Instead of discussing such details within the main text, he opted to give generalized overviews with inadequate pictures of fractals that have nothing to do with finance. Now, I know that since I read graduate-level textbooks on Computer Science in my spare time, I’m not the target audience for this book, but I would have expected to see many, many more price charts and elucidating discussion of features within such charts, esp. considering that he’s so big on empirical data. As it was, even when the book had pictures to convey the geometric ideas within the text they came out piss-poor and confusing. Tufte would be appalled.

Mandelbrot also seems to have a healthy dose of self-assurance (deservedly so, for he is quite accomplished). He didn’t fail to mention that one of his students (Fama) formulated the Efficient Market Hypothesis, and that his early paper on cotton prices help to form a pillar of econophysics. He certainly deserves recognition for developing a very important part of mathematics, but I consider his abilities to write for the layperson to be severely lacking.

I’ve also been reading up on Component-Oriented Software Construction. It’s not a panacea that will solve all the industries woes, but I consider it a significant step towards solving many of our current problems. The traditional Object-Oriented inheritance paradigm is fundamentally incompatible with parallelism, and OO in general suffers from systemic rot as shown by the Circle-Ellipse Problem and the Fragile Base Class Problem. The move toward a Component-Oriented architecture is, in my opinion, a beneficial one. But it comes at a high cost; instead of having a (complex and rigid) framework for message passing and method calling, the programmer must handle request forwarding and chaining themselves; functionality is derived through composition instead of inheritance. In my experience, programmers are the most unreliable piece in the software construction business, and relying on humans to successfully adapt their minds (already trained on the OO model) to a new methodology is a mistake. Furthermore, the Component-Oriented message passing system is so flexible (best formulated as a general directed graph) that a programmer could easily get themselves into the opposite of a deadlock (messages getting passed around continuously in a Hamiltonian path). Debugging could be a real nightmare in such a system, and we’d really best develop techniques for tracing and visualizing information flow throughout the program.

I watched a recording of Guy Steele’s infamous lecture Growing a Language (because of the poor video quality, you really want to read the article as you watch), which he gave at OOPSLA ‘98. This was a delightfully instructive video, I recommend that everyone interested in programming language watch it. I also watched a presentation he gave about his newest language, Fortress, because it was mentioned at LtU. I especially like the mathematical nature of the language, and his willingness to go back and try syntax experiments (APL, PL/I) that failed due to requirements of specialized hardware.

I also read Vannevar Bush’s famous article As we may think, wherein he introduces the memex. I found the proposed interface to the memex to be both antiquated and mechanically cumbersome, when compared to the modern computer. But, given the technology in his day this is to be expected. Some of the issues related to search, recall, and annotation, were unfortunately glossed over; in fact, these same issues still plague us today, everybody consistently underestimates the complexity of the task; reliable associative search is a hard problem. He did have the remarkable foresight to envision how people would wish to use such a system, and, were he alive today, would probably be greatly enamored with the collaborative efforts of knowledge sharing that places such as wikipedia represent.

I keep finding interesting stuff on this old HD; Here’s a documented e-mail conversation between myself and a high-school friend Jeff Peoples on materialism and the mind. It was dated 2004-04-07 and appears to have been written in response to a missing article titled “Enlightenment” that was itself dated 2004-03-02.

Eric:
I think I have figured out what enlightenment is. It occurs when a neural network achieves the capacity to look at itself as it looks at any other object. ie. when a person fully understands consciousness itself, the phenomenon of ‘I’. Furthermore, this insight halts the normal categorizations of Aristotle’s knife, so that you are able to see things as One complete form.

Associated with this insight is the ability to treat oneself and others with a deep holistic respect, friendliness, and complete impartiality.

Enlightenment might be more quickly arrived at by attacking the inherent gaps in logic directly with koans.

Jeff:
Very interesting. However, I think attaching consciousness to the brain is a mistake. For one thing, the one thing we are certain about is our conscious awareness, all else is in doubt; including the brain. Solipsism must be taken seriously, and to use that which is in doubt: the body, to explain that which is certain–the mind–sounds to me like backward thinking.

I had the realization that even the body is a creation of the mind. For example: phantom limb; the experience that one is aware of pain in a member of the body that has been recently removed. It is to the senses, that is to the sight, obvious that the limb is not there and if the location of pain were actually in the body, then one would not experience pain there. But because the location of pain is actually “in” the mind, one still experiences pain in the phantom limb. Thus it is feasible to assume that one could place awareness of mind outside of the body, and in fact anywhere, for the awareness of the mind is not limited to the body, as is shown in the phantom limb. Furthermore, if the mind is capable of creating pain where there is in fact no location for the pain to occur, it must also be possible for the mind to eliminate pain where one thinks pain can occur; for the experience of pain is actually sensed by the mind, and not the body, and sensations of the body are at least partially a projection of the mind, as is the case in the phantom limb. It has been demonstrated that people under “hypnosis” can “block” out pain from awareness. I contend that hypnosis is simply a term used to apply to the inherent power of the mind that when fully mastered is its natural and perfected state. When one can produce “self-hypnosis” by choice and will, the term hypnosis is no longer an appropriate term, for it implies that one is under the control of another and ones freedom is partially usurped.

The idea of the koan is very good. I wish I had a koan.

Now that you know what enlightenment is, achieve it. Otherwise it is like describing an orange without ever tasting it.

I hope that you find true happiness.

If you want to talk more about these things, like in person, I would be happy to.

Eric:
Your appeal to the phantom limb as an attempt to justify the existence of the body as a realized idea of the mind is poorly justified. Although it is true that a person can feel many things from the phantom limb, only one of which is pain, this phenomenon lends more credibility to the concept of a ‘body image’ that the mind creates than it does to a solipsistic reality.

I’m a materialist (physicist by training) so I think that the mind is a phenomenon created by a sufficiently complex processing system. Actually in light of Wolfram’s _A_New_Kind_of_Science_ the system may not need to be that complex to achieve consciousness. But the point is that mind is a side effect of the body. To prove this, I just point out that there is no mind without body, and in fact mind seems to be much more elusive than body, just compare physics to psychology.

If the mind and consciousness are just side-effects of certain matter arrangements comprising the brain. It is part of the functioning of this matter that ‘you’ ‘think’ you exist. ie. the brain has manifested an internal process that you identify as yourself, and some other processes, more correspondant with reality, that constitute your ‘body image.’ In virtue of this conceptualization we can explain phantom limb, and other feelings of Oneness with objects distinct from the body as hallucinations. It should be remembered, however, that I think everything the mind creates is a hallucination.

This interpretation does bring into question, free will. ie “can the mind will itself to do things.” to which I am bound by logical consistency to respond “Yes, it appears that way, but No, it’s all self-delusion.”

Jeff:
Well your understanding of the mind, although it is consistent with materialism, which is based on the axiom, (faith), that the mind exists, does not do any mind any good.

If all conceptions of the the mind are “delusions” as you call them, then nothing is a delusion. Indeed, if all things are delusions the word delusion loses meaning. Delusion and hallucination are two pejorative words that are less science and more fear of the unknown. We are confused by hallucinations and therefore claim they are “unreal” or manifestations of the mind; but of course, ALL THINGS are manifestations of the mind.

For me to know mind I need not think, I need only to be, and I need not have any faith; to believe in the body I must think, and I must also have faith.

You think there is no mind without the body, but how can you prove this? When is the last time you did NOT see an invisible mind? And, can you prove that the body can exist without a mind to perceive it? And most importantly, can you prove that YOUR body exists without your mind to perceive it?

Science cant even prove the existence of mind. The materialist, before even studying the “mind” must assume its existence. If the materialist actually kept to its primary axiom: that only observable phenomenon exist and only observable phenomenon are areas of legitimate study, it would not waste its time trying to prove that an invisible ghost called the “mind” is a side effect of the body.

The materialist can put brains, hearts, and fingers in jars, but it cannot put a mind in a jar. And until it can, he has no business studying it.

And for all the materialists theorizing about the mind, and how much they think they know about it, they don’t even have control over their own mind; the Buddha did, so I have much more reason to believe he knew what he was talking about.

The most important thing about the phantom limb example is that it shows that all experience occurs in the mind and not in the body. That is, what we think is pain in our body is actually pain in our mind. Pain is a subjective experience, not objective; pleasure is a subjective experience, not objective. Although pain and pleasure are often correlated with body, they are not caused by the body.

It is the beginning of all mystical practice to understand that pleasure can be had without the senses, without the 5 delights–sights, sounds, tastes, smells, and tactile sensations—and with this beginning one can work on the joy that can be produced directly by the mind. In this first step people realize that imaginations and intellectualizations can produce pleasures. Some people get stuck on the intellectualizations, and some people on imaginations. Once you then rid yourself of both of these, you can produce joy with just the will.

From this joy of will comes the obvious connection with morality. For if one can will joy, one does not need the pleasures of anything else; so one does not want sex, and thus is not lustful and adulterous, one does not want “things”, and thus is not covetous, one does not want honor or the approval of others, thus is not envious or angry or jealous or lonely etc. And one also recognizes that such negative emotions such as anger, envy, fear–they are all impurities of the will, which is pure joy.

Nevermind the “scientific” reasons for this. It can be had.

Eric:
I’m quite surprised that you did not bother to point out that although I was arguing that ‘I’ is an illusion and does not exist the entire e-mail was written in first person, quite an irony.

And it’s not that the mind’s conceptions are delusions, but that they are not real in the same manner that physical objects are. I have used the terms delusion and hallucination, to refer to mind-like activities of a biological neural net. The net has convinced itself that it has a self and that that self exists, and somehow came to doubt everything acquired it. The net has acquired language as analytical tool and uses it so well that thought and reason cannot occur without it. Paradoxically, your doubt of things other than yourself, can only be expressed in a language that you had to acquire from others, which is why I doubt my ’self’, but not the external world. So we have that ALL PERCEPTIONS are manifestations of the mind, not all things.

Unfortunately, the way in which neural nets adapt makes it so that you cannot ignore signals of pressure and temperature relayed to the brain from neurons in the extremities. A neural net with no inputs will never get anywhere, will never learn anything. Your ’self’ exists, and all the ideas about yourself exist because you have acquired these thoughts from interaction with others. Take for example: a researcher discovered a primitive tribe in a rain forest. This tribe had hitherto no knowledge of the outside world. Fortunately, the researcher learned the language of this tribe, only to find that there was no word ‘I’ ‘mine’ or ‘You’(singular) ‘Yours’(singular) only ‘We’ ‘Ours’ and ‘You’(plural) ‘Yours’(plural). These people had no concept of singular possession, they could not exist, even in concept, by themselves without their family. Apparently the most basic ideas you have about yourself are borrowed from your culture.

I may be misunderstanding, but I don’t think I have ever encountered a mind that was not derived from some physical process. Furthermore, I’m quite sure that rocks and planets exist, and would exist if I were not here to perceive them, because of (1) China exists and I’ve never been there, and (2) China existed before I was born, and will continue to do so after I die. Although I cannot know this from experience, my parents could, and they are people like me.

The primary reason Science cannot prove the existence of mind, is because science needs a much better set of parameters by which to measure mind. Mind doesn’t have a sufficient definition that enables testing. But consciousness seems to exist as a direct subjective experience of every person. If you put a brain in a jar very carefully, it’s processes can be studied. For example: Some scientists took some manta ray brains (they last about 2 weeks disembodied) and connected electrodes into them, wired to wheels of a little cart and a photo-detector. The brains successfully navigated the cart toward a flashlight in a darkened room.

I do agree, most people could use some practice controlling their own minds, esp. the minds’ perception of itself. Such control would be very convenient to have in today’s world. Joy and Happiness have been found to be related to brain chemistry and activity of certain areas.

• Love as a chemical in the brain
• God center of the brain

So it seems with sufficient training, you can get the brain to pleasure itself, and ignore external stimuli (the usual trigger of pleasure/pain). But I will not believe that anything we do has an intrinsic morality, though it does have a survival value, and other subjective, linguistic, cultural rubbish heaped upon it.

If the consistency of the external world is greater than that of your own mind, you must believe in the existence of the former over the latter.

Jeff:
Well I wrote a long response originally but my computer crashed. And I’m not going to write another one. Sorry :(

But here is a summary without argument:

1. Science is based on the observation of materially objective phenomenon. The mind is not materially objective and thus is not a legitimate area of study. People having consciousness and subjective experience is not grounds enough to study such a thing. The fact that other people have minds is hearsay, and science is not based on hearsay. Millions of people claim to believe in God but science is not studying that. Indeed they cant. Anymore than they can study the mind.
2. The brain is not the mind anymore than a glove is a hand or a correlation a cause. And thus anything claimed about the brain cannot be claimed about the mind. To understand this do not go to scientific journals, go to philosophy journals. Scientists tend not to know the philosophical foundations they use in their own claims.
3. Intrinsic morality exists insofar that one must be moral to be happy. This is so because to have happiness one must eliminate the causes of unhappiness, and the causes of unhappiness include such things as envy, greed, lust, anger, sloth, gluttony, and pride, fear, guilt, shame, etc. The presence of such things implies a lack of something, and in joy and happiness there is no lack, there is only abundance. And in abundance comes virtue, which includes: sympathetic joy, generosity, continence, patience, industry, moderation, humility, peace, forgiveness, and mercy.
4. I don’t adhere to the popular conception of the self; that is of the individual ego or personality. The self is as empty as the world is. And my description of the self’s emptiness and the world’s emptiness is based on language I acquired from the world, but my experience of emptiness is not. For I experience emptiness when I am without thinking and imaginations. It is only after that experience do I apply language.

This was a very truncated summary.

Eric:
Sorry for taking so long to reply, I usually do very little during weekends.

Science is only capable of experimenting on the well defined. We are much closer to defining consciousness than we are God. To this end, we have much more information about the brain than we do about any so called ‘Creator.’ Our language has many terms for our varied subjective experience, so I find it very conclusive that subjective experience exists as an illusion perpetuated by ourselves’. Furthermore, the existence of minds other than my own is verifiable by direct observation, the people I see, look like me, communicate like me, etc. etc. That should be proof enough for a materialist. Consciousness has many levels and forms, which can be objectively studied through psychological exams and brain scans.

Since you insist on drawing such a fine line between mind and brain, and since you have defined mind as not having any material manifestation, it must necessarily be beyond the reach of Science, which is limited to the objective/rational world. I have been thinking this entire time that mind = consciousness, which, to my understanding, cannot occur without a brain of some sort, otherwise there will be no objective place for information storage and processing that the consciousness needs to operate on. Also many Philosophical arguments get rather semantic in nature, something that Science has avoided with precise, formal, mathematical definitions.

Since happiness is really just a class of brain chemistry, you need not be moral to achieve it. It could be acquired through drugs, sadism, or whatever, induces the chemical state of happiness. Though this seems a very superficial outlook, what you have invented is a hierarchy of things which you have not clearly defined.

Logically, the elimination of a negative does not imply the succession of the positive. ie. the difference between nonnegative and positive is the element 0. You just might end up completely devoid of any emotion.

My point with the language argument was that, it inherently changes the manner in which you evaluate your personal experiences. That is, any description is colored with categorization inherent in the system in which you are trying to express the event. Thus, inasmuch as enlightenment is a truly subjective experience that must be treated holistically, any description of it in any language will necessarily fall short. But more than this failing, the system you operate under will also affect how you approach, and what you concentration on of any repetition of the experience.

Jeff:
You in fact do not have any evidence to believe other people have separate minds anymore than you have evidence to believe that dream characters have separate minds. Behavior is not evidence of separate minds.

The very curious thing about dream characters is that they seem to be independent beings, but in fact they are a creation of your mind, as is the “Self” that exists in the dream that seems to be who you are. But in fact, in the “reality” of the dream, you are both the characters and the “Self”; for your mind creates them both. And you discover this when waking up. A dream is just–at the best–your mind playing games with itself and the worst, your mind in complete confusion: a nightmare.

In a dream, any physical thing is simply a manifestation of mind; even that which appears completely solid. If you were to study a brain in a dream it would behave the same as it would if you studied a dream in “reality.”

Happiness is not just a “class of brain chemistry.” It refers to a subjective state not an objective state. The subjective state may correlate with certain pattern of brain chemistry, but sadly our ability to trace “brain chemistry” is extraordinarily poor. Our understanding of the brain is nil. Every new discovery about how the brain works is replaced by a new discovery that refutes it or contradicts it. There is still crave over “right brain” and “left brain” thinking even though in reality it is not that clear cut; science just likes to simplify their discoveries so that it seems more correct. Any deviation in a rule of subjective experience correlating with certain brain activity (say on a EEG scan) refutes the rule completely. It is therefore just a tendency, a correlation and not a cause; otherwise the subjective experience would correlate ALWAYS with the specific brain patterns/chemistry. Any study you read you are going to see patterns of brain chemistry correlating with subjective experience not absolute correlation with subjective experience. So 80% of the time when someone smiles these parts of the brain lights up (and the parts aren’t always as highly lit as other times) the other 20% of the time when someone smiles an entire other part of the brain lights up. There goes any causal relationship.

And before you say that happiness is “just a chemical state” realize that the brain is a lot more complicated than chemicals. In fact much of brain activity isn’t even chemical it is electrical, and much of brain activity isn’t even electrical, its unknown. It is like saying that the world is “just made up of atoms” as if an “atom” is anything. Science thinks that because they can label things they have it all figured out.

I don’t even want to bother trying to explain why math does not explain reality. I will just say reality cannot be separated into parts. And that is the first thing math does.

The foolishness of reducing mind to brain is like this: say someone is enlightened, in extreme bliss, joy without suffering, love without hate, the messiah, the Buddha: he is brought into a laboratory and his brain is monitored; the scientists watches the activity in his brain: it fluctuates, different parts of the brain are lighting up, blah blah blah; and then after analyzing his brain activity the scientists go up to the Buddha and they say: “we know what enlightenment is” and they show him all their charts and pictures. The Buddha would respond: “no, you know what enlightenment looks like on an EEG chart; and that is not enlightenment”

The foolishness of reducing mind to brain is like this: A person who has never known pain wishes to know pain so he goes to the hospital where pain is plentiful. He gets to the hospital and sees people in the waiting room with broken bones, coughing, moaning, crying. He then goes home satisfied he knows what pain is. When his friend who also does not know pain asks him what he discovered pain is, the person tells his friend: pain is when a bone is broken, a person coughs, a person moans, or when water comes out of someones eyes. Pain is when the body squirms and moves in strange ways. I don’t know why people are so wanting to get rid of it; all of it didn’t bother me.”

Science is no closer to “defining” consciousness than they are at defining God. They are only closer to defining states of the brain that correlate to different experiences in consciousness in people who say they have conscious that science cannot be sure in fact they do have.

If you really wish to be skeptical, try to doubt science. Your faith in it has only brought you misery.

Once a long time ago (2003) I took an English course to satisfy UCLA’s bureaucratic notions that I should have a ‘well-rounded’ education. As part of this course we read short stories, and were required to write a mini-essay each week about those readings. The grading system was arranged such that 1 of the grades on those essays was to be dropped, essentially we were given 1 freebie. About the middle of the course, I became rather tired of writing essays about short stories, and thought it would be more instructive to write a short story myself, and hand that in instead. (I was also feeling rebellious, and curiously wondered about how the graders would respond to this ‘daring creativity’). It was customary to receive last weeks graded essay in the TA session when we turn in this weeks homework. To my great amusement my paper was marked “see me after class”, whereupon I had a small discussion, and stated my reasons for rebellion, and ultimately caved in by agreeing that this was how I chose to use the freebie. My grade didn’t really suffer, but I was disappointed that the TA and teacher didn’t really seem to care that I’d tried my hand in creativity rather than analysis. So much for English majors caring about creativity.

During this process, I also learned that I’m not especially good at creative acts, my talents lie more in analysis, picking apart logical deductions and revealing the fallacies, or in applying work that others have already done to solve problem. This is why I’m a programmer, It’s a relatively well-defined task, and offers the constraints that I need to bounce off of during algorithmic construction. When presented with the much freer realm of linguistic expression of pure Ideas, I feel presented with too many choices and not enough of a formalism to help guide me towards the ‘optimal’ choice. I can construct when my world is made of Legos but not when made of clay.

Fortune is Fated.

Fusilli was painting a portion of the New Jersey coast, grand and with a truly beautiful sunrise; a masterpiece of Meaning, Purpose, and Form. Thousands used these docks everyday, loading and unloading ton after ton of raw cargo with giant skeletal cranes, while millions more depended on the efforts of this monotonous labor. None of this was reflected in the painting. In place of a fish carcass was rendered a glint of sunlight, the cargo ships were transformed into pastoral dinghies holding fisherman bronzed from the sun, the entirety of the docks were sunk into a deep blue ocean, rich with aquatic life. The New Jersey coast was replaced by something resembling the Ideal.

At the pinnacle of his career as an artiste, Fusilli’s work was compared to the grandmasters of the business, Da Vinci, Raphael, Rembrandt. He produced works of Beauty owned by financial tycoons but held in museums and frequented by the public. Through his renditions patrons caught a glimpse of Truth. The hidden meaning of their experience was communicated by still shape and color alone, an utterance beyond words.

As the sun made its slow path toward midmorning Fusilli realized that further painting would have to wait for another day, he had to prepare himself. Tonight he must make an appearance at an exhibition of his work hosted by the Guggenheim. Many fabulously wealthy capitalists and persuasively powerful art critics would be in attendance. His personal servant washed his brushes and stowed the canvas in the trunk, while he entered the limousine and reflected on the Beauty he had so far recorded.

As expected, the museum was populated by batty intellectuals, accompanied by their silenced mistresses adorned in the most expensive jewelery and precious gowns, in fervid discussion over the artwork. There were grand and eloquent speeches together with diminutive cocktail weenies. The artwork supported the walls and was gazed at in awe. When Fusilli finally arrived, having planned a fashionable entrance, he was much praised and fawned over. With people lauding him as he traversed the halls he waded to his favorite piece, The Grandure of New York.

He stood to gaze and appreciate the majestic power he had captured in this piece. So absorbed was his admiration that he became immune to all around him, without sound or movement he stared. It was a gigantic work, 10 feet high, it caught the Empire State as cleanly as an architectural landscape. With lofty cotton clouds and royal blue sky the building stood as a monument to mans constructive power. The windows, like mirrors, sublimely reflected the surround structures as if they were made of Oriental porcelain.

Slowly, Fusilli came back to reality, and in so doing became aware of snappy conversation near him. An elderly man, bedecked in ordinary tuxedo, enhanced with a crimson rose that was mirrored by impeccably shined pearl black shoes. His aged face held noble austerity with twinkling eyes framed behind gold rimmed glass, which spoke more of his vast wealth that the old fashioned silk top hat. He was nonetheless enjoying himself in heated conversation with some creature left vilely garbed in a raincoat. Though young, his eyes lacked the sparkle of the old mans, and were kept hidden as he refused to speak in any forthright manner. His shoes were beaten and ragged, his hat an ordinary bowler. Indeed, having dressed minimally for the occasion, his entire demeanor seemed to subversively seek out and destroy all the pretensions of fashion.

“But don’t you see what is behind the painting?” cried the gentleman.

Curtly, and with no attempt to look deeper, the truant replied, “Impossible, the painting covers it up.”

Fusilli had to put a stop to this conversation. This man’s view was dangerous. Ideas like that could infect the entire art community. They’d stop funding his work, he’d be destitute once again. Oh! How hard it was to appreciate Form and Beauty when only he could see it. Bitterly, he remembered the hunger that ate him alive as he sacrificed food for canvas and paint. He must stop this foreigner.

“But the Beauty, It is real!! I captured it for you to look at,” Fusilli tried in vain to tell the man.

“All you did was put some color on some matte, and not very well at that.”

Pleading hopefully, “You see the Form, though, behind the work. Its Meaning and Purpose?”

“If by form you mean the blobs of color, yes. But meaning and purpose, there is none. Not in anything. You haven’t even painted the real thing. We’re in New York, it looks nothing like that.”

This man was obviously stubborn. He wouldn’t be swayed by visual appeals to the idealistic, nor would he listen to statements of the Divine. Fusilli needed desperately to convince this critic. “I was on an observation deck when I painted this, And this is what I saw. I painted Life: the Air that gives it breath, the Water that quenches its thirst, the Fire that ignites passion, and the Earth that supports us all. Can’t you see the Divine?”

Cold-heartedly, came the crushing response. “You painted a fantasy, a delusion in your mind, though shared by many. You have painted the Maya. That is no skill; to paint what you think you see.” The cloaked man turned and left. Walked slowly away with the burdened footsteps of Atlas.

Fusilli with tears in his eyes, on bent knees, his World being taken away called out “I painted Beauty!! I painted Beauty!!” while other critics and investors eyed each other knowingly.

I was going through a saved home directory from a HD that died a couple years back, and found this piece, which deserves to be saved. The file it came from is dated Mar 8 2004. (if it looks like crap it’s because I didn’t want to reformat it for the web)

I’ve been dwelling on the contents of this e-mail for more than an hour, couldn’t sleep because of it. So, for any e-mail that I write, this’ll be epic. Also, this is what I really learned over last summer break, while I took, and was supposedly learning, History of Science, and Life Science 4: Genetics.

Statements of Personal Philosophy, and the books I got it from, in order of importance.

BOOKS I’VE READ
==================================
Gödel’s Proof — Ernest Nagel
delightfully short and exciting work, captures the philosophical essence of Gödel’s work without the cumbersome set-theoretic notation.

Gödel, Escher, Bach: An Eternal Golden Braid — Douglas R. Hofstadter
A wonderful book that has taught me more about math, reason, and consciousness than Zen and the Brain, even though I’ve only read half of both.

The Fountainhead, Atlas Shrugged, Anthem — Ayn Rand
nice fictional pieces that tell a good tale. though I think she holds logic as an absolute, which, in my opinion, is a mistake. Her philosophy is pretty sound, and is nicely expounded upon in some of her other works. I particularly enjoyed Anthem for its narrative style. Atlas Shrugged is a culmination of all her thought and effort, if you’re only going to read one.

Zen and the Art of Motorcycle Maintenance — Robert Pirsig
a lovely frame story of a philosophical journey in search of a platonic Quality (which can probably be substituted for just about any platonic Ideal) during a physical trip through the midwest and down memory lane. Gets even better when you read about the history of it’s author (Guidebook to Zen and the Art of Motorcycle Maintenance — Ron Di Santo)

Heart of Darkness — Joseph Conrad
a nice read about the depths of the human psyche, gotta love the depiction of the British.

Zen and the Brain: Toward an Understanding of Meditation and Consciousness — James H. Austin
big thick volume that reads like a scientific journal article that won’t stop. Much can be learned about the physical structure of the brain itself

I feel that I should take a brief walk through Gödel’s Proof….

THINGS YOU SHOULD KNOW
==================================
Paradox by Bertrand Russel.
Let S be the set of sets which DO NOT contain themselves as an element, most sets are like this.
Some sets that DO contain themselves as elements are very strange.
Example1: the set of all thinkable things, is, itself, a thinkable thing, and therefore contains itself as an element.
Example2: the set of all possible combinations of numbers, is, itself, a possible combination of numbers, and therefore contains itself as an element.
So far we’re good. But wait: is S an element of S ?
well, logically, by the way we defined S: S is an element of S if and only f S is not an element of S.
What a paradox!!!

Self-Referential Statements are a common source of paradox, and my special categories BOTH and NEITHER.
Ex1: This statement is True.
well, if you assume so, then it is. if you assume not then it is not.
so, really, since it is consistent both ways, the statement is BOTH True and False.
Ex2: This statement is False.
well, if you assume it’s true, then it says it’s false. if you assume it’s false, it says it’s true.
so, really, since it is inconsistent both ways, the statement is NEITHER True nor False.
Historically, Ex2 was taken to be a paradox and to be avoided.

Definitions: Mathematical, Meta-mathematical, axiom.
Mathematical statements are those describing relationships between numbers.
ie. 1+1=2
Meta-Mathematical statements are those statements which are about numbers.
ie. 2 is the first and only even prime
Most mathematical work is accomplished through meta-mathematical arguments.
Axiom is some statement to be assumed true, usually self-evidently. It’s what you build your Theorms on.

HISTORY AND MOTIVATION
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The mindset of mathematicians at the turn of the 1900’s was to axiomize all of mathematical work up to that point, and remove any and all self-referential statements that might breed inconsistencies, and thereby cleanse the entire field of doubt, because, of course, doubt is the bane of logic and truth. It was with this mindset that Alfred North Whitehead and Bertrand Russel, both [mathematical philosophers/philosophical mathematicians/philosopher mathematician/mathematician philosopher] (best type of person, in my opinion) devoted 20 years to compiling a veritable tome of mathematics known as Principia Mathematica (yes, Newton also published a different book under this title). The idea was to define logic as mechanical notation shuffling according to preset rules, such that a computer, with no intelligence or knowledge of the underlying ‘meaning’ of the symbols involved, could proove stuff, if you supplied it with a starting position, the axioms. So detailed was the language of Principia that they never got around to 1+1=2 until somewhere around page 200 of the 3 volume set. I don’t think that anyone has actually ever read the whole work.

It was in response to this work that Gödel published his _On_Formally_Undecidable_Propositions_of_Principia Mathematica_and_Related_Systems_. A work that was humorously devoted to Whitehead and Russel, and which in 20 pages completely underminded what they had done in 20 years and 3 hefty volumes. Naturally his argument rests on something they were trying to get rid of: the self-referential statement.

GEOMETRY REFERRED TO IN RESULTS (best to skip and come back)
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Axioms of Euclidean Geometry:
1. It is possible to draw one and only one straight line from any point to any point.
2. From each end of a finite straight line it is possible to produce it continuously in a straight line by an amount greater than any assigned length.
3. It is possible to describe one and only one circle with any centre and radius.
4. All right angles are equal to one another.
5. (Euclid’s fifth axiom). Through a given point not on a given straight line, and not on that straight line produced, no more than one parallel straight line can be drawn.

Ax5 is important because it was for some 100’s of years thought to be derivable from the other 4, but nobody could find out how. Eventually someone got smart and figured out that if you had instead:
5. (Hyperbolic axiom). If P is any point and AB is any straight line not passing through P (even if produced), then through P there are straight lines YPZ and WPX such that: (1) YPX is not a single straight line. (2) YPZ and WPX are each parallels to AB. (3) no straight line through P entering ^ZPX is parallel to AB.
You get Hyperbolic Geometry. Then there’s also Reimannian Geometry, and lots others, none of which are True in the absolute sense of the word.

THE PROOF
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1. assume that mathematics is complete, that we know all axioms and can, from them, derive all things (given the time)
2. It is now, in principle, possible to have some algorithm test all possible statements in our symbolic language, namely Principia Mathematica, to see wether or not that statement is derivable from the axioms.
3. At present no such algorithm is known to exist, and if we can show it to be impossible, then 1 is null and void.
4. To do this you start out making some statements about numbers (meta-mathematical statements), you organize all these into a table and number them.
5. Now you start asking things like, is statement X true ?
I sorta forget what happens next, but eventually you get some statement somewhere that can be looped back to talk about itself, and the whole system comes crashing down. ie. your mathematical statements have some mapping to your meta-mathematical statements, so the meta-math is really talking about itself not math.
6. because this inevitable happens somewhere, it must be that not such test algorithm can exist, and therefore that mathematical systems, all of them, are incomplete.

RESULTS
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Take, the historical example about geometry. You have some axioms 1-4 and you have a statement 5 that you want to derive from 1-4. well someone showed it couldn’t be done, that 5 had to be taken as another axiom. Then, if you assume it, you get Euclidean Geometry, if you assume something else, you get a Noneuclidean geometry. There will always be some statement out there that you can find, which must be assumed as another axiom in your system. In this way the field of mathematics will branch out into some sorta intricate tree.

The results of all this can be taken two ways:
1. mathematicians have prooven themselves into good job security, ’cause there shall always be some statement out there waiting to become an axiom
2. it’s a lost cause, because you can no longer find absolute Truth, nor will your search ever end if you try.

I’m gonna go with the 1st interpretation myself.

Mathworld states Gödel’s work a little differently, but it’s really all the same.
Beware ye seekers of truth, those that claim to have it:
If you have a system that claims to be able to prove itself true(consistent), then that system is inconsistent.

PERSONAL PLUG
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I could ramble on more about consciousness and its manifestations (Gödel, Escher, Bach) or about subjectivism (Zen and the Art of Motorcycle Maintenance) or the logic of atheism (Ayn Rand, with support from Godel and Hofstadter). But, though I be atheist, all is not lost. If you show me somewhere that I might be wrong, I’ll readily go back and rethink everything, atheism doesn’t make me particularly happy. (Assuming they are mutually exclusive, given the choice between happiness and knowledge, I choose knowledge.) You’ll have a tough time, though, ’cause Gödel ruined my belief in the absolute.

Is the maxim ‘There are no absolutes.’ itself an absolute? is probably the best place to start, ’cause I don’t really have that answered.

Also, during the summer, inspired by Gödel, i came up with a new way of looking at the manner in which the field of mathematics can be derived, you have but to ask, and I’ll write another installment. In retrospect, that brief walk wasn’t so brief.

I usually really enjoy having to design a computer application. Lately I’ve been trying to design a multithreaded server that’ll process image frames from a video. Right, that’s MPI, Network and video decoding all rolled into one. Decoding video into an event-driven stream of frames is difficult enough by itself, without having to worry about threads and network driven state changes simultaneously.

The task of the designer is to take complicated processes like the above, and distill them into a set of pieces that integrate together. The programmer will ususally loathe or relish the design process. It’s the point during which all the creative juices that brew during years of drudgery and long hours of typing finally get to surface. On a good day, the designer will get to wield Occam’s Razor like a sleek katana as they nimbly cut through all the conceptual cruft and end up with an elegantly trimmed and simplified piece of core functionality that not only “Just Works” but that’s easy for others to use, and provides aesthetic appeal. On a bad day, the cruftsman grafts parts together in ad-hoc fashion with duct-tape and a club until something works by sheer accident, some hideous kluge that deftly defies programmer and user expectations at every turn, dooming the sanity of everyone involved thereafter. Mostly the poor designs result from the designer not having the singularly clear vision of a guru, from not having spent enough time in deep meditations about the subtleties involved, from neglecting to see the ephemeral thread of commonality that hides neatly behind each of the disparate pieces being conjoined.

Unfortunately for me, I know next to nothing, and have no real experience with everything needed in this project. I’m not familiar with network programming or protocol design and implementation; I’m not familiar with event-driven architecture; I’ve only just figured out how to decode the video; and I’m only just now turning my attention to threads. Concurrency without Idempotency is Hard. The other real difficulty is that when I’m given the choice of where to allocate processing resources (via threads and MPI) there are several different, competeting ways to design the application. I’d much rather just code up a series of small idempotent functions and offload the difficulties of resource allocation to a well-designed multi-purpose scheduler.

As I think through the different designs, and read up on all of the skills I lack, I think it’s inevitable that I’ll design a kluge rather than a piece of art. I keep having moments of lucidity where I think I’ve got an elegant design, only to find later that there’s a gaping chasm surrounding a detail I overlooked in my ignorance. *sigh* I should probably resign myself to writing an inelegant hack, and plan on re-coding the whole thing, chalking up the initial attempt as a learning experience.