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Friday, May 18, 2007

TP Part II : Insight


I was more than pleased to see so many comments. It was a greatdiscussion. So why delay for Part II ? Of course the observations and "comments" affect the system ( A sleek example of Uncertainity Principle like effect is real life ) so now the posts I had thought of are no longer going to be the same. I was supposed to write about all this an year ago, but got lazy. To me, this is DAMN interesting ! I hope you all too would realize the importance, consequences, and implications of the ideas that follow.

Temporal Programming
Hats off to Time and all of you for mentioning this. For this ceratainly is a great field of current research. A hot field indeed where people fix neuro-networks with electric chips and try to control them and stuff. The aim of course is to combine electrical and biological systems to create "cybernetic organic matter"... sounds Terminator-ish ehh ? lol

However TP is NOT equal to Temporal Programming. If I were to mention it, it might sound 'dubious' and trivial/unimportant/crazy. But I'd insist, that if not of all the importance, it sure is what I began with. So more about TP on Part III. Till then I would like to have a time travel session ( yoh Time get the machine ready man ... ) back to history (a subject I hate from the core of my heart ) ...

Many of you ( Im sure Arun would ) would already know about many of these facts. However, please bear patience, for the others would be fascinated indeed. Countdown Time...
10
9
8
7
6
5
4
3
2
1
0
-1
...
(oops forget it)

Old Hilbert had Problems
In the early 1900s ( not early... infact the very year 1900 ) the great mathematician Hilbert listed out a few "good" "classical" problems in mathematics. Many of these have been solved now. What he emphasised further, was a need to organize mathematical reasoning. He said that a formal axiomatic system should be both `consistent' (free of contradictions) and `complete' (it represents all the truth). Further argued that a mathematical problem should be "decidable" in the sense that there exists an exact procedure or set of instructions (however complex) to decide whether a proposition is TRUE or NOT... an algoritm !

Around the same time, people were talking about unification of physics. This, in a sense, was a unification or generalization of Mathematics. But it's been tested ... that nature seldom appreciates such acts of (folly???). The 2 problems can be listed...

  • a complete system of axioms
  • an algorithm ( procedure ) to deduce a give proposition as TRUE or FALSE
But things have never been simple...

Everything is Relative
While other mathematicians were working, trying to formulate a standard set of axioms, the genius of Kurt Godel prooved (Boolean Algebra) that there can never exist a complete logical system, all by itself. For the daredevils and brave-hearts the two theorems of "incompleteness" can be found below :

Wikipedia - Incompleteness theorems

The exact proof ( With Godel's history and stuff )


PARENTAL ADVISORY is Required... click at your own risk ! (I'd advise not unless you have chewing gum for a brain cuz thats what is going to happen lol)


How to do it ?
People yet searched for Hilbert's second quest... the algorithm. But a wise guy called Turing was wise enough to show that this too was impossible. Now I am not explainging how because I take the liberty to post about it as a follow up, for its a favourite topic of mine and deserves special credit.

Implications
Hilbert's dream was shattered. My history is not good enough to tell you, whether he lived to see that day, but I guess not. The two quests were PROOVEN to be impossible. There could not be a self-consistant set of axioms. Hence mathematics must rely on (some) assumptions. Also, there was no set of algorithms. So there was no way to predict if a proposition was TRUE or NOT ... infact... you could proove it TRUE, but never FALSE. Its like Physics. U have a theorem. U keep experimenting. But cant proove it. Same applies to maths for some of these classical ones. An infamous example is Fermat's Third Theorem, which reamained unprooved for decades, and was finally prooven in the 1980s. Who who' s ? Maybe it could have been wrong. The point is, is it true that ALL THINGS TRUE CAN BE PROOVEN ?

Back to the Brain
Now most of you must be thinking " This crackspot ... last I knew he was talking of the brain and something wierd called TP ... and now he switches to abstract mathematics ... "
I empathieze with you (my brain does). But explaining all of the above was important. The implications are not small.

AI
This aint another TP... but Artificial Intelligence yeaah... So now Im talking about a field, which promised to change the world in the 1950s but over these many years, has been an utter failiure. When people expected to see walking talking humanoid robots, all they get is stupid toy dogs that act like pets. The technology has failed to deliver. Now Ill dismantle and disect certain subtle points of the subject.

Humanoid or not ?
An aim... one of them... has been to make machines "think". There are two basic problems. One - we hardly know what is "thinking". Two- The approach. By the approach, Ill bring out a certain result that recently, wierd looking robots have outperformed human-like (humanoid) ones for various tasks. They are as effecient, if not more, while imitations of humans have been unsuccessful. The point is, we are trying to COPY nature.
Switch to an analogy. Aeroplanes. ( Im sure TIME wouldn't agree but I still believe that conventional aerofoil based planes are better than ornithopters ). Initiall people fixed wings and tried to fly resulting into calaities. Most the designs they thought of comprised of moving wings. However imitations of nature failed. The flying planes we have today are based on different design principles.
So why IMITATE human thought at all ?
I mean... machines, lots of them, can do better than human at lots of things. Like... playing scrabble, chess, even football ... and I am not talking about humanoid ones ! So why make a humanoid thing at all ? I guess this has more to do with the curiosity and understanding ourselevs than imitating a birds flight. Ohkay now Im diverting from the topic ... ( but wats the topic ? )


My Doggie is Conscious
Forgive that subheader. I am getting wierder with each passing hour. Though my point is, can machines be conscious ? Back to the game eh ? Well to understand this, we must look into our own machines... our brain... Now how exactly our brain works is not known. Perhaps we can say (or we do) that it follows algorithms. Like a computer program or a computer. So a machine can follow algorithms too. Whats the big deal ? The deal is... that we have prooven... that there is no perfect algorithm. Infact for the set of all algorithms, there is another which is unbounded, or not an algorithm at all ! ( Turing did all this )
How exactly it says what it does would be clear only when we study Turing's method(s). But the result is... maybe our brain does not follow an algorithm !
Hah ! I can hear God laughing. "Do what you can *.......* you cant copy your own mind"
Now our kind of machines follow algorithms. What can be done if a thinking machine does not follow an algorithm ? Nothing. Hopeless. Maybe somewhat like, popping of the wave function! (Arun's comment - deserves a post on its own).

Wrapping Up
I mentioned ( or you did... ) yoga and hypnotism. I was to write about them, related to my own escapades(TP). However, my brain tells me its tired. So Ill let those two hang up.

Till then something to think about.

(1)
Is it the mind which carries out experiments or the world which provides inuput ? If its the mind... what about my mind and your mind ? Are u a figment of my imagination ? ( Ive tried conveying this message to ppl. The replies were not very positive so Ill not try it again hehehe )

(2)
This publish button I see below is ORANGE. This Save Now button I see is BLUE. Ohkay. I can differentiate between frequencies. But then... do you see ORANGE too ? Yes you would say you do. But do you see the SAME orange as I do ! ... I guess there is are no means to answer this, that I can think of. MAybe you see my RED as your YELLOW and my BLUE as your RED. Maybe its not of much importance... but will the beauty of the RAINBOW be the same for both of us ? If not... this could be a reason why things like art,beauty are subjective ... that is ... "lie in the EYES of the beholder".

(3)
I believe that the EARTH is conscious. Only it doesn't bark.

Ill quit writing before you book me for the asylum. lol.

Ill be Bak

~ Twist ~




11 comments:

sandeepan said...
This comment has been removed by the author.
obiwankenoby said...

so you are now talking of perspective reality now- right.thats what we were discussing in the comments section as well.
so the blindman does not see that the grass is green, but ask him and he says that it is green.
there was some film about a person who was unblinded by a recent dicovery of surgical science -- and his experiences following.
so does this man think of green as i do-in the visual way? or he associates it with the chirping of birds, and warm sunlight.
infact i think can yet bypass the danger of being tagged THE cracked un when i say that try THIS-literally--
close your eyes for half an hour(yes, u heard it right) and taste your best food,or pinch yourselves.
SENSITIVITY---women have it more than men (because men are more out of themselves) and feel and smell roses better than we do.
so the close-your-eyes-experiment should work better in a closed room(you wouldnt want your parents to get the wrong notions) and feel about.
for me the result was that i didnt want to open the blindfold anyway; that is till my sister called me out and i HAD to go and level her up-quite a different story.
so heightened perceptions of smell and taste can be quite liberating - painful as well when you fall down.

so there is perception for you.


and so i think it will suffice to say that consciousness(measured in complexity) is proportional to the perceptory capacity an organism has.
????

another question-
do you think a congenitally blind person actually visualizes green color through his race\group consciousness??

Arun Chaganty said...

Hey!!! Both Godel's Work and Turing in the same post! That's great. While I do know what they've done, to be honest, I really didn't get most of the proof. I know it centers around proving that there are infinite possible statements in the axiomatic system that basically say:
You can not prove this statement.

I've seen a lot of the arguments (all three actually), and they're all real interesting.

(1): The dream paradox: Well, from my frame of view, your the figment of imagination, and your posted just to fool me. Well there is no way to prove that this is NOT true, but I'd ue Occam's Razor to prove it false.

(2): Well, I DON'T see the same orange as you. It's only slightly different, that we can speak on a common basis. The fact is this, if we both can understand that the publish comment is orange, then well, thats all that matter right? If I wanted to I could call orange poopsy-green, and as long as both of us agree on the same thing, it doesn't matter. The poopsy-green ball may look orange-ish to you, but both of us call it poopsy-green. Remember that whenever you see orange, you'll call it poopsy-green. Ok, i've confused you all. Thank you very much ;). I hope you get the point. It doesn't matter. (But it's a fun topic to discuss anyway).

(3) Earth conciousness; Hmm... I guess obiwan's comments spill into this. How do you judge whether something is concious or not? This becomes especially complex when it comes to things with no input/output. My view is rather simple: you can't tell whatsoever. It's hidden from you (read Cosmic Censorship Theory ;)).

My comments seem to be pretty negative, but I'd just like to say that this is my conclusion after a lot of debate. But it's always fun to talk about it.

@Obiwan: I fully agree with the blindfold bit. But I'd like to point out that it isn't just proportional to the number of "perceptrons" or sensory organs, but also to the capacity of the processing unit. So the fineness of our conciousness increases using particular sensory organs only (via blindfold), but isn't that level of conciousnesss nearly equal the extra conciousness (of lower detail) you get with vision? How does that balance out? I think actually that you have a higher sense of conciousness without the blindfold (like you said. Just elaborating that point). There was a novel with 3 short stories of differently abled childredn saving the day via their heightended sense of skills. Don't remember the author, but it was Indian.

Another question I'd like to raise: How can you measure the level of conciousness? Surely we would say/like to think that a human is more concious than a butterfly, but how can we say that? My views are that the "metric" for conciousness should again be how well that sense, is networked into your brain. How deep it reaches into your brain.

For example, if a car crashed right infront of me (godforbid), then I would immediately rush to help. Why? Because the visuals have reached so far as to make me remember: car crash means that ppl may get hurt. That means I should see if I can help them." Furthermore, I'd be recollecting past accidents I've seen/heard about. An entire plethora of activity occurs in my brain because I am "concious" of the crash. If a butterfly aw that, it wouldn't do anything. Of course, it could be because it is concious that it couldn't do anything. Can't really go past that no can I?

Final Question about race conciousness: No. To me, race conciousness does not deal with highly personal traits like vision, but more with things like: hmm. he's moving towards the fridge, he's going to get a bottle of water. Let me get a glass". That kinda of unspoken understanding. This is a weak example, admitted, but I'm having some trouble thinking of an example that can't be explained in atleast 2 different other ways ;).

Another would be the understanding that a mother is boss. No one says it anywhere. You just know that she's your mother, and she's the boss. From birth. That's probably a better example.

Anyways, point being that group/race conciousness shouldn't extend into so personal areas as vision.

I think why we are able to comment so much on this post is because its a good topic, and a general one. Also, its one that every one of us have thought about already ;). Still I'd like to see some new faces (and more of Rash). Obiwan and me can keep a great discussion going, but it's always fun to have new (old) guys joining in!

Arun Chaganty said...

BTW: You forgot to mention a very important aspect of Godel's proof. It says that their are truths (and "lies") that a consistent axiomatic system can not prove. And the more important part is that the human mind can perceive these truths.

For example the statement:
This statement can't be proved.

Is inherently true to the human mind. But you can't prove that axiomatically can you? Its a truth that the system can't prove, but a truth nonetheless.

This inspired a lot of talk of: you can't prove god exists because he's out of the system, and its the same thing". It's gotta be one of the most misused theories after Occam's Razor (which isn't really a theory, more of a conjuncture I guess).

obiwankenoby said...

another aspect i would like to come to the fore would be the basis of axioms.
godel's theory from what i got off the wikipaedia site says that if you dont accept axioms as the truth, you cant find any truth in the world.


now why did addition (i consider multiplicaion as addition too) become the central nervous system of the human number system?
our hands! we have five fingers on each hand and five on each feet.this made the additon principle appear out of nowhere.so this was the elementary addition axiom.
but what do you say if the morphology of humans was a cause and the effect was the addition axiom?

but what if some other creatures on some other part of the universe (dont rule out extra dimensions) had a different way of approach? maybe if they are 6d creatures, the celebrated theory of relativity was an axiom to them.

so how can we visualize extra dimensional maths?


of course i am treading irrelevant paths, but then who isnt.
so say an yes to the basis of axioms or not?

Navneet said...

i really don't get it when you bring in perception of colours.

biologically speaking, all humans (who aren't genetically compromised) have the same photoreceptors lining their retina and thus will sense the same wavelengths of light.

however the difference in perception might come when comparing say a human vision with that of the bee...so my point is that MY orange and YOUR orange are exactly the same.
now having said that, the difference in perception that we frequently refer to during our many arguments comes from the emotional centres of the brain...thus physical realities remain the same, however emotional ones might vary according to one's nature(that's another hot topic to discuss sometime)

TwIsTeR said...

Id clarify the color part of the post.

My brain and your brain are certainly not the same, even though it can be assumed that the retina lining cells would be "similar".

It is certainly logical to say that my ORANGE and your ORANGE is similar. But I dont think it would ever be the same.

For example, hearing range of people differs. While my littel brother can hear sounds upto 14KHz... I can even manage 22KHz !!! ( Ive tested ) My mother hears upto around 18KHz and same for Dad.

Similarly, the range for light sensaton might differ. Apart from that, I am not really aware of this, but tell me, do we have a special organ for visual perception ? I dont think so. Infact just like a memory is stored in the brain, visual perception is also a stored "script" not a program preexisting from birth. Dont we develop our own visual perception ? ( Babies cant see clearly ... )

So now, why would it be that my orange and your orange be, even similar ?

Now picturize the scenario with 2 colors swapped in a rainbow. Or maybe jumbled up. What would be the result ? Would it be the same ?
Yes its about frequencies but WHAT WE SEE must make a difference too.

TwIsTeR said...

@ arun

Yes I did miss out that part of Godel's proof where he gives references to STATEMENTS which can refer or relate to themselves. Creates alot of fallacies/contradiction etc.

Wwanted to stick to the relevant points though I diverted alot.


And the same issue... would be clearer if Turing's work is discussed.U know wat that is ?

At this point, I wont talk about the EArth being conscious. Its less of a belief more of an idea actually, but yes it is logical. Some other time for that.

@ obiwan
Interesting thought about axioms. I remember when I first heard about the ( was in a geometry class in 8th i think ) The teacher told me that Euclidian geometry was based on ASSUMPTIONS else different geometries could exist.

Its strange indeed. we can mess up with any assumptions at all right ?
And u cant even test them because all are abstract and VALID for different things !
(Eg : Lebacheskian Geo, )

And yes...
you can take theory of relativity as an acxiom cuz its maths were talking here. axioms shud be the most fundamental, and give rise to higher levels of understanding. I dont think there is much of a higher level to deduce ( assume it ofcourse no1 knos ) higher.
So ull have to work your way backwards to simpler truths.
( I hope u see the resulting problems )

Yet we are free to choose, from a set of basic axioms, any of them. I guess its beacuse maths is abstract. It lets you experiment with mayny different (possible) realities.

TwIsTeR said...

And please comment on the new look of the blog ! If its bad, plz provide some suggestions for the color.

Arun Chaganty said...

Twish, I'm posting another article on Turing, because its just soooo long! Well, back to the discussion. Regd. the Godel statement, I think it is very much on topic, because it shows that there are things that our mind can cross. We can see something is true, though we can't prove it.

Cool that your prof took the effort to mention them. (shakes fist at old maths teacher). Well, either way, your talking about Non-Euclidean Geometry. Awesome topic that I don't know much about. I think Rash or Time mentioned it here earlier.

Now, at Obiwan, I guess I agree with Twish in that, when you have a truth, if its a real truth, then well, it doesn't matter where you start from. BUT our mind needs somewhere to begin thought (that's why we go to school. To gain some ideas for thought). Thus, yes human morphology and thought cycles are very interlinked. But more than that, you will recognise that the nature of invention itself changes as time progresses. From needs to luxury.

I've been thinking about the alien argument for a while now (since well 8th class). The thing how can we assume that aliens will be like us? That they will require the same things for growth? IS water important to them, if it was to us? What if they walk among us, but are in such a shape that we can't see them (and perhaps they can't see us either)?

Then I learn't Occam's Razor ;) Well, when I look into mirror, it could be that light reflects, or theres an alternate dimension to which this mirror is a door to. And theres a guy on the other side whose doing the same things I am...

I don't mean to sound bad here, just narrating my story on how I dealt with this subject. I'm still struck by; "how can you say that for sure" waves.

Now to extradimensional visualisations, I don't know how, but after a certain amount of time, I am in a way able to be "concious" of that extra dimension while visualising things or just dreaming. I'd like to know how to visualise it too, but till then, I'm just going on gut-feeling. What I do is visualise 3D and some how in that same vision, i put another layer, which "feels" at 90* to the plane. I have no idea what I'm doing, but it works ;)

Arun Chaganty said...

P.S. I've put a lot of axiom stuff in a new topic.