Talk

Talk from Brett Russell Dougherty on Vimeo.


This here is really a pretty ordinary video, but still it isn´t. I found it on Vimeo when I just browsed around for some intresting content, and intresting it was (Ok, I´m starting to sound like Yoda here).

It´s really just a simple portrait of something we probably do to litte. Talk. And I don´t mean idle talk among our friends. We´re perfectly fine at doing that. No, I rather meen talking to strangers. People we don´t normaly communicate with in our own neighborhood, on the bus, at the store, in the park or whereever you go during the day. We´re meeting more people during a single day then most people did during a whole year a hundred years ago, but still I can´t shake the feeling that we´re becoming more and more isolated from eachother. Sure, most of us probably have big circle of acquaintences but what about all the other outside of our realm of familiar faces? One could argue that you can let those people mind there own buisniess, which is partially true, but we´re still working on a common project - forming an society together with them - which meens we can´t ignore them all together.

All this is of course very utopic when applied to the population as a whole. It would be really great if everybody had this mindset I´m talking about, but unfortunately that´s not the case, and frankly I don´t think it will be either. However, from a pure subjective point of view, I don´t think that that´s relevant to the behaviour of the single individual. You can gain a lot just by making this your own reality, no mather what other people are doing.

Well, anyway. This video made me feel good.

Incompleteness: The Proof and Paradox of Kurt Gödel

I recently finished Rebecca Goldstein's book "Incompleteness: The Proof and Paradox of Kurt Gödel" (Swedish translation (which I read): "Ofullständighet: Kurt Gödels bevis och paradox"). For those of you who aren't familiar with Gödel (I hardly was before I read this book), he was a logician, by many people though of as the greatest thinker of the last century along with Albert Einstein. This book tries to explain why, but often gets stuck in its vivid description of this somewhat strange and esoteric character. The fact that Kurt Gödel died of malnutrition due to paranoid delusions maybe explains why there's a lot of intresting anecdotes about this strange man well worth brought up, but it sometimes feel that the author is more excited about Gödels odd life than what he actually accomplished. With that said, the book is, in my opinion, a great and captivating introduction to his work.

The fact that everything isn't centered on hard scientific facts all the time makes this book a pretty easy and convenient read. More speculative philosophical discussions are blended with stories of Gödels life and his own ideas in respect to his logical claims. In the middle, there is a pretty technical, although pretty talkative, presentation of the work that made him almost immortal. The reader who wishes to really dig down into Gödels theorems - and at the same time spare oneself from those vauge discussions on different implications of it - will probably be pretty disapointed by this book though. However, if you know that you wouldn't last more than a couple of pages reading a book filled page up and page down with stringent logical arrangements, but still wants to grasp the main idea about Gödels theorems, look no further. This book will probably get you intrested enough to go on to the last page.

The fascinating thing about this book is how it's almost structured as good detective story. In the beginning, intresting implications of Gödels work is suggested, and when your half way through the book, you could recite all the passages about how great and novel his theorems was, without having read a single conclusive description about it. Sort of like this review.

***

Well, I feel I can't publish this post without at least taking a shot at trying to explain what Gödel's pioneering results were. This attempt, sprung from my megalomania, shouldn't be taken too seriously though. Ok, here we go.

Gödels proof of incompletness is really based on the old liar paradox. It goes something like this (there's countless different versions of it):

This sentence is false.

If you look at it, it soon becomes clear why it's a paradox. If the sentence is false as it claims, the statement that it's false is true, which makes the sentence true and hence contradicts itself. If the sentence is true then the statement that it's false isn't true, hence the sentence is false, which contradicts the fact that we said that is was true. As you can see, it becomes pretty complex, but the main idea should be pretty easy to grasp.

What Gödel does is to expand this paradox into the domain of mathematics. First, he construct a system, that translates logical statements to aritmetic statements. In this way, he can represent every logical statement with a specific number. Let's say for example that the statement "If A then B" in this system is represented by 10230. It doesn't really matter what the actual system is (although If it did, I couldn't give an account of it) but the important part is this. What is demanded from the system is that it is isomorphic with standard logic (which Gödel, a couple of years before his incompleteness theorem, prooved was complete). What this means is that there have to be a given set of rules to combine different numbers, depending on what rellation you want them to have to eachother, so that the output produces the correct logical statement. Let me try to illustrate this (since I don't know Gödels system, and since I don't really think I have the time nor the knowledge to create a coherent one myself, you have to ignore that this example is taking some liberties).

Let's say I want to make this series of statements (this is a so called syllogism):

(A) If A then B.
(B) A is true.
-----------------
(C) B is true.

Let's say that (A)=1, (B)=2 and (C)=3 after the translation. What we now want to do is to find some rule that we can use whenever we have two statements and want to know what the consequenses of those statements are. Well, in this example it's pretty easy. 1+2=3. So let's say that plus holds that function. The trick with Gödels system is to work out something that always is interchangeable with simple logic. In this case, you could clearly see that my model doesn't get very far. Let's try to state:

(A) If A then B.
(A) If A then B.

What's the result? 1+1=2. In other words:

(A) If A then B.
(A) If A then B.
-----------------
(B) A is true.

Hopefully not true. Well, let's move on.

Why did Gödel go through all this fuzz then? Well, his goal was to create an aritmetic system that could make claims about itself. If you can represent every logical statement with a number, then you can say something about the aritmetic system and then translate it into a number being part of an aritmetic system, hence make it say something about itself. It's almost like if you, everytime you said something about a pig, was turned in to one, and therefore said something about yourself (anyone who's ever been told by a parent that he or she eats like a pig, and witty responded that pigs usually have pigs for parents, know what I mean).

So, what's the point of doing this then (we're soon home free)? Well, this takes us back to the liars paradox. The reason why it is so effective is that it says something about itself. "This statement is false" get problematic because it refers back to itself, creating somewhat of an infinate loop (Yes, I'll get to "Gödel, Escher, Bach" in future posts).

Gödel now make this statement:

This statement is impossible to prove in an formal system capable of aritmetics.

He then translates this statement into a number and get something like, well, let's say:

52352359875239823987609238765987234987587237865982309589723

Yes, I just made that up. What the numbers above now is saying is this:

This statement is impossible to prove in a formal system capable of aritmetics (and this is a statement in a formal system capable of aritmetics).

What this statements says, given that it's true, is that there is true statements within a formal system capable of aritmetic, that still are impossible to prove. And what it says given that it's false, is that it actually can be proven. But since the statement is false, it could possible be proven, hence we have a contradiction.

So, what follows of all this? Well, when we construct a formal system, we don't want it to be able to contradict itself. That's really the worst thing that can happend. We can't have a system that says that 1+1 is 1 and that 1+1 is 2. That would mean that 1=2, which would make it possible to prove any kind of statement. 3+3=8? Sure.

1+1+1=3--->3*2+2=8--->3*1+2=8--->3*1+2+1-1=8--->
3+2+2-1=8--->3+2+1=8--->3+3=8

Since 1 and 2 are interchangeable at the same time as they have different meaning, we can prove whatever we want. We can't have that. Our only option is to accept the other outcome. There are true statements in formal systems capable of aritmetics that can't be proven. This made a huge impact on the mathematical world (to the extent that mathematicans were willing to accept it) when Gödel presented it in the the 30's. Untill then, the general idea was that every true statement in mathematics could be proved. That was by many though of the very analytic meaning of true. That it could be proven. Gödel showed that that wasn't the case.

***

Gödel's incompletness theorem spawns a lot of different implications in respect to how you choose to see it. From platonism to conscioussness, people have tried to apply Gödels famous work in a lot of different areas. I'll definitly come back to this topic in the future, but this will be all for now.

If anyone have any objections against how I've presented Gödels incompletness theorem, please tell me. I'm eager to improve.

For a kind of halfly vauge parallel to Gödels theorem, see my post titled "The epistemology of consciousness". What I try illustrate there is a (hypotetic) true statement that cannot be proved, although this one is not within a formal system. In you are a sceptic, you could come up with countless of examples of situations were this holds. I'll get to this too in due time.

The epistemology of consciousness

One of the biggest and most beautifull puzzles in the universe is, according to me, the question of consciousness. Therefore, I've decided to write a couple of texts about it, to see if I can shed some light on this mysterious phenomena. I'll start with an epistemological view of the subject, namely the fact that our inability to ever prove that consciouss exists in any other enteties than ourself spawns a sort of paradox.

***

That I am conscioussness is self evident. It is something that I feel, and since a feeling is defined as something consciouss, I really can't be mistaken. Let's also assume that there is somebody else who's consciouss too. This person can also prove his or hers own conscioussness, but have no way of accessing mine, and can therefore not prove that it exists.

What we have here is a sort of a stand of. My knowledge proves my own conscioussness and the other persons knowledge proves his or hers. It's important to see here, that my knowledge isn't transferable in some sense. It isn't the content of my knowledge that is the important factor for the proof here, but rather the experience itself. The experience proves the phenomenon by beeing the phenomenon itself.

Let's say that for some reason, you don't know the answer to 7+5. You lack that knowledge. Now imagine I show up and tell you that the answer is 12. You gain that knowledge. But have you gained my knowledge? Well, no. You now have a replica of my knowledge. Its content is the same as mine, but it's still not the same experience. You have your experience, I have mine. They might post the exact same thing, but that doesn't mean that they aren't seperated. It's not the same knowledge. It's two different set of knowledge with the same content.

Most knowledge is of the type that can be combined and thereby extended itself to embrace more than it did on its own. If I know that Stockholm is the capital of Sweden and you know that Sweden is in Europe, we can combine our knowledge and get the statement that Stockholm is in Europe. What matters is the abstract contents of the knowledge, not the knowledge itself. I can give you all the reasons why I think that Stockholm is the capital of Sweden and once you got them, your knowledge is as good as mine.

The paradox, which is more of a dilemma rather than a paradox, is this: If it's the case that I am consciouss and know it, and you are consciouss and know it, we can't combine our knowledge and get the true statement that there exists more than one consciouss entity. I can't just tell you that I know that I'm consciouss, since the abstract content of the knowledge isn't the important factor for the proof here. To know that I'm consciouss, you actually have to be me. If there were some way to merge two minds togheter, we could merge our knowledge, but at the same time we would both share the same conscioussness, and thereby the statement that there exists two consciouss entities would't be true anymore. To prove the statement, you have to make the statement false, and thereby you have nothing left to prove. The catch 22 of consciousness.

Creativity

After reading the article "Creativity - The last human stronghold?" by Israel Beniaminy over at TFOT, I got inspired to jot down some of my own thoughts on the subject. Let me just emphasize, that even though I might sound like I'm lecturing about the objective truth in the matter, this is only me speculating. To much "I think that..." and "It's my firm belife..." just gets irritating in the long run.

So, what is creativity? What I find especially fascinating is that behaviour, carried out by a machine, seldom is acknowledged as creative. What is it that we have, that the machines are missing?

Would you trust this guy to repaint your bedroom?

Let's first ask ourselfs: Is creativity present under circumstances we normaly don't associate with this skill?

Imagine you're searching for something in a limited space. Let's say you're trying to locate your keys which are somewhere in your house. How do you proceed?

Strictly speaking, there are more places where they could be than you could posibly cover in a somewhat reasonable time. However, some places are meaningless to even consider. You won't look in the shower or in the dishwasher, simply because you never would put your keys there. Many options are in other words excluded from the begining. Of course, you could ask yourself the question whether these alternatives is processed by the brain at all. In the same way as you don't consider traveling to another country to try to retrive your keys, you probably don't either take the bathroom alternative into account. Some other, more plausible options, may however be taken into consideration and rejected.

Anyhow, you could attack the problem using a lot of different strategies, but you'll probably make some kind of mental list over posible places. This list is probably hierarchic organized too. You look in your jack pockets before you start to get really desperate and search through your loundary basket. Sometimes you'll get an spontaneous idea just by being in a certain situation. You might for instance look in the top drawer when you've just gone through the one on the bottom. Not because you had that intention when you walked up to the bureau, but because the situation generated that idea.

Has this whole search process something to do with creativity? Well. Let's leave these infernal keys for a moment and go to an other area which is highly accosiated with creativity. Let's go to another set of keys. The piano.

What happens when you sit down by the piano, ready to compose a masterpiece? Well...If it's your first time playing, chances are that what you accomplish probably will sound like crap. But let us say that you have some experience.

First of all, like in the last example, there are a lot of key combinations that you simply even won't consider. You have a sort of repertoire with acceptable moves and combinations. The first thing you play, if you don't really have a plan of what your going to create, will probably be something random. However, from there, there are a lot of options that will make your ears hurt. As soon as you've started playing, your options are limited and you have to apply your, either implicit or explicit, knowledge of scales, harmony, counterpoint and so on. However, it isn't a strict formal process that always will lead to the same result. The outcome depends on your current mood, what you focus on in the music, your habits, what you happend to associate with what according to certain circumstances and so on. Everything is connected in an extremely complicated network of calculations, and the slightest change of a parameter can have profound impact on the outcome.

Compare this situation to something simmilar (I will try to tie up all these examples in the end. Bare with me). Imagine you're producing linguistic statements. The statements doesn't really have to make sense. The only thing that matters is that you keep producing them, even if you really can't think of any meaningfull content to put into them. For example, this is what I produced right now: "I wan't to think that then it isn't really that bad but couldn't you say that again if that's no big problem." Even though I probably would be institutionalized if this was how I usually talked, you can clearly see somewhat of a pattern here. If you read the the whole sentence it's just confusing, but by looking at segments of it, it's actually coherent. "I want to think that", "it isn't really that bad" and "no big problem" are all fully understandable and usable segments that can be put into meaningfull sentences.

Could one argue that this situation is similar to the piano example? Clearly you're following a given set of rules. You have a grammar that you really don't violate and exactly which words you choose to utter depends on a lot of different factors that togheter decide the outcome. So, are both the latter and the former situations examples of someone using their creativity? That naturally depends on how you choose to define the concept of creativity, but let me try to distinguish what's really differs beetween the two.

A computer could carry out the latter task, producing linguistic sentences, without any bigger problems. You just have to give the program at hand a couple of words, assign them to different clause elements and then put down some rules of how it's allowed to combine the different grammatic parts. It won't be perfect, and noone has so far managed to make a fully explicit description of a gramatic system in any human language, but it would be fairly easy to put something togheter that performed about as good as a real human. Is this an example of creativity? Well, some people maybe say so, but it really just boils down to a given set of rules and a couple of randomly asigned values. Not so exciting.

Well, let's turn to the other example. Playing the piano. Isn't this really just a set of patterns, rules and learned behaviours? Well, yes it is. But what makes this behaviour special is all in the feedbak process.

Think about the key example again. What kind of feedback process does take place in it? Well, nothing really. It's pretty simple. If you find the keys, you stop looking. If you don't, you continue the search. There isn't any kind of situation where you sort of find them. So, the feedback response is binary and purely used to decide whether the behaviour should be canceled or not.

Let's get back to the piano. Now, things get a little more complicated. There isn't one way to play it that is the right way. The performance is constantly being judged by the brain on the basis of a lot of different factors. Rythm, harmony, tension, mood, constancy...The list could go on for a pretty long time. If something sounds good, we reinforce the behaviour that led to it. If it sounds bad, we repress it. Of course, this process is at work when we search for our keys too, but to a lesser extent.

I suggest this is the key (there are an awful lot of keys in this text) to creativity. The reason we haven't been able to successfully inplant this preciouss behaviour into computers, is because we haven't figured out what makes us tick, when it comes to these areas accociated with creativity. It's a complicated process to create a computer program that does something we want. It's even harder to make it do it in the same way we do.

I would like to say that computers, in theory, can be just as creative as us humans. The problem is that they're working with another set of preferences than us. Of course we are going to look at the result and say it's worthless when it's created by something that doesn't share our views on what's good. If you would let a cat compose its own meal (don't ask me how that could be carried out) we probably wouldn't like that either. That doesn't mean that the cat did something wrong according to its own measures. It just means that we don't like tuna that much.

Mark lives in IKEA

I saw this guy on the news this morning and it made my day. Or at least my morning. Well, the first ten minutes of it anyway. You see, I descided not to go to sleep this night in an desperate atempt to sync up my diurnal rythm to the rest of the world now when the school starts up again after the holidays. With that said, nothing really stays in my head for more then a couple of minutes today. Anyway, that's not the point. The point is...I forgot. No, got it. The point is that I thought this was hysterical. Or...Well, let's pretend I thought it was hysterical. That sound better than moderatly funny and pretty clever.

Anyway. Mark is some kind of comedian/filmmaker/lunatic who obviously like to get everybodys atention. Apperantly he is famous for that he, and I cite right of his homepage here, "visited and consumed purchases at all 171 Starbucks locations in Manhattan in one day". Well, since I'm not New York based I haven't really heard about him before, but when he commits to his next rather bizarre project, living at IKEA for a week, he's bound to get some atention here in Sweden. I'd be lying if I said I hadn't thought about doing this myself. Who hasn't?

Randy Pausch

I stumbled upon this video when it came out about half a year ago and it fascinated me. It's the last lecture of Randy Pausch, a professor at Carnegie Mellon. The reason it's his last is that he's going to die from pancreatic cancer in the very near future. So, what he tries to do is to sum up his life and at the same time pass something on. The theme of the lecture is "Achieving your childhood dreams", something Randy himself confidently states that he did.

I like this video. Allthough the serious circumstances, Randy is so optimistic you almost get suspicious. Kinda makes you think.

As far as I know, Randy is still alive, and you can follow his progress on his personal site.

Update: On the morning of July 25th, 2008, Randy passed away.

Bring rock'n'roll to the music box

When I searched google for any suitable pictures for the header to this blog (which you can see I haven´t found yet), I stumpled upon an adorable little product over at Grand Illusions. If you're anything like me (I understand that the chanse of that isn't that big), you've also always wished that you could replace the tune that your old music box plays to something funkier. Well, here's an intresting little toy that lets you do exactly that.

It's basicly a hand cranked music box which uses stips of papers, with strategicaly placed holes, to play different songs. The whole process reminds me a little of the good old days when computers where programmed using pasteboard cards with holes punched through them (well, it reminds me of reading of those good old days...The floppy disk ruled the earth when I was a kid).

I'm going to have to try to resist the temptation to order one of these, mainly because I know how frustraded I will get by trying to program Bach's fuga in D-moll, on a piece of paper. Heck, I have trouble geting it right on the piano. However, for all of you musical sadist out there, I recomend a peek at the demo video of this fascinating little device.

Of course...If you want to be really extreme, you can always get yourself one of these.

First post

New year. New blog.

Welcome to Speldosa, my personal blog. Who am I then? Martin is the name I usually respond to. I live in Stockholm, Sweden, and I'm currently studying a wonderfull mixture of fields at Stockholm University. So far I've had the pleasure to learn more about philosophy, cognitive science, linguistics and mathematics and I plan to keep on trying to structure this crazy world through expanding my knowledge.

What I hope to accomplish with this site is pretty simple:

I want to write an intresting blog for you, my dear audience, to read. The blog hasn't got a totaly clear direction, so you might find that the subjects I write about differs quite a lot, ranging from everyday observations to scientific related stuff. I feel that the secret recipe to keeping a project like this alive is to not put to many restrains on it. That is an excelent way to kill your creativity and motivation. At least that's how my sick mind works.

Anyway, I'm sure a red line eventually will reveal itself and if it doesn't....well...I'll just deal with it then.

I should probably mention what "Speldosa" means, for those of you who are feeling your swedish is a bit rusty. Speldosa is the swedish word for music box. I won't tell you the complete backround story to why I choosed to call my blog this (partly because I really don't know myself and want to keep some of the mystiqe), but it will probably, as everything else, get clearer down the road.

Oh, one last thing. Since my native tounge isn't english, I happily listen to anyone who have any complains on my writing. My expectation is that I will develop my skills as I go along with this blog, but there's nothing wrong with a little help from outside. So go ahead. Tear my apart.

Well, enough said. Let's get started.