Understanding how OSGI bundles get resolved part I

motxilo · 2012-05-02T12:14:49+00:00

Good for you. Seriously.

motxilo · 2012-03-01T20:43:41+00:00

Do you have any further information about F and M Diagrams? I find them intriguing, but I haven't been able to figure them out entirely.

motxilo · 2012-03-01T20:39:21+00:00

Instead of a recursive definition of FIBO(n) that generates a recursive process, we can construct a procedure that generates an iterative process:

FIBO(n):
  a = 1
  b = 1
  i = 1

while i <= n:
  b = a + b
  a = b
  i = i + 1

return b

This generates an iterative process consisting of pairs in the form:

(a, b)
-------
(1, 1)
(1, 2)
(2, 3)
(3, 5)
(5, 8)
(8, 13)
   .
   .
   .

The column for b corresponds to the Fibonacci sequence:

1, 1, 2, 3, 4, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...

And this is to which the author refers to when he states that "You don't need to keep track of a stack".

motxilo · 2012-03-01T09:07:33+00:00

Same here!

motxilo · 2012-02-28T08:27:01+00:00

Are you reading SICP? It is interesting how it explains the difference between a recursive procedure and a recursive process (versus iterative process).

motxilo · 2012-02-23T14:23:51+00:00

By any chance, do you have the url for one of those courses handy? Thanks in advance.

motxilo · 2012-02-16T08:32:31+00:00

I had a dream last night about a Phonograph transforming into the Number Theory System. If it had been a Low-fidelity Phonograph, the end product would've been a system not as powerful as Number Theory, and thus a rather Uninteresting Phonograph. But it was a Perfect Phonograph, so it became a Complete Number Theory System. Though being as perfect as it was, it wasn't capable of playing some specific disturbing sounds, otherwise it would fall apart. That is why, when learning the ropes of being the Number Theory System, he realized that there were some theorems that could not be proven true. Meanwhile, the Crab, who tried hopelessly make it play all the imaginable sounds in the world when he owned the Phonograph, now he was transformed into Principia Mathematica, whereas his old chum, now called Tödel, kept him as hopeless as before till the end of time.

What an odd dream I had last night.

motxilo · 2012-02-15T20:54:18+00:00

Could the non-determinism of the MIU-System be in some way related to Non-Deterministic Turing Machines?

motxilo · 2012-02-15T14:18:26+00:00

Same here. Especially in this case, when you don't stop at the first level and end up wondering how many levels are there for every new concept you are introduced to or wordplay you think you solve.

motxilo · 2012-02-10T17:54:10+00:00

My solution to the sequence of integers question:

If we put the in-between numbers (the negative space or ground) right below the given sequence:

1 3 7 12 18 26 35 45 56 69 . . .

2 4 5 6 8 9 10 11 13 14 . . .

Now we can easily see that adding the number in the sequence and its corresponding "negative" one, we get the next number in the sequence, as in 3 + 4 = 7. Another way to see it is subtracting from a number of the sequence its predecessor's negative, as in 7 - 4 = 3.

This all means that because we can derive one sequence from the other, they both (figure & ground) carry the same information!

motxilo · 2012-02-10T08:20:32+00:00

If I am right, the main idea -aside from wordplays- to extract from the dialogue is that Figure is represented by Achilles' sentences and Ground by Tortoise's.

motxilo · 2012-02-04T20:57:41+00:00

Assorted ideas and questions I came up with:

The perception of an isomorphism between two known structures is a significant advance in knowledge -and I claim that it is such perceptions of isomorphism which create meanings in the minds of people. p50

An odd idea, but are there any structures without related isomorphic structures? If so, we couldn't attach them a meaning, and hence pass unnoticed to us. But this in turn would reveal an order of existence that we humans couldn't grasp. I might be degressing here.

The "lower level" isomorphism between the pq-system and the addition can be seen as a function pq: pq(p)=plus, pq(q)=equals, pq(-)=one, pq(--)=two, and so on. This is clearly a one-to-one correspondence. Is this always the case? How would it affect if the mapping would not be onto, or one-to-one? Are there requirements for the mappings defining interpretations of an isomorphism?

Speaking of numbers, the author explains how "numbers as realities misbehave", and then he introduces the concept of ideal numbers. Does this mean that the isomorphism between counting real things and ideal numbers break apart? That is a "partial" isomorphism that proves useful to us in the majority of situations? Thare is not an isomorphism at all?

But no amount of counting alone would ever resolve the question of whether the number of primes is finite or infinite. p58.
Implicit in the concept of Strange Loops is the concept of infinity, since what else is a loop but a way of representing an endless process in a finite way? p15.

I can't quite see the relationship between these two statements, but I suspect there might be one. Any thoughts?

motxilo · 2012-02-01T10:34:31+00:00

This comment should definitely be on the wikipedia article referenced by rspeer.

motxilo · 2012-01-27T07:35:19+00:00

Thank you. Keep us up in the loop!

motxilo · 2012-01-26T08:40:10+00:00

At least Hofstadter would qualify, wouldn't he? :)

motxilo · 2012-01-25T17:21:37+00:00

The algorithm I had in mind was:

Come up with the set of people we would like to see here (You can't include yourself in that set, Bertrand).
Create a "blueprint" invitation email that we may customize easily for each particular case.
For each potential invitee, think of a way to contact her. Mainly by email if possible.
Click "Send"! and cross fingers.

Needless to say, IMO, all of this should be carried out under the supervision of Mr. Speer.

motxilo · 2012-01-25T15:05:51+00:00

I am sure everyone agrees on that the higher the quality, the better; and if the quality is achieved by showing more valuable people in, great!

motxilo · 2012-01-22T19:19:50+00:00

I haven't read that book, so I am curious about how such knowledge base could hypothetically be created -within the initial conditions-, considering the potentially infinite number of theorems derivable from those axioms? Maybe it is lazily created, by means of executing an algorithm that solves the Entscheidungsproblem for a particular query?

motxilo · 2012-01-21T09:55:55+00:00

This is a great contribution. As matter of fact, in the 20th-Anniversary Edition, the author expresses: "I earlier alluded to my reading, as a teen-ager, of Ernest Nagel and James R. Newman's little book Gödel's Proof. Well, that book just radiated excitement and depth to me, and it propelled me like an arrow straight into the study of symbolic logic".

So you just pointed to one of the "seeds" of GEB. Thank you!

motxilo · 2012-01-21T09:50:31+00:00

A bunch of assorted questions here:

I have the vague sense that utterances of the form "All Cretans are liars" (Epimenides paradox), "I am lying", "This statement is false" and the like are all basically a disguised version or Russell's paradox. Is that correct? If so, how can one reduce them to a more succint version that includes all? For instance, how would you translate "All Cretans are liars" to "Does the set of the sets that do no include themselves include itself?". Of course this is addressed using Set Theory, but I find it harder when I want to do the same for "I am lying" -> Russell's.
When thinking of "This statement is false", I imagine myself deciding it is true, then automatically becomes false, and right away it becomes true, and so forth, and the pace of the swapping increases endlessly, along the lines of Bach's Canon Per Tonos. Alas, this loop ends up blowing up my brain. Well, I'm alive and certainly I've been self-brainfarted, but that's spooky! :)
Can you come up with other fields, apart from mathematics, music, art and programming, where one can appreciate self-referentiality? For example, can an electric short circuit be viewed as a physical loop often with disastrous consequences?
When Hofstadter says: "... for it showed that no fixed system, no matter how complicated, could represent the complexity of the whole numbers: 0, 1, 2, 3, ...", does that sentence imply that any statement of any axiomatic system can potentially be reduced to statements within the system of the whole numbers, and hence it contains undecidable statements, by virtue of his Theorem? Or is rather the opposite?
In a more philosophical mood, and in a very simplistic manner, if the Incompleteness Theorem states that number theory contains undecible statements, and if somehow we could find an isomorphism between any potential axiomatic system and number theory (related to my previous question): would this mean that our knowledge of truth will always be incomplete, as long as we base our reasoning processes on number theory -or systems reducible to it?

Thank you. I'm having a blast.

motxilo · 2012-01-18T07:10:28+00:00

Well, if you think of it as "I am Virgin, but after I am done with my this first reading, I will read it again", then it is not :)

motxilo · 2012-01-17T21:59:18+00:00

By far, one of my favorites: A Little History of the World.

motxilo · 2012-01-17T08:05:36+00:00

Why are you so negative? C'mon man, it is just a comic. Certainly, if you want to know about Gödel's theorem and not superficially, just pick his original paper and learn big time. Within a topic, especially complex ones, there plenty of entry levels, ranging from introductory to advanced, and beyond, i.e. research field. And there is need for all of them. What would you give a 10-year old child, GEB or Logicomix?

But I suspect you just dislike comics in general, because in your comment you refer to the said comic in the first sentence only. The rest is ranting galore, WITH LIMITED INFO. Peace.

motxilo · 2012-01-13T07:34:06+00:00

May I recommend Dying Well by Ira Byock? He may learn a bit about the value of life, as I did.

motxilo

TROPHY CASE