Beyond Brute-Force Dictionaries

In the pattern of letting the reader tip-toe in the dark while shouting: “A little bit more left, than you went backwards just before!” Hofstadter carries on with the Jumble puzzles throughout the second chapter. Jumbo, the program which he leaves us so unclear about, supposedly can solve simple and more complex anagrams by bonding letters, syllables and word parts together and forming ever more probable (but not necessarily more meaningful) chunks.

In metaphorically rich language, the author explains how such bonding between such atomic (letter) or molecule-like entities (syllables or intrinsically well fitting pairs or triplets) would carry out. That potential partners could first spark on sight of each other and eventually bond together if no other potential partner in sight would exert even more attraction. This way, all elements mingle first on a very small and detailed level and would then try to bond again with other more evolved structures further up in the hierarchy.

Yet, it does not seem quite plausible, how Hofstadter wants to realize such ranks of attraction level between the potential bonding partners. He suggests a very subjective approach, by bonding the first atomic elements with the help of his own intuitions. I would have rather suggested a probabilistic approach which had the underlying knowledge of how often certain letters proceed others in a certain language. This can be easily done by consulting just a small sample text and analyzing what letters normally occur in the environment of others.

Maybe Hofstadter is going to go into this, and I am being unjust to him. But I would have wished that he went into more detail of the actual realization than using two metaphors over like 5 pages to describe a process that most people have understood from the previous text.

Numbers Go Up, Words Come Down!

Foreword to this post: The reader might not take the lighthearted humor and hidden allusions contained in this post for a mischievous criticism of Douglas Hofstadters work but rather as a funny commentary about the complementary reading experience.

As well written the first chapter of "Fluid Concepts and Creative Analogies might have been and as thrilling Douglas Hofstadter know how to present the topic at hand, in the end it is merely sequences of numbers and their hidden pattern which seem to absorb the authors interest. Hence, I was relieved to find that he found practical application for such specialized cognitive ability by transferring his expertise to the realm of linguistics. - Well not quite yet, but at least since page 87 we are now juggling with words, or rather letters. But better than 86 pages about numbers anyway.

The task of rearranging letters in a word to form meaningful anagrams naturally involves almost the very same processes as in finding the underlying pattern in sequences of numbers. The proximity to everyday usage and implicitness for humans to learn a language, though, spawns totally new approaches to finding solutions for such kind of problems. Also, this way we are able to apply the found methods to other, more practical problems and formulate strategies which do not ground on sheer numeric templates but rather understandable words, found in a dictionary.

Take for example: P A R L E N I A (Try it!!!exclamation mark!!!)

After some time of memorizing the single letters used in this word, one might easily come up with the partial PLAIN and then we would only have A R E left. There are not too many combinations of order we could put the remaining three letters in: ARE or ERA. Both would make sense alone, but would not really form a proper word, put together with PLAIN. So we shuffle again and come up with other partials.

To stay in the tradition of the author I will not reveal which word I have originally come up with, solely to mock the baffled reader.

Mee-To-Phone-Me-None

In one of the last sub-sections of chapter one, Hofstadter explains the “Me-Too”-Phenomenon, which I haven't actually thought about but struck my interest immediately. The concept of this problem (or rather effect) is that people develop their own independent line of thought during a conversation. Either we come up with our own imagery which by definition has to differ from the other person's, we might even think into a different direction, though starting from the same original thought or we just think in analogous to the described story. The outcome, especially but not exclusively of the latter, can be the so-called “Me-too”-Phenomenon, where we answer according to the presented circumstances but just reflect/project them on our situation.

Example: “My dog used to literally eat my homework.” - “Yeah, mine too.”
Clearly in this example the two persons do not mean the first ones homework but theirs individually in analogy. The “Me-Too”-Phenomenon shows how easy it is for humans to think in analogies, sometimes even without noticing it. Applying the same ability to pattern-matching algorithms for example inevitably has to be a tough job, though.

Making a Program more Human

In the current part of Hofstadters text, he explains his approaches to more complex sequences that may be easy to human cognition but are generally hard to crack by computer algorithms. Sequences for example where patterns or numbers move around in lawful manners (e.g. singlers or bouncing doublers) are generally easy to spot by the human eye, but make hardly any sense if deciphered by counting the occurrences of certain numbers or interchanging sequences.

It is their notion of figure and ground according to the Gestalt laws which make these features so salient to us, having to cope with similar effects in nature. Other such features like plateaus (strings of the same number "1111"), up- and down-runs (continuous up- or down-counting sequences, "2345", "98765") and palindromes (symmetrical sequences, "014410") are also salient to the eye, but had hardly any mathematical relevance in the existing sequence-seeking programs before.

Hofstadters suggests some kind of bottom-up approach for finding such 'islands' (as he calls them) first and making sense of them, by finding their connections in the next step. This approach is by far more natural than the previous methods, the author briefly touched in the first sub-chapters. In my opinion, the notion of similarity should also play an important role among the other mentioned features. Even though this criteria would be much harder to implement, due to its broad definition, similarities among islands or slightly deviating sub-sequences reveal most of the connections between them and therefore useful hints about the generation process itself.

After this part of the book, I am actually sorry Hofstadter does not let us in on the actual realization of Seek-Whence program, because I imagine some details of it even more useful than the mere description of problems it can deal with.


[This blog post has been edited after the assigned deadline, because the original post was embarrassingly short and general.]

Perceiving Patterns

Isn't it surprisingly human to seek for patterns in a chaotic world? Douglas Hofstadter tries to do exactly this with naturally or synthetically occurring sequences of numbers in his book "Fluid Concepts and Creative Analogies". Recognizing patterns in the natural environment around us is a viable part of cognition and Hofstadter goes as far as calling it the potential key to intelligence. It comes into play in everyday use as grouping of letters in written language, sounds to meaningful spoken words, perception of geometric structures according to the Gestalt Laws.

Yet, Hofstadter concentrates on stripped down, purely mathematical sequences of numbers which can mostly be explained by repeating the same generation pattern (in his words: templates) over and over. And even though the mathematical construct standing behind such generative sequences, including arithmetic expressions and numbers, was arbitrarily thought up by humans, this kind of miraculous sense-seeking works for the most random sequences. Therefore it is easy to believe in some kind of higher power like Mathgod ("Zahlengott"), Einstein supposedly described as cagey but not wicked.

No matter how random something might be, if you break down the problem in finite space, there always seems to be a pattern emerging from it. I am just not that sure whether there actually can be patterns to all irrational sequences. Because once you thought you figured out the template behind the nth number of permutations, there might be a ‘n+1’th packet that screws up the previous template all together.

The Thinking Machine

For a long time, intelligence was supposed to be the one thing that set us humans apart from the other animals. But as we come to think about it, there is no such clear-cut definition of the term intelligence. It clearly involves the ability to solve problems in general but also to comprehend one's own environment and reflect this comprehension in appropriate behavior. To come up with entirely new ideas or to draw analogies is certainly the strength of humans. Therefore creativity makes up a great deal of the intelligent human being.

But the most ingenious idea the human mind has ever come up with is the idea of a machine or device, which extends its own ability to calculate, think recursively, memorize, communicate, etc... Inventing the computer and similar devices might turn out to be the biggest revolution in intelligence so far, but it might also mark a turn point from which intelligence could regress.