Gödel, Escher, Bach
Introduction
Bach
Stages of complexity of a cannon:
Escher (1902-1972)
Bach and Escher were playing with loops. Such as Bach does with the crab cannon, Escher does with his loops . They are both playing with something that never ends.
Gödel
Essential abilities for intelligence:
How is it that we can make a programmed machine conscious if we built it ourselves?
Bach
Stages of complexity of a cannon:
- Dual, triple, quadruple role (more than one voice singing at different times).
- These copies or repetitions vary in pitch.
- Invert the theme
- Retrograde copy (played backwards in time) (crab cannon).
Escher (1902-1972)
- Notion of strange loops (never ending loops).
- Paradox, illusion, double meaning
- Based on mathematical principles of symmetry and pattern.
- Visions of infinity.
Bach and Escher were playing with loops. Such as Bach does with the crab cannon, Escher does with his loops . They are both playing with something that never ends.
Gödel
- Strange loops in mathematics
- Converted the Epimenides paradox into mathematical terms.
- Math in unprovable.
Essential abilities for intelligence:
- Respond to situations flexibly (choice).
- Take advantage of circumstances.
- Make sense out of ambiguous / contradictory messages.
- Recognize the importance of elements in situations.
- Find similarities against differences.
- Draw distinctions against similarities.
- Synthesize new concepts /ideas.
How is it that we can make a programmed machine conscious if we built it ourselves?
Chapter 1
The MU-Puzzle
Difference between machines and men:
Difference between machines and men:
- Human consciousness notices facts about the task it is set out to do, meanwhile the machine/computer does not. That is why it can go infinitely on searching for answers.
- Machines do not learn patterns, we always look for patterns.
- Humans act observant, machines are totally unobservant. Machines do thing without complaining or getting bored
The MU system with shortening and lengthening, never getting to MU is like a strange loop.
Chapter 2
Meaning and Form in Mathematics
Problem of this book:
Do words and thoughts follow formal rules, or do they not?
Another formal system: pq system
Well-formed string: hyphens, p, hyphens, q, hyphens
P = plus
Q = equal (meaning)
-p-q--
Isomorphism:
Information preserving transformation.
“When two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other, where “corresponding” means that the two parts play similar roles in their respective structures.”
Our multiplications are assumptions.
Numbers as abstractions are different than every day numbers we use.
Problem of this book:
Do words and thoughts follow formal rules, or do they not?
Another formal system: pq system
Well-formed string: hyphens, p, hyphens, q, hyphens
P = plus
Q = equal (meaning)
-p-q--
Isomorphism:
Information preserving transformation.
“When two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other, where “corresponding” means that the two parts play similar roles in their respective structures.”
Our multiplications are assumptions.
Numbers as abstractions are different than every day numbers we use.
Chapter 3
Figure and Ground
Tq system : t = times
Wholes:
Numbers that form non-theorems are negatively defined.
Figure – ground:
A figure or a positive space is drawn inside a frame, a consequence happens, its shade (background, negative space) is also drawn.
Tq system : t = times
Wholes:
Numbers that form non-theorems are negatively defined.
Figure – ground:
A figure or a positive space is drawn inside a frame, a consequence happens, its shade (background, negative space) is also drawn.
Cursively drawable: ground is an accident.
Recursive figure: the ground can be seen as a figure in its own right.
Recursive figure: the ground can be seen as a figure in its own right.
Chapter 4
Consistency, Completeness and Geometry
Music:
Which is the explicit and implicit meaning of contracrostipunctus?
Comparison with the record player and Gödel’s theorem:
Euclid´s Elements:
“The elements began with very simple concepts, definitions, and so forth, and gradually built up a vast body of results organized in such a way that any given result depended on foregoing results.”
“The more common the word, the more associations we have with it, and the more deeply rooted its meaning is.”
How can you define something of which everyone already has a clear concept? Ex: the case of Euclid´s definitions.
You can give isomorphism to different words, but you must be sure of what meaning you are giving to them. (the case of the line in non-Euclidean geometry).
“Consistency is not but a property of a formal system per se, but depends on the interpretation which is proposed for it.
Consistency: every theorem, when interpreted, becomes a true statement.
Inconsistency: there is at least one false statement among the interpreted theorems.
Two ways of looking at consistency:
Music:
- Vibrations in the air that causes us to have emotional responses.
- Gödel’s phonograph theorem.
Which is the explicit and implicit meaning of contracrostipunctus?
Comparison with the record player and Gödel’s theorem:
- “Tortoise says that no sufficiently powerful record player can be perfect (in the sense of being able to reproduce every possible sound from a record).”
- “Gödel says that no sufficiently powerful formal system can be perfect (in the sense of reproducing every single true statement as a theorem.”
Euclid´s Elements:
“The elements began with very simple concepts, definitions, and so forth, and gradually built up a vast body of results organized in such a way that any given result depended on foregoing results.”
“The more common the word, the more associations we have with it, and the more deeply rooted its meaning is.”
How can you define something of which everyone already has a clear concept? Ex: the case of Euclid´s definitions.
You can give isomorphism to different words, but you must be sure of what meaning you are giving to them. (the case of the line in non-Euclidean geometry).
“Consistency is not but a property of a formal system per se, but depends on the interpretation which is proposed for it.
Consistency: every theorem, when interpreted, becomes a true statement.
Inconsistency: there is at least one false statement among the interpreted theorems.
Two ways of looking at consistency:
- Externally consistent:
- Internally consistent:
Chapter 5
Recursive Structures and Processes
Recursive:
When you leave something unfinished and move on to the next thing and don’t come back to the original until you are done with the ones that appeared afterwards. (Unlike recursive in chapter 4, which meant things inside of things.)
Push: suspend operations on the task you are currently on, in order to take up a new task.
Pop: close operations on one level and to resume operations where you left off (in another lower level).
Stack: what restores you to your context once you have returned to a certain level.
Recursive Transition Network (RTN): is a diagram showing various paths which can be followed to accomplish a particular task.
Sameness-in-differentness: in recursion the same thing happens on a different level.
Recursive:
When you leave something unfinished and move on to the next thing and don’t come back to the original until you are done with the ones that appeared afterwards. (Unlike recursive in chapter 4, which meant things inside of things.)
Push: suspend operations on the task you are currently on, in order to take up a new task.
Pop: close operations on one level and to resume operations where you left off (in another lower level).
Stack: what restores you to your context once you have returned to a certain level.
Recursive Transition Network (RTN): is a diagram showing various paths which can be followed to accomplish a particular task.
Sameness-in-differentness: in recursion the same thing happens on a different level.
Chapter 6
The Location of Meaning
Is meaning always inherent in the message or is it manufactured by a mind or mechanism?
Everybody sees things differently.
Exotic isomorphism: two can be mapped onto each other.
Prosaic isomorphism: parts of one structure are easily mappable onto the parts of the other.
“Generally, we can say: meaning is part of an object to the extent that it acts upon intelligence in a predictable way.” (No matter who is decoding it, the meaning will always be the same).
Layers of information:
Chromatic fantasy and feud might be an example of what happens when our meanings of the same thing are different.
Is meaning always inherent in the message or is it manufactured by a mind or mechanism?
Everybody sees things differently.
Exotic isomorphism: two can be mapped onto each other.
Prosaic isomorphism: parts of one structure are easily mappable onto the parts of the other.
“Generally, we can say: meaning is part of an object to the extent that it acts upon intelligence in a predictable way.” (No matter who is decoding it, the meaning will always be the same).
Layers of information:
- Frame message: structural aspects of any information-bearers. Needs a decoding mechanism.
- Outer message: how to decode 3. Trigger.
- Inner message: the one that is being transmitted. Meaning that is intended by the sender.
Chromatic fantasy and feud might be an example of what happens when our meanings of the same thing are different.
Chapter 7
The Prositional Calculus.
Propositional reasoning: reasoning which depends on the correct usage of “if, then, or, not”.
Propositional calculus:
Rule of joining: if X and Y are theorems of the system, then so is the string ( X )
Well-formed strings:
Atoms: p, q, r
Propositional reasoning: reasoning which depends on the correct usage of “if, then, or, not”.
Propositional calculus:
Rule of joining: if X and Y are theorems of the system, then so is the string ( X )
Well-formed strings:
Atoms: p, q, r
Formation rule: if any X and Y are well-formed, then you can form (lengthening rule)
This chapter relates to Fire in the Equations, because you have to have a leap of faith in order for this logic to work. It also relates to A Philosopher Looks at Science, because you assume many things.
Chapter 8
Typographical Number Theory
Otherwise known as TNT.
Numerals: the successor of the successor of zero. ( 0, S0, SS0, SSS0)
Formula: string of TNT.
When a formula is neither true nor false it is called open. The variable that makes it opened is called free variable.
Otherwise known as TNT.
Numerals: the successor of the successor of zero. ( 0, S0, SS0, SSS0)
Formula: string of TNT.
When a formula is neither true nor false it is called open. The variable that makes it opened is called free variable.
The variables that express numbers are quantified.
Parts of Well-formed formulas:
Terms:
Smallest well formed formula: atom
Parts of Well-formed formulas:
- Classes of stings:
- Numeral (SS0)
- Variables (a, b’)
Terms:
- definite (no variables (S0 + S0))
- Indefinite (contain variables ( b + S0)
Smallest well formed formula: atom
Rule of specification: allows the desired string to b e extracted from axiom 1. (takes off universal quantifiers).
Rule of generalization: undoes the action of specification. (allows back a universal quantifier).
Rule of interchange: you can change
Rule of generalization: undoes the action of specification. (allows back a universal quantifier).
Rule of interchange: you can change
Rule of existence: change a term for a variable
Rule of equality:
Rule of succesorship:
Rule of equality:
- Symmetry: P = S, S = R
- Transitivity: R = S, S = T, R = T.
Rule of succesorship:
- Add S: R = T, S = T, R = T
- Prop S: Sr = St, R = T
Chapter 9
Munon and Gödel
General Zen attitude: No words con compare truth.
“Only by stepping outside of logic, can one make a leap to enlightenment.”
Enlightenment: transcending dualism
Dualism: dividing the world into categories
Once we name something we are getting the fact but not the reality as a whole.
“Words lead to some truth, but not all truth.”
What Zen strives for:
Essence of Zen/ism: suppress perception, logical, verbal, dualistic thinking. Un-mode.
Escher’s drawings:
Trying to break the mind of logic.
Show reality and unreality.
General Zen attitude: No words con compare truth.
“Only by stepping outside of logic, can one make a leap to enlightenment.”
Enlightenment: transcending dualism
Dualism: dividing the world into categories
Once we name something we are getting the fact but not the reality as a whole.
“Words lead to some truth, but not all truth.”
What Zen strives for:
- Ism: a way of being without thinking.
Essence of Zen/ism: suppress perception, logical, verbal, dualistic thinking. Un-mode.
Escher’s drawings:
Trying to break the mind of logic.
Show reality and unreality.
Chapter 10
Levels of Description and Computer Systems
Sometimes we have more than one description of a single system. And we maintain both descriptions separate from each other. (We can think of one description without thinking of the other). They are maintained in separate mental compartments.
This is why we are confused about who we really are.
“The many levels of a complex computer system have the combined effect of ‘cushioning’ the user, preventing him from having to think about the many lower-level goings-on which are likely totally irrelevant to him anyway.”
Sometimes we have more than one description of a single system. And we maintain both descriptions separate from each other. (We can think of one description without thinking of the other). They are maintained in separate mental compartments.
This is why we are confused about who we really are.
“The many levels of a complex computer system have the combined effect of ‘cushioning’ the user, preventing him from having to think about the many lower-level goings-on which are likely totally irrelevant to him anyway.”
Chapter 11
Brains and Thoughts
Holism: the whole is greater than the sum of its parts.
Reductionism: A whole can be understood completely if you understand its parts, and the nature of their ‘sum’.
“Fantasy and fact intermingle very closely in our minds, as this is because thinking involves the manufacture and manipulation of complex descriptions, which need in no way be tied down to real events as things.”
Most important cells in our brain: Neurons, and each has a synapses (entry-parts) and axons (output channel).
If all brains have more or less the same composition, what makes each person different? Maybe it's the experience…
Prototype principle: the most specific event can serve as a general example of a class of events.
Could this symbol recognition work the same way as Pinker’s Rules? (We store and relate.)
Knowledge is stored in a spread-out manner. (through out the brain).
Holism: the whole is greater than the sum of its parts.
Reductionism: A whole can be understood completely if you understand its parts, and the nature of their ‘sum’.
“Fantasy and fact intermingle very closely in our minds, as this is because thinking involves the manufacture and manipulation of complex descriptions, which need in no way be tied down to real events as things.”
Most important cells in our brain: Neurons, and each has a synapses (entry-parts) and axons (output channel).
If all brains have more or less the same composition, what makes each person different? Maybe it's the experience…
Prototype principle: the most specific event can serve as a general example of a class of events.
Could this symbol recognition work the same way as Pinker’s Rules? (We store and relate.)
Knowledge is stored in a spread-out manner. (through out the brain).
Chapter 12
Minds and Thoughts
Isomorphisms between brains don't happen, because of the simple notion that everyone has different experiences and different memories.
If brains were isomorphic we would all have or need to have the same memories. (Not even twins are isomorphic)
Our brain from this instance is not isomorphic to our brain of a few moments ago.
The only way to describe how people are more or less alike, in the sense that they think alike can bring up the theory of partial isomorphism.
Global property: the overall shape (not focusing on details too much)
Local property: specific details.
What makes people alike?
Many of the symbols are universal in every human’s network.
“The relationship between the symbols of people with different native languages have every reason to be quite similar, as far as the core is concerned, because everyone lives in the same world. When you come down to more detailed aspects of triggering patterns, you will find that there is less in common.”
Those things that we don't have in common are the experiences that we have had.
Isomorphisms between brains don't happen, because of the simple notion that everyone has different experiences and different memories.
If brains were isomorphic we would all have or need to have the same memories. (Not even twins are isomorphic)
Our brain from this instance is not isomorphic to our brain of a few moments ago.
The only way to describe how people are more or less alike, in the sense that they think alike can bring up the theory of partial isomorphism.
Global property: the overall shape (not focusing on details too much)
Local property: specific details.
What makes people alike?
Many of the symbols are universal in every human’s network.
“The relationship between the symbols of people with different native languages have every reason to be quite similar, as far as the core is concerned, because everyone lives in the same world. When you come down to more detailed aspects of triggering patterns, you will find that there is less in common.”
Those things that we don't have in common are the experiences that we have had.
Haz clic aquĆ para modificar.
Chapter 13
BlooP and FlooP and GlooP
Recursive:
I believe that people believe more in the regularity and predictability of numbers because it sounds more coherent and may appear more beautiful than a chaos theory.
TNT is at least complete with respect to primitive recursive predicates.
George Cantor: founder of set theory. Diagonal method.
Cantor’s infinity types:
1. How many entries there can be in an infinite directory or table.
2. How many real numbers there are.
Recursive:
- Primitive recursivity
- General recursivity
I believe that people believe more in the regularity and predictability of numbers because it sounds more coherent and may appear more beautiful than a chaos theory.
TNT is at least complete with respect to primitive recursive predicates.
George Cantor: founder of set theory. Diagonal method.
Cantor’s infinity types:
1. How many entries there can be in an infinite directory or table.
2. How many real numbers there are.
Chapter 14
On Formally Undecidable Propositions of TNT and Related Systems
TNT is capable of introspection / Self-reference.
Proof-pair: a pair of natural numbers related in a particular way.
Quinning: Self-reference
TNT is capable of introspection / Self-reference.
Proof-pair: a pair of natural numbers related in a particular way.
Quinning: Self-reference
Extra numbers beside natural numbers: supernatural numbers.
Natural # + supernatural # = generalized naturals.
Natural # + supernatural # = generalized naturals.
Chapter 15
Jumping Out of the System
When TNT is extended ad infinitum and still can’t be made complete, then it is said to suffer from, Essential Incompleteness.
The possibility of constructing, in a given system, an undecidable string via Gödel’s self-reference method (alternate of TNT) depends on:
1. The system should be rich enough so that all number statements can be expressed within it.
2. All general recursive relations should be represented by formulas in the system.
3. Axioms and typographical patterns defined by rules should be recognizable by decision procedure.
According to J.R. Lucas:
“For a computer to be considered as intelligent as a person is, it must be able to do every intellectual task which a person can do.”
He is claiming that computers can Gödelize.
Lucas says computer programs can never know as much as we know because we are always outside the system, where we can perform the Gödelizing operation, which the program can’t do because it is within the system.
But then again…. Humans are also incomplete (or the brain).
Just as we can’t jump out of the system ourselves to see our face, TNT can’t jump out of itself.
When TNT is extended ad infinitum and still can’t be made complete, then it is said to suffer from, Essential Incompleteness.
The possibility of constructing, in a given system, an undecidable string via Gödel’s self-reference method (alternate of TNT) depends on:
1. The system should be rich enough so that all number statements can be expressed within it.
2. All general recursive relations should be represented by formulas in the system.
3. Axioms and typographical patterns defined by rules should be recognizable by decision procedure.
According to J.R. Lucas:
“For a computer to be considered as intelligent as a person is, it must be able to do every intellectual task which a person can do.”
He is claiming that computers can Gödelize.
Lucas says computer programs can never know as much as we know because we are always outside the system, where we can perform the Gödelizing operation, which the program can’t do because it is within the system.
But then again…. Humans are also incomplete (or the brain).
Just as we can’t jump out of the system ourselves to see our face, TNT can’t jump out of itself.
Chapter 16
Self-Ref and Self-Ref
René Magritte
Examples of self-reference:
1. This sentence contains five words.
2. This sentence is meaningless because it is self-referential.
“The Quine construction is quite like the Gödel construction, in the way that it creates self-reference by describing another typographical entity which, as it turns out, is isomorphic to the Quine itself.”
Description of the new typographical entity is made by:
1. Instructions telling how to build a phrase.
2. Template; the construction materials to be used.
Pointer phrases are interpreted by the context.
Self-rep: self-reproducing.
Self-ref: self-referential.
What is the original (examples):
There can be a parallel between:
1. Formal systems and strings
2. Cells and strands of DNA
3. Record players and records
Examples of self-reference:
1. This sentence contains five words.
2. This sentence is meaningless because it is self-referential.
“The Quine construction is quite like the Gödel construction, in the way that it creates self-reference by describing another typographical entity which, as it turns out, is isomorphic to the Quine itself.”
Description of the new typographical entity is made by:
1. Instructions telling how to build a phrase.
2. Template; the construction materials to be used.
Pointer phrases are interpreted by the context.
Self-rep: self-reproducing.
Self-ref: self-referential.
What is the original (examples):
- A program, when interpreted by some interpreter running on some computer, prints itself out.
- A program, when interpreted by some interpreter running on some computer, prints itself out along with a complete copy of the interpreter.
- A program, when interpreted by some interpreter running on some computer, not only prints itself out along with a complete copy of the interpreter, but also directs a mechanical assembly process in which the second computer, identical to the one on which the interpreter and the program are running is put together.
There can be a parallel between:
1. Formal systems and strings
2. Cells and strands of DNA
3. Record players and records
Chapter 17
Church, Turing, Tarski and Others
Crab: “The sense of Beauty is the exclusive domain of conscious minds, minds which through the experience of living have gained a depth that transcends explanation by any mere set of rules.”
One of the main theses of the book:
“That every aspect of thinking can be viewed as a high-level description of a system which, on a low level, is governed by simple, even formal rules.” System = Brain.
AI(artificial intelligence)
Aim = “To get what is happening when one’s mind silently and invisibly chooses, from a myriad of alternatives, which one makes most sense in a very complex situation.”
In other words, our intuition. How do we know what to choose? We almost do it intuitively. When we talk to someone, we are choosing relevant information to analyze.
Church’s theorem: There is no infallible method for telling theorems of TNT to non-theorems.
Tarski-Church-Turing theorem: there is no infallible method for telling true from false statements of number theory.
PICTURE FIGURE 106
“A number theory problem, once stated is complete in and of itself. A real-world probles, on the other hand, never is sealed off from any part of the world with absolute certainty.”
Problems in real life are affected by many external things, things that don't have really anything to do with the problem. That's why is can never be sealed off.
Church-Turing thesis, soulists’ version: Some kinds of things which a brain can do can be vaguely approximated on a computer but not most, and certainly not the interesting ones. But anyway, even if they all could, that would still leave the soul to explain, and there is no way that computers have any bearing on that.
This could be related to what Kemeny in A Philosopher looks at science and what Armando says in class. You can never reach the whole of something, we will always have approximations to things, and that is was far as we can get.
FIGURE 109
Crab: “The sense of Beauty is the exclusive domain of conscious minds, minds which through the experience of living have gained a depth that transcends explanation by any mere set of rules.”
One of the main theses of the book:
“That every aspect of thinking can be viewed as a high-level description of a system which, on a low level, is governed by simple, even formal rules.” System = Brain.
AI(artificial intelligence)
Aim = “To get what is happening when one’s mind silently and invisibly chooses, from a myriad of alternatives, which one makes most sense in a very complex situation.”
In other words, our intuition. How do we know what to choose? We almost do it intuitively. When we talk to someone, we are choosing relevant information to analyze.
Church’s theorem: There is no infallible method for telling theorems of TNT to non-theorems.
Tarski-Church-Turing theorem: there is no infallible method for telling true from false statements of number theory.
PICTURE FIGURE 106
“A number theory problem, once stated is complete in and of itself. A real-world probles, on the other hand, never is sealed off from any part of the world with absolute certainty.”
Problems in real life are affected by many external things, things that don't have really anything to do with the problem. That's why is can never be sealed off.
Church-Turing thesis, soulists’ version: Some kinds of things which a brain can do can be vaguely approximated on a computer but not most, and certainly not the interesting ones. But anyway, even if they all could, that would still leave the soul to explain, and there is no way that computers have any bearing on that.
This could be related to what Kemeny in A Philosopher looks at science and what Armando says in class. You can never reach the whole of something, we will always have approximations to things, and that is was far as we can get.
FIGURE 109
Chapter 18
Artificial Intelligence Retrospects
Turing test:
An interrogator, a computer and a human.
Through a series of questions, the interrogator must figure out which one is human and which one is a computer. The computer will most likely answer complicated mathematical problems faster than humans.
Larry Tesler’s Theorem: The AI is whatever hasn’t been done before. Once it has been programmed, people stop believing it is AI.
Problem reduction:
Whenever one has a long-ranged goal, there are usually sub-goals whose attainment will aid in the attainment of the main goal. So, it breaks up the problem into sub-problems.
Depending on how you perceive the problem, you can have many different solutions (each time you pick a route, it has different outcomes)
“Are there highly repetitious situations which occur in our lives time and time again, and which we handle in the identical stupid way each time, because we don’t have enough of an overview to perceive their sameness?”
To notice if this happens we would have to step out of our system onto a higher level. This relates to how our brains, also work as programs from time to time.
“When a human forgets, it most likely means that a high-level pattern pointer has been lost – not that any information has been deleted or destroyed.”
Turing test:
An interrogator, a computer and a human.
Through a series of questions, the interrogator must figure out which one is human and which one is a computer. The computer will most likely answer complicated mathematical problems faster than humans.
Larry Tesler’s Theorem: The AI is whatever hasn’t been done before. Once it has been programmed, people stop believing it is AI.
Problem reduction:
Whenever one has a long-ranged goal, there are usually sub-goals whose attainment will aid in the attainment of the main goal. So, it breaks up the problem into sub-problems.
Depending on how you perceive the problem, you can have many different solutions (each time you pick a route, it has different outcomes)
“Are there highly repetitious situations which occur in our lives time and time again, and which we handle in the identical stupid way each time, because we don’t have enough of an overview to perceive their sameness?”
To notice if this happens we would have to step out of our system onto a higher level. This relates to how our brains, also work as programs from time to time.
“When a human forgets, it most likely means that a high-level pattern pointer has been lost – not that any information has been deleted or destroyed.”
Chapter 19
Artificial Intelligence Prospects
Almost:
“In every day thought, we are constantly manufacturing mental variants on situations we face, ideas we have or events that happen, and we let some features stay exactly the same while others ‘slip’.”
This is like the essay I wrote. What if this is something that we are programmed to do? Everybody creates scenarios in their heads when things should’ve gone one way or another. Also when an event has passed we always think or imagine what could’ve been. Even strange but possible replays.
“I believe that ‘almost’ situations and unconsciously manufactured subjunctives represent some of the richest potential sources of insight into how human beings organize and categorize their perceptions of the world.”
Bongard problems: intended for patter-recognizers (human or machine)
Fission: gradual divergence of a new symbol from its parent symbol (symbol from which it was copied)
Fusion: two or more originally unrelated symbols participate in a ‘joint activation’, passing messages so tightly back and forth that they are bound together and the combination can thereafter be addressed as if it were a single symbol.
Conceptual mapping: a process that can be seen as a succession of mappings of ideas, at varying levels of abstraction.
kind of what we do at the MPC. (meta-essays, meta-dialogues)
conceptual skeletons: abstract structures which connect up to two different ideas.
“One of the major characteristics of each idiosyncratic style of thought is how new experiences get classifies and stuffed into memory, for that defines the ‘handles’ by which they will later be retrievable. And for events, objects, ideas, and so on – for everything that can be thought about there is a wide variety of ‘handles’.”
If our brain really does work like frames and slots then it works the same way as Pinker’s concepts.
“If I tell ‘picture a river bank’ you will invoke a visual image which has various features.”
Almost:
“In every day thought, we are constantly manufacturing mental variants on situations we face, ideas we have or events that happen, and we let some features stay exactly the same while others ‘slip’.”
This is like the essay I wrote. What if this is something that we are programmed to do? Everybody creates scenarios in their heads when things should’ve gone one way or another. Also when an event has passed we always think or imagine what could’ve been. Even strange but possible replays.
“I believe that ‘almost’ situations and unconsciously manufactured subjunctives represent some of the richest potential sources of insight into how human beings organize and categorize their perceptions of the world.”
Bongard problems: intended for patter-recognizers (human or machine)
Fission: gradual divergence of a new symbol from its parent symbol (symbol from which it was copied)
Fusion: two or more originally unrelated symbols participate in a ‘joint activation’, passing messages so tightly back and forth that they are bound together and the combination can thereafter be addressed as if it were a single symbol.
Conceptual mapping: a process that can be seen as a succession of mappings of ideas, at varying levels of abstraction.
kind of what we do at the MPC. (meta-essays, meta-dialogues)
conceptual skeletons: abstract structures which connect up to two different ideas.
“One of the major characteristics of each idiosyncratic style of thought is how new experiences get classifies and stuffed into memory, for that defines the ‘handles’ by which they will later be retrievable. And for events, objects, ideas, and so on – for everything that can be thought about there is a wide variety of ‘handles’.”
If our brain really does work like frames and slots then it works the same way as Pinker’s concepts.
“If I tell ‘picture a river bank’ you will invoke a visual image which has various features.”