Chapter 1. What is Knowledge?
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5. Free Will
1. Essence of Knowledge
⑴ Truth Exists.
① Overview
○ Some argue that influenced by postmodernism, truth varies according to individuals. However, developing logic after truth’s existence is uncertain becomes meaningless. The conclusion that truth exists in this world is obtained through a simple thought experiment.
② Proof of the Existence of Truth
○ Step 1. Assume there is no truth in the world.
○ Step 2. “The fact that there is no truth” becomes a truth itself.
○ Step 3. The assumption of no truth leads to a contradiction.
③ Examples of Truth
○ p ∩ ~ p = ø
○ p = p
④ Nothing (void) = Empty set ∅ = Complement of the truth set
⑵ Mathematics is Precise. Because the Universe Exists.
① There are no contradictory theorems in mathematics that we can understand. Because we exist.
② Example: Double Counting in Combinatorics
○ Represents the same number of cases whether counted by path A or path B for the same event
○ Although it’s always assumed that the same conclusion is reached, if this weren’t the case, the universe couldn’t exist.
⑶ The Physical World Resembles Mathematics.
① There are several axioms in the laws of physics that cannot be proven.
○ Concept of energy
○ Concept of momentum
○ F = ma
○ Curved space concept
○ Law of entropy
○ Standard model
② If the physical world unfolds with some axioms, combining these axioms can yield derived theorems.
○ Example 1. Using F = ma and the concept of energy, energy conservation can be derived.
○ Example 2. Using F = ma, conservation of angular momentum can be derived.
⑷ A Perfect System Isn’t Perfect in Itself.: This proposition could deny the existence of truth, so further study is needed.
① Here, let’s consider a perfect system as one that is static and stable.
② Reasons
○ Reason 1. Water stagnates and rots.
○ Reason 2. Stable systems can’t cope with unexpected uncertainties.
○ Reason 3. It can’t save the losers. Thus, it continues to carry elements like dissatisfaction.
○ Reason 4. Constant problems arise because the world is interesting.
③ Reference
○ Reference 1. Karl Popper: Accumulate the knowledge system based on continuous refutations rather than perfect proofs. However, because historically there hasn’t been much history of refutation, the credibility of this hypothesis is being questioned.
○ Reference 2. Psycho-Pass: “A completely perfect society is an illusion.”
○ Reference 3. Gödel’s incompleteness theorems mathematically prove that no system can be perfect.
④ Conclusion: Ultimately, I think stable systems fall into one of two categories.
○ Systems constantly in dynamic equilibrium
○ The problem is that dynamic equilibrium systems change into static equilibrium the moment they lose dynamism.
○ Systems constantly advancing: Note that I believe humanity can endlessly progress and should progress.
○ However, stable systems could be either of these systems or neither.
⑤ Application 1. If knowledge is organized once and never revised, it’s imperfect knowledge.
○ Thus, knowledge must be alive and evolving.
○ Just as food must be broken down into molecules for digestion, knowledge must be broken down into concepts for digestion.
○ This can be seen through the history of Einstein challenging Newtonian dynamics.
○ Forgetting, that is, removing unnecessary and incorrect knowledge, is also important.
○ Knowledge systems can also be alive; refer to here.
⑥ Application 2. Elections induce political dynamism, paradoxically stabilizing society.
⑦ Application 3. The fact that humans undergo a complete change in atomic composition in 7 days(?) supports this dynamic equilibrium hypothesis.
⑧ Application 4. Science and technology create constant new changes, thus placing society in dynamic equilibrium rather than static equilibrium.
⑸ It’s impossible to define certain concepts perfectly.
① Since there are exceptions to every concept,
○ (Negative) Can it be said that there are exceptions to the various geometric laws in Euclid’s Elements?
② Is there a limit to understanding concepts based purely on rules, and is pattern recognition based on deep learning necessary?
○ (Positive) Google DeepMind’s AlphaGeometry successfully performing symbolic deduction proves this.
⑹ Knowledge transcends emergence.
① In bioinformatics, even data of the same modality often do not integrate well because they are at different stages of emergence.
○ Example: Even if all data are liver spatial transcriptomics, whether liver zonation can be identified depends on spatial resolution and gene expression intensity.
② Knowledge, although syntactically the same as “A is B,” may vary in its valid scope.
③ By exploring the boundaries of the valid scope of each piece of knowledge, the principles of emergence can be discovered.
⑺ Knowledge is an indeterminate proposition.
① Exception: Mathematical knowledge
② Each piece of knowledge also contains indeterminacy, and sometimes it does not hold true even within its valid scope.
③ Knowledge generally possesses the attributes of an indeterminate proposition, and it can only be asserted as true based on logical consistency and statistically significant frequency.
④ Instances where the knowledge is deemed true can be called a signal, while instances where it is deemed false can be called noise. (cf. Error theory)
⑤ Between uncertain propositions, there are reinforcing and canceling interferences, but between certain propositions, there is no interference, only contradiction.
○ Example: If multiple similar pieces of evidence are found, the reinforcing interference becomes stronger, making the uncertain proposition closer to the truth.
2. Generation of Knowledge
⑴ Humans Have the Ability to Attain Truth.
① Through the thought experiment earlier, we came to know that “truth exists” by proving the existence of truth.
② Furthermore, we can identify two additional examples of truth.
○ p ∩ ~ p = ø
○ p = p
③ Through ① and ②, the ability of humans to attain truth has been demonstrated.
⑵ Humans Can Grasp Abstract Concepts.
① Fundamentally, humans need concrete objects in their minds to understand.
② However, using other knowledge and mathematical principles, humans can understand knowledge beyond the physical world.
○ If there were mathematical principles in 1, 2, and 3 dimensions, we can confirm them in the 4th dimension.
○ Since the mathematical principles modeled by the brain are concepts that transcend the physical world, this is possible.
⑶ Humans Can Understand Contradictions.
① People focus on several key pieces of knowledge corresponding to the general principle.
② Then, they connect new knowledge around those principles.
③ This forms a hierarchy (e.g., causal relationships, logical relationships) between the two pieces of knowledge.
④ Continuously forming hierarchical relationships between knowledge leads to situations where two conflicting higher-level pieces of knowledge connect to one lower-level knowledge.
⑤ This process is similar to Euclid’s “Elements.”
⑷ We can understand the universe, which includes us.
① (Negative) However, we believe that we cannot observe emergent properties beyond the macro-level society. We think that AI is necessary to overcome this cognitive limitation. (
[Cognitive Horizon and AI as a Breakthrough](https://jb243.github.io/pages/2410))
⑸ Nature is always repetitive and orderly.
① Therefore, even following a single thread of thought can lead to discovering the truth.
② The lesson from backpropagation in deep learning is that by gradually approaching the truth, one can eventually reach it.
⑹ Knowledge can also undergo M & A (mergers and acquisitions).
① In other words, through the power of categorization, a single concept can encompass many other concepts and be considered a more fundamental concept.
② These higher-level concepts are commonly referred to as meta-knowledge.
③ The key to the success of philosophical bestsellers was ultimately creating higher-level knowledge.
○ General relativity
○ Selfish gene
○ What is justice?
④ I describe the integration of knowledge into deeper and more abstract concepts as the “Tower of Babel of knowledge.”
Figure 1. Tower of Babel of knowledge
⑺ AI can generate knowledge.
① Example: AlphaFold3, FunSearch, AlphaGeometry
② (Negative) Writing has its own personality, but is it reasonable to automatically generate that?
③ (Negative) How can we control hallucinations caused by AI?
④ (Positive) Just as there is an event horizon in human understanding, there might be a boundary of human understanding, and we might need to use AI like a telescope.
○ It seems that the information derived by AlphaFold3 in the molecular world really acts like a microscope. And this role as an observational tool seems more suited to diffusion models than transformers.
○ Even if AI measures knowledge, humans should be the ones to accept it as truth. Therefore, AI’s hallucinations might not be a significant problem.
○ If AI can expand the human event horizon, perhaps the AI’s event horizon should be expanded by a super AI (AI of AI)?
⑻ How far can our understanding go?
① Can we eventually understand all the complexity of biology?
② For instance, trying to understand down to the atomic level becomes impractical due to the overwhelming amount of information.
③ This is where coarse-grainability can be important.
⑼ The emergence of ChatGPT encourages the creation of new knowledge.
① New knowledge is often gained through experimentation or errors, but can machines do that?
② (Agreement) Just as Einstein’s theory of relativity emerged from thought experiments, machines can also acquire new knowledge.
③ (Agreement) As seen with The AI Scientist, it seems quite possible to generate knowledge in the realm of programming or coding.
③ (Disagreement) Relativity became knowledge due to Eddington’s observational experiment.
④ (Disagreement) Human errors or thought experiments might arise from unique quantum mechanical errors in humans.
⑤ (Disagreement) I’ve tried JavaScript coding with ChatGPT 4.0 recently, and not only did not all the code work, but unintended effects also emerged. This is because the in-silico world with semiconductors as working units is relatively deterministic, while our real-world with quantum units is significantly noisier and less predictable. Thus, experimentation is essential in this world.
3. Organization of Knowledge
⑴ All knowledge can be ordered.
① (Agreement) Every piece of knowledge can be expressed as an individual sentence, and each sentence can be vectorized using a sentence embedder. For example, the
all-MiniLM-L6-v2sentence embedder maps variable-length sentences under a certain maximum length to a 384-dimensional embedding space. As a result, sentences with similar meanings are placed close together in this multidimensional space. Therefore, it is possible to map each piece of knowledge on a virtual map and assign an order to the knowledge, similar to how paths on a map are navigated.
② Additionally, the order of knowledge is more one-way than expected.
○ This is because the world is composed according to the principle of emergence. The laws of atoms apply to cells, but the laws of cells do not apply to atoms.
○ Following the principle of emergence inherent in nature, I envision the order of knowledge progressing from natural sciences to life sciences, to social sciences, and then to historical sciences.
③ Because we can order knowledge, all concepts are continuous.
○ Thus, all knowledge can be placed on a single map.
○ For example,
F = mais close to Maxwell’s laws (in terms of being physics), but it is far from game theory.
Figure 2. Various pieces of knowledge laid out on a single map
⑵ Memories aren’t eternal. However, records can be.
⑶ The amount of knowledge can be quantified through information theory.
① The amount of knowledge is proportional to the level of interest.
② Deeper knowledge leads to more complex relationships between knowledge.
○ [LTP](https://jb243.github.io/pages/464#:~:text=%E2%91%B5-,LTP,-(long%2Dterm%20potentiation)(long-term potentiation): The more connections between knowledge, the longer it remains in memory.
③ Perhaps the amount of knowledge isn’t substantial.
○ Therefore, organizing all human knowledge might not be difficult. Thus, achieving equality of knowledge might not be challenging.
○ The success of ChatGPT shows the limited amount of knowledge.
④ Among natural science, applied science, social science, and historical science, applied science (human realm) has the most information, followed by natural science (divine realm).
○ However, this is from a human-centric perspective; practically, natural science has the most information.
○ However, just as there is an event horizon in natural science, there might be a boundary of human understanding, and we might need to use AI like a telescope.
⑤ There are core concepts with vast amounts of information.
○ For example, “F = ma,” theory of evolution, etc.
○ It’s possible that humanity could gather all core concepts in this world.
⑷ With ChatGPT’s appearance, the importance of organizing knowledge might diminish.
① (Negative) Creating an easily comprehensible system of organizing knowledge might be beyond ChatGPT’s capabilities.
○ Reason: It belongs to the realm of art that machines can’t replicate.
⑸ The amount of knowledge should be infinite.
① Since human progress should be eternal. Even if humanity does not last forever, knowledge at least is eternal.
② The fields in which humans, who are based on quanta, outperform AI, which is based on transistors, are areas where the amount of knowledge forms an entire universe.
③ When Einstein was a teenager, he reportedly asked his mother, “What if there’s nothing left to research when I grow up?” However, he went on to develop quantum mechanics and the theory of relativity. So, what about now?
④ A breakthrough called AI has been found that can greatly expand the total amount of human knowledge, if not to infinity. (ref)
⑹ Humans understand knowledge as a tree.
① Reason 1: There is a thought process that starts from the self because the thought process, with the self as the root node, has been preserved throughout a long history of evolution.
② Reason 2: The principles of nature endorse a one-way knowledge tree derived from emergent properties.
③ Whether the system of knowledge is a tree or a graph, the value of that system is proportional to the square of the number of nodes (propositions).
○ Having value means containing more information.
○ This conclusion is an application of Metcalfe’s law.
⑺ Learning Volume Over Time
① The amount of information acquired when learning a discipline generally increases over time, provided that memory remains largely unaffected.
○ Once knowledge is acquired, it is usually retained. By learning new information, even if previous errors are corrected, the overall amount of information collected on the subject increases.
② Stage 1: Initially, learning speed is slow.
○ To master a field, one must effectively overcome the bottleneck that hinders exponential growth.
○ For example, in physics, understanding F=ma can be the bottleneck.
③ Stage 2: During the intermediate stage, exponential growth is experienced.
○ This is due to Metcalfe’s law.
④ Stage 3: Afterward, the acquisition of new information slows down.
○ Reason: This happens because most of the information offered by the discipline has been learned, or accessing additional information becomes significantly costly.
○ Due to inherent human forgetfulness, the amount of learning may even decrease.
⑻ Dunning-Kruger Effect: Wisdom-Confidence Curve
① When a person experiences exponential growth in a particular field, it is usually accompanied by a rapid increase in confidence.
○ (Negative) The Dunning-Kruger effect does not necessarily need to be limited to a ‘specific field’.
② In later stages, confidence is undermined for the following reasons:
○ Reason 1: It becomes prohibitively costly to learn additional information.
○ Reason 2: Discovering new higher-level knowledge (root nodes) and realizing that one knew only half of it.
③ However, if a person studies the field for a long time, confidence gradually increases due to the perception that they have experienced most aspects of the field.
⑼ Curiosity and Indifference
① Curiosity: The motivation to explore knowledge outside one’s own domain. The knowledge system can collect information across various aspects, which is beneficial in the long term.
② Indifference: The motivation to explore depth within one’s own domain. Maximizes Metcalfe’s law by enhancing the efficiency of one’s knowledge system. Short-term benefit.
③ If curiosity leads to acquiring knowledge from different domains, resulting in n knowledge systems, the amount of information only increases n times. However, if these knowledge systems are integrated and organically connected, the amount of information increases exponentially according to Metcalfe’s law.
④ The reason people choose between curiosity and indifference is due to the historical context in which they have lived and the energy needed to broaden one’s domains.
⑽ The connectivity of knowledge not only benefits learning but also enhances the reliability of the knowledge system.
① Reason 1: The better organized the knowledge, the easier it is to find logical relationships and contradictions.
② Reason 2: The truthfulness of a specific fact can only be inferred through the logical relationships of existing propositions.
③ Question: What is correct when two logical systems, each without inherent contradictions, contradict each other?
○ This may be related to Gödel’s incompleteness theorem.
4. Sharing of Knowledge
⑴ Objectives
⑵ Methods
① Taking blockchain as an example, sharing knowledge could be a method to preserve knowledge eternally and completely.
② Encouraging public participation through knowledge sharing is an example of crowdsourcing.
③ Science values openness, while technology values secrecy.
○ The openness of technology, such as open-source, might stem from a new era where the impact and preemptive effects gained from revealing technology outweigh exclusive gains from keeping it hidden.
○ Copyright laws that prioritize idea protection are fundamentally at odds with sharing knowledge. Therefore, sharing knowledge might supersede copyright laws.
⑶ Effects
① Through sharing knowledge, one can gain power (whether an entity or individual).
② Does the realization of knowledge equality signify the end of elitism?
○ Is the realization of equality synonymous with justice?
○ Does the end of elitism equate to justice?
○ Does knowledge equality inevitably lead to the end of elitism?
○ Sub-conclusion: Currently, partial elitism is advantageous (because it is unclear who the elites are), but opportunities for the future should be provided equitably.
5. Free Will
⑴ Does a distinct human free will exist compared to machines?
① Human errors or random thoughts ultimately stem from quantum mechanical errors that naturally occur in organic matter, which can provide the driving force for thought experiments. I consider this the greatest difference between humans and machines.
② If thought experiments are based on quantum mechanical errors, could humans challenge divine-determined causality?
③ Recently, research has been conducted to explain free will through chaos theory.
○ Chaos theory suggests that even a very slight difference in initial conditions can lead to completely different outcomes. Quantum biological signals can also create differences in these initial conditions.
○ Is free will the same as predestined fate?
⑵ Instances when free will manifests
① Problems not applicable to paradigms: New problems demanding creative solutions.
② Inherent contradictions in paradigms: Can be one’s own paradigm or humanity’s as a whole.
③ Experimentally generating networks between concepts arbitrarily: If unsatisfactory, inappropriate knowledge is discarded.
Input: 2023.02.02 12:09
Modification: 2023.03.15 21:18