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tanszek:oktatas:techcomm:information_-_basics:sciences

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tanszek:oktatas:techcomm:information_-_basics:sciences [2024/09/09 20:33] – [What is science?] kneheztanszek:oktatas:techcomm:information_-_basics:sciences [2024/09/12 17:53] (current) – [Deductive Sciences] knehez
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 //Science// has been highlighted because of the following criteria from our historically established social forms of consciousness: //Science// has been highlighted because of the following criteria from our historically established social forms of consciousness:
  
-  * they possess high-reaching concepts or logical tools to formulate or express broad, general or universal **principles** or **laws**.+  * they possess high-reaching concepts or logical tools to formulate or express broad, general or universal **principles** or **laws** (e.g. gravity, axioms, [[https://en.wikipedia.org/wiki/Maxwell%27s_equations|Maxwell's equations]]) 
 +   
 +  * they can describe the objective **conditions** under which these principles or laws will prevail.
  
-  * they possess the required logical tools or methods that can help us to calculate or predict **results** in given circumstances+  * they possess the required logical tools or methods that can help us to calculate or predict **results** in given circumstances,
  
-  * they can describe the objective **conditions** under which these principles or laws will prevail.+According to **principles**, **conditions** (circumstances), and **results** (these three general aspects) we can categorize every scientific problem into the following problem groups.
  
 ====== Inductive Sciences ====== ====== Inductive Sciences ======
- 
-According to **principles**, **conditions** (circumstances), and **results** (these three general aspects) we can categorize every scientific problem into the following problem groups. 
  
 **Induction**: the physical conditions are known, just like the results, and we are seeking for the general principle. this is the classical type of experimental physics problem. **Induction**: the physical conditions are known, just like the results, and we are seeking for the general principle. this is the classical type of experimental physics problem.
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   - **Inductive Hypothesis**: Assume that for any binary tree with \(k\) nodes, the number of edges is \(k-1\).   - **Inductive Hypothesis**: Assume that for any binary tree with \(k\) nodes, the number of edges is \(k-1\).
   - **Inductive Step**: We must prove that if the statement holds for a binary tree with \(k\) nodes, then it also holds for a binary tree with \(k+1\) nodes. \\ Suppose we add one more node to the binary tree, bringing the total number of nodes to \(k+1\). When we add this node, we also add exactly one edge connecting the new node to an existing node in the tree (either as a left or right child of a parent node). \\ \\ By the inductive hypothesis, the tree with \(k\) nodes has \((k - 1)\) edges. Adding one more node introduces one additional edge, so the number of edges in the tree with \((k + 1)\) nodes is: $$ (k-1) + 1 = k $$ This matches the formula for the number of edges in a tree with \((k + 1)\) nodes, which should be \((k-1) + 1 = k\).    - **Inductive Step**: We must prove that if the statement holds for a binary tree with \(k\) nodes, then it also holds for a binary tree with \(k+1\) nodes. \\ Suppose we add one more node to the binary tree, bringing the total number of nodes to \(k+1\). When we add this node, we also add exactly one edge connecting the new node to an existing node in the tree (either as a left or right child of a parent node). \\ \\ By the inductive hypothesis, the tree with \(k\) nodes has \((k - 1)\) edges. Adding one more node introduces one additional edge, so the number of edges in the tree with \((k + 1)\) nodes is: $$ (k-1) + 1 = k $$ This matches the formula for the number of edges in a tree with \((k + 1)\) nodes, which should be \((k-1) + 1 = k\). 
 +
 +https://en.wikipedia.org/wiki/Mathematical_induction
  
 ====== Deductive Sciences ====== ====== Deductive Sciences ======
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 Logic can only state that the results will be true if the premises are true (and consistent) and the arguments are logically correct. Logic can only state that the results will be true if the premises are true (and consistent) and the arguments are logically correct.
  
-//Bonus Content//:+**Example**:
  
 János Bólyai – a famous Hungarian mathematician – wrote this famous sentence to his father: János Bólyai – a famous Hungarian mathematician – wrote this famous sentence to his father:
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 {{:tanszek:oktatas:techcomm:information_-_basics:pasted:20240908-180605.png?320x220}} {{:tanszek:oktatas:techcomm:information_-_basics:pasted:20240908-180605.png?320x220}}
 +
 +The quote from [[https://en.wikipedia.org/wiki/Niels_Bohr|Niels Bohr]], //"In the Institute, we only have one piece of experimental equipment: a ping-pong table"// is a good example of reductive reasoning in science. It suggests that groundbreaking discoveries can be achieved not through extensive experimental setups but rather through the adjustment of theoretical laws and conditions. Bohr highlights the power of thought experiments and abstract reasoning, emphasising that manipulating underlying principles can lead to new insights without always needing physical experimentation.
  
 ====== Reductive Sciences ====== ====== Reductive Sciences ======
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-**Explanation**: these type of tasks are typical examples of technical sciences.  However, sadly the solution cannot be inverted from the end results, therefore there can be an infinite number of terms which can get us to the known results. In this case we have to accept a few  possibilities (or more usually only one). We usually get to this term in heuristic ways.+**Explanation**: These types of tasks are typical examples of technical sciences. Unfortunately, the solution cannot be inverted from the end results; therefore, there can be an infinite number of terms that can get us to the known results. In this case, we have to accept a few possibilities (or, more usually, only one). We usually get to this term in **[[https://en.wikipedia.org/wiki/Heuristic|heuristic ways]]**. 
  
-We can face another interpretation of reduction in the classification of elementary scientific problems (the so-called ’Trinity’ of sciences).+We can face another interpretation of reduction in classifying elementary scientific problems (the so-called ’Trinity’ of sciences).
  
  
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     - The performance depends on factors like indexing, table size, query structure, and features of database engine.     - The performance depends on factors like indexing, table size, query structure, and features of database engine.
     - The result of the query must remain the same regardless of the optimization.     - The result of the query must remain the same regardless of the optimization.
-  - **Seeking Appropriate Conditions:** +  - **Seeking Appropriate Conditions:** The task is to optimize the query by structuring it to minimize response time and resource usage.
-    - The task is to optimize the query by structuring it in a way that minimizes response time and resource usage.+
     - **There’s no single “perfect” solution**  for optimizing the query, because different query structures can yield the same result, but with varying degrees of performance based on the specific context (e.g., hardware, data distribution, and load).     - **There’s no single “perfect” solution**  for optimizing the query, because different query structures can yield the same result, but with varying degrees of performance based on the specific context (e.g., hardware, data distribution, and load).
     - Additionally, the same query might perform differently on different database engines (e.g., MySQL vs. PostgreSQL), and therefore there can be an infinite number of ways to structure a query that achieves the same end result.     - Additionally, the same query might perform differently on different database engines (e.g., MySQL vs. PostgreSQL), and therefore there can be an infinite number of ways to structure a query that achieves the same end result.
-  - **Reducing the Number of Solutions:** +  - **Reducing the Number of Conditions:**: The database administrator (DBA) or developer uses **heuristic methods** like: 
-    - The database administrator (DBA) or developer uses heuristic methods like: +    - Query profiling tools (e.g., EXPLAIN in SQL) to examine how different query structures perform. 
-      - Query profiling tools (e.g., EXPLAIN in SQL) to examine how different query structures perform. +    - Applying **best practices** like indexing the right columns, minimizing nested queries, and using joins effectively.
-      - Applying **best practices** like indexing the right columns, minimizing nested queries, and using joins effectively.+
     - By profiling and tweaking different versions of the query, the developer reduces the number of possible query structures to a few that perform optimally in the given context.     - By profiling and tweaking different versions of the query, the developer reduces the number of possible query structures to a few that perform optimally in the given context.
-    - There may not be a “single” optimal solution, but the best solution is found by reducing the possibilities through trial and error, experience, and tools. +    
 The //reductive approach// in database query optimization involves narrowing down many possible solutions (query structures) to a few practical ones. The solution can’t simply be inverted from the final result (i.e., retrieving the data); instead, developers use heuristics, profiling, and experience to eliminate inefficient options and find the most effective query structure for their specific environment. The //reductive approach// in database query optimization involves narrowing down many possible solutions (query structures) to a few practical ones. The solution can’t simply be inverted from the final result (i.e., retrieving the data); instead, developers use heuristics, profiling, and experience to eliminate inefficient options and find the most effective query structure for their specific environment.
tanszek/oktatas/techcomm/information_-_basics/sciences.1725914003.txt.gz · Last modified: 2024/09/09 20:33 by knehez