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tanszek:oktatas:techcomm:information_-_basics:sciences [2025/09/08 19:40] – [Inductive Sciences] kneheztanszek:oktatas:techcomm:information_-_basics:sciences [2025/09/15 17:52] (current) – [Inductive Sciences] knehez
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 ====== What is science? ====== ====== What is science? ======
  
-According to the definition: //Science// is understood as a provable and fact-based system of the objective relationships between //nature//, //society//, and //thinking//.+According to the definition: //Science// is understood as a provable and fact-based system of the objective relationships between //nature//, //society//, and //human thought//.
  
-//Science// is not just a collection of knowledge, but a **discovery process**. //Science// aims to discover new information, facts, and answers about our world or the universe. +However, science is not only a set of theories stored in textbooks. It is a dynamic process of exploration and innovation that directly shapes technology, industry, and daily life. Science is the reason we can design sustainable energy systems, create AI-powered applications, or even send rockets into space. 
 + 
 +//Science// is not just a collection of knowledge, but an ongoing **discovery process**. It aims to discover new information, facts, and answers about our world or the universe, while also solving real-world engineering problems.
  
 Science, among our historically established forms of social consciousness, is distinguished and emphasized by the following characteristics. Science, among our historically established forms of social consciousness, is distinguished and emphasized by the following characteristics.
  
-  * 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]])+  * It possesses high-reaching concepts or logical tools to formulate or express broad, general or universal **principles** or **laws** or **axioms** (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.+  * It 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,+  * It provides logical methods and computational tools that enable us to calculate, simulate, and predict **results** under specific circumstances.
  
-According to **principles**, **conditions** (circumstances), and **results** (these three general aspects) we can categorize every scientific problem into the following problem groups.+From a modern engineering viewpoint, these features mean that science is not abstract—it is applied, testable, and useful. Every time an engineer uses mathematical models to optimize a production line, simulates a digital twin of a factory, or analyzes big data to predict outcomes, they are applying these scientific principles. 
 + 
 +According to the three general aspects — **principles**, **conditions**, and **results** — we can categorize every scientific problem into the following groups. 
 + 
 +----
  
 ====== Inductive Sciences ====== ====== Inductive Sciences ======
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 ---- ----
  
-**Example 2**: Sum of consecutive natural numbers +**Example 2**: Sum of consecutive natural numbers. **Claim**:
- +
-Claim:+
  
 $$ 1 + 2 + \cdots + n = \frac{n(n+1)}{2}. $$ $$ 1 + 2 + \cdots + n = \frac{n(n+1)}{2}. $$
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 so the statement holds. so the statement holds.
  
-Inductive step:+**Inductive step**:
  
 Assume the formula is true for \(n = k\): Assume the formula is true for \(n = k\):
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 $$ 1 + 2 + \cdots + k = \frac{k(k+1)}{2}. $$ $$ 1 + 2 + \cdots + k = \frac{k(k+1)}{2}. $$
  
-Simplify: +Then for \(n = k+1\): 
-$$ \frac{k(k+1) + 2(k+1)}{2} = \frac{(k+1)(k+2)}{2}. $$+ 
 +$$ 1 + 2 + \cdots + k + (k+1) = \frac{k(k+1)}{2} + (k+1). $$ 
 + 
 +**Simplify**: 
 + 
 +$$ \frac{k(k+1)}{2} + (k+1) = \frac{k(k+1) + 2(k+1)}{2} = \frac{(k+1)(k+2)}{2}. $$ 
 + 
 +Thus, the formula also holds for \( n = k+1 \). Thus, by mathematical induction, the formula holds for all \(n\in\mathbb{N}\)
  
-Thus, the formula also holds for \( n = k+1 \). 
  
 https://en.wikipedia.org/wiki/Mathematical_induction https://en.wikipedia.org/wiki/Mathematical_induction
 +
 +----
  
 ====== Deductive Sciences ====== ====== Deductive Sciences ======
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 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. 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 ======
tanszek/oktatas/techcomm/information_-_basics/sciences.1757360427.txt.gz · Last modified: 2025/09/08 19:40 by knehez