What is the Meaning of Taking Square? - Explained

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Discussion Overview

The discussion revolves around the mathematical and physical implications of taking the square of quantities, particularly in the context of energy calculations and other formulas. Participants explore the reasons behind squaring numbers and the interpretations of such operations in both mathematical and physical frameworks.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the necessity and meaning of taking squares in calculations, specifically regarding energy and other formulas.
  • Another participant suggests considering dimensions, using the example of area to illustrate the concept of squaring.
  • A participant explains that mathematically, squaring a number means multiplying it by itself, and for vectors, it involves taking the scalar product of the vector with itself.
  • There is a request for clarification on the physical interpretation of squaring, indicating a desire for personal insights or expressions on the topic.
  • One participant argues that squaring quantities does not have a special physical interpretation and that the occurrence of squared terms in physical laws is somewhat arbitrary, though they acknowledge that certain conclusions can be drawn from specific formulas, such as kinetic energy being a scalar and always positive.
  • A later reply emphasizes that mathematical concepts do not inherently possess physical meaning, reflecting a viewpoint that separates mathematical operations from their physical interpretations.

Areas of Agreement / Disagreement

Participants express differing views on the significance of squaring quantities, with some emphasizing the mathematical aspect while others challenge the notion of a physical interpretation. The discussion remains unresolved regarding the deeper implications of squaring in physical laws.

Contextual Notes

Participants have not reached a consensus on the physical meaning of squaring quantities, and there are unresolved questions about the implications of squared terms in various contexts.

Naimbora
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Taking square?

Why do we need to take square? What does it mean? For instance, calculating energy, why do we need to take square of the velocity or taking square of time in some other formulas?

In general, what is the mathematical meaning of taking square?
 
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Think dimension? If I told you that area of your room was 50 feet what would that mean to you?
 


Naimbora said:
Why do we need to take square? What does it mean? For instance, calculating energy, why do we need to take square of the velocity or taking square of time in some other formulas?

In general, what is the mathematical meaning of taking square?
The mathematical meaning of taking the square (of a number) is simply multiplying a number by itself, raising it to the second power etc. In the case of a vector this means taking the scalar product of the vector with itself.

The physical interpretation on the other hand is something completely different.
 


Hootenanny said:
The physical interpretation on the other hand is something completely different.

Ok, i think that i asked the question in a wrong way.. I did mean the physical interpretation of "taking square" as Hootenanny said above.

Could you help me about this question, at least a personal idea or expression?
 


Naimbora said:
Could you help me about this question, at least a personal idea or expression?
There is nothing particularly special about a squared quantity, the fact the some quantity is squared simply arises as a matter of course from their derivations.

Of course, some people would say that its strange that so many physical laws contain powers of two; but conversely there are many that don't. Personally, I don't feel that there is any special physical interpretation to physical laws or equations containing terms to the second power.

Of course, one can draw conclusions from certainly formulae. For example, you cite kinetic energy; from this equation one can conclude firstly that kinetic energy is a scalar quantity and secondly that kinetic energy is always positive.
 


Thank you, Hootenanny. I seem to get barked at everytime I make the point that mathematical concepts do NOT have "physical meaning".
 

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