Am I wrong? Is this correct thinking? Am I weird? Am I crazy?

In summary, the conversation discusses the concept of pi and its exact value, which cannot be known due to its irrational nature. This leads to the idea that the surface area of a sphere cannot be calculated exactly, but can be approximated depending on the precision of measurements. The use of units and algebraic expressions to represent numbers is also mentioned.
  • #36
pwsnafu said:
Before one can do that you need to define the problem of finding "area of a circle" without analysis.

if by this question, you mean: "what is 'area' "? then i agree.

the most delicate and complicated mechanisms underlie our spatial notions of "n-dimensional content" (length/area/volume/etc.). it is not immediately clear that a region has such a number associated with it (i can think of some very bizzarre regions in the plane), nor is it clear how to find a coordinates-free method of assigning such a number.

the answer (if i recall correctly) has something to do with pull-backs, determinants and n-chains. and even this appeals (at some level) to assigning "1" to some basic figure (a unit interval, disk/square, ball/cube, etc.).

frankly, i am quite impressed that people even decided (long before calculus came around) that the circumference of a circle was rectifiable.
 
<h2> Am I wrong about my beliefs or opinions?</h2><p>It is important to remember that everyone has their own unique perspective and experiences that shape their beliefs and opinions. What may be "wrong" to one person may be "right" to another. It is important to consider different perspectives and have open-minded discussions rather than labeling oneself as "wrong."</p><h2> Is my way of thinking correct?</h2><p>There is no one "correct" way of thinking. Our thoughts and beliefs are shaped by a combination of our upbringing, education, and life experiences. It is important to critically examine our thoughts and beliefs, but also recognize that there is no one "right" way to think.</p><h2> Am I weird for having certain thoughts or beliefs?</h2><p>Being "weird" is subjective and often based on societal norms and expectations. It is important to embrace our individuality and not conform to societal expectations. As long as our thoughts and beliefs do not harm ourselves or others, there is nothing wrong with being different.</p><h2> Am I crazy for thinking a certain way?</h2><p>The term "crazy" is often stigmatized and should not be used to label someone's thoughts or beliefs. If you are concerned about your mental health, it is important to seek professional help. Otherwise, having unique or unconventional thoughts does not make someone "crazy."</p><h2> How do I know if my thoughts or beliefs are valid?</h2><p>Validating our thoughts and beliefs is a personal process. It is important to critically examine them and consider different perspectives. It can also be helpful to seek out information and evidence to support or challenge our thoughts. Ultimately, what matters is that our thoughts and beliefs align with our values and do not harm ourselves or others.</p>

FAQ: Am I wrong? Is this correct thinking? Am I weird? Am I crazy?

Am I wrong about my beliefs or opinions?

It is important to remember that everyone has their own unique perspective and experiences that shape their beliefs and opinions. What may be "wrong" to one person may be "right" to another. It is important to consider different perspectives and have open-minded discussions rather than labeling oneself as "wrong."

Is my way of thinking correct?

There is no one "correct" way of thinking. Our thoughts and beliefs are shaped by a combination of our upbringing, education, and life experiences. It is important to critically examine our thoughts and beliefs, but also recognize that there is no one "right" way to think.

Am I weird for having certain thoughts or beliefs?

Being "weird" is subjective and often based on societal norms and expectations. It is important to embrace our individuality and not conform to societal expectations. As long as our thoughts and beliefs do not harm ourselves or others, there is nothing wrong with being different.

Am I crazy for thinking a certain way?

The term "crazy" is often stigmatized and should not be used to label someone's thoughts or beliefs. If you are concerned about your mental health, it is important to seek professional help. Otherwise, having unique or unconventional thoughts does not make someone "crazy."

How do I know if my thoughts or beliefs are valid?

Validating our thoughts and beliefs is a personal process. It is important to critically examine them and consider different perspectives. It can also be helpful to seek out information and evidence to support or challenge our thoughts. Ultimately, what matters is that our thoughts and beliefs align with our values and do not harm ourselves or others.

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