I Analyzing Infinitesimal Motion

[Dale]

The relevant post I'm referring to is post 14, post 16 also might be useful and interesting, let me know if they're visible.

It is not a more correct formulation. It has the exact same issues as the OP.

 

[Chenkel]

It's logical only if the "fool" learns from his mistakes, not if he persists in his folly (i.e., continues making them).

I might be able to illustrate my idea in this way: a person who persists in his folly is not wise, but he will be wise.

It's like if I do something painful, I cannot do the same painful thing for eternity, reality requires I learn from my mistake and correct the action.

There are many kinds of fools, willfully ignorant fools, malevolent fools, benevolent fools, the list goes on.

Just to clarify, I'm not claiming special knowledge to wisdom, I'm just telling you what I choose to believe that has given me a sense of equanimity in my own life.

 

[Chenkel]

It is not a more correct formulation. It has the exact same issues as the OP.

I want to discover my misconceptions, so I apologize if I made the mistake of adding to the confusion with my own lack of knowledge, I'm looking to know what it is that I don't know so I can be logically consistent.

If I find something that doesn't make sense to me in physics, I tend to illustrate where the potential misconception is, and in the process I might show my own misconceptions and learn which concepts explain reality better than the ones I currently have.

 

[PeterDonis]

I might be able to illustrate my idea in this way: a person who persists in his folly is not wise, but he will be wise.

It's like if I do something painful, I cannot do the same painful thing for eternity, reality requires I learn from my mistake and correct the action.

There are many kinds of fools, willfully ignorant fools, malevolent fools, benevolent fools, the list goes on.

Just to clarify, I'm not claiming special knowledge to wisdom, I'm just telling you what I choose to believe that has given me a sense of equanimity in my own life.

@Chenkel, none of this is relevant to the thread topic. The thread topic is not general philosophy of wisdom, but a specific question about how motion in a continuum is analyzed. @Dale has several times now pointed out that your formulations of the problem using real numbers (and that means all of them, not just the one in the OP) are not well-defined and thus cannot be answered, and has asked you to reformulate the problem and given good advice on how to do so. You have not responded to that advice at all. Other posters have pointed you at measure theory, and you have not responded to that suggestion either. Those are the sort of responses you need to give to move this discussion forward. Continuing to talk about your general ideas about knowledge and wisdom, as you have in several posts now, does not do that.

 

[PeterDonis]

I want to discover my misconceptions

@Dale already told you the misconception: that you can use real numbers to formulate your question using infinitesimals. You can't. There are no such things as "infinitesimals" in real numbers (except for the edge case of $0$ itself being called an "infinitesimal" in some sources, but that doesn't help for what you want to do). So you can't formulate a meaningful question that talks about "infinitesimals" using real numbers. As @Dale has already told you, you need to either pick a different number system, one that includes well-defined "infinitesimals" other than $0$, or reformulate your question in terms of limits, which would allow you to use real numbers.

 

[Dale]

I want to discover my misconceptions

OK, are you clear now? If so how do you want to fix it? Are you going to reformulate your question in terms of limits using real numbers or if not then what numbers do you want to use instead of the reals?

 

[PeterDonis]

I'm not asking you to believe it, I'm asking you to challenge it.

Again, this is off topic for this thread. Please keep discussion focused on the actual specific question at issue and avoid tangents into other topics.

 

[Chenkel]

@Chenkel, none of this is relevant to the thread topic. The thread topic is not general philosophy of wisdom, but a specific question about how motion in a continuum is analyzed. @Dale has several times now pointed out that your formulations of the problem using real numbers (and that means all of them, not just the one in the OP) are not well-defined and thus cannot be answered, and has asked you to reformulate the problem and given good advice on how to do so. You have not responded to that advice at all. Other posters have pointed you at measure theory, and you have not responded to that suggestion either. Those are the sort of responses you need to give to move this discussion forward. Continuing to talk about your general ideas about knowledge and wisdom, as you have in several posts now, does not do that.

Thank you for bringing this to my attention. I apologize if my previous posts have not been directly related to the specific question about motion in a continuum. I understand that this is the focus of the thread and I will do my best to stay on topic in future posts.

I appreciate the suggestions and advice offered by @Dale and others about how to reformulate my question and make it more well-defined. I will take this into consideration and try to address any issues with my formulations. I am also open to learning more about measure theory and how it might be relevant to this topic.

I understand that it is important to stay focused and stay on topic in a discussion forum, and I will make an effort to do so in the future. However, I do want to acknowledge that I feel there is a human side to physics that is sometimes overlooked. Science, and specifically physics, is not just about logic and numbers, but also about understanding the world and our place in it. I believe that considering the human element and the impact of our work on society and humanity is an important aspect of scientific inquiry.

 

[Mark44]

I understand that it is important to stay focused and stay on topic in a discussion forum, and I will make an effort to do so in the future.

Good.

However, I do want to acknowledge that I feel there is a human side to physics that is sometimes overlooked. Science, and specifically physics, is not just about logic and numbers, but also about understanding the world and our place in it. I believe that considering the human element and the impact of our work on society and humanity is an important aspect of scientific inquiry.

This part is off-topic relative to the question you've asked in this thread.

 

[Chenkel]

OK, are you clear now? If so how do you want to fix it? Are you going to reformulate your question in terms of limits using real numbers or if not then what numbers do you want to use instead of the reals?

Thank you for your help, Dale. I am still trying to fully understand the information and how it applies to my question. I appreciate your patience and understanding as I take the time to process this.

I understand the importance of reformulating my question in terms of real numbers or another suitable set of numbers, and I will consider the suggestions you and others have made. I am committed to finding a solution and moving forward with this discussion.

I also want to express my appreciation for your efforts to help me understand this topic better. I recognize that we are all human and that it is important to approach discussions with respect and consideration for one another. I hope we can continue this discussion in a collaborative and respectful manner.

 

[Chenkel]

Good.

This part is off-topic relative to the question you've asked in this thread.

What is off topic?

 

[PeterDonis]

What is off topic?

The whole paragraph that @Mark44 quoted.

Not only that, at this point you have posted quite enough to tell us that you are going to try to reformulate your question and that you appreciate the feedback. The next post from you in this thread should be you actually doing what you say you're going to do, namely, reformulating your question. Anything else is off topic at this point. It's ok if that takes you some time. This forum is not going anywhere.

 

[PeterDonis]

Thread closed for moderation.

Edit: Thread will remain closed.