It's not clear to me what happened. You're complaining you have been falsely accused of being @keystone?

No. I'm complaining that things I have never said - and do not know enough mathematics to articulate - have been attributed to me.

All I know is that a link to a message that I did post, on the Infinite Staircase thread, has been added to text and quoted by fishfry in this post on the Fall of Man thread. Judging by this post and my exchanges with them on the Fall of Man thread, they did not do this. I don't know who did it and have no way of finding out. The suggestion that it came from keystone came from .

I hope that's clear. I would like the false attribution to be corrected or removed.

I've done all I can. We're at a point where our interests have diverged. I need to wrap up my end so perhaps if you have any final questions, or perhaps if you come back now and then with more ideas formed over time, we can chat. So a pause, if nothing else. — fishfry

You stuck with me for an incredibly long time, and while I wasn't specifically looking for a sounding board, it turns out that's exactly what I needed. However, we've now reached a point where this discussion requires more than just a sounding board; it needs someone who can truly digest and engage with what I'm saying. Given this, it makes sense for you to disconnect now. This isn't due to a lack of topics to discuss, but rather because you're not interested. As such, I don't foresee us picking up this conversation again in the future, but who knows. Thank you so much for staying with me up to this point. I've gained a lot from our discussions, and I wish you all the best!

Or, do your thing and persist until the thread dries up and vanishes. Good luck. — jgill

Well it's been a couple of months but we're finally at the state you predicted. I know you've been on the bleachers largely but now and again you've injected a comment which suggests that you've been following. Do you care play a more active role in the discussion or would you rather leave it at that and let this thread 'dry up and vanish'?

Do you care play a more active role in the discussion or would you rather leave it at that and let this thread 'dry up and vanish'? — keystone

Some time back this thread shifted to the idea of starting math with continua and deriving points, rather than the other way around. MU has spoken of this, but has yet to put any meat on the bones. You, on the other hand, got into the discussion with some sort of ideas, and I was intrigued. I assumed you might begin with something akin to contours in the plane, but you went another direction, and sticking with one dimension I think was very limited, and rather boring I fear.

There are many thousands of ideas, large and very small, floating around in the world of mathematics these days, each one championed by one or more individuals. I enjoy playing with contours in the complex plane, and I hoped what you had to say would somehow involve this concept. But, instead, the discussion moved towards reconstructing the reals, devolving into an obscure approach - interesting I am sure to a few - but not to the, relatively speaking, many.

If you were to return to the beginning and speculate continua that precede points, or something similar, the thread might continue. Just my opinion.

I assumed you might begin with something akin to contours in the plane, but you went another direction, and sticking with one dimension I think was very limited, and rather boring I fear. — jgill

Indeed, I went in another direction and 1D is boring.

If you were to return to the beginning and speculate continua that precede points, or something similar, the thread might continue. Just my opinion. — jgill

This is exactly what I want to return to. Here's what I'm thinking:

If we keep going, I'll summarize the 1D story so far and then spend a couple of messages discussing the visual representation (using lines instead of intervals). After that, I'll move on to 2D, exploring higher-dimensional analogues of intervals/lines, namely equations/faces. Then, I'll spend a few messages examining the meaning of roots, derivatives, and integrals from this top-down perspective.

However, I'm not sure if your advice was about how to appeal to you specifically or more about attracting a new audience. If you're not interested, that's totally fine, and I'll move on. If you want to continue but prefer to take it one message at a time, then we want the same thing. I'm not asking for a long-term commitment like the one fishfry gave me. But if we proceed, I want to ensure it's a conversation, not just me 'lecturing' to the bleachers. What do you think?

Why not go directly into 2D. If you stay away from the SB-tree and Niqui arithmetic I might linger a bit longer. Let's see. You might even tempt fishfry back.

That is my message. It is on the "Infinite Staircase" thread, and does not include any of the passages attributed to me in your quotations. So I have no idea who wrote them. — Ludwig V

Oh I'm terribly sorry. That was for @keystone. I think I know what might have happened. Sometimes when I'm responding to someone, I have their quote tag in my copy buffer. Then I go to a different mention to reply to that, and when I was talking to keystone, I might have had your quote tag there instead.

No harm no foul I hope.

No. I'm complaining that things I have never said - and do not know enough mathematics to articulate - have been attributed to me.

All I know is that a link to a message that I did post, on the Infinite Staircase thread, has been added to text and quoted by fishfry in this post ↪fishfry on the Fall of Man thread. Judging by this post ↪fishfry and my exchanges with them on the Fall of Man thread, they did not do this. I don't know who did it and have no way of finding out. The suggestion that it came from keystone came from ↪jgill.

I hope that's clear. I would like the false attribution to be corrected or removed. — Ludwig V

Did I screw up the quoting? Are we having an interesting convo about infinity and time or did I hallucinate that?

I do confess that on this site I process my mentions and don't always know what thread I'm in. It all kinds of blends together. Just for my curiosity, what did I say you said? Like I said earlier, I probably just copy/pasted the wrong quote tag.

You stuck with me for an incredibly long time, and while I wasn't specifically looking for a sounding board, it turns out that's exactly what I needed. However, we've now reached a point where this discussion requires more than just a sounding board; it needs someone who can truly digest and engage with what I'm saying. Given this, it makes sense for you to disconnect now. This isn't due to a lack of topics to discuss, but rather because you're not interested. As such, I don't foresee us picking up this conversation again in the future, but who knows. Thank you so much for staying with me up to this point. I've gained a lot from our discussions, and I wish you all the best! — keystone

You're very welcome. You know you had a profound effect on my life. I had been away from this board for quite some time, a couple of years or more I think. I did read it on occasion; and when you posted your original question in this thread, I jumped in because I happened to know that the answer to your puzzle is that there is no uniform probability on a countably infinite set. Your top post lured me back from my vacation. For what that's worth. The jury's still out or maybe they're measuring the rope.

I enjoyed our chat. Thank you.

No harm no foul I hope. — fishfry

OK. No problem. I was just annoyed because I didn't understand what was going on.


Thanks for your message. As you see, it's sorted out now.

Your top post lured me back from my vacation. — fishfry

Our relationship was mostly one-sided, with me being the main beneficiary of our conversations. I'm glad to hear that you found some benefit in meeting me as well. This is a great way to conclude our conversation. Cheers!

If you stay away from the SB-tree and Niqui arithmetic I might linger a bit longer. — jgill

I see no need to mention those topics any time soon.

Why not go directly into 2D. — jgill

Without sufficient priming, you will almost certainly reject the 2D images I intend to share. I'm going to just spend this message covering the remaining 1D topics and if you're still following and interested I'll follow up with a message on 2D.

----------------------------------------

In 1D, figures adds no value as they are equal to the k-interval union. However, this is an ideal situation as it allows us to ease into unorthodox top-down figures.

Here's a k-interval union:
<-∞, 1-ε> ∪ 1-ε ∪ <1-ε, 1+ε> ∪ 1+ε ∪ <1+ε, +∞>

Below is that same k-interval union placed above a grey box containing an illustration of k-line geometry (with matching components vertically aligned and color coordinated such that k-lines/k-intervals are green and k-points/fractions are red).




I wrote <1.0> as a k-interval and placed it below <1-ε, 1+ε> because they both describe the same k-line.

I want to highlight one important difference between k-line systems and Cartesian systems.

All k-line system properties (such as order and length) are preserved under continuous deformations. In other words, all of the 3 systems illustrated below correspond to <-∞, 1-ε> ∪ 1-ε ∪ <1-ε, 1+ε> ∪ 1+ε ∪ <1+ε, +∞>. It is for this reason that complete k-line systems can fit on a finite page, since 'k-points' at infinity need not be far off in the distance. From our discussions, I've learned not to call these systems topological as that term comes loaded with meaning that doesn't apply. However, to capture the idea that properties are being preserved under continuous deformations I'm going to say these systems are k-topological. So if in 2D you see a graph that looks weird, I will likely justify the weirdness by saying that it is k-topological.



Also, please note that if ε were allowed to equal 0 then a k-topologically different system would result. As such, ε must never equal 0.

What do you think?

I'm done here. Sorry. Maybe another mathematician will appear.

[deleted]

Sounds good!

Our relationship was mostly one-sided, with me being the main beneficiary of our conversations. I'm glad to hear that you found some benefit in meeting me as well. This is a great way to conclude our conversation. Cheers! — keystone

Likewise.