keystone

Great. And if it seems like you're no longer making debatable points or asking questions, I'll take that as a hint that the conversation has reached i...

Time is valuable, and it's perfectly fine for you to express that you're not interested in continuing our conversation; we can leave it at that. If yo...

ZENO'S PARADOX Quantum Jump - Abstract space (as opposed to physical space) cannot be discrete because any minimum unit you propose can be halved. Thi...

Okay, now I'm wondering if it was me...it is possible...and likely... I've delete my message from here and posted it in the correct thread. @"Metaphys...

EDIT: I think I made a mistake by incorrectly posting in this thread a message that was meant for another thread. I've since deleted that post. No it ...

EDIT: I think I made a mistake by incorrectly posting in this thread a message that was meant for another thread. I've since deleted that post. @"fish...

EDIT: I think I made a mistake by incorrectly posting in this thread a message that was meant for another thread. I've since deleted that post. All of...

@"fishfry": Let's recast Zeno's ideas using contemporary terminology. In his era, the dominant philosophical view was presentism, which posits that on...

Great! It does feel nice to feel heard. I didn't bring up transfinite numbers as examples of abstract impossibilities because I knew you might disagre...

Do you truly believe that Achilles is unable to surpass the tortoise? Do you think that Icarus's deeds influence the passage of time? Is there a concr...

How is it possible for him to ascend the stairs if there isn't a first step? Or do you think that he might not be able to fully descend the stairs?

What's your take on this? Do you believe he never finishes descending the stairs? If that's the case, then where would he be after one minute has pass...

If that statement is logically unacceptable, then it could be considered a paradox. However, many people today might not see an issue with it, so you ...

I understand you're asking which of the following four scenarios interests me: 1) Tangible and possible - for example, a horse. 2) Tangible and imposs...

@"fishfry": I just realized I might have misread the tone of your second-to-last post as suggesting we were wrapping up, even though your latest post ...

@"fishfry": While I would love to continue this conversation, it sounds like you see this as a good endpoint. I'm going to post a new paradox now that...

@"fishfry" For what it's worth, here's how I would construct a random number generator on N in our physical universe: 1) Employ a quantum event that h...

Now you're introducing narrative elements into our discussion, mentioning God and fishbowls. If we assert that God can do anything, then we could just...

I agree with you that a uniform probability measure on N is impossible. I think the resolution to this paradox lies elsewhere. While I initially used ...

@"fishfry" I've given much thought to your critiques of my proposed resolution, and largely, I find myself in agreement with you. While I believe I'm ...

@"fishfry": I previously posted a message here but have decided to retract it and spend more time reflecting on the comments before continuing our dis...

Thanks for sharing that. The Quora post is definitely relevant. However, I believe the chart I just shared demonstrates a different perspective.

Love it. But with this approach, probabilities can only be considered in retrospect, which seems insufficient.

I believe this probability chart captures the all of the essentials of the infinite dice game and yet I do not see how it violates Kolmogorov's treatm...

Are you certain? By definition, a roll of tickets that has no end can't be completed (for that would mark the end of the roll) —attempting to do so is...

Wow, if the last time you went to a theater they were still using those raffle-like ticket stubs, you've missed out on quite a few great theater exper...

@"fishfry" : Considering the significance I attribute to the tie outcome in resolving the paradox, it's surprising how carelessly I addressed it in my...

I wouldn't venture to disagree with Kolmogorov on this matter. Although it's not an easy undertaking, particularly for me, I find it relatively easier...

Thanks @"sime" for the mathematical treatment! I'm quite fond of this potential infinity solution and believe it may be the correct direction to pursu...

I don't think you understand my position. I'm playing in the "paradise" which Cantor created (involving infinite sets) not because I believe in it but...

: First off, thanks so much for your insightful and kind response! Are you suggesting that the gambling event can occur but that we can't discuss it i...

In my initial post I wrote "Rest assured, the dice are fair." In the very post you mention I wrote "All that's left is a little divine magic to ensure...

Thanks for the discussion!

In the game with an infinite-sided die, suppose Adam rolls a 1000. What are his chances of winning? Consider the infinite set of larger numbers the se...

Doesn't the effectiveness of classical computers contradict your perspective? I have a tough time accepting the use of limits to define reals as numbe...

In our physical universe, a perfect circle cannot exist, nor can pi be fully represented as a decimal number with infinite digits. However, the univer...

Your message begins stating that "infinity is an unreasonable stipulation" and concludes by stating that there are an "infinite amount of numbers". It...

Although I presented the 'paradox' in the form of a story to make it engaging, it could just as easily have been described purely as a mathematical pr...

Yes, this post. To me, the story presents a paradox because the probability of Adam winning appears to drop from 50% to 0% simply by observing his die...

No problem, and thank you for the discussion. I will say that, in my view, the conflux of mathematics and magical thinking was formalized by Georg Can...

Why not? In a recent post to Javra, I described an object of finite size with infinite sides that could function as a die. Adam could certainly hold i...

Do you believe that the set of all natural numbers exists? Is it reasonable to stipulate its existence? If infinite sets can exist in some realm, why ...

Your argument merely skims the surface, focusing only on the impossibility of the story occurring in our physical world. Let's remember, this is a die...

I concur that this narrative couldn't unfold in our physical reality, but your argument doesn’t address the core of the paradox. The inclusion of God ...

No, the die in the story remains unchanging and complete with a side for every natural number. This distinction matters because the potentially infini...

Agreed, however, this is precisely why I find the sequel valuable. As I stated in my latest post to @"flannel jesus", the sequel is not paradoxical be...

Yes, but he will never be certain that that moment is the first moment the guillotine is going through his neck. I agree that there's nothing paradoxi...

While I concur that this sequel shares conceptual similarities with Zeno's paradox, I diverge in the assessment that its resemblance to the hanging pa...

That's why I called it a hopeless task. Yeah, this is a fair point. But then again, I'm presenting it as a sequel, not a remake of the original.

Fair enough. Formalization is the way for an idea to be treated seriously. Learning how to get there would require a huge investment of time and money...