The Edge Is A Ghost?

[Synov]

Here's a more interesting problem: You have a closed PM2 in your hand. After 1/2 a minute you flick it open. 1/4 a minute later you close it. 1/8 a minute after that you flick it open. You repeat this process until 1 minute total has passed. At that time will the knife be open or closed?

[ZrowsN1s]

........ Without stopping, constant speed. Will You have reached the end by 75s? no, You're 75% of the way there. Will You get there after 99.99999999999s? No, You're 99.99999999999% there. But will You get there after 100s? Yup, welcome to the other side .

Yes you will get there at a 100%. But first you need to go 99.99% of the way there. Then 99.999, 99.999, 99.9999, 99.99999999, 99.9999999999999999999, 99.99999999999999999999999999999999, '...' infinity. You can always add another 9. FOREVER. Whats the last 9 you add to the end before 100%? There isn't one.

Remember, You're never stopping, so it doesn't matter how small You've divided the distance into and how many parts there are as You always cover them at the same speed, so the sum of time to travel a certain distance at constant speed is always the same.

You're trying to argue, that by the sole fact that You can still imagine dividing the remaining part into smaller bits disproves the fact of how long it takes to get to the other side.

Not exactly how I'd word it, but now you're getting it. It doesn't disprove the total sum of anything. A mile is a mile, and an hour is an hour. But no matter the constant nature of the sum of the total parts, you can stay in the process of incremental division FOREVER. Welcome to the paradox.



In the interest of not derailing this thread anymore, if anyone wants to discuss further, DM me or start a thread in off topic and @ me. I think I've made all the points I have to make though. Mostly just repeating myself so I won't answer here (on this topic) anymore. Lets talk edges!

[ZrowsN1s]

Here's a more interesting problem: You have a closed PM2 in your hand. After 1/2 a minute you flick it open. 1/4 a minute later you close it. 1/8 a minute after that you flick it open. You repeat this process until 1 minute total has passed. At that time will the knife be open or closed?

You would have to skip to the end to know the answer. And the answer at the end will always be the same. BUT... If you stay in the process of dividing the time smaller, you can stay in the process of flicking that knife forever. 1/4, 1/8, 1/64, 1/128, '...' infinity. It doesn't matter how you word it, the paradox remains the same. See my above post.

[Synov]

But no matter the constant nature of the sum of the total parts, you can stay in the process of incremental division FOREVER. Welcome to the paradox.

Forever is a statement of time. The infinite division will be done after 100s, not forever. You're again confusing amount of actions with time, and confusing not having a final action with not being completed in finite time. There is no connection between the two.

You would have to skip to the end to know the answer. And the answer at the end will always be the same.

Why skip to the end? It only takes a minute.

BUT... If you stay in the process of dividing the time smaller, you can stay in the process of flicking that knife forever.

No, it's impossible for that process to go beyond 1 minute, let alone forever. Please explain which fraction you'll be in at 1 minute and 1 second. Or two minutes, or any time you want above a minute. You can't, because the sum of the first n divisions of time is 1-1/2^n which can never go above 1.

the paradox remains the same. See my above post.

You haven't shown a paradox, just made incorrect assertions based on intuition and confusion of terms.

[ZrowsN1s]

I think you are the one who is confused. I feel like you keep shouting A Minute Is A Minute. Yes, I hear you, we agree. What you are missing is the act of dividing '1' into infinite parts can continue forever. A minute, mile, a square. Again write out ALL of the smaller increments of '1'. .9, .999, .9999999, .99999999999999999. Let me know when you've written out that last 9. You can't. All you can do is say... But It's Still '1' if I add it all up, '1' minute still passes after a minute. Yes. And you can divide that mile and minute endlessly. That pretty clearly shows a pardox. Please DM or start a thread in off topic if you wish to discuss further.

[JSumm]

...Please DM or start a thread in off topic if you wish to discuss further.

Now this is a paradox (maybe a ghost) I'll never understand. Usually when these things go too deep, this step gets lost in the abyss. Doesn't bother me. I just find it fascinating in the online human psyche. It would be interesting to explore this deeper. I guess harder to pick up the side eye, the arm grab, the dad voice or whatever to move it along.

[Synov]

What you are missing is the act of dividing '1' into infinite parts can continue forever.

It can, but it doesn't have to. And dividing up a minute cannot continue "forever" by definition. You mean you can divide up the minute infinitely, which doesn't somehow magically make the parts sum to more than a minute. You're not making a logical argument or responding to my proof, just asserting it will take forever. Can you tell me the difference between amount of steps and time to complete them?

Again write out ALL of the smaller increments of '1'. .9, .999, .9999999, .99999999999999999.

Why? I've already given you a procedure for completing infinite steps in finite time. Saying there is some other procedure that doesn't do that shows nothing. Try responding to what I said directly.

Let me know when you've written out that last 9.

There's no such thing, so that's a pointless challenge.

But It's Still '1' if I add it all up, '1' minute still passes after a minute. Yes. And you can divide that mile and minute endlessly. That pretty clearly shows a pardox.

Where's the paradox? Show the contradiction clearly instead of just calling it a paradox.

[ZrowsN1s]

If you can't understand 'move it to off topic' not much hope of explaining the rest to you. Nothing to say that hasn't been said. Either I'm not capable of explaining it, or you're not capable of understanding it. I know which way I'm leaning on that Either way I'm done talking to you about it. Move on man.

[bullets_bandaids_blades]

Thanks @sal , @Steveng and @Bolster for the welcome. Happy to be on the ghost ship with everyone here. What a thread to start on haha.