- #51
curiousBos
- 29
- 0
Hey thanks for all the info. and i hope I am not coming across as rude, but i honestly have been told what I'm telling you by teachers, and find it troubling that you can't even at least see how one could think this is a paradox.
This is in fact zeno's paradox. It's called a paradox for a reason (or at least it was, since you claim we've solved it.) So clearly I'm not the only one who has found this situation to be paradoxical.
You seem to have solved it the exact way i predicted you would. I had said one can easily say that after 10 seconds I've ran 100 meters and you've ran 10 meters, so clearly I have surpassed you. But that is because this logic, along with yours, starts the time that has passed AFTER 1 second. That is the key to the paradox. The example i just gave a sentence ago works because it starts at 10 seconds later. The example you gave works because it starts at 1.1 seconds.
The example i gave starts at 1 second and then goes through an infinite series of ever decreasing time intervals (1 second later, then 1/10 second after that, then 1/100 second after that, etc.). This is the where the "limit" I am talking about comes in. Mathematically, you can never go past 1.11111111111... seconds if you choose to keep moving in an ever-decreasing fraction of time.
I don't understand how you don't understand this point. You agreed with me before! :
Me: "Yes but this is my whole argument in the first place. The universe we live in let's time flow... 2 seconds will take 2 seconds. But if you use math, you could argue that in order to get to 2 seconds you have to first get to 1 second and in order to get to one second you have to get to 1/2 a second and so on and so on. It's the same paradox as stated earlier. Thats why i think that the fundamental unit of time must be discreet, which would allow you to stop cutting it in half, and eventually, reach 2 seconds. The infinite cutting of time is what prevents you mathematically from ever reaching 2. It sets a limit. If time is discreet (if there's a fundamental smallest unit of time), that issue doesn't exist.
So when i say you can never reach 2 seconds, I mean mathematically".
You: Yes, you could argue that, but there'd be no problem as long as you accept that 1 + 1/2 + 1/4 + 1/8 + ... has a sum of 2, as is assumed in calculus. I still don't see what your actual argument against this would be.
**The reason we don't agree is because you are ASSUMING that you can reach 2 seconds. I'm saying, in the real world, as we move through the flow of time, how do you reach the 2nd second if you can keep moving a smaller and smaller fraction of time forward (such as 1/10 of a second later, 1/100 of a second later, 1/1000 of a second). You are assuming you can reach the 2 seconds, but I'm asking HOW we actually do it in the real world. That is why I brought up the notion of discreet time and fundamental units.
This is in fact zeno's paradox. It's called a paradox for a reason (or at least it was, since you claim we've solved it.) So clearly I'm not the only one who has found this situation to be paradoxical.
You seem to have solved it the exact way i predicted you would. I had said one can easily say that after 10 seconds I've ran 100 meters and you've ran 10 meters, so clearly I have surpassed you. But that is because this logic, along with yours, starts the time that has passed AFTER 1 second. That is the key to the paradox. The example i just gave a sentence ago works because it starts at 10 seconds later. The example you gave works because it starts at 1.1 seconds.
The example i gave starts at 1 second and then goes through an infinite series of ever decreasing time intervals (1 second later, then 1/10 second after that, then 1/100 second after that, etc.). This is the where the "limit" I am talking about comes in. Mathematically, you can never go past 1.11111111111... seconds if you choose to keep moving in an ever-decreasing fraction of time.
I don't understand how you don't understand this point. You agreed with me before! :
Me: "Yes but this is my whole argument in the first place. The universe we live in let's time flow... 2 seconds will take 2 seconds. But if you use math, you could argue that in order to get to 2 seconds you have to first get to 1 second and in order to get to one second you have to get to 1/2 a second and so on and so on. It's the same paradox as stated earlier. Thats why i think that the fundamental unit of time must be discreet, which would allow you to stop cutting it in half, and eventually, reach 2 seconds. The infinite cutting of time is what prevents you mathematically from ever reaching 2. It sets a limit. If time is discreet (if there's a fundamental smallest unit of time), that issue doesn't exist.
So when i say you can never reach 2 seconds, I mean mathematically".
You: Yes, you could argue that, but there'd be no problem as long as you accept that 1 + 1/2 + 1/4 + 1/8 + ... has a sum of 2, as is assumed in calculus. I still don't see what your actual argument against this would be.
**The reason we don't agree is because you are ASSUMING that you can reach 2 seconds. I'm saying, in the real world, as we move through the flow of time, how do you reach the 2nd second if you can keep moving a smaller and smaller fraction of time forward (such as 1/10 of a second later, 1/100 of a second later, 1/1000 of a second). You are assuming you can reach the 2 seconds, but I'm asking HOW we actually do it in the real world. That is why I brought up the notion of discreet time and fundamental units.
