“Preposterous twaddlecock Time travel is impossible!”

“But Professor, you time traveled yourself. Remember? When we went back to Roswell?”

“That proves nothing! And furthermore, you’d think I could remember a thing like that! Plus, who are you anyway?”

Don’t forget his birthday and his mother’s maiden name too

One of the effects of me getting medicated is being able to make phone calls and schedule meetings. Do I still hate that everyone would rather I call and stumble over my words and forget what I’m going to say rather than let me write an email that allows me to clearly and concisely ask my questions? Yes, fuck them for doing that. Hell, it’s stupid and inefficient to try and find times your schedules are both open to have a meeting when you could just write a fucking email and reply to it when your schedule allows. But yeah, anyway, now I actually have enough executive function to make those phone calls and meetings when I have to.

Also here’s a reminder to take your meds because I definitely would have forgotten to take mine if I hadn’t seen this post and remembered.

Yes, but if the universe is quantum, then there also exists a minimum finite space step. So the fractions never get infinitely small. So you either stop moving in which case of course you never reach the destination; you stopped before you did. OR you take an extra step and surpass your distance by a negligible amount which means you did move all the way.

So even in a quantized universe, the paradox is still false right?

Not that anyone cares but I just realized that this is not actually paradoxical and I can prove it mathematically! (I think) Bear with me since I’ve like just barely learned this stuff this week.

Proof Let S be the set of all steps needed to be taken. It can be written as S = {(distance to be traveled)(2^-n): n in the Natural numbers}. Thus, S shares cardinality with the natural numbers and is countably infinite.

However, time is continuous. Thus, it has the cardinality of the continuum (real numbers) which means any time interval contains an uncountably infinite amount of moments. Let us denote an arbitrary time interval as T.

Because | T | > | S | there is no injection from T to S. Thus if each step has only 1 time value, there will be moments of time left over, and since the hand is not in two places at once we know each step must have its own time value, so this must be the case.

Therefore, when moving in steps like this, one will run out of infinite steps before they run out of moments in time to complete those steps. Hence, any finite distance can be traversed in this way over some bounded interval of time. QED.

Basically, you can traverse any distance in any time interval as long as physics allows you to move at a fast enough speed. Even if it doesn’t, there may be a limit to how fast you can traverse the distance, but it is still bounded. You can traverse any finite distance like this before existence runs out of time.

(I’m still learning. So if there’s an error in my proof please be gentle lol)