Professor Martin Rees, the astronomer royal, searches for extra-terrestrials in a film that gets inside the minds of the scientists considering whether we’re alone in the universe.
The Chernobil exclusion zone is arguably a nature reserve. It has been 30 years since the world’s worst nuclear accident, yet it is still not clear how badly the local wildlife has been affected by the radiation.
2021 seems pretty close for such a mission. And would mean that China has licked the life sciences problems NASA hasn’t yet, and a multitube of other problems.
What is a fact, is that China might just do it. But not manned mission by 2021. We know little about the true state of its Moon and Mars program.
don’t know if it’s the good topic but I have a stupid question, about the dichotomy paradox…
If I want to go from point A to B (the distance is 1), I need to do the first half, then the first quarter of the second half, etc… I have the feeling that mathematically it’s impossible to reach B (because it’s impossible to reach infinity), where in real life it’s obviously simple. Does that mean our universe is not infinitely divisible ?
The series 1/2 + 1/4 + 1/8 + 1/16 + … is convergent. I understand why its limit is 1 but I suddenly can’t understand why in real life we are able to move… I’m sure physics answer simply to this, sorry for the stupid question…
edit : I read that the paradox is solved by considering the move is continuous, but I don’t understand why it solves it…
A silly ancient argument that’s meant to illustrate infinities in my opinion rather than confound people.
A practical solution would be to walk the entire distance and then declare that you have just walked a finite distance using an infinite number of infinitesimal steps each lasting an infinitesimal amount of time all of which took a finite amount of time…which seems fairly continuous I might add.
The answer is found by arriving at your destination, not by never arriving at your destination. Don’t stop at each mid point to consider how far the next step is…just get to the end.
You’re going down the right rabbit hole. You should research the definition of continuity and what it means to be continuous.
The universe we live in is pretty discrete. You have either traveled 1 meter or you haven’t, you’re either on or you’re off, +5v or 0v, etc. However in math we get to make the abstraction of continuity and let it explain some things for us… calculus is one example.
I wrote this up a few hours ago and just came back to it so I forgot where I was so I’m going to assume that this is possibly correct…
To move the progressively shorter distances requires that you consider progressively shorter periods of time. That is an artificial condition that creates an artificial problem. The problem doesn’t actually exist because time continues to progress at a uniform rate (ignoring relativistic considerations).
If the time to move each progressively-shorter interval was constant, then you’d have a real problem on your hands. It would be just like the problem of trying to accelerate a massive object to the speed of light. That’s one destination that you really can’t reach.
it’s impossible to use an infinite number of something no ?
So the space-time continuum is discrete ?
Same problem than space. In space-time, if you prefer, you can always divide the remaining distance and time by 2…
I know that in real life it’s obvious (I made a lot of experiments :D), but your answers are not satisfying IMO (or I missed something in your explanations…)
edit : another possibility is that if universe is not discrete, then for a reason that I ignore, I cannot compare the serie and the distance I want to travel. If so, why ??
edit2 : in fact the problem doesn’t need my example. Even with a distance of 1 meter, or with 1 second… if space-time is infinitely divisible, 1 meter is infinitely divisible… haaaaaaaaaaaa… I am totally going down right rabbit hole…
According to latest theories, look up “quantization of space and time”.
As to the paradox…
A mathematician and an engineer are sitting at a table drinking when a very beautiful woman walks in and sits down at the bar.
The mathematician sighs. “I’d like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. There’ll always be some finite distance between us.”
The engineer gets up and starts walking. “Ah, well, I figure I can get close enough for all practical purposes.”
You can always divide the time, yes. However, the time will also be constrained to a fixed boundary. If you are willing to never pass that boundary, you get an infinite approach.
That’s the key as to why this works, though. Because it takes proportionately less time to cover a proportionately smaller distance, you’re able to cover those infinite steps in a finite amount of time. If it took you progressively more time to cover those progressively smaller distances, you would eventually reach a gap that you wouldn’t be able to cross.