131–140 of 264 posts
While practically true, this isn't technically correct. If you knew the masses, velocities, and location with infinite precision and could perform all operations with infinite precision, (also assuming no external interaction and quantum mechanics doesn't come into it), you could know the state of the system for long time periods. The problem is we can't measure things that accurately.
This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…
> Americanism ( which also spreads to non-Americans working inside American companies ) views on the world suggest if you work hard you will get it. America is a big place. I'm seventh generation American, with a patriotic family. I wasn't raised to believe that if you work hard you WILL get it. No, it's that if you DON'T work hard, you WON'T get it. You see, success is hard work + luck. You can have luck without har…
Depends on how much you start with.
> one cannot simply specify the system evolution over long time-scales. While practically true, this isn't technically correct. If you knew the masses, velocities, and location with infinite precision and could perform all operations with infinite precision, (also assuming no external interaction and quantum mechanics doesn't come into it), you could know the state of the system for long time periods. The problem is…
Earlier quoted context omitted.
> For a two body problem, you nudge one of the bodies and it is forever off by a small amount, but your predictions into infinity require only a small adjustment to compensate. How does this even work? Where is a place in the universe where there are only two bodies?? Where would the nudge come from if not from a third body?! A ghost?
You're taking it too literally. The 'nudge' means a change in initial conditions, and could result e.g. from measurement uncertainty, not necessarily a literal nudge. It also doesn't necessarily matter that much if there are more than two bodies, if the gravitational influence of other bodies is small enough, then you can model as a two body problem.
This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…
My two cents: A well thought out design process tries to augment luck with a controlled progress: where you try to move towards your goals in a systematic, more controlled, way so the final outcome is less dependent on luck but more dependent on your ability to properly adjust and execute your design plan. It might be that luck was more important than the process in your case, but that hard to build on, and more importantly, to make any learnings for the future, it still good to analyze how the process could be made better, how you could better take advantage of the lucky circumstances you had.
This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…
I agree. I’m writing a book about why people play MMORPGs, and you just got at the heart of (part of one of my) theses.
Earlier quoted context omitted.
The question is what happens with a small perturbation and how does it "grow". For a two body problem, you nudge one of the bodies and it is forever off by a small amount, but your predictions into infinity require only a small adjustment to compensate. For a three body problem you nudge one of the bodies and only for a very short time do your previous predictions stay true, the change amplifies until nothing you tho…
> For a two body problem, you nudge one of the bodies and it is forever off by a small amount, but your predictions into infinity require only a small adjustment to compensate. How does this even work? Where is a place in the universe where there are only two bodies?? Where would the nudge come from if not from a third body?! A ghost?
Each planet and the sun can be done like this, ignoring all of the other planets. Each moon and its planet can be considered a two body system ignoring the rest of the moons.
If you just randomly generated a bunch of massive bodies and pressed play, you would have few 2 body systems and a lot of chaos, but that’s a problem that solves itself as the chaos results in either collisions or ejections.
Earlier quoted context omitted.
Trust me, mathematicians do not sit in libraries.
they walk and wander around ;) https://jorgenveisdal.medium.com/the-mathematical-nomad-paul... https://medium.com/@vovakuzmenkov/poincares-creativity-8e31d...
> one cannot simply specify the system evolution over long time-scales. While practically true, this isn't technically correct. If you knew the masses, velocities, and location with infinite precision and could perform all operations with infinite precision, (also assuming no external interaction and quantum mechanics doesn't come into it), you could know the state of the system for long time periods. The problem is…
It’s true even with arbitrarily good measurements when you get to the level of quantum mechanics.
This may be a Rant, or an unpopular opinion. Life is strange. As if God is reminding me something. It was only yesterday Overthinking [1] was submitted on HN. A little over 10 years ago many of my friends and colleagues told me to stop overthinking about things. It was causing me some stress and depression because when you start doing analysis many level deep the only conclusion is any small variance will simply caus…
> Americanism ( which also spreads to non-Americans working inside American companies ) views on the world suggest if you work hard you will get it. America is a big place. I'm seventh generation American, with a patriotic family. I wasn't raised to believe that if you work hard you WILL get it. No, it's that if you DON'T work hard, you WON'T get it. You see, success is hard work + luck. You can have luck without har…
Rich people. It's the result of survivor bias, "I worked hard and got rich, so if you work hard you can get rich too." And they discount the "luck". And it is reinforced by the fact that being born to wealthy, well connected parents is really luck.