I have been seeing many videos on aging and how dance is a good option to delay dementia as it uses both the mind and body (assuming you try new dance moves as the old ones become automatic). What is the best way to get into dance if you are above 40 and have heavy feet? For me this is purely for mind-body benefits and not to get 'good' at a particular style. I guess same can be said for picking up a musical instrument although the physical aspect seems less involved (unless you are drumming). Some sort of weekly progression chart.
If you're male (or want to dance as a leader), there are universally not enough of you to go around in partner dancing (with occasional exceptions), so any partner dance you pick you should be well received if you aren't a creep and just do the work to improve.
Some of these dances are easier to get into than others. So your area might have salsa classes. Salsa is nice because it's easy to get into, but you can keep getting better at it forever. Bachata is similar but it's a bit more intimate in my view, so depends what you're after.
Some places just have "social dancing" classes, which is a different thing each week, but they might require you bring a partner, so look into it.
If you're from the US, or less commonly outside of the US, line dancing is a non-partner dance, so a group dance. One of my best friends does it and he loves it. Again don't need to be good to start.
Even if for most areas and most partner dances, there are less leaders than followers, this is not universally true. For instance in Turkey and Buenos Aires, there are many tourists of both sexes, while local women are culturally biased not to participate while local men are culturally biased to participate, hence creating a different gender balance.
Salsa is definitely not easy to get into, at least as lead. Salsa music itself is quite complicated for beginners and to keep time and lead moves all while having to improv on the spot. its a really tough partner dance imo. but the rewards are that much more satisfying once you get out of the beginners hell.
Why are there less leaders generally? That is not intuitive to me since it feels like men generally want to fill that role in any context. Are there just less male dancers?
To address all of the peer comments at the same time: I don't know.
There are places where men dancing is gay-ish and that deters them. That's an easy answer, but it's not enough because very progressive countries don't do much better on this, by my experience.
I would agree learning to follow in the very beginning can be easier, so that sounds like maybe men don't remain because their job is harder, but I wouldn't agree with this explanation because I observe fewer men showing up for beginner classes, when they don't know their job might is harder (whether or not it actually is).
Maybe men are more asocial on average? I'd be willing to believe that, especially in these times.
A comment above yours comments that this isn't true in Turkey, Buenos Aires, and I would add Paris to this list from experience, and then there's the entire continent of Africa we haven't mentioned and I can't really comment on, but what those places have in common is a cultural presence of dance, often a deep connection to dance where families dance together, maybe mom dances when she's cooking, dance isn't something you pick up as an exotic hobby, it's just that thing everyone does, and maybe you decide to do it a bit more than others.
Every culture with a lot of cultural dance presence would have a different view on this, I suspect.
When the balance gets skewed too hard one way or another, lead/follow becomes less sex-discriminated. Which usually means that women lead too. But in the past few years it's become much more acceptable for men to follow as well, at least in some contexts.
My 2 cents on this question – it's easier to learn the follower part: you get some basics and then go to social dances events and practice with a good leaders. But to learn the leader part you can't just go to dance events and practice with good followers. It takes more deliberate practice in classes to get the leading part.
There are just fewer male dancers. I've gone to events with insane ratios either way (3x more leaders/followers) but it's rare. Usually there are more leaders at the beginner level and decreasing amounts as you go up (but more followers who can also lead to mitigate).
Every group thing where men play a big part alongside women or kids have a shortage of men. Men are simply way less social than women in today’s world.
Would 100% recommend any kind of partner dancing. my personal favorite is salsa. Granted I love the music, but there is so much to learn in salsa you will never get bored. The connection to music and your partner whilst dancing is some of the best feeling i have ever had. and its a great way to socialise and meet new people.
Just go to any beginner class for social dancing (salsa, bachata, etc etc). They'll have had older/less co-ordinated, trust me. It's fantastic physical, mental exercise and a great way to meet people/be part of a community. I don't regret any of the time I spent dancing.
The writer appears to touch one important point. Many of us are mind-oriented, have lost touch with our emotional and physical side. For us, body is just for moving brain around.
While we all have all of the sides, for such a person, other sides are atrophied from under-utilization, while mind is hyper-trophied from overuse for for things it is not so good at. The primary obstacle for a person like that is to start developing the atrophied sides.
If this is the case, the best way to start is with the simplest possible partner dance, because mind-oriented people naturally approach learning complex body movements through mind, which is exactly the opposite you need to be doing.
So something where steps are one step per beat, like Swedish bugg.
if you avoid the ideological capture of "getting good at [dance style]" then what you dance means is "playing with the physical energy stored in the body"
muscles store physical energy in the form of tension, if you can create a bit of tension [here] then smoothly transfer it [there] you are "dancing".
how it looks to an observer is irrelevant. stretch this game enough on every dimension and it will eventually start to look [positive valence] to observers
I guess I misunderstood or mis-scoped the problem. Does the 3-body problem state 'the general case' has no solution, but that does not preclude some configurations from having a solution?
The three-body problem only states the problem to solve, it doesn’t itself state anything about the existence or non-existence of solutions. It has been proven that there is no general closed-form solution. And there are obvious solutions for trivial special cases, such as three equal masses in an equilateral triangle rotating around each other.
There is no closed-form solution for finding the roots of >4th degree polynomials in general, but that doesn’t preclude many families of >4th degree polynomials from having closed-form solutions. As a trivial example, x^5 - 1. The exact same thing with the three-body problem.
In the case of a planet going around the sun we know that the planet travels in an ellipse, more generally a conic section including interstellar comets. Orbital periods and everything else can be computed straightforwardly with formulas.
In the three body problem you can always do a numerical integration (e.g. simulation) and this is valid for a certain amount of time but will not be valid forever because of: (1) chaotic motion which amplifies small errors exponentially over time and (2) celestial mechanics is symplectic which means it conserves certain geometric properties and most integrators are not symplectic and must have different long term dynamics. There are symplectic integrators but they don’t work as well overall as ordinary integrators.
We do not know, for instance, if the solar system is stable. In the short term the planets seem to be basically doing their own thing in their orbits with just minor perturbations. We know the orbits vary a bit over millions of years. We aren’t sure which side of the sun Pluto will be on in 30 million years. It’s very believable that the planets are doing the same thing in 4 billion years but we can’t rule out that the orbits could change in a big way or one could get ejected.
> In the case of a planet going around the sun we know that the planet travels in an ellipse
That's a Newtonian approximation. Under General Relativity it is not true - the possible solutions are time varying, and I'm not even sure there are periodic orbits, nor even stable orbits. All N-body patterns radiate gravitational energy till the system collapses. I'm pretty sure there are no general closed form solution, and I think it's true there is not even a single case where the path is a closed form solution.
In general relativity it is closer to quasiperiodic.
Classical motion under an 1/r^2 field is really strange as a dynamical system because the periods of rotation, in-out and up-down motion are all the same which is why the motion closes as an ellipse. It is beautiful in a lot of ways but a godawful mess from the viewpoint of perturbation theory because these are always in resonance as opposed to only in resonance occasionally.
Ignoring gravitational radiation, in GR (or with secular perturbations from other planets) those periods no longer match up so the orbit goes in-and-out in not quite the same time it goes around and then you get a precession so it is still basically an ellipse but the angle of the ellipse changes and you'd see something like a spirograph if you draw it. It's a quasi-periodic orbit.
You can write down closed forms (often with special-function integrals) for things like 1/r^3 and it is the same story, the variables separate nicely because angular momentum is conserved.
It's worth noting that the Sun-Earth-Moon "system" is much more complex than a three-body problem just due to momentum transfer from tides/bending. That's ignoring the effect of all of the other planets and asteroids or solar wind.
The 3BP is just the simplest chaotic system showing the limits of simple models and approximations.
Well there are simpler chaotic Hamiltonians like Henon–Heiles.
There are a lot of things wrong with how we teach classical mechanics and one of them is that the two index problems that are used in the undergraduate course are the harmonic oscilator and celestial dynamics and these are the worst non-generic problems that there are. The harmonic oscillator is generic in quantum theory and is a good place to start doing perturbation theory from but the fact that the frequency doesn't change with amplitude makes it non-starter in classical perturbation theory.
In the 2-body case the periods to: (1) go around the sun, (2) go in and out towards the sun, and (3) go up and down out of the plane are all the same which again breaks perturbation theory... and of course classical perturbation theory is difficult and doesn't work that well even in cases where it does work. Contrast that to quantum mechanics where you can start doing simple calculation with perturbation theory, like to calculate the lifetime of an excited state, right away with paper and pencil.
Note that, in general, you can get chaos with as few as two position variables. In the case of the two body problem you have six position variables, but because of conservation of momentum the center of mass doesn't really matter, so you can pick a coordinate frame where the total angular momentum is zero and there are just three variables that matter which is the vector between the two bodies. There are a lot of conserved quantities here, especially angular momentum so the (1) and (2) and (3) motions all do the same thing coincidentally with the same period!
One you add a third body you are adding three more variables but not any more conserved quantities so it is a problem with a lot of dimensions.
Mapping out the orbits of the three body problem has gone pretty slowly because, compared to simpler Hamiltonians, we have to search for those orbits in a high dimensional space. You can find a periodic orbit numerically if you know where it is, but it takes a systematic approach to find many of them.
The general case always has a solution. At least until the point where two of the three bodies meet (which is a singularity). We can approximate that solution numerically.
The problem is that the solutions very strongly tend to be chaotic. Meaning that small differences in initial conditions, tend to grow exponentially with time. Which means that if you measure everything to 3 digits of precision, in finite time it will stop looking like the actual solution. Every additional digit of precision adds a similar finite time to how long the approximation is good for.
So when finally found, say, the 1953 BC conjunction described in https://en.wikipedia.org/wiki/Conjunction_%28astronomy%29?#N... - that was a very good stress test for our estimated planetary data. Because surprisingly small errors in modern data would have kept that conjunction from happening.
Yes. It's kind of like the halting problem: You cannot write a general computer program that will analyze the source code of any random other computer program and tell you if it will halt.
You can write a program that will analyze the code of a few specific other programs and tell you if they will halt. You just can't do it in general.
The 3-body problem is like that. Except it's much harder to find stable 3-body problems than computer programs that are predictable.
I'm pretty sure there is always a unique solution to the equations of motions (safe for some pathological edge cases perhaps). Classical mechanics is deterministic, after all. But for more than two bodies, there is in general no solution in closed form, and it's often chaotic, so not even computeable for arbitrary time frames.
The "about" info states that all of these are computed numerically.
There is a general solution to the three body problem due to Sundman, in the form of an infinite series. Unfortunately it converges so slowly that it's useless in practice.
Being unable to state the solution of a problem in closed form doesn't prevent solutions from existing.
It's also not computable, as in chaotic. Small differences in initial positions will lead to unpredictably large differences in trajectory (with small and large having specific meanings to match the formal definition of a chaotic system).
Its a little too much.... I have to ask it to explain some of the terms in the context they are used and I am getting tired of it. 'Seam', 'overload', 'spine'.... having to mentally 'reinterpret/flatten' the sentence is tedious. When asked to re-explain it starts with some half apology. Then, on the next query it does it all over again.
> KOSPI is crashing because the memory manufacturers are priced for continued bubble orders books. Those orders cannot be sustained
Could you explain what that means? Are they overbooking and will not be able to meet those particular projections? Would a single segment of one industry cause a reverberation throughout?
It means that there will not be this level of memory demand for much longer. I tend to agree. Right now there is far more demand than supply, so they are cashing in while they can. It will be resolved one way or another eventually, current margins are not sustainable for the long term and will be resolved either via demand destruction or an increase of supply. Likely a combination of both.
"Anchor is not a diagnostic tool. Instead, its greatest value lies in the questions it could help answer."
and
"Users can zoom from the whole brainstem seen on MRI down to individual neurons while maintaining their precise spatial relationships."
Thats pretty cool. The diagnosis/evaluation is still in the hands of another entity (doctor/scientist/AI assistant). More samples (via end of life donations) would help understanding, early diagnosis, and hopefully/eventually cures.
This is wonderful and well done. I wanted to do something with a single NFL game using the play by play you see on websites. Do you have precise enough coordinate data or do you interpret and extrapolate from a play-by-play description? Is the feed data free?
reply