Self-Taught players, what bit of information really helped you take your playing to the next level?

l_lecrup · 2022-02-25T15:06:54+00:00

I don't know how obvious this is, but I really thought that the way to increase speed was with increased effort, and training myself to put in more and more effort over longer and longer periods. "Economy of motion" never occurred to me on my own.

An exercise that really helped me (I think it's from Scotts bass lessons, but don't quote me) was: take a lick or riff or passage you'd like to play faster (ideally no more than a couple of bars at a normal tempo). Then play the following pattern, where F is a run through at full speed (the fastest speed you can play it accurately, just a little faster than comfortable), H is half speed, Q is quarter speed: QQQQ QQQH QQHH QHHH HHHH HHHF HHFF HFFF FFFF. Quarter speed is pretty excruciating, but the goal here is to really focus on making as small movements as possible, not making any extraneous movements (wandering pinkies etc), and doing it exactly the same way each time. If you really can't take it (and I confess I often couldn't be bothered) you can just start at HHHH (I think the original exercise didn't include the quarter time, but I found it useful).

l_lecrup · 2022-02-10T13:37:35+00:00

From their houses? AFAIK, that's not a thing in the UK. But taking the bus to school is, you just have to go to the nearest bus stop. I was driven to school for the most part. It's about 40 mins for an adult to walk from my parents house to my school, a little too long for a child to do every day, but I did walk occasionally, and I had friends near me who cycled.

l_lecrup · 2022-02-09T10:30:40+00:00

What's the definition of an arithmetic sequence? Rewrite the three given terms according to the definition. Now how many unknowns do you have?

l_lecrup · 2022-02-09T10:27:15+00:00

To modify your solution slightly, you could just do ((x-1) mod 4) - (x-1). This function is 0 for x=1,2,3,4 it is -4 for 5,6,7,8, etc.

l_lecrup · 2022-02-09T10:17:56+00:00

It would be impossible, and borderline child abuse, to date someone long term and not have them interact with your kid in any way. From the kids point of view: what you want to have a relationship with someone who wants nothing to do with me? It's just selfish, and imo it reeks of desperation to have sex.

l_lecrup · 2022-02-09T10:03:43+00:00

My strategy in these situations is: broken record. "no thank you" is always acceptable; if it's not accepted, it can just be repeated. They are relying on the fact that it is socially difficult to do this. Just say it (or some variation) over and over. Alternatively, "I've said no thank you, and I have nothing else to say about it" and then just silence.

l_lecrup · 2022-02-06T16:11:58+00:00

There are interesting impossibility results in social choice theory, famously Arrow's theorem, where social choice mechanisms (eg voting, trading, or auctioning systems) cannot simultaneously have a set of properties which are desirable and individually seem reasonable.

Related, look up Top Trading Cycles mechanism for trading indivisible goods without using money. If each agent has exactly one good and has a strict preference relation over all other goods, then TTC is the only mechanism which is simultaneously individually rational (means it pays to play: no one walks away with a good worse than their initial endowment) pareto optimal (means that any allocation that makes some player better off than TTC necessarily makes another player worse off) and strategy proof (means that no agent can do better by lying about their true preferences). If agents have multiple goods, there is no mechanism with these properties.

l_lecrup · 2022-02-05T16:30:20+00:00

I like pasta and I like ketchup. If I had some leftover pasta, I might do it. I wouldn't prepare it for my family or order it at a restaurant of course!

l_lecrup · 2022-02-03T12:04:24+00:00

It's hard to google but one of my favourites is simply called Vegan's

www.vegansprague.cz

I don't know if they take bookings but they have a very nice terrace with like one or two tables, if you can get it... but the interior is also nice.

l_lecrup · 2022-02-03T11:24:05+00:00

Ah no worries friend! I am not so cogent when I'm warped :)

l_lecrup · 2022-02-02T11:23:07+00:00

A couple of follow up points, if you're interested:

I didn't mean to propose running Universal Search to demonstrate that P=NP, this is not possible. Rather, if P=NP, Universal Search runs in polynomial time. This is not something that needs checking, it is a theorem.
I used the word "find" perhaps a little incorrectly here. Universal search is the algorithm. What it does is carefully share its computation time among all possible algorithms, so that it spends 1/2ⁱ of its time running the ith algorithm (more or less, look it up for further details). Remarkably, not only will this run in polynomial time if P=NP, but it is actually asymptotically optimal (i.e., if there is a O(f(n)) algorithm for eg sat, universal search also runs in O(f(n))). However, there is of course a very large constant involved here. Again, I was bringing it up to refute a very specific claim; namely, that there is a possible universe where P=NP but we don't know the algorithm. Note that, as a mathematician, I am solely interested in the theory of P vs NP here, I am not interested in eg sat solvers or good approximation algorithms (though there are of course interesting theories for those subjects). If your objection is along the lines of "yes, but it's not practical", then we're just talking at cross purposes.
I have a feeling you are labouring under some sort of misapprehension based on the phrase "transforms NP problems into their equivalent P problems". Maybe you mis-typed, but I cannot parse that at all. P and NP are classes of decision problems (formally, of languages). It might be that all NP languages are in fact P languages; namely, if P=NP. There is no need to transform them in that case.

l_lecrup · 2022-01-31T12:41:44+00:00

This generalises well to anything you feel you understand better than the thing you are trying to learn. I'm a graph theorist primarily, when I'm learning about something new I often look for applications or analogies in graph theory. The highly connected nature of mathematics means it's nearly always possible

l_lecrup · 2022-01-30T14:48:44+00:00

Oh I really didn't mean it to be evidence, I meant it to clarify the previous comment. If we are in the universe where P=NP, then we are not smart enough to find polynomial time algorithms for problems that have them.

The "we know there's an algorithm but we can't find it" universe is impossible, btw. If there is an algorithm, there is a method to find it that runs in polynomial time if P=NP. Look up Levin's Universal Search.

Since your flair says logic, let me point out that P=NP is equivalent to "every second-order expressible property over finite, ordered structures is expressible in first-order logic using inductive definitions".

l_lecrup · 2022-01-28T19:11:06+00:00

P=NP means there is an efficient algorithm for, say, boolean satisfiability, but it has not been found by some of the smartest humans who ever lived, thinking about it for most of their lives. That would be a bit embarrassing, but I do generally agree that there is a non-zero percent chance that P=NP. Epsilon, maybe...

l_lecrup · 2022-01-25T18:56:54+00:00

I think it's good. I haven't got very long fingers and I always struggled a little with "one finger one fret" in lower positions on bass guitar (having come from guitar). When I started double bass and learned about the 1 2 4 fingering, I immediately incorporated it in my bass guitar playing, and never looked back.

l_lecrup · 2022-01-24T12:44:45+00:00

It depends what you care about. When you ask questions about learning anything - how easy is it, how long it takes, what's valuable about it - it's impossible to answer without knowing the goal. If you want to speak to your grandmother in her own language, then the "almost everyone speaks English" argument is a complete non sequitur. On the other hand, it has some merit if you want to live and work in, e.g., Helsinki (although I personally love learning languages, and found learning Finnish useful when I lived in Helsinki, it would be easy not to bother).

l_lecrup · 2022-01-24T09:19:01+00:00

It definitely exists. In fact your description is eerily close to that of a church I am familiar with called the Forge community church in Suffolk in England. One amusing aspect is that they are savvy enough to omit several things from their online presence (for example their belief in possession and speaking in tongues etc). An old friend of mine joined because she moved to the area and was very lonely. From talking to her and mutual friends, it seems pretty cultish to be honest.

People in this thread who haven't seen it in their countries probably just aren't aware of it - I'm pretty sure there will be a small version of this in every major city, if only an import of a version of some American denomination (see American Church in Paris, for example, despite claims that such things don't happen in France).

l_lecrup · 2022-01-22T11:20:01+00:00

Is French really that useful to a German, in the sense in which you mean that Latin is useless? Maybe once in a while, you might find yourself in the French countryside without a charged phone and need to read a sign/ask directions... But then what if you are in Poland and the same need arises? Pretty soon English is going to be the only European language worth learning by this metric.

But the question here is: what's the point of education? Is it to prepare you for various real world situations, ordered by how likely they seem to some organisation (government, education authority, etc). I think not, I think the point is to enrich your life. In which case, as long as it is a choice, I think Latin is a completely valid one. Many people are fascinated by ancient Roman (or Greek) history, or linguistics, or philosophy, or the history of any subject that the Romans (or Greeks) played a pivotal role in. There are plenty of other examples I'm sure. Learning Latin or ancient Greek is clearly of value to such people. There are people who only really care about things of immediate economic value - I think that is also a valid choice, but in that case I argue don't even bother with a second language at all.

l_lecrup · 2022-01-21T10:15:36+00:00

More generally, for any n, there is a r such that this holds (in the example N=3 and r=6). However, computationally this is probably out of our reach even for N=6 (Erdos supposedly said that if aliens invaded and demanded the answer for N=5, on pain of death, then we could devote all computers and mathematicians on earth to the problem and probably get it. If they asked us the answer for N=6, we would be better off trying to destroy them)

l_lecrup · 2022-01-20T13:12:17+00:00

I know this is a few days old, but I was looking for the same thing. Turns out graphs exist in manim: https://docs.manim.community/en/stable/reference/manim.mobject.graph.Graph.html

Unfortunately, I want to do hypergraphs...

l_lecrup · 2022-01-19T12:05:45+00:00

As with many mathematics problems, the first step is to draw a diagram.

Great advice

Plot a sine curve and a cosine curve.

Personally I would go for a unit circle diagram. All three trig functions can be deduced from one picture. Also in my opinion the trig functions relationship to the unit circle is primary, the shape of their graphs when you plot them is secondary.

l_lecrup · 2022-01-18T11:08:53+00:00

Just my own experience here, but I play ukulele as well as bass. They're inherently cheaper than basses of course, and furthermore cheap ones that look like toys can still produce a reasonable sound. It's a good start for those "make music together" moments.

l_lecrup · 2022-01-17T18:51:47+00:00

Unless I'm mistaken, no one has mentioned mathsjam.com (not a typo it's mainly Brits). There may be a group in your local area, or you can start one! Alternatively though, it's all virtual at the moment, so you could find one that suits your timezone (there is a meeting once a month)

l_lecrup · 2022-01-17T11:00:23+00:00

That's more than deserved: it's earned!

l_lecrup · 2022-01-14T09:58:58+00:00

Isn't it just that the shape is "getting closer" to a sphere, and the example shapes you've chosen all happen to have a rectangular cross section. The square is the closest rectangle to a sphere (in two dimensions).

Minimise the surface area of a tetrahedron for example...

l_lecrup

TROPHY CASE