11,359 karma · joined December 2, 2014
The players know if they're ahead or behind, which affects how much risk to take. Do you take the safe shot, or go for the tricky shot that could potentially save you a stroke if you get it right but could lose you more if you fail?
If I want to understand some mathematics, my first step is always translating it to code. Modern code (excluding array languages) no longer has a culture of minimizing character count, and omitting "obvious" steps is not possible. LLMs are based on an architecture (transformers) that was originally designed for natural language translation, so it doesn't surprise me that they're good at this.
The purpose of a browser is to make network requests. If I use a browser, I am implicitly giving it consent to make the network requests necessary for the web browsing I do.
This implied consent does not cover unnecessary requests, e.g. the adverts Firefox displays on new tabs by default are unacceptable, because I did not consent to them being downloaded. It also does not cover the network requests made by opening the "Extensions and Themes" menu, because merely looking at a configuration menu does not imply consent to make network requests.
But that fact that modern web browsers are a privacy disaster does not excuse bad behavior from other software.
No software should ever make network requests without your consent.
The whole point of formal verification is to remove the necessity of understanding most of the work. We only need to trust the formalization of the problem statement, the proof verifier, and the formalization of the result. We already have proof verifiers that humans understand to a high level, and the formalizations of the problem statement and the result are much simpler than the full proof.
I'm confident that the Navier-Stokes equations can blow up because I'm confident that Lean works correctly, and I'm confident that the mathematicians verified the problem statement and result correctly. This is despite the actual proof not being human verified yet (as far as I know), and despite the "human-readable" version not actually corresponding to the formal proof. The formal method still worked.
It doesn't because it only has a single row of keys. Piano music is full of awkward finger crossings that could be avoided with multiple rows of keys like on the Jankó keyboard.
>or feeling
You can texture or raise/lower the keys on any keyboard as you please. No layout has an advantage here.
>the range for one hand is smaller than the guitar's
True, but the traditional keyboard is even worse.
>there's no bending/sliding/vibrato
Exactly the same as a traditional keyboard.
The problem is "a third apart" means different things depending on where on the diatonic scale that third is. What I actually care about is how many MIDI note numbers apart it is, because that's what corresponds to the finger positions on the instrument.
>G# and Ab aren't even played the same on some instruments
Seeing as we've freed up the sharp and flat symbols, we can repurpose them to mean adjustments by whichever comma is relevant.
I want more than 6x as much light as I had in the incandescent bulb era. Indoor lighting is usually very dim compared to outdoor lighting, and that makes it harder to see things. As I get older and my eyes degrade I expect I'll want even more light. People running offices understand this and provide more lighting than typical for homes. See:
It's IMO crazy that going up seven scale degrees makes an "octave".
This is actually another reason to use an isomorphic/"chromatic" staff. If you prioritize data compression (traditional notation), you have 7 notes per octave + modifiers. If you prioritize linearity (isomorphic/"chromatic" notation), you have 12 notes per octave.
12 is an even number, meaning you can stack octaves and have consistent notation for each one. With traditional notation, you always have to keep track of which octave you're reading and adjust accordingly.
Having to learn a different notation system for every key is IMO no longer a good tradeoff.
I assume you're in good health, not poor, in a stable living arrangement, etc. The burden of "minor personal inconveniences" depends greatly on how many inconveniences you already suffer. Somebody working two jobs doesn't have much spare energy for optimizing utility use.
True, but it's not a fatal flaw of the notation, because you can annotate it with written chord names above the notes. This is common in guitar tabs (which are almost isomorphic in standard tuning, and fully isomorphic in regular tunings).
There's a web site you might be interested in with many examples of isomorphic notation at:
But traditional notation is more compact, and for music based around diatonic scales, implies information about the harmonic function of notes that could be useful for interpretation.
I don't believe this is true. High street banks are still common. 99% closed means we previously had 100 times as many, which would be absurdly high. It's probably closer to 50% closed.