Yes, it seems intuitively obvious, which is why mathematicians spent a long time trying to prove that the conjecture was true. It turns out The conjecture is false in a non-obvious way. The result described in the blog post is a specific counterexample: the conjecture fails, just barely, for a specific graph with several thousand nodes and edges. It's not the kind of counterexample you would intuit in your head or even on a whiteboard.
It would seem the next logical step would be to come up with a series of examples where the conjecture fails and then extrapolate from there what new rules you come up with. And then possibly attempt to draw an isomorphism from another field. At some point mathematics will turn into an LLM problem (I know hype cycle). I'm interested in knowing if there are branches of mathematics which are near inaccessible to non computational methods of proof. And then there would be levels of mathematics where the proof itself would be true, but it would be much like me asking you for the intuition except it would be man versus the computer. If you do this level of mathematics and you put it in a box you have some real world result the operations of which are non comprehensible but demonstrably have an analogy to something understandable. Schrodinger's AI.
It's floor(_) - as in, floor(1.999) = 0, but floor(2.001) = 2. If you look carefully the upper flange of the [] square brackets is missing, which makes it a floor.
Many solid state guitar amps are made by the tube amp companies, who have a vested interest in treating those models as entry-level stuff from which the real pro is supposed to upgrade to the inconvenient tube stuff.
The mistake with most solid state guitar amps is that they have similar wattages to tube amps. At
stage volumes, it's easy for a measly 50 or 100W thing to go into clipping.
If you want solid-state guitar amplification, skip guitar amps and use a high wattage power amp used for sound reinforcement. E.g. something that puts out like 800W or more into a 4 Ohm load. This will have the headroom not to crap out when competing with the other guitarist's 100W head.
Not only that, but it will cost you less $$$ (particularly in the second hand market), and likely weigh less than your friend's 100W tube head.
Solid state guitar amps from guitar amp companies are snake oil, basically. They are not representative of what you can do with solid state.
Did you know Eddie Van Halen used solid state amps? One thing he did was to use a Marhsall tube amp head as a giant guitar pre-amp: capture the speaker output, reduced to line level, and re-amplify with a power amp, like a H&H V800.
I haven’t been able to tell the difference for a while. I switched from a Marshal JTM45 to an Axe FX III w/ a big FR/FR cab and it sounds damn good and is a lot more flexible.
The other benefit to the new modellers (which for the past 5 or so years have been really high quality) is they are far more versatile and weigh a lot less.
Now the key is to invest in a good speaker cabinet, just like with a tube amp. Unfortunately there aren’t a ton of places where you can test drive them at least where I live. There’s another company that makes high quality modellers (Kemper) and they make a matching cab, but I’ve never seen one in person.
Yeah, hard for me to wrap my head around why you would throw high speed digital circuitry, DSPs, and complex algorithms into a box to try and emulate the sound that a simple heated cathode in an evacuated glass tube can produce. $24 can still get you a decent 12AX7, I believe.
