I have a tangent question: is there a formal language definition of mathematical grammar the same way there is for a programming language? If so, is it context sensitive or context free?

I was daydreaming about how someone would model symbolic algebra in computer code, and naively thought it would be easy, but the more I thought about it, it seems to get exponentially (pun intended) more complicated.

Yes, people are using the programming language Lean for that, and there are a few less popular alternatives as well.

Fundamentally, there is a one-to-one correspondence between mathematical proofs and programming. Proofs are isomorphic to type checking.

https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...

Thank you for this.

Why get a canvas print when you could put up a TV and display the picture digitally?

I'm guessing you're not a musician or studio worker, or I wasn't clear.

If I am using an analog device (in my case tube amplifier) I want to listen to something that was mastered on analog equipment. If it's square wave pressed on to vinyl you might as well stream.

You should save the exaggerated euphemisms for your audiophile subreddits. "square waves pressed on to vinyl" just proves you have no clue of the physics to an HN audience.

Yep, never studied physics. Do know the difference between a sine wave and a square wave, though.

We can debate whether people can hear the difference, and mastering has as much (or more) to do with it, but I will take an AAA or AAD over an ADD all day.

There are some phenomenal sounding DDD masters from the late 80s. I believe it requires all 3 of these, which were present then:

1. Digital recording equipment had significantly improved

2. Audio engineers learned how to use the equipment

3. Heavy digital compressors weren't in use yet.

Hooboy. Where do I even start with this?

Because the TV wouldn't be as good a representation of the original painting as the canvas print would be. Similarly, vinyl wouldn't be as good a representation of the original sound as CDs would be.

> This means that not only does a singular snapshot of our universe exists in pi, but every single one does

The word 'exist' is doing a lot of work here. Could any computer actually find the value in pi? Each computation takes energy, and there is a finite amount of energy in the universe. Does the value 'exist' in pi if it could never be rendered? How much different is that claim from "our simulated universe is a file on gods computer, located just past the edge of the observable universe or 18 inches away in the 4th dimension"?

A similar thought experiment I've had is with the lottery. With just a few sheets of paper, there exist a sequence of numbers that would completely shut down both major US lotteries - ossibly even get you arrested - if they contained the winning numbers for the next 50, 20, or even 10 consecutive draws. Think about the consequences. You would win, and win again the next draw, and they would be certain you cheated. Then confiscate your pad, and draw again and win a third time. They would have to shut the contest down because this is "mathematically impossible ". But it's not. Just like your thought experiment, it's "just numbers"

It's not glamorous but I want to see SpaceX do a 6 month antarctic mission to prove they're capable of supporting life on Mars. No assistance from any existing antarctic base, fully self contained.

Rather than a one off mission, why isn't NASA operating a permanent base there along those lines? Locate it reasonably close to mcmurdo so they can get help in an emergency. I realize we have the ISS but there's probably still a lot to be learned about keeping a fully self contained system running in a hostile environment.

Any permanent lunar outpost (with maybe the exception of some of the coastal ones) needs to be fully self sufficient during the winter, that is nothing new.

No one is going to go rescue you tracking or flying thousands of kilometers in total darkness, snow storms and ~-80C temperatures.

This is the first time I've heard of that. What are some of the carcinogens? I know the radiation is bad there, but I didn't know the regolith was toxic.

I'm risking being wrong here, but I think the difficulty is getting conforming behavior across all device and browser combos.

This is the only correct answer in this entire thread! Congrats!

Monolithic codebase though

I'm counting the liths and I'm getting a lot more than mono

That's because I think it's more accurate to call it a megalithic codebase. :)

Don't threaten me with good times.

It's still modular.

And probably a prototype deployed to production!!!

> while leaving the musicians looking like neutral parties.

Then why wasn't Pearl Jam able to shake them in the mid 90s?

Several things can be true at the same time.

I truly believe that Pearl Jam and many others who have been harshly critical of TM and Live Nation genuinely want to fight back.

However, a person much more cynical than me could make the argument that a band can fight Ticketmaster, still get their bag AND look like folk heroes in the process.

They make low power AM transmitters as well. I bought one for my dad so he could "stream" old music from the Internet to his old tube radios.

What's the audio quality of AM transmission?

I've used an FM dongle to play a tablet through car speakers, which works pretty well.

Terrible in one word.

The bandwidth for AM transmissions in North America is only 20 kHz and radio emissions has to STRICTLY fall within that bandwidth. Technically, it allows an audio BW of 10 kHz, but in practice it is close to 4 kHz which is telephone quality.

Not suitable for Music.

There are monied interests that do not want inexpensive Chinese successors to Scam Altman's creation.

They're inexpensive because they're derived from his creation.

The creation--which isn't "his" in the first place, by any standard definition--was not only itself "derived from" our creations but was always supposed to be "open".

> which isn't "his" in the first place, by any standard definition

I was saying that because of the previous comment:

> to Scam Altman's creation

It wasn't derived in the same way though - I can read loads of books and so can write my own book, but that's not derivation in the same way as the Deepseek's derivation.