Great observation. I have observed the same thing in my own life.
The solution: do things that you really believe people need. Then you owe it to them to find out if you actually are “good enough”, and you don’t care what others think because all you care about is whether the people who need it are happy with it.
- If you just run the previous generation of games on the newer graphics, it's only a tiny bit better. But games designed for this generation will have more of a difference. Ultimately, it's all about giving the creators more freedom in making the game. Amazing games have been made with much less capability than today.
- You're going to get another big jump in graphics and immersiveness once the current neural rendering techniques are productionized. (though PS5 Pro probably isn't going to be important for that.)
Maybe so. But the part of the article I resonated with is that it just doesn't matter. I don't care. I buy games for gameplay, and better graphics -- which once opened up kinds of gameplay -- just doesn't matter anymore.
And this has been thing for good long while. One could even argue that some previous titles that played well with art style in their limitations look better than some later one. And this is even when doing "realistic" games. Games have looked good enough for many years now.
I really feel that we are still often lacking in other areas, or not enough care is put in there or lot of work and effort is being misdirected for various reasons...
Real life use cases for theorem proving I am aware of:
- Formal verification of implementations for applications that require extreme security and reliability. (banking, aerospace, ...)
- Automated theorem proving would increase the pace of theoretical work. In some cases, that helps guide useful work. There are better examples, but a simple one: nobody is looking for faster (worst-case) sorting algorithms because there is a proven theoretical limit. Don't believe in theory, but don't be without theory! It definitely won't hurt if theory-building is cheaper and faster.
Also, it's the most complicated pure reasoning task you can build. So working on theorem-proving AI may help in reasoning and reliability.
It's called Acoustic Echo Cancellation. An implementation is included in WebRTC included in Chrome. A FIR filter (1D convolution) is applied to what the browser knows is coming out of the speakers; and this filter is continually optimized to to cancel out as much as possible of what's coming into the microphone (this is a first approximation, the actual algorithm is more involved).
Remember that convolution is multiplication in the frequency domain, so this also handles different responses at different frequencies, not just delays
This assumes that the parts of number theory that ended up being useful could not have been developed after people realized you could do public key cryptography with primes.
If the work is undertaken for its own sake, there should not be a need to argue about how it will be useful in the future.
No, we could not wait to start doing number theory until after we discover that it's useful for cryptography. It took thousands of years to get to the point where we understood it well enough to use it. Its use would never occur to us if we had not discovered it beforehand. That's completely the wrong causal direction.
What completely undiscovered branch of mathematics do you think we should explore based on an immediate need that we have right now? Not so easy, is it?
What specific, useful things in cryptography would never have happened if we had not been studying number theory for thousands of years? Even if there are some examples, would we be significantly behind in useful capability if we didn't have those specific results?
It's more efficient to work backwards from the problems you have and build out the math. That's what they did with a lot of linear algebra and functional analysis when quantum mechanics came about. I am not saying discovery-based exploration would never work; I am saying it's inefficient if the goal is technological progress.
It just feels like asking which bits of a human wouldn't have been possible without having evolved for billions of years. It's an interconnected body of work that made cryptography possible at all. So ... all of it? I know it sounds like I'm copping out of the question, and maybe I am, because it's a really complicated question you're asking. I just don't know how you're imagining humanity came up with the ideas for:
- Diffie-Hellman key exchange without a deep understanding of quotient groups (and their properties, and proofs of their properties), large (co)prime numbers, and computability
- Quotient groups and its applicability to this problem without a deep understanding of group theory, equivalence classes, isomorphisms, etc.
- Large (co)prime numbers without work by Euler, calculations of GCD, proofs of infinite primes, understanding their densities and occurrence on the number line, etc.
- Computability without tons of work by Turing, von Neumann, Church, Babbage, Goedel, etc. relying on ideas on recursion, set theory, etc.
- Ideas on recursion and set theory without work on the fundamental axioms of mathematics, Peano arithmetic, etc.
- Group theory without modular arithmetic, polynomials and their roots, combinatorics, etc.
- Polynomials and their roots without a huge body of work going back to 2000 BC
- Calculations of GCD without work by Euclid
Most of these generalized abstractions came about by thinking about the more specific problems: e.g. Group Theory only exists at all because people were thinking about equivalence classes, roots of polynomials, the Chinese remainder theorem, modular arithmetic, etc. Nobody would have thought of the "big idea" without first struggling with the smaller ideas that it ended up encompassing.
You can't just take out half of these pillars of thought and assume the rest would have just happened anyway.
I agree that it's hard to imagine an alternate history when things happened through a mixture of pure and application-motivated work. In each example, I can see how people arrive at these notions through an application-driven mind-set (transformation groups, GCD through simplifying fractions during calculations, solving polynomial equations that come up in physics calculations). Computability and complexity, in the flavor of Turing's and subsequent work, I already see as application-driven work, as they were building computing machines at the time and wanted to understand what the machines could do.
As a former mathematician, I completely agree. Academic math is good stuff but you end up making too many assumptions that end up being hard to reconcile with a working system.
Personally, I stopped caring much about beauty because doing work guided by some beauty heuristics didn't make me happy. Doing work that is useful to many people does make me happy; and there ends up being beauty in it somehow.
Not my experience at Amazon. If an employee is performing but not growing, then their manager has some explaining to do as it is usually the case that the employee wants to grow but manager is not developing them the way they should be. I have seen plenty of cases where an employee just does not want to get promoted, the manager explains, and it’s fine.
Chip War focuses a lot on the personalities and comparatively little on the business/industry itself. It provides an entertaining read, I guess, but especially in the second half, I found myself reading on just to finish the book, rather than out of a desire/expectation to get informed.
Some representative paragraphs from the book. Some people probably like this style, but it's not for me.
> In 1985, Taiwan's powerful minister K. T. Li called Morris Chang into his office in Taipei. Nearly two decades had passed since Li had helped convince Texas Instruments to build its first semiconductor facility on the island. In the twenty years since then, Li had forged close ties with Texas Instrument's leaders, visiting Pat Haggerty and Morris Chang whenever he was in the U.S. and convincing other electronics firms to follow TI and open factories in Taiwan. In 1985, he hired Chang to lead Taiwan's chip industry. "We want to promote a semiconductor industry in Taiwan," he told Chang. "Tell me," he continued, "how much money you need."
...
> Lee Byung-Chul could make a profit selling almost anything. Born in 1910, just a year after Jack Simplot, Lee launched his business career in March 1938, a time when his native Korea was part of Japan's empire, at war with China and soon with the United States. Lee's first products were dried fish and vegetables, which he gathered from Korea and shipped to northern China to feed Japan's war machine. Korea was an impoverished backwater, with no industry or technology, but Lee was already dreaming of building a business that would be "big, strong, and eternal," he declared. He would turn Samsung into a semiconductor superpower thanks to two influential allies: America's chip industry and the South Korean state. A key part of Silicon Valley's strategy to outmaneuver the Japanese was to find cheaper sources of supply in Asia. Lee decided this was a role Samsung could easily play.
...
> Vladimir Vetrov was a KGB spy, but his life felt more like a Chekhov story than a James Bond film. His KGB work was bureaucratic, his mistress far from a supermodel, and his wife more affectionate toward her shih tzu puppies than toward him. By the end of the 1970s, Vetrov's career, and his life, had hit a dead end. He despised his desk job and was ignored by his bosses. He detested his wife, who was having an affair with one of his friends. For recreation, he escaped to his log cabin in a village north of Moscow, which was so rustic that there was no electricity. Or he'd simply stay in Moscow and get drunk.
The solution: do things that you really believe people need. Then you owe it to them to find out if you actually are “good enough”, and you don’t care what others think because all you care about is whether the people who need it are happy with it.
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