Approximate relative to what? All actual measurement is implicitly or explicitly approximate such as L = x meters +/- epsilon. There is no infinite precision by which to discount rational measures as "approximate" and thus "invalid" in any way.
>What do "real" numbers buy you? That is, what do you get for the trouble of building your formalism around numbers that are not computable? Basically nothing.
You "buy" all of mathematics which operates on the assumption of "infinite" precision. It is an abstraction necessary to prove theorems and relationships of math. Abstracting from precision isn't a denial that it exists, it is the assumption that I can ignore it or leave it undefined. This is the assumption that distinguishes math from physics/engineering. Mathematicians deal with abstract e or pi but in the real world pi=3.14 if you are tiling your patio and 3.14159265... or whatever is necessary to get to the moon.
pi and e and sqrt(2) are real numbers and not rational, to be sure. But they are computable! Computable just means that they are arbitrarily approximable. "approximate relative to what" is that whatever criteria defines the number. You can't represent the "true" value of a non-rational number in the rationals, but you can prove that the error of an approximation is (rationally) bounded above and below, and you can have another approximation with a tighter bound.
Rational numbers are already infinitely precise relative to other representations -- finite decimals are another representation that is functionally equivalent to the rationals, but even a simple rational like 1/3 does not have a finite decimal value.
You can prove all the interesting theorems with computable numbers and rational/decimal numbers. You don't need the real numbers because you can't name a real number that exists and is not computable, BY DEFINITION! No mathematical construction can define a real number that is not constructible. These numbers are useless and there's no reason to continue even in abstract mathematics to pretend that they are useful because we have the formalisms to ignore them.
I'm on your side for most of what you say. This topic has been interesting to me for years. I've considered going back to school to build on my math degree, specifically because of this topic.
However, I thought things like Chaitin's Constants (you could make one per programming language) are real numbers you can name but not compute. I think you could do this from any undecidable problem.
Of course there only a countable number of those Reals. And they still don't seem useful for much more than naval gazing.
Unless things change we are going to end up like Cuba keeping old '57 Chevys running into the 80's. From what I've read nobody wants these modern ipads on wheels and used car prices of pre-2015 cars, regardless of miles, will continue to rise. The most telling thing is that the industry knows that if their customers knew about all the spying and there was an off switch then 99% would choose off. Perhaps they should think about something other than money.
Yes, this is the same argument used when the Biden admin during covid pressured the media companies to cancel people and news they did not like for "misinformation" instead of calling it censorship. This and LEOs buying data from Big Corp is just end-running the 1st and 4th amendments which is ultimately fascism.
The Biden administration both asked nicely for actual, factually incorrect information to be corrected by sites and pressured sites. They were taken to court over both, and they prevailed on the former and lost on the latter: the administration (any administration) is permitted to ask a site for a correction, and it is then truly at the site's discretion. They are not permitted to pressure them.
you are factually correct but realistically the office of the president cannot ask for anything without pressure, by nature of being the office of the president
I am old enough to remember when the fax machine first became ubiquitous in the 80's and read about how the Soviets were threatened by it. Unauthorized use was a crime and they stationed guards at fax machines to prevent mis-use. Perhaps I naively fell for CIA propaganda at the time but if true we can hope/estimate that California Commies will fall in less than 10 years since things are moving much faster in today's world.
It wasn't just fax machines. Throughout the Eastern bloc, typewriters were strictly controlled and registered. There's a great scene in The Lives of Others [1], a German movie about a Stasi agent and a dissident writer, in which the Stasi (East German secret police) have recovered a typed manuscript that was smuggled to the West, and are interviewing a forensic expert to determine the make/model of typewriter used, in an attempt to cross reference against anyone who owns that typewriter.
We still do similar things now, though for ostensibly different reasons. Inkjet and laser printers have long had various signatures they add to every printed page, barely noticeable to the naked eye, that can lead back to the specific printer used. The stated motivation is to prevent counterfeitting. Similarly, there is a pattern of "O" symbols called the EURion constellation that, if present in an image file, most commercial image editing software will refuse to print [2].
It's not surprising that politicians are trying these sorts of strategies with 3D printing, because they've already tried and used them often in the past.
Perhaps the CIA wanted people to use fax for secret communications, so they could use automated means to read the text instead of having people listen to hours of phone conversations?
So everyone is on the same page on this issue. The First Amendment is the right to anonymous free speech. I doubt they teach it in the govt schools but the Federalist papers, which argued for the US Constitution, was published anonymously.
I think the human "driver" of that car will be charged with at least recklessness. Even if you are in a botcar you still have ultimate responsibility for safe operation. From the vids I've seen and the damage to a brick wall it had to be going at least +60 MPH in a residential neighboorhood. If he was paying attention he would have disconnected auto mode and hit the brakes long before it crashed. He was probably on his phone at the time or asleep.
You can take a nap in the backseat of Waymo. There isn't even a remote driver, just a remote advisor for cases where the car can't make a decision on its own,because latency and connection issues would make remote driving inherently unsafe. It has to actually work otherwise it wouldn't work at all.
In other words, there is no responsible human. That's not an excuse for Tesla. The opposite really.
>Now, to be sure, the end product of science is supposed to be science, not grants or tenure.
"To be sure" and "supposed to be" are doing some heavy lifting here. I am not so sure about that so I suppose that for many "scientists" the end product is not science at all. I'm not impugning the whole field as there are many good and honest scientists but the SYSTEM is corrupt. I think a significant portion are gaming the system for status or money or sinecures. P-hacking, fake data scandals, the replication crisis and various fake articles getting published in top journals are omens that something isn't quite right in the science world.
My own view is that it is all due to govt funding of science and especially the NSF which should be closed ASAP. Ayn Rand discusses the problem in her article "The Establishing of an Establishment" in her anthology "Philosophy:Who Needs It". Handing out govt grant money invariably locks in the status quo, i.e. an establishment. She also points out that under such terms it is impossible even for an honest man to make good choices which is why such rackets attract scammers and con artists, even fully credentialed PhD's.
> we made the intentional decision to not include email on the dumbphone 2 to stay aligned with our values. we created a communication device with essentials that help guide you off your smartphone screen, while still being able to operate in the modern world.
I'm looking for a dumb phone and this looked promising until no email. Email is underrated as a time saver, if you aren't getting hundreds of emails daily which is a choice. Email is not as urgent as text or phone calls and its main advantage is that it separates the sender/receiver schedule or timezone.
People need to learn to guard their time and schedule like a hawk and not operate in chronic reaction mode, i.e. someone else setting your priorities for the day.
> People need to learn to guard their time and schedule like a hawk and not operate in chronic reaction mode, i.e. someone else setting your priorities for the day.
Why not just use a smartphone if you’re able to guard your time effectively?
I feel like the main reason people are interested in dumb phones is because they’ve identified that they personally can’t, for whatever reason. (Certainly that’s why I’m intrigued by them.)
Plus, email access is assumed for identity verification these days. Whether that's porting a number out from a wireless carrier or any service that has your email but not your phone number.
I receive emails that need immediate attention and texts that can wait a day or two. The only urgency attached to these communication methods is the urgency you assign them.
The limited communication options and the frankly weird choices for what to include and what not to include (no email, WhatsApp and Uber are included?) make this a very weird product in my opinion.
Approximate relative to what? All actual measurement is implicitly or explicitly approximate such as L = x meters +/- epsilon. There is no infinite precision by which to discount rational measures as "approximate" and thus "invalid" in any way.
>What do "real" numbers buy you? That is, what do you get for the trouble of building your formalism around numbers that are not computable? Basically nothing.
You "buy" all of mathematics which operates on the assumption of "infinite" precision. It is an abstraction necessary to prove theorems and relationships of math. Abstracting from precision isn't a denial that it exists, it is the assumption that I can ignore it or leave it undefined. This is the assumption that distinguishes math from physics/engineering. Mathematicians deal with abstract e or pi but in the real world pi=3.14 if you are tiling your patio and 3.14159265... or whatever is necessary to get to the moon.
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