I would rewrite it as follows: " If a country had some good and working components a few years or centuries ago, it doesn't mean that it is still working fine today". E.g. If a country had a working legislative branch 50 years ago and it was one of the best at that time, it doesn't mean it is good or even working at all today, despite having the same name.
I'm implying that parliaments in multiple developed countries are rapidly devolving and ceding their powers and/or work to the unelected or unrelated officials.
We didn’t have laws but every TV at the dawn of the era came with full schematics and documentation.
That said, I’m not arguing that we don’t need laws today - we do, or at least I have no other idea how to do a course correction from where we are. Preferably wide-range ones that alter the whole consumer-producer relationships.
But the key thing is not the laws, it’s the attitude (individual and corporate) towards others. Can’t legislate that, I’m afraid.
There's probably something to do with volume and mfg capacity. The TV companies were doing everything they could and still not meeting the demand for TVs, so they might as well make them repairable. Signals quality. But now we have much more ability to make TVs than demand for TVs, and making them not repairable stimulates demand.
I'd say: Shortages after the world wars, combined with the teething problems of new technology made customers acutely aware and capable of repairability. That lesson is now forgotten.
It also wasn't universally true. E.g. the story of Mad Munz creating TVs that worked only for 90% of the customers (who had good enough reception and needed less signal cleanup). His idea was to capture 90% of the market with a cheaper product, while shafting 10% of the consumers and shamelessly send them to other vendors when they reported their troubles and he already had their money.
yep one of the first rules of any market should be
you sell a product -> you are responsible about the product
with a ".. -> you must be honest about the product (/what the products does, provides, etc.)"
to see how absurdly not followed this common sense(^1) is in the us look at supplements
1. provider are not hold responsible, non small parts of sold supplements are harmful in one way or another. Even cases like supplements advertised for pregnant woman with highly dangerous components for pregnant woman existed, no major change followed.
2. high amounts (AFIK 80% or so) of supplements sold in the US are severely dishonest and don't quite contain what is advertised. And this isn't just about it technically containing the supplements, but in a form the body can't absurd. But it goes so bad that "it's just sugar pills" is more on the harmless side... (and even that is dangerous given that many people take supplements for fixing health issues caused by to little of what the supplement).
not only has the US not fixed it when it started going out of hand, they went explicitly out of their way to not fix it.
(^1): (Common sense for anyone looking a bit into market dynamics/consumer protection etc.)
I don't think the supplement information you quoted is correct. There are issues, but I don't think it is that prevalent. I subscribe to consumerlab.com, they do regular testing.
(1) is certainly correct, they're poorly understood when it comes to interactions and they almost never have much clinical evidence for claims (thus they say "support"). There are also heavy metal contaminants in all sorts of things, certainly stuff bad for babies.
Just to make clear that while (2) is at least an exaggeration unless you really stretch the issues with GRAS components not being adequately safety tested, it's certainly true that evidence of benefit is thin.
Personally I'd love to see the FDA actually regulate supplements, including actually testing additives for safety rather than falling back on GRAS sketchiness.
But we can't even test food for parasites and bacteria so I guess it falls to the consumer to somehow get enough information to make an informed decision.
Absolutely. First let's install an extreme surveillance state and give them full police power unlimited by the Constitution. Then, later, if we have any regrets, no problem. Just restore democracy.
Lets me help you since you seem confused, i put the parts you should pay close attention to
> > The request PROPOSES $4 billion for NSF, a 54% cut from the fiscal year 2026 enacted level. The amount echoes last year’s proposal of $3.9 billion, which Congress soundly rejected, FUNDING THE AGENCY at $8.75 billion.
The current FUNDING is $8.75b, not the $4b he PROPOSED. Here's the wikipedia. Hope this helps.
Your statement is irrelevant to the fact that, on the executive branch's insistence, NSF has distributed far fewer funds this year (approximately 30%) than were required by Congress. We know and have repeatedly stated that the amount of money that Congress ALLOCATED TO the NSF has not changed. It is the amount of money DISTRIBUTED BY NSF that has been restricted. I don't know why you insist that allocations and disperment are the same thing. Repetition does not make it so. If you wish to present convincing evidence for your position, you must provide evidence that DISPERSEMENTS FROM the NSF have not changed. Otherwise, I see no point in continuing this circular conversation.
"Online" is not one place. And what the author is complaining about is not happening in the places I spend 99% of my online time on.
That's just the saying as I know it. Regarding the post it would be along the lines of "if you think everyone is a predator/grifter/scammer, it may be a problem with you or the places you roam"
1^x is multi-valued, and like with all other multi-valued complex functions it is possible to select a branch of the function that is a proper function.
Defined correctly, the value of 1^x for any rational x is the corresponding smallest root of unity, and for irrational arguments it is defined by continuity.
Therefore 1^x rotates on the unit circle for increasing x.
The standard complex exponential and complex logarithm functions are defined exactly in the same way, because they are also multi-valued, so the same kind of equalities like yours would also be true for them.
With the correct definition, 1^x = 1 only for integer x, not for any x. As I have written above, the useful 1^x is defined only for real arguments, not for complex arguments. Only its values are complex numbers of unit modulus.
>The standard complex exponential and complex logarithm functions are defined exactly in the same way, because they are also multi-valued, so the same kind of equalities like yours would also be true for them.
The author's not talking about doing math, but about porting math into code. Counting turns is the same as counting cycles. People do that all the time. It works fine.
And this math is kind of a mess. exp(x) is its own derivative but the log is not. (d/dx)log(x) = 1/x
But, agreed, if you're going to do calculus, use radians.
The derivative of log x being 1/x is "clean", free of arbitrary constants. If we change away from e being the base, we lose that.
The derivative of log_b x is 1/(x ln b), where ln b is 1 if b is e.
The computational aspect of it is totally compelling. The library routines are already using turns internally, so it is wasteful to go from/to radians when the caller doesn't require it, and many callers can be rewritten not to. Plus the part argument about common angles like multiples of the right angle having to be irrational numbers under radians is also compelling.
Assume people have read the article and understood it.
If you look at the implementation of sqrt for a computer, it's usually implemented with Newton's algorithm, which is an iterative numerical method with high speed convergence. It is computationally efficient and looks approximately zero how √ looks.
Sometimes a person will tell a story which is untrue, with the purpose of bringing levity to a conversation. This may be termed a joke. These stories may also be used to illustrate a point.
It's important to note that such cases are not always clearly signaled as being humor or untrue. It is a part of the joke's effect that the reader or listener will not at first know it is a joke, but will realize it after noticing an absurdity.
I’ve been writing code for 46 years. Not once have I had to code a derivative.
And for all the people who are concerned about how sin' 2πx = 2π cos 2πx, in actual code, it doesn’t matter. Let’s say that I’m writing a basic graphing function and I want to be able to display the slope of the sin curve at any point.
I am not going to expose the turn-based units to the user. Caring about slopes implies that I’m doing calculus and thus assuming radians. So even though my internal values are [0,1], I will label them as [0, 2π] (and the actual numeric values on the display may actually be something like [50,450] which is yet another numeric value we don’t display). So to get the slope at π/4, I’ll calculate cos_t 0.125 and display that value.
We do all kinds of unit translations in computing without worrying about it. This is just another case of that which observes that numerically speaking, using turns is better aligned with the underlying numerical algorithm for calculating trig values.
> I’ve been writing code for 46 years. Not once have I had to code a derivative.
Haha !
I have been coding for much shorter time but having done some ML on orientations and on spheres in my time, I have had to take their derivatives all the time.
It will be interesting to consider folks who do machine learning on robot trajectories or analysing dynamics of robotic arms.
I've also seen public information (from SEC filings) being sold by a consulting firm as competitive intel. Which I guess it kind of is competitive intel, but you can download it for free.
I can remember when this simple point was obvious to almost everyone.
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