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Another interesting thing is that these seem to work:

base 16: 123456789ABCDEF~16 * (16-2) + 16 - 1 = FEDCBA987654321~16

base 10: 123456789~10 * (10-2) + 10 - 1 = 987654321~10

base 9: 12345678~9 * (9-2) + 9 - 1 = 87654321~9

base 8: 1234567~8 * (8-2) + 8 - 1 = 7654321~8

base 7: 123456~7 * (7-2) + 7 - 1 = 654321~7

base 6: 12345~6 * (6-2) + 6 - 1 = 54321~6

and so on..

or more generally:

base n: sequence * (n - 2) + n - 1


This is in the original post, in the form

  num(b)/denom(b) = b - 2 + (b-1)/denom(b)
so you just need to clear the denominator.


It's very tiring to see these kinds of comments, even as a bystander. I can't imagine how it is for the developers. People have spent a fair amount of time building this thing and deserve better than to have their efforts dismissed by the likes of you. Please, do better.

The current browser engine landscape is a monoculture, so this is a very welcome addition IMO.


Also see David A. Wheeler's work on countering trojan horse attacks: https://dwheeler.com/trusting-trust/


To me, the most interesting part of Wheeler's work is formal verification. As an extra argument, he converted his verbal arguments into a set of logical statements, and then used a theorem prover to show the DDC argument is flawless (within its assumptions).


What if the theorem prover was compiled with an infected compiler?


I remember seeing a post on MathOverflow, the OP asked about the consequences of using malicious code to fool a theorem prover to certify lies and falsehoods.

It's a valid question and has deep philosophical implications. Unfortunately, mathematicians are not tech workers, so they were not impressed, and closed the question as off-topic. I personally think the main reason resposible for the lack of enthusiasm from mathematicians is that formal methods are rarely used in our society, and mathematicians in general (with the exception of logicians) also do not really value formal axiomatic systems as the something especially important for setting a standard of truth. If formal methods are used in decision and policymaking in the far future, the picture will be different. Nevertheless, right now, malicious proofs are just a hypothetical thought experiment.

https://mathoverflow.net/questions/63816/consequences-of-tec...


I did think of that :-) ... and I explained how I countered that in the paper and during my public defense.

First, the proofs were verified by a separate prover that was itself independently formally verified.

Second, the proofs were manually verified by multiple people. Once you know how to read first order logic notation (which is easier to learn than most programming languages), it's not hard to verify the steps by hand. The paper walks through the key parts.

For more details see the paper :-).


> some services are literally impossible to provide without a cookie of some form.

You seem to be under a misapprehension about what GDPR is about. It is not about cookies, it's about PII.


At this point it's largely semantics. The ePrivacy directives were included in the same piece of GDPR legislation. And when people talk about GDPR they are talking about both.


>At this point it's largely semantics. The ePrivacy directives were included in the same piece of GDPR legislation.

What? No. That's backwards.

The ePrivacy Directive referenced the Data Protection Directive. The GDPR replaced the DPD, and references to the DPD are now references to the GDPR.

That's really not the same as saying the ePD is "included in the same piece of GDPR legislation".

>And when people talk about GDPR they are talking about both.

And those people are wrong.


>This honestly doesn't really strike me as a major issue.

You're saying this from a position of privilege. There are a lot of people that don't enjoy the same financial security that you and I do that will be affected immensely by this. I know a few and this is not news in their favor.


Working in PC repair, a majority of my customers can't just up and buy a new PC just because Microsoft arbitrarily decides that whatever they have isn't good enough, even though it has sufficient performance.


And they don't have to. They can keep using the PC they have until 2025. After that, there's always Linux Mint.


I don't think it's a silly argument at all. Windows 10 will meet its EOL in 2025, meaning that our computers only have 4 more years left in them (or you switch to something like linux, but that's not really an option for most people for obvious reasons). This will make the computers unattractive on the second-hand market. IMO a computer should be serviceable for longer than 7 years.


>IMO a computer should be serviceable for longer than 7 years.

How many Windows PCs are actually getting security updates for less than 7 years? Your CPU will have to be like 8 years old when you stop getting security updates for Windows 10 and you can't upgrade to Windows 11.


>Your CPU will have to be like 8 years old when you stop getting security updates for Windows 10 and you can't upgrade to Windows 11.

Yes, and I'm saying that's unreasonable. Look no further than this very thread and you'll find plenty of people using 10-year old computers without issue.


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