I have internalised that in mathematics nice things come in bouquets. If there is a thing defined with properties A, B, C, and there is an other thing defined with properties D, E, F, then chances are that those 2 things are the same thing, because there are only so few nice concepts.
There are many types of examples, and many different reasons why I don't find a particular connection or connection type surprising. So I can concentrate on memorising them, and building intuition.
For the Fundamental Theorem of Calculus:
- int f' = f: the sum of the change is the thing itself. E.g. pour water in the bathtub, if you sum the rate you pour, that's the total water in the bathtub
- int f' = f(t2) - f(t1) : same but water differences between 2 times.
- (int f)' = f: the rate of the sum is the function itself. If you go and integrate your function f, the integrate function's change rate at x is f(x)
- and so on.
Also someone mentioned discrete functions, partial sums and difference series are indeed easier. Say, F is your gross money and f is your monthly salary, or F is gross amount of rain and f is daily rain. Summing a series or taking differences between 2 consecutive data points are each other's inverses.
> the area under an entire curve being related to the derivative at only two points
This is a very wrong sentence. The area under f on [a,b] is not related to the derivative of f at a and b. The area under f on [0,x] is a real function F(x) by definition, and there is nothing surprising that the area of f on [a,b] is F(b)-F(a). Simple interval arithmetic. Granted F, the integral function, is related to f: F' = f.
tl;dr : in the "fundamental theorem of calculus" there are 2 main observations:
- the operators 'sum of' and 'change rate' are each other's inverse and commute:
(int f)' = int (f') = f
F' = f <==> int f = F
- from interval arithmetics:
S(a,b) = S(0,b) - S(0,a)
You can ask for a syllabus first, then go through it.
It's interactive, and it covers in detail everything you don't get. You can ask for an unlimited amount practice material, exercises, flashcards, or anything you want.
Smoking in Paris is harmful to the health of UK citizens residing in Paris. I'm not sure why UK hasn't banned that yet.
When OSA was announced I really expected the US to state clearly that they wouldn't let UK to threaten US citizens with millions of fines if they practice their rights to Free Speech.
Because this is what's happening, the UK is making open threats against US citizens when they practice their rights to Free Speech. See e.g. Lobsters' take on it: they just wanted to have a webforum in the US but they couldn't because a foreign country threatened them with huge fines. No protection from the US.
"Just geoblock UK" seemed like a good enough in practice solution, although it is more action needed than I'd prefer.
I don't know how I missed this. Yes, geoblocking should be on ofcom. If they don't like my forum, then instead of sending me a ridiculously big check, putting me on interpol, capturing me at the airport etc, just tell their ISPs to block my forum.
I know, but I've been always confused why a gzip file would have a filename field in its header if it's supposed to contain only one file. Obviously it's good to keep a backup of original filename somewhere, but it's confusing nonetheless.
And both are poor interchange formats. When things stay in their lane, there is no "problem." When you try to make an interchange format using a language with too many features, or comments that people abuse to add parsable information (e.g. "type information") then there is a BIG problem.
It caused all kinds of problems, though those tend to be more directly traceable to the "be liberal in what you accept" ethos than to the format per se.
Yes, but the compatibility is very very easy to support for both hardware vendors, softwares, sysadmins etc. Some things might need a gentle stroke (mostly just enlarge a single bitfield) but after that everything just works, hardware, software, websites, operators.
A protocol is a social problem, and ipv6 fails exactly there.
What stymies IPv6 is human laziness more than anything else. It's not hard to set up. Every network I run has been dual stack for 10 years now, with minimal additional effort. People are just too lazy to put forth even a minimal effort when they believe that there's no payoff to it.
> What stymies IPv6 is human laziness more than anything else. It's not hard to set up.
I think the biggest barrier to IPv6 adoption is that this is just categorically untrue and people keep insisting that it isn't, reducing the chance that I'd make conscious efforts to try to grok it.
I've had dozens of weird network issues in the last few years that have all been solved by simply turning off IPv6. From hosts taking 20 seconds to respond, to things not connecting 40% of the time, DHCP leases not working, devices not able to find the printer on the network, everything simply works better on IPv4, and I don't think it's just me. I don't think these sort of issues should be happening for a protocol that has had 30 years to mature. At a certain point we have to look and wonder if the design itself is just too complicated and contributes to its own failure to thrive, instead of blaming lazy humans.
Sage Accounting is prone to various connectivity gollywobbles between the server and workstations. The first troubleshooting recommendation is to turn off IPv6. About 75% of that time, the problem then goes away.
> People are just too lazy to put forth even a minimal effort when they believe that there's no payoff to it.
For me just disabling IPv6 has given the biggest payoff. Life is too short to waste time debugging obscure IPv6 problems that still routinely pop up after over 30 years of development.
Ever since OpenVPN silently routed IPv6 over clearnet I've just disabled it whenever I can.
This goes the other direction too. I just this second fixed a problem with incredibly slow SSH connections because a host lookup which returned an IPv4 address instantly was waiting 10+ seconds for an IPv6 response which would never come.
Now I'm sure I can fix DNSmasq to do something sensible here, but the defaults didn't even break - they worked in the most annoying way possible where had I just disabled IPv6 that would've fixed the entire problem right away.
I'm confused by the argument that replacing equipment is something that is always possible. It doesn't matter that it's easy to support by updating or replacing the hardware - a lot of hardware isn't going to be updated or replaced.
ISPs are used to this though, and tunnel a lot of packets. If you have DSL at home, your ISP doesn't have a router in every edge cabinet - your DSL router sets up a layer-2 point-to-point tunnel to the ISP's nearest BRAS (broadband remote access server) in a central location. All IP routing happens there. Because it's a layer-2 tunnel it looks like your router is directly connected to the BRAS, even though there are many devices in between. I don't know how it's done on CATV and fiber access networks.
If an ISP uses an MPLS core, every POP establishes a tunnel to every other POP. IP routing happens only at the source POP as it chooses which pre-established tunnel to use.
If an ISP is very new, it likely has an IPv6-only core, and IPv4 packets are tunneled through it. If an ISP is very old, with an IPv4-only core, it can do the reverse and tunnel IPv6 packets through IPv4. It can even use private addresses for the intermediate nodes as they won't be seen outside the network.
A simple solution would be:
There is absolutely no need to identify everyone on the internet, or forbid kids to talk to other kids.reply