>> "Probability" does not mean "maybe yes, maybe not, let me assign some gut feeling value measuring how much I believe something to be the case."
That's exactly what Baeysian probabilities are: gut feelings. Speaking of values attached to random variables, a good Bayesian basically pulls their probabilities out their ass. Probabilities, in that context, are nothing but arbitrary degrees of belief based on other probabilities. That's the difference with the frequentist paradigm which attempts to set the values of probabilities by observing the frequency of events. Frequentists ... believe that observing frequencies is somehow more accurate than pulling degrees of belief out one's ass, but that's just a belief itself.
You can put a theoretical sheen on things by speaking of sets or probability spaces etc, but all that follows from the basic fact that either you choose to believe, or you choose to believe because data. In either case, reasoning under uncertainty is all about accepting the fact that there is always uncertainty and there is never complete certainty under any probabilistic paradigm.
If I give you a die and ask about the probabiliy for a 6, then it's exactly 1/6. Being able to quantify this exactly is the great success story of probability theory. You can have a different "gut feeling", and indeed many people do (lotteries are popular), but you would be wrong. If you run this experiment a large number of times, then about 1/6 of the outcomes will be a 6, proving the 1/6 right and the deviating "gut feeling" wrong. That number is not "pulled out of somebody's ass" or some frequentist approach. It's what probability means.
I see, you don't know what I'm talking about. My apologies, I assumed a common background. Here's some introductory materials on Bayesian vs frequentist interpretations of probability:
Bayesian and frequentist reasoning in plain English
What you're hinting at is the fact that proofs created by human mathematicians are not complete proofs but rather sketch proofs whose purpose is to convince mathematicians (including the person deriving the proof) that a statement (like the Reimann hypothesis) is true. Such human-derived proofs can even be wrong, as they sometimes turn out to be, so just because a proof is given, doesn't mean we have to automatically believe what it proves.
In that sense, proofs can be seen as evidence that a statement is true, and since one interpretation of Bayesian probabilities is that they express degrees of belief about the truth of a formal statement, then yes, proofs have something to do with probabilities.
But, in that context, it's not proofs that probabilities should be attached to. Rather, we can assign some probability to a formal statement, like the Reimann hypothesis, given that a proof exists. The proof is
evidence that the statement is true and we can adjust our belief in the truth of the statement according to this and possibly other lines of evidence. In particular, if there are multiple and different proofs of the same statement that can increase our certainty that the statement is true.
The thing to keep in mind is that computers can derive complete proofs, in the sense that they can mechanically traverse the entire deductive closure of a statement given the axioms of a theory, and determine whether the statement is a theorem (i.e. true) or not but without skipping or fudging any steps, however trivial. This is what automated theorem provers do.
But it's important to keep in mind that LLMs don't do that kind of proof. They give us at best sketch proofs like the ones derived by human mathematicians, with the added complication that LLMs themselves cannot distinguish between a correct proof (i.e. one where every step, however fudgy, follows from the ones before it) and an incorrect one, or an automated theorem prover, are still required to check the correctness of a proof. LLM-based proof systems like AlphaProof work that way, passing an LLM-generated proof to an automated theorem prover as a verifier.
Mechanically-derived, complete proofs like the ones generated by automated theorem provers can also be assigned degrees of probability, but once we are convinced of the correctness of a prover (... because we have a proof!) then we can trust the proofs derived by that prover, and have complete belief in the truth of any statements derived.
>> Yeah, EU is super fucked too since it outsourced its energy dependence to Russia, consumer manufacturing to China, defence and tech services to US, and only just woke up in the last 3 or so years that it was all a huge mistake that's now costing us dearly since we're at the whims of all 3 belligerents who know that now is the time they can squeeze us.
The EU policies makes sense if the goal is peace and prosperity. You can't reach that goal without collaboration and trade. If you're going to blame someone, blame the Great Powers, the US, China and Russia, in order of importance, who have suddendly gone ballistic and can only talk of war, War, WAR, and nothing else.
Oh, sorry, President Trump is all about trade... tariffs.
I mean if the world has gone mad, don't blame the EU for trying to be sane.
>The EU policies makes sense if the goal is peace and prosperity.
How can EU maintain peace and prosperity with no military? With hugs and kisses?
Because if that was their goal, then they really fucked up because they delivered the exact opposite: war next door and lowest purchasing power of the working class in years/decades.
You see, people like this are so detached from reality, they don't understand that peace and prosperity comes from strength, not from weakness. When you don't have military strength you invite conflict, since everyone else now sees you as an easy target and wants your slice of the global GDP.
The world leadership is composed of competitors and bullies fighting for dominance of land and resources, not of nice guys who bend over to your demands just because you're nice and peaceful. If you don't have any leverage, you get run over and colonized. It's wild this hasn't sunk in yet, especially given Europe's colonial past.
>If you're going to blame someone, blame the Great Powers
Ah yes, it's always everyone else's fault that the EU kicked its military, IT, energy, economy, manufacturing industry (and now farming too) in the balls for the past 20-30 years, allowing the US, China and Russia the opportunity to exploit this self inflicted weakness for their own benefits.
All countries are economic competitors to each other. Every fuckup you make is an opportunity for the rest to enrich themselves from your stupidity. They aren't obliged to save you from your mistakes when they can profit from it. It's how Europe got rich in the first place during colonialism.
>who have suddendly gone ballistic and can only talk of war, War, WAR, and nothing else.
Doesn't matter what other sovereign countries choose to do on the global stage, they're not accountable to you. But it's your job to have a strong military to deter others from having chimp-outs with you or in your backyard. Unless you live in a fairytale, you would know that world peace was never the default state in human history, but only a temporary state created by wielding orders of magnitude more force than everyone else who will then have to follow your rules and ideologies creating a state of compliance which you interpreted as peace. You should prepare for the worst even, or especially in times of peace, as other countries won't keep world peace for you or in your favor, but will try to free themselves from compliance to your game and try to enforce their own rules that benefit them. It's the EU's fault it slept at the wheel in terms of defence and lets itself get bullied around.
>Oh, sorry, President Trump is all about trade... tariffs.
For all Trump's problems, the US still got TSMC to build a cutting edge fab there, they're getting south Korea to build new ships there, and attract cutting edge tech companies like Infinera to close shop in EU and move everything to the US. What did EU get from being nice and generous with others? Other than illegal welfare scammers.
>don't blame the EU for trying to be sane.
I CAN blame the EU since that's where my taxes go so they're accountable to me. Being weak and powerless is not being sane. There's no virtue in letting everyone walk over you and exploit you. "Turn the other cheek" does not work in competitive international politics. Your weakness and complacency will always be used against you. I know what I wrote above isn't popular to hear but it's how the world works. Ignoring it doesn't help anyone.
Asian/Asian British: A very large majority, with some reports showing over 70%, including a significant Pakistani community (around 38% of the total population).
Black/African/Caribbean: The second-largest group, making up about 26%.
White British: Around 18%.
Foreign-Born: Over 44% of the population was born outside the UK.
Religion: Islam is the most prominent religion (around 54%), followed by Christianity (26%).
The local community near Aston Villa's grounds, Villa Park, is predominantly Muslim.
Take a look at this map of data from the 2011 census. The dark green lumps in the north-west (>70% Muslim) and the green lumps surrounding them (45%-70% Muslim) are Perry Barr. The whitish lump (0%-5% Muslim) immediately to the east of a dark green lump is Aston.
> But the decision has been welcomed by Ayoub Khan, the MP for Birmingham Perry Barr, the constituency where the match will take place. He organised a petition calling for the match to be either cancelled, relocated or held behind closed doors [...]
> Khan is one of the five independent MPs elected at the last election wholly or partly because of their outright opposition to Israel’s war in Gaza and his petition suggests that his opposition to the match going ahead is motivated as much by the desire to make a political point about Israel’s conduct as by concerns about the risk of violence. The petition cites three reasons why the match should not go ahead. One is the “track record of violence by Maccabi Tel Aviv fans”, but the others are the “ongoing genocide in Gaza” and the “wider European context”. The petition says:
> As Israel continues its assault on Gaza, killing thousands and devastating civilian infrastructure, sporting fixtures involving Israeli teams cannot be separated from the wider political context. Hosting such teams sends a message of normalisation and indifference to mass atrocities.
With this in mind, perhaps you can see there was as much a political and sectarian religious element to WMP's decision as there was a security element.
Don't know what the "wider European context" is, but a public official campaigning to boycott and sanction a country carrying out a genocide is not in any way bad. That the UK authorised that match to happen instead of sanctioning Israel is the shameful part, not Khan's conduct.
And your opinion about there being a "religious sectarian element" is very subjective even though it's presented as fact. People from Arabic/Middle-Eastern countries (who are majority Muslim) are indeed especially sensitive to Israel's apartheid/killings, but that has much more to do with their own marginalisation and history than with their religion I'd wager. As evidence, I'm sure these matches were happily going along before Israel started killing 100 people per day, no?
In short, that a public official did the right thing when his country's government couldn't is, again, laudable.
This is I think the third reply I make to you, not because I follow you around, but because every time I read a post full of "implications" and concern for the innocent citizens having to deal with evil people, it happens to be you posting it...
The people of Gaza are a bit like a somebody that climbed into a cage with a lion, hit it with a cricket bat, and then start crying when it retaliated.
If the people of Gaza actually possessed the inclination to create a functioning state with a football team, that team would obviously have been banned after the mass rapes and murder on October 7th.
You seem to have chosen one specific viewpoint, and are lauding those that you already agree with.
Birmingham's Jewish community is under attack. That's not coming from nowhere, it's coming from people riled up about Gaza, finding an excuse to attack innocent people in the UK:
I have no love of football hooligans. But I'm not blind to the implications of a police force favouring one group of people over another. It's WMP's duty to protect all citizens, including from each other. They clearly failed in their duty here, especially because they were caught out with a hallucinated post-hoc justification for their decision.
I'll repeat what I said earlier: If you're angry about Israel and Palestine, don't take it out on Jews in the UK. Don't assume Jews support Israel or the IDF, don't assume Muslims support Palestine or Hamas. Thanks.
First: before speaking about the Jewish community, go to a protest, you'll find plenty of them there. The Jewish community is not under attack, the tired "antizionism/antigenocide = antisemitism" trope doesn't fly much nowadays. I'd be extremely certain that a lot of those who voted for that mayor, and who campaigned for the football match to be cancelled, and who got ready to bash the fans if need be were Jewish people (haven't been to a single protest without Jews being represented and very vocal about their protest of the genocide).
Second: believe it or not, but for hours after writing that comments, it kept popping up in my head until I realised what I was doing.
I'm arguing with someone who:
- during an ongoing genocide harps on about the great injustice done to genocide-celebrating football fans
- plays the moderate by saying we should all defer to the public authorities (the good ones, those that don't do anything, not the public authorities like Khan, who is a dishonest guy who wouldn't even have gotten elected if there hadn't been a genocide around in the first place)
- mentions that indeed, it's complicated, there are problems on both sides, etc. The sides you're equivocating being a group of pretty much Nazi football fans and the (gasp) the Muslamists!
- jumps into a comment about Muslims being the problem whipping out a Muslim map of Birmingham. Imagine any other discussion about risks of violence and someone helpfully jumping in with a "Jew map" or "Chinese map" and making dark innuendos about the Jewish mayor. And then has the gall to squeak out "and don't you dare be an islamophobe"!
- is all over the discussion, making disingenuous, weaselly arguments.
Again, stop reading opinion pieces on WP and looking at Muslim maps, go to a protest, you'll see you're imagining things.
>> The problem? Every compound interest calculator online is terrible. Ugly interfaces, ads covering half the screen, can't customize compounding frequency properly, no year-by-year breakdowns. I've tried so many. They all suck.
While you can't do anything about (other peoples') interfaces, you can absolutely do something for ads. You can install an ad-blocker on your browser. This is not just for you, OP, it's for everyone: get an ad blocker. Your experience of the internet will be radically changed.
I am reminded of this anytime I sit at someone else's computer who doesn't have an ad blocker, or whenever I see internet conversations complaining about ads; I wonder "what ads"? Then I remember: the ads I'm blocking.
So do yourself a big, warm, fuzzy favour and make the internet better for you. Block ads today.
Choose your own ad blocker, obviously.
What, you thought this was an ad for a specific ad blocker, didn't you? Nah, any one will do. Just block bloody ads.
Using an ad blocker just shifts the cost of creating/providing content onto people not using ad blockers.
The enshitification of the internet is largely driven by people ad blocking, as is incentivizes more click bait, more ads, and sloppier cheap content.
For engineering/software related content, the impact is immense since the audience is largely people ad blocking. I won't name names, because they fear backlash from their "ad block is awesome" audience, but some well known youtubers in the hard nerdy tech space report 40-50% of views they receive no compensation for.
So you can evangelize how great it is to not have to compensate for content, but don't think it's some kind of everyone wins victory. It's just a cost shift onto someone else, which largely manifests as bad content being needed to cover costs.
The correct approach is paying for what you use, and avoiding ad-supported content to send the message that you want a paid option.
> The enshitification of the internet is largely driven by people ad blocking
This is unfairly putting the blame on only one rational actor in a prisoner's dilemma.
Content providers are free to put their content behind a paywall with no ads, but they choose not to.
They choose not to because people don't pay for content when they can get it from other providers who don't use a paywall.
Consumers then are left without the option to pay for an ad-free experience.
But ads are run on hardware the consumer owns, consuming their resources and harvesting personal information on the consumer, which is a security concern.
So even if they want to support content creators by viewing the ads they run, they need to also accept the security trade-off, which many reasonably do not
Just a note that many creators integrate the advertisement of their sponsors into their content presentation and not all of that can be stopped by ad blockers (most, in fact, can't). Those creators also tend to have a Patreon or similar so their content can be supported directly. And I'd wager that's a much better model for the creators than relying on ads they don't even select themselves and that possibly clash with their content. This also makes it much more clear to users that the creators directly benefit from those integrated ads, so those kinds of ads are probably much better tolerated.
Which btw doesn't work. Users have to first watch the video, identify "sponsor blocks" and then update the blocker's database. So between the Sponsorblock users who have to watch the video and the multitudes who don't even know it exists... Sponsorblock won't block many sponsors.
Yes it's crowd-sourced, so of course it's not perfect. Saying it doesn't work isn't true though, and as more people get onboard, improves. I don't think it's the final solution, but it helps right now.
40-50% of people are ad-blocking some rather beloved content creators. That means, not paying for premium, and not viewing ads.
Ok, so maybe they are suscribing to patreon? Maybe Nebula?
Well those two have conversion rates around (on a good day) 1%.
You can swim in the waters of cognitive dissonance because ads really do suck and ad block is a great way to stop the pain while still getting what you want.
Understand though, the statistics are so damning against the ad-block crowd, that you come off like the people screeching about human generated CO2 being totally fine for the environment (It helps plants grow!) because they cannot imagine having to give up commuting in their diesel monster pick-up truck everyday. (Ad block does no damage because I cannot imagine having to see ads...)
As an aside, ironically, security nightmare ads are really only served to people with tracking blockers, because those people are the lowest value visitors and only scammers/bottom feeders really bid on their views. Regular tech illiterate people get ads for Tide and Toyota. The more you know.
>> The enshitification of the internet is largely driven by people ad blocking, as is incentivizes more click bait, more ads, and sloppier cheap content.
In Bizarro World. In our world, enshitification of the internet is driven predominantly by ads. For example, click bait, more ads and sloppier cheap content are all motivated by the need to create ever more content in order to serve ever more ads.
In the same way, spam blockers don't cause more spam, vaccines don't cause more disease, eating fish deosn't cause more fires, etc.
The internet is shitty in many ways and ads are one reason. You can pay for ad-free streaming but still get low bitrate although you paid enough to cover traffic costs for higher bitrate. You can pay to have ad-free instagram but still see all this shitty AI-generated crap and bot posts. You can pay for Youtube Premium but Google will still massively invade your privacy.
Do you really think that if everybody turned off their ad blockers and paid for premium services, the internet would become better? The way I see it, corporate greed would milk consumers even more.
Instead of surrendering to ads, we should promote directly donating to (or supporting) YouTubers or websites that provide value to us.
Funny, but as a speaker of Greek I never realised that it's in principle possible to basically create infinitely many, infinitely long new Greek words by stitching together word-roots and connectives, like "λόπαδ-ο τέμαχ-ο", etc.
I mean, has any linguist noticed this? The ability to (again in principle) embed infinitely many sentences is AFAIK an argument for the infinite generativity of natural language. Can the same argument be supported at the word-level also? And does anyone know whether it has?
Also, I think in German it's very common to string together words like that to form longer words. Are there more languages with that characteristic?
From what I've read, the German phenomenon isn't actually German-specific after all, and English does it too; the difference is just that English keeps the spaces when written. Like, linguists apparently consider "vending machine" to be a perfectly cromulent compound word (among other things, consider that the stress falls on "vending" instead of "machine," which wouldn't(?) happen if "vending" was being used as a bona fide standalone word). Turns out, there's not even an accepted general definition of what a "word" even is in the first place, because different languages vary so much.
> Also, I think in German it's very common to string together words like that to form longer words. Are there more languages with that characteristic?
Yes. All of them.
> Can the same argument be supported at the word-level also?
Here it depends what you mean by "the word-level". "Words" are commonly taken to be compositionally opaque. Compound expressions are not compositionally opaque and are not "words" in this sense.
Well, sometimes you can gain a few LIPS by cutting strategically but it's not a big deal. Most textbooks will tell you that cuts help the compiler optimise etc, but most of the time you're not writing e.g. a raytracer in Prolog, so the efficiency gains are slim.
It's the other way around. We kind of stumbled on the whole idea of computation thanks to work on First Order Logic, that Prolog borrows its syntax and semantics from.
It's all the other programming languages that have weird syntax, including LISP btw. Prolog's syntax is the quintessential syntax of a formal language for computation.
As to the "data description" part this is just a leaky abstraction almost universally adopted by programming languages, other than LISPs and logic programming languages. In truth, there is no separation between data and computation. And so there is no need for special syntax for either. Prolog is a "data description" language only in the sense that you can describe data and computation in one go.
That's exactly what Baeysian probabilities are: gut feelings. Speaking of values attached to random variables, a good Bayesian basically pulls their probabilities out their ass. Probabilities, in that context, are nothing but arbitrary degrees of belief based on other probabilities. That's the difference with the frequentist paradigm which attempts to set the values of probabilities by observing the frequency of events. Frequentists ... believe that observing frequencies is somehow more accurate than pulling degrees of belief out one's ass, but that's just a belief itself.
You can put a theoretical sheen on things by speaking of sets or probability spaces etc, but all that follows from the basic fact that either you choose to believe, or you choose to believe because data. In either case, reasoning under uncertainty is all about accepting the fact that there is always uncertainty and there is never complete certainty under any probabilistic paradigm.
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