I have never seen a "wizards are idiots" complaints about harry potter ever that had to do with that assumption.
Wizards ARE idiots. This comes entirely 100% from reading the harry potter books and has nothing to do with any assumptions.
You clearly haven't
read the books, so no.
They have zero concepts of safety, or security, or logic.
Such as?
And they vastly under utilize their own magical power.
How? You literally cannot know that they 'underutilize it' because you have no idea of the limitations of it.
They give time machines to 11 year old kids without any adult supervision on its use.
and the time machine is made entirely of fragile glass and yet does not even come in a carrying case for when it is not being used.
McGonagoll was supervising it's use, that's what Hermione went off to see her about at the start of PoA. The time travel they gave her isn't capable of causing problems as it works on a closed loop system, not a freeform system, so it's relatively safe to use for 'inconsequential things'. The Time Turner isn't 'made of glass' it's an hour reversal charm stored in glass, which - considering the fact that Herimione falls over, is thwacked by the whomping willow, and in general is physically knocked around - likely has a very common 'unbreakable charm' on it to prevent it from being damaged.
The Cursed Child -
blech - which Rowling has said is effectively second canon also implies that Hermione got a gimped shitty version of a Time Turner, because the Time Turner they used there can be used to create true alternative timelines. (One of them in which Voldemort wins is just 'Hitler, but bald', with Death camps, and all that jazz.). But I'm about a million times more than okay with disregarding that crock of shit.
children can break into their government with a simple potion, even though they have countermeasures that should have caught it (a simple sneakoscope should have caught a polyjuiced infiltrator).
A sneakoscope lights up and whistles whenever anyone nearby is doing something untrustworthy. You want to put that in a government building? Why would an alarm that goes off 24/7 be at all useful? A Foe-glass would be slightly better, but not by much as that just shows you if someone who dislikes you is in proximity. They could track wands, but Harry swapped his out, and Hermione/Rons had already had their trackers broken, they could by keycards, but Harry, Ron and Hermione ambushed three low level employees; and took their magical tokens that let them get in. The only thing we've ever seen defeat polyjuice potion - a high level, extremely delicate brew, that needs expensive reagents, a full month of constant attention, and your victim already immobile - is a piece of Goblin magic called Thieves downfall, and IIRC snape directly blasting someone in the face with magic. You can't assault your public workers, they're just not going to turn up for work if you do that.
Above all that, there's the issue that the Ministry is a public building. The offices are guarded, the entrance and general paperwork areas - of which we see, the public courtrooms, the police department, including general administration, and improper use of magic - you are seemingly free to move about, if you have a token that you work there and you are disguised as the person who is supposed to be there. What sort of realistic counter to that would you suggest?
If you mean the Order of the Phoenix, then sure; it was easy since Voldemorts people had already prepped the way for them as an ambush.
They are amused by a sport whose rules are utterly idiotic (get rid of the seeker, that position is retarded).
This is entirely cultural, Americans like Football, football is retarded and idiotic, people get brain damage from football. The rules of Basketball are retarded, the hoop is too high. You have to use a horse to play Polo, that is retarded.
TikTok exists. Gangnam style peaked at number two in the entire world in 2012. In terms of 'retarded culture', we've got wizards beat for sheer mass of it, by far.
They think giving a hostile foreign nation complete control over their economy is a good idea (goblin nation) despite it having failed spectacularly multiple times in the past (the multiple goblin rebellions) they keep on doing it.
Goblins aren't a hostile foreign nation. Goblins aren't even a nation. Goblins are a minority peoples in the wizarding world. The times that they have 'rebelled' have been as a direct response to wizards murdering them, wizards literally oppressing them, and wizards keeping them as slaves. The rebellions as described seem to be small scale, enough so that they are actually just riots. Since the 'biggest' consisted of them taking over a small village and using it's Inn as their HQ. (Though I assume the upcoming game will change that.)
I mean, you can also look at the real world as well. Goblins caused a ruckus and were seen as second class people during their rebellions of the 16th and 17th centuries. But they occupy the position of importance right now.
This is Clarence Brown. Below, is what the law says about people like Clarence Brown during the same time as the Goblin rebellion.
Clarence Brown is one of the highest points of authority in America right now. Jews throughout Europe were expelled, demonised and exterminated for the past five hundred years, now they're largely upper middle class/elites in western society. You're thinking of Goblins as being something alien, because to you, they are alien; to the average wizard Goblins are a fact of life. No different to a black person, or a chinese person. What would you suggest? They toss out the Goblins, seize their assets, round them up and ship them off to some smoke belching magical death camp?
Their govt are literally comedically inept. And so are their terrorists.
I would like you devise a way of stopping people who can teleport, cast a undetectable spell that controls peoples minds, have large scale popular support among your rich upper classes; along with large scale popular support among the lower classes. And you can't kill him. because he comes back if you do that. You also cannot use those same spells on people.
The other side has magic as well; and a willingness to use the really messed up stuff that damages your soul, and large amounts of money.
if you're talking general day to day activities. The ministry operates a surveillance network of problem individuals so pervasive that when one of them committed a crime, five minutes after he got home, he received a summons from the government to come and stand trial. The first escapee from Azkaban had to spend his entire life underneath and invisibility cloak, minded by a house elf because otherwise he'd have been found out. In order to run the world cup, they created a stadium large enough and tall enough to fit ten cathedrals end to end; and nobody saw a dammed thing. In one experiment, this happened:
What is more, her five days in the distant past caused great disturbance to the life paths of all those she met, changing the course of their lives so dramatically that no fewer than twenty-five of their descendants vanished in the present, having been “un-born”.
‘Finally, there were alarming signs, during the days following Madam Mintumble’s recovery, that time itself had been disturbed by such a serious breach of its laws. Tuesday following her reappearance lasted two and a half full days, whereas Thursday shot by in the space of four hours. The Ministry of Magic had a great deal of trouble in covering this up and since that time, the most stringent laws and penalties have been placed around those studying time travel.’
In spite of the many Muggle fantasies around the subject, time travel is possible in only a limited sense even in the magical world. While the subject is shrouded in great secrecy – investigations are ongoing in the Department of Mysteries – it appears that magic can take you only so far.
www.wizardingworld.com
Which they then managed to cover up. A giant destroyed an entire town in the UK; wizards altered the news and reporting so it was told to the public as a 'freak tornado'. A wizard casually walked in, and assimilated himself into the cabinet of the Prime Minister for months, without the Prime Minister or anyone else realizing it, a member of that same cabinet was then quietly removed to their magical hospital to fix a curse, and again, no one realised. Pettigrew flattened an entire street: Gas main went off. A dragon attacked a town: No one remembers seeing a dammed thing. Until 1689 wizards and witches were fully integrated in the wider world, and were commonly known about. They had departments that liased with the muggle kings and queens, laws regarding each other. Once it was signed, they managed to convince us they didn't exist. Despite a Malfoy nearly becoming
King of England at one point.
That's insane. That's like...well, that's like wizards running around and being a fact of life until 400 years ago, we have food recipes on record from the Greek era, plays from before that, records that stretch to some of the earliest civilizations. When Wizards segregated themselves from us, the East India company was a growing power, we had firearms, the earliest threads of industrialization were being thought up. This wasn't ancient history, the Bill of Rights was written when it was signed. Two thousand years of history had to be effectively edited to make this work, tens of thousands of people had to have their minds altered. The sheer scale of the act is fucking terrifying.
The wizarding government is
disgustingly corrupt, and in bed with their upper class money powers; but they don't seem particularly inept. It's just really dammed hard to fight back against people that can arrive without warning, completely suborn your will; and send you off without anyone being the wiser.
Oh also their education... math is an optional elective (arithmancy) that most don't even bother taking, they have no basic education, start their education at 11, and the only thing they learn is magic.
Arithmancy is not mathematics, it's a way of predicting the future due to the magical nature of numbers and numberology. They start their education like all British Schoolchildren at age 6, either through home tutors or at a primary school if muggleborn.
Regarding the teaching of more advanced (GCSE and A-level) Maths, why would they bother? The majority of the principles that maths is needed to understand, don't apply to magic. Anything more advanced than basic Algebra, some geometry and counting is completely superfluous for the average wizard, and largely superfluous to the people that are making things that may actually require an advanced understanding of physics/mathematics. An engineer needs to know Maths because if he doesn't, then whatever he's making won't work. Arthur Weasley created a sentient, flying, invisible car as a side hobby whilst having no clue - we assume - about anything more advanced than year 6 mathematics. Don't get me wrong. I think they should probably learn more maths. But for their day to day life, magic is the more useful skill.
It also has the neat effect of preventing Muggleborns from working muggle jobs, and keeps them inside the wizarding world. Probably not intentional on Rowlings part, but definitely creepy none the less.
They have a history class, but for hundreds of years it has been taught by a ghost who only teaches the goblin rebellions and nothing else (and yet they STILL trust goblins with total money control despite that)
This is what Binns teaches.
1st year
Werewolf Code of Conduct
Soap Blizzard of 1378
The Gargoyle Strike of 1911
2nd Year
Medieval Assembly of Wizards.
International Warlock Convention.
3rd Year
Witch Hunts
4th Year
Goblin Rebellions.
5th year
Werewolf code of conduct (Again, weirdly)
Dissolving of the Wizards Council.
14th Century Wizarding Economic Bubble.
etc, and so on until 7th year. I also left out some of the stuff I couldn't click source to from the wiki.
The whole Goblin Rebellions thing was literally the subject major of one year. I'm not sure what you'd like doing with Binns either? If you fire him, he ceases to exist. That's kinda close to murder to cavalier with the idea of getting rid of the man; wizards say that ghosts are just 'imprints' of people, but an 'imprint' in the paintings beg not to be killed sometimes, so I'd be cautious about randomly getting rid of ghosts.
Have you just read fanfiction? Because that's what it feels like. The wizarding world as presented in the books and expanded materials is this horrible mix of 1984, Brave New World and a weird communist dystopia. No one really seems to work for food, they work for clout or influence. Even the poorest family - Weasleys - are fully self sustaining. At the drop of a hat you can be named a criminal and whisked away in the night, tried in absentia at random (As what nearly happened to Harry), and then sentenced to a stone hole in the ground forever. You could lose all control over your life, without a way of escaping because someone sprayed you with a perfume bottle (Love potions are contact based, not just drinkable) or decided to Imperius you. The only way Harry and his friends got through Voldemorts reign, was moving every day, living in the woods like animals, sleeping in their expanded tents and eating scrounged food. Even then they eventually got caught because one of them said a word that had been cursed to instantly pin point your location - Breaking their magical defences at the time as well - to the secret police.
Rowling tried to make a pretty, fantastical world, and what she instead made is a nightmare.