Self Learning Math/Physics

[WWGD]

Come to physicsforums for help with mathematics and get a desiccated lecture on Kierkegaard vs. Max Stirner’s “The Ego and it’s Own” with a side dish of nihilistic ontologism.

Quoting @fresh_42 :


I remember learning about unions and sets as some of the earliest math lessons I had. At the time it was ineffable and boring; later though I’m glad we had those lessons as they made many other concepts accessible. Without that ballast I highly doubt that a book like Hofstadter’s GEB would have made any sense to me.

Took me a few months to even be able to pronounce his last name without my tongue convulsing.

 

[WWGD]

Welp, same in Britain. Though embarrassingly despite still learning basic maths in school I am so insanely reliant on my calculator it is crazy. I never mark my little sister's maths work without a calculator in my hand, despite most of the maths being basic arithmetic...

For set theory? Either times have changed or you're doing something wrong.

 

[fresh_42]

Took me a few months to even be able to pronounce his last name without my tongue convulsing.

Which one? Gödel, Bach, or Kierkegaard?

I only met two people in my life who grew up with American English and were able to pronounce German correctly. The difference to Danish isn't so big then. I think that the main reason is actually how the tongue is used or placed. This is something you cannot easily switch between languages, and the reason why you cannot say Schrödinger and I break my tongue pronouncing clothes.

 

[WWGD]

Which one? Gödel, Bach, or Kierkegaard?

I only met two people in my life who grew up with American English and were able to pronounce German correctly. The difference to Danish isn't so big then. I think that the main reason is actually how the tongue is used or placed. This is something you cannot easily switch between languages, and the reason why you cannot say Schrödinger and I break my tongue pronouncing clothes.

Hofstadter.

 

[fresh_42]

Hofstadter.

I mean Hofstadter is an American, so where is the problem? Ok, he has a German name, which was at some point in time probably written Hofstädter. But the "ä" is the least problematic for English-speaking people. You use it anyway, only pronounced longer than it should as in "can". And most Germans would pronounce it Hofstedter so that the "ä" is basically not heard at all. The only real difference that I see is that the "o" should be long, not short, since the "f" isn't doubled.

 

[sbrothy]

Excuse for cutting away some of the above quote...

Something is bothersome about what is said in post #22, from @TensorCalculus.

Within main computer programming languages each of them has several dialects (and I am just guessing that the word "dialect" is chosen well). A program during development and at a finish still needs to be TESTED extensively or not, in order to look for and remedy problems in coding. How The infierno will Artificial Intelligence take care of all that?

Tell it to write unit tests along the way?

Sorry, just a silly chivalrous attempt at coming to the rescue of @TensorCalculus ‘s idea. Don’t know if it’s possible. Lots of similar links and citations though. (Also, I never personally liked them.)

 

[TensorCalculus]

Excuse for cutting away some of the above quote...

Something is bothersome about what is said in post #22, from @TensorCalculus.

Within main computer programming languages each of them has several dialects (and I am just guessing that the word "dialect" is chosen well). A program during development and at a finish still needs to be TESTED extensively or not, in order to look for and remedy problems in coding. How The infierno will Artificial Intelligence take care of all that?

Yes there will definitely be a need for programming in the future, such as what you've highlighted above.

I decided to take the absolute worst-case, most extreme scenario and try and show that even then, the OP should not care about the fact that AI can do what they're doing because their aim is to do it to satisfy their curiosity.

For set theory? Either times have changed or you're doing something wrong.

Nonono, not for set theory. Basic arithmetic. My sister is preparing for the 11+, she's doing her last year of elementary maths. I use a calculator to check her long division, her column addition, subtraction, multiplication... things like that. I could probably check it properly but... I would probably be slower than her. I relied on my calculator ever since COVID (so, when I was 8,9,10) when I started trying to teach myself physics...

Beyond a couple of lessons on Venn Diagrams here and there we don't do much set theory anymore. I don't think many secondary-aged children would even know what you were talking about if you mentioned set theory (It's introduced formally in A-level maths I believe).

 

[sbrothy]

Which one? Gödel, Bach, or Kierkegaard?

I only met two people in my life who grew up with American English and were able to pronounce German correctly. The difference to Danish isn't so big then. I think that the main reason is actually how the tongue is used or placed. This is something you cannot easily switch between languages, and the reason why you cannot say Schrödinger and I break my tongue pronouncing clothes.

I actually just assumed it was Hofstadter, even though Kierkegaard is probably more tongue-twisting. In fact, the double As are replacements for the Danish Å. It’s pronounced somwhat like the vocals in “duh” or “or”.

Danes pronounce Kierkegaard like “Keerguegor”. Both G’s, and the “ue” like the G and “ue” in “guest”. The D is silent.

 

[martinbn]

Beyond a couple of lessons on Venn Diagrams here and there we don't do much set theory anymore. I don't think many secondary-aged children would even know what you were talking about if you mentioned set theory (It's introduced formally in A-level maths I believe).

It is done in year 10 and 11.

 

[fresh_42]

I actually just assumed it was Hofstadter, even though Kierkegaard is probably more tongue-twisting. In fact, the double As are replacements for the Danish Å. It’s pronounced somwhat like the vocals in “duh” or “or”.

Danes pronounce Kierkegaard like “Keerguegor”. Both G’s, and the “ue” like the G and “ue” in “guest”. The D is silent.

I love Ångström for that reason. Two for the price of one.

 

[sbrothy]

I love Ångström for that reason. Three for the price of one.

Three? Were’s the third? But that’s Swedish. Swedes don’t have the Æ. They use ä.

(Couldn’t find umlaut on my phone.)

 

[TensorCalculus]

It is done in year 10 and 11.

Huh? I asked a year 11 that I know if she knows what set theory is and she had no idea (and she got 9 on her maths GCSE... so...)
Oh well. I haven't done y10 and y11 yet (even though our school usually teaches us things a year early) so I guess I can't say much.

 

[fresh_42]

Three? Were’s the third? But that’s Swedish. Swedes don’t have the Æ. They use ä.

(Couldn’t find umlaut on my phone.)

I first thought "ng" would be a problem, too, but I corrected it as it might be a bit far-fetched. I copied the name from the German Wikipedia page; that's faster than looking for the ASCII code of the letters. Nevertheless, we have the open "a" and the "ö"; ˈɔŋːstɾœm. Neither of which occurs in English.

 

[martinbn]

Huh? I asked a year 11 that I know if she knows what set theory is and she had no idea (and she got 9 on her maths GCSE... so...)
Oh well. I haven't done y10 and y11 yet (even though our school usually teaches us things a year early) so I guess I can't say much.

I might be wrong. I saw a textbook once that had a bit more than Venn diagrams. It may have been A levels or uni. It looked completely pointless, so I assumed it had to be uk's gcse curriculum.

 

[fresh_42]

It is done in year 10 and 11.

It was in elementary school (or shortly after) here, which is why it was so controversial.

 

[TensorCalculus]

I might be wrong. I saw a textbook once that had a bit more than Venn diagrams. It may have been A levels or uni.

Oh well, we'll see.
I've set a reminder for year 11 me to come back and say whether I learnt set theory or not
This is what the AQA curriculum says for GCSE Maths

It looked completely pointless, so I assumed it had to be uk's gcse curriculum.

 

[TensorCalculus]

It was in elementary school here, which is why it was so controversial.

We do Venn diagrams in Elementary here, but nothing more than that I guess.

 

[fresh_42]

We do Venn diagrams in Elementary here, but nothing more than that I guess.

Yes, that's why I said "set theory" was an exaggeration. However, they called it as such, and it was kind of revolutionary back then since people were used to considering math in early classes as a drill for arithmetic only. I guess, calling it "set theory" and thereby sounding like something new wasn't the best idea. However, I will not dive into the realms of didactics of mathematics in order to avoid ranting.

I basically share the opinion of my former mentor.
(Me, seeing a parcel addressed to a didactician in his office while he was dean): "You send ... a parcel?"
(My mentor): "This was submitted here by mistake. At most, I'll send him something that ticks."

 

[TensorCalculus]

Yes, that's why I said "set theory" was an exaggeration. However, they called it as such, and it was kind of revolutionary back then since people were used to considering math in early classes as a drill for arithmetic only. I guess, calling it "set theory" and thereby sounding like something new wasn't the best idea. However, I will not dive into the realms of didactics of mathematics in order to avoid ranting.

Ah yeah you did mention...
Do they still teach it in elementary now? Considering the fact that it wasn't considered the best idea?

 

[fresh_42]

Ah yeah you did mention...
Do they still teach it in elementary now? Considering the fact that it wasn't considered the best idea?

I don't know, I haven't checked. The problem was not the content; the mistake was labelling it by a name. I assume you will learn this on several occasions in your hopefully long life: People oppose everything new by default! Have a look at the AI discussions here! Or even better, look at "I am a chipper, I am no melter!"

You can easily introduce these basic concepts by, for instance, considering divisors and looking at $\operatorname{gcd}$ and $\operatorname{lcm}.$ The key is to sneak in new concepts rather than calling out a revolution!

 

[sbrothy]

Yes, that's why I said "set theory" was an exaggeration. However, they called it as such, and it was kind of revolutionary back then since people were used to considering math in early classes as a drill for arithmetic only. I guess, calling it "set theory" and thereby sounding like something new wasn't the best idea. However, I will not dive into the realms of didactics of mathematics in order to avoid ranting.

I basically share the opinion of my former mentor.
(Me, seeing a parcel addressed to a didactician in his office while he was dean): "You send ... a parcel?"
(My mentor): "This was submitted here by mistake. At most, I'll send him something that ticks."

To be clear I also didn't mean we had proper Set Theory that early. But the concepts of sets and subsets and the use of the symbols like ⊂ and ⊆ were present.

 

[Muu9]

I might be wrong. I saw a textbook once that had a bit more than Venn diagrams. It may have been A levels or uni. It looked completely pointless, so I assumed it had to be uk's gcse curriculum.

What's pointless about set theory, or the set theory covered in the book?

 

[sbrothy]

Heck, a Venn diagram is just the most basic representation of shared sets isn't it? Why is it mentioned so much? I mean why does it seem so important to people? I'd expect the logical symbols representing the relationships between sets much more important.

 

[martinbn]

What's pointless about set theory, or the set theory covered in the book?

They only introduced notations and names without any motivation or use.

Heck, a Venn diagram is just the most basic representation of shared sets isn't it? Why is it mentioned so much? I mean why does it seem so important to people? I'd expect the logical symbols representing the relationships between sets much more important.

I agree. I don't know why they are taught.

 

[symbolipoint]

Heck, a Venn diagram is just the most basic representation of shared sets isn't it? Why is it mentioned so much? I mean why does it seem so important to people? I'd expect the logical symbols representing the relationships between sets much more important.

Visualization!

Symbols can be nice. Visualization can also be nice. More to say, but that should be enough.

 

[jtbell]

I love Ångström for that reason. Two for the price of one.

That's why we have people named Engstrom in the US. Their immigrant ancestors probably figured that was as close as they could expect their new neighbors to manage. I knew one in high school.

 

[CrysPhys]

Visualization!

Symbols can be nice. Visualization can also be nice. More to say, but that should be enough.

Yes. And I'd like to point out that Venn diagrams are particularly effective for communicating with non-mathematical audiences. At one time, I needed to make presentations to business executives (backgrounds were in business, finance, and project management). Venn diagrams they could readily grasp; they would have been lost with "symbols like ⊂ and ⊆".

 

[weirdoguy]

Why is it mentioned so much?

Why drawings are mentioned so much, when one can write equations without them? Some of you didn't have to make living out of teaching math/physics

 

[sbrothy]

Why drawings are mentioned so much, when one can write equations without them? Some of you didn't have to make living out of teaching math/physics

Well OK. I just meant that this particular name popped up very frequently. What I maybe didn’t consider was how widespread a concept it is and how often it applies.

No harm meant. I was certainly not out to ridicule your profession!

 

[weirdoguy]

I just meant that this particular name popped up very frequently.

Long time ago I read a set theory textbook where author said that Venn diagrams are way more general tools then most people think. He talked way more about that, but I was reading it just for fun, and it wasn't fun, so I don't remember more. Anyways, in polish schools they are taught just as a tool, without naming them. They are also used in the context of some exerices in probability (eg. to write $P(A'\cap B)$ in terms of other sets - for me Venn diagrams are the best way to see things).