I mostly comment on my iPad. When using an iPad it’s hard to get spelling correct. Also, language changes over time. For instance, “I could care less” is starting to mean “I couldn’t care less”. When enough people say or use a phrase incorrectly enough then it becomes the new correct way.
Please spare me that "war" simile, it only shows you're an American who can not write too well.
It’s understandable that you don’t like the desensitization of war that comes from our over usage of the word. Perhaps it speaks to a defect in American culture but this is how we communicate in our language. I think Arabic has too much emphasis on allah related phrases. But that’s how they speak. Nothing I can do about it. I don’t think said usage implies anything about their writing abilities.
The “war on Christmas” was thought up by a think tank and agreed upon by a group of conservative media that meet weekly to decide agenda to push across talk radio, tv, online. Truly an American phenomenon.
Think tanks that create agendas for groups who meet regularly to decide how to push those agendas through the media and through their politicians are not an American phenomenon, and not specifically conservative.
The people who you work for (and who everyone works for) are probably loosely associated with tons of them.
It was pointed out that in American English we overuse "war". I pointed out a language that overuses a different word. I imagine most languages have a bunch of phrases involving an overused word. My point was that this phenomenon isn't unique to American English.
Your response is that English also overuses another word. I don't understand the point you are trying to make.
Not even close! I only have experience in the Gulf but they use "allah" words all the time!
"Alhamdulillah" (thank god) is pretty much part of the standard greeting (Pretty much just two people rapid firing a list of phrases at each other simultaneously "peace be with you / and also peace with you / how are you / thank god / how's the family / thank god") and a frequent response to almost any question.
Anything dealing with the future or uncertainty will bring in "Inshallah" (God willing). I remember the first time I asked my cab driver to take me to my destination and he said "Inshallah" that did not give me confidence!
Then there's "bismallah" and "mashallah" which I heard a bunch. And I'm not sure if we can count "yallah, yallah" which is like "hurry, hurry, let's go" which you hear all the time and is derived from "Ya Allah".
I would be willing to bet that Gulf Arabic speakers say "Allah" literally at least 10x if not 100x more than Americans say "God".
> "Alhamdulillah" (thank god) is pretty much part of the standard greeting
Same goes with English! When parting ways, people commonly say "bye" or "goodbye" which is an evolution of "Godbye" - a contraction of "God be with ye"
I had a photoshoot scheduled with a young Somali man. He was late by over an hour, and I had another shoot after so I had to cancel. I rescheduled and told him if he was late for the next shoot I wouldn’t be rescheduling again.
He said he wouldn’t be…inshallah.
I know it’s part of their language but just as with your cab example it can be a bit annoying as an outsider, as it feels like they’re passing off responsibility. I feel the same way about some of the things Christians say too, for what it’s worth.
Anyways, that’s my infuriating inshallah story. He was late again - and he needed to find another photographer after that.
On the other hand. For example in Kiswahili "Shauri ya Mungo" (God's business). Perhaps not exactly the same, but sufficiently similar to be interesting: that some things are in fact beyond human capability and comprehension has largely disappeared from the English language (or any language from predominately secular countries).
> that some things are in fact beyond human capability and comprehension has largely disappeared from the English language (or any language from predominately secular countries
It's still common in insurances agreements or other contracts that have to consider force majeure - natural disasters and other phenomena fall under the blanket term "Acts of God".
Also, plenty of "secular" curses/exclamations have religious connotations (because it was taboo, and cursing and the taboo are inextricably linked). "Geez", "Gazooks" (God's hooks), etc.
Inshallah is just a fun and useful word, I've been hearing it a lot lately from people who aren't even Muslims. I think it's on track to become a common loan word in English.
Sounds similar to "mei ban fa" (it can't be helped) in Chinese. The words suggest something is impossible but in practice it generally just means, nope, don't feel like it.
For one of your next trips I suggest a few months in Ireland, and if you could in particular spend time living in a slightly more rural or at least small-town type family.
Jaysus lads, that chap...Christ, sure how would ya...Holy lord! I've never heard...My God, did you hear...Lord help us and save us, she'd only...
And I'm leaving out the more vulgar variants here.
I'm not saying we'd beat some of the Arabic countries, but I definitely am saying we very well might give them a good run for their money. I'll consciously try tone it down if I'm conversing with a non-Irish person, and then with my family I'll let loose.
Maybe Americans use God-related idioms a lot less than us, of course. The U.S. is a relatively big place though, so I'd be curious to know if there aren't some corners closer to (rural?) Ireland's usage.
Nah. English speakers use God-based exclamations from time to time but they generally do not pepper their sentences with "God willing", "praise God," etc like Arabs do.
That said, I do not care at all that Arabs used "God" a lot or that Americans (supposedly) use "war" a lot. If anything, I like these sorts of differences.
The point I was making is that this phenomenon occurs in other languages. Arabic and its phrases involving "allah" first came to mind. So how was this "needlessly"? I needed to give an example of this occurring in another language.
Nah, even a short interaction with a muslim would key you into the fact that they use allah based phrases way more often than the typical american or christian.
People can be convinced that vaccines are bad and that they shouldn’t vaccinate their kids against polio. You can convince someone of just about anything. Sometime in the future measures against false information will need to be taken to prevent a tyranny of simpletons.
This checks the meaning box because Peterson is doing something meaningful that I agree with and identify with on the world stage, which I’m afraid is where the bar is for me if I’m not going to be the frontman.
That's definitely a way to narrow down potential employers. Hope it works for him but he comes across...off to me.
Can you be more specific? I wasn't sure if I'd got the idea across there but maybe it seems narcissistic/sycophantic anyway. I'm not married to the idea at all, but it is something that's occurred to me. Also not sure about Peterson himself recently, especially with the video on Trump's character leaving out anything about the bad business deals and Trump University stuff.
Students don’t like “real world” problems. They say they want more of that but when you actually do those types of problems they complain or do poorly on them. Word problems are even more confusing to students than non-word problems.
The vast majority of so called real world problems aren’t things people who use math in their jobs actually do.
I guess you are referring to the "Steve has 17.5 credits, how many pizzas can he buy?" type problems?
For me, when learning calculus it was that it seemed pointless. They were teaching me to do this mechanical task, but why? Why not another task like increasing every other number in the equation by 6? It wasn't until I learnt about velocity and acceleration that it all started to make sense. The task of differentiating/integrating seemed far less important than the understanding that functions have derivatives and anti-derivatives and what that means.
Calculus 3 in the U.S. is multi-variable calculus. Sometimes and introduction to linear algebra is given in this course. Calculus 4 is differential equations. It’s almost never officially called Calculus 4. Sometimes an introduction to linear algebra is given in this course.
Okay that makes sense, that's how the classes went for me in the US, with Calc 3 being multi variable (and as you say, a brush with linear alg via vector-valued functions), and 2 sideways steps from there, one being a course on PDEs and the other on linear algebra, both called by those names rather than listed as a step in the calculus sequence itself.
The removal of such emotional baggage from a subject greatly nerfs the ability of people to manipulate public perceptions by tugging at heartstrings with phrases like "underclass of migrant labor whose human rights are always in jeopardy".
Do you believe migrant labor in the U.S. are treated with dignity and are treated well? What about illegal immigrants working in slaughterhouses? More generally speaking, do you believe there are classes of people who are treated poorly?
If such people exist then isn’t it valid to describe them accurately and to describe how “the system” treats them?
Every healthcare system rations care. In the U.S. that rationing is largely based on quality of employment or how much wealth you have. To some this is a largely immoral way to ration care.
As with all healthcare systems if there is a shortage of workers or it is not properly funded it will deteriorate. The U.S. healthcare system sucks for people who have no real access to it. The wait time of someone with no access to the system is effectively infinity.
Socialism, capitalism, communism, fascism, etc. are merely economic systems and all of them suck if not properly administered.
What argument? I’m not making an argument. I’m pointing out what I think are facts. Apparently you don’t have enough wealth provided you are in the U.S.
The term "function" sadly means different things in different contexts. I feel like this whole thread is evidence of a need for reform in maths education from calculus up. I wouldn't be surprised if you understood all of this, but I'm worried about students encountering this for the first time.
Don’t know if you are a mathematician or not but mathematically speaking “function” has a definition that is valid in all mathematical contexts. Functional clearly meets the criteria to be a function since being a function is part of the definition of being a functional.
The situation is worse than I thought. The term "function", as used in foundations of mathematics, includes functionals as a special case. By contrast, the term "function", as used in mathematical analysis, explicitly excludes functionals. The two definitions of the word "function" are both common, and directly contradict one another.
By contrast, the term "function", as used in mathematical analysis, explicitly excludes functionals. The two definitions of the word "function" are both common, and directly contradict each other.
This is incorrect. In mathematics there is a single definition of function. There is no conflict or contradiction. In all cases a function is a subset of the cross product of two spaces that satisfies a certain condition.
What changes from subject to subject is what the underlying spaces of interest are.
> What changes from subject to subject is what the underlying spaces of interest are.
I'm not sure I understand what you mean here. I need some clarification. How does this have any bearing on whether functionals count as functions or not? What is the "underlying spaces of interest" in this example?
In some trivial way, every mathematical object can be seen as a function. You can replace sets in axiomatic set theory with functions.
Everything I wrote was assuming set theory as the foundations for mathematics and applies only to that setup. At any rate a functional is function since the definition starts with: a functional is a function from…
Some books will say: a functional is a linear map….
You genuinely don't know what you're talking about. The word "function" means different things in different areas. So does the word "map" or "mapping". In analysis, what you personally call a "function" instead falls under the term "mapping". In foundations - which is a different area with incompatible terminology - the terms "mapping" and "function" are defined to mean the same thing.
This situation is a consequence of how mathematicians haven't always been sure how to define certain concepts. See "generating function" for yet another usage of the word "function" that's in direct contradiction with the last two. So that's three incompatible usages of the term "function". All this terminology goes back to the 1700s when mathematics was done without the rigour it has today.
I find it aggravating how you're so confidently wrong. I hope it's not on purpose.
I am looking at the whole development of this thread with amusement, but I also find it somewhat shocking.
I see that you are desperately trying to distinguish "foundational" and "analysis" contexts from each other. If you are writing a book about analysis, it might be helpful to clarify that in this context you reserve "function" for mappings into ℂ or ℝ, for example [1] defines "function" exclusively as a mapping from a set S to ℝ (without any further requirements on S such as being a subset of ℝⁿ). Note that even under this restricted definition of function, a distribution still is a function.
In a general mathematical context, "function" and "mapping" are usually used synonymously. It is just not the case that such use is restricted to "foundations" only.
It seems to me that squabbles about issues like this are becoming more frequent here on HN, and I am wondering why that is. One hypothesis I have is that there is an influx of people here who learn mathematics through the lens of programs and type theory, and that limits their exposure to "normal" mathematics.
[1] Undergraduate Analysis, Second Edition, by Serge Lang
I learned mathematics the regular way. So you're wrong - and not just about this.
> I see that you are desperately trying to distinguish "foundational" and "analysis" contexts from each other
They literally are different. The proof is all the people here saying that distributions aren't functions, while displaying a clear understanding of what a distribution is. Maybe no one's "wrong" as such, if they're defining the same word differently.
I think you're the naive one here. Terminology is used inconsistently, and I tried to simplify the dividing line between different uses of it. I agree it's inaccurate to say it's decided primarily by Foundations vs Analysis, but I'm not sure how else to slice the pie. It's like how the same word can mean slightly different things in French and English. I agree it's quibbling, but it's harder to teach maths to people if these False Friends exist but don't get pointed out.
I never expected some obsessive user to make 6 different replies to one of my comments. Wow. This whole thing thread was a bit silly, and someone's probably going to laugh at it. I need to take another break from this site.
I never expected some obsessive user to make 6 different replies to one of my comments. Wow.
You have 6 posts in the thread started by my top comment. I had multiple replies to one of your posts because HN requires one to wait a while to reply and I was in a hurry. The order of posts doesn’t matter. At least not to me.
Insinuating I’m obsessive has a negative connotation. Along with outright insults such comments make you look bad and unreasonable.
It’s strange to hear a fellow mathematician say that if I’m in set theory class then a functional is a function but isn’t one in functional analysis. In Rudin’s Functional Analysis book he proves that linear mappings between topological spaces are continuous if they are continuous at 0. I’ve never heard of someone believing that a continuous mapping is not a function.
Terry Tao writes in his analysis book:
Functions are also referred to as maps or transformations, depending on the context.
Tao certainly knows more about this than I ever will.
Yeah, the whole argument felt somewhat unhinged and silly. It is fine to point out that sometimes "function" is used in a more specific manner than "mapping", particularly in analysis, but I doubt any mathematician would think that a functional is not a function, in a general context such as a HN comment.
You genuinely don't know what you're talking about. .... I find it aggravating how you're so confidently wrong.
This is a fine example of irony.
Let V be a vector space over the reals and L a functional. Let v be a particular element of V. L(v) is a real number. It is a single value. L(v) can't be 1.2 and also 3.4. Thus L is a function.
A function is simply a subset of the product of two sets with the property that if (a,b) and (a, c) are in this subset then b=c.
Can you find a functional that does not meet this criterion? If so then you have an object such that L maps v to a and also maps v to c with a and c being different elements.
Find me a linear map that does not meet the definition of function. Give an example of a functional in which the functional takes a given input to more than one element of the target set.
I think you are not a mathematician and you also don't appear to understand that a word can have different meanings based on context. "generating function" isn't the same thing as "function". Notice that generating is paired with function in the first phrase.
Example: Jellyfish is not a jelly and not a fish. Biologists have got it all wrong!
> Example: Jellyfish is not a jelly and not a fish. Biologists have got it all wrong!
You have a problem with reading comprehension. I never said any mathematician was wrong.
Think about namespaces for a moment, like in programming. There are two namespaces here: The analysis namespace and the foundations namespace.
In either of those two namespaces, the word "mapping" means what you're describing: an arbitrary subset F of A×B for which every element of a ∈ A occurs as the first component in a unique element (x,y) ∈ F.
But the term "function" has a different meaning in each of the two namespaces.
The word "function" in the analysis namespace defines it to ONLY EVER be a mapping S -> R or S -> C, where S is a subset of C^n or R^n. The word "function" is not allowed to be used - within this namespace - to denote anything else.
The word "function" in the foundations namespace defines it to be any mapping whatsoever.
If one has a “thing” that “maps” elements of one set to another that satisfies the condition I previously gave then that thing is a function. Every functional satisfies that definition. Therefore every functional is a function.
[edit] I've finally blown it. You're a moron. Your definition of "function" as some subset of AxB is how it's defined in foundations. It's not how it's defined in analysis. In analysis, your definition would describe the term "mapping". What a crackpot and idiot. I'm done wasting time and sanity on this.
Interesting. So you think there are functions in real analysis that are studied that don't meet the definition I gave? Is there a functional that does not meet the definition I gave?
In all contexts a function is a subset of the product of two sets that meets a certain condition. Anything that does not meet this definition is not called a function.
Every functional meets the definition of function.
The word "function" in the analysis namespace defines it to ONLY EVER be a mapping S -> R or S -> C, where S is a subset of C^n or R^n. The word "function" is not allowed to be used - within this namespace - to denote anything else.
In real analyis one is interested in functions from R^n to R. They don't define function to be only something from R^n to R. It's just that these are the functions they wish to study. They don't define function to exclusively be a map from R^n to R. It’s just that these are the types of functions they care about.
No mathematician can possibly think function is anything other than a subset of the product of two spaces that meets a certain condition.
