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Terry Tao on some desirable properties of mathematical notation

mathoverflow.net

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Re: Terry Tao on some desirable properties of mathematical notation

#211

Post by gspr »

an_android wrote: post #200
foobar_ wrote: post #197

Earlier quoted context omitted.

I'm not insane ... you are just the type of person who will defend roman numerals. Maybe you just have OCD. 1. Socrates is mortal 2. Mortals die 3. Socrates dies Deduction is really like amazing. Holy shit we really proved something spectacular here. I guess you would be really impressed if I used tau and sigma and defined death with vietnamese alphabet. Almost the entirety of calculus was derived from problems relat…

Don't use phrases as "Maybe you just have OCD". This is offensive and trivializes the problems those with OCD face. OCD is a serious disorder and your use of that phrase illustrates your lack of mental maturity. Further, that phrase is bigoted. What you are implying is that someone with OCD is "lesser" or "other" as you are using the phrase to discount the person you are talking with. Hence it is bigoted. In fact, it…

> If you want a more concrete example, show that the sum […]

He won't. I keep running into people like this all the time. They are hellbent on the idea that anything they don't understand must be meaningless, useless, or the fault of others. If you get a reply at all, I suspect it will be something like "pi is just a meaningless approximation to a real physical concept" or "infinite series don't actually exist in real life, I'll sum the first 1000000 terms on a computer and that's all that exists".

Re: Terry Tao on some desirable properties of mathematical notation

#212

Post by foobar_ »

gspr wrote: post #211
an_android wrote: post #200

Earlier quoted context omitted.

Don't use phrases as "Maybe you just have OCD". This is offensive and trivializes the problems those with OCD face. OCD is a serious disorder and your use of that phrase illustrates your lack of mental maturity. Further, that phrase is bigoted. What you are implying is that someone with OCD is "lesser" or "other" as you are using the phrase to discount the person you are talking with. Hence it is bigoted. In fact, it…

> If you want a more concrete example, show that the sum […] He won't. I keep running into people like this all the time. They are hellbent on the idea that anything they don't understand must be meaningless, useless, or the fault of others. If you get a reply at all, I suspect it will be something like "pi is just a meaningless approximation to a real physical concept" or "infinite series don't actually exist in rea…

Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers.

The internet makes it easy for pedantic losers to have a loud opinion. Hell I have even run in to pedantic losers who have the time to create multiple new and fake accounts and use old sock puppets to create the illusion of an audience because these friendless, loveless losers literally have no one to talk to IRL.

> I keep running into people like this all the time.

Psychological attacks, amazing! I'm guessing you are one of those deeply insecure symbol twiddlers. Let me guess, as kid you were crap at everything, especially sports except symbol twiddling so you latched onto those praises your teacher gave you and as an adult that is the only source of your self-esteem. And you can't handle it when someone on the internet thinks abstract mathematicians are full of shit.

Re: Terry Tao on some desirable properties of mathematical notation

#213

Post by Smaug123 »

ChrisLomont wrote: post #199
Smaug123 wrote: post #162

Earlier quoted context omitted.

I think you've got the same misconception as quietbritishjim above. Start stacking quantifiers, and the symbols get hairy much faster than the English does.

Maybe you're not used to reading quantifiers. I also find them much easier, faster, and more accurate to read, because it's from practice. Sure you can take simple English statements, and write them with quantifiers, and claim the English is simpler. But going the other way, expressing complex items in English, is a non-starter. English is far too sloppy, whereas the quantifier version is mathematically precise. Try…

Look, do you really want me to wade through sixteen pages to discover the notation first (written by someone who doesn't know about \langle and \rangle, either)? I would consider it bad argumentative form of the same water as Euler's apocryphal "does God exist" debate with Diderot.

At the very least, you will struggle to persuade me that the use of \wedge is easier to understand than the English word "and" with line breaks.

Also you've picked a specific example where the objects of study are these long strings of symbols. Of course any paper worth its salt is going to use them - they're literally the things that the paper is there to examine. It's the metamathematical statements in this context, not the quotation of the formulas under study, that I want to replace with English.

Re: Terry Tao on some desirable properties of mathematical notation

#214

Post by gspr »

foobar_ wrote: post #212
gspr wrote: post #211

Earlier quoted context omitted.

> If you want a more concrete example, show that the sum […] He won't. I keep running into people like this all the time. They are hellbent on the idea that anything they don't understand must be meaningless, useless, or the fault of others. If you get a reply at all, I suspect it will be something like "pi is just a meaningless approximation to a real physical concept" or "infinite series don't actually exist in rea…

Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers. The internet makes it easy for pedantic losers to have a loud opinion. Hell I have even run in to pedantic losers who have the time to create multiple new and fake accounts and use old sock puppets to create the illusion of an audience because these friendless, loveless losers literally have no one to…

> Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers.

Mathematicians will not say anything like "infinity is real" or "infinity is not real". We are careful creatures, and will ask what you mean by "infinity". In this subthread we've been discussing infinite series. What part of the definition of those do you have a problem with? (Prediction: you'll never answer this, but instead go on ranting with no ability to focus on the topic at hand. I can definitely see why math is hard for you, you have a severe problem with focus).

> The internet makes it easy for pedantic losers to have a loud opinion.

I can see that.

> Hell I have even run in to pedantic losers who have the time to create multiple new and fake accounts and use old sock puppets to create the illusion of an audience because these friendless, loveless losers literally have no one to talk to IRL.

That's pretty sad. It's also very sad that this is the conclusion you jump to when someone speaks out against your insane ravings in an entirely logical and coherent way.

> Psychological attacks, amazing!

It's a bit entertaining that you can go from what you wrote above (and what you write below) straight into accusing me of this.

> I'm guessing you are one of those deeply insecure symbol twiddlers.

I am indeed quite insecure. I'm working on managing that. If you by "symbol twiddler" mean mathematician, then yes – and quite proud of it too. You'll do well to get back on track to the topic at hand though, seeing as you're currently coming off a bit like the people one sometimes see yelling incoherent nonsense on subway trains.

> Let me guess, as kid you were crap at everything, especially sports except symbol twiddling so you latched onto those praises your teacher gave you and as an adult that is the only source of your self-esteem.

Not at all. While I was quite mediocre at sports (though far from crap), I did really well in most things. I was not a favorite of the teachers, because I had (and probably still have) a bit of problem with authority. Are you done derailing the discussion now? I'll remind you: we're discussing the usefulness of mathematics, not my childhood or athletic abilities.

> And you can't handle it when someone on the internet thinks abstract mathematicians are full of shit.

I can handle it just fine, primarily because what raving lunatics believe has no influence on the extreme actual power and usefulness of mathematics. The reason I care to have the discussion is to set the record straight for third parties' sake.

Re: Terry Tao on some desirable properties of mathematical notation

#215

Post by foobar_ »

gspr wrote: post #214
foobar_ wrote: post #212

Earlier quoted context omitted.

Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers. The internet makes it easy for pedantic losers to have a loud opinion. Hell I have even run in to pedantic losers who have the time to create multiple new and fake accounts and use old sock puppets to create the illusion of an audience because these friendless, loveless losers literally have no one to…

> Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers. Mathematicians will not say anything like "infinity is real" or "infinity is not real". We are careful creatures, and will ask what you mean by "infinity". In this subthread we've been discussing infinite series. What part of the definition of those do you have a problem with? (Prediction: you'll nev…

I would not reply if not for the delicious irony the georoge cantor was a schizophrenic lunatic who died poor and homeless.

I too am concerned about mentally ill lunatics who have taken over mathematics who think gibberish and number puzzles need to be the concern of others, hell even funded by others.

Unlike you I welcome the death of mathematicians and mathematics as we know it, I am all ears on how we can get rid of mathematics from obsessive compulsive lunatics, pea counters, hypocrites, schizophrenics and symmetry worshipers.

> we're discussing the usefulness of mathematics

Internet narcissists do like to imagine insults.

No we are not. The post was about the value of notation and my thread was about the refutation of notation as useless and programming as a better alternative to it.

Re: Terry Tao on some desirable properties of mathematical notation

#216

Post by gspr »

foobar_ wrote: post #215
gspr wrote: post #214

Earlier quoted context omitted.

> Mathematicians who think infinity is real should be treated with the same disdain as Neptune worshiping astrologers. Mathematicians will not say anything like "infinity is real" or "infinity is not real". We are careful creatures, and will ask what you mean by "infinity". In this subthread we've been discussing infinite series. What part of the definition of those do you have a problem with? (Prediction: you'll nev…

I would not reply if not for the delicious irony the georoge cantor was a schizophrenic lunatic who died poor and homeless. I too am concerned about mentally ill lunatics who have taken over mathematics who think gibberish and number puzzles need to be the concern of others, hell even funded by others. Unlike you I welcome the death of mathematicians and mathematics as we know it, I am all ears on how we can get rid…

> I would not reply if not for the delicious irony the georoge cantor was a schizophrenic lunatic who died poor and homeless.

Do the mental problems and drug addiction of a brilliant musician detract from his or her music? Do you yell "madman" at a painting by van Gogh?

> Unlike you I welcome the death of mathematicians and mathematics as we know it

Even you, with the most pedestrian definition of what is "useful", must surely acknowledge that a lot of mathematics is immensely useful. Yet you wish for its death. You have nothing to replace it with. You sound like Trump and his non-existent healthcare "plans". You're hell-bent on destroying something simply because you cannot grasp it.

> No we are not. The post was about the value of notation and my thread was about the refutation of notation as useless and programming as a better alternative to it.

Yes, and in a sub-thread of the post you've made it clear that you doubt the usefulness of mathematics. So now we are having a sub-discussion about that. Yet you've still to contribute anything of value. On several occasions have I and others invited you to comment on very concrete mathematical constructions. You evade those invitations. I can only surmise that that is because you do not understand the questions you are being asked, or are unable to provide an alternative to the current standard mathematics. That standard mathematics is done in a somewhat formal language built around the very notation that this thread is about.

Re: Terry Tao on some desirable properties of mathematical notation

#217

Post by omaranto »

cryptica wrote: post #206
omaranto wrote: post #186

Earlier quoted context omitted.

If informal descriptions confuse you, skip them and read actual definitions instead. I actually like informal definitions a lot. I think they serve two different purposes: 1. For beginners they usually soften the blow of a fully rigorous definition, letting them get an idea of the concept before getting it exactly. 2. For experts they can often suggest what the exact definition is faster than it would be to read a pr…

It's not about 'informal definitions'. I also really like informal definitions but not the way that most mathematicians currently tend to write them.

Wait, are you complaining about how mathematicians currently tend to write informal descriptions of concepts or about the informal descriptions in the intros to Wikipedia articles? I think those things are pretty different.

Re: Terry Tao on some desirable properties of mathematical notation

#218

Post by foobar_ »

gspr wrote: post #216
foobar_ wrote: post #215

Earlier quoted context omitted.

I would not reply if not for the delicious irony the georoge cantor was a schizophrenic lunatic who died poor and homeless. I too am concerned about mentally ill lunatics who have taken over mathematics who think gibberish and number puzzles need to be the concern of others, hell even funded by others. Unlike you I welcome the death of mathematicians and mathematics as we know it, I am all ears on how we can get rid…

> I would not reply if not for the delicious irony the georoge cantor was a schizophrenic lunatic who died poor and homeless. Do the mental problems and drug addiction of a brilliant musician detract from his or her music? Do you yell "madman" at a painting by van Gogh? > Unlike you I welcome the death of mathematicians and mathematics as we know it Even you, with the most pedestrian definition of what is "useful", m…

> Do the mental problems and drug addiction of a brilliant musician detract from his or her music? Do you yell "madman" at a painting by van Gogh?

Yes. Completely ignore the degenerates. There are many sober people who have made art and science. You should not allow mentally ill lunatics to define art, music, religion, maths or politics anymore than you will allow them to be your cab driver or spouse.

Clearly science is about sobriety and not schizophrenia. I guess mathematics was hijacked by schizophrenics, music and art by depressed losers. No wonder you are out of touch with reality, practicality and are defending symbols which you think have magical "powers" beyond mere convention.

You can also see this in physics with the string theory garbage, however unlike "pure" mathematics ... in physics people need to test experimentally.

> Yes, and in a sub-thread of the post you've made it clear that you doubt the usefulness of mathematics.

No, I said proofs were tautological and pointless and notation is useless. Formal mathematics is bullshit.

> On several occasions have I and others invited you to comment on very concrete mathematical constructions.

Your sock puppets ?

1. You were asking about fundamental theorem of calculus

This has a very geometric proof. Why would I have a problem with that ? I am all for geometry, visualization, simulation , testing ....

2. A number puzzle

I don't care for number puzzles. I will try to solve that number puzzle if you can write vietnamese jokes.

Re: Terry Tao on some desirable properties of mathematical notation

#219

Post by ChrisLomont »

Smaug123 wrote: post #213
ChrisLomont wrote: post #199

Earlier quoted context omitted.

Maybe you're not used to reading quantifiers. I also find them much easier, faster, and more accurate to read, because it's from practice. Sure you can take simple English statements, and write them with quantifiers, and claim the English is simpler. But going the other way, expressing complex items in English, is a non-starter. English is far too sloppy, whereas the quantifier version is mathematically precise. Try…

Look, do you really want me to wade through sixteen pages to discover the notation first (written by someone who doesn't know about \langle and \rangle, either)? I would consider it bad argumentative form of the same water as Euler's apocryphal "does God exist" debate with Diderot. At the very least, you will struggle to persuade me that the use of \wedge is easier to understand than the English word "and" with line…

>do you really want me to wade ....

No - just pointing out that no matter how hard you studied that an English equivalent of such a terse expression will be a mess, vastly harder to understand.

>At the very least, you will struggle to persuade me that the use of \wedge is easier to understand than the English word "and" with line breaks.

You're making my case for me :)

The word "and" and "or" are ambiguous in common English, and have no common or even technical well-defined precedence. "Or" in English both can mean "inclusive or" or "exclusive or," yet most people simple write "or".

In math they have well defined precedence, and math has parentheses to order correctly, unlike English.

The only reason you find English easier to understand is you have used more than math symbols at a ratio that makes that true for you. It's not true for everyone, especially professionals, that use some set of notation a lot.

>Also you've picked a specific example where the objects of study are these long strings of symbols

Avoiding the point. The math does not have to self-referential to use complex expressions not amenable to writing in English. This expression is not complex because it's a meta argument. Such expressions can occur in all sorts of places.

At this point I'm sure your present these red herrings to avoid considering that your opinion is not common among professionals that can read symbols much faster and more accurately than can be done in English.

No sense in continuing.

Re: Terry Tao on some desirable properties of mathematical notation

#220

Post by gspr »

foobar_ wrote: post #218
gspr wrote: post #216

Earlier quoted context omitted.

> I would not reply if not for the delicious irony the georoge cantor was a schizophrenic lunatic who died poor and homeless. Do the mental problems and drug addiction of a brilliant musician detract from his or her music? Do you yell "madman" at a painting by van Gogh? > Unlike you I welcome the death of mathematicians and mathematics as we know it Even you, with the most pedestrian definition of what is "useful", m…

> Do the mental problems and drug addiction of a brilliant musician detract from his or her music? Do you yell "madman" at a painting by van Gogh? Yes. Completely ignore the degenerates. There are many sober people who have made art and science. You should not allow mentally ill lunatics to define art, music, religion, maths or politics anymore than you will allow them to be your cab driver or spouse. Clearly science…

> Yes. Completely ignore the degenerates. There are many sober people who have made art and science. You should not allow mentally ill lunatics to define art, music, religion, maths or politics anymore than you will allow them to be your cab driver or spouse.

What a vile attitude.

> Clearly science is about sobriety and not schizophrenia.

Of course. No endeavour is about schizophrenia. That doesn't mean the contributions of sufferers of schizophrenia should be discarded. Evaluate the contributions on their own merits. Which is something that you can do with science and math and art.

> No wonder you are out of touch with reality, practicality and are defending symbols which you think have magical "powers" beyond mere convention.

I and others have repeatedly challenged you to reproduce "useful" math without these tools. You consistently avoid the topic.

> You can also see this in physics with the string theory garbage, however unlike "pure" mathematics ... in physics people need to test experimentally.

That is because physics is about deducing facts about the natural word. Mathematics is about deducing truths within a logical framework, given certain assumptions. If the assumptions are reasonable, the things math deduce can very often be extremely useful in describing said natural world. You have clearly not understood this.

Said differently: given a mathematical model for the physical world, mathematics can predict its behavior. This is, needless to say, extremely powerful. It is the job of physicists to determine whether the underlying model is a good one.

> No, I said proofs were tautological and pointless and notation is useless. Formal mathematics is bullshit.

And I will have to repeat myself then: Is calculus useless? If you say yes, you're clearly deranged, as physics and much of engineering die with it. If you say no, then I challenge you to construct a useful and consistent version of calculus without formal mathematics. Come on now! Enough with the ad hominems, get cracking! Put your money where your big mouth is.

> Your sock puppets ?

No.

> 1. You were asking about fundamental theorem of calculus. This has a very geometric proof. Why would I have a problem with that ?

Care to give that proof? Or point me to it? I bet you that it will either turn out to be correct and I can show you how it uses formal mathematics, or it will turn out to be incorrect or not a proof at all.

> 2. A number puzzle

What the hell are you on about? What's the number puzzle you're talking about? The series mentioned? It's not at all a "number puzzle" – it's a direct consequence of (among other things) Fourier analysis. Ask any "real life" signal processing engineer whether Fourier analysis is "real" or "just a number puzzle".

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