Mathematics - 2013-11-29 (page 4 of 5)

Hal

6:00 PM

All those sense representations are called 'qualia'

Charlie

very interesting!

Hal

We could be automatons with no qualia - and nobody would no the difference. Even a brain scan wouldn't show it. The automatons would still process and recognize red. It just wouldn't be represented to them.

So we can't ever point to the qualia and say 'here it is!'

or disprove it

but we know it exists.

IMO, that leaves a crack in the best arguments against the existence of a soul, even those made by most well reasoned, empirical skeptical secular person you might ever meet.

So if you believe in the soul - that's a useful thing to have at your disposal if you need to defend the belief.

Charlie

yes, as i told you

Hal

Yep. I'm in the same boat.

But I have to play the game I'm in.

Imagine philosophical discussion proceeding up a tree.

Charlie

hahaha

Hal

6:04 PM

The idea of personal identity relying on the soul is fully explored

So now we're exploring the, 'what if there is no soul', and somehow our living experience doesn't depend on that. Then what would personal identity consist in

Charlie

our memories, feelings, sensation

Hal

Got it

We can still distinguish between 'mental states' (the experience of those things, as we just discussed) and 'brain states' (the corresponding activity in the brain)

If our mental states could somehow happen on a positronic brain (again, just say it were possible)

Charlie

@Hal can a person have more than one identity?

Hal

we wouldn't care about our physical brain so much either

Mats Granvik

Is the power series for the Lambert W function known up to infinity

?

Hal

6:07 PM

Charlie, the anal answer is no.

What do you mean by identity?

Mats Granvik

Eulers identity?

Charlie

@Hal there are some psychiatric cases of multiple identities

Hal

Personal identity - we're chatting about an idea in philosophy to apply some math to it

Yep - good question

That's why thought experiments can be useful

Because before we knew about multiple identities

we were thought experimenting with the idea of two people being fused into one (as a counterpart of one person being fissioned into two)

Then in the 80s - multiple personalities became a big thing

and we had been discussing it before. So it wasn't like this tsunami that toppled all of the thinking on identity up to that point. I think that's the merit in these weird 'what if' cases

Okay, but to answer the question.

Chris's sis

@robjohn an interesting closed form (a lovely one)

Hal

Actually - come to think of it, it's more like one person being fissioned into multiple persons

Well, that's part of the problem really.

Charlie

6:12 PM

created identities

Hal

The person can have multiple 'selves'

robjohn

@Chris'ssis Okay. Just checking.

Charlie

are we creative enough to live as different people?@hal

Chris's sis

@robjohn aha, ok

Hal

Your 'self' is what we usually mean when we say 'who am I' and you say - I am a 99 year old man from kentucky who votes republican and plays the saxophone

So multiple personality is like 'multiple selves'

But the problem is that in multiple personality

each personality cannot access the memories of the others (or often cannot)

Charlie

6:14 PM

yes, it's curious

Hal

so you don't have that psychological continuousness we were talking about

Charlie

I see

Hal

I'd say that none of the new identities are 'one and the same' as the person who preceded them, as it were.

Only so long as they can't access each other's memories - because there's none of what we just said we care about - psychological continuousness

So thinking back to our thinking of the mental content being what matters

Chris's sis

hmmm, I need to write some proofs ... (I become lazy)

Hal

If I told you all your feelings, sensations, memories were going to be erased from your mind

Charlie

6:17 PM

@Chris'ssis this heat makes me sooo lazy

Hal

and a new personality, memory, etc

were going to be written into them

Charlie

got it

Hal

I think that's as good as dead.

Do you?

Chris's sis

@Charlie I believe you! :D

Charlie

@Hal yes, but, personally, i don't believe that our brain is capable of "forgetting"

Hal

6:18 PM

Yeah - neither do I

Charlie

@Chris'ssis I don't even feel like eating

Chris's sis

@Charlie I'm preparing to eat some honey with milk:D

Hal

So then Charlie - you could say this.

Charlie

@Chris'ssis is it good?

Hal

If the one of the personalities is continuous with the original person (but in a less explicit way) then he is still mentally continuous - so he is the same

Charlie

6:19 PM

?

Chris's sis

@Charlie They make me really clever. Sure, it's tasteful! :D

Hal

If he is not, then he is not mentally continuous - so he is entirely different.

Charlie

@Chris'ssis I don't like drinking milk much

Danny

can sumone help me with theorem 6.4 in rudin

if not asking to much

Chris's sis

@Danny I drink milk almost every day!

Danny

6:21 PM

:)

Charlie

@Danny post it here, the statement of the theorem

@Chris'ssis really, I do'nt like much, only with cereal

@Hal curious, curious....

@Hal i don't think i understood

Chris's sis

@Charlie toast+honey+milk=a great meal :D

Hal

Okay, I can probably fix that in three quick questions

Charlie

@Chris'ssis hehehe

Hal

You remember that we established that what we care about in identity is our mental content (thoughts, feelings, memories, etc)?

Charlie

6:23 PM

'yes

Danny

if $p*$ is a refinement of $p$ then $L(p,f,\alpha) \leq L(p*,f,\alpha)$

Hal

and our identity-as-persons is established by the relation our mental content has now with the mental content we had earlier.

(e.g. - you can remember you from some time ago, and that lets you concieve of yourself as being the person you were as a child)

Charlie

i remember

Hal

(sometimes you might not remember things from your life, but all of your thoughts and everything in your mind at each earlier point lead your mind to the state it is in at this moment. That chain is personal identity, and memory lets us know that there is such a chain and about our chain)

Danny

i would have to right down the hole proof ,but i takes time

maybe i could find some link on the net

Charlie

6:25 PM

@Danny I think if you post on main, you will get more help

Hal

Okay. So then. If you have multiple personalities

Charlie

@Hal I got it

if there is a linearity between your "content", then you are you

Hal

And one personality is entirely unaffected by the things before - then he is not continuous with that person from before

Bingo

Charlie

if you have gaps

Danny

yeah ok...

Charlie

6:26 PM

discontinuities, like functions

Hal

Gaps are okay.

Because the linearity is maintained causally.

If not by a direct memory

I.e. I am not experiencing hunger now, because I decided to eat something for breakfast, but I don't remember what it was

my decision caused my experience now - but I have no memory of the decision.

Charlie

but your body remembers

Hal

right.

Charlie

it's not conscious

Hal

I could also say that I am in a pissy mood because I decided to think about how much I dislike bats (I do) all day. and then got hit in the head and forgot I was thinking about bats

but my mood is still a little pissy.

Or that I create the intention to go shopping when I find I am out of gummy bears

Later that day, I go shopping - but I don't remember when I decided to go shopping

Maybe just 'why'

Charlie

6:30 PM

hmmm

i am understanding

Hal

But memory gives us important access to bits of the chain that we can piece together to see we are the same person overtime

It's like this

mental causality is what justifies calling one person the same over time

Memory is how that person knows about it.

I met someone once who had a brain injury - and a 3 minute memory

He didn't stop being concieved of, or concieving of himself as being, the same person

Charlie

ohh!

this is a really fascinating subject

Hal

But he'd have a heck of a hard time grasping the concept of identity if he were born with that condition

or if his brain injury erased all his past knowledge and understanding of things (like identity)

Danny

guys what countries are u from

Hal

and then started re-erasing every few minutes

Danny

6:33 PM

iam from sweden...

Canada

oh nice

Brazil

wow

Yeah - it's pretty cool, right.

So taking it back to the = sign

Danny

6:34 PM

so i guess mathematics is really a uniform language that works in all countries

Charlie

:DDD

Hal

You can probably see how silly it is to say A=B

As in person at time 1 = person at time 2

Especially if we're allowing for there to be 'different' people at time 2 who are both also = to person at time 1

So this is why I am saying that if you must maintain that identity is always a 1:1 relation overtime

Charlie

got it

Hal

then that relation definitely is not represented by =

Charlie

this is very mathematical for me

Hal

6:36 PM

It is mathematical

Charlie

but i see mathematics everywhere

Hal

I think it is.

Chris's sis

@Charlie Do you remember that interview I told you about some time ago? I failed there for a stupid reason.

Hal

IMO, all thinking is math. Math is thinking without descriptors

Charlie

@Chris'ssis Oh no!! what reason?

Hal

6:37 PM

like 'chair, duck, red, bald' etc.

What interview?

For work?

@Charlie, now that I've explained it all to you - I'm trying to solve this thing mathematically. Would you like to work on it with me over email?

Charlie

@Hal sure, sounds nice

Chris's sis

@Charlie I was told it should be preferable to tell them the truth about the knowledge I possess. They claimed I didn't want to tell them about all schools I graduated from.

Charlie

if you use my thoughts, i want my name on your paper

@hal

Hal

Yeah for sure

Charlie

@Chris'ssis ???

Hal

6:40 PM

That'd be cool. Two people from a chatroom who havent met credited on the same paper

Might be a first in the discipline

Chris's sis

@Charlie Indeed, it's strange (in a way).

Charlie

@Hal :DDD

@Chris'ssis do you have any problem in telling that information?

@Hal it happened a lot in math

Hal

I bet.

Charlie

people talked via letters

Hal

True.

Chris's sis

6:42 PM

@Charlie I told them the truth, but they thought there should be more than that. (to tell I mean)

Hal

But this has the coincidence element to it, which I think makes it novel.

Charlie

@Chris'ssis oh!

Hal

@Chris'ssis That's annoying. What about taking a test that might make your story more believable

(I'm presuming you knew more than they believed you could know given your education)

Maybe you could take some sort of mathematical aptitude test or something

Ian Mateus

@Chris'ssis there's something more, this reason doesn't make any sense.

Hal

Actually, yeah - I agree with Ian on that

(and interviews are part of my job)

Charlie

6:45 PM

@Hal really?

Hal

@Charlie About interviewing?

Charlie

yup

Chris's sis

@IanMateus yeah, it doesn't make sense.

Hal

Yeah. www.windowbutler.ca I started that in high-school. It took about 8 years, but it runs itself now.

So I'm taking philosophy with the time.

Ian Mateus

@Chris'ssis That's just like "you're too good to be here". There must be another reason they didn't want you there, given your mathematical knowledge.

Hal

6:48 PM

But, I interviewed a lot of people - we had to get really good at it, because qualifications arent exactly important to be a window cleaner, so we had to look at other things that I think are more subtle. That was the hardest part, by far.

Yeah, but that they said that - to me that says they were pissed off

Or annoyed

Because it's a bit of a kick in the nuts.

I mean, maybe it's just me, but of all the ways you could decline a candidate - that one's one of the bitchiest ways you could do it (for want of a better word)

Chris's sis

@IanMateus I perfectly answered all their questions. (it was a kind of test) Anyway, it never happened to me such a thing before.

Hal

It feels like they were a bit angry about something.

Chris, were you arrogant?

Remember, people have egos.

What if you showed-up one of the guys there who thought he was awesome.

Or if they thought you were lying about something else (even if you held back a bit)

That might have spilled over into everything.

Chris's sis

@Hal Yes, I was a bit arrogant, but I HAD A REASON ...

Hal

Doesn't matter

Ian Mateus

@Chris'ssis my father always told me stories like this, when someone didn't pass for some stupid/obscure/arbitrary reason

Hal

6:52 PM

That's why you didnt get it

I hate this, but the world doesn't give a rats about justifications.

even if they're excellent

Charlie

@Chris'ssis what.reason?

Hal

What matters is 'how do I feel right now'

and if the answer isn't 'positive' whenever you're around - you aren't getting their favour

I don't mean smile and tell jokes, necessarily

Positive feelings can come from seeing you be awesome and math and a promising productive employee

but they can also be pushed away by things that dont matter to the content of the work

(arrogance, whatever else)

If the amount of positive feelings you generate is less than your competition, your competition gets the persons favour.

IMO, that's what happened if you were at all arrogant.

But that's just my view, I don't have a lot to back that up on other than my experience

Chris's sis

@Hal it's my belief - they couldn't have someone better than me on that position.

Hal

Yeah, man - you're thinking rationally

Put it this way

Math is rational and logical

If you are the most mathematically talented guy

Ian Mateus

*girl

Hal

6:56 PM

then it follows you are probably the most rational and logical girl*

so don't expect others to think as rationally or logically as you do

Charlie

Chris never said if was girl or boy....hm..

Chris's sis

@Hal You're right.

Hal

Well you just made me feel good

:p

Love hearing that more than I should.

Don't judge me.

Charlie

hahaha

WE all do

Hal

Haha. Okay, so Chris' Sis - what now?

Chris's sis

6:58 PM

:-)

Ian Mateus

I am beginning to like a little bit to be wrong, at least I'm learning something

Hal

Yeah I agree

I had a chess coach - his theory was that you were learning the most when you were losing 25% of the games you played, and playing your best each time.

Chris's sis

I love to learn ... (from others).

Mats Granvik

LambertW(50) as power series in Mathematica:

Clear[x, a, nn, b, z]
nn = 120;
z = 50
a = Series[Exp[-x], {x, N[Log[z], 500], nn}];
b = Normal[InverseSeries[Series[x/a, {x, 0, nn}]]];
x = z;
N[b, 20]
N[LambertW[x], 30]

Hal

@Chris'ssis have you read 'how to win friends and influence people'? It's not as flashy a book as it sounds. It's short, simple, and gives examples of what makes a person likeable.

You probably are likeable - but even more so. I read it, and it changed how I approach people

Charlie

7:01 PM

oh

Chris's sis

@Hal I didn't read it, but I heard of it.

Charlie

it doesn't work with mathematicians

Mats Granvik

Dale Carnegie wrote the book.

Hal

Yeah, I remember reading about some autistic or high-asbergers kid with no social intuition (not that that's anyone here) who read it. And he just followed its rules like they were rules in a program

and seemed to have a low-average quality social life after that

Chris's sis

@Hal They were also upset I didn't give details about my life. This was very annoying.

Hal

7:02 PM

Going from absolutely none or negatives.

(repelling people)

@Chris'ssis read the book.

For one afternoon

It's worth it.

Mats Granvik

What is all this code? Could you translate this into usual mathematical notation? — dfeuer 28 mins ago

Chris's sis

@Hal OK, I'll try to do it. Thanks.

Mats Granvik

Is this a known result?

^^

I got this link pasting wrong.

Hal

K here. Chris

bookfi.org/dl/1482465/db058a

There's the link

Mats Granvik

0

Q: Power series to calculate LambertW up to infinity?

Is this an allowed operation to calculate the Lambert W function as a power series up to infinity, or is there some trouble in defining it this way? Mathematica programs: Clear[x, a, nn, b, z] nn = 40; z = 2; a = Series[Exp[-x], {x, N[Log[z], 50], nn}]; b = Normal[InverseSeries[Series[x/a, {x, ...

Chris's sis

7:05 PM

@Hal Great. Thanks!

Hal

Welcome.

And one more thing specific to job interviews

- Do what they want

Charlie

what you mean?

Hal

- Show you're obedient (because they are going to assume the 'hired' version of you is more independent and less easy to manage)

Mats Granvik

Programming and mathematics is really one and the same thing, except that mathematicians don't understand programming and programmers don't understand mathematics.

2

Hal

- Also, when they ask about things that connect to negative parts of your life

Chris's sis

7:06 PM

@Hal I want only one thing, only one thing - a clever boss, and I do anything!

Hal

Talk about the shit that happened to you

Mistakes that make

@Chris yeah but you don't get to interview the boss in the interview

Charlie

@MatsGranvik hahaha great

Hal

And when you do - it's a joke

I mean, you don't really get to interview the boss. You're always the 'applicant'

Chris's sis

@Hal Yeah, right.

Hal

They will often ask you 'do you have any questions'

Maybe then - you have a question that is a very rough gauge of how clever he is.

Chris's sis

7:08 PM

@Hal Indeed. I always ask them a lot of questions.

Hal

"Like, what's you're favourite part of math."
He answers.

"Oh, yeah X subject. What do you like about it?"

Then just let him talk.

Chris's sis

@Hal Oh, it's not for me this kind of dialogue. I'm very direct.

Hal

Well

That can offend people

"How clever are you? - Prove it"

That is the most direct version of what you want

Charlie

@Chris'ssis you gotta be a bit more flexible

Hal

Inflexibility will kill you in an interview

Chris's sis

7:10 PM

@Hal I'm always very flexible.

Ian Mateus

@Chris'ssis was this a job interview? Which job? It seems a little distant from me by now, like cars and houses :s

Hal

Anyone who shows that they're willing to be stubborn in an interview - probably values being stubborn over a job - and I don't want to have to manage that person(if you even can manage that person)

"By cars and houses" haha

Charlie

hi @anon

Hal

You meant that the memory is decades old? I like that

anon

@Charlie hello

Charlie

7:12 PM

@anon how are you?

anon

alright

Ian Mateus

@Hal no, that I'm still young (not so) for it. Not so in some countries

Hal

Ahh

Chris's sis

@IanMateus Yeah, it was a job interview.

Hal

@Charlie, I gotta run - do you have email?

Charlie

7:14 PM

@Hal yes

@Hal I'll put here you copy

Hal

Thanks

Okay

Once more

Charlie

got it?

@Hal you didn' t get?

Hal

Nope

Got it

Charlie

:)

Hal

Thanks

I'll write you

Charlie

7:16 PM

you're welcome

ok

Hal

By the way - do you know how one could write a proof that a 1-to-1 relation can't be a 1-to-2 relation

Charlie

i think so...

Hal

I think it's trivial, but some way of formally expressing that might help with the proposal.

Charlie

yes, fine

anon

Chat guidelines | $\LaTeX$ in chat

9

Ian Mateus

7:18 PM

@Chris'ssis you are a very intelligent person, you'll get way better opportunities soon! Such people are rare in whatever field you think of.

Chris's sis

@IanMateus Thank you very much! I hope to have some more luck next time.

Hal

Chris, I don't doubt Ian's right. But only because I actually want you to get this. May I say my experience has taught me never to underestimate how little what ought to matter matters.

Ian Mateus

Gauss would hurt some feelings in a job interview.

Hal

I think it's frustrating, because it's unjust, in my opinion. But - it's not something we can change. So in such cases we have to adapt so that our talents can be made useful.

Yeah - and that was Gauss!

I don't know if you're a Gauss or not

Vrouvrou

pleaaaaaaaaaaaase help me

0

Q: Question about saddle point

i have this paper http://www.sysmath.com/jweb_xtkxyfzx/CN/article/downloadArticleFile.do?attachType=PDF&id=10691 and i dont understand how to prove in page 3 that $\overline{c}$ is a critical value please help me Thank you.

homework analysis morse-theory

Hal

7:21 PM

But, that guy had piles of what was supposed to matter in his field

What about the very best of us mortals?

Danny

@Vrouvrou nice approach

Hal

Who aren't renowned for our proofs

and don't have an illustrious reputation coming in the door before we do

If you do, great. If not, maybe you will one day and you can play on that. But until then -

All that said, the boss' failure to put what matters ahead of what doesnt is a mutual loss.

Some employer will be lucky to have you. (It just might happen sooner than later if you grease the process a bit)

I need a vice grip to keep my mouth shut sometimes, gawd.

Charlie

@Hal your advices were very helpful! you should come more often and give us some tips!

Chris's sis

@Charlie Did you manage to ponder a bit over this very lovely question? :-) $$\sum_{n=1}^{\infty} \arctan\left(\frac{1}{F_{2n-1}}\right)$$

@Hal Indeed, you show a lot of experience. Glad to have you around. :-)

Hal

@Charlie & Chris, thanks for saying so.

Charlie

7:30 PM

@Hal :)

@Chris'ssis not exactly

:P

Chris's sis

@Charlie :D

(brb - I'm writing up some proofs)

Charlie

@Chris'ssis have fun!

Chris's sis

@Charlie :D

Charlie

@Chris'ssis :D

Hal

Alright, I'm out for now. I have to be productive. - Tragic.

Thanks for the chat. It was nice meeting you Charlie, and you too Chris, and Ian.

Charlie

7:33 PM

@Hal nice to meet you too :)

vzn

wow quite a party in here

Charlie

yeah!

oow freak out, le freak c'est chic

vzn

@MatsGranvik interesting, a thought just occurred to me recently of some ideas floating around quite awhile.... "mathematical proofs are like computer programs that run in a human's head".... =D

Charlie

@vzn runs in a hardware named brain

vzn

yep.

Vrouvrou

7:46 PM

@Danny i don't understand

vzn

is there a history of math.se somewhere? am amazed its up to 206.6K questions, wow. seems like its not that old...

anon

go to meta
search "history of"
????
profit

Vrouvrou

@Danny are you there ?

please i need help can someone help me ?

Charlie

@anon what??

anon

I am telling vzn how s/he can answer their own question

using a standard internet instruction format

Charlie

7:51 PM

@anon I'm so sorry, my brain had a bug

vzn

ok thx

64

Q: History of Math.StackExchange

This thread is used to record significant events in the life of Math.StackExchange. (There are also anniversary posts written from personal perspectives of contributing users.) Where this idea comes from. Long ago, on a distant website, a user asked "What's the story behind MathOverflow?". Mari...

discussion statistics

interested in collatz. anyone else who likes hard unsolved problems, empirical attacks, datamining-like approaches, TCS-angles etc... plz drop by my blog!

15

Q: Collatz Conjecture & Grammars / Automata

I was wondering if there is a good bibliography of attempts to investigate the Collatz conjecture as a formal grammar? (or any other attempts in the CS community to deal with this class of generative phenomena & their "halting" properties).