The h Bar

2:48 AM

@Slereah Let $V$ be an $n$-dimensional vector space which is also a $C^\infty$ manifold. For any $v\in V$, we can find a unique natural isomorphism $\phi_v:T_vV\to V$.

Proof. Let $\omega\in V^*$. We can view this as a function $\bar\omega:V\to\Bbb R$ in the sense of manifolds. We seek an isomorphism $\phi_v:T_vV\to V$ such that $\omega(\phi_vw)=\mathrm d\bar\omega(w)$ for each $w\in T_vV$ and $\omega\in V^*$.

For existence, pick a basis $\{\theta^i\}$ of $V^*$ and a basis $\{e_j\}$ of $T_vV$. Then if we define $(\phi_v)_i^j=\mathrm d\bar{\theta^i}(e_j)$ we obtain the desired isomorphism.

For uniqueness, suppose $\psi_v$ has the same properties. Then $\omega((\phi_v-\psi_v)w)=0$ for all $\omega\in V^*,w\in T_vV$. It's obvious that this implies $\phi_v-\psi_v=0$. $\Box$

Now this can be used to turn a Lorentzian vector space $(V,\langle \cdot,\cdot\rangle)$ into a Lorentzian manifold $(V,g)$ if we define $g_v(w,z)=\langle \phi_v w,\phi_v z\rangle$.

This is now one should "properly" define Minkowski space.

ZeroTheHero

@dmckee Thanks for you recent prompt action.

0celo7

3:35 AM

@yuggib What is Yosida trying to say in the Theorem on page 80? The statement is not what is proved, unless I am misunderstanding what "for any large positive constant $C_1$" is supposed to mean.

Is he trying to say this only works for $C_1$ above some critical value?

Because he seems to be proving that if $|\eta|$ is bounded, so is $|\zeta|$. I checked LH's original paper, his statement is completely different.

Prashant Gokhale

4:39 AM

@JohnRennie Could you solve my question here

0

Q: What will be pressure of gas measured by manometer if mercury starts to rise on the other side?

What will be pressure of gas measured by manometer if mercury starts to rise on the other side? The $P_a$ side is open to the gas container and the $P_0$ side is open to the atmosphere with atmospheric pressure $P_0$. The pressure of gas $P$ here is $P_0 + \rho g H$ where $H$ is as given in i...

2017

@PrashantGokhale Just draw a free body diagram of the mercury column and balance forces.

The total length of mercury in the u-tube will remain constant.

It should'nt be a tough job to write the equations.

user228700

5:30 AM

@Sir: Have u received the book yet?

Secret

Quantum mathematical framework inspired psychology and cognitive models applied to analysing humor

user228700

@Secret Hi :-) How dyou post a link and write over it?

Secret

[description](url)

user228700

Thanks!

Secret

The same format you use in the main site when writing link embedded comments

Please note that linebreaks cause the formatting to fail

user228700

5:38 AM

When you add a "---" after you've said something, it's an indication that a brief account of "last night's dream" is going to follow :-P

Secret

no, I add --- to indicate whatever I said next has nothing to do with the previous message. It forces the chat to break up that chat bubble into 2 so for each bubble I am only focusing one topic at a time

user228700

I know. Usually, what u say next is about your dreams is all :-)

Secret

I see

Secret

Yes, I know this is a Frontier article (and how it is surrounded with controversy including its possible predatory status). But I actually took the time to read this article and the sources in detail, including some breif checks on the background of the authors. So far, everything mentioned there seemed legit, and there are reputable past models of psychology that employed the mathematics of quantum mechanics in the context of psychology

One thing to note that despite they both shared similar mathematical frameworks, there are actually many differences between the phase space of physical systems and psychological, sematic systems:

1. Most sematic, psychological and cognitive systems are highly sensitive to contextual elements. For example, a joke's interpretation is sensitive to the phrasing of the joke and the prior information available to the audience, whereas physical systems, usually their dynamics are controlled by the hamitonian and the hamiltonian contains all information about the evolution of the system

This is why in that article, they mentioned that it is still a work in progress in figuring out how the funniness of jokes interacts with the sematics and phrasing of the joke, (which is why readers will have trouble finding anything that suggests an analogue of schrodinger equation in that article)

vzn

@Secret a remarkable find, wild mix of soft/ hard science, thx for sharing. esp intrigued by all the "QM outside of physics" refs 2-28, quite a collection worthy of further perusal.

MartianCactus

5:53 AM

LMAO NARUTO'S SEXY JUTSU ON KAGUYA

actually idk if you guys know about it i just HAD to write about it as it was such a plot twist

write it somewhere that is and this tab was close to me :P

Secret

Quantum cognition

Quantum cognition is an emerging field which applies the mathematical formalism of quantum theory to model cognitive phenomena such as information processing by the human brain, language, decision making, human memory, concepts and conceptual reasoning, human judgment, and perception. The field clearly distinguishes itself from the quantum mind as it is not reliant on the hypothesis that there is something micro-physical quantum mechanical about the brain. Quantum cognition is based on the quantum-like paradigm or generalized quantum paradigm or quantum structure paradigm that informatio...

Information in general for this field of study

user228700

Oh, @JohnR: Morning! :-)

John Rennie

Morning :-)

Secret

> there are actually many differences between the phase space of physical systems and psychological, sematic systems

Sorry typo, actually there isn't much differences other than the dynamical law cannot be precisely known (yet)

Secret

Hmm, I guess we can call a model quantum whenever its mathematical framework contains vector spaces (superposition), noncommutativity (uncertainty principle) and measurement

O btw at the introduction they also mentioned a future plan to develop a QFT inspired model for cognition. However reading this, the first thing that came to my mind is: Well, what will be the analogue of number of particles in a sematic processing of information...?

The dying moments of a red giant

The cool thing about astronomy is it is pretty

John Rennie

6:39 AM

@PrashantGokhale it isn't clear to me what you are asking. The pressure difference is $\Delta P = \rho g h$ as you say in the question, so $P_a = P_0 + \rho g h$. The level of the mercury will start to rise if $P_a$ increases above this value.

Secret

6:58 AM

Why water splashes, because the layer of air the liquid film trapped prevent it from flowing smoothly, and some droplets fly off

The nature of fluids, even in these seemly mundane scenarios, are extremely important in the context of manufacturing

2017

7:39 AM

Does my edit seem okay? physics.stackexchange.com/questions/319650/…

0

Q: How I can see electron

Anybody can explain me that one can see electron or any other particle by our nicked eyes using any apparatus? Regards

particle-physics

I suppose the OP wants to know why electrons can't be seen with naked eyes.

The initial framing of the question was horrible :-P

physics.stackexchange.com/review/suggested-edits/166970

It's going to be a part of the HNQ list pretty soon :'D

user228700

7:57 AM

@JohnR: Did u take to activities such as these back in Wookey Hole to ease the pain of acute boredom:

user228700

(^ Sitting by the railway tracks, waiting for trains to show up to wave to them) Or this perhaps:

user228700

2017

@Kaumudi.H wtf is that?

Secret

@2017 Seems fine. since from a layman perspective, this is how questions of this type usually implies

user228700

7:59 AM

@2017 I've edited my message.

2017

who does that :-P

@Kaumudi.H Ah, I've done that with tyres in my childhood at our ancestral home.

user228700

@2017 Bored people of the 50s and 60s :-P

John Rennie

@Kaumudi.H for little children (sub puberty) the countryside around Wookey Hole is a fantastic place to grow up.

Secret

3

Q: Physical explanation of seeing sparkles?

I know this might look more appropriate to ask this kind of question on the biology or medical stackexchange but since this kind of cross-science question I'll ask it here. Sometimes when sitting and working on my computer I get to see sparkles which look like particle trajectories. Sometimes th...

electromagnetism biology

user228700

@2017 I've tried but I never got the hang of it :-(

user228700

8:00 AM

@JohnRennie :-) I can only imagine.

Secret

Well, it is kinda cool to have a cloud chamber in your eyes if that claim really holds

John Rennie

It's hilly and heavily wooded so there are dozens of little (secret!) valleys to play in.

And because it's on the edge of limestone hills there are lots of small caves - big enough to be fun exploring while too small to get lost in.

It's only when I started comparing childhoods with friends who had grown up in cities that I realised just how fantastic a place it is.

user228700

It sounds so lovely :-) In my village, the only options are tree-climbing and swimming in the pond.

John Rennie

The problem comes when you get to your mid-teens and want more from life ...

Secret

Most of my desires are nonmaterialistic, which is why I tend to be quite content with my life

John Rennie

8:03 AM

Your village? Chennai? :-)

user228700

@JohnRennie I understand this; until my teenage years, I used to yearn to go to my village every summer. And then around 14 or 15, I sort of started getting depressed around there.

user228700

Chelakkara

Chelakkara is a small town in Thrissur district of Kerala. One of the famous pooram ( Vela ) in Trissur dist - in fact in Kerala. Anthimhakalan kavu located in Chelakkara, Which is famous for fire works and traditional celebrations called Kala kali. == Geography == Chelakara is located at 10.70°N 76.35°E / 10.70; 76.35. It has an average elevation of 6 m (20 ft). == Festivals == One of the famous pooram (Vela) in Trissur dist Anthimhakalan kavu located in Chelakkara, which is famous for fire works and traditional celebrations called kala kali. The town has many temples including Narasimhamurthy...

John Rennie

> It has an average elevation of 6 m

Fairly flat (and boring?) landscape then?

user228700

Precisely.

user228700

There was nothing to do other than tree-climbing and swimming.

user228700

8:06 AM

They've literally cut off all the trees now and the pond is beginning to dry up.

John Rennie

I have a sneaking suspicion that 14-18 years olds are always dissatisified. You could put them in a paradise and they'd still be complaining :-) I include the 14-18 year old version of me in this category!

user228700

@JohnRennie -__- You oldies, always mocking us teenagers.

John Rennie

That wasn't intended to be mocking. It's just an observation.

user228700

Besides, that's not even true.

user228700

Not all of us are dissatisfied.

John Rennie

8:09 AM

I'm not even sure it's a bad thing. I think it takes dissatisfied people to change the world. It's probably down to the chronically dissatisfied that we aren't still leaving in caves and hiding from sabre tooth tigers.

user228700

Sure sure. I'm merely noting that there is a subtle difference between despairing dissatisfaction and hopeful dissatisfaction.

Secret

user228700

@JohnR: This is what it looks like:

Secret

How to beat a frustrator: Easy, make your choice, but flip the opposite switch, so the frustrator get slapped onto its face by its own rules

Then you win the prediction game, always

user228700

John Rennie

8:12 AM

Palm trees :-) I remember trying to climb date palms in Khartoum but the bark is so rough it tears your skin.

user228700

Dyou see the yellow building at the back of that picture?

John Rennie

How far away are the hills in the background. Five miles?

@Kaumudi.H Yes?

user228700

@JohnRennie That's the hospital in which I was born :-)

John Rennie

Aha - a future famous landmark :-)

user228700

@JohnRennie I really dunno. Although they seem close, I doubt if it's only 5 miles...

John Rennie

8:14 AM

I don't know where I was born.

A hospital somewhere in Khartoum I suppose ...

user228700

@JohnRennie My mom was born in my house (back in Kerala)

John Rennie

@Kaumudi.H too far to walk then, but within cycling distance?

user228700

@JohnRennie I doubt whether it's within cycling distance.

user228700

I went cycling one time and never came close.

John Rennie

So you were stuck in the middle of an alluvial plain with no escape possible? :-)

user228700

8:18 AM

I usually do enjoy my time over there but three years ago, I had to spend close to 1.5 months over there and that sort of messed me up.

user228700

At least one good thing came of it tho--I ended up taking really great pictures before most of the trees were cut down.

user228700

Dyou wanna see the pond?

John Rennie

Pond?

Secret

They are now thinking about moving to the infrared bandwidth to get around the wifi congestion problem. Well let's see how it goes...

user228700

Yes. My house is beside those fields you see. It used to be situated in the midst of a dense forest of rubber trees but they've been cut down now. The pond remains.

user228700

8:23 AM

Dyou want to see?

John Rennie

Yes, please post a picture.

user228700

It's not so wonderful, I dunno why I built it up but here :-P :

user228700

I dunno what these are called but we have these and they're so beautiful:

user228700

8:28 AM

(All these pictures I took on a lazy afternoon whilst in the depths of boredom :-P)

John Rennie

I suspect Chennai is less pretty but more fun for someone in their mid to late teens :-)

user228700

No, not really; without friends, it gets boring anywhere :-)-:

John Rennie

Yes, I found that as a teen in Wookey Hole. Going to university was my escape route! :-)

user228700

:-)

John Rennie

Look on the bright side. Life gets better as you get older ... then you die! :-)

Secret

8:36 AM

If these phenomenon are gone, then we all die

Sometimes, war leftovers are good. That does not mean we encourage them

It appears that the most irreversibly destructive process to an ecosystems are often the long term, slow ones, such as human development and land exploitation

Why try so hard to bring back the past that no longer was. Are you even sure that literally transferring a fragment of the past to the present it will survive and not cause trouble. O, and let's not get into the issue that they are a flawed copy of the original, technically speaking

Secret

10:11 AM

[Memory correlations] they are a flawed copy of the original ->http://submachine.wikia.com/wiki/Secret

That's a very fun flash game I played in the past

The memory correlations lead to revisiting this game's wiki, and via reading a bunch of articles from layers->karma->karma portal->outer rim -> ... -> eventually result in a new question:

in Mathematics, 21 mins ago, by Secret

What is an example of a space where it is impossible to place any charts and coordinate systems on it?

MartianCactus

10:23 AM

anyone here?

what does e + 22 mean?

prntscr.com/elfhpx

2017

@MartianCactus wolframalpha.com/input/?i=1+megaparsec

Figure it out yourself now!

John Rennie

3.086e+22 is a way of writing 3.086 times 10 to the power 22.

MartianCactus

or 3.086 + 10 to the power 22 ?

John Rennie

@MartianCactus No, times 10^22

2017

$3.086*10^{22}$

MartianCactus

10:29 AM

oh, alright!

John Rennie

The plus is there because it's $3.086 \times 10^{+22}$. If you wrote 3.086E-22 it would mean $3.086 \times 10^{-22}$.

MartianCactus

oh!!

John Rennie

It's a notation that arose in the early days of computers because early displays didn't have a way of writing exponents.

Secret

and it is still used in excel

MartianCactus

lol

so its just a approximation, right?

John Rennie

10:42 AM

@MartianCactus an approximation? No, it's a way of writing $3.086 \times 10^{+22}$ using ordinary characters that is simple and easy to read.

Secret

I have been seeing this convergence phenomenon everywhere, what does that even mean...?

John Doe

Hi all

2017

@MartianCactus $3.086 \times 10^{+22}$ has 4 significant digits. So it is indeed an approximate value. You can find a more precise value of megaparsecs (having more significant digits) if you do a bit of googling!

MartianCactus

@JohnRennie but a megaparsec isn;t exactly 3.086×10+223.086×10+22, is it?

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