Mathematics - 2016-09-04 (page 1 of 2)

Unknown123

01:08

Please help, i don't understand with my homework

I don't understand how to simplify product of sum function and i can only find in google how to simplify sum of product function

I understand how to simplify this function by watching a youtube video
https://www.youtube.com/watch?v=8jUN-w0yQSI
F = ABC + A' . B . (A' . D')'

but how do I simplify the product of sum function?
I can't find an example of question like this
F = (A' + B) . ( A + B + D) . D'

How should I do it? Please help me

um, I must do it with K map and not allowed using boolean algebra

Unknown123

01:40

It's even more confusing because it is not written in standared POS

Unknown123

02:08

Okay thank you I have solve it

The Pointer

05:17

Can anyone help me with a linear algebra problem please? I've spent literally tens of hours on it and am desperate.

It is a simple problem but I have issues understanding the trigonometry aspect.

Martin Sleziak

@ThePointer As the room description says: "Just ask; don't ask to ask."

The Pointer

Ok

Using the standard basis of ℝ2 to determine the matrix of the following linear transformation

Martin Sleziak

Simply state your problem and maybe somebody will help maybe not. (And certainly link to the question if you posted it on main, too.)

The Pointer

1

Q: Using the standard basis of R2, determine the matrix of each of the following linear transformations

I've asked questions about these problems before but thus far, no one has been able to help me understand. I've been attempting these problems for tens of hours over a couple of weeks now. I'm desperate for some help. The problem are as follows: The issue is not the linear transformation aspe...

Martin Sleziak

The reason for this suggestion that without seeing the problem it is difficult to say whether I will be able to help you.

The Pointer

05:25

This is the problem. I am having issues with solving (2)

I have solved (1).

Martin Sleziak

So to find a matrix of the reflection w.r.t. the line which has the angle $\theta/2$ to the x-axis.

How did you want to deal with the problem?

The Pointer

I was using trig ratios to try and calculate the values for (x,y)

Based on the image that was provided

Martin Sleziak

I am not sure what you mean by values for (x,y).

The Pointer

sorry, (x,y) values for f(e_1) and f(e_2)

Martin Sleziak

Ok, so you have $e_1=(1,0)$.

The Pointer

05:28

I calculated f(e_1) to be (cos(theta), sin(theta))

Martin Sleziak

The you immediately see that $f(e_1)$ will have unit length and angle $\theta$.

Exactly as you wrote.

The Pointer

However, I am not getting the correct answer for f(e_2)

Martin Sleziak

Now you need to find $f(e_2)$.

$e_2$ is at angle $\pi/2$. The line is at angle $\theta$. So the angle between them is $\pi/2-\theta$.

So to me it looks like we need the new angle $\frac\pi2-2\left(\frac\pi2-\theta\right)=2\theta-\frac\pi2$.

Is $2\theta-\frac\pi2$ the correct result @ThePointer?

The Pointer

I see a lot of $ symbols in your text, making it hard to understand. Am i doing something wrong?

$\frac\

Martin Sleziak

To get math rendered, you can use bookmarklet from here: math.ucla.edu/~robjohn/math/mathjax.html (The link is both in the room description and in the rules of this chatroom.)

Anyway my results was 2*theta-pi/2. Is that what you are supposed to get?

Sorry, I used $\theta$ instead of $\theta/2$ as the angle of the given line.

So the result changes to $\theta-\pi/2$ if we use $\theta/2$.

The Pointer

05:38

Ok i see it now

working

The solution is

imgur.com/a/VN0Sr

Not that :(

Martin Sleziak

Well, that's exactly what we got, just written differently.

The Pointer

Ahh, I see.

Martin Sleziak

We got $f(e_2)=(\cos\left(\theta-\frac\pi2\right),\sin\theta-\frac\pi2)$, right?

Le't have a look whether we can simplify it.

$\cos\left(\theta-\frac\pi2\right)=\cos\left(\frac\pi2-\theta\right)=\sin\theta$

$\sin\left(\theta-\frac\pi2\right)=-\sin\left(\frac\pi2-\theta\right)= -\cos\theta$

The Pointer

Ahh, I see.

So since we are reflecting both points on either side of the line

it creates an angle of pi/2?

between f(e_1) and f(e_2)?

Martin Sleziak

No, that's not true. Why should it be $\pi/2$?

Just draw a few pictures and you will see that the angle between the two images can be various, depending on $\theta$.

The Pointer

05:45

You said e_2 is at angle pi/2

Martin Sleziak

Yes, that's true.

And angle between $e_1$ and $e_2$ is $\pi/2$.

The Pointer

Oh, I see.

Martin Sleziak

But the angle between $f(e_1)$ and $f(e_2)$ can be different.

The Pointer

I thought you were referring to f(e_1) and f(e_2) my apologies

Hmm

Is there any way to calculate these using trig ratios?

Martin Sleziak

I don't know what are trig ratios.

The Pointer

05:51

That is how I calculated the previous ones but for some reason am not getting the correct answer for f(e_2)

sin(theta) = opposite/hypotenuse, ect

Martin Sleziak

Isn't that what we just did? We found angle for $f(e_2)$ and then expressed it using cos and sin.

The Pointer

Unfortunately, I do not understand :(

Martin Sleziak

BTW in this answer you have a different solution, which uses projection matrix.

@ThePointer So let us try once again.

The Pointer

Yes. However, I am not supposed to solve using the projection matrix.

Martin Sleziak

If it does no help, maybe you can spend some time looking at other similar problems on the main, I listed a few here:

The Pointer

05:55

Ok will do

Martin Sleziak

So we have $e_2=(0,1)$ and want to calculate $f(e_2)$, right?

The Pointer

Yes. It is in the 4th quadrant

Martin Sleziak

First, the angle between x-axis and $e_2$ is $\pi/2$, do you agree with this?

The Pointer

Yes

Martin Sleziak

And we have the axis of reflection, which is the line with the angle $\theta/2$.

The Pointer

05:57

Yes

Martin Sleziak

So the angle between $e_2$ and the axis of reflection is $\pi/2-\theta/2$.

So far, ok?

The Pointer

Yes

Martin Sleziak

In fact, let us denote $\alpha=\pi/2-\theta/2$ for simplicity.

The Pointer

Ok

Martin Sleziak

So $\alpha$ is the angle between the vector we want to transform and the reflection axis.

Now we should ask how the angle changes if we look at $f(e_2)$ instead of $e_2$.

We have to subtract the angle $2\alpha$.

The Pointer

05:59

well f(e_2) is in quadrant 4

Yes

Martin Sleziak

Notice that if we rotate $e_2$ by the angle $-\alpha$, we get a vector which is in the direction of the reflection axis.

If we do it once again, it is the result of reflectoin.

So we need to calculate $\pi/2-2\alpha$.

Is this ok?

The Pointer

Yes

Martin Sleziak

Now it is some simple algebraic manipulation $$\frac\pi2-2\alpha = \frac\pi2-2\left(\frac\pi2-\frac\theta2\right) = \theta-\frac\pi2.$$

We know that the angle is $\theta-\pi/2$ and the vector has unit length, which means
$$f(e_2)=\left(\cos\left(\theta-\frac\pi2\right),\sin\left(\theta-\frac\pi2\right)\right).$$

Now it only remains to simplify $\cos\left(\theta-\frac\pi2\right)$ and $\sin\left(\theta-\frac\pi2\right)$.

The Pointer

I got most of it

The part where you say rotate e_2 by angle -a

and then we do it once again, won't that be along the x-axis?

Martin Sleziak

Not necessarily.

You probably drew the picture where the $\theta=\pi/4$.

Try to draw several picture, with various reflecion axes.

What you wrote is true only if the reflection axis is exactly in the middle between $e_1$ and $e_2$.

The Pointer

06:15

Yes

That is true

so pi/2 - 2a gets us to f(e_2)?

Martin Sleziak

Yes.

The Pointer

Hmm. This method is difficult for me to understand conceptually and generalise.

How would one do this using purely the sin, cos ratios?

And drawing the image?

Martin Sleziak

I think that we did exactly what you said.

The Pointer

Hmm this must be the only way

Yes I think so

Martin Sleziak

If you draw the image you could see that the the reflection works like this.

@ThePointer That is certainly not the only way.

I don't think you can say about any mathematical problem that there is only one way to solve it.

BTW I have posted an answer summarizing what we discussed here in chat.

The Pointer

06:23

Yes it is very elaborate thank you

I am reading it now

Martin Sleziak

And I have also tried to retype your question. (It is better not to use images if possible.)

The Pointer

I was going well all semester

until I got to these two questions

I've spent literally tens of hours trying to understand these. There must be a deficiency in my previous knowledge

Feels very bad :(

Martin Sleziak

Do you mind if I point out some things which I think the question you posted is lacking @ThePointer?

The Pointer

Yes please do

Martin Sleziak

1) You knew what the solution is supposed to be. (You mention this in chat.) But you did not say so in the post. (That's why I have edited your question.)

2) You did not mention where the problem comes from.

It is always good to give all the available details which might be useful for answerers.

The Pointer

06:26

My apologies. I will do this in the future.

Martin Sleziak

It might be useful to read How to ask a good question?. The things I mentioned are in the part about context

@ThePointer Why in the future. You can still improve this post by adding at least the source of the problem.

You can also remove the image if you are satisfied with the transcription.

The Pointer

Ok.

Martin Sleziak

@ThePointer I know looked at the list of your questions and I see that you have asked the same question as part 2 of this one here.

You should not post the same question twice.

The Pointer

Yes. I became desperate :(

I will not do it again

Martin Sleziak

The only difference seems to be that the other question does not require calculation of the determinant.

Probably the best thing to do is if I delete my answer and post it to the other question - it is more suitable there.

The Pointer

06:33

Ok that is fine

Yes I am reading your answer and it is making complete sense now

:)

Martin Sleziak

Ok, I'll have to go - I have other things to do.

Good luck with your studying!

The Pointer

Thank you very much!

You helped a poor student this day!

I will never forget :)

r9m

09:10

@Idomathart pls check mail :-)

I do math art

@r9m wait a second.

@r9m Ah, just read once again what was the point with the problem (otherwise I wouldn't have cared). I send you the email now.

r9m

@Idomathart I can take it down no problem .. just say the word!

I do math art

@r9m No, it's OK. Anyway, such problems I can create in the future again.

@r9m I didn't want to have possible problems with publishing, that's all.

r9m

@Idomathart nah .. now that you mention it .. I should take it down. Btw you can check Tauraso's solution too .. the generalization ain't far from his approach either :-)

I do math art

@r9m Anyway, let it there. Just in case anything happens, hope you can mention to the publisher one, two words.

Hope all will be fine.

r9m

09:19

@Idomathart I am taking it down with a note .. no worries. It's better to take it down now than to have publication problems later

them publishers are so annoyingly nitpicky about these things .. it's better

I do math art

@r9m Only if you want. I would appreciate that a lot!

@r9m Yeah, that's the exact point.

r9m

@Idomathart I agree to the proposition wholeheartedly. The thought should have crossed my mind b4 .. sorry for causing annoying trouble late at night! :(

I do math art

@r9m Please check your email and see that I told you in the past about that article I want to publish. Maybe you simply forgot.

@r9m Thanks a huge lot!

r9m

@Idomathart I edited my blog with a note .. see if it's agreeable now :-)

I do math art

@r9m :D No need for that long comment. ;)

r9m

09:29

@Idomathart that's the least I should mention .. :)

I do math art

@r9m I see ... :-)

I do math art

09:51

@r9m almost forgot to ask you about the integral I posted here

Just to find it

Can you calculate without pen and paper $$\int_0^1 \left(\frac{\log(1+x)}{1+x}-\frac{\log(1-x)}{1+x}\right) \arctan(x) \textrm{d}x=\frac{\pi^3}{192}+\frac{\log(2)}{2}G$$ ?

It's not a joke or anything like that, it is simply possible.

Then there are other nice two versions you might like to try

$$\int_0^1 \left(\frac{\log(1+x)}{1+x}-\frac{\log(1-x)}{1+x}\right)^2 \arctan(x) \textrm{d}x$$

and

$$\int_0^1 \left(\frac{\log(1+x)}{1+x}-\frac{\log(1-x)}{1+x}\right) \arctan^2(x) \textrm{d}x$$

@r9m I'm sure you might like to try them all. And finishing them all in the spirit of the art. :-)

Just to say it is for Sunday a full of fun! :-)

Ah, I meant a Sunday full of fun.

The connections of these integrals with some class of series are simply amazing.

And as far as I know not-known to the present date.

Balarka Sen

10:35

@Alyosha 'Sup.

Alyosha

I've just woken.

What are you up to?

Balarka Sen

Learning some topology.

Good morning, by the way.

Alyosha

And the same to you, modulo time shifts.

whereabouts

11:38

Hi everyone :) "modulo time shifts" hah, hey I was thinking about this solution here math.stackexchange.com/questions/652721/… - very nice and helped me to understand induced mappings in M-V sequences, but I don't catch this final equality, that ends with Z^{k-1}\oplus Z / (2,...,2)Z = Z^{k-1} \oplus Z_2. Z^{k-1}\oplus Z = Z^k since it is finite product or am I wrong? And then it would be (Z_2)^k... where am I wrong??

r9m

@Idomathart should be doable with that fun transform ;) .. I will try later .. :-)

Agawa001

12:25

@r9m cool blog, i bet chriss will be owed mutual credits as in your blog in her book :)

HiHello

12:57

Hello! Some hint about summation of i.a^i from zero to n?

Semiclassical

13:14

@HiHello Consider the summation of a^i from 0 to n and then differentiate w/r/t $a$.

0celo7

I was wondering...one usually proves "if $f,g$ are continuous, so is $f+g$" in analysis using sequential continuity. Can one prove it using topological continuity?

i.e. preimage of open sets is open

HiHello

@Semiclassical The sum is the same that from 1 to n. What does it "differentiate w/r/t $a$" means? I differentiate the sum of a^i in a, and the result isn't the expected.

Balarka Sen

@0celo7 Adding two functions cannot be done just using the topology on $\Bbb R$.

0celo7

what do you mean?

Balarka Sen

Also, it can be done using the $\epsilon$-$\delta$ definition.

0celo7

13:27

I'm sure it can.

bbl, will explain

Semiclassical

also, morning chat

@HiHello w/r/t means 'with respect to'

Balarka Sen

@0celo7 The epsilon-delta definition of continuity is not distinct from the topological defn of continuity (preimage of open set is open).

HiHello

@Semiclassical Ok. That didn't work

Semiclassical

the point being, you've got one sum that looks like 0+1a^1+2a^2+etc

and another that looks like a+a^2+a^3+etc

if you differentiate the second, you get 1+2a+3a^2+etc, which differs from the first one only by a factor of a

that's a pretty standard technique for this kind of problem.

HiHello

@Semiclassical I got it. Worked. Now it seens so obvious... hahah Thanks

Mithlesh Upadhyay

13:36

Please, help me write a letter to extend my job for more 6 months workplace.stackexchange.com/questions/75385/…

Semiclassical

@HiHello no problem. another useful technique is to multiply by 1-a. this is handy here because (1-a)(a+2a^2+3a^3+etc) = a +(2-1)a^2+(3-2)a^3+etc = a+a^2+a^3+etc.

doing that again gives (1-a)(a+a^2+a^3+etc) = a+(1-1)a^2+(1-1)a^3+etc

If this was an infinite series, then that etc. of zeroes in that last expression would continue forever. for the finite case, though, it won't.

so you'll end up with something like a-a^m (i'm too lazy to figure out what m is here)

0celo7

@BalarkaSen I know.

Balarka Sen

@0celo7 Then I don't understand your question.

Mithlesh Upadhyay

13:51

@did, how to do next? Sorry for pin you.

And @JyrkiLahtonen ?

HiHello

@Semiclassical Yes. a-(a^(n+1))*(b+1)+n*a^(n+2)

Semiclassical

right.

the details are easy enough to work out if you're not careless when multiplying by 1-a.

0celo7

@BalarkaSen My analysis book defines continuity in general topological spaces and then asks the reader to show $f+g$, $fg$, $f/g$ are continuous, something that was not mentioned in the section on continuity.

So I'm wondering if there's a really slick way of proving this using open sets.

Semiclassical

hence, that sum ends up being some rational function whose numerator is a polynomial in a and whose denominator is (1-a)^2.

0celo7

I'm fine with the sequential proof or $\epsilon-\delta$, but the book makes it seem like there's a third proof

Balarka Sen

14:00

No, there is no abstract way to do it. You have to get your hands dirty.

0celo7

Ok, just checking.

Balarka Sen

Addition, multiplication etc of functions to $\Bbb R$ cannot be done just using the topology on $\Bbb R$, is the reason.

You need the vector space structure of $\Bbb R$. Hence, get your hands dirty using epsilon-delta whenever you try to use that.

0celo7

Ok.

@BalarkaSen Do you have access to Helgason?

I do math art

@r9m OK. There I used a new tool I created. Not sure what you want to use, but let me know if you did it using your way.

Balarka Sen

No.

HiHello

14:04

@Semiclassical After first (1-a), it works fine, I guess. Because appears (a+a^2+a^3+...+a^n) - na^(n+1). Putting (a+a^2+a^3+...+a^n) as a(a^n -1)/(a-1) I get the answer dividing a(a^n -1)/(a-1) - na^(n+1) by (1-a). No?

Semiclassical

that should be right.

i'm not really checking the details, tbh, just signaling that one needs to

HiHello

@Semiclassical I really liked the differentiation. haha. I've never aplied that on some problem like that, I'm starting university. So, thank you so much.

0celo7

@BalarkaSen some definitions and a theorem. I'm miffed as to why this is important.

Semiclassical

glad you like it, heh

both of them are nice tricks for summations like that.

0celo7

@BalarkaSen Helgason is in the same vein as Kobayashi-Nomizu, geometry in the Bourbaki style.

They both have weird theorems that don't pop up anywhere else.

Balarka Sen

14:13

@0celo7 What's $u(\varphi_1, \cdots, \varphi_n)$?

0celo7

It says that $u$ is a diff. function on $\Bbb R^r$.

Balarka Sen

Oh, missed that.

0celo7

If you take $r$ smooth functions on $M$ and plug them into a smooth function on $\Bbb R^r$, you get a smooth function on $M$.

Balarka Sen

@0celo7 These are important because it's an alternative definition of manifolds.

Essentially it says a manifold is something which locally admit the coordinate functions of $\Bbb R^n$.

0celo7

Ah, that's how Bredon defines manifolds.

But why is that better than the usual definition?

Balarka Sen

14:21

Because the usual definition doesn't take account to the information about the smooth functions on the manifold, @0celo7.

0celo7

But why does one need that?

Balarka Sen

Why does one need smooth functions on a manifold?

0celo7

No, why does one need this weird definition?

Balarka Sen

Need? You probably wouldn't need this.

It's simply of a pedagogical importance, is all.

Carry on Smiling

15:14

hello

Leon Aragones

15:33

Hello, Carry on.

Agawa001

@Idomathart which tools you have created ?

I do math art

@Agawa001 I'll share some of them at some point.

Agawa001

@Idomathart you code ?

I do math art

@Agawa001 No. I did that in high school. Turbo Pascal, some FireFox.

Agawa001

15:48

lol lool firefox isnt a language lmfao

php / css / html ?

ok nvm

just asking about what kind of tools you create

I do math art

@Agawa001 There is not much to describe in these circumstances, but to show. Let's say there are some special identities that connect some integrals and some series in a very nice helpful way.

Agawa001

i didnt ask you to make them public, just wondering about their usability/ language created by

with mathematica ?

I do math art

@Agawa001 I suspect they are not known. Mathematica couldn't invent such identities. :-)

Agawa001

me also i create some tools that help me in my work

I do math art

@Agawa001 Researching you discover all you need. Well, sometimes it takes a lot to get where you want.

Agawa001

15:54

and my coworker wanted them for gold lol they are not available in internet

I do math art

@Agawa001 don't you share them? :-)

Agawa001

after they become outdated

evil me

I do math art

:-)

@Agawa001 I would need a whole team for all my ideas, no jokes at all. I'm excessively tired these days, I cannot handle with all the stuff I have anymore.

That means that I have to neglect a lot at least for a while.

Agawa001

noone would handle working solo

I do math art

4, 5 people would be a good start

Agawa001

15:58

btw that reminds me of AI program i designed in my teens, it integrates by part

I do math art

@Agawa001 Really? Did you have such stuff?

Agawa001

some intelligent stuff working by decision tree (branch and bound)

I do math art

@Agawa001 Cool!

Agawa001

oh it is amateur work, i can now design cooler things

I do math art

@Agawa001 In the past wolframalpha implemented something like that, showing you all the steps, including the variable change.

Agawa001

16:01

@Idomathart you could be twice overwhelmed if you studied AI, better than maths

I do math art

@Agawa001 Maybe. :-)

Agawa001

well they are deeply and drastically connected

I do math art

I see.

Agawa001

but regarding innovativity and creativity, AI can hand you many many doors

and ways

I do math art

@Agawa001 Also in mathematics I like much much more to create than to solve, but I admit that at the same time I love to attack some crazy classes of integras, series that seem impossible and humiliate them a bit. :-)

Or classical problems that seemed impossible by elementary means, never done in history like that.

Agawa001

16:08

but the mathematics area lacks innovations and contemporary discoveries, it is abandoned relating to computer science, AI is the science of the modern age

I do math art

(by the way, I have some issues with my network connection, I can't even edit what I type here)

Agawa001

not underestimating it, because maths stays eternal

once maths stops progress, i assume dozens maybe hundreds other fields stop in parallel

I do math art

@Agawa001 Maths never stops. :-)

Agawa001

they may hold some years but finally become very infertile without maths

I do math art

Indeed.

Semiclassical

16:13

it's also true that certain instances of mathematics have been forgotten/rediscovered over the years

stuff which some classical mathematician may have considered a century or so ago, say

0celo7

16:42

@Semiclassical like?

Semiclassical

i'll confess, i don't know a lot of examples off the top of my head.

but it's inevitable, given the sheer plenitude of publications over the decades

This MathOverflow question has some examples: mathoverflow.net/q/176425/55904

0celo7

@Semiclassical in that same vein, AFAIK diff geometry was a relatively obscure field until Eisntein "discovered" it in ~1910

I wonder why it wasn't more popular

Perhaps because we didn't have a good definition of manifold until ~1935

The foundations were pretty shaky

Semiclassical

17:19

one way to get a feel for the timeline of a subject is to look at the names associated with it

Agawa001

@Idomathart these weird postures

Semiclassical

So, for instance, Levi-Civita's book on tensor calculus was published in 1900, and as I understand it that's the text which Einstein used to master the subject

0celo7

@Semiclassical I can name like 4 geometers before Einstein.

Riemann, Levi-Civita, Ricci, Christoffel.

After Einstein the field exploded

Semiclassical

I presume you mean 'differential geometers'

0celo7

@Semiclassical Yes.

Agawa001

17:22

@Semiclassical the fft was introduced by ptolemy as far as i know

Semiclassical

I thought it was Gauss, at least in some sense

I haven't seen any reference to Ptolemy having a sense of it

Agawa001

@Semiclassical guass developped it, but talking about the first time it was abandonned

Semiclassical

That was to Agawa, though I think an argument can be made for him re: differential geometry

He worked on curvature of surfaces, for instance.

I do math art

@Agawa001 cool. I would like to able to stay like that, however my belief in the power of these exercises tends to $0$.

Agawa001

lol, me i can, im somhow flexible (at a limited point)

I do math art

17:25

Religions spread too much BS during the time, and this is like a religion.

Agawa001

@Semiclassical who was the first scholar who discovered the true earth rotation (double-sin motion) isnt euclid

Semiclassical

What?

Do you mean, the fact that the earth rotates about its axis and also revolves around the sun?

I do math art

@Agawa001 Science gave people back the power to look at themselves with dignity.

Agawa001

forgive my lack of knowledge, i forgot

who discovered the double-curved motion of earth

yes around itseld + around sun

I do math art

@Agawa001 However it is clear (for me) that people also live in a spiritual dimension which the science cannot feed. It's complicated.

Agawa001

17:29

@Idomathart yes indeed, but earlier philosophers like socrates paid for their knowledge

0celo7

@Semiclassical It was Riemann who first dreamt of $n$-manifolds.

Semiclassical

The tricky thing is that there's a difference between someone proposing that the earth both rotates and revolves, and someone offering evidence thereof.

0celo7

But his treatment was very handwavey, akin to an undergraduate GR text really.

Semiclassical

@0celo7 Have to start somewhere.

Agawa001

qph.ec.quoracdn.net/…

Semiclassical

17:31

Looks like Aristarchus is generally credited with the first suggestion of heliocentrism

I do math art

@Agawa001 Does the science answer to the question Who are we??

:32109438 Just typing too fast.

Semiclassical

@Agawa001 is that the retrograde motion of mars?

Agawa001

religions have propositions and they force humandkind to consider it true with no right to criticise, philosophy tries to set some dogma-free assumptions and they are considered false until proven right, science gives experience based facts which are considered true until proven wrong

Semiclassical

ahh, metaphysics

Agawa001

this is a general overview about where we come from refering to many sources

and i priorize science then philosophy then religion

my brain does it in this order, while my heart force it in counterclockwise order

@Semiclassical i guess this is the solar system map as firstly proposed by ptolemy

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17:46

@Agawa001 Here is something interesting related to any system that (in my view) also has a spiritual side. If you have a friend which is doctor and you can stay and talk to him/her, just asking him/her: Is it true doc that many of the truths in the medicine 20 years ago are not truths anymore? And we talk about science, to be clear.

Semiclassical

Depends on what one means by 'truth', I suppose :)

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Let me find a relevant article.

Semiclassical

If one means a fact that is supposed to be in literal correspondence with reality, then probably most of the things we take to be 'truths' are not so and never were.

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sciencedaily.com/releases/2016/05/160521071410.htm

Low-salt diets may not be beneficial for all, study suggests
Salt reduction only important in some people with high blood pressure

Semiclassical

But eh. Most of the time it doesn't matter if there's a perfect 'mirroring', so to speak, of reality by thought.

What matters is whether those facts are reliable within some domain.

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17:49

Eating too LITTLE salt may INCREASE your risk of a heart attack or stroke, claims controversial new research

dailymail.co.uk/health/article-3601799/…

Please if you have time check how things were treated for many years related to the salt intake!!!

Semiclassical

well, you're assuming that the new research is right and the old was wrong.

maybe so. maybe the reverse. maybe it's more complicated than either.

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It's all over the place just science!

Semiclassical

Just because one source claims it, doesn't mean it's true. Doesn't mean it's false either, to be sure.

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No, medicine is full of such situations, and possibly in 20 years, what was considered good is then bad.

Semiclassical

Considered good/bad by whom?

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17:51

@Semiclassical Accepted as recommended in medicine based upon studies.

@Semiclassical Really, it's a waste of time before you talk to a doctor, maybe you have a friend which is doctor, and then we can continue.

Semiclassical

Sigh.

Agawa001

what is common is taht salt increase the exposability to blood flow diseases

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Before it was Eating too MUCH salt may INCREASE your risk of a heart attack or stroke, but now we have other titles in papers (based upon studies) Eating too LITTLE salt may INCREASE your risk of a heart attack or stroke

It's science!

Agawa001

wierd

Semiclassical

I think that points to the lack of consensus on the subject and the difficulty of actually testing it

Agawa001

17:54

but cholesterol is never contestable

Semiclassical

And how easy it is to make a bad study in either direction

The other example of this that circulated fairly recently was flossing

Agawa001

i know what is the general sight is, science is prone to change anytime, but as science changes, circumstances change also, like food,life instruments transport etc, many things change that makes this morphological nature of scientific statements reasonable

Semiclassical

Dentists recommend it, but a study came out saying that they didn't find a statistically significant effect from it

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