help-39

[west sapphire]

yea i hate writing out the long thing with the division by |n|
so i just assume n has already been normalized, makes the formula easier

[mellow pine]

let my mind process this haha

[west sapphire]

sure

[mellow pine]

so we have
newV = oldV - A(oldV)

[west sapphire]

yep

[mellow pine]

and the question is asking us to find what A is?

[west sapphire]

actually it wants a P such that
newV = P(oldV)

but if you find A you're almost done, because then

let P = I - A

[mellow pine]

so
P(oldV) = oldV - A(oldV)

[west sapphire]

then you can see that:
P(oldV) = (I - A)(oldV) = I(oldV) - A(oldV) = oldV - A(oldV)

I here is the identity matrix

[mellow pine]

gotchya

so to find the matrix for the ANSWER

we do
I - A
where A is what?

ugh

how do we calculate A

here we know what Av is, but not A...

just divide by v?

[west sapphire]

nah it's not that simple

[mellow pine]

but we don't even know v!!

[mellow pine]

how close are we bungo 💀

this seems a very very hard problem lolz

[west sapphire]

you need to find an A that does the following job:
given an arbitrary v, we need
Av = (v.n)n

[mellow pine]

so A is the hard part, then finding P is trivial

[west sapphire]

yes pretty much

[mellow pine]

is this even possible 💀

[west sapphire]

well let's take it a step at a time

suppose I start with a matrix which has 3 identical rows
each row is just n

let's call that matrix B

what would Bv be?

[mellow pine]

hmmm

[mellow pine]

so like
a a a
b b b
c c c

[west sapphire]

no the other way around

a b c
a b c
a b c

[mellow pine]

ohh yeah mb

[west sapphire]

where n = (a b c)

in row form

[mellow pine]

v would get cross producted with a matrix that is the normal of a plane

[west sapphire]

maybe it's easier if i just give a formula for A and then we see why it works

[mellow pine]

😭

okie

[west sapphire]

let's try $A = nn^T$

[mellow pine]

I feel like we gave up on me tho

[mellow pine]

got it

what are the dollar signs

[west sapphire]

no, the problem is that it's easier to do this if you already know how to do it haha

[jolly parrot]

Bungo

[mellow pine]

gotchya

[west sapphire]

sorry that was supposed to format,

ah there, delayed reaction

bot is slow today

[mellow pine]

so matrix A is equal to the cross product of n and the transpose of n

where the transpose of n is just like flipping the matrix

[west sapphire]

no it's the ordinary matrix product of n and n^t

where n is expressed in column form

so in other words

(column form of n)(row form of n)

as a matrix product

[mellow pine]

what is n^t?

[west sapphire]

that's what A will be

[west sapphire]

sorry, lazy notation for transpose of n

[mellow pine]

wait so I know transpose is flipping rows with columns

but what does that actually do

[west sapphire]

example:

suppose your normal vector is just n = (1, 2, 3)

[mellow pine]

okay I understand what this is now, but I don't understand how you got this formula

[mellow pine]

yepp i'm listening

[west sapphire]

then what I mean is
$$A = \begin{bmatrix}1 \ 2 \ 3\end{bmatrix} \begin{bmatrix}1 & 2 & 3\end{bmatrix} = \begin{bmatrix} 1 & 2 & 3 \2 & 4 & 6 \ 3 & 6 & 9 \end{bmatrix}$$

[jolly parrot]

Bungo

[mellow pine]

mhm

[west sapphire]

i'll address that next, let's first make sure we agree about what i mean, sounds like you're cool with that part

[mellow pine]

yeppers

[west sapphire]

ok so why does that work

[mellow pine]

WHY

🥺

[west sapphire]

lemme write some more formatted stuff, be patient

[mellow pine]

yes Bungo

🫡

[west sapphire]

it's harder to write formatted but it's easier to read

one moment

[mellow pine]

you got this Bungo

i'm cheering you on

[west sapphire]

let's say we defined A as above

then:

$$Av = (nn^T)v = n(n^T v) = n(n \cdot v) = (n \cdot v)n$$

[jolly parrot]

Bungo

[west sapphire]

the key that i'm using here is that $n^T v$ is just the dot product of $n$ and $v$

[jolly parrot]

Bungo

[mellow pine]

got it

[west sapphire]

so you see why this choice of A does the job

[mellow pine]

WAIT HOLD UP

[west sapphire]

and you see it's also easy to compute once you have n

[mellow pine]

so by transposing t and multiplying it with v, you get a scalar?

yes makes sense

[west sapphire]

yea i'm assuming here that n and v are both column vectors

[mellow pine]

I wrote it out

[west sapphire]

so n^transpose is a row vector

then row vector times column vector = scalar

the order of multiplication here is important

[mellow pine]

ahhhhhh
and since Av = nn^Tv
A = nn^T

[west sapphire]

if it was the other way around:

[mellow pine]

omg how did you even figure that out

that was genius

[west sapphire]

(column vector) times (row vector), that's a matrix

[west sapphire]

i 100% did not figure that out, i've seen it before and remembered the trick

it's actually quite genius

and i am not a genius haha

[mellow pine]

shush

you are

IN MY OPINION

[west sapphire]

reminder:

[mellow pine]

wait so

[mellow pine]

mhm

[west sapphire]

remember that we assumed here that n is a unit vector

[mellow pine]

yepp

[west sapphire]

none of this works if you just take n as the cross product of the two given vectors

remember to normalize it

[mellow pine]

ie divide by the magnitude of n

[west sapphire]

yep

[mellow pine]

SO JUST GONNA put all of the equations in one place rn

we know that

AnswerVector = I - A

[west sapphire]

well P = I - A

AnswerVector = Pv for given arbitrary vector v

[mellow pine]

where I is the identity vector
and A = (n . v )n

[mellow pine]

oops I meant answer matrix

like wut the problem wants us to find

[west sapphire]

no

Av = (n . v)n

A itself doesn't depend on v

A is n n^T

product of n (column) times n (row)

[mellow pine]

wait how does A not depend on n when you write it in terms of n?

[west sapphire]

oops typo

A doesn't depend on v

[mellow pine]

makes sense yeah

cuz if it did, then we wouldn't be able to solve the problem! as we don't know v

[west sapphire]

yea exactly

luckily the same A works for any v

[mellow pine]

yepp lemme rewrite
P = I - A
Av = (n . v)n
A = n n^T
So P = I - n n^T
n = normalized version of cross product of the two vectors

WRITE

RIGHT*

[west sapphire]

yes

100%

[mellow pine]

THANK YOU SO MUCH BUNGO

I LOVE U

[west sapphire]

n = normalized version of cross product of the two vectors

done deal

[mellow pine]

oops yes lemme edit and eadd dat

TADA

[west sapphire]

yep

complete

[mellow pine]

aight lemme try it out

and see if it works in the problem

[west sapphire]

sure

[mellow pine]

I got it wrong Bungo 😭

Let me show you my work!

We know that N is sqrt(3) * [-1, -1, 1]

We know that A = N * N^T
so A =
3 3 -3
3 3 -3
-3 -3 3

so I - A =
-2 -3 3
-3 -2 3
3 3 -2

BUT IT SAID I GOT IT WROGN

: (

@west sapphire

[west sapphire]

let me check

[west sapphire]

you need to divide by sqrt(3), not multiply!

unfortunately this means you get ugly noninteger numbers

[mellow pine]

OH CRAP

[mellow pine]

sqrt(3)*sqrt(3) --> 3 so we just multiply by 1/3 in the end

[west sapphire]

that will work as far as A

but you'll have to recompute I - A

[mellow pine]

gotchu

thank u bungo!

[west sapphire]

depends on what you mean here

if you take your wrong A, there you effectively multiplied by 3 instead of dividing by 3

so if you start with the wrong A you would need to divide by 9 to get the right A

[pearl pond]

@mellow pine Has your question been resolved?

[pearl pond]

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[dry lintel]

I need help...

[dry lintel]

For the LOVE of GOD!

Can someone explain to me the Halting Problem

from whatever Alan Turing was trying to explain

[crystal lion]

Theres a pretty good veritasium video about it i think /or something else but it contains it

[dry lintel]

yeah I tried looking at the videos...

NONE of them makes sense to me

Like wtf was Alan trying to prove?!

Alan: "Let me create a computer/program that solves everything"

World: "THank you Alan!"

[rough stream]

long story short:
There exists no algorithm that can take a program, and answers "Does this program halt?"

[dry lintel]

5 seconds later,
Alan: "Now I'm going to prove that its wrong and no computer can ever solve everything"

I don't understand the paradox aspect

[rough stream]

Turing does use a contradiction argument to do this. He says "Okay, let's pretend there is such an algorithm" and then shows the logical failure of that assumption

[dry lintel]

What..paradox?

https://www.youtube.com/watch?v=VyHbd6sx5Po

I found this video...

But I don't understand where "the paradox" part comes into play

https://www.youtube.com/watch?v=macM_MtS_w4

same with this

[rough stream]

This being the paradox I think you're referencing, to be clear.

[dry lintel]

but what algorithm?

He creates a program...thats always right

[rough stream]

.

[dry lintel]

But...

what?

but...he does?

[rough stream]

He tries to and fails

[dry lintel]

I'm confused...what is the process?

All I know, there's a program that answers correctly if a program says if it halts or runs forever

and then we put that program in another machine and then....sh*t gets weird

ALL I know, we start off with a program that DOES answer and says if the machine stops/halts or if it runs forever

[rough stream]

Let's be SUPER CLEAR here, there's actually no such algorithm. That's the halting problem!

How does Turing prove it? Let's begin by PRETENDING there is one.
But as you've mentioned, shit gets weird when we pretend this.

[dry lintel]

god damn it

Ok so we are pretending there is a program that answers if the machine stops/halts or runs

and then what?

We put that program, in a machine that does...what?

[rough stream]

Then Turing constructs a machine that "beats our algorithm".

[dry lintel]

huh...

[rough stream]

If the algorithm exists, then this machine causes our algorithm to lie.

But that's not possible, our algorithm should work on every machine!

[dry lintel]

what...

[dry lintel]

basically this?

Basically we put our perfect program/algorithm in a machine that says the complete opposite?

[rough stream]

Yep. our perfect algorithm is not so perfect anymore

[dry lintel]

but...

ok so...what's the paradox?

the algorthm is still perfect

its the machine...

that's the problem

[rough stream]

Our algorithm should work on every machine!

[dry lintel]

cause its designed to lie/say the complete opposite

[dry lintel]

ok so:

• There's a perfect program that detects if something is supposed to run forever or halt.
• We put that program in a machine that just says the complete opposite.
• Program says "Halt", Machine runs forever / Program says "Run forever", Machine Halts..
• We blame it on Program

[rough stream]

That's true! And perhaps profound. This machine is specifically designed to defeat our algo. The halting problem could also be stated as: these machines exist.

[dry lintel]

so what's the paradox part?

[rough stream]

What's the video referring to with the word "paradox"?

[dry lintel]

Ok dammit, can I dm you what my prof is saying?

and his explanation?

[rough stream]

Just post it! Let's see.

[dry lintel]

or screw it, I'll post it here

[rough stream]

They might be referring to the "unsolvability" of the halting problem. That is, given a program, can you determine if it's possible to write an algorithm that determines HALT/NO HALT?

The answer ends up being "we can't know!" We need to actually see that program before we can say.

[dry lintel]

here ^

This professor sucks so much

I understood NONE of what he just said

[rough stream]

The "paradox" here is the proof by contradiction. There exists a program for which we cannot determine HALT/NO HALT, when we assumed such a progrram isn't possible.

[dry lintel]

ok, I'm sorry I'm awful at this

Can we do this step by step

cause I'm not getting it still

[rough stream]

No you're good. This is a pretty tricky proof

[dry lintel]

literally explain to me like im a 5 year old

who doesn't know anything cause this is too confusing for me

[earnest schooner]

There's a video on youtube about diagonal arguments, and it talks about the halting problem if I'm not mistaken

[rough stream]

• Let's PRETEND we have perfect program that detects if something is supposed to run forever or halt.
• We put that program in a machine that just says the complete opposite (NOTE the construction of this machine is non-trivial!)
• We get a logically impossible contradiction

[earnest schooner]

I remember watching it even before starting uni

[rough stream]

(Says HALT, but the program doesn't halt / says NO HALT but the program halts.)

[earnest schooner]

So it's probably straightforward

https://youtu.be/dwNxVpbEVcc?si=VAW7jSZLyE75SAPu

Hope it helps

[dry lintel]

So the perfect Program is orange box from the clip

[rough stream]

ye

[dry lintel]

so my prof was just too dumb to add the part

"we put it in a machine that says the complete opposite"

Ok so we take a program that's perfect which says correctly, "this will halt" or "this will run forever", and we put it in a machine that says the opposite

and obviously, that will not give us the right answer

[rough stream]

There's some detail there that does need to be fleshed out. Is it possible to construct such a machine? Turing was able to logically construct it.

[dry lintel]

so even though the Program says in an instance, "Oh this will halt"
the machine will say, "this will run"

[earnest schooner]

Most of the time u just argue about a machine's existence using the TCT

For every algorithm there's a machine that does that

I don't think Turing proved that

But it works most of the time

[dry lintel]

a machine that says the complete opposite?

LITERALLY the professor posted the video I showed above...

https://www.youtube.com/watch?v=macM_MtS_w4&t=105s

This one...which Im still confused about

[rough stream]

What's up?

[dry lintel]

just my dumb professor saying, "oh yeah, I said it awfully and explained it badly"

"watch this video instead"

Ok here's where I am stuck on:

This part of the video

How...this...

this makes no SENSE!

[dry lintel]

This guy is saying, "Ok, H+ is the entire program that tells it correctly!"

How does...

fucking

the program says, "it halts! It can't run!" translate to a machine saying, "IT CAN FOREVER RUN!" when it can't!

what it just says, "halts, halts, halts, halts, halts, " until the computer explodes?

[rough stream]

Or it calculates digits of pi for eternity

[dry lintel]

im so frustrated at this im going to cry...

[rough stream]

For whatever reason, the "loop forever" branch doesn't stop computing.

[dry lintel]

I don't understand the video starting at the 5 minutes timestamp...

[rough stream]

Can you elaborate on this? Why shouldn't this happen?

[dry lintel]

Ok...i'm trying

1. We have a perfect algorithm that says if machine stops/halts or runs forever

2. We add something that to algorithm where it will say the complete oppposite

like shown in the video

[rough stream]

Worth noting, H itself is the "perfect program"

[dry lintel]

so if it halts, we make it so it runs forever. And if it doesn't halt, we make it halt

Ok!

[rough stream]

H+, which depends on H, is the "defeating program"

[dry lintel]

then we package allll that crap together

which is H+

so now we feed H+ into H sort of again.

which agian H+ is this:

[rough stream]

We want to know what the output will be, when H+ takes H+ as an input

[dry lintel]

If....its supposed to Halt, instead of halting, it will run forever.
If its suppoed to run forever, instead of running forever, it will instead halt

[dry lintel]

ok so the inputs is H+ got it

[rough stream]

Here's a question.
Does H+ halt when we feed H+ into it?

[dry lintel]

but...what do you want to originally? To make it halt or run forever?
If you want to make it run, I'm assuming H+ is going to make it halt.
And if you want to make it holt, H+ is going to make it run forever...

....I hope this is correct?

[rough stream]

• Let's assume it halts.
  H would print "yes".
  But then that goes to the "loop forever", so H+ doesn't actually halt like we assumed.
  So our assumption must be wrong.

• Instead, let's assume it runs forever.
  H would print "no".
  But then that goes to the "halt!", so H+ doesn't actually run forever like we assumed.
  So our assumption must be wrong.

[dry lintel]

ok...wait

so I was right?

[dry lintel]

with this

...right?

[rough stream]

Yeah that's basically it

But instead of "want", it's more like "what actually happens"

[dry lintel]

so essentially....
Whatever the intention was, its doing the opposite

[rough stream]

H+ has to halt or loop. One of those two options.
Except... it doesn't!

[dry lintel]

if its thinking that its going to halt, its actually going to run forever.
If its thinking that its going to run forever, its actually going to halt

[dry lintel]

what?

[rough stream]

That's the paradox. H+ neither halts or loops.

H+ can't exist. H can't exist.

[dry lintel]

https://tenor.com/view/jontron-what-excuse-me-confused-gif-15932709

but...

its doing it?

its..

how does it not exist?

like you mean it literally?

[dry lintel]

wdym?

but it is halting or going in a loop

[rough stream]

If H+ halts, it doesn't halt.
If H+ loops, it doesn't loop.

So it... doesn't?

[dry lintel]

huh?

what do you mean it doesn't?

its doing that...

[rough stream]

Basically, it can't halt or loop, so what is it?

[dry lintel]

if its not halting, it isn't...

[midnight haven]

if it halted or went in a loop, then the inner machine, H, incorrectly predicted which it would do

[rough stream]

Every program's gotta halt or loop. But H+ here can't do either.

[dry lintel]

....back to being confused

But...it is

[rough stream]

Which?

[dry lintel]

ohhh my god I haaaate this sooo god damn much

https://youtu.be/macM_MtS_w4?t=298

I added the time stamp already

4:58

if the machine says, "Yes it holts!" but we see in run forever/going on a loop

if the machine says, "Its not holting", we see it holting

[rough stream]

That's based on the assumption that H+ halts, however.

[rough stream]

And this is based on the assumption that H+ loops

[dry lintel]

yeah so H is correct, its just H+ screwing it up

[rough stream]

Skip ahead to 5:16.
"If H+ halts, then it doesn't halt. If H+ doesn't halt, then it halts"

[dry lintel]

but we are blaming it on H

[rough stream]

Forget about H atm. The question is "when does H+ halt, or loop?"

The answer ends up being "there is no case where either happens"

[dry lintel]

like yeah I get that part...
But why are they wording it different/weirdly?
Isn't it basically:
"If H+ Halts, then it doesn't halt and it runs forever"
If H+ doesn't halt, then it stop running forever/loop and halts"

its just...the opposite

of what Program H is saying

[rough stream]

Yeah!
So does H+ halt or loop?
Neither.

[dry lintel]

if its origianlly meant to Halt, its not going to

huh...

?

what do you mean...

H+ is doing the opposite of what H is doing

[rough stream]

You're saying here.

• If it halts, it doesn't actually halt. So, it can't halt.
• If it loops, it doesn't actually loop. So, it can't loop.

[dry lintel]

yeah

isn't it that?

[rough stream]

So if it can't halt or loop, what does H+ do?

H+ just... kinda logically fails to be a real thing

[dry lintel]

I don't understand the question.
H+ is just...doing the opposite

of whatever was intented for H to do

[rough stream]

No. We are assuming what H+ was intended to do

[dry lintel]

what...

https://tenor.com/view/byuntear-baby-cry-crying-gif-25019897

[rough stream]

If H+ halts, it doesn't.
If H+ loops, it doesn't.

[dry lintel]

H is saying:

• If it halts, it halts
• If it runs, its runs

H+ added the craps that made it do the opposite

so:

• If it halts, its actually going to run
• If it runs, its actually going to halt

[midnight haven]

Regardless of who is screwing everything up, H is still in H+, H still gets fed the question of whether H+ halts or not, and H still makes a prediction

[rough stream]

Maybe the "it" is confusing. I'll restate without.
We've determined this:

• If H+ halts, H+ doesn't halt.
• If H+ loops, H+ doesn't loop.

[midnight haven]

H+ makes the prediction wrong, but the point is the prediction was wrong

[rough stream]

H+ niether halts, or loops.

[dry lintel]

Ok! I get this!
But, ok you said:

• "If H+ halts, it doesn't." So its going to run instead
• "If H+ loops, it doesn't." So its going to halt instead

right?

[rough stream]

It can't run if it halts though haha

Can't just say "H+ halts. Therefore H+ loops." We've already stated that H+ halts.

Maybe in better words:
If we assume H+ halts, it makes no sense to say "H+ loops instead".

Because of course, you can't do both

[dry lintel]

https://tenor.com/view/taeuvre-berleezy-berleezy-confused-berleezy-math-math-gif-26165413

well...yeah

[rough stream]

lol the GIFs are good

[dry lintel]

its not going to run if it halts

cause its on halt

...

I don't get this

[rough stream]

Right. But if it's on halt, it's not on halt.

[dry lintel]

......

[rough stream]

Obviously, that makes no sense. So, our assumption that H+ can halt is BS. H+ cannot halt!

[dry lintel]

ok run through me again...

H+ added the craps where it does the opposites of whatever H was intended

so now the package is H+

but its designed to do the opposite

so when we run it again

when its on "Does this halt?", if its going to respond with "it does!", instead its not going to

or if "Does it halt?", and instead it responds with "it doesn't", its actually going to

.......right?

[rough stream]

Well, I do believe this is an issue as well.
But to specifically address the video and timestamp earlier, this is the problem:
If we take H+ and feed it as an input to H+, it neither halts or loops. This makes no sense, and so H+ can't exist.

[dry lintel]

but how?

how does neither halts or loop when it does that?

instead of halting, its going on a loop

and instead of going on a loop, its halting

[rough stream]

Not "instead". More like "despite".

Despite halting, it loops.
Despite looping, it halts.

[dry lintel]

why despite? Is it a huge difference?

so like...

[rough stream]

• Assume H+ halts. (Argument goes here). Therefore H+ loops. But that's impossible, so H+ must not halt!
• Assume H+ loops. (Argument goes here). Therefore H+ halts. But that's impossible, so H+ must not loop!

[dry lintel]

its INTENDED to loop, but its not going to

or its intended to halt, but its not going to

[dry lintel]

https://tenor.com/view/michael-scott-the-office-steve-carell-explain-like-im-five-eli5-gif-5356727

[rough stream]

Let's pretend H+ halts. What does it do?

[dry lintel]

its not going to halt

its going to loop instead

...right?

[rough stream]

But that makes no sense. We're pretending H+ halts!

[dry lintel]

i want to punch a pillow so badly

[rough stream]

No I'm not saying you're wrong lol

You're correct:
If we pretend H+ halts, it loops.

[dry lintel]

so I was right!

[rough stream]

But that's nonsense. We're pretending H+ halts. It can't just loop

[dry lintel]

so basically we need to act like idiots

and pretend we don't know whats going on

when we know whats going on

[rough stream]

No we pretend we know what's going on, but we actually don't haha

[dry lintel]

...but we know its doing the opposite cause we added something to H that made it do the opposite and put that together in H+

[rough stream]

We act like geniuses, and end up showing there's no sensible answer

[dry lintel]

Ohhh my fricken god who I don't know if he or she or it exists...

is it just doing the complete opposite...

right?

that's the whole gist of this thing?

[rough stream]

Forget H, and the relation to H+.

We ask ourselves a question:

• Does H+ halt?
  The answer:
• H+ cannot halt, because doing so would be a logical impossibility.

We ask ourselves a question:

• Does H+ loop?
  The answer:
• H+ cannot loop, because doing so would be a logical impossibility.

[dry lintel]

so basically...

we can't get

...I don't know

what we are looking for?

[rough stream]

It ends up being impossible because halting implies looping implies halting implies looping implies...

[dry lintel]

so like

If I say, "I want it to loop", its going to be impossible because its going to halt instead

or if I say, "I want it to halt", its going to be impossible because its going to loop instead

[rough stream]

Right. But halting is actually going to make it loop.
And looping is going to make it halt.
And...

[dry lintel]

over and over and over again

[rough stream]

Okay that's the paradox haha. Must have been what your prof meant.

[dry lintel]

But now, we cant say or think,
"Ok KNOWING this doing the opposite to what I want. If I want it to loop, I will say, let it go on halt, so it can then loop"

we can't do that?

or is different cause machines are not like us

[rough stream]

We're not "wanting" it to loop.
We're asserting it loops.

[dry lintel]

wdym by asserting?

[rough stream]

It loops.
(Argument goes here)
It does not loop.

But that means it both loops, and does not loop, which is impossible.

Therefore, the assertion that it loops must be a bad one. H+ cannot loop!

[dry lintel]

ok so that's the paradox?
Basically when its looping, its actually not going to loop.
And when its supposed to be running, its actually not going to run

or...in other terms to make it weirder

[rough stream]

Yeah that exactly

[dry lintel]

when its supposed to halt, its not going to halt.
and when its supposed to not halt, its going to halt

[rough stream]

Therefore H+ can't either halt or loop

[dry lintel]

Im having a brain moment

ok ok just...

OK !

[rough stream]

Because if it does one, it does the other... then the other... then the other...

[dry lintel]

I think I get what you mean

!

[rough stream]

I shouldn't really say this though, because the take away is that it can't do either

[dry lintel]

so please bare with me! I think I got it:

H+ can't halt or run.
because again:

when its supposed to halt, its going to run.
and when its supposed to run, its going to halt

So its that, it THINKS that its doing one thing, but its doing the other thing

[rough stream]

Yeah, sounds good!

[dry lintel]

I...

HATEE this sooo god damn much

but fucking finally

my brain understood this crap

it only took me around 1h and 45 god damn minutes

[rough stream]

Now. H+ neither halts or loops.
So... what does it do?
As a program must choose one of those two

[dry lintel]

it will...

do neither?

[rough stream]

But that can't happen!

[dry lintel]

is this what you said, that it doesn't exist?

aka, the paradox part

[rough stream]

That's exactly it. The takeaway is that H+ can't be real.

And, H+ is a simple modification of H.
So, H can't exist.

[dry lintel]

maybe I'm being too literal

cause ok, I get it

I just find it dumb

but I get it!

I hope

[rough stream]

Ultimately, Turing proved that some things are not computable. There exists no algorithm that can take any program and determines HALT/NO HALT.

[dry lintel]

But its weird cause wasn't his whole thing about creating a perfect computer?

[rough stream]

Well, let's say he did create a perfect computer.
This algorithm is something the computer cannot do

[pearl pond]

@dry lintel Has your question been resolved?

[pearl pond]

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[unkempt saddle]

I need help finding the pattern in this integer sequence
1 3 5 9 15 17 19 27 45 51 57 ...
I already tried wolfram and oeis

[acoustic path]

is there strictly a pattern? or does something like "ordered factors of 43605" suffice

[unkempt saddle]

that doesn't help me but it's possible that there's no answer that will help me

I can explain where the sequence comes from

that might help you help me

[acoustic path]

sure

well this does look similar to some sequence involving modulus

[unkempt saddle]

so this table is a table of the ratios of the overtones which you get by taking the "frequency" rounding it down to the next power of 2 and dividing by that.

+----------+--------+---------+-------+
| Overtone | N      | Ratio   | Ratio |
+----------+--------+---------+-------+
| 1        | 1      | 1       | 1/1   |
| 3        | 8      | 1.5     | 3/2   |
| 5        | 5      | 1.25    | 5/4   |
| 7        | unused | 1.75    | 7/4   |
| 9        | 3      | 1.125   | 9/8   |
| 11       | unused | 1.375   | 11/8  |
| 13       | unused | 1.625   | 13/8  |
| 15       | 12     | 1.875   | 15/8  |
| 17       | 2      | 1.0625  | 17/16 |
| 19       | 4      | 1.1875  | 19/16 |
| 21       | unused | 1.3125  | 21/16 |
| 23       | unused | 1.4375  | 23/16 |
| 25       | unused | 1.5625  | 25/16 |
| 27       | 10     | 1.6875  | 27/16 |
| 29       | unused | 1.8125  | 29/16 |
| 31       | unused | 1.9375  | 31/32 |
| 33       | unused | 1.03125 | 33/32 |
| 35       | unused | 1.09375 | 35/32 |
| 37       | unused | 1.15625 | 37/32 |
| 39       | unused | 1.21875 | 39/32 |
| 41       | unused | 1.28125 | 41/32 |
| 43       | unused | 1.34375 | 43/32 |
| 45       | 7      | 1.40625 | 45/32 |
| 47       | unused | 1.46875 | 47/32 |
| 49       | unused | 1.53125 | 49/32 |
| 51       | 9      | 1.59375 | 51/32 |
| 53       | unused | 1.65625 | 53/32 |
| 55       | unused | 1.71875 | 55/32 |
| 57       | 11     | 1.78125 | 57/32 |
| 59       | unused | 1.84375 | 59/32 |
| 61       | unused | 1.90625 | 61/32 |
| 63       | unused | 1.96875 | 63/32 |
+----------+--------+---------+-------+

in just intonated 12 tone music we use these 11 overtones 1 3 5 9 15 17 19 27 45 51 57

I'm trying to figure out why

in order to figure out how to do 24 tone or N tone just intonation

maybe it's just a thing of "they are closest to the P_n = P_a2^{(n-a)/X} way of diving the range 1-2 into X parts"

[pearl pond]

@unkempt saddle Has your question been resolved?

[tulip ore]

the ratios of 12-tone equal temperament are:
1/1
T/1
T^2/1
T^3/1
T^4/1
...
T^11/1
T^12/1
where T is the 12th root of 2
this is because:

• sounds at equal ratios have the same interval
• an octave 2:1 needs to be split into 12 equal intervals
  so the 12th root of 2 as a ratio can be continuously applied to get from 1 to 2, 3, 4, ... 12

the fractions youre seeing are what happens when a number happens to get close to one of these ratios

but really theyre always slightly off

https://www.youtube.com/watch?v=1Hqm0dYKUx4

you can think of it as

using 12-tone equal temperament, they are all made to sound equally spaced between each other and together

the gap between the points is like multiplying by T

now here's what 3/2 looks like:

the gap it has with C is very close to 7/12

now heres the lowest three ratios

you can see it vaguely suggests a sound of some sort split into 12ths

and so the other ratios are found from sounding close to being split this way

@unkempt saddle do you have any questions so far

[pearl pond]

@unkempt saddle Has your question been resolved?

[tulip ore]

so for N-tones you just need N fractions that sound close to the various powers of the Nth roots of 2
To find those, idk

[pearl pond]

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[pearl pond]

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[drowsy tendon]

Hey guys
I need help calculating this system of equations and where to start:

[cunning comet]

e.g. write the second one as x = ... and then plug this in the first.

[pearl pond]

@drowsy tendon Has your question been resolved?

[burnt minnow]

Start by simplifying the first equation. You can then derive the value of x from the second equation. Substitute the value of x in equation 1.

[drowsy tendon]

This is What I’ve done until now

[burnt minnow]

You could actually simplify the first equation to make things easier.

[drowsy tendon]

how?

[burnt minnow]

I'll give a hint- you can divide the equation with 5

[light helm]

you didn't sub properly

[burnt minnow]

Also whenever multiplying with two terms, don't forget the parentheses.

[light helm]

regardless, i don't see how you're getting 14y

[pearl pond]

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[drowsy tendon]

.reopen

[pearl pond]

✅

[drowsy tendon]

I made calculation error/mistake

[burnt minnow]

yes

[drowsy tendon]

thanks for the help

.close

[pearl pond]

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[pearl pond]

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[fervent ginkgo]

how to solve this?

[pearl pond]

@fervent ginkgo Has your question been resolved?

[pearl pond]

@fervent ginkgo Has your question been resolved?

[fervent ginkgo]

what theoorem?

[pearl pond]

@fervent ginkgo Has your question been resolved?

[neat harbor]

maybe use the fact that CO, DO and BO are of same length

[pearl pond]

@fervent ginkgo Has your question been resolved?

[pearl pond]

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[midnight haven]

<@&286206848099549185> Tanya is having a bake sale and must bake cupcakes. She has cupcakes donated by a friend and after her first hour of baking, Tanya has a total of 60 cupcakes. She has 84 cupcakes after the second hour of baking. Tanya continues baking the same number of cupcakes each hour. - The graph for the number of cupcakes baked will have a slope of _________________ and a y- intercept of ___________

[pearl pond]

Please don't occupy multiple help channels.

[midnight haven]

ok

[midnight haven]

your rate would be determined by the amount change between hour 2 and hour 1

so for this instance, do 84-60, what do you get?

24

oh the slope is 24

60-24 = 36 so the y-incpt in 36

yes

there you go

thanks

np

@midnight haven do you mind doing .close here?

.close

[pearl pond]

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[midnight haven]

alright thanks

[pearl pond]

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[midnight haven]

can someone help me solve this? i started on it but idk where to go from there (for context i’m trying to split it into two different fractions, or do partial fraction decomposition)

[feral leaf]

Since you know this part, you can multiply by x(x - 3) on both sides to remove the fractions

[blissful salmon]

next what you do is let A+B=0 and A=-1, therefore B=1

[midnight haven]

does the A+B=0 come from taking the derivative

[feral leaf]

You don't need the derivative

[midnight haven]

oh okay

[feral leaf]

Doing this, you should get 3 = A(x - 3) + Bx

Then you can solve for A and B

The easiest, is using the roots of the denominator from the original fraction, x(x -3)

x(x -3) = 0, solve for x, then use that to solve for A and B

[blissful salmon]

it doesnt come from taking the derivative, you can just see that since the numerator has no x, therefore the coefficent of x (aka A+B) has to be equal to 0

[midnight haven]

ohh ok

[midnight haven]

so here the x values would be 0 and 3 right

[feral leaf]

Yes

So now knowing 3 = A(x - 3) + Bx, and x = 3 and x = 0, plug in each value of x separately then you can find A and B

So for example, plugging in 0 for x, you get 3 = A(0 - 3) + B * 0 which is 3 = A(-3) + 0

So then A = -1

Repeat using x = 3

[midnight haven]

ohh okay that makes sense, thank you

[pearl pond]

@midnight haven Has your question been resolved?

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[snow sail]

presumably it should say x,y >= 0?

on e

I don't think youre correctly interpreting e

There exists an x, such that for any y,

x and y nonnegative implies their sum is non-negative

[pearl pond]

@signal lynx Has your question been resolved?

[surreal ocean]

d & first 2 good. works for counter with -1, 3. reev e. for the other one... let x < 0. when y < 0, is x+y>0? klds

[signal lynx]

yeah thats what ijm assuming

[signal lynx]

ohhhh

wait

isnt it still false if x is 0 and y is negative?

[snow sail]

y wont be negative

[signal lynx]

no its not so wouldnt c be false? sorry im a little confused on ur phrasing

[signal lynx]

how do you know?

isnt it for any y in R?

[surreal ocean]

x doesn't need to be 0 right

[signal lynx]

yeah

but

if its not

x+y is always <0

nO?

[snow sail]

i dont wanna cross talk lemme know when youre done with fluffy

[signal lynx]

fair enough

[surreal ocean]

fine you then-

[signal lynx]

?

[signal lynx]

hi

[snow sail]

howdy

so

Ignore the part that x and y are reals, just assume it in the back of your head

what this says is that, for any nonnegative number, there exists another nonnegative number, such that their sum is nonnegative

[signal lynx]

the only issue i have with that is that while its a non negative number, it could be comprised of negative numbers could it not?

since its only the product of the two thats non negative?

[snow sail]

its not clear what that is supposed to say

so, who knows

to me i'd assume it says $x,y \geq 0$

[jolly parrot]

jan Niku

[snow sail]

but its not clear, since theres a typo

[signal lynx]

i mean the previous 4 have it as the product of x and y

so why wouldnt it be the same as well?

[snow sail]

okay, then sure

they could both be negative

then it would be false

[signal lynx]

so its just entirely depends on the typo then lol

i was operating with it as xy

thats why i was getting it

[snow sail]

sure

[signal lynx]

can u help me w c then if there isnt anything else to be said for e

[snow sail]

all this excludes is x or y being 0

[signal lynx]

for c?

[snow sail]

yea

[signal lynx]

okay yeah that makes sense. that makes the statement true then right? because as long as y isnt 0 it continues to hold?

[snow sail]

its not true

its false

by an identical counterexample

to e

[signal lynx]

oops

yeah

so for the final overall lineup it would be:
a) true
b)false
c) false
d) false
e) false depending on the typo: if the typo is xy >= 0 it's false. if x,y then true

sound abt right to you?

[snow sail]

i havent checked the other

[signal lynx]

:p theyre simple enough it should be fine

[snow sail]

does seem weird to only have one true

but you know you get what you get

[signal lynx]

yeah 😭

im not gonna get all freaked out over though

these answers make sense to me so

[snow sail]

you know a bunch of these are symmetric

because multiplication and addition are commutative

so b and c are identical.

e is mostly identical, too

[signal lynx]

so it makes sense for the majority to be false

[snow sail]

i think so

you know

for e

what if x=0 and y=4

then xy>=0

but 4 >= 0

then again, it says such an x exists for all y

which isnt true

0 wont work for all y

[signal lynx]

yeah

[snow sail]

even though 0y>=0 for all y

so moot

[signal lynx]

as long as theres a single y that disproves it (which there is) we should be good

[snow sail]

yea

[signal lynx]

thanks for the help 🙏

[snow sail]

[signal lynx]

..close

.close

[pearl pond]

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[pearl pond]

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[sinful hemlock]

I have to solve this Indefinite integral using trig sub, I have no idea where to even start, I've pulled out a factor of 4 from the sqrt but the numbers aren't exactly working and I've no clue how to do trig sub when both numbers in the sqrt have an x. Any help in understanding what to do would be excellent, thank you!

[merry carbon]

May want to complete the square...

[sinful hemlock]

can I ask how you know to complete the square there? is there a form you just see that immediately lets you know that?

[plush bramble]

Something x^2 + something x without anything else

[sinful hemlock]

I feel like I have made a mistake somewhere. I am unsure how to proceed. A hint would be excellent

[merry carbon]

The x in the numerator, you also want to deal with that too...

If x - 1 = sec(theta) then x = 1 + sec(theta)

[sinful hemlock]

This is what I have so far. I want to look at some of my other material to make sure I'm resubbing theta to x right. How does it look? any issues?

I am very likely not subbing it back right lol

need to square x's under sqrt I think

[merry carbon]

Yep or note as tan^2(theta) = sec^2(theta) - 1 of course

[sinful hemlock]

I'm rather stuck here wondering if this is the correct answer. I tried subbing tan for sec^2theta - 1, but I'm not competent enough at trig to figure out what happens when sec^2(arcsec(x+1)) occurs

[pearl pond]

@sinful hemlock Has your question been resolved?

[merry carbon]

Well remember that sec(theta) was (x - 1), so you want rather (x - 1)^2 - 1 under those roots

[sinful hemlock]

would that eliminate the roots or is there another piece I'm missing? I feel like there is

orperhaps I have to expand

[merry carbon]

Doing so of course simplifies to x^2 - 2x

,w int (x + 1)/sqrt(4x^2 - 8x)

[jolly parrot]

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[merry carbon]

Meh, it should be fine, can’t be bothered to check equivalence

[sinful hemlock]

I will believe you, math wizard

[merry carbon]

Hehe

Could always check by differentiating the answer of course

[sinful hemlock]

me when fundemental theorem of calculus

[merry carbon]

,w diff sqrt(x^2 - 2x)/2 + ln(x - 1 + sqrt(x^2 - 2x))

[jolly parrot]

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[sinful hemlock]

yeah so it does work

[merry carbon]

When you make the changes you get the same thing

[sinful hemlock]

OKAY I WAS SO CONFUSED HOW WA GOT THAT ANSWER I GUESS IT WAS THROUGH CRAZY SIMPLIFICATION

[sinful hemlock]

dw I fixed it

[merry carbon]

Haha you’d be surprised, integration can get you many results that look different

[sinful hemlock]

that headache is over. I am so terrible at trig but I'm slowly getting there

thank you for your help, I very much appreciate it

.close

[pearl pond]

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[vast holly]

Confused on the 2nd part of question B. I don't fully know for which functions you can / can't setup a hessian matrix

[pearl pond]

@vast holly Has your question been resolved?

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[vast holly]

.reopen

[pearl pond]

✅

[vast holly]

<@&286206848099549185>

I guess it should only be the first one right?

since its a scalar function?

[pearl pond]

@vast holly Has your question been resolved?

[vast holly]

.close

[pearl pond]

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[royal pelican]

Can some1 please check for me the last question in this page

[pearl pond]

Please don't occupy multiple help channels.

@royal pelican Has your question been resolved?

[jolly shuttle]

why n+3?

[pearl pond]

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[sly dagger]

what are the possible values for |z| and arg(z) if z satisfies |z+2-2i|=2?

[sly dagger]

im unsure what to do, i know that there is a cricle with radius of 2 centred around -2+2i

[ashen geyser]

draw it

like on the plane

maybe youll get a better idea

[sly dagger]

yeah i have drawn it now, i can see that the pi/2<=arg(z)<=pi

but I have no clue what to do to find possible values for |z|

[pearl pond]

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[wicked creek]

How do you solve this?
(2x+1)(x-4)(1-x) is strictly less than 0

[blissful raptor]

find the critical points of the same after converting all equations in such a form that all your coefficients of x are positive

[wicked creek]

I don't know how to do that.

[blissful raptor]

(2x+1)(x-4)(1-x) < 0 means (2x+1)(x-4)(x-1) > 0

do you follow thus far?

[wicked creek]

yes

how do you continue?

i found the answer
a friend of mine explained it

.closed

[pseudo oxide]

no it's .close

@wicked creek

[blissful raptor]

sorry, didn't see this

[wicked creek]

/close

[blissful raptor]

critical point means a point where the equation would return the value of 0

[wicked creek]

.close

[pearl pond]

Channel closed

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[blissful raptor]

oh you're done alr

[fading lance]

Hi everyone

[pseudo oxide]

?

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[pseudo oxide]

it isnt occupied, but just to help if u need it @fading lance

[fading lance]

Ok got it

[pearl pond]

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[sick galleon]

Simultaneous equation

[pearl pond]

Please don't occupy multiple help channels.

[pseudo oxide]

^^

!1c

[pearl pond]

Please stick to your channel.

[sick galleon]

Simultaneous equation

Question C

Please help

Don’t know what to do

[unborn abyss]

wow your book hates you

[pseudo oxide]

@sick galleon close your other channel

[sick galleon]

Oh

Where

[unborn abyss]

get rid of the fractions by multiplying each equation by a common denominator

[sick galleon]

there

[unborn abyss]

you'll have big numbers but they'll be integers at least

[sick galleon]

which common denominator

[unborn abyss]

like see the first one has /17 and /4

just multiply that equation by both of those so you don't have those mixed fractions anymore

or you could convert those into improper fractions

but once you've done that it's the same as any other system

[sick galleon]

how does that work with the 3 again

if i times it by 4

where does the 3 go again I forgot

wait

[sick galleon]

combine the numbers into a full number

Then multiply ?

[unborn abyss]

i don't know that term

[sick galleon]

Like

7754/17

is 456 2/17

I do that ?

[unborn abyss]

whatever it takes to get out of $\text{Mixed}\frac{\text{Fraction}}{\text{Hell}}$

[jolly parrot]

hayley!

[pseudo oxide]

LOL

[unborn abyss]

you're going to have some absurd numbers here. you absolutely should have a calculator handy

[sick galleon]

AHHHHH

[unborn abyss]

remember to multiply on the right by all relevant things

you missed the 22 and the 17

actually in general you need to do that

like 3951y didn't get hit with the 17 bat

[sick galleon]

did I ?

I multiplied the fraction

by the other number

FUCK

MY BRAIN

WHY R THE NUMBERS SO WEIRD

[unborn abyss]

this problem sucks

the solution has a denominator of like 1.2 billion it's stupid

[sick galleon]

5 C

Is the answer

[unborn abyss]

oh they just cheated by estimating

that would be much easier sigh

[sick galleon]

I’m fried

[unborn abyss]

,w rref {{456 + 2/17, 987 + 3/4, 1}, {233 + 13/22, -94 - 2/3, 4}}

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by kitten.in.a.teacup

[sick galleon]

What to do

😭

[unborn abyss]

what I would do I think

is convert all your numbers to decimal with 4 decimal places

and then just use those

much easier to deal with in the calculator that way

or? just don't worry about this kind of problem, it doesn't really teach you much beyond precision

[keen ore]

Uhm, Peter, this is just a passing remark for you - unless this is a question you need to submit later, consider skipping it. This tests nothing except your ability to multiply big numbers, which is worthless in my opinion.

I apologize for being blunt.

[sick galleon]

but i’m mad that i can’t solve it

i’m gonna do it later

[keen ore]

Don't beat yourself up for these, it's okay

Try the other and similar problems.

[pearl pond]

@sick galleon Has your question been resolved?

[pearl pond]

Channel closed

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[pearl pond]

Available help channel!

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[livid bolt]

is this if it is no raining then there are no clouds in the sky

[pseudo oxide]

no

its "if there are no clouds in the sky it is not raining"

[livid bolt]

huh

why

[pseudo oxide]

its contrapositive

if there's a statement "if p, then q" then the contrapositive is "no q means no p"

wait no sorry

[livid bolt]

switch the hypothesis and conclusioon?

[pseudo oxide]

i got that wrong

[pseudo oxide]

its like the inverse

[livid bolt]

weird

[pseudo oxide]

sorry it's like

[livid bolt]

is there a reason for dis

[pseudo oxide]

well its the definition

of contrapositive

[livid bolt]

oh

so u just memorise dis?

[pseudo oxide]

well not really

but sorta

[livid bolt]

ahhh ok

[pseudo oxide]

if done do .close

[livid bolt]

.close

[pearl pond]

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[pearl pond]

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• Show your work, and if possible, explain where you are stuck.
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[kindred parcel]

hey guys I need help

[merry carbon]

May help to explain what you want to do with those (e.g. sketch them, find domain/ranges, etc)

[kindred parcel]

yeah

I need help with understanding

like for the first question C

how and why do I need to find the factor

and for d I have no idea how to do

how to graph them and find the points

<@&286206848099549185>

[midnight haven]

Yeah

[kindred parcel]

I'm having trouble with C

I don't understand why and how to find the factor

and also for d I don't know how to do it in general

[midnight haven]

If x = 20 and y=40 then x and y are

[kindred parcel]

?

[midnight haven]

Idk

[kindred parcel]

<@&286206848099549185>

[daring roost]

add the six to both sides then take an x outside parenthesis and solve as normal by factoring or quadratec formula (pretty sure)

[kindred parcel]

.close

[pearl pond]

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[red trail]

does this solve the question? cuz it has a good amount of points in an exam

[tulip ore]

looks good to me

[merry python]

What did you do in the last step?

a + b <= a is false if b is positive

[red trail]

why?

[merry python]

take 3 + 4 <= 3 for example

[tulip ore]

oh wait thats facing the opposite direction than what I expected

thats not good at all

[red trail]

😂😂😂 i just noticed

[merry python]

You could prove that f is increasing and then assume that x >= y

that way you'd get rid of the absolute values

[red trail]

i used Lagrange mean value therom

i think it worked

[merry python]

lol

[pearl pond]

@red trail Has your question been resolved?

[pearl pond]

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[pearl pond]

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[ivory shadow]

help with this please

[ripe cobalt]

You put in where f(x) =0 while the question is asking for the value of f at x=0

In other words, at what y value does the parabola cross the y axis?

[pearl pond]

@ivory shadow Has your question been resolved?

[pearl pond]

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[pearl pond]

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[undone bough]

hey

[undone bough]

sp

so

theres this thing

calculate the value for x = 2
and one of the calculations is
3x+2+(2x+1)

can anyone explain this nonsense?

why isnt anyone here?

[pearl pond]

@undone bough Has your question been resolved?

[undone bough]

nah fuck off

[plush bramble]

Just wait

[undone bough]

i am solving this issue via DMs

.close

[pearl pond]

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[strong ether]

The following information is provided about a function
Dm(f) = {x E Rix -::f:.-61\x-::/:- 6}
f(-1 1) = 0, f(-7) = 0 and f(-3) = 0
f(O) = 2
f(x) > 0 in the intervals]-11; -7[,]-3; 6[ and ]6; oh [
f'(-9) = 0, f'(0) = 0 and f'(9) = 0
fer growing in the intervals ]-oo;-9], ]-6; 6 [ and ] 9; oh [
a) Write down the coordinates of the curves of the graph with the coordinate axes.
b) Sketch the graph of a function that fits the given information.

[strong ether]

I need some help 😊

We need to find x and y coordinates and how do you do that?

[pearl pond]

@strong ether Has your question been resolved?

[pearl pond]

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[vernal hill]

Let's say that when moving the coordinates, the origin is reflected at the point (-1;3); Then at which point will the point (1;-3) be reflected in the same parallel translation

[vernal hill]

.close

[pearl pond]

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[pearl pond]

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[small drum]

f1,f2:R->R
is {f1,f2} linearly independent over R?

[small drum]

is there any work free method to solve that?

like of course they are dependent the dimension of R is 1

[hollow cobalt]

Hm?

Why is dimension of R relevant

f1 and f2 are vectors from the vector space of real functions

[small drum]

ohh yee I get it sry

[hollow cobalt]

I would start by solving for real a, b such that ax^2sin(x) + b(cos(x) - 2x) is the zero function

If you find a solution where a, b are nonzero, then {f1, f2} is linearly dependent

But if a = b = 0 is implied, then it's linearly independent

[tired violet]

I think you might be thinking about a basis on the vector space R but in reality you’re working in a vector space of functions which is likely infinite dimensional

[hollow cobalt]

Try plugging in some values for x to solve for a, b

[tired violet]

So the dimension of the field underlying it is irrelevant here

[small drum]

is that allowed?

[hollow cobalt]

Of course