Archived threads in /sci/ - Science & Math - 1385. page

homework goes in >>>/hm/

OP here. I think infinity is infinite because that is just the way it is and why it exist. There are not multiple sizes of infinity just like there is only one GOD. Honestly, I'm not even sure if infinity exist. It could just be a made up concept. GOD on the other hand is not. I know for sure imaginary numbers are crap because they are imaginary. They wouldn't call them that otherwise. OP out. Just wanted some opinions.

>>8334272
That wasn't even funny. I'm not gay.

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>>8334251
>If you're so smart, woman, why do you have a X chromosome?

>>8334761
Holy shit you're bad at basic biology

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>>8334761
fyi men have a x chromosome too

>>8334236
What part do you not understand?
They just use the Euler's formula and substitute x by pi/2 and then raise both sides by i.

>>8334236
The problem lies within the question: How do you even define exponentiation of a general complex number? In the reals, you can easily define
[math] a^b := \exp(b \cdot \log(a)) [/math] for positive [math]a[/math] and arbitrary [math]b[/math]. The definition for general complex [math]a[/math] is a little involved, because the logarithm isn't uniquely defined if we allow complex numbers.
To see this in more detail, consider the basic example
[math]\exp(0) = 1 = \exp(2 \pi i) [/math]. We usually define [math]\log(1) = 0[/math], in line with the first equation here, but following this, [math]\log(1) = 2 \pi i[/math] would be equally sensible. It all comes down to choosing a sensible region, because we can't have multiple function values for the same argument, choosing a so called principal branch.
https://en.wikipedia.org/wiki/Principal_branch

So to come back to your original question:
Considering that [math] \exp( i \pi /2) = i [/math], we could choose our principal branch for the logarithm so that [math] \log(i) = i \pi/2 [/math]. Using our previous definition of complex exponentiation, we then find [math]i^i = \exp( i \cdot \log(i)) = \exp(i \cdot i \pi/2) = \exp(- \pi/2)[/math], which is a real number.
However, consider a different principal branch: For example, [math] \exp(i \pi/2 + 2 \pi i) = i [/math] is also completely viable, and would lead us to [math]i^i = \exp(- \pi/2 - 2 \pi)[/math], which is a different real number. And of course we could do this in infinitely many different ways, by adding different multiples of [math]2 \pi i[/math]. So our definition of complex exponentiation depends on the choice of branch, and thusly we won't have a well defined value of [math]i^i[/math] in general without any specification.

Let's see how broken my Tex is here now.

>>8334265
wrong
>>>/b/

>>8334201
>if we human were wired better for logical thinking, a smarter race so to say, would we be happier or off worse? discuss

Intelligence in the general population is bad for buisiness.

we are wired for logical thinking, people just lack the motivation to apply it

>>8334201
There are plenty of smart people that do awful things. We need more morality, not more intelligence.

The article is wrong in all possible ways.

The brain does store and retrieve memories.
It moves information around for processing and storage. Memories are processed and transformed before they're stored.

And you can find Beethoven’s 5th Symphony in the brain of some people, certainly including Beethoven.

The article is written by a psychologist that had his feelings hurt when the human psyche moved from some abstract concept to a more concrete model.
I'm sorry that he doesn't like it, but this is the reality.

>>8334199
>The model could help explain some parts of human intelligence but in the end it will always fail, for it's way too simplistic.

It's actually abstract enough to work.

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Not a peer-reviewed scientific journal?
Into the trash.
Why is /sci/ so fulled of /x/ and /pol/ these days?
At least when /his/ was here they avoided using fallacies.

Section 0(>>8266952) text: http://pastebin.com/50w9MYjD
Section 1 text(>>8282778): http://pastebin.com/fMdRzhTf
Section 2 text(>>8317513): http://pastebin.com/GfdvBDML

Definitions and notations: https://www.dropbox.com/s/ia4m7s0fy59z9jv
Axioms, Theorems, and other statements: https://www.dropbox.com/s/6ch0btu3adiz2ob

>muh axioms
into the trash

In Euclidean space dimensions 3 and higher, there are three relevant cases for two distinct lines:

-intersecting
-parallel
-skew(non-coplanar)

Axiom 3 doesn't have to deal with the skew case, so our task is to show how to correctly treat the skew case projectively. Recall that one of the arguments for the line at 'infinity' was continuity. If you 'nudge' a pair of parallel lines so they aren't skew, then they intersect at a point 'far away', which justifies the idea that they intersect 'at infinity'. On the other hand a 'nudge' to a pair of skew lines almost always keeps them skew. This suggests the correct way to handle projective 'skew' lines is to not let them meet.

This means Axiom 3 must be replaced by a statement like 'All coplanar lines meet.'. The problem with this statement as it is is that it make reference to a plane and thus the plane axioms. Since this is supposed to be a generalization of projective planes, this situation is not ideal.

To resolve this we look back at Euclidean space. Here three distinct points are always coplanar, but not so for four points. Thus, we would like our axiom to involve four distinct points. A way to ensure that the points are coplanar is to have the line through two of the points be coplanar to the line through the other two points. This then ensures all pairs of lines incident to two of the four points are coplanar.

That then suggests the following axiom in the projective case:

Axiom 3-(Veblen-Young axiom): Given 4 distinct points a, b, c, and d, if the line through a and b meets the line through c and d, then the line through a and c meets the line through b and d.

Using our point and line naming conventions, we can restate the axiom as follows:

'Given four distinct points a, b, c, and d, if [ab][cd] exists, so does [ac][bd].'

With the axioms now settled, we can define some important terms in the next post.

>>8334131
No, your idea dies with you because nobody will believe and/or fund you, unless you're very lucky.

>>8334143
Simple and true.

Unless you manage to acquire a freak grant that allows you to do whatever the fuck you want (e.g. Bill Gates believing in your 'vision'), you ALWAYS word your grant in such a way that you maximise the chances of success. This means that the funding call is already limiting what you can or can not do. Sure, there's always a bit of wiggle-room and most scientists like to invest a tiny portion of their money into their pet projects, but other than that - progress in tiny steps.

>>8334131
Your ideas are actually shitty, you just haven't thought about them enough.

>>8334080
Look it up, then swallow some rat poison.

>>8334080
I think you're a vegetable anon

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>>8334080
somebody's never eaten bark before

>>8333971
Gonna guess, you entered physics because of the money

Just switch to whatever you like, dumb frogposter

>>8333982
Why would he enter physics for money? If he wanted money he would enter something like petroleum engineering.

>>8333982
I chose to enter physics because I like it

Cant register bruh

>>8333833

Post pic for reason? I put rules but theres a chance I fucked it up.

The username must be >=6 characters, right?

HOW ABOUT YOU WRITE THAT BELOW THE REGISTRATION FORM?

Also, this is /sci/, not /g/

>>8333754
I have very good concept about research in my field but i have no idea who to talk to since everything is about knowing the right people which I dont.
I dont even know who to pander to lmao

>>8333758

Assuming you have graduated you should know how this works.

When I say pandering I'm talking about institutions, not individual people.

Do you not understand how funding works in STEM

>>8333766
>Do you not understand how funding works in STEM
No not really.
I know im retarded

read that one monologue from Hamlet

Who the fuck checks 4chan during a funeral?

>>8333751

What the fuck did you just fucking say about me, you little bitch? I’ll have you know I graduated top of my class in the Navy Seals, and I’ve been involved in numerous secret raids on Al-Quaeda, and I have over 300 confirmed kills. I am trained in gorilla warfare and I’m the top sniper in the entire US armed forces. You are nothing to me but just another target. I will wipe you the fuck out with precision the likes of which has never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of spies across the USA and your IP is being traced right now so you better prepare for the storm, maggot. The storm that wipes out the pathetic little thing you call your life. You’re fucking dead, kid. I can be anywhere, anytime, and I can kill you in over seven hundred ways, and that’s just with my bare hands. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Marine Corps and I will use it to its full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy retribution your little “clever” comment was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit fury all over you and you will drown in it. You’re fucking dead, kiddo.

>>8333698
Hard work, passion, it may not be enough for 4.0 but with 4/5 hours of work a day it will get better every day

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>>8333701
I've currently been doing pic related. I haven't seen drastic improvement I usually glide through questions no problem but get stuck for hours on one due to holes in my math foundation. I want to know how to fill in these holes but I don't know what I don't konw

>>8333698

old highschool maths teacher told me i'd never amount to anything

now i'm starting my post-grad thesis, and that bitch is fuckin' dead

Sure. You could get a few drops back into the reservoir by the time it empties completely.

>>8333588
Weeell... This is basically how the atmosphere works, so...

>>8333599
I assume he meant an isolated system. A reservoir that doesn't refill from groundwater.

>>8333574
>determinant of 3x2 matrix

Sounds like you failed.

>>8333580
oops was looking at the wrong matrix/question

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>>8333580