/sci/ - Science & Math

[Anonymous No.4643118]

Anything you find amazing, all subjects welcome. Pictures and facts encouraged.

[Anonymous No.4643124]

I'll go ahead and get the "It's amazing how much of a faggot OP is" over with.

[Anonymous No.4643146]

http://www.youtube.com/watch?v=9D05ej8u-gU

[Anonymous No.4643147]

God, peak oil, tulpas and qualia.

[Anonymous No.4643150]

[Anonymous No.4643158]

>>4643150

Just so damn original.

[Anonymous No.4643189]

Consciousness.

[Anonymous No.4643201]

>>4643146

>this

[Anonymous No.4643245]

bump

[Anonymous No.4643254]

The most incomprehensibly thing about the Universe is that is comprehensibly.

[Anonymous No.4643268]

i find it amazing that leftover shit from the formation of our solar system sometimes collides with earth and acts like a cosmic reset button. if life was reverted back to single celled organisms and another intelligent animal species evolved to our state of awareness in say a billion years - would there be any evidence of us? would oil deposits regenerate in that time?

[Anonymous No.4643269]

every time.

[Anonymous No.4643279]

>>4643254

English, motherfucker, etc.

[Anonymous No.4643289]

>>4643146
fuck lsd. all you need is a conscious mind and access to the right information to be in awe what we are and where we came from.

[Anonymous No.4643306]

[Anonymous No.4643310]

[Anonymous No.4643314]

[Anonymous No.4643329]

[Anonymous No.4643331]

[Anonymous No.4643340]

[Anonymous No.4643341]

>>4643289

But you should still try it anyway.

[Anonymous No.4643348]

[Anonymous No.4643363]

[Anonymous No.4643380]

It is absolutely amazing, there is no ultimate reason for physical reality's emergence, because it and causality are one in the same. A reason for reality existing would also be the cause of an ultimate cause. What use is logic here?

[Anonymous No.4643386]

>>4643146
i literally just finished watching ''in the shadow of the moon'', edgar mitchell, one of the astronauts said this (what degrasse says in that video) towards the end and it hit me.

we are the cosmos.

[Anonymous No.4643405]

>>4643386
We're the universe, perceiving itself from within.

[Anonymous No.4643804]

Even if I live to see the sun swallow the earth, see the milky way be smashed to bits by another galaxy. Even if I live long enough to see the universe grow cold and dark. Eventually the very proton I am made of will fade out of existence.

[Anonymous No.4643811]

>>4643804
I hope you live to learn correct grammar.

[Anonymous No.4643832]

>>4643380
what? What do you mean by that?
Are you talking about how the universe could have evolved to have any number of different realities with different physical laws and constants, and you find it amazing? Explain.

[Anonymous No.4643841]

>>4643269
My nigga Fibonacci and his pet phi

[Anonymous No.4643844]

>>4643832
Dude what
Reread the post. It's just applying logic to cause and effect.

[Anonymous No.4644767]

I can't into the math for quantum mechanics, but I find it to be fascinating. Even more so that because we can't see it, we make up math to describe what we can't see. Sometimes it is right, sometimes it is wrong. I always liked the idea that the universe could be infinitely small as it is big, then strings said they're the smallest, and then the 6-26 dimensions....its all just insane.

[Anonymous No.4644780]

It is well known that if you draw a loop on a 2-sphere - that is, the set of points in 3d space such that x^2+y^2+z^2 = 1, then the surface of the sphere will be split into do pieces that look like discs. (Basically, if you draw a loop, the inside will be a circle). The same is not true if you take it up a dimension. You can embed a 2-sphere into three dimensional space such that the 2-sphere does not enclose a ball.

Also, if you stir your cup of coffee, there will always be one point on the surface that isn't moving.

[Anonymous No.4644969]

i Still canit beleive that penies go into gineys and the willy shoots spermies and they swim to an egg but mmillions die and only one makes it and that you!

[Anonymous No.4644974]

The Mandelbrot set.

[Anonymous No.4644989]

The most amazing thing I can think of is how so many people are totally scientifically illiterate.

[Anonymous No.4644992]

>>4644969

Why did I laugh so fucking hard at that .gif and post

[Anonymous No.4645004]

Right now we have man made artifacts visiting moons of other worlds. At the same time we are controlling temperatures comparable to the sun on our own planet. I fucking love this new century of ours.

[Anonymous No.4645013]

tupac hologram

j/k

Technology does blow my mind though. Maybe because I'm someone with an interest in history and I'm always reading about, or watching something about life in the past. Then I end up realizing something like I have instant access to the vast majority of human knowledge, and I can carry out live conversations with somebody on the other side of the planet with absolute simplicity. I can even catch a routine jet flight and fly through the stratosphere to any location of the planet in less than 24 hours.

I think the future is going to amaze me even more. Artificial intelligence? Synthetic biology? Cybernetics, ubiquitous computers, etc. I know if I live through at least half of this century I'm going to get blown away.

[Anonymous No.4645027]

>>4643380
I'm not sure if I it's better to ask why, or how.

[Anonymous No.4645064]

Hoag's object, ring galaxy. Old yellow stars inside, young blue stars outside. Nothing inbetween.

What's cool? There's a ring galaxy that's visible through Hoag's object, in the background.

[Anonymous No.4645094]

>>4645004
>Right now we have man made artifacts visiting moons of other worlds. At the same time we are controlling temperatures comparable to the sun on our own planet. I fucking love this new century of ours.

I fucking hate you so much. You are the cancer than has killed everything. In 1000 years people like you will still be marveling at their navels.

[Anonymous No.4645097]

>>4643147
yeah fiction is fascinating

[Anonymous No.4645098]

>>4643254
but it doesnt make sense at all.

[Anonymous No.4645099]

<div class="math">1! + 2! + 3! + 4! + 5! = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17</div>
<div class="math">(1 + 2 + 3 + 4 + 5 + ... + n)^2 = 1^3 + 2^3 + 3^3 + ... + n^3</div>
<div class="math">e^{i\theta} = \cos{\theta} + i\sin{\theta}</div>

[Anonymous No.4645101]

>>4645094
Oh look, it's that guy who ruins every good thread with his fearful luddite crap.

Stand back bitches, I got this.

[Anonymous No.4645113]

>>4645094
What the fuck is this? What's wrong with acknowledging that we've accomplished some pretty cool shit?

[Anonymous No.4645221]

>>4645099

The latter two are interesting, but the first one is kind of dumb. It's just a stupid coincidence. The sum of factorials isn't generally a triangular number.

[Anonymous No.4645245]

<div class="math">\sum_{n=2}^{\infty}{1 \over n^2 - 1} = {3 \over 4}</div>
<div class="math">\sum_{n=1}^{\infty}{1 \over n^2} = {\pi ^2 \over 6}</div>
<div class="math">\sum_{n=1}^{\infty}{1 \over n^2 +1} = {\pi \over 2}-{1 \over 2}+{\pi \over e^{2 \pi} -1}</div>

[Anonymous No.4645334]

[None !!w5CHYddUvhS No.4645466]

>>4645245

You know what's even cooler (in my opinion)?

<span class="math">\int_0^{\infty}~\frac{sin^2(x)}{e^x}~dx=\frac{2}{5}[/spoiler]

<span class="math">\int_0^{infty}~\frac{cos^2(x)}{e^x}~dx=\frac{3}{5}[/spoiler]

[None !!w5CHYddUvhS No.4645470]

>>4645245
You know what's even cooler (in my opinion)?

<div class="math">\int_0^{\infty}~\frac{sin^2(x)}{e^x}~dx=\frac{2}{5}</div>

<div class="math">\int_0^{infty}~\frac{cos^2(x)}{e^x}~dx=\frac{3}{5}</div>

[None !!w5CHYddUvhS No.4645474]

>>4645245
You know what's even cooler (in my opinion)?

<div class="math">\int_0^{\infty}~\frac{sin^2(x)}{e^x}~dx=\frac{2}{5}</div>
<div class="math">\int_0^{\infty}~\frac{cos^2(x)}{e^x}~dx=\frac{3}{5}</div>

[Anonymous No.4645485]

<span class="math">\sum_{n=1}^\infty n = -\frac{1}{12}[/spoiler]

[None !!w5CHYddUvhS No.4645492]

>>4645474
Also, where G represents the Gauss constant....

<div class="math">Limit_{w\to\infty} \left(w-\int_1^w~\frac{1}{x^2}\left(1+x^4\right)^{1/2}~dx\right)=\frac{1}{\sqrt{2}G}</div>

[None !!w5CHYddUvhS No.4645495]

>>4645474
­Also, where G represents the Gauss constant....

<div class="math">Limit_{w\to\infty} \left(w-\int_1^w~\frac{1}{x^2}\left(1+x^4\right)^{1/2}~dx\right)=\frac{1}{\sqrt{2}G}</div>

[Anonymous No.4645499]

>>4645221
True. In fact that's the only non-trivial case for natural n. Proving it isn't too difficult either. I'm just fond of the number 17.

[Anonymous No.4645502]

>>4645495
>>4645495
>infinity-infinity >0
>not trolling

[None !!w5CHYddUvhS No.4645503]

>>4645495
Pic related.

(By the way, in case you're wondering why you should be shocked, that integral is the function for the arclength of <span class="math">\frac{1}{x}[/spoiler] from <span class="math">1[/spoiler] to <span class="math">w[/spoiler].)

[None !!w5CHYddUvhS No.4645510]

>>4645502
Learn to indeterminate forms, dumbass.

Also, more mindfuck in pic.

[None !!w5CHYddUvhS No.4645527]

>>4645499
>I'm just fond of the number 17.

I ascribe the alternate prime successors of 2 "good luck" and the alternate prime successors of 3 "bad luck". So 2, 5, 11, 17, and 23 are lucky; 3, 7, 13, and 19 are unlucky.

I know it's irrational of me. I don't know why I do it.

[None !!w5CHYddUvhS No.4645531]

Here's another mindfuck.

<div class="math">Limit_{n\to\infty} \left(\frac{d}{dn}~\left(n!\right)^{1/n}\right)=\frac{1}{e}</div>

[Anonymous No.4645537]

>>4645510
Oooh. I like this one.

[Anonymous No.4645541]

>>4645531
Well the first mindfuck I see is that you differentiated with respect to a discrete variable

You should have used the Gamma function

[Anonymous No.4645542]

I find this pretty amazing, OP.

http://www.youtube.com/watch?v=RGyOQR6mu2M

[None !!w5CHYddUvhS No.4645548]

>>4645531
Pic related.

[None !!w5CHYddUvhS No.4645550]

>>4645541
See >>4645548.

[Anonymous No.4645557]

http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

[Anonymous No.4645560]

>>4645548
I think it's more honest to show the relative difference between the functions.

[Anonymous No.4645565]

>>4645557
I don't understand why it is a paradox.

Isn't it the same problem than the graph of the characteristics function of the rational numbers.

[None !!w5CHYddUvhS No.4645578]

>>4645560
The relative difference is irrelevant if I'm merely trying to demonstrate that the slopes of the two functions approach identity.

My point is that factorials, while ordinarily representing fucking gigantic numbers, can instead be represented as a comprehensibly small number, taken to the power of the base of the factorial. Go ahead. Find <span class="math">\left(100!\right)^{1/100}[/spoiler]. It is a small and manageable number. Somewhere in the vicinity of 38, if I recall correctly.

[Anonymous No.4645584]

>>4645578
>The relative difference is irrelevant if I'm merely trying to demonstrate that the slopes of the two functions approach identity.

Then you ought to plot the relative difference between the derivatives, it's hard to make anything out of that other graph.

[None !!w5CHYddUvhS No.4645595]

>>4645584
>why not plot the derivative

Because this.

[Anonymous No.4645617]

>>4645578
well there's Stirling's formula, then.

<span class="math"> n! = \sqrt{2 \pi n} (\frac{n}{e})^{n}[/spoiler]

[Anonymous No.4645627]

>>4645595
If that's a problem for you, I don't think you understand the whole concept of using a computer algebra system.

[Anonymous No.4645633]

>>4645578
well there's Stirling's formula, then.

<span class="math"> n! \sim \sqrt{2 \pi n} (\frac{n}{e})^{n}[/spoiler]

[Order of Entemos !!04oa9mCAgoe No.4645636]

>>4643269
>cigarette paper
what?

[None !!w5CHYddUvhS No.4645644]

>>4645627
>If that's a problem for you, I don't think you understand the whole concept of using a computer algebra system.

The problem isn't doing it myself; the problem is that it's much, much quicker to just type in the goddamned functions and compare the obviously visibly similar slopes than it is to bother typing out the entire, grotesquely long slope function just to compare it to <span class="math">\frac{1}{e}[/spoiler].

[Anonymous No.4645645]

>>4645510

Thats neat, but I dont think they lie tangent do they?

http://www.wolframalpha.com/input/?i=arctag%282pi%29-Si%282pi%29

[Anonymous No.4645649]

Saturn's rings are only 10m thick.

>>4643269
It amazes me that viruses look like this.

[Anonymous No.4645652]

>>4645644
Did you see me writing all that out? No.

[Anonymous No.4645668]

>>4645645
No one said they were tangent at <span class="math"> 2 \pi [/spoiler] though

[None !!w5CHYddUvhS No.4645681]

>>4645649
>It amazes me that viruses look like this.

Is there as yet a working hypothesis on the origin of viruses? I've always wondered if perhaps viruses do not share a common ancestor with the rest of life on earth, either because abiogenesis occurred more than once, or because either we or the viruses or both arrived via meteorite from different origin worlds.

[Anonymous No.4645692]

>>4645681
viruses are not considered life, they are more like organic replicators

[Anonymous No.4645697]

Trig.

What's the first example of using trig in a practical environment? Measuring how tall a tree is without cutting it down. I know it's simple but still, there's something really amazing about it to me.

[Anonymous No.4645698]

>>4645649
>Are as little as 10m thick.
Many of the rings are much thicker.

[Anonymous No.4645700]

>>4645633
<span class="math"> n! = \sqrt{2 \pi n} (\frac{n}{e})^{n} + \frac{1}{12n} + o(\frac{1}{n^2})[/spoiler]

[Anonymous No.4645707]

http://www.youtube.com/watch?v=oLjEulT6ssM

[Anonymous No.4645708]

Fucken nerds.

[Anonymous No.4645711]

>>4645708
Nerds having sex ?!!
Where ??!!!

[Anonymous No.4645720]

>>4645681

Virology isn't something I study too much, but I was under the impression that viruses have DNA the same as our own--using ATGC for the base pairs. That would strongly imply that viruses do have a common origin with us, because for that to happen twice on one planet...I mean the odds are astronomical.

And yeah life may have been embedded by meteorites in the Earth's early history. It's not impossible.

[Anonymous No.4645744]

>>4645707
This one is easy, actually.

10 cards then 1st card then n random cards then 15-n random cards then 2nd card then m random cards then 15-m random cards then 3rd card then 9 cards.

which makes 10 cards - 1st card - 15 cards - 2nd card - 15 cards - 3rd card - 9 cards.

the placement is exactly the same, regardless of the way you cut the decks.

[Anonymous No.4645754]

>>4645744
Thank you.

[None !!w5CHYddUvhS No.4645932]

>>4645692
>viruses are not considered life

Fuck off, purist. Viruses are life.

[Anonymous No.4645940]

>>4645932

>Proposing vague definitons of life.

I seriously hope you don't do this.

[None !!w5CHYddUvhS No.4645956]

>>4645940
>I seriously hope you don't do this.

I have a simple, single-requisite definition of life.

"If we found it on Mars, would we call it life?"

[Anonymous No.4646070]

>>4645956
well if we found a autonomous homeostatic self-replicating physical entity on Mars, well yes we would call it life.

[Anonymous No.4646096]

you can cut a ball in a finite number of pieces, and arrange them to have 2 (full) perfect balls of the same size of the first

[Anonymous No.4646102]

>>4645474
cos^2+sin^2=1....
says sumthing about integral of 1/(e^x) from 0 to inf, dunnit?

[EK !EKFnQG0UBo No.4646104]

>>4646096

[Anonymous No.4646105]

>>4645485
>>4645485
ruawizard.jpg?

[Anonymous No.4646107]

>>4646105
Ramanujan is.

The definition of the sum isn't the same though, but still.

[SAGE No.4646109]

>>4646104

[EK !EKFnQG0UBo No.4646112]

>>4646109
aww, you took the time to make an image especially for me. how cute.

[Anonymous No.4646126]

>>4645485
what? the sum is clearly positive, and diverge to infinity

[Anonymous No.4646190]

>>4646096
axiom of choice fucks everything up. mfw

[Anonymous No.4646204]

>>4646126
That's only if the definition of the sum is the limit of the partial sum, which is not the case with Ramanujan.

[Anonymous No.4646225]

>>4646112

[Anonymous No.4646231]

Every goddamn time

[Anonymous No.4646242]

>>4645094
Please tell me more, you sound like an interesting person

[Anonymous No.4646264]

>>4646126
This is a trick, and not a particularly enlightening one. It is merely a changing of your definition of metric.

What is weird is that if you extend the function <span class="math">\sum n^{-s}[/spoiler] to the left of 1 you get the result that <span class="math">\sum^{\infty} 1=-1/2[/spoiler]

[Anonymous No.4646276]

>>4646264
Analytic continuation is your friend there.

[Anonymous No.4646281]

>>4646104
>>4646096
Can somebody explain how this is physically possible?

[Anonymous No.4646296]

>>4646281
Here's a quick half ass take on it:

Consider the closed interval [0, 1].

It has the same cardinality as the closed interval [0, 2] because we can pair each point from the first interval with a unique point of the second interval. Each x inside the interval [0, 1] can be paired with 2x inside the interval [0, 2]. Notice how the second interval is twice as large.

It's similar to that, cardinality and such.

[Anonymous No.4646298]

>You will live to see the technological singularity

[Anonymous No.4646312]

>>4646298
Don't things break down at singularities?

[Anonymous No.4646313]

>>4646281
Well it is not "physically" possible, just mathematically possible.

My guess is that seeing the physical volume as a Lebesgue integral is slightly flawed.

[Anonymous No.4646324]

>>4646313
I see.

[Anonymous No.4646343]

>>4646312
I'm not exactly sure. I am refering to the point where we create a machine that is smarter than a human. That machine will create a smarter machine and so on. We will see phenomenal exponential growth in AI up to Go like intelligence within our lifetime

[Anonymous No.4646370]

>>4646298
>Implying the energy trap won't put an end to that
Also pic related

[Anonymous No.4646374]

lots of people actually think like this and still survive long enough to breed

[Anonymous No.4646376]

>>4646370
>>4646298

[Anonymous No.4646427]

>>4646376
Meh. Something to dream of, and cool reading about it.

[Anonymous No.4646450]

>>4643289

this should be the /sci/ slogan

[Anonymous No.4646471]

>>4646450
I second that idea

[Anonymous No.4646509]

>>4646281
The ball on the left is solid and the ones on the right are hollow.

Geez guys I thought you were smart.

[Anonymous No.4646531]

I find consciousness to be utterly amazing.

[Anonymous No.4646548]

its funny, i go browse the other boards, get bored, and come back to threads like this. its like coming home. /sci/ people are awesome :D

on topic, this picture. I find it amazing that people can believe that we are the only intelligent life in the universe, when there are such an incredible amount of places out there. the size of it has never ceased to amaze me

[Anonymous No.4646596]

>>4646376
>Ignoring the third of the world without electricity
The funny thing about computers; not everyone in the world needs to use them for them to be influential.

Nerds who dream of singularity are under the impression that AI must be contained within a single computer. But the Brain is made out of a collection of interdependent cells, and we define thoughts by the cells that are active. Artificial intelligence would be the same way. It wouldn't be independent of human thoughts. It would be composed out of them instead.

In the past 30 years, we have witnessed a technological boom on a scale far beyond anything we have seen before. The World Wars have ended. Religion and Nationalism are slowly fading away. And birth rates are declining worldwide.

It's hard for me to dream about Singularity when I'm already living in one. Fuck what anyone else says, the world is an awesome place and it's only going to get better.