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/sci/ - Science & Math

 Name Options Subject Comment Verification 4chan Pass users can bypass this verification. [Learn More] [Login] File Please read the Rules and FAQ before posting.Use TeX with $tags for inline and [eqn] tags for block equations.Right-click equations to view the source.  08/21/20 New boards added: /vrpg/, /vmg/, /vst/ and /vm/ 05/04/17 New trial board added: /bant/ - International/Random 10/04/16 New board for 4chan Pass users: /vip/ - Very Important Posts [Hide] [Show All] ### Self-serve ads are available again! Check out our new advertising page here. [Catalog] [Archive] File: sciguide.jpg (9 KB, 200x140) 9 KB JPG https://sites.google.com/site/scienceandmathguide/ >> Reminder: /sci/ is for discussing topics pertaining to science and mathematics, not for helping you with your homework or helping you figure out your career path. If you want advice regarding college/university or your career path, go to /adv/ - Advice. If you want help with your homework, go to /wsr/ - Worksafe Requests. File: sol.png (19 KB, 1024x1024) 19 KB PNG Anyone else feeling like flexing their brains in a bit of fun? Take a puzzle leave a puzzle! >You drop a pin of length 'a' on the floor >Floor is made from parallel wooden planks of width 'b'. (just think parallel lines) What are the odds the pin will lie on two planks (cross a line)? 20 replies and 1 image omitted. Click here to view. >> File: Sc6S3NxWSx.png (17 KB, 300x250) 17 KB PNG One places nine beetles on a circular track, where the nine distances, measured in meters, between two consecutive beetles are the first nine prime numbers, 2,3,5,7,11,13,17,19 and 23. The order is arbitrary, and each number appears exactly once as a distance. At starting time, each beetle decides randomly whether she would go, traveling at a speed of 1 meter per minute, clockwise or counter-clockwise. When two beetles bump into each other, they immediately do "U-turn", i.e. reverse direction (like billiard balls). We assume that the size of the beetles is negligible. At the end of 50 minutes, after many collisions, one notices the distances between the new positions of the beetles. The nine distances are exactly as before, the first nine primes numbers! How to explain this miracle? >> >>12394147 It's doable, I swear. >> >>12394271 is the answer 24,901 mi? >> >>12394234 Primes are multi dimensional 1st order identities >> File: pic_related.png (96 KB, 1940x672) 96 KB PNG >>12393869 Well right now I only manage to make it work in cases where we know b>=a, if that is the case then what I did was, first parametrize the angle of the stick such that: [math]-\frac{\pi}{2}\leq \theta\leq\frac{\pi}{2}$
Notice now that the "length" of our stick can be calculated as follows:
$a\cos\theta$
Let's look at it from the perspective of the leftmost plank on which the stick lands. Then, the probability that our stick will ONLY be on that plank is:
$\frac{b-a\cos\theta}{b}$
We can make a little graph of this the x axis is gonna be our angle, refer to the first part of pic related. We are interested in the area outside the curve and such that y is less than 1, since we're looking for the probability the stick lands in two or more planks. We then divide this area by the total and we get our answer:
$\frac{2a}{\pi b}$

Now, if you look at the right part of pic related, this is what happens when b < a. As you can see, just calculating the integral raw as before is not gonna be enough, we're gonna have to start integrating from the point on which the curve starts being positive:
$\int _{\arccos \left(\frac{b}{a}\right)}^{\frac{\pi }{2}}\:\frac{b-acosx}{b}dx$
Notice that I'm only doing it in one half since the other is symmetrical. So if you calculate that and then from there calculate the shaded area, I think the answer is:
$\frac{2b\arccos \frac{b}{a} + 2a - 2\sqrt{a^{2}-b^{2}}}{\pi b}$
Tho I'm not sure since it looks pretty ugly and generally that's not a good sign, so hopefully some anon can give me a hand for the second half.

If you keep going in any one direction without consideration for how long it takes to get there what is at the edge?

No cop out answers that start with "you are like a...". "You are like a 2D person not able to visualize 3D, that's you trying to visualize 4D". Or the "You are like someone at the center of the North Pole asking how to go further North".
>No "you just loop around to where so started" answer without any proof.
>>
it goes on forever
you loop around
nothing
something different
a big fucking wall

probably one of of the above, nobody actually knows
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>>12394372
>it goes on forever
I think you have to say this....

>you loop around
Unless you discover some extreme mechanisms we don't have physics for(?) that can allow the universe to do this.
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>>12394372
>you loop around
I mean, for all we know it's like trying to find the edge of the earth, maybe there is no edge. Maybe like everything else in the universe, it's a big sphere.
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>>12394375
einstein's theory of gravity is that mechanism
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>>12394358
Probably more space

Hey guys. So what do you math guys think about the implications of high N density in the neighborhood of infinity, such that is suggests all numbers in the neighborhood are the same and prime?
Also on reals there are two neighbor hoods the positivities and negatives. Which is cool because signage is it's own dimension and that's awesome.
Also I've come to understand complex numbers as relating to negative length, meaning it points in a way that is abbreviate to reality. Or I like to say it points "away."
I've been working on some stuff with space, and I've been defining neighborhood of infinity on.
Though I was originally only working with natural numbers and negative naturals, or unnatural. As well as N*C X N graphs as well as it's unnatural inclusion.
I've also been thinking about the J set a lot. What are your thoughts on the J set? Also honorary known as the Hitomi set or the O"J" Cosby murder rape set.
Also a*x = x where x =/= 0. pretty cool right? I'm pretty sure the number in the neighborhood of infinity acts this way.
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>>12393763
Redpill me on the neighborhood of infinity. What is it?
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>>12394231
Is this what the mathematics of Gods looks like?
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>>12394231
Is this mathgen?
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>>12394231
Thanks god for procedurally generated autism

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Tropical Soyuz edition.

On sunday, a Soyuz launch from Kourou. Also, a Japanese launch of a H-IIA will take place that same day.

Also also: SN-8 hop soon.
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>>12394329
maybe NSF's calendar? https://forum.nasaspaceflight.com/index.php?action=calendar
All of my autism sensors are saturated by that place so their calendar may be more accurate and up to date
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>>12394337

That is because of ILS:

https://en.wikipedia.org/wiki/International_Launch_Services

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>>12394359
>exclusive rights to the worldwide sale of commercial Angara and Proton rocket launch services
>Lockheed-Martin
lel what
>>
That's it. I'm sick of all this "Super-dense methane" bullshit that's going on in the solar system right now. Hydrogen deserves much better than that. Much, much better than that.

I should know what I'm talking about. I myself commissioned genuine hydrogen in Florida for \$20,000 (that's about 2 jobs in Alabama) and have been practicing with it for almost 2 years now. I can even produce 7000kN of thrust with an engine.

Aerospace chemists spend years working on a single tank of hydrogen and crack it up to a million times to produce the finest fuel known to mankind.

Hydrogen is thrice as powerful as hydrocarbon fuels and thrice as forceful for that matter too. Anything propane can push; a hydrogen can push better. I'm pretty sure a hydrogen could easily lift a moon mission with a simple booster-sustainer rocket.

Ever wonder why space agencies never bothered using non-hydrogen fuels to go to the moon? That's right, they were too scared make the attempt using inferior fuels. Even during the Space Race, Soviet spies targeted the American engineers with the hydrogen knowledge first because their power was feared and respected.

So what am I saying? Hydrogen is simply the best fuel that the world has ever seen, and thus, require better stats in the solar system. Here is the stat block I propose for hydrogen:

(Upper Stage Exotic Fuel)
Thrust coefficient of 3
550s specific impulse
+2 to storage density
Counts as Masterwork

(Booster Stage Exotic Fuel)
Thrust coefficient of 4

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>>12394369
You glorious motherfucker.

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In 100 years there will be two types of people.
Those who leave earth to help colonize the galaxy
and those who stay on earth to live in VR dreamland.
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>>12392926
>post most obvious lazy cgi psyops since the moon landings
>has the balls to speak about fantasy land
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>>12393084
I don't believe you. And even if you're right we should try anyway.
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>>12394168
why do you think putting a big piece of metal in to space needs to be faked? You know the falcon heavy is capable of doing this without any trouble. Unless you think all rocketry is fake.
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>>12393015
Tell us how long in your opinion
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>>12394087
Based...

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I want to study number theory at a research level. I plan to start my studies with this book by HARDY. I'm just worried that my IQ of 130 will not be enough! I scored at the 95th percentile on the SAT but standardized tests vs research level math is a completely different beast. Where to even begin when completing your first proofs in even elementary number theory is a challenge compared to the rigorous nature of complex analysis, which is where I have a background. I just want to learn number theory to potentially tackle the Riemann hypothesis, since I have a load of complex analysis in my brain.
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>>12394226
Liquid IQ is a good starting point. You have a good engine. But if you don't drive anywhere it doesn't matter. Like having a muscle car for city commutes. You need to develop your experience to really tackle these concepts. Find out where people in the field today started and then read where they are at by developing a habit of reading published papers. Save the YouTube summaries for subjects you are not interested in.
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>>12394226
>130 IQ
That's 30 higher than you'd need for number theory. Just work hard! There's no smart people in number theory, only people willing to work hard and throw everything at a wall until something sticks.
What to expect from NT research: useless results that will force you to beg for money.
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>>12394233
Ramanujan's partition function is hot af
>>
I want to study double and triple integrals at a research level. I plan to start my studies with this book by LANG. I'm just worried that my IQ of 130 will not be enough!

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broken kidney -edition

We discuss research, DO NOT offer advice (just see your family physician), make fun of premeds and shitpost.

>inb4 not science
>>
Stop looking down on us you smug pieces of shit
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>>12394276
They go finger blast their nurses or teenaged assistants, they don't have time for your shit.
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>>12394305
What the fuck am I paying him for then?
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>>12392419
dont start studying until orientation lol
memorize pathoma and sketchy
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>>12394363
To finger blast his nurses and assistants. Fuck dude can't you read?

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Imagine choosing to major in something that was literally founded by an autistic faggot.
>>
Earlier thread said he was a super faggot, aka a nonce. Brave Norf FC lads took him down.
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>>12392803
To elaborate, most Brits say that faggotry was perfectly acceptable by the elite so Turing had no problem in that regard. However, he was supposedly a nonce which, unlike today where elites do it, back then it was frowned upon. He got a light sentence of being given drugs.
>>
It wasn't. Computing is much older than Turing, Babbage being the father of the computer itself and Kurt Gödel laying the foundations for theoretical computer science.
>>
He wasn't autistic, faggot
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>>12392801

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Before I go into the details of the debate itself, it's important to point out that scientific models aren't good or bad because they're "true" or "untrue", but because of how well they can describe or predict things.

In order to falsify if human race exists, we need to define what race is. While it'd require a lower standard of evidence to compare to other biological use of the term "race", "breed", or "variety", I'm going to use subspecies as a means of comparison to race because it's the most well defined of the aforementioned taxonomical ranks.

Because most work on human subspecies is ethically charged, here's a definition used by biologists in regard to subspecies of wolves (source: https://www.ncbi.nlm.nih.gov/books/NBK542546/):

1. shared phenotypical/morphological attribute(s);

2. genetic compatibility with the species (i.e. two subspecies can mate with each other);

3. partial restriction of gene flow (i.e. just because they can doesn't mean they do);

Starting off with the phenotypical requirement, it's well established by physical anthropologists that it's possible to separate human skeletons into three or four morphological "ancestries" (Negroid, Caucasoid, Mongoloid, and possibly Australoid). Besides that we obviously have skin colour, hair colour, hair texture, face shape, etc.

Because no one genuinely thinks modern human races are different species, I'm going to skip #2.

Humans most certainly have partially restricted gene flow. Even in relatively diverse parts of the world like the United States, you have pretty high population heterogeneity in regards to race: https://www.vox.com/2018/3/5/17080218/school-segregation-getting-worse-data and a rate of interracial pairings substantially below what we would find by random pairing (lookup: OkCupid data, Tinder data, interracial marriage rates).

By the standards of how we define subspecies in other animals, we have subspecies in humans.
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>>12394317
OP you're not saying anything revolutionary. Most genetic/anthropological researchers worth a damn believe there are different races. Most people with a brain do. The people that don't are brainwashed into not believing something that should be obvious and aren't worth arguing with. The reason that people of merit who do believe in race don't make public statements is because they like having jobs. We don't have free speech OP. I'm glad you have a scientific subject you've found some passion in though.
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>>12394324
>>12394317
Also don't use words like mongoloid and caucasoid, they're cringe and dated, scientists haven't used those words for centuries. Just say European, Caucasian, Asian, etc. most people will write you off as "racist" immediately if you start throwing around the word "negroid" even if you're using it in exactly the same way as you'd use the word "African." Just say African, it's not 1890.
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>>12394317
You would have to make an argument from a y chromosome / mDNA perspective. The phenotype that controls skin color expression can be made while having people belong to same haplogroup but different skin color. Fundamentally making the critical race theory utter nonsense since it focuses so much on phenotypes
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>>12394338
Even these are overly broad and do not account for migration patterns across regions

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Since math systems are axiom based, is it safe to say that "logic" is an axiom? If so, then the re are other mathematical systems that we can never understand since our brains work with logic.
That's not helpful, but if we allow such things, then we can actually call math truly right, bc it will envelop every axiom, and every method of linking those axioms.
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>>12390866
Yes, when setting up your mathematical foundation you also have to specify which underlying logic you'll be using. By default, if it isn't specified, first order logic is assumed.

I'd like to point out though that there's probably a difference between formal logics (like first order logic) and your idea of what it means to be logical.

A formal logic is just a set of rules to manipulate symbols. For example, I can decide that whenever I have the sequence of symbols "p or q" that I'm allowed to write the sequence of symbols "p" by itself.
A formal logic is just a set of rules of a game we call formal math.

There are many other logics like intuitionistic logic, modal logic, and even different fuzzy logics.

Which logic is the "real" logic (if any)? We're now entering philosophy.
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>>12390886
> no real barriers prevent anybody from creating their own set of mathematical rules and operators
Imagination by default compells you to the usage of rules of mathematics
You can say 2+2=5 but you cannot even imagine a real example of yourself breaking that rule
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>>12392033
Brainlets can imagine 2+2+1, but NOBODY can imagine 2+2=5
NOBODY.
You cannot break the rules of this Universe, period. You are made by them, you will conform to them. You WILL eat all axioms without bugs.
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>>12392034
This is the thing, we're actually not sure that 2+2=4, it's something that our way of thinking, u can call it logic, made us think so, that's why we're using axioms and that's pretty much the reason why I thought of this.
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>>12392016
Fantastic response, do you have any papers/textbooks/books you would recommend for more on the subject?

I was taught that they are not. This is starting so seem like bologna.
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>>12393207
>They are usually said to be not alive because they have no metabolism and can't reproduce by themselves.

that definition of life excludes a shit ton of parasites and also incels
>>
>>12392341
Our definition of life is a set of shitty guidelines. Viruses are just a form of life that is different from cellular life.
>>
Viruses are the Borg.
>>
It just depends on what you consider life, it is a container of RNA that can't reproduce on its own.
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>>12394128
>>12394134
This is what I think. If they dont metabolize how to they generate energy to move or preform RNA deposits?

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why is there only one "octave" for our perception of colours, unlike for sounds where there are multiple octaves.

Like why can't we see red but an octave higher like we can hear an A note but am octave higher?
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>>12394320
you just described brightness
>>
brightness is intensity you fuck

like sounds can be louder just like colours can be brighter, but that doesn't change there pitch
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Yeah I'm not sure OP.
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>>12394336
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>>12394351

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how come nobody gets influenza anymore?
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>>12394133
Uhhh, because everyone is social distancing. Also, COVID deaths are up because people aren't social distancing.
Yes, this must be it. If you think otherwise you're a right wing conspiracy racist.
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>>12394133
Coronavirus and influenza compete. These viruses usually ward each other off. This is one reason why I won't take a vaccine. My ancestory is well adapted to coronaviruses and having them is symbiotic.
See human coronavirus nl-63
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>>12394141
lol

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i live in a virus hotspot shithole (staten island). The cases are on their way to being what they were in april and nothing can stop it. America won't survive this winter.
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>>12394285
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>>12394106
Yeah yeah like last time right
The trend is actually logarithmic, the relative period rate of change approaches zero as cases increase
This makes sense intuitively as well if you take two seconds to think about how a virus spreads
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>>12394292
Your lack of reading comprehension skills has /pol/ written all over it. GTFO idiot brainlet.
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This guy was right afterall huh bros?