Is there even the slightest chance that at some point in history a white woman got knotted by a dire wolf

>>16893511
Given when and where they lived the answer is definitely no.

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if i have a scientific theory that i want to publish can i do it while being just a normal guy?
where to publish for people to care
how to check if something like my idea has already been published
how to format the thing i want to publish- any guides on that
etc.

>>16893860
You can. Anyone can submit to arxiv though you would have to follow the strict latex guidelines - https://info.arxiv.org/help/submit_tex.html - downloading existing papers or templates would be a good starting point.

For checking already published articles try using Google Scholar.

>>16893204
What are some other people like:
>Cumrun Vafa
https://www.physics.harvard.edu/people/facpages/vafa
>Semën S. Kutateladze
https://ncatlab.org/nlab/show/Sem%C3%ABn+S.+Kutateladze
>Dingding Dong
https://math.uchicago.edu/~may/REU2017/REUPapers/Dong.pdf
>Arjum Nigam
https://math.uchicago.edu/~may/REU2022/REUPapers/Nigam.pdf

Quote from Wikipedia: "Under string theory, strings are bundles of energy vibrating in complex ways in both the three familiar dimensions of space as well as in extra dimensions."

Simple question: is this a symptom of schizophrenia?

>>16893204
Is there any point in doing problems you can't check the answers for?

what's the best approach to learning AI/ML/DL in 2026? Should I do freecodecamp, codeacademy or Deeplearning.ai specialisations?

>>16894074
No, but your question might be.

>>16894074
So, basically, harmonic oscillators with extra steps? It seems more like a lack of imagination than schizophrenia (imagination led astray)
https://arxiv.org/pdf/2407.06856

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2/3 of the perimeter of the pentagon is visible. Is that too much? That's a rhetorical question.

>>16894278
Harmonic oscillations happen in something. String, gas or field. What the hell are "bundles of energy" and what's their vibration means? It's nonsense. If an equation looks like vibrations that doesn't mean you should postulate vibrations.

>>16894302
Things like the wiki quote are just dumbed down pop-sci answers, not detailed scientific explanations. If you want the latter go look elsewhere.

> Harmonic oscillations happen in something
In the theory "strings" are fundamental, in the same way you are taught in high school particles like electrons are thought to be. The energy strings have then comes from their modes of vibration just like any vibration you are familiar with has energy.

>>16894302
The point is, harmonic oscillations are a related physical phenomenon but harmonic oscillators are a formalism. Even if unispired, looking for new applications of the same old formalism may be naive but it is not schizophrenic. Your complaint seems to be about the word salad coming from taking said formalism at face value.
>>16894366
It seems that this is no different from the "luminiferous aether" word salad of 19th century electromagnetism

>>16894372
The aether wasn't a terrible idea, it was actually good science. Until then every type of wave scientists had encountered required a medium. When the newly discovered electromagnetism turned out to be a bunch of wave equations it wasn't a stupid assumption to believe there also had to be some unseen medium they moved in - the aether. It took breaking that mindset, and some experiments, to advance physics.

String theory has many problems, it could very well be wrong, but it's very different to how the concept of the aether arose.

>>16894409
>String theory has many problems, it could very well be wrong, but it's very different to how the concept of the aether arose.
The analogy with aether is not about string thery as whole, but about said dumbed down pop-sci talk of "bundles of energy vibrating", because something has to be vibrating, right? Just like every wave needs a medium. Even better, let's throw in a semantically overloaded word like "energy".

>>16894438
Actually vibration and energy are the most scientifically accurate and precise words in the whole description. Their use is no different to that of QM or QFT.

>>16894366
Thanks for the answer.
>just like any vibration you are familiar with has energy
The vibration I'm familiar with has constant or dissipating energy, energy is not the thing that vibrates, that's why it's frustrating. I'm bachelor in biomech.

Electrons... they feel kinda fundamental because they match fundamental math idea of a point. Even if electron somehow consists of other particles, they better to be points. There's nothing less than a point.

>>16894806
Unfortunately, even if points make the math simple and and easy, they can't physically be true. If electrons really were zero-volume points they would have infinite mass and charge densities. That's simply not possible.

What is the purpose of the Neutrino? It travels at the sped of light, but there are claims it has mass which cannot be true if it travels at c. Or, is the rest mass so small it can actually travel at c? Is it just excess energy and not actually a particle?

>>16895250
Our best understanding is that neutrinos have a very very tiny but nonzero mass, and that they "travel at c" simply because we have no detector sensitive enough to pick up on the difference.

>>16895250
The neutrino masses as so small that they 'effectively' travel at the speed of light (but NOT at c). The difference is so tiny that a neutrino coming from another galaxy millions of light-years away would only be delayed compared to a photon by a few seconds, if that.

>>16895263
>"travel at c"
>>16895323
>'effectively' travel at the speed of light
If time slows as velocity approaches c, from the nuetrino's perspective how does it have time to interact with anything since it essentially is emitted and travels across the universe instantly?

>>16893204
Why doesn't science acknowledge the biological reality of race when there are numerous genetic distinctions/adaptations that every race has?
How many more distinctions need to exist before they recognize that we are clearly not all the same?

>>16895851
>Why doesn't science acknowledge the biological reality of race
Race, and species, but politics has overridden science and deformed it to not hurt people's feelings. How do you tell the retarded race they are a subspecies?

>>16895843
Interactions are about position, not time. They aren't affected by time dilation. However scattering cross sections are dependant on energy and that dependency can be complicated, so in that regard the likelihood of a particular interaction does depend on kinetic energy (velocity).

>>16895851
> Why doesn't science acknowledge the biological reality of race
Because there is no scientific way to rigorously define some biological category and label it as race. It's a purely social construction.

can the fastest cameras that take a photos of light be used to gain additional info about the double slit experiment and quantum eraser version?

>>16895070
>infinite mass and charge densities
We could ignore this

>>16895920
No. It doesn't matter how fast your camera is, it's still a measurement and any measurement collapses the wavefunction and removes any uncertainty in the location of the particle.

>>16895895
The retarded race wouldn't exist if it didn't have some strength in it. Race reality doesn't entail superiority necesarrily, people should at least acknowledge different climate based strengths.

>>16895906
Except there are distinctions like:
>Muscle Structure
>Bone mineralization
>Skeletal Structure
>Skull shape
>Temperature regulation
>Temperature sensitivity
>Melanin content
>Pore size
>Fat distribution
>Cellular adaptations such as Europeans Mitochondria producing more Heat.
>Hair color, eye color, facial structure
>Nose shape/size differences following Thomson's Nose Rule
And the list goes on. So how are you going to say:
>there is no scientific way to rigorously define some biological category and label it as race.
When there are very clear distinctions between Europeans, Asians, Blacks, and every group in between?

Around how many different axis is it possible for an object to spin simultaneously?

>>16896153
Of course there are differences but then how do you use them to define a 'race' without using some ad-hoc or subjective rules?

>>16896153
You listed about 10 physical characteristics which were correlated with geographic location. Now pick any other arbitrary list of 10 characteristics and define races using those characteristics. This new racial classification will look nothing like your original classification.

What is an effective way to find a recipe/synthesis for LSD?

>>16896159
3. And there cool way to name them: rotation, precession and nutation.

>>16896185
Ask FBI

I once read about a book online that teaches how math should be done. It wasn't about something specific like calculus.
I think it lets the student find its own formulas to solve the problem and the solutions were open.
Does anyone know the name of the book?
Thanks

>>16896166
You don't use any kind of subjective rule, it's simply acknowledging that people who have lived in a particular climate for hundreds if not thousands of generations are generally better suited for that climate, thus making them a distinct race, with a distinct subset of traits.
More obviously, look are somebody with Blonde Hair and Blue eyes, you would clearly acknowledge that they descend from Nordics, provided they're not mixed.

>>16896170
Why would I pick arbitrary characteristics? These traits are generally persistent in racial groups, and they are so numerous it isn't even a matter of debate.
Clearly somebody with less melanin isn't going to do well in a hot climate, how is this not obvious? There is no obfuscating the fact that we are genetically acclimatized for certain climates, and if your argument is that "Mixed People Exist," you'd have to acknowledge that they aren't acclimatized to any one particular argument, because they have disparate genetic adaptations.

>>16896205
he said "simultaneously"
>>16896159
In three dimensions: One. Rotating around multiple axes at once is going to be equivalent to rotating around another individual axis. See Euler's rotation theorem.

what is the largest particle/atom that can be used in the double slit experiment, and how does particle size affect wave-particle properties, and if a particle is large enough can it me monitored with a photon without altering the outcome?

>>16896364
There is no limit and the particle size doesn't affect the wave-particle properties. However it does affect the angle of diffraction. The interference pattern depends on the distance between the slits and the detector, the width of the slits, and the de Broglie wavelength of the particle, molecule, buckyballs, whatever. The tl;dr is that it's easier to perform the experiment and see the interference with small, single particles.

I keep thinking about creep. How it never stops. But surely it must stop eventually, right? Gravity is a constant load but atoms will run out of places to move. Assuming proton decay isn't a thing, won't the earth eventually become a sub-atomically perfect sphere of iron? Then it won't creep anymore from gravity. My question then is what happens then when you place a cube of lead onto this perfect iron sphere. It's softer than the iron so gravity means it will slowly collapse until the cube has become a 1 atom thick layer coating on the sphere, right? But will the atoms distribute in a perfectly uniform distance from eachother or will it be like a splotch on one part of the sphere which introduces new forces onto the once perfect sphere making the entire thing shift around slowly until it evens out again... idk, this is a stupid thing to post. Just musing.

>>16896403
It the inter-atomic bonds are stronger than any other forces acting on them then no, there will never be any creep no matter how long you wait. That is almost the definition of what a solid is. You also have to realise that electromagnetism is *way* stronger than gravity. It's why a small magnet can lift objects despite the gravitational force of the entire planet.

Is there a rate limit at which particle interactions can occurr - two particles are moving past each other too fast, even if very close, to have any interaction (as depicted on a feyman diagram). What the speed/rate of the gluon interactions, or does that question make any sense? I think 'science communicators' have filled the space with inaccurate gibberish and everywhere I look I see incorrect info.

>>16896339
>These traits are generally persistent in racial groups
"These traits are generaly persistent in groups which I've defined using these traits"
Okay, and others can define groups based on other traits, so it's obviously a social construct.
>somebody with less melanin isn't going to do well in a hot climate, how is this not obvious?
How is it relevant? Another trait you mentioned is eye and hair color, which are obviously not important to survival in humans.

Do we have any scientific evidence of gods or souls existing?

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>>16894297
sin(π/5) of the pentagon's perimeter is visible.
Is that enough?
An AI assistant wrote, that it's the minimum.

>>16896515
None. And no scientific mechanism they could or should exist.

>>16896420
Why does creep cause objects to permanently deformed at under half their yield strength and melting temperatures tho

>>16896630
It depends on the specific material you are talking about and it's purity. There are lots of mechanisms for "creep", it's not a simple process. For example if something is full of grains and dislocations those inter-region bonds are weaker and can break under stress from say temperature changes, especially in materials with lower melting points (i.e lead) - thermodynamics after all does state that statistically speaking there will randomly be a few particles with enough kinetic energy to affect weaker bonds.

>>16893204
String theory is literally just math with extra flair. Could I get into string theory research with ease as a pure mathematician?

>>16896642
It's an extremely mathematical field so if that's your strength it will absolutely help in topics like AdS/CFT correspondence, but in the end you still need to a good grasp of the physics you're trying to create a theory for. However, getting into ST right now might not be a smart idea. Depending on who you ask, ST is either a dying field of research - there's still plenty of people working on it but not as many as there once was - or one that needs to move in new directions since the work of the last several decades hasn't led to anything testable or a eureka moment that says "yup, this theory is correct and how the universe works." For example AdS and supersymmetry and extra dimensions are the only way the math of ST works, unfortunately all we have ever seen in our 3D universe is dS and no supersymmetry.

>>16896153
>very clear distinctions between Europeans, Asians, Blacks
>and every group in between
Then those "groups in between" are the biological reality, while race is not.

>>16896721
Those groups in between are the product of historical examples of mixing in the past between the preestablished racially homogenized group, which once faced with their own selection pressures form their own unique subset of people who are acclimatized to their particular environment.

>>16896511
>Okay, and others can define groups based on other traits, so it's obviously a social construct.
Your argument is absurd, we could use this same line of reasoning to deconstruct everything:
>"A bird has wings and eyes, which you've arbitrarily selected to make your argument, therefor it's impossible for birds or dogs to be different from one another, Animals are all a social construct.
>How is it relevant?
Because we are defining the traits of a particular thing. A dog does not have wings, because it is a dog, not a bird. A White person has less melanin, because a White person is not a Black person (among other signifiers).
>not important to survival in humans.
Well if civilization is important to humans, then clearly the homogenization of external features would hold weight for their survival. Society does not function as well from disparate values, the more people have in common, especially on a surface level, the stronger their sense of identity will be. Conversely a society where nobody looks like one another is going to be less trusting, and have a less stable sense of its own identity, hence every historical and modern example to date.

>>16896806
> the homogenization of external features would hold weight for their survival.
I think that statement needs something called proof.

Double pendulum system requires 4 variables (2 angles and 2 angular momentum).
Are there any chaotic systems with less variables/less dimensional phase space?

>>16896830
Double pendulum or 3-Bodies are almost always the examples given. The simplest mathematical system I can think of that is chaotic would be the logistic map. I'm not sure there is a physical equivalent.

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I'm terrible with coordinates. How far away are the two little red X's from each other? I guesstimate something like ~4,500 miles but want to know if I'm correct.

>>16896825
Infants begin to show preferential treatment for same-race faces over other-race faces by approximately 3 months of age
>https://pmc.ncbi.nlm.nih.gov/articles/PMC7349221/
It's no secret, if you study history Multi-Ethnic and Multi-cultural societies are not typically healthy or functional, not as long lasting as ethnically homogenized cultures. The examples are so numerous: Rome, Greece, Babylon, etc.
People trust somebody who looks like them more then somebody who doesn't share their physical features, there are a lot of studies on this, most try to falsely attribute it to socio economics and exposure to other faces, but the fact that this pattern even exists in the first place suggests a preference for ones own racial group. I'll try to find some more later when I got time, busy rn.
>https://www.nature.com/articles/s41599-022-01248-8

The the sequence 1, 2, 3, 4... increases linearly, how do you describe the sequence 1, 1/2, 1/3, 1/4... ? Does it decrease inversely linearly? Logarithmically? What is the correct word to describe the decreasing property of the sequence?

Got a simple question about genetics and relatedness
If you take a mouse from a litter lets call L1 and backbreed it to its own dam to create a 2nd litter we'll call L2, then how closely related is one of the other L1 littermates to this new L2 litter?
The sire from L1 would be 75% related to L2 so I thought maybe 62.5% as a halfway point?

>>16896901
I would call it harmonic decay but there is probably some better term for this.

Question on ftm:
I know its not healthy, but what are changes on the body, on personality and overall life expectancy if a female decides to troon?

>>16896950
Hormonal imbalance quite literally affects every part of your body, your mood regulation, your organs, even your cellular health, cognition, literally everything is thrown out of wack when you introduce hormones that set you out of natural sex based balance.
It's different for men who take testosterone because their bodies are already conditioned for testosterone, though I'd argue steroids aren't healthy just because they're unnatural and it's a lot harder to keep your body in balance.
It will fuck you up for life.

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>>16896901
It's decreasing hyperbolically.
Don't you know anything?

>>16896806
Clearly, nothing in what I said implies that dogs are birds. In taxonomy, what is not a construct is the existence of animals and their ancestries. The classification into different species is done to reflect facts about animal ancestries. These facts constrain the classifications into species but cannot uniquely determine them so there are still lots of free choices involved in defining species. In that sense, it is a construct but unlike 'race' it is done by zoologists, etc. rather than laypeople who are afraid of other skin colors. All of this, except perhaps the last sentence, should be obvious.
>Society does not function as well from disparate values [...]
All of this pseudoscientific pop-sociology is really irrelevant to the fact that having certain eye and hair colors is unimportant for the survival of humans in certain climates.

I've been going through Gensler's Intro to Logic and everything has been fine, no real difficulties. Now I'm on chapter 9 in the section on identity proofs and it feels like the first time in the book where he just doesn't explain anything nearly enough, provides barely any examples before giving problem sets, and to make matters worse, I believe there's an incorrect answer given in the solutions manual (only the second one I've found so far) but I can't confirm this and I haven't seen any info elsewhere online about errata in the manual. I had no problem with the LogiCola problems assigned for this set either, which seemed more complex but at least I felt prepared for them. Am I suddenly retarded or has he shit the bed in this section? Can anyone suggest another book I could look at to get a better explanation of this topic (identity proofs)?

An even function is a function f(x) = f(-x)
An odd function is a function g(x) = -g(-x)
But why are they called even and odd? I keep forgetting which is which.

>>16897253
Assuming the function is always raising or falling, for every element of codomain(result value), even function has even number of possible inputs and odd functions have odd number of possible inputs. Or in other words, if you draw a horizontal line on the function graph, even function will intersect if even number of times, vice versa.

>>16897260
For periodic functions this assumes a function plot of an integer number of periods, right?

>>16897265
No. I just made up that definition of the fly and it does not hold under any scrutiny.
Don't think too hard on this, it's just the rough idea.
Another thing you can do to memorize them is to consider f(x)=x^n. For even powers you are going to get even functions and for odd powers you get odd functions.

>>16897253
Even functions have only even terms in their power series expansion, and likewise for odd ones. At least, for infinitely-differentiable ones, with the terms being generalised to their current definition
At least, that's what I was taught

>>16897271
*even exponents for terms in their power series expansion, obv

What would be a fast and easily digested explanation or at least motivation (non-Grothendieck like) for motifs in algebraic geometry, more precisely for varieties concering quadratic forms over fields?
This subject really seems more like hieroglyphs to me the more I get into it and I am in such a deep shit that my thesis has become this topic, lol.
People, please do not go into algebra if you are not completely living this with every fiber of your being...

>>16897271
>>16897272
Thanks

>>16897173
>Clearly, nothing in what I said implies that dogs are birds.
Right, so clearly you didn't understand the rationality behind what I was saying.
>laypeople who are afraid of other skin colors.
Who said anything about fear?
The fact is, there are clear biological distinctions between different races of people, beyond simple skin tone even, distinctions of which you ignore in order to make your claims more tenable. There are very clearly Europeans, Africans, Asians, Easterners, etc, regardless of the semantics of the issue, there are clear distinctions, these distinctions don't disappear just because you don't want to acknowledge them.
We apply distinction to all things, that is the purpose of zoology, I'm simply stating that we can easily extend those definitions into different classifications, who despite sharing basic similarities, possess numerous climate based adaptations. Ignoring this fact shows that you're the one who is afraid, perhaps of reality.
>unimportant for the survival of humans in certain climates.
If a society is relevant to the survival of humans, then yes, being surrounded by people that look like you is important for society, and by extension survival.
Show me an example of a successful multi-cultural society, I'll wait.

Can someone please make an idiot's guide to: slit plane, branches, branch point, branch cut, principal branch. I've just started my complex analytics course and these aforementioned things are all Chinese to me after finishing the first chapter

>>16897354
>so clearly you didn't understand the rationality behind what I was saying.
No, I just dismantled the caricature you put up.
>Who said anything about fear?
You said people are afraid to trust those who don't look like them, right?
>these distinctions don't disappear
Haven't we already gone through this already? The distinctions you draw depend on the traits you choose for making those distinctions. You choose to make distinctions based around skin color, others are free to choose different traits.
> possess numerous climate based adaptations
So far, the only trait that you mentioned which is clearly adapted to the 'climate' is skin color, and you've repeatedly failed to explain how eye and hair color are adaptations to the climate rather than just byproducts of different melanin levels.
>Show me an example of a successful multi-cultural society, I'll wait.
Most societies which have existed are 'multicultural' unless they were isolated from the rest of the world. Also, evolutionarily speaking, natural selection can't work if there's no variation and sexual reproduction guarantees that there will always be significant variations, so your idea that societies can be homogeneous is just a fantasy.

>>16897377
>slit plane
a restricted domain where the inverse function
is defined and contains branch points and cuts

>branch
a choice of plane to select the value of the function
[think: [math] \sqrt{x} [/math] has 2 answers, one per branch]

>branch point
a point where the function is undefined and is
attached to the branch cut

>branch cut (aka slit)
a line on the plane where all branches are
separated from (crossing it leads to next
branch up/down); function assumes a single
value ONLY when evaluated on branch cut
pertaining to a particular branch

>principal branch
the "default" branch to get values of a function
(or, where k=0 on a multivalued function)
[think: principal branch of [math] \sqrt{x} [/math] is usually the positive]

Let [math]a,b \in \mathbb{N}_{>0}[/math] and let [math]X,Y[/math] be two independent integer valued random variables.
[math]X[/math] takes an uniformly random value from [math]\{1,2,..,a\}[/math] and [math]Y[/math] takes an uniformly random value from [math]\{1,2,..,b\}[/math].
What is [math]P(X \geq Y)[/math]?

>>16896350
Imagine you have straw, and the straw is spinning like a helicopter blade. Then, it you're also turning it simultaneously around the axis that goes though the straw. How is that rotating around just one axis?

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I just found a question on the internet which was asking which triangle has the maximum surface area for constant perimeter.

Of course the obvious answer is an equilateral triangle (proof by being obvious) but it made me wonder the following. What if you used the Heron's formula, and then you made a four-dimensional graph (since it has three variables instead of one, the graph is 4D) and then you found the maximum just like you would find a maximum by using derivatives for a normal 2D graph. Could you solve the problem in this way (it's probably not the easiest way but that's besides the point) and how would it work?

Or to simplify my question: is working with derivatives possible in higher dimensional graphs or multivariable graphs like that in the same sort of way as you would normally work with them?

should I put acetone in my lighter to get a better/bigger/cooler looking flame or is this stupid?

>>16896938
I thought on this a little more, but if the L1s share 50% with their dam and 50% with their brother then would the L1 littermates be 50% related to the L2 litter? 25% from their shared dam as they're half sibs, then 25% for the niece/nephew, which implies they're only the equivalent of littermates while I thought the increased homozygosity from the inbreeding would somehow bump up the relatedness to maybe 62.5%.

I don't know how to properly calculate this.

>>16897426
>No, I just dismantled the caricature you put up.
You played a semantic game to reject terms and definitions, reconstructing reality, and then claiming victory despite never confronting the essence of what the conversation is about.
>You said people are afraid to trust those who don't look like them
I said people generally trust those who look like them more then those who don't, that doesn't necessitate the notion of fear, but a greater degree of trust then would otherwise be had.
>others are free to choose different traits.
So then I can choose to acknowledge bones and tendons are all that is necessary to create a bird, and thus dogs become birds simply because I dismiss all the other traits that differentiate them? The issue is not a matter of subjective classification, there are clear genetic distinctions between races, just as there are different kinds of dogs, and different kinds of birds, so would you say that separating a Blue Jay from a Cardinal is a subjective classification, or do you acknowledge that there are objective differences between the two?
>So far, the only trait that you mentioned which is clearly adapted to the 'climate' is skin color,
See >>16896153, Thomson's Nose Rule, Cellular adaptations, diet adaptions (Differences in Oral and Gut Microbiome), I have listed many differences already, and I can continue to list even more if it would satisfy you. There are numerous climate based adaptations.
Melanin content is a climate adaptation, hair and eye color are reflective of melanin content, thus they are one of the ways to signify the environment for which a person is adapted to genetically. Outside populations who have blonde hair is typically due to race mixing in the past.

>>16897426
>>16897783
>Most societies which have existed are 'multicultural'
Demonstrably false, we would not have the genetic variation we have if not for thousands of years of isolation and homogeneity, distinct traits would not have emerged. Also, Genetic Diversity already exists in every environment, too much genetic diversity results in a population who is not acclimatized to their environment, hence Outbreeding Depression.
You don't know what genetic diversity means.
Humans have existed homogeneously throughout all of human history, but you will try and dismiss this reality by deconstructing it
>Well what is race? Is race even real? I don't see race. None of those distinctions matter. Sure we can clearly see what region a non-mixed individual comes from from the traits they possess, but that doesn't mean anything, it's arbitrary, and you're delusional if you think otherwise.
>natural selection can't work if there's no variation and sexual reproduction
Selection pressure means that some traits are favored for their environments more than others, variation already exists even in a small population, as following the 50/500 rule you only need 500 people to avoid genetic recession, so clearly a large degree of genetic mixing from populations on entirely different corners of the world isn't necesarry, nor does it result in bettr health outcomes.
You may then try to cite hybrid vigor, a contradiction in itself as how could hybrid have greater vigor if we are all the same in the first place? Yet Hybrid Vigor only applies to immunological advantages to F1 hybrids (First Generation) which quickly dissipates in all subsequent generations.
Most studies on race are prefaced by saying they lack most the data they need, because the research is being gatekept. So I ask again, if all these traits and distinctions occur, why does science refuse to ask this question, why does it refuse to do the research?
You're illiterate, and it shows.

>>16897679
It's not one of your standard axes, but it is a single axis nonetheless.
The actual mathematics get kind of ugly here, and, more importantly, writing matrices in LaTeX is a pain in the ass and I don't want to do it.
So to provide an example based on yours, let's say I rotate the straw about the Z-axis by 90 degrees and then about the X-axis by 90 degrees. I'm picking those numbers and making them completely discrete because it makes the calculations work out much easier. You can imagine the same principles applied to smaller and smaller movements until you're looking at something virtually continuous, should you feel so inclined.
Using the relevant yaw and roll matrices (not typing them up here because, again, matrices in LaTeX are a pain), we take their product and calculate its λ=1 eigenvector to find it is [math]1,-1,1[/math]; that would be the axis of such a combined rotation.

>>16897725
Look up lagrange multipliers. This is a problem you can learn to do in hs.

>>16897757
acetone dissolves many plastics and rubbers. If you try it, tell us how it went, id be curious

>>16897647
draw a graph and literally count them

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>>16897725
Well, we obviously can't picture graphs in higher
dimensions in a convenient way (unless we use
colors or something), but yes indeed we can take
multivariable derivatives of the function and classify
certain points to highlight features of that function
(max, min, saddle point, etc...). Pic related is a 3D
sphere with colors representing temperature as the
fourth dimension as an example.

Video I found that does an example problem without graphs:
https://www.youtube.com/watch?v=z1pjNmjldwM

So, you can take Heron's formula and apply it to
part of the surface residing in the first octant (+,+,+).
The constraint of constant perimeter are all possible
triangles as points forming the surface. The colors
forming a heatmap on the surface getting red at the
point of max surface area. Hopefully, you'll see that
it should match your answer.

>>16897783
>and thus dogs become birds
See >>16897173. Your inability to understand simple facts about how classifications are made is striking.
>Thomson's Nose Rule
No evidence of being an environmental adaptation.
>Cellular adaptations, diet adaptions
Too vague to respond to.
>hair and eye color are reflective of melanin content
So, as I mentioned already, they are not adaptations but accidental byproducts to the actual adaptation which is melanin. You can have mutations for producing light skin with brown eyes and not face any environmental selection pressure.
>I can continue to list even more if it would satisfy you.
What would satisfy me is if you learnt some critical thinking and stopped making fallacious generalizations which are unsupported by any data.
>Demonstrably false
>too much genetic diversity results
>a large degree of genetic mixing
Of course you fail to demonstrate that in any sense because there is no way you can quantify what amount of genetic variation is healthy and what amount isn't. This means your entire worldview is built on vibes-based reasoning, just like the concept of 'race'.
>why does it refuse to do the research?
The research has already demonstrated that the concept of race is pseudoscientific for all the reasons discussed already. This is my last response to you.

>>16897874
>Your inability to understand simple facts about how classifications are made is striking.
You're basically just saying that classification only exists if it complies with your arbitrary guidelines of how things can be classified, all other forms of classification are non-existent to you simply because you refuse to acknowledge it. Object reality holds no weight against you.
>No evidence of being an environmental adaptation.
Okay, so there is no reason whatsoever that people in northern climates have thinner noses, and people in warmer climates have wider noses. Cool story bro.
>Too vague to respond to.
Since you can't fucking read: Europeans and other northern races have a cellular adaptations that allows their Mitochondria to produce more Heat as opposed to energy, allowing them to handle colder climates easier.
>accidental byproducts
You're a fucking moron, they obviously faces selection pressure for lower melanin content because they were living in a climate that favored lighter complexions for sunlight absorption, jesus fucking christ dude. The fact that this variation exists whatsoever is enough to create some kind of classification, so you're just blatantly wrong about your claims.
>can quantify what amount of genetic variation is healthy and what amount isn't
There is actually
>can quantify what amount of genetic variation is healthy and what amount isn't
>https://pubmed.ncbi.nlm.nih.gov/18258915/
There is, 4th and 5th cousins have the best fertility outcomes, and allows them to retain their optimal stronger adaptations. Iceland faced a lot of selection pressure. Once again, you're projecting onto me that my reasoning is emotional when you have absolutely zero reason to believe as you do, and instead of confronting your cognitive dissonance, you're just redefining things to avoid reality.
>This is my last response to you.
Good, you're illiterate and I hope somebody more intelligent will reply.

>>16896806
>A dog does not have wings, because it is a dog, not a bird. A White person has less melanin, because a White person is not a Black person (among other signifiers).
If you try to reproduce a dog with a bird you'll fail. If you reproduce a white and a black person you'll get fertile offspring. Humans are a single race/species but many different breeds, like dogs and cats are

>>16897795
My lighter is made of metal and has no plastic or rubber parts

>>16897995
You can reproduce different breeds of Dog together, that doesn't make it right. Even amongst dogs they have numerous traits that make them better suited for different tasks, though after 100 years of selective breeding, we have created modern mutts who: Have more organ and heart related problems, have issues with hip dysplasia, nasal cavity deformity, lower intelligence, lower life spans, etc.
Your argument is a platitude without sufficient justification.
>If you reproduce a white and a black person you'll get fertile offspring.
Less fertile then monoracial couples, there is plenty of literature supporting this.

>>16898185
> You can reproduce different breeds of Dog together, that doesn't make it right.
Hahahahahahahaha. Wtf am I reading. Have /pol/tars become so brainwashed they have now moved onto canine purity?

>>16898204
you can breed a chihuahua with a great dane.
should you?

>>16897995
>are a single race/species
A race is not the same as a species it's at most a subspecies.
and mixed race couples do have lower fertility rates

>>16898204
Have you never owned a mutt? They have so many health problems dude, everyone in my family who has owned a mutt, 90% of them die early, or have some massive heart failure.
I understand it's easier for you to belittle the conversation, but seriously consider the reality of the discussion. Your cognitive dissoance should not own you, you should be able to engage in an informative discussion.
At the least, people of your mentality not being able to handle a genuine conversation without typing shit like
>Hahahahahahahaha.
Just kind of shows why more and more people are becoming racialists, because at least the racialists can articulate their points, you just say
>Oh, you don't agree with the scientific consensus? I don't even need to debate you, lmao

>>16898223
Racialist? Is that a subspecies of racists which is more mentally retarded than the usual racist?

>>16898441
People who believe that Race Exists, y'know, people who trust the evidence of their eyes and don't just believe what the TV tells them?
But no, you're right, White people should just abandon their countries, abandon their cultures, abandon the ancestors whom they owe their life towards, and accept infinity migrants into their country, because we're all the same, right? We're all no different then the 70IQ Somalians, or the Australian Aborigines?
Hey Anon, you know you're not supposed to sniff Petrol right, you're supposed to put it in your car!
https://www.youtube.com/watch?v=s1yeBmSFkC4&list=RDs1yeBmSFkC4&start_radio=1

>>16898450
The rest of us are trying to argue the lack of scientific basis for a definition of 'race'. You are talking about culture and immigrants. You are trying to use science to justify your racist bias and it couldn't be more obvious.

>>16898453
There is already an entire thread up that is focused on debunking the scientific consensus behind Race. Not to mention I've cited plenty of examples that my opponent has not even mentioned once in reply, despite providing no research or studies in return.
I'm the only one in this conversation who has cited studies.
>>16881343

>>16898456
> mixed-race people are rated as more beautiful
> https://pubmed.ncbi.nlm.nih.gov/15895630/
We can all cherry pick studies and simplify / misconstrue their conclusions (causation is not correlation).

>>16898462
Pertaining to the point I was trying to make, it was valid. How about you cite some studies, wise guy?

>>16898462
>>16898467
Studies pertaining to the notion that we are all one race, show them. Show me evidence that contradicts the truth of observable reality.

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I look into hard sci-fi concepts from time to time and one idea I see for a heat radiator in space is the curie point one. It's really interesting to me but I always find myself thinking won't the iron dust just fly away before it can remagnetize? If the craft is moving at speed or just by the nature of spewing it out that it will lose amounts every time?

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If dividing the power (any power) of an even number by the product of two odd numbers gives us an integer number, how can we prove that the even number to the power of 1 is (or isn't) greater than the product of those two prime numbers?

>>16899318
> those two prime numbers?
What prime numbers? That's the first time you mentioned any.

>>16899329
sorry, I meant odd. I was thinking about prime numbers and got confused, they are just odd not necessarily prime (y and z)

>>16899318
>>16899408
What are you even trying to prove? All you seem to be asking is if 2x > yz? What's wrong with just a comparison test?

>>16899318
>if (given this), how can we prove (that)
Set n to be equal to 1? Cause then it's given

>>16899318
I'm a bit confused by the wording, do you mean that yz divides (2x)^n for all n or that there exists an n such that yz divides (2x)^n?

If it's the former, 2x>yz because yz must divide x in the special case n=1; if it's the latter nothing can be said, previous special case is still in play but so is, say, x=15 y=3^100 z=5^100.

What's a good way to discover obscure crank theories? Besides Rational Wiki, of course.

>>16899811
I dunno, but lurk on 4chan long enough and you'll see plenty of schizo threads.

>>16899412
>All you seem to be asking is if 2x > yz
Yeah. Is this true for every n if the result is always an integer number?
>>16899561
Yes, the former. Could you expand on this? the case n=1 is to be found, it is not an initial condition.

>>16899811
https://github.com/veorq/crackpots
https://jamesrmeyer.com/blogs/blog-cranks-and-crackpots

>>16899910
> Is this true for every n if the result is always an integer number?
No. A counter example would be [math]x=3, y=9, z=9, N=4[/math]. Then [math](9.9) | (2.3)^4 = 16[/math] but [math]6 < 81[/math]

What you are essentially asking is if [math]yz|(2x)^N[/math] does [math]yz|2x[/math]? In general this is not true unless you impose more restrictions like gcd(y,z)=1

Is there a formal taxonomy of "cognitive operations" or "epistemic actions" for conceptual understanding?

I have been analyzing high-quality explanations in physics and mathematics (specifically the work of Grant Sanderson/3Blue1Brown) trying to "reverse-engineer" what happens in the learner's mind.

I noticed that successful understanding of complex topics often requires the learner to actively execute very specific "mental maneuvers". I am NOT looking for instructional strategies (like PBL or Spaced Repetition), but rather the atomic learning operations which any person could learn anything.

Is there a specific field of study, author, or framework that attempts to catalog or taxomomize these specific "operations of understanding"?

>>16900269
Read George Lakoff and Rafael E. Núñez, although it may not be what you want

>>16900234
>unless youimpose more restrictions like gcd(y,z)=1
so if y and z are coprime 2x would always be bigger?

>>16900386
Nope, I think it's still too general, there are still exceptions. If you also enforce the condition that y and z have no repeated prime factors then I believe it will always be true.

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>>16900269

Is there any way to measure if fusion is occurring in the Earth's core? Considering the temperature, pressure, and size of the core, and quantum tunneling, is it probable that some slow rate of fusion is occuring slowing the rate at which the core cools?

>>16901039
Fusion produces neutrinos so in theory they could pass through the planet and into our existing detectors. However they are incredibly hard to observe, detection rates even from the sun are so low, tens in a single day, that any from the Earth would be lost in the background noise.

> Considering the temperature, pressure, and size of the core
While "high" they just aren't high enough for fusion to occur. For one it needs millions of degrees in temperature, not the thousands at the core.

>>16893204
Did the /sci/ wiki page for mechanical engineering ever have a ballistics textbook?

Can someone tell me if there's any real reason we aren't all just using sink dish soap to wash clothes, or using clothing liquid soaps to wash dishes in the sink (not the dishwasher). Both make suds. Both clean off grimey shit. You can find both that are neutral scented. There are peopl who talk about little hacks of using one as a substitute when you're in a pinch, but I can't see any real reason why not just use them all the time. I don't know why Dawn and Tide aren't interchangeable

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Could a platonic solid be defined with one concise sentence: a solid whose faces are regular polygons identical in shape and size.

In wikipedia for example the definition seems to have more conditions, so is there something wrong with my concise version? Or can there even be solids that meet my definition but are not platonic solids?

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>>16902575

>>16902823
Oh why didn't I think of this. If you add a condition that it must be convex as well, are we now left with only platonic solids?

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Does Galactic mass determine the speed that the galaxy operates at for a base observational foundation relative to other galaxies?
Does a bigger galaxy have a different observed time frame reference in relation to another smaller less mass containing galaxy?
Does then star mass size play into account as as second frame of reference/observation/ratio/relative after galaxy size plays in?

>>16903058
All time-dilation effects are ignored, taken to be zero. While galaxies are very, very massive they are also very, very big. Their average density per unit volume is far too low to require any adjustments. What can't be ignored however when it comes to reference frames is the expansion of the universe. That is why astronomers distinguish between comoving and proper distances.

If you have A people in a room, what is the probability that at least B of them have the same birthday? Assuming of course that B<A.

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I got asked this in a fluid mechanics class, if both containers have the same dimensions and on top of the water we have ambient pressure, which one will empty the fastest? Intuition tells me the first one but I don't know how to prove it

>>16903818
https://math.stackexchange.com/questions/3550700/is-there-a-generalized-solution-to-the-birthday-problem

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If you pick seven uniformly random points on the interval between zero and one, what is the probability that there's at least one pair of adjacent points whose distance between each other is less than 1/20?

>>16903895
There were literal threads over this problem on /sci/ weeks ago. The left side goes down fastest.

>>16904231
If the min gap is x, then that means you're able to shift the leftmost point by 0*x, the next point by x, the next point by 2x,... the last point by (n-1)x, and still keep the order of the points. So you can just work backwards and start off with a distribution of the compressed points, and uncompress them by adding 0, x, 2x, ... and seeing if they're all withing the range upper bounded by 1. So that means choosing n compressed points such that all of them start off within the range upper bounded by 1-(n-1)x, because all points in this range can be expanded to gaps whose size is lower bounded by x.

So the point is that the set of all n points whose min gap is x or more (pidgeonhole can tell you the max gap) can be bijectively mapped to the set of all n points less than 1-(n-1)x. The domain and codomain are the same, so intuitively the sizes of the sets are the same. Would need a proof though.

You want 1 - prob that none are less than 1/20, or 1 - prob all are greater than 1/20, so it's pretty straightforward.

Am I cooked as a stem student if I excel more at the theoretical and writing papers than the practical?

In a normal substitution reaction, what happens first? Detachment of the old atom, or attachment of the new one?

>>16904835
It depends on the reaction. It could be either or even simultaneous.

is khan academy good to pass a university course on calculus provided i spend most of my time doing old math course exams + some AI to flesh out my knowledge and ask for help?

I have some sort of ADHD and dont want to read that much I just want to solve math problems while taking literal m3th.

also, the book recs link seems empty:

>book recs?
>4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html

>>16904912
wait the link works nvm

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How many times do you have to roll a dice at least so that the probability of rolling two sixes in a row at least once is greater than 50%?

>>16904927
30 times

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How do I empty one of these without spilling the boiling chemical on myself?

>>16905626
Carefully.

isn't it possible black holes don't even exist? i personally do not think they are real.

>>16905714
Yes, strictly speaking it's possible. After all you can't see a blackhole, only their effects. But it's extremely unlikely. You would have to explain all the (indirect) astronomical observations we have, using an object no one has ever thought of before. For example https://www.youtube.com/watch?v=A2jcVusR54E

Only a super massive, compact object could cause those orbits and the only object our theories predict could fit are blackholes, and those predictions exactly match all our observations. A single neutron stars is simply not dense enough.

If it looks like a duck, swims like a duck, and quacks like a duck, it's probably a duck.

>>16905719
i believe in God

i think the only explanation of a physical world is God there's really no way around it

>>16905721
Bless your heart. You may be dumb as rocks but god loves you.

>>16905706
Bullshit. There has to be some sort of a jig for these. Anyone else?

How do you solve something like the following?

You have a ball. If you have, for example the function f(x) and that is the acceleration of the ball as a function of its distance travelled. So maybe it's something like acceleration = distance + 1, so after exactly X meters travelled, its acceleration in that point is X+1 m/s^2. That's just one example how it could work.

Now that you have this informaion, how do you turn this into a function which now describes the ball's velocity as a function of time? Or time as a function of distance? Or any other combination of functions?

All that this does it give me a head ache trying to think of all this because I'm a brainlet.

>>16905714
>>16905719
We also have images of the rim of black holes like Sagittarius A*. Black holes are basically proven at this point.

>>16906339
[math] y'' y' = f(y) y' = d_t \tfrac{(y')^2}{2} = d_t F(y) \ \Rightarrow\ y' = \pm \sqrt{2F(y)+c} [/math]
[math] \ddot{x} \dot{x} = f(x) \dot{x} = d_t \tfrac{\dot{x}^2}{2} = d_t F(x) \ \Rightarrow\ \dot{x} = \pm \sqrt{2F(x)+c} [/math]

It's sorta a trick you learn. If you didn't get it yourself, maybe you haven't taken those classes yet.

>>16906368
What happens if you have something more mad, like the power used to accelerate the ball as a function of its velocity? And then from that figure out the distance as a function of time for example.

>>16893204
What's the best way to understand KKT points and convex optimization.

>>16906375
[math] \tfrac{P(v)}{v} = F(t) = mv' = m \tfrac{dv}{dt}\ \Rightarrow \ t = \int \tfrac{mv}{P(v)} dv + t_0 = G(v, v_0) \ \Rightarrow\ v(t) = G^{-1}(t) \ \Rightarrow\ x(t) = \int_{t_0}^t G^{-1}(t')\ dt'[/math]

You learn how to do this in normal calculus. You're just moving symbols around, this one was pretty straightforward..

>>16906397
wikipedia?

>>16893204
I had my first glass of raw milk. That shit is delicious. How long do I have before all of the unpasteurized bacteria kill me?

>>16906451
It tastes good because it's not been UHT treated like all the milk you drank before. Stick to pasteurized fresh milk and you get great tasting milk that's safe to drink. Raw milk is some schizo bullshit, that's why pasteurization was invented in the first place because it was such a health risk.

>>16906451
This retard is jewish >>16906478
Safe to drink just means Pussified Substances for babies who have under developed immune systems.
I'm in my mid 20s, I've been drinking Raw Dairy since I was 6 years old. I'm also starting a homestead where I'm going to be getting my own dairy cows. Never had any issue whatsoever.

>>16906478
>Raw milk is some schizo bullshit
So the majority of human history drinking Raw Dairy is schizophrenic? You retards like to retroactively define history, yet know nothing about it.
The reason Pasteurization was necessary is because mass industrial farming was unhygienic and farmers were less sanitary.
That issue is completely overcome with local farms who practice basic hygiene, without the loss in nutrients, or more importantly the Bacteria which is crucial for your Oral and Gut microbiome. (Kefir is pussified, you need to challenge your system with a wider range of bacteria.)

>>16906478
>>16906451
>In 1946, Victor Rothschild, 3rd Baron Rothschild, championed the cause for mandatory dairy pasteurization in the UK House of Lords.
>The only other time Lord Rothschild spoke before the House of Lords was to advocate for the creation of Israel
>https://api.parliament.uk/historic-hansard/lords/1946/apr/10/pasteurization-of-milk
>https://pmc.ncbi.nlm.nih.gov/articles/PMC5758418/
It is basic Jewish Fear mongering. As vindicated by the Epstein files, Jews do run the world, and they want everyone to be sick and unhealthy. They manufacture plagues (Sanitation), that way they can sell you the cure (Pasteurization), all the while making you weaker more easier to control Goycattle.
Read the Epstein Files, Conspiritards continue to win again and again. Calling people Schizo for eating a substance that their ancestors have been consuming for generations just doesn't work anymore.
It's like calling White People racist for wanting to live around their own people, it's an empty statement.
Try it for yourself, if you don't like it or it makes you sick then don't try it. Simple as. No need for Jewish Fearmongering.

>>16906495
>>16906497
Our ancestors also did blood letting, used cocaine to treat hayfever, and radium tonic for pain relief. Why not go back to using them as well?

>>16906502
Modern day people (Jews) rape children on Eptseins Island, does that mean everything in the Modern Day is Bad and everything in the past was good?
Or maybe you can understand the absurdity of your argument in acknowledging the nuance of history. If everything in history is bad and unhealthy, there is no way we could have gotten this far.

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No matter how I do it, I'm unsure how the left side resolves to that integral, rather than [eqn] v_{ter} \Big| ln (1 + (\frac{v}{v_{ter}})^2) \Big|_{v_0}^{v} [/eqn] The trick in question referred to in the problem statement is such that [math] \frac{dv}{dy} = \frac{1}{2} \frac{d(v^2)}{dy} [/math]

>>16906478
It has been 9 hours and I am not dead chat. Thoughts? Scientifically speaking.

>>16906649
Scientifically speaking, you appear to be a moron.

>>16906647
Look up u-substitution

>>16906656
You aren't science sweetie. The science is an institution.

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Can you prove this relationship?

>>16906873{}
Don't you just start by rewriting:
[eqn]x^{x^2} = e^{x^2 \ln{x}} = \sum_{n=0}^{\infty} \frac{\left( x^2 \ln{x} \right)^n}{n!}[/eqn]
Then do the (painful) integrals for each term, and you spot a pattern.

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>>16893204
gold is used in electronics, but it is very expensive. why not lead?

>>16906956
Gold isn't poisonous, doesn't tarnish, and has ten times better conductivity than lead. Yes it's more expensive but the quantities involved are tiny so the cost isn't actually that important. The reason silver isn't used despite being much cheaper is because it's too hard and difficult to work with, unlike gold which is ductile.

>>16906956
If you have to ask why lead isn't used for a purpose, it usually ties back to the heavy metal neurotoxin thing.
It is god's greatest joke to man that lead happens to be very good (even if it's not always the absolute best) at damn near everything, except for the heavy metal neurotoxin thing.

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anyone know anything about array processing? array signal processing? beamforming?

i wanted to read https://sps.ewi.tudelft.nl/Education/courses/ee4715/reader.pdf

couldn't understand. no matter how much i learn, i don't have enough prerequisites to understand anything besides lectures

also did you guys invent a cure for akrasia yet?

>>16907146
i want to learn array processing (sometimes called array signal processing) with somebody please add me on discord username is 5xw8

>>16907146
>>16907463
i'm really cool i read gwern btw and might be schizoid

Are there infinitely many numbers 3*10^n-1 which are divisible by seven for integer n?

>>16907493
Yes.
Proof: There exists at least one such case in n=5 (7*42857+1)
If 3*10^n-1 is divisible by 7, then it means that 3*10^n is congruent to 1 mod 7. Multiplying this by something else that is congruent to 1 mod 7 will give you a product that is congruent to 1 mod 7. By Fermat's Little Theorem, 10^6 is one such number.
So, putting this together, any n of the form n=5+6k for k=1,2,3,etc. will work

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You are put blindfolded into an infinite hallway in which the two walls are hundred meters apart. You only know that you are in a random location in such hallway, and you get out once you touch a wall.

Which curve do you start walking so that the distance that you will walk before reaching a wall is going to be on average as short as possible? And assuming that you use this optimal path, what is the average distance that you walk before touching a wall?

>>16907508
Probably the logarithmic spiral but fuck knows how to prove it.

>>16907508
My guess is that you assume the wall is directly in front of you and move 45 degrees in a straight like for the length of Rsqrt(2), where 2R is the distance between the two walls. If you don't hit a wall any time during your walk (50% of the time), Assume the two walls were slightly rotated by angle d(theta), then you move in a straight line to that wall. If you didn't hit it, then assume walls again were rotated, then move in a straight line again.

>>16907857
its more like F(x, A), where A is your original facing angle relative to a wall and x is distance from the wall.
then your goal is to rotate -A and move x distance.
Or if x is > 0.5 L, then rotate -(A + 180) and move x distance

So, short version of my assignment.
I'm supposed to analyze data based on distance from certain points using ArcGIS Pro.
I thought the right thing to use was Geographically Weighted Regression but it's asking for Input Features and not any features based on the locations.

Does ArcGIS get easier at any point?
It feels like it was designed just to cause pain and misery. I'm terrible with it, and I think picking Geoscience as a major was a huge fucking mistake.

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>>16907857
So this was quite wrong; in pic rel, the purple path is way too long,

If theta represents the angle of the red dotted line touching the red wall, when theta is between 0 and pi/2, the 45 degree green line is hit by the solid red line pretty quickly. Same will happen to the blue line at pi to 3pi/2. I'm just gonna go off from the 45 degree green line, so I have no real proof of any answer

The curved dashed green line is such that at the point where the red tangent line intersects it, the line from the point to the end of the 45 deg solid green endpoint is perpendicular to the red line. And this green dashed curve is a much better answer than the purple. The straight dashed green line seems like a reasonable path too. I have no intention of integrating to see which is better, since it was an arbitrary straight linel. In pic rel, that particular position it sorta looks to me that the path lengths for both green curves are the same, and angles below that the curved green line beats the straight green line

Still have no answer, but I thought to find a minimal equation, IF I can use the 45 deg green line. The two walls means theres probably some point where the derivative of the floor integral doesn't exist, and I don't wanna think about that

Unfortunately, I can't exactly solve it. Still, the curve I seek past the 45 deg line should satisfy the altered Euler lagrange (as the action functional is a 2x integral)
[math] (\tfrac{\pi}{2} - \theta ) \tfrac{\partial L}{\partial x} \big|_{x(\theta)} - \tfrac{\partial}{\partial \theta} \left[ ( \tfrac{\pi}{2} - \theta) \tfrac{\partial L}{\partial \dot{x}} \big|_{x(\theta)} \right] = \lambda_x(\theta) \tfrac{\partial g}{\partial x}[/math] ,
where [math] L = \sqrt{1 + (\dot{y} / \dot{x})^2} [/math] and the constraints g are that the parametrized curve outta intersect the red line somewhere [math] 0 = \sin\theta[ y(\theta) - R\sin\theta ] + \cos\theta [ x(\theta) - R\cos\theta ] [/math]

It's so unwieldy written out

>>16908474
Idk, it's probably something easier, like to the the circles edge then go around the circle, idfk

I never understood why Divergence is equal to [eqn]\nabla \cdot \vec B[/eqn] when it's defined as flux over volume of an infinitely small volume. Does someone have a proof relating the two definitions?

>>16909257
Are you asking about divergence in general or specifically about Maxwell's equations?

>>16909263
Just divergence in general.

>>16909267
> when it's defined as flux over volume of an infinitely small volume
The divergence operator is not defined that way. What you are getting confused by is the similar sounding "divergence theorem" - the volume integral of the divergence is equal to the surface integral of that volume (the flux).

>>16909296
I meant why is the formula [eqn]\frac{\partial B_x}{\partial x} + \frac{\partial B_y}{\partial y} +\frac{\partial B_z}{\partial z} [/eqn] when https://en.wikipedia.org/wiki/Divergence#Definition gives it as flux divided by volume as the volume goes to zero?

>>16909411
I'm surprised wiki didn't give any info on it. Suppose you have infinitismally small box with side area A = (2dx)^2 and volume V = (2dx)^3. The center of the box is your origin of focus. B is a vector field with derivatives, and consider B(0). The only 6 values we only have to consider are B(dx, 0, 0), B(-dx, 0, 0), B(0, dy, 0), ...). So what would the flux of this box be? Factor out the A, divide by V, then set the limit down to 0. Voila

This was the easy one. Now do the same for curl. Not that much harder but more writing. After you do the curl one yourself, look up a proof for the generalized div/curl/gradient for a change in coordinates (don't do it yourself). If you can't find it, Griffiths has it in his Electrodynamics appendix I think.

>>16909257
>>16909411
The combinarions of the following two links should help you:
https://math.stackexchange.com/questions/300024/formal-definition-of-the-divergence-of-a-vector-field?rq=1
https://proofwiki.org/wiki/Justification_for_Geometrical_Representation_of_Divergence_Operator

>>16909450
I think that did it. Is there something similar for the curl?

Do standard genetic tests give enough resolution to tell if someone is inbred or are they only filtering for genes?
Can they estimate how far back their parents are related?

is it true computer science isn't considered a real field by /sci/ standard? just found out that there used to be a /cspg/ general on here.

>>16910061
It's considered not a real science in the real world by many people too - it's partly a meme and party the truth how upset those with CS degrees get when you tell them that. That's not to say CS isn't a rigorous academic field, but the argument is over the word "science". No one would call Economics or Architecture a science.

>>16910070
>Economics
ummm actually that's a social science and therefore a science (it's right in the name)

>>16910073
Fair, but just having science in the name comes back to anon's original question.

> While referred to as the formal sciences, the study of logic, mathematics, and theoretical computer science are typically regarded as separate because they rely on deductive reasoning instead of the scientific method as their main methodology.
It's all a question if you consider the physical and social sciences the only ones that deserve the label.

>>16910061
In practice, it's closer to engineering in that you're engineering/developing solutions by construction of some object that in this case is digital. You might think a graphics artist would be doing the same thing, except their work requires much less logic and very little mathematical reasoning as would an engineer.

Work is work. No shade on any field

>>16910118
And actual computer science theory is basically math

>>16910061
Do computer scientists, for the most part, work with any hypotheses?

>>16910073
Economics is not and has never been a (natural) science no matter how much economists try to dress it up in math, its no more of a hard science than biology is.

>>16910061
It covers the TEM in STEM, but not the S.

>>16910119
It's the converse. Math is a computer science.

/med/ says it doesn't give advice so I'll ask here
my upper back/neck are kinda fucked and now I can often feel some very light sensation in my back by the left shoulder blade right next to my spine
also got some scoliosis but have had that for a while
anyway to not aggravate this? no time to go to the doctor anytime soon

>>16910674
Math is not a science.
It wouldn't take a million years to figure out that dividing by zero is just cutting something zero times, leaving it untouched.

>>16911083
Go to the doctor.
Make time for it now or it will be made for you later.

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I have a retarded question.

V(t)=dPhi(t)/dt

Our exam is without calculators. And the task would be to draw the voltage graph

I totally get it first part is 1/10 then 0,...

To the quadratic part. I know its x^2=2x and that it's just a straight line with a positive slope but how do I calculate it where to start and where to end without a calculator

>>16911294
You have to make the parabolic equation regarding that section.
Check for yourself that this equation in terms of milliseconds is [math] y={1\over 200}(x-70)^2 [/math].

Calculate the derivative from this and evaluate the two endpoints at 70 ms and 90 ms.
On the derivative graph it's a straight line from (70,0) up to (90, 0.2).
The numbers are simple enough without a calculator.

>>16906451
It has been a week fellow scientists and I have not died from the raw milk. What are the chances of someone surviving a substance with 100% kill rate and does this scientifically confirm the superiority of my whole raw white milk drinking genes or will death come at a later time?

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>>16911294
Φ/2 = [(t – 70)/(90 – 70)]^2

>>16911294
>V(t)=dPhi(t)/dt
?

Your graph shows phi as volts V?

>>16911333
1) No one survives a 100% kill rate, hence the 100%.
2) No one has ever claimed that raw milk has a 100% kill rate.
3) Raw milk has a higher risk than treated milk. It might be only be slightly higher due to modern hygiene standards, but it's still higher.

i think I did bad on my set theory test, "test" is generous considering it was only 6 simple questions. lack of reading carefully and encountering a variation of a problem that i didnt know how to solve fucked me over. i want to die

>>16911323
>>16911370
Thanks a lot!
>>16911403
No it's Vs (voltseconds=weber)

I fail to see what's been the matter with Euclid's fifth postulate, it looks pretty self-evident to me.

>>16911781
Explain, do you mean self evident enough that you should assume without proof using other postulates, or evident enough that it should be provable with the others?

Btw, if you and a person start face forward north and start walking north, you eventually run into each other.

>>16911781
I'm not clear what you're asking about here? There are a few 'matters' regarding the fifth postulate. I guess the main one is that despite it being 'self-evident' it cannot be proven. Which means it's an axiom, one that isn't even needed to have a fully consistent geometry.

>>16911792
>>16911794
I thought Definition 7 on plane surfaces was enough for it to be evident. Well looking at it again, Euclid mentions no plane on his postulate.

>>16893204
Why do negative ions go toward Zinc electrode and positive ones towards Copper?
Shouldn't it be the other way around considering Copper is more electronegative than Zing?

>>16893204
Is it worth it to get dental X-rays? I know dentists try to bill you excessively to make money, but I haven't had dental X-rays in about 12 years, after having radiation therapy for cancer my radiologist told me to minimize radiation exposure. I'm 28 now. My teeth look and feel fine on the surface. By dentist hasn't said a word about X-rays until my last appointment but now he's been bugging me more about it.

>>16912539
What negative ions?
Copper being more electronegative means the copper cathode attracts the electrons from the zinc anode through the metal conductor, which is why current flows that way.

>>16912749
*electron current, not conventional

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what's the speed of magnetism? I know it's c, but two magnets with opposite poles do not exactly snap together at the fucking speed of light, breaking my hands in the process if the force is large enough.

>>16913598
F = ma = qvB

Metaquestion: Why the fuck is barely anyone giving push back to the schizoniggers here e.g. Gwaihir and HyperAdvanced?

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>>16913664
Divergent thinking is a prerequsite to advancement, otherwise we would be simply repeating orthodoxy from the 1600s (and eaier.) We therefore can and should tolerate a certain level of divergence.

what the fuck are particles made of? are they really just volumeless points that move through space with charge and mass just because?

>>16913830
> are they really just volumeless points that move through space with charge and mass just because?
Essentially, yes.

According to Quantum Field Theory they are modes of vibration of a field that pervades all of space. So every electron is nothing more than a quantized vibration in the single electron field. It is the properties of that field that defines what change, mass, and spin the particles have. It's also why every electron is identical.

>>16913664
Autism speaks, and it has nothing good to say: I ignore it instead of wasting my energy on engagement.

>>16893204
How can someone be ethically racist?

>>16914310
Racism is not innately unethical.
Everything racist you do that causes harm is already unethical regardless of your motivation.
If you target black people for charity because you think they're inferior, don't believe that is innately unethical.

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>>16914310
>How can someone be ethically racist?
When I see pic related types of people, I realize they are genetically incapable of thriving in a modern society and it only reinforces my intuition that they should be left alone to live their lives as they please. They don't bother me in any way and they shouldn't be bothered. Many "racist" retards feel irrational rage at the very sight of these hopelessly primitive people. They make "racism" their identity, but they're clearly not racist enough, because they're implicitly judging these tar-black atavistic hominids by "normal" human standards and expectations to conclude they are somehow at fault for being this way. Likewise, many "anti-racist" retards feel a deep discomfort looking at this picture and feel an irrational urge to "civilize" and "uplift" these people, whom they perceive as their inferiors and dependents. They make "anti-racism" their identity, but they're clearly racist (just not racist enough). I conclude that the problem with racism is that people just aren't racist enough. To be ethically racist, you need to racistmaxx.

>>16914512
>>16914518
I didn't mean an argument for how the category exists. I meant based on the distribution of populations. How can one be certain they are behaving in an ethical manner. For example, just avoid them or never relax heuristics already presumes this question cannot be answered. Incredulity or ignorance is not sufficient grounds to act. The signaling of various beta-types is obvious, fags virgins etc. I think about the Bateman diatribes and psychopathy where maniacs game the status quo, but its a hack on retards who interact based on checklists.
I get this real schizo feeling. How do people talk about laying tripwire when the coolies are in the meeting.

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Is there a name for projecting a perspective based on projectile trajectories(at least parabola) instead of typical straight lines?

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Are the lengths a and b enough information to solve the surface area of the crescent moon looking shape?

>>16915058
No. You can vary the radius of a circle that defines an arch over the horizontal segment from b/2 to infinity and get arch heights anywhere from b/2 to 0, so you have infinitely many options for two arcs with heights 'a' units apart.

Femoid here. I bathed with my brother for shit and giggles last Sunday. I can't stop thinking about our genitals, holy fuck. The skin around his penis was all clear like the rest of his body, but the skin around my vulva is all dark and ugly, what the hell!? Shouldn't be have the same traits as siblings? Someone explain

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A ladybug lands on the number 12 on a clock. It then takes a step either clockwise or counter-clockwise to the next number with both having 50% probability. What is the expected (average) number of steps that the bug takes before it reaches seven o'clock?

>>16915216
> How long is a piece of string
> How far is a lady bird step

>>16915216
Let f(n) be the expected number of steps to arrive at 7 if you start on the number n.

Trivially:
f(7) = 0
f(12) = f(2)
f(11) = f(3)
f(10) = f(4)
f(9) = f(5)
f(8) = f(6)

Also it's easy to see that:
f(6) = 1 + (f(5) + f(7))/2
f(5) = 1 + (f(4) + f(6))/2
f(4) = 1 + (f(3) + f(5))/2
f(3) = 1 + (f(2) + f(4))/2
f(2) = 1 + (f(1) + f(3))/2
f(1) = 1 + f(2)

Just solve this linear system with GauB.

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>>16915058
You drew or posted a fine drawing. There are two arcs. If each arc is a horizontal-directrix parabola, then yes, the lengths are enough information.

what kind of math do i need to learn to do project euler problems? any textbook recs

>>16915058
The answer to your question depends on this symmetric curve's degrees of freedom.

For the lower curve, the center point (worth 2 degrees of freedom) is confined to the x=0 line (1 restriction). A second random point (worth only 1 degree of freedom) is confined at (b/2, 0). So you've restricted two degrees of freedom so far. Saying that the center point has y > 0 isn't enough to lower a degree of freedom because it isn't a concrete number.

For the upper curve, same deal with the two degrees of freedom, but you also set the height to be "a" higher than the lower curve. But this only becomes a 3rd degree of freedom taken away if the lower curve is already restricted.

So how many degrees of freedom do your curves have? How many random points are needed? If a center point is given, how many random points are needed?
For a line, you have y-b=M(x-a);
for a parabola, you have (y-b) = A(x-a)^2;
for a circle, you have (y-b)^2 + (x-a)^2 = r^2;
for an ellipse/hyperbola, you have (y-b)^2/d^2 +/- (x-a)^2/c^2 = 1

Do you have enough information, or do you need more?

>>16915462
There's no one fits-all answer to that. The first ~100 problems or so are essentially coding challenges that require only basic math. Everything you need to know is in the question. The challenge as you progress is writing algorithms that complete quickly, seconds or minutes rather than hours or days. However, eventually the questions do require more advanced mathematical knowledge you might have to do research on, but it tends to be question specific. I dropped the project when it got to the point if you didn't know what esoteric math field the question was about (and it no longer tells you) the questions become neigh-impossible to answer.

I need to understand analog video signals for a hobbyist project I'm doing, what kind of math do I need for that shit?

>>16916016
look up a signals & systems course and check the prereqs?

Considering all the photons flying around in space.
If I were to take snapshot of 1m3 of "empty" space. How many photons there would be? What would be their energy? Could it be the "dark matter" we are missing?

>>16916367
Your question isn't well defined. It's not the number of photons that matter, it's their frequency and density (and hence mass equivalence). Most of the photons in empty space will come from the Cosmic Microwave Background. Since that energy can be measured, you get a mass of around [math]4 \times 10^{17}[/math] kg per cubic light year. Compare that to the mass of the sun at [math]2 \times 10^{30}[/math] kg and the answer to your question is no. It doesn't even come remotely close to explaining "dark matter" and anyways, it was already factored into astronomers' calculations of all known / visible mass.

>>16916376
>Most of the photons in empty space will come from the Cosmic Microwave Background.
Yeah, but their energy will be low. How about all that star radiation. That will have much more energy per photon.

>per cubic light year
But there will be a lot of cubic light years, compared to single star.

>>16916376
I just found out that I can bench press 35,552,111,811,601,841,387,986 cubic miles of empty space

>>16916378
> How about all that star radiation. That will have much more energy per photon.
Correct, but it's radiated from a point source. The falls off as [math]1/r^2[/math] so it very quickly becomes irrelevant. The CMB on the other hand is *everywhere* with a constant mass-energy density. Which brings us to your other point:

> But there will be a lot of cubic light years, compared to single star.
Yes, but look at those number again. You would need [math]~10^{13}[/math] cubic lights years of space to match a single average star. Now think about how many stars are in a galaxy, and galaxies in the observable universe. The mass of the CMB just doesn't compare even with all that empty space out there.

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I don't get it... not the sin stuff, I get all that... the graphs... these are both 2d graphs and yet the graph on the left contains all the information in the graph on the right as well as the relationship between x and y in the unit circle...

>>16916867
Are you also surprised that zip files exist?

>>16916867
I mean, they're essentially the same thing graphed in two different ways. They're interchangeable. You can derive theta from the left graph and you can derive x from the right graph.

>>16916867
[math] F: \mathbb{R} \rightarrow \mathbb{R^2} [/math]

[math] \theta \rightarrow (\cos\theta, \sin\theta) [/math]
vs
[math] \theta \rightarrow (\theta, \sin\theta) [/math]

If you go into 3D, then you can get all three, wooooh
[math] \theta \rightarrow (\theta, \cos\theta, \sin\theta) [/math]

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>>16915378
In the image, a = 1 and b = 6.
Thus the area of each colored region is 2*a*b/3 = 4.

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How would you make an equation that defines how an animation walk cycles, idles and even sequence to sequence work

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I can't do it
I can't visualize a graph with a real x axis, imaginary x axis, real y axis, and an imaginary y axis

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>>16914606
>How can one be certain they are behaving in an ethical manner
Ethics is based in outcome, as is most the modern behavior of racism. When you see a Grizzly Bear act in a particular way, you don't base your conduct towards it by catering to the exceptions, i.e. you don't run towards it expecting a hug.
When you see that Blacks are typically belligerent and violent, you don't conduct yourself by pandering to the statistical exceptions, because it's safer to assume that an animal that typically acts in a certain way is going to keep acting in that way. Furthermore, even if you do manage to find the exception in some instance, you're basically establishing a precedent that gives future credence to them in the future. I.e. A grizzly bear might actually be chill and let you hangout, but then somebody is going to get the wrong idea and now you have a bunch of tourists coming around trying to hug the bears at yellowstone.
The same rule applies, they started giving blacks lighter sentences because of "Systemic Racism," which allows for guys with upwards of 30 Felonies to get released back into society without any prudence to determine his elligibility, which they almost never have, hence pic rel.
>who interact based on checklists.
If somebody says they're a murderer, are you going to hangout with them anyway? Afterall, that checklist of people who Murder being bad guys is retarded by your logic.
>How do people talk about laying tripwire when the coolies are in the meeting.
You just stop associating with them, or mitigate your association to whatever extent you can. It's that simple, don't support their business, keep words to a minimum, don't go into areas infested by them. That's literally all there is to it. Put your people first.

>>16917690
that's why you imagine two

>>16917690
imagine a 3d graph with a slider that lets you scroll between slices of a 4th dimension?

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>>16917683
Fine!

Does it make sense to read apostol's calculus after serge lang's calculus or is it going to be mostly the same

If I have a superscript that says 0+x, but x never shows up, what is it equal to?

>>16918094
But x does show up. It's right there, I can see it.

>>16918095
Maybe the question is not so simple... But please try to help me. I guess my question is how to phrase that x doesn't appear
Knife will get the the job (x is knife)
Music album with knife on track 2: W1^0+x = W1^2
Music album with knife on track 10 = W2^10
Music album with no knife: W3^0+x =W3^???

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I speedran Khan Academy from kindergarten to calculus 2 over a week. I can answer all the questions but I feel like I'm just pattern matching rather than really understanding what's going on most of the time. How to fix?

>>16918098
just leave it at zero mate

>>16918099
>I feel like I'm just pattern matching rather than really understanding
They're the same thing, so your question is meaningless.

>>16918112
maybe if you're a llm

>>16918117
You should take the khan academy class for neuroscience next time so that you don't say stupid things like this.

>>16918132
if I wanted to learn neuroscience I would just pirate a proper book on it rather than watching a series of slop videos produced by a grifter

>>16918137
If you were smart enough to do things on your own, you wouldn't be here asking stupid questions.

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>>16918112
>They're the same thing, so your question is meaningless.
If they were the same thing, LLMs (including bio-LLMs like you) would have impressive performance at actual science and not just at standardized testing and homework.

>>16918099
Now you attempt the questions in a standard textbook like >>16918092 and see if you understand or not. And if you don't you have the book to fix that.

>>16918098
That may be one of the worst attempts at a description I have ever seen.

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>>16918112

>>16918214
>>16918141
>Incoherent seething

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How to make equation for a walk cycle?

>>16918229
modulo

>>16918231
Please show.

>>16918229
Not everything has an equation

>>16918229
You don't. Animation isn't equations, it's fixed arrays of positions.

>>16918240
Procedural animation does.
>>16918241
Physics guide these motions in reality, somehow.

>>16897757
You shouldn't. But if you do, be careful

>>16918252
>>16918229
From the perspective of the walker, the motion is periodic, so you should look at sin and cos functions.

>>16918267
How about using only F=m.a can one tell how much spacing from there or what guides spacing in limbs,appendages and cycles, tandems etc>>16918234
>>16918234

>>16918229
>How to make equation for a walk cycle?
Get a bunch of data points from a mo-capped walk cycle and fit quintic polynomials to the data points for joint trajectory. Differentiate the quintics and you'll get smooth linear acceleration signals for the joints. As a bonus, I think you could apply a Fourier transform to the accelerations and get a frequency domain representation that decomposes the walk into its cyclical components. If you vary some of those parameters, do an inverse transform and integrate the new acceleration signals, you'll get new funky walk cycles.

>>16918280
How about something more basic like those in cartoons. Like maybe how walk cycles parallels work. What's the physics driving it or just maybe a diagram of how things moves.

>>16918280
Or do you have the paper for this. Or infographics.

>>16918285
>How about something more basic like those in cartoons
Same thing. You can go over the frames and mark where the joints are, fit some quintics and you have a differentiable trajectory you can derive accelerations from.

> What's the physics driving it
You mean how to deduce the accelerations from first principles instead of given trajectories? I dunno. That would be an optimization problem over an entire articulated rigid body system involving balance and energy expenditure and constraints for human biomechanics... so quite a bit more involved, but it's been done. Just look up procedural walk animations or something...

>>16918277
So you want something more general than just walking. If a limb is a rigid body with mass M and length L, the force required to change its angular velocity by an amount [math] \Delta \omega [/math] in a time [math] \Delta t [/math] is of the order [math] M L \frac{\Delta \omega}{\Delta t} [/math]. This force is supplied by chemical reactions in the muscles in the limb and the timing of these reactions is controlled by electric signals from the nerves, so the force acting on the legs is a function of the signals received from the nerves. You can hard code a bunch of signals, each for controlling the movement of a limb/appendage/etc by a certain amount and apply the force according to the nerve signal received. Walking can be simulated by sending a sequence of signals in a certain order.

>>16918298
>Quintics
>Frames
>Marks
Do you have actual examples? This seems to be Abit overcomplicated.
>Deduce
No, it's vector math at least, with force being constant, I assume the mass is gonna be the same thus, acceleration will tell speed and then tell distance.
That is supposed to be the basic.
Getting the spacing.
>>16918310
>Certain order
What order then?
There's only so much limbs for so much signals.

>>16918343
JFC. Go play your Xbox or something, kiddie.

>>16918345
>What is even jfc
And become a dumbass moron with a smartmouth of a wookie? Maybe after this.

>>16918343
>What order then?
Up up up up down down down down, on repeat. Something like that for each leg.

>>16918346
>And become a dumbass moron
You've already maxxed that out.

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Is optimization really worth the amount of time spent trying to figure out the function of a system? I'm studying it from Stewart but I find no use cases for it in real life.
You can only optimize simple systems while assuming lots of constraints and I don't see it being useful enough to be worth the trouble. Any anon ever used it for something really useful beyond simple practice or thought experiments?
Stats based optimization seems far more versatile and useful.

If you pick two uniformly random points on the surface of a truncated icosahedron whose side length is one unit, what is the average distance between the two points? And can this have a closed form solution?

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If the atomic nucleus were 38 millimeters across, the farthest distance the electron cloud would...angular momentum propagate materialize away...would be 2 kilometers (2 million millimeters), the outlier maximum, but with an average that was much shorter around 1 million millimeters or so...
Given that the difference in energy between the weak and strong nuclear forces is roughly 1 million, is there a measured, observed relation in distance ratio scale to the difference in the strong and weak nuclear forces somehow?
What do I not understand? I am sure it is simple.

>>16918464
What is the nucleus made out of? How do you know where it starts and where it ends? What is matter anyway?

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>>16918566
So is reality simply distance averages between the next smaller observational parts layers angular momentum propagation materialization orbit clouds?
Distance averages theory?
Just endless pressure field distance averages, things floating in those fields, and those things themselves possessing Russian doll pressure fields of things floating in them...
Clever
Very clever young orbital cloud....
But its pressure fields all the way down

https://youtu.be/WsuBBd9W4hk?si=86NZblkxHqEMb5Mk

>>16918263
already did it a month ago, nothing interesting happened, the whole lighter flashed the moment I ignited it and my hand got engulfed in fire for a split second and then it just burned normally and the flame got slightly bigger but that could've been for any other possible reason. could be because i put in a very tiny amount because i really don't have a lot of acetone left and i don't even know where I can more (yes i'm that dumb).

>>16918347
This is not a console bro. How about more precise.
>>16918348
And you are the goddang professor. Archaic literal fossil of its Einstein, duh. Actually no, you can't even make a four letter linear math of it.

>>16918464
Why are you mentioning the weak force? The nucleus us bound by the strong force, the electrons by the electromagnetic force.

>>16893204
Is she the girl who solved that old harmonic analysis problem?

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I suck so much at solving equations and factoring. I hate myself so much, how can I get better at it, anon?

>Yoda bird nasal noise
If object has predefined actions, how would it's distance per frame be"
There.