/sqt/ - Stupid Questions Thread: Why Do Things Move Edition

>you
>reading comprehension
Try again.

What about secretions? Both male and female would have secretions that you couldn't simply wash away.

You would need a universal killing mechanism that could instantly kill contagions before they infect the host (i.e. one of the sex partners). Yet, this universal killing mechanism would need to not hurt the host.

I think that if we have a solution like that, many, many diseases, including cancer, would have been eradicated or greatly reduced by the same technology.

How would I prove that any finite language over the finite set of symbols making up the alphabet, is regular?

Stationary (stop) is death.
Cardiac arrest. Arresting is about stopping people from exercising their freedom to roam free and kill more people. Only for a moment, the smallest unit of time measure, can anything be in the same place doing the same nothing.

I'm trying to find the time it would take an electron to fall into the nucleus according to classical mechanics. The thing is, in the total energy equation, I have to ignore the radial component of kinetic energy to get "the right answer". How is this allowed? We're assuming circular orbit at all times, so is the radial component just negligible compared to the angular? I guess that must be it.

Well the radial component wouldn't contribute to any radiation emission.

ah that's true, just did the proof of that as well. cheers

Thought fluids was implied in my post, but yeah

>You would need a universal killing mechanism that could instantly kill contagions before they infect the host (i.e. one of the sex partners). Yet, this universal killing mechanism would need to not hurt the host

also it might have the added bonus of killing sperm, so it might work as a contraceptive too.

I'm not sure of the virility of all the different std causing pathogens, but surely its not outside the realm of reason that it could be eventually done.

Studying basic set theory, can someone help me understand why the set of natural numbers is complete? From the definitions I've been given, a lattice is complete if, for every subset, there exists a least upper bound and a greatest lower bound. I understand that the bounds don't necessarily need to be in the set. If we take N and a subset of itself, we have the greatest lower bound of 1 but what exactly is the least upper bound?

what lattice are you talking about? subsets of natural numbers ordered by inclusion? natural numbers ordered by divisibility? natural numbers ordered by the usual < sign?

Ordered by

wouldn't the LUB of a natural number n just be n+1 and the GLB would be max{n-1,1}?

>can someone help me understand why the set of natural numbers is complete?
Let [math]\left( u_n \right)_{n \,\in\, \mathbf N}[/math] be a Cauchy sequence in [math]\mathbf N[/math]. Choose [math]n_0 \,\in\, \mathbf N[/math] such that [math]\forall \left(p,\, q\right) \,\in\, \mathbf N^2,\, \text{if } p \,\geqslant\, n_0 \text{ and } q \,\geqslant\, n_0 \text{ then } \left| u_p \,-\, u_q \right| \,\leqslant\, \frac{1}{3}[/math].

We have therefore [math]\forall n \,\geqslant\, n_0,\, \left| u_n \,-\, u_{n_0} \right| \,\leqslant\, \frac{1}{3}[/math] and since [math]\left( u_n \right)_{n \,\in\, \mathbf N}[/math] is an integer sequence, [math]\forall n \,\geqslant\, n_0,\, u_n \,\in\, \mathscr B \left( u_{n_0},\, \frac{1}{3} \right) \,\cap\, \mathbf N \,=\, \left\{ u_{n_0} \right\}[/math] then [math]\forall n \,\geqslant\, n_0,\, u_n \,=\, u_{n_0} \,\xrightarrow[n \,\rightarrow\, \infty]{}\, u_{n_0}[/math].

Therefore [math]\left( u_n \right)_{n \,\in\, \mathbf N}[/math] is convergent and therefore [math]\mathbf N[/math] is complete.

Let's say that we create perfect nanobots that can identify viruses (nm scale) and other contagions and kill them without damaging the host. This type of system would only reduce risk, not eliminate risk.

A more perfect solution would be to eradicate the disease from the Earth or find a way to provide immunity to the diseases (e.g. genetically enhanced humans).

Currently, it is hard to imagine a world where either solution will be feasible. I could, however, imagine a world where you could reduce the chance of catching specific diseases (e.g. a non-perfect "nanobot" in the form of some chemical like you were describing).

>surely its not outside the realm of reason that it could be eventually done

I enjoy having an optimistic stance when discussing possibility.

This would probably be very helpful if I had a firm understanding of what a Cauchy sequence really is what exactly the criteria for convergence are but I don't have any background in analysis, only multivariable calculus and basic linear algebra.
This is basically what I was thinking but I wasn't sure if that was really a proper argument to make. I always second guess myself when I'm thinking about infinite sets because I feel like I don't properly understand what it means for a set to be infinite but that could just be lack of confidence. Thanks user.

Need some help understanding how one changes a divergent sequence into a convergent one for analysis. The example I'm reading about (don't know Latex but this is simple):
(2n+1)/(n+5), and because both the numerator and denominator are divergent, they divide by n on both, getting (for example) a new numerator of (2 + 1/n) and denominator (1 + 5/n).

How is this allowed? If the original sequence was divergent, how can you just change it this way and say it's the same sequence, just now convergent?

Think I made a mistake in saying that the original sequence was divergent, because that's not what I meant. Meant more about how changing the original (2n+1) sequence from divergent to convergent makes sense. Obviously the original is convergent (obviously)

Factor out n. 1/n->0 as n->infinity.

done part a, but on part b I got a factor of gamma when I did the integral. :/ also, any hints for part c?

when you divide BOTH the top and bottom by n, it's the same as multiplying by 1 (since 1=n/n) so this doesn't change the convergence at all (it's still the exact same sequence)

how could you tell the difference between reality, and say, being in a very realistic dream in a coma for the last 10 years without being aware of it?

Mind explaining why the perfect nanobots you described only reduce risk but don't eliminate it?

The 'perfect' part of these nanobots would be specificity and lethality, not coverage.

The nanobots cannot be everywhere at one time and, consequently, a contagion could infect the host before a nanobot was able to locate and destroy it.

>The nanobots cannot be everywhere at one time

Well if they plenty of them would they not act similar to a liquid? Or maybe have them applied along with a liquid?.
So if the inside and outside of genitals are covered in this nanobot fluid, then there would be and army of nano's protecting us.
This would solve the coverage problem and if they were fast enough to detect, apprehend and neutralise the contagion then they would eliminate the risk.

I'm trying to derive the intensity of the double-slit diffraction pattern as a function of θ (angle between the rays and the normal).
I get the amplitude at point P
U = 2Acos(kdθ/2)sin(wt - kD)
where D is the distance to the scree, and d is the distance between slits. not sure how to get rid of the sin term, since I'm not supposed to get a time-dependence

How do I into Lagrangian mechanics? Are there any good books on the subject? Also what are the prerequisites if any

>Will condoms always be necessary for safe sex?

There already exists a way to have safe sex without a condom.

Have your partner take an STD test.

How much LSD will a 6'0 270 pound person need to take to go completely out of this world?

pinch yourself

LSD dosing is largely independent of your actual body mass. It depends on what you mean by "out of this world" and if it's your first time or not.

Done 100ug twice.

No real halucinations, vivid colors, everything I saw looked differently, some bleeding, was able to hear noise.

I want to have a trip where I journey through the Universe and leave the planet

Try 400mcg. That'll put you around the "heavy" threshold. It's pretty setting dependent too, for example if you keep yourself in a dark room you'll have a much stronger trip.

Classical Mechanics by John Taylor is a pretty good book in general, but learning the Lagrangian method is pretty simple as long as you are fluent in calc and diff eq. In my opinion it should be taught alongside the newtonian method or at least touched on in the high school level. All you need to know is that the Lagrangian is equal to the kinetic energy minus the potential energy (L=T-U) and the partial derivative of the Lagrangian with respect to a coordinate is equal to the time derivate of the partial derivative of the Lagrangian with respect to the derivative of the coordinate. I realize that sounds super complicated but when put into equation form it looks much more simple and beautiful: [eqn] \frac{ \partial L}{ \partial x} = \frac{d}{dt} \Big( \frac{ \partial L}{ \partial x'} \Big) [/eqn]
The biggest take away from Lagrangian mechanics is that this works with any coordinates you choose (and a decent amount of the time the resulting equations are not solvable analytically if you don't choose the right coordinates). I recommend taking a few examples like a spring or pendulum, assigning a coordinate (you only need one for these simple examples) and using what you know about kinetic and potential energy plug everything into the equation and verify that it agrees with Newtonian mechanics. And if you already knew all this and you're just looking for a more advanced book on the subject, sorry for wasting your time.

>sorry for wasting your time.
No, thank you. This helps a lot user

Thanks, mate!

I'll give that dosage a try next time I trip.

Just remember that you can take more, you can never take less. Don't get too over your head with a huge heroic dose like a milligram unless you're willing to commit to it.

How does one go about proving a conjecture on infinite quantities? There are numerous unproven conjectures on various primes, so how can you prove a number does or does not occur infinitely many times?

>How does one go about proving a conjecture on infinite quantities? There are numerous unproven conjectures on various primes, so how can you prove a number does or does not occur infinitely many times?
this is really unclear, is there a conjecture you have in mind?

How to into lab reports in a nice and concise way?

I'm taking a lower division physics class where we base a lab report on a relatively simple pre-written lab. It's exhausting, and I'm having difficulty writing about what is essentially nothing.

Any of you guys have to deal with this sort of thing?

The question is a little too general for me to give you specifics.

However, in general, if I have to write an intro which simply requires me to rewrite an intro from the lab manual, that's what I do.

I combine 2-5 sentence into a reworded sentence and get free/easy lab points. Yes, very tedious, but I never say no to free points.

>en.wikipedia.org/wiki/Perfect_number
"It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist."

>en.wikipedia.org/wiki/Quasiperfect_number
Searches have been done up to 10^35, but I'm not a fan of the computational approach to mathematics. I would hope there's a more intelligent method than just counting upwards and checking. How would one go about determining whether a type of number exists without taking this kind of approach?

As for primes...
>Cousin primes
We have an established rule for these primes (they must differ by four) therefore we know how to identify them. How can we determine whether or not they continue to occur infinitely?

There are others I'm interested in but I feel these are sufficient examples.

Why did my homework problem say this was correct?
I honestly do not get where it got the 4.2 from. I get 3.66666...

I'm in retard math class for a reason.

convert hours to years

Mother fucker!
Thank you.

There's not much that can be answered to you about these questions. You should know that nobody can tell you how to prove that there are infinitely many cousin primes, because it's not even known. If anybody knew how to prove it it wouldn't be a conjecture.

If you'd like a related but reasonable example for "how do I prove something about infinitely many integers" there is a nice simple proof that an even number is perfect if and only if it takes a certain form, which shows there are infinitely many and also how to find them.

I was merely using cousin primes as an example, not expecting an answer on how to go about proving that specific conjecture. I'm just looking to understand how problems like these are solved in general (how to work with the infinitely many).

>If you'd like a related but reasonable example for "how do I prove something about infinitely many integers" there is a nice simple proof that an even number is perfect if and only if it takes a certain form, which shows there are infinitely many and also how to find them.

I would greatly appreciate a reference or link. That may be exactly what I need.

en.wikipedia.org/wiki/Euclid–Euler_theorem

Thank you very much!

Veeky Forums, there's a certain faculty member at my school who I have a massive crush on, and I have reason to believe she browses this board.

What's the best way to let this eat at me for weeks, then get drunk one night and confess my lust over several forms of media, and turn this into an awkward and uncomfortable situation for everyone involved, possibly leading to arbitration and ending one or more careers?

blogshit goes on

>So if the inside and outside of genitals are covered in this nanobot fluid
> nanobot condom

OK, stupid question. This has bugged me for years. A guy at work found an air conditioner (a/c) in the dumpster, so we lugged it inside. He put it in a bathroom, plugged it in and turned it on, and when it seemed to work ok, unplugged it and took it home.

So, my question is, taking a normal a/c unit, if you put it in a well insulated, air tight room (no exhaust) at, say 80 degrees F, and run it at it's highest cool setting for an hour, what will happen to the ambient temperature?

Yes, I am this retarded.

No exhaust? Do you mean to say the room has no ventilation? Or are you saying the a/c unit produces no exhaust heat?

I read that in her voice

Thanks for asking. It's about the room. I don't know if I should make it airtight for the experiment or not. If not, let's say there is some airflow, but the outside air is the same temp as inside (80F). Obviously, the unit takes in air and blows it out, but I mostly wonder what would happen if it only circulated air within the room.

Tempting to say the cool air and heat exhaust would balance out, but I think there'd actually be a net increase in heat due to the massive amount of electricity a/c units use

That's my guess, too. No unit is going to be 100% efficient and the excess is mostly going to come out as heat. I wish I had a chance to test it. Also, there would be a lot of condensation of water out of the air. I'm not sure how that would effect the ambient temp in a closed system where it turns into a puddle on the floor.

Yep, A/C units are a type of heat engine, which have an absolute maximum efficiency that is thermodynamically possible (don't quote me on this but I think it's ~60%) Another issue is that it's an electric device, which adds in another layer of inefficencies. In the end, running a 600 W A/C unit in a closed room would be no different from running a 600 W toaster.

So, the "magic" is in the exhaust and the draw throwing the heat out the window. I don't know why it bugged me so much, but "testing" an a/c in a closed bathroom really fried my neurons. Thanks.

I'm not sure how A/C's work exactly, but I do know that air being blown by a fan (or the wind or whatever) feels cooler because it is moving at a higher speed, and thus more air is hitting you per second and stealing heat from your body faster. So even though the temperature of the room may have gone up because the average kinetic energy of the particles has increased, it may also feel cooler to you because it's stealing some of the energy from your body to keep the room hot.

Any good books on game theory?

A/C generally works by compressing gases. When a gas is compressed, its temperature increases (governed by the simple PV/T equation), because the molecules of gas collide much more often. For cooling devices, the gas is compressed until it becomes a liquid. In A/C, the hot fluid is run through a radiator positioned outside of the room and gets nearer to ambient temperatures. The fluid then enters an expansion chamber where it expands into a gas. This is the reverse of the compression, so it logically becomes colder, just like why aerosol cans get cold. The cold gas is then run in a radiator in the room that draws in heat, bringing it nearer to ambient temperatures. This process goes in a cycle. So exhaust is key here, since you're not getting rid of heat, because that's impossible; you're just moving it elsewhere.

What would happen if the sun got split in two, moved just a kilometre apart and then let go to have gravity pull it back together?

Would it just wobble back together and go on shining or explode due to the exposed core?

Brainlet Linear algebra question:

I'm taking my first linear algebra course and we just went over the dot product of two vectors the second day. I have used the dot product before in calculus and physics, but I am having a hard time deciphering what the dot product means conceptually. You are multiplying the x,y,z components of two vectors, then finding the sum of the products, but what does the scalar number that you get when you do this actually mean? I initially thought the sum was the magnitude of a resultant vector from multiplying two vectors, but that doesn't quite fit.

You can consider it as the magnitude of the projection of one vector onto another multiplied by the magnitude of the other vector. It's like projecting one vector onto another and then stretching or shrinking the projection by a factor of the vectors magnitude. So it does produce a new vector in a sense, but you've collapsed 2D/3D space into 1D space during the act and so the result is a scalar. If you did this with higher dimensional matrices, let's say the dot product of two 3x3 matrices, the result would be a vector rather than a scalar.

cool thanks that makes a lot of sense, I wish books had good definitions like this for exactly what a theorem means

The dot product is in some sense a measurement of how much two vectors "influence" each other (e.g. when they represent forces). You can interpret it geometrically as the combined area of two parallelograms, but it's not really useful to think of it like that.

Why does gravity affect light if it doesn't have mass?

photons have mass though

Anyone with access to this 2013 paper, please?

dx.doi.org/10.2174/157017941006140206102255

How do you go from ii -> iii?

By adding one

The inner product of a complex vector space is still a map to the reals, so clearly Re()=

Is there a way to mathematically write this or should I just write that down?

>The inner product of a complex vector space is still a map to the reals

So I found this lens. I believe it to be a Plat-convex lens (flat on one side) and was wondering of making a telescope.
It's 150mm (~5.9 inch) in diameter and 28mm (~1.1 inch) height.
What other lenses do I need to make a decent telescope to be able to possibly watch and take photos of the moon.

tl;dr Need help for telescope

Do you enjoy studying? Like do you get a kick out of it every second like when you're playing a video game, watching a movie or anything else less productive?

I didn't study too much when I was in high school and now that I'm going to uni to study chemistry I need to study a lot to apply. And when it comes to studying I do like it, but sometimes it's more challenging and requires more willpower to do compared to something like playing League of Legends. I love the outcome of learning new things and concepts, but I can't study for 8 hours straight like I could when I'm doing something less productive.

I'm just trying to find out is it normal to sometimes feel like you're grinding new information to your head. I think the answer is obvious, but the thing is still bothering me.

use the polarization identity for complex hilbert spaces

scratch that. that's probably circular logic.
I would try a different approach, since (iii) => (ii) is trivial, try to prove (ii) => (i) or (ii) => (iv) and go back from that to (iii)

Where can I find supplementary instruction on college physics? Because of bum fuck public education, I never had an algebra teacher, or a trig teacher, or a pre-cal/cal teacher and now I'm one semester away from finishing my god damn degree and physics is just not happening for me. Vectors and kinematics ( 2D projectile motion, circular motion) is what we've covered so far. I don't follow how to solve problems or how to algebraically fuck with equations to find certain unknown values. What the fuck can I do. Please help.

Unfortunately the height doesn't tell you much. You're going to need to find the focal length, either by measuring the curvature of the lens or by shining a source of light through it and seeing where it comes to focus. If you want to make a telescope out of that you want your total focal length to be infinity and to get that your next lens will have to be diverging (concave). You want the beams of light to remain parallel but you still want an increase in magnification. You can find all the necessary equations online.

(reposting because i fucked up the latex tags)
It's the product of their length, weighted by how much they overlap.

- If the two vectors are pointing in the exact same direction, then the dot product is just the simple product of their lengths.

- If the two vectors are slightly offset (e.g. one is pointing North and the other is pointing Northwest) then the dot product is a little bit less

- If they are at right angles, there's no overlap at all so the dot product is zero

- If they're pointing in opposite directions then they have "negative overlap", so the dot product is the negative of the product of their lengths.

This gives a natural equivalent definition of dot products:

[math]\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos{\theta}[/math]

Where [math]\theta[/math] is the angle between the vectors and [math]|\vec{a}|[/math] is the length of a vector. You should verify for yourself that this is equivalent to the dot product as defined by the sum of the products of the components.

ughghg fucking hell i messed it up again, cba to redo it. hopefully you can work out what i meant to say

How good my foundations should be for me to be able to do the exercises on Apostol/Courant/Spivak's Calculus textbook?

What kind of cloud is this. Bottom is flat

Which software is used to make this trajectory simulation of J002e3?

you can write this kind of stuff with a few lines of code in basically any language
it's basically an approximation to the solution of a 3 body problem ode

is there any real difference between column vectors and row vectors?

least upper of any number k in N is k + 1....right?
there's no number in between unlike in Q.

when you said cauchy sequence in N, does that mean im working with a sequence that only contain integers?

>1/3

the choice is arbitrary right? In general i can choose any number n < 1/2