So im reading up on chaos stuff right now but I have a few questions.
So essentially there is chaos (deterministic) and real randomness. Chaos is almost everything we declare as random (rolling a dice for example) while real randomness is essentially really rare, for example in radioactive half-life.
Are there any other examples of actual randomness?
>>8093939
>Are there any other examples of actual randomness?
Everything that depends on quantum effects. Tunnelling (radio decay) is the easiest to explain, but basically all of quantum mechanics.
>>8093949
Layman here. Can we prove their randomness or we just don't know what happen behind the scenes and use this approximation?
>>8093949
Thanks, gonna read up on that and try to understand it at least a little bit
historical accuracy aside, is this a viable idea?
how difficult would it be to make it work?
>>8093894
They tried to do it on mythbusters
>>8093894
Archimedes was straight balling.
>>8093894
It's unlikely that the wood will burn
You can however burn the sails
So what I had gathered is that maths was for the most part discovered, meaning that it would exist regardless of what we do. But does all forms of math fit this? For example: are matrices something that were discovered or something that is governed by man made rules?
>>8093701
axioms are invented
the resulting objects and their properties are discovered.
Math wouldn't exist without us because our logic is not universal, it only makes sense to us. And that's what we use to do math.
>>8093701
Philosophy is just structuring and formalizing in natural languages.
mathematics are about formalizations of your speculations (which you form from your desire to see things that you experience [the empirical world, once you chose to objectify what you feel] through induction, as similar or dissimilar) to the point that you have a structure more formalized than your speculations structured in natural languages.
Logic is just a the formalization of your speculations about *validity of inferences*, so here logic is a formal part of mathematics.
It turns out that plenty of mathematical structures are cast into some formal deductive logic (like set theory formalizes your structures of numbers).
I meant your usual set theory cast in FOL. Set theory is just a structure too and it turns out that you can interpret a part of this structure as some kind of numbers.
Science is just claiming that your formalized structures (in formal languages or not) gives you access to some *reality*, more or less hidden with respect to what you are conscious of[=the empirical world, once you choose to ''externalize, objectify'' what you feel].
Same thing for the religions which go beyond empiricism [=claiming that you feel and think is **not** enough from which you choose to dwell in your mental proliferations].
Some mathematicians, typically Brouwer, think that mathematics should, equally to the speculations (however formalized) of the scientists, talk about the empirical world. So typically, your formal symbols are real entities: these entities belong to some world and they connect or not back to the empirical world.
to be clearer, the symbols are names of real entities and, since you begin always from the empirical world, this world constrains you on the creation and usage of these real entities. then these real entities can or cannot belong to some other world as well.
A lot of math, historically, came from "standard" (ie. euclidean) geometry.
So thats mostly discovery, because you can draw pictures and see how things work out.
(Our real world is approx. Euclidean 3d space)
However, once a certain formalism is established (like Cartesian coordinates, defining algebraic equations for plane curves, or axioms for deriving all known properties of geometry), one can twiddle around with that and invent new things.
Probably the most trivial example would be Euclidean 4d space, or more interesting, alternative axioms for geometry, in particular relaxing the parallel axiom in Euclidean geometry leads to hyperbolic geometry, which is a lot of fun.
pic related shows a bunch of lines going through some point and parallel to a given (thick) line, visualized in the poincare disk model of the hyperbolic plane.
Does your college run moodle? Do you like it?
I work for IT in a college and I have some weight regarding what platform we migrate to next semester. I want to know students' opinions
>>8093608
Buggy as shit, could be worse. Homework on moodle can go suck every dick in existence though.
>>8093618
Second
I hear Canvas is pretty good.
What if we just took all the CO2 from Venus and gave it to Mars
We'd have two more habitable planet just like that. It's probably LITERALLY what ancient Aliens want us to do with them, and we're sitting here wondering how to send a robot there. Fucking pathetic.
>>8093541
CO2 won't sustain alien life. Mg4O5(g) does. The Drake Equation (d×t×x) proves this.
>>8093541
Oh, just like that.
>>8093541
How would you do it?
Alright /sci/ I'm doing some tutoring for some freshmen at my uni and I stumbled upon pic related.
How can we prove it by mathematical induction and just induction? I think it'll be a fair exercise.
>>8093523
a^2+b^2=c^2 is the best avenue of solving that equation.
>>8093523
[math]10\nmid(k^{2}+2k+2)(k+1)[/math] though, try n=3, you get 17*4 which is 68.
>>8093528
Incorrect.
k+1=60
60-1=k
K=59
What percentage of the planet's relative gravity is do to the fact that the planet is spinning? What percentage less would we feel if the planet was stationary?
>>8093425
Standard gravity is inferred directly from the density of the earth at given points. This isn't the 19th century any more senpai, we don't use pendula to measure g. So if you were to drop a particle it would undergo an accelerating less than g because of the coriolis force.
>>8093425
https://en.m.wikipedia.org/wiki/Gravity_of_Earth
Check out the part in apparent gravity. It also varies by a little bit depending on your distance from the earth's axis of rotation.
What is /sci/'s opinion on AP Physics?
>inb4 europe
>>8093364
Mechanics C is the only useful one.
The "algebra-based" ones are retarded.
E&M needs mv-calc to be done correctly. So E&M C isn't very useful.
>>8093376
Thank you for your input.
>>8093364
It has an abismal passing percent, only 30% get a 3 or higher. I took it and it was very hard but very informative. Take it with no expectation to get college credits but just to learn. I'd recommend it.
If maths is just a set of rules made by people, how can you call it objective when people could change those rules?
>>8093359
math exists whether or not we discovered the "rules"
they aren't invented they're discovered, please commit sudoku
>>8093368
This. Math is discovered, not invented.
You can in fact define your own sets of mathematical rules across a space you define, and this is often done in fields such as modeling. However, such systems will either be a subset of an overall vector space, or will be inconsistent.
(Took linear algebra 101 eight years ago so I know what I'm talking about)
I was mulling over some GR equations, when something hit me. We often say in physics that certain things can't be possible because they would violate causality, but just how well-founded is the invocation of causality to constrain a physical theory anyway?
Starting from classical physics, [math]F = ma[/math] really doesn't say anything, except to provide a meaning to the word "force", until we start attaching the implication that a force *causes* a mass to accelerate. Otherwise it, and everything else in Newtonian physics, is just a bunch of acausal couplings between expressions.
The problem gets hairier under relativity, because simultaneity now goes out the window. Two observers in different inertial frames cannot agree on the simultaneity of events, yet it is asserted that they can still agree on a partial ordering of some events, so long as a lightlike or timelike interval seperates them.
(cont.)
(cont'd)
While Newtonian gravity expressed the interaction of bodies in a basically acausal, yet simultaneous way, GR suggests that the bodies (represented by the stress-energy tensor) have an effect on the geometry of spacetime (the metric tensor), which then affects the bodies in turn (the geodetic equations). This might not be a problem, except for the fact that their exist valid solutions like the van Stocktum, Gödel, and Alcubierrie metrics allow you to create a circle of events which are still seperated by timelike intervals (closed timelike curves), which means you could have a seemingly paradoxical cyclic causality. To date, all responses to these metrics have been the suggestion of ad-hoc conjectures that invoke causality as some kind of universal force field, something which strikes me as desperate and unsound.
When one tries to natively combine the equations of relativity and QM, we get the timeless, acasual, and nonlocal Wheeler-DeWitt equation. This is presently interpreted as showing some essential incompatibility between GR and QM, but what if what that equation has been demonstrating, and we've been ignoring, is that this is precisely how the universe operates? That time, space, and therefore causality and locality, are merely emergent properties of laws which are have none of those things?
What would the implications be of ditching the reliance on causality? Is it even possible to make a coherent theory without it? Can we even prove that the universe is logically consistent in the first place?
because we have absolutely no experimental evidence for acausality
also metrics such as godel's do obey causality, and also just because it's a mathematical solution doesn't mean it's in any way a good physical solution
EFE break down at certain extremes, we already know this. is meme theory the way to fix that breakdown? probably not, but it sounds like you don't actually care about physics being a science (rather than physics being a study of mathematics), so i guess you'll be a great meme theorist
>>8093369
I didn't say acausality as such had been observed, certainly not at normal scales. My question is if it's possible that causality might a) be an emergent phenomenon of something which is acausal, and b) if that causality might itself break down under extreme conditions.
As for the "not all mathematical solutions are good physical solutions", well, then we still have to explain what those constraints are and why they exist. Physics tends to follow the math quite closely. No one had ever observed antimatter when Paul Dirac first wondered what would happen if he did't discard the negative solution to a particular quadratic term in the relativistic Schrödinger equation.
Researchers say the "sperm crisis" is a tough nut to bust, and "that if we keep fixing the problem, in 10,000 years no men will be producing sperm."
http://discovermagazine.com/2011/nov/12-impatient-futurist-sperm-crisis-tough-nut-crack
Good. Women have become so cancerous to this species that we'd better be extinct than let this continue.
>>8093291
>implying half the world's population doesn't sill live under 19th century conditions.
>>8093291
seewhatyoudidthar
Why are there so many theorems that are completely obvious/common sense? IVT/EVT are the first ones that come to mind. Do there really need to be theorems for those things? They just state the obvious. The logic behind them just can't be refuted. So what purpose do they serve?
yes there does
>>8093289
yes
>muh rigor
That's the only reason, OP. """"Higher level"""""" math is just mental S&M
During the summer my room gets super fucking hot from the sun beating on my room in the second half of the day . We have AC and there is a vent in my room but it still gets super warm especially with a computer going.
I notice that when I walk out into the hall from my room, that there is a noticeable different temp, much cooler in the hall.
If I have a fan positioned at my room doorway, should I have it positioned in or out to make my room as cool as possible, and should it be directly at the door bounary or offset in some way?
For the record, I think I should have it pointing into my room. I figure that the air will be coolest lower down outside my door, and forcing that air into my room will help the most, but I don't know if that is helpful with the AC also blowing into my room
since you dont have a source of cold air input, only heat input (computer + sunlight and hot air from outside) you'll want to have the fan blowing cold air into your room
blowing the air out wont help since new hot air will replace it immediately.
blowing cold air in will reduce the temperature of the hot air in your room
>>8093024
oh i missed that you have an AC vent. then what you could try is positioning the fan over the AC vent so it passes that cold air better through your room.
i tilt a small desk fan over my AC vent so it isnt blocking the grate and it blows cold air all through my room, whereas with the vent alone, it just hovers around that area.
since you have a lot of heat sources this would probably work best, and just leave your door open for air circulation
How do you guys stay motivated to study?
atm I feel really burnt out on math..
pic unrelated
>>8092998
getting good grades
Because if you dont study youre gonna end up like the guy who picks up your trash every week and barely make enough to support yourself.
>>8093005
But sanitation workers make solid money, senpai
http://america.aljazeera.com/watch/shows/real-money-with-alivelshi/articles/2015/1/13/sanitation-gold.html
Find a non-trivial function f(x) that satisfies:
f(ab) = a*f(b) + b*f(a)
(trivial being obviously f(x) = 0 would work -- pick something else)
>>8092974
Looks like the product rule of differentiation...
>>8092974
Let a = b = 1/2, f(x) = 1. Your welcome.
>>8092982
Good one, I didn't think of that.
Now suppose a and b are real numbers not functions.
