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HELLO AND WELCOME TO THE BOARD DEDICATED TO THE DISCUSSION OF MATHS, SCIENCE, TECHNOLOGY, ASTRONOMY AND ALL THINGS RELATED! Now, perhaps ill-advisedly, I will trust that if you're scientifically inclined, then you're more likely to be a reasonable, logically-minded fellow. BUT, since we're all also human (fine, mostly human), I know that fervor and heated arguments are bound to pop up once in a while, and that's fine. You need to be passionate in order to absorb and interact in the ways of the hard sciences. Keeping this in mind, I've crafted a few basic rules that must be followed by all:
First Rule: 1+1=2
Second Rule: L = -1/4F^2+iΨDΨ+ΨØΨ+h.c.+|Dϕ|^2-V(ϕ)
Third Rule: We're here to share knowledge, and we're here to learn. That is to say I don't want any kind of dick measuring contest, and NO SHAMING of any kind. If someone doesn't know or understand something you do, you teach them. If I catch you being all "lol how can u not no dis shit wat r u retrreaded" you're getting a ban the size of VY Canis Majoris.
Fourth Rule: This is not /phi/, this is not /x/ and this is most definitely not /pol/. You're welcome to consult this board on any topic that is relevant to it if your genuine interest is learning something new. But bring forth magic thinking, tinfoiled pseudoscientific arguments and biased political propaganda to this board for the sole purpose of trying to get the "sheep" to "stop being closeminded" and you'll be promptly proven wrong, laughed at and banished from the premises.
Fifth Rule: Similarly, you must at all times keep in mind that science is a method. Not an ideology or a cult or some tool to further your metaphysical/political agenda. This is important.
Sixth Rule: Much like in science itself, rules are bound to change once we find that something doesn't quite work or fit. Have fun, nerds.
The earth is flat and this book proves it.
Are all of your contributions going to be random Amazon links and feeble topics?
Do you think infinite numbers really exist? Or if they do exist, can we manipulate them in ways that are meaningful?
The reason I ask is that I've noticed there's a lot of finitists on various chans and prominent people like Wilderberger are espousing a dogma that doesn't permit any "completed" infinities despite their applications.
Infinity is where all of the interesting Mathematics happens. Pretty much all of (in)computability theory focuses on that. Church out some of Godëls theorems.
Research in large cardinals has shown that accepting the existence of a sufficiently large number is logically equivalent to statements that on their surface have nothing to do with infinite numbers.
For instance, if you accept the existence of infinitely many Woodin cardinals and a measurable cardinal above all those, you can create a model that satisfies ZF + Determinacy.
My point is that even if these numbers don't exist, they are extremely useful for consistency results and other applications I don't know about. I would put infinite numbers on the level of transcendental numbers- we will never be able to fully "Exhaust" one in the real world, but accepting their existence is useful and intuitively true. So yes, we can clearly manipulate them in meaningful ways.
finite numbers don't exist, yet we maniplulate them in ways that are meaningful.
Yes they do! Numbers exist not in themselves but as properties of objects. 2 exists as the number of cups of coffee I've had today, the infinite cardinality of the continuum exists as the number of points between my fingers and the keys.
>infinite cardinality of the continuum exists as the number of points between my fingers and the keys
Don't push your pet topology on me. One can produce a model of the space between your fingers and the keys with any cardinality.
Hello, this is my first post and it is here because i was permabanned in all the 4chan boards
Here is the question, i have been reading Serge Lang-Basic Mathematics-Addison-Wesley (1971) and i can't solve a problem, it is "Prove that there is no positive rational number a such that a^(3) = 2" while a = m/n which is specified before, i tried and i failed
The book gives an example with a^(2) = 2 which is the picture posted so can anyone explain the exercise and if possible the other two which is the same but a^(4) = 2 and a^(2) = 3
Suppose that a^3=2 with a rational. Then we can write a=m/n for some natural m and n such that m/n is in lowest terms (that is, m and n have no common factor other than 1). It follows that a^3=(m/n)^3=m^3/n^3=2, so m^3=2n^3 and we find that m^3 is even. Since m^3 is even we know that m itself must be even, so m=2k for some natural number k. Then m^3=(2k)^3=8k^3, so 8k^3=2n^3. Divide by 2 to find that n^3=4k^3. It now follows that n^3 is even an hence n is even, a contradiction since we also have that m is even but m/n is in lowest terms.
The arguments for a^4=2 and a^2=3 should be quite similar.
ah i get it now, i couldn't figure out what it truly meant, now i know thanks alot anon
So, according to Godel's incompleteness theorem any sufficiently complex system is inconsistent, such as arithmetic or ZFC. However, the proof hinges entirely on expressing meta-mathematical statements within a mathematical system, which seems kind of silly to me. Is it possible to prove that a system such as ZFC is consistent, inconsistent, complete, or incomplete with a formalized meta-mathematical language?
As an example, ZFC is a system meant to be interpreted as statements about sets and classes from my naive viewpoint. In other words, it is a system "about" sets. The meta-system I'm talking about would be about the system that is about sets, making statements not about sets themselves but making statements about the statements that are themselves about sets.
What kind of axioms would this meta-ZFC have? What symbols could be used to express it? What would the rules for derivation of theorems from these axioms be?
If you have anything to say about this I'd love to hear what you think. This post was probably a little confusing, so in short what I'm trying to do is get around or avoid Godel's incompleteness theorem.
It's not that it's inconsistent, it's that it is either inconsistent or incomplete.
You could prove the inconsistency of ZFC within ZFC by showing a contradiction. Similarly, you could show the incompleteness by proving that a theorem is unable to be proven true or false.
No one has been able to do the first; as far as we know ZFC is consistent. If it weren't, that would be a really, really big deal. Like, rewriting the foundations of mathematics big.
On the other hand, incompletenesses have been shown. There are statements in ZFC that could be true or false without violating any of the axioms.
The only way to get around Goedel's incompleteness theorem is to lose one of the conditions. Either your system is incapable of expressing arithmetic on natural numbers (meaning that counting is impossible) or it is inconsistent (meaning that some statement is both true and false).
Systems unable to express arithmetic on the natural numbers are probably very uninteresting, but you might be able to come up with something novel; that's something I don't know much about. Breaking consistency, on the other hand, means that everything is true and false. Those systems are very uninteresting.
Unless I misunderstand the premise of what you are saying, it sounds a little like you are trying to reinvent type theory. There are plenty of other, more abstract languages that can be used to reason about ZFC in the way you are describing. Type theory, category and (the nascent but probably most interesting) homotopy type theory among others.
I recommend a text on abstract algebra if you are just interested in learning about reasoning about algebraic structures, such as sets, in general or a text on category theory or something if you want to know more about higher level mathematical languages.
Can you recommend me a good category or type theory text? I've become fairly comfortable (still learning of course) with the fundamentals of set theory and logic since the OP, but I know nothing about those two topics.
The big question is this: why should I bother learning type theory or category theory if (nearly) the whole of the mathematical edifice has been done in the context of set theory? I don't mean to be argumentative at all, but what's the point of having an entirely different system that is for all intents and purposes equivalent? What do you mean by reasoning about ZFC with category or type theory?
Are you talking about propositions as types?
Category theory and (homotopy) type theory are able to serve as foundations for mathematics just like set theory does. They are not directly equivalent to each other in any way that I know. Things that are easy to prove using category theory might be hard to prove using set theory or vice versa, so each possible choice of "foundation" has its uses.
This board doesn't look too heavily trafficked, so I'll try to remember to come back in a week or so to check in and answer any questions.
I'm in my first year of a doctoral program. I have a background in statistics, but applied looking to cross over to pure mathematics. The school that I'm at right now has math and stats as a singular department. I think they misread my application and thought I was applying to a doctoral program in statistics. Now that I have my foot in the door, they can't really take away my acceptance. However, they've tried to chase me off by not making me a teaching assistant or giving me any financial support. On the road to getting a master’s in statistics, I racked up about 30k in debt, which I don't think is that bad considering the job prospects. But without any aid here, I've already had to take out 10k in loans for this semester, AND had to drop a class in order to afford that. Next semester brings another 10k loan to take out.
I decided to stay here so that I could build up a transcript and show potential schools that I can work at this level. At the end of this semester I'll have 2 A's in Abstract Algebra and Real Analysis. Next semester I'll repeat that with Advanced Linear Algebra and Complex Analysis. Part of me is hoping that after seeing me excel at this level, that the school I'm at will throw me a bone and start to support me. However, I want to have a contingency plan if that doesn't work.
The only thing that sucks about my grad application is my GRE subject test. I'm pretty sure there were schools who automatically turned me down simply because I wasn't good enough on that test. Any school who can get past that should see me as a very capable student, but because of the automation of the application process, I'm not sure which schools actually have human eyes seeing my application. Of course retaking the GRE seems to be the most appropriate option, but the window for doing so in the Fall had expired by the time I thought about retaking it. I'm signed up for April, but it will be too late to have a new score on my application by then.
Do you know of any mathematics programs that don't require the Math GRE for the application process? Or any schools that are fairly lax with entry requirements? (After being denied so much because of my GRE, I've got some pretty low self-esteem, and would love to have an "easy in" school as a confidence booster). Or any general advice for someone who has had a tougher time with the admission process than the actual material?
Right you are, but I'm glad I got back to you!
I'm currently residing in the wonderful town of Rochester studying my eyes out because I was accepted with tuition waived and everything. Who would your friend be?
Please come back, I want to know this friend connected to a friend from 99chan ;-;
I came back, his name is in this image.
I'm also from Rochester and do math there. Nice to know I'm working around like-minded people.
">The Hellza Ballza School"
It's there such a thing as obsessive compulsive posting? The objective of this question is to discover a commercially viable reserve of crude oil suitable for extraction and piping to a refinery.
I want to talk to you a little bit about closed jar terrariums. Basically, you create a small ecosystem within a jar that has three main things: producers, consumers and decomposers. Once you have those three in their, you seal it shut for good. No food, no additional water, just those three things. This way, you create a natural balance within the jar, so that for life to go, all you need is sunlight.
Now, there are some challenges involved because you need to make sure that you have the proper species of plant and animal, or else you are doomed from the start.
For the plants, any freshwater aquatic plant will do. With the proper amount of soil and decomposers, they can help bring food and filtration to the system. For your consumers, you want to choose a species of that eats plants and gives live young. If you choose a fish that lays eggs, the decomposers will eat them, causing them not to reproduce, thus ending the cycle. For the decomposers, you want a creature like snails or shrimp. They will eat the poop and dead consumers, and return that to the soil, thus restarting the cycle.
Now the tricky part is getting the balance right. I've attempted to create one myself, but all of my consumers died one month later. I believe that I chose fish that were too big for the jar, because I could only fit 6, two males and four females. The two males died after two weeks at the same time, which meant that there was no chance of reproduction. I think if I have smaller fish, I can have more in there, which means that if a few die without reproducing first, then the experiment can continue. Plus the added biodiversity is always good.
Has anyone else tried this before? Or perhaps, does anyone want to try this now? I'd be willing to do it again if I had people to share results with.
My ex girlfriend was very into these. I think the idea is that the simpler the system the more stable- so some mosses or small plants should be self sufficient for a long time. Try going down to your local river and just picking up random shit that seems alive, then seal it up and see how it goes. Mason jars and dirt are cheap.
How can I perform this kind of analysis on my own brain MRI?
Looks more like positron emission tomography scan.
How do I grow something like this around my house or in setting up a hotel? Any links?
It's a bit difficult to discern what this is, are those hanging vines? Or are they stalks growing from pipes at the ceiling level?
It looks like some kind of hanging moss that's growing on top of the tree
Anybody here a staunch intuitionist?
I've been reading about categorical logic and it has opened my eyes. Before I thought intuitionist logic was silly but it turns out to be very natural from this point of view.
That said, from what I've seen there is a sense that a given person either is or isn't an intuitionist, which is a very classical thing. Anybody here contest that?
It's not about believing in a certain type of logic. What matters is that it is able to produce useful ideas (extrinsic results), which both intuitionistic and first order logics etc. do very well. As far as it being more natural, that could be viewed as a good justification but it still would be silly to say that you are either an intuitionist or not as the latter could be viewed as either an extension or a restriction depending on how you look at it.
It would be foolish to abandon first order logic in favor of intuitionist views, they are both good things.
For a lot of ideas in math there are "Deep" truths, where both sides of the coin are useful and productive things to use a metaphor. Although this kind of math is evidence based, you can't make determinations like "intuitionistic logic is right" or "first order logic is right" as can be done in other fields in the way that we say the sun is yellow or the sky is blue.
My understanding is that it is a logic where the law of the excluded middle and the double negation principle are disposed of. i/e
--p != p & -(pV-p)
>>552 Can you recommend any good texts on the theory of intuitionist logic? I have read only some background overviews about it's theory and history, and learned a little of the theory in the context of substructural logics and linguistics. I just want to know what intuitionist logic is really all about.
Sorry, you're probably better off doing some google searches and finding a book that is good for your background knowledge. If I were to suggest you anything it would just be me googling and posting what I'd buy for myself.
I sometimes think intuitionist logic is cool.
I also think it's unfortunately named, as the name itself draws ire (as you yourself have experienced). Similarly I think Complex/Imaginary was a poor choice in wording.
I'm working on a project that amplifies an 1-6mV output voltage from a pressure sensor by a factor of 500, to get voltages in the range of 0.5V to 3V
Problem is, the op amp is actually amplifying by a factor of 60, not a factor of 500. Does any electrical people know why this is? What about op-amps causes an order of magnitude in amplification? Is it because the circuit diagram calls for R1 to be 470Ohms but in my real life circuit R1 is actually 270 ohms?
data sheet for all three OP-amps (LF256N)
I'm a non-electrical guy doing electrical work :(
I failed high school math. I didn't understand many concepts because nobody would clarify my queries - until I got comfortable with Wikipedia and it showed me the foundations of maths and killed my cognitive dissonance. When I first learned algebra, I was confused over whether the concept of x could represent x's in itself. That is, self referentiality or x = 2x. This made things very difficult. I didn't see why a pronumeral couldn't stand for another pronumeral and it refer to itself. I realised that maths problems was unsolvable this way and implcitly accepted that for analysis to be completed I could make the proceedural ontological assumption that anything cannot be a part or element of itself. Excuse my spelling, I'm drunk.
How do you study, man? Share your secrets? I mostly get what is happening in a example, but I can't practice longer to put it my head.
How do hormones affect sensory perception and subject experience?
Hello /calc/, I found this on Kickstarter: http://kck.st/1gVCcrB , it's literally a low-cost alternative to Project Tango, you can DIY it for 50$ and do not need to buy a specific smartphone model just for having a 3D camera, it's adaptable to all Android and iOS smartphones, Raspberry Pi and have ROS drivers for Robot Operating System middlewares!
I really love the idea of using this for SLAM Augmented Reality and 3D scanning, quality look pretty good for such small device.
If it succeeds, I think it would be very beneficial for the DIY community, pledging for the developer edition give you the source code, the 3D CAD files, B.O.M. and it's possible to build one completely from scratch, unlike other commercial solutions you become completely independent (spare parts, repairs, support, etc.), the possibilities are endless, so far I've not found a way to do it DIY on a smartphone, if anyone knows an open source solution like this please let me know, I searched hard for it.
However, if this continues like this I'm afraid they won't make it with the funds, honestly this leave me a bit disappointed, because commercial solutions like the Structure Sensor by Occipital has reached over a million dollars, and it's not completely DIYable, as we speak lacks support for Android, it's much more expensive and at first glance the resolution doesn't seem much better or worse.
Apple bought PrimeSense, blocked sales, pulled down OpenNI website, stopped the development of open source solutions, I hate to be forced to depend on them.
So, it's not my intention to spam, but I think this would greatly benefit the DIY community, I always wanted to be able to build these from scratch, so I can customize/tweak according to my needs, if it interests you, please spread the word, I've already funded it.
fuck you and your spam. I remember getting you bann from /diy/ like 10 times.
Here is my situation:
I am returning to school in the fall, I need to know calculus by september. I took it back in highschool, but I remember absolutely nothing.
I can find tutors no problem, but I can't really find someone to provide me with a curriculum that will get me up to speed. I don't really know what I don't know, if that makes sense.
If there are any good resources online, I would really appreciate it. I found an interesting website that had videos with people going through math equations step by step on a tablet, but I can't remember what it is called.
If anyone has any advice, I would appreciate it.
Thank you /calc/
Picture unrelated: An undercover NYPD officer busts a mugger on the subway in the early 80s
Also, if someone can suggest to me an excellent math textbook, preferably available on amazon, I would be incredibly grateful. I am currently searching local bookstores for textbooks, preferably older ones since I have been told they're better, but no luck thus far.
I spent the last couple of years teaching math, and whenever a colleague needed to brush up on something for a class they were teaching they would use Khan Academy.
When I learned calculus I used a book called Calculus: Early Transcendental Functions by Larson and Edwards. I liked it well enough but I used it with a class (actually two) so I can't speak to it's efficacy for those who are self teaching, but it is used by my school for calc 1, calc 2, calc 3, differential equations, and one more I think so it can't be all that bad. The derivative/integral cheat-sheet in the front is handy so if you can get it with that I'd say go for it. Hell, if you're in the greater Philadelphia area I wouldn't mind lending it to you.
Here it is on amazon:
I learned calculus from Morris Kline's "Calculus: An Intuitive and Physical Approach". Absolutely amazing book, costs $22 on Amazon, and the full solution manual is on the publisher's site.
I would also recommend you try Jason Gibson's series on Calculus. It's on mathtutordvd.com but you can just torrent it (it's on the pirate bay, etc).
Just choose the Calculus ones in your torrent client instead of downloading the whole thing.
Great explanation with examples.
I like to understand things in terms of how they relate to other concepts. I generally use Wikipedia as my ontology. I'm trying to understand the relationship between the words in white, and I use philosophy as the organising concept that it all comes back to. I can automate the process of generating what hypoerlinks links the white words together with a nice app available online (xefer.com). Can someone help illuminate what the white words mean here with reference tot he black words. I mean, if I wanted to differentiate reduction in complexity theory, with forecast, I could explain it most broadly as ne relates to properties and the other relates to what necessary and sufficient...but I don't understand what this even means. Can you think of an alternative way of carrying out my suggested method of analysis?
It seems that patterns exist in numbers such that there can be (en.wikipedia.org/wiki/Mental_calculation) mental calculation shortcuts?
Can we analyse the trends to infer how the mind works?
Hello. I need to make a sound-related experiment on my physics class for a project. Do you have any interesting ideas? There's plenty of various equipemnt in my school that may be necessary.
You could make one of these. Or some sound powered phones, which is a non-powered communications system used on navy ships. Or make a giant speaker out of a room or small building that has a large opening.
You could try that, but I don't know how viable it is without knowing more about your school.
Or you could try soundproofing your class with egg boxes and then detail the principle of how it works. Failing that, just a classic string vibration to prove one of the early scientist's work.
Ruebens tube will allow you to display waveforms with fire, and it's not all that tricky to make.