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/sci/ - Science & Math

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4801721 No.4801721 [Reply] [Original]

einstein once said

"if you cant explain it simply, then you dont understand it enough"

explain what you think you know well in the most simplistic way possible.

>> No.4801729

OP is a male who is attracted to other males

>> No.4801734

>>4801729
We need to stop pushing the boundaries of what we know and leave a little bit for the soul to believe in.
Nanu nanu... hahahaha

>> No.4801779

schrodingeys cat

the cats put in box. inside the box is a device that, if the cat does something, will kill it.

the cat is inserted, the box is closed.

from that point on, to you, the cat is both dead and alive. which one it is in unknown to you, so to you, the cat is in limbo.

>> No.4801783

godel's first incompleteness theorem is the assertion that any theory of mathematics powerful enough to express truths about number theory will either have unprovable truths or contradict itself.

a counterexample to the converse can be found by creating a theorem which asserts its own unprovability, through a combination of a theorem-numbering system called godel numbering in conjunction with an application of W.V.O. Quine's method of indirect self-reference.

this is as simple as it gets without writing another GEB.

>> No.4801788

I'd like someone to explain Galois theory simply. I tried abstract algebra:

Suppose you have a collection of objects which has nice properties, e.g., the collection of real numbers, with arithmetic as the nice property. Let's say you figure out the rules where these nice properties come from (for our example, it would be a rule for making an object out of two objects, namely addition). Then you can consider the class of collections which satisfy these rules, and prove theorems about it. So now, if you show for some collection that it satisfies these rules, you've automatically shown that these theorems are true for that collection (for example, the symmetries of a pentagon also have a sort of addition, so in a way they're kind of similar to the real numbers).

>> No.4801800

Niggers act like animals because they are animals.

>> No.4801815

>>4801779

hehehe you don't really understand it at all.
"to you" - it's not just to you, it's to everyone. the cat's state is fuzzy in mortality. only when its measured does it live or die.
that's the problem with the analogy; intuition tells us the cat is either dead or alive at any instant of time. but in QM that's not the case - its a mixture of dead and alive.

>> No.4801817

Quantum physics: everything is a wave, but you only notice it when stuff becomes small enough.

Relativity: Gravity is only the effect of mass bending space-time.

Thermodynamics: 1st principle says energy cannot appear from thin air. 2nd principle says heat will always go from hot stuff to cold stuff, never the opposite.

Electromagnetism: An electric field is either created from electric charges or a dynamic magnetic field. A magnetic field is either created from a current or a dynamic electric field.

Gödel's incompleteness theorems state that: if a theory has enough axioms to do standard stuff with numbers, then you can't prove that theory is correct using its axioms (incompleteness in coherence). Moreover, there will always be truths that will never be proven using these axioms (incompleteness in decidability).

P = NP states that for every problem qualified as "hard" (for which algorithms running with polynomial costs haven't be found), there exists an algorithm solving it "easily" (i.e. using an algorithm with a polynomial cost).

Light is an electromagnetic field. The thing you see is the field's mean energy being radiated toward your eyes.

>> No.4801819

>>4801783
>W.V.O. Quine's method of indirect self-reference

I don't think this qualifies as simple. :P


>>4801721
I don't agree with Einstein. For some subjects, if you simplify the explanation, it fails to be an explanation. I mean, I could tell someone the whole dead/alive cat thing and leave it at that, but they would be no closer to having a clue what QM is about. It's simple, but it's not an explanation.

I'd be pretty amazed if someone would be able to explain simply the notions of pseudodifferential operators, De Rham cohomology, the Grassmannian, or even tensor calculus.

>> No.4801824

>>4801721
I thought that was a quote from feynman.

>> No.4801829

>>4801819

obviously specialized topics need further understanding

>> No.4801895

>>4801819
strictly speaking, it's not a required part of the simple explanation of godel's incompleteness theorem, only the concept behind it; that is, the fact that indirect self-reference is a usable thing. indirect self-reference, in a few words, is when an object refers to an object exactly like itself, a description or composition of which is [usually?] created within the object.

bonus content follows.

quine's specific method of indirect self-reference (which is, to my knowledge, the only one) is most accurately explained with examples, due to the sheer number of words that would likely be required otherwise.

consider the following sentences:
- "is a sentence fragment" is a sentence fragment.
- "when preceded by its quotation, forms a proper sentence" when preceded by its quotation, forms a proper sentence.

the second sentence is the exemplar of indirect self-reference. in a programming analogy, if you have code which replicates its given data as both code and data, then subsequently describes or acts upon that result, then passing a data representation of the code to the code will force the code to describe (or act upon) the unit composed of the code and its passed data: namely, itself.

it's easier to talk about when you define the verb "to quine X" to be "to precede X by its quotation X". the second sentence can be rewritten '"when quined, forms a proper sentence" when quined, forms a proper sentence.'

(in case you catch on yet i really loved reading GEB)

>> No.4801976

we are biological machines, natural and artificial don't mean anything.

>> No.4801993

>>4801976
>>4801976
>>4801976
>>4801976

>> No.4801998

1+1=2. If you take 1 stick and put it together with another stick then you have 2 sticks.

>> No.4801999

>>4801819
To be fair, the cat was never really inetended to explain QM.
Also, I tried explaining De Rham Cohomology once to non-science friends, failed completely.

>> No.4802046

>>4801721
Einstein's expertise wasn't in the nature of understanding, or teaching.

>> No.4802061

>>4801721
and others.

This is not a genuine quote from Einstein. Seems to be derived from something he said that was similar.

http://en.wikiquote.org/wiki/Einstein#1930s

>> No.4802102

>>4802046

doesnt matter. if you dont understand something enough to explain it in easily understandable and simplistic terms, then you simply dont understand it enough.

its not that fucking hard of a concept, but trend fags liek you all think you know the world when in reality you dont know shit.

case in point, this entire thread. not one of you shit asses explained some easy to understand concept. you all came in trying to sound smart. youre fucking failures. get off 4chan. your life is shit.

>> No.4802110

Apparently Einstein said the thing this is derived from to discredit quantum physics.

Obviously this demonstrates that this saying was created for the wrong reasons.

A description of the universe should be simple, but there's no philosophical basis for the idea, which Einstein vainly clung onto, that it should be intuitive; that is to say, that it should correspond to every day, macroscopic experience.

>> No.4802111

>>4802102
Trend fags? What does that even mean?

You're just plain wrong, some things are simply too complex to be simplified to that point. Besides which, why do you have so much hate? We're not failures, our lives aren't shit, and why should we get off 4chan if we enjoy it here? It seems like you're projecting.

>> No.4802116

>>4802111

i wish. what im getting at is, none of you really know what youre talking about.

if you really understood what its like to really understand something, like you all seem to claim (when apparently explaining something complex), then youd fully understand what the quote means, and none of you would be getting into the piss fests you all get into.

fact of the matter is, a majority, if not all of you, dont understand anything you all claim to understand in the level that you claim. youre trying to sound smarter than you are.

youre trying. youre sheep.

>> No.4802118

>>4802116
That's rather rich coming from someone who doesn't even use punctuation. But enough feeding you, I have things to understand.

>> No.4802129

>>4802118
>criticizing punctuation after facing the facts of the matter.

prove me wrong know-nothing

>> No.4802135

>>4802110
>philosophical
>basis

Besides this oxymoron, I think the idea that everything should be intuitive on some level IS the basis.

>> No.4802138

bs
understanding and putting it into words are 2 different things. Plus the fact that the person your telling maybe idiotic in understanding as well. Not to mention the fact that they can just ask "what?" or "huh?" or "why?" at the end of your explaining anyway
i understand this and if you dont, tough beans

>> No.4802143

>>4801721

fuck

>> No.4802145

>>4802135

its true. we should be trying to understand it to the point that we can explain it to children. if we cant explain it to a child, then we dont fully understand it.

at one point, teaching basic mathematics was considered too complex to be explained simply.

>> No.4802163

Weed is fun and if you consume it primarily through a vaporizer and edibles its good for you

>> No.4802161

>>4802145
>>4802135

no, it's a bullshit basis. we have moved on from this philosophically and scientifically a long time ago. philosophically: there is no logical argument you can give to imply that reality outside of the domains we naturally observe should be amenable to be comprehension of faculties solely to conceptualise said natural domains. scientifically: it is impossible to give an intuitive description of various scientific facts, much of which can only be described with abstract mathematics. try to give an intuitive explanation of a spinor, for instance. or intuitively describe a wave of probability.

>> No.4802177

>>4802161

K Godel / Hilbert.

>> No.4802181

>>4802161

again, if you cant simply explain the concept, not the actual mathematics or the theory in every detail, but the concept, in a way even a child could understand, then you dont fully understand it.

take the concept of a radio wave. how do we get sound out of a radio wave?

sound works like a wave in water. if you can repeat that wave over and over, you could make a wave on that wave. a radio takes that wave that you constantly made, and extracts the the wave you put on that.

again, if you cant explain a concept ina simple way, ignoring all the irrelevant specifics, then you dont understand what youre talking about.

how is this not getting through?

owait, thats right, everyone here thinks they understand their "advanced complex" sciences.

bullshit, you just memorized the equation. you dont understand it.

its why teachers nowadays suck.

>> No.4802180

I tried to teach my girlfriend (who has only done basic yr 10 maths) cantor's diagonal argument once on a whim. It wasn't to bad, although in a weird autisic moment I got way to carried away defining a bijection in terms of injective an surjective functions instead of 'one-to-one correspondance' or some more intuitive manner.

And it didnt really have the impact it usually has because, well, she didnt really care at all.

>> No.4802185

>>4802161
A rather limited viewpoint. As knowledge increases, so does what is intuitive.

What is "intuitive" today was just a complicated mess of thoughts in the best minds of the past.

>> No.4802191

>>4802181
>again, if you cant simply explain the concept, not the actual mathematics or the theory in every detail, but the concept, in a way even a child could understand, then you dont fully understand it.

Explain homeomorphisms on topological spaces in this manner. Go right ahead.

>> No.4802194

This quote is just wrong.
If you are able to explain anything you understand un basic terms, it means that the person you explained it to as mastered the subject.
If they had mastered the subject, they should be able to do whatever you, with your hours of trying to grasp the concept of whatever theory, can do.
I can see plenty of subject where even if you think you understand the basic idea, you can't predict anything
Some subject need pre requisite to be understood.
I could try to introduce maxwell's equations to a 5years old using simple terms but without deeper explaination, he won't be able to build a telegraph.
Since you seem to like quotes, here is one from feynman
"If I could explain it to the average person, I wouldn't have been worth the Nobel Prize."

>> No.4802199

>>4802191
"If YOU can't explain it simply, YOUdon't understand it well enough."

You're trying to prove a point on the fact he might understand some very specific and arbitrary topic?

>> No.4802205

>>4802181
> again, if you cant simply explain the concept, not the actual mathematics or the theory in every detail, but the concept, in a way even a child could understand, then you dont fully understand it.
> again
> i'm just going to reassert my assertion with no counter argument

uh... okay.

giving examples of things which can be explained intuitively isn't relevant. some things can be, and when they can be, they should. it's just that not everything can.

>>4802185
i don't see any reason to think the intuition of laymen has increased by any measurable about. come on dude just think about this, newton's been dead and buried for about 300 years now and yet the average man on the street still couldn't explain how orbits work.

>> No.4802208

>>4802191

i cant. i dont understand them.

case closed.

>> No.4802209

>>4802199
Its hardly 'very specific and arbitrary' this is a maths and science board, you'd expect at least a passing familiarity with Topology from most posters. My point is, you can't ask a mathematician to explain the things he understands 'without going into the mathematics'. That's just plain ludicrous.

>> No.4802216

>>4802208
Then why are you here telling us we don't understand things? What do you understand?

>> No.4802217

>>4802205
yet calculus was probably complicated as shit coming out of his books, yet there most highschoolers can handle it easily

>uh we fly around the sun because gravity keeps us in orbit?
its a start.

>> No.4802234

>>4802209

thats funny. my dad was a mathematics major (ba and masters). alot of times, friends and his coworkers would have issues with mathematics. what he'd do is sit them down, and explain each step in a simple manner. he'd make a comparison they could easily relate to, then build off that with equally relatable comparisons. itd get to the point where he'd have them understanding fairly complex shit thatd go right over my head.

its how my sister and my mum both learned what they did. its not about getting across how complex something is. things arent complex if you understand them. theyre very simple if you understand them. and with simplicity comes sharing.

if you dont understand, then you cant share the idea.

like an above poster said, what we consider now as simple, was complicated at some point. what made it simple was real understanding.

things arent "complex". theyre complex to the mind that doesnt fully understand. once people stop thinking that theyre learning something complex and start just learnig, realating and understanding, then we'll start making progress.

so what im getting at is, stop thinking what you know is complex. start trying to simplify it. once you simplify it, you can teach it and we can start making some progress. right now we're just circlejerking and this addy is only halfway done.

and imo, if you think what your field of focus is is complicated then youre full of yourself and wont get anywhere.

>> No.4802235

>>4802217
no it isn't. there's no intuition there at all, they are just parroting some half-remembered fact from school. if you actually probed their knowledge with a simple question which required only the most basic understanding of the concept, such as 'are people in low lying orbit totally weightless', they would founder.

i don't see what the complexity of newton's calculus was. newton made his calculus overly complex on purpose, i doubt even a versed student would find principia readable. it's only because we now have better approaches like that of leibniz. a student reading leibniz 300 years ago would have no more difficulty than a student reading leibniz today.

>> No.4802246

>>4802235
*what the relevance of newton's calculus is

>> No.4802249

>>4802216

i know radios, programming and how to fix shit. i also know that i understand these things to the point that each and every one is simple.

when i come here, people are busy trying to explain complex things, but nobody ries to explain it in a simple way. they all try to explain it in a convoluted manner only they would understand. and so everyone argues and tries to understand eachother.

so nobody here really undertsands what theyre talking about.

so stop trying to sound smart. stop trying to explain how complex something is, and just try to understand it. explain it simply and in pieces. do that and this board will be full of useful info and some real progress.

>> No.4802250

Let me explain why the converse to Lagrange's theorem in group theory is false:

Let the alternating group <span class="math">A_4[/spoiler] be our group of focus. This group is a subgroup of <span class="math">S_4[/spoiler], which has 24 elements, so <span class="math">A_4[/spoiler] has 12 elements. Now, the converse of Lagrange's theorem suggests that there is a subgroup with 6 elements. You can look at exactly what <span class="math">A_4[/spoiler] looks like, but essentially it has 8 cycles with length 3. Thus, a subgroup of <span class="math">A_4[/spoiler] with 6 elements must have 2 cycles with length 3.

Let's call this subgroup <span class="math">H[/spoiler]. For all <span class="math">a \in A_4 \setminus H[/spoiler], we have <span class="math">A_4 = H \cup Ha[/spoiler]. (that is, <span class="math">Ha[/spoiler] and <span class="math">H[/spoiler] are disjoint)

Let's consider <span class="math">Ha^2[/spoiler]. Because <span class="math">Ha[/spoiler] and <span class="math">H[/spoiler] are disjoint (and because the index of <span class="math">H[/spoiler] in <span class="math">A_4[/spoiler] is 2), either <span class="math">Ha^2 = Ha[/spoiler] or <span class="math">Ha^2 = H[/spoiler]. If <span class="math">Ha^2 = Ha[/spoiler], we can do right multiplication by <span class="math">a^{-1}[/spoiler] to get <span class="math">Ha = H[/spoiler]. But this would imply <span class="math">a \in H[/spoiler], which can't be true. So <span class="math">Ha^2 = H[/spoiler]. By group closure, for all <span class="math">h \in H[/spoiler], we have <span class="math">Hh^2 = H[/spoiler]; therefore, for all <span class="math">g \in A_4[/spoiler], we have <span class="math">Hg^2 = H[/spoiler], which then implies <span class="math">g^2 \in H[/spoiler]. If for some <span class="math">g[/spoiler], <span class="math">g^3 = e[/spoiler], then <span class="math">g^2 = g^{-1}[/spoiler]. So <span class="math">g^2 \in H[/spoiler] implies <span class="math">g^{-1} \in H[/spoiler], which by subgroup closure implies <span class="math">g \in H[/spoiler]. This would imply that every cycle with length 3 is in <span class="math">H[/spoiler], and we already know that there are 8 such cycles. But <span class="math">H[/spoiler] is supposed to only have 6 elements, so there's a contradiction.

>> No.4802254

>>4802234
I don't care about your anecdotes, you're talking out of your arse. Have you noticed we have these institutions about the place for education? These universities, they call them. Now, I spend 10 years at one of these institutions to get a good understanding of my field. Why? If it can be simply explained then its not necessary. Has human education throughout all of history just been a sham? Is research pointless?

Of course it isn't, because your idea is wrong. But if you can prove that everything is simple, please do, I'd like to have super technology and immortality and what not come the end of the week if at all possible.

>> No.4802259

>>4802191
Homeomorphisms of topological spaces are functions that tell you that topological spaces are in some way "the same" under continuous change. This way, a donut is the same as a cup, because the cup could be continuously deformed into a donut, and that continuous deformation has a continuous inverse, so the two spaces are homeomorphic.

>> No.4802273

>>4802259
Whoa buddy throw some math equations in there. maybe some jargon. You're not respecting the true complexity of the subject. You need to start at the middle and work your way to the beginning and back to the end.

>> No.4802277

>>4802249
You're a fucking idiot, I'm sorry to say. This is a science and mathematics board, not a tinkering forum. The matters of worthwhile discussion here are not so simple to understand. You need grounding to understand certain ideas, not everything is introductory level. For example, no matter how hard I might try, there is no way I could teach you to understand measure theory without you first understanding real analysis. I could 'simplify' it as you say by first teaching you real analysis, but that will take AT LEAST a week. Now what if you don't even understand elementary algebra? There's no way I'm sitting down and explaining measure theory to you, because its fucking impossible to do so.

>> No.4802281

>>4802259
Now, what are these topological spaces you speak of? You haven't explained. What is a continuous deformation? Continuous inverse? Makes no sense.

You haven't explained a homeomorphism at all, you've said some words and delivered no meaning.

>> No.4802282

>>4802235
indeed, I've seen a show recently where a woman thought that if you put an object in a vaccum chamber, it would drop because there was no air.

>>4802249
the problem is that what people who study a particular field find interesting is at the edge of this field, where intuite definition doesn't always work. You need a proper definition that works for every single case even if it means a less intuitive definition. But I agree with you, people on this board should at least try to exlpain it simply first and intuitively and then be more precise

>>4802250
Is this the layman terms explaination? because I'm not quite sure you explained things to children in the last 200years

>> No.4802286

>>4802281
Unless of course the person you're explaining it to already has a reasonable understanding of topology, in which case you haven't simplified anything, you've just lost some rigour.

>> No.4802289

>>4802259

^ there we go. understanding. i understand the basic concept. and now im intrigued.

if we teach more info liek this in this manner, then it would draw more interest.

imo, the scientific fields think theyre special because their ideas are complex. all its doing is alienating otherwise interested people. figure out how to explain them in simple terms, and maybe actual understanding will come around. keep trying to explain things in the convoluted complicated forms they are and nobody gives a fuck.

>>4802254
and that right there is the reason public education is shit and colleges are a waste.

>> No.4802295

>>4802282
The point is there is no fucking layman introduction. There is a hierarchy of understanding, if you don't understand the most basic idea, you can't understand those ideas which stem from it, or those which stem from them, and so on. This is why we have education.

>> No.4802297

>>4802277
I think you miss the point.

Simple is a relative concept.

If you can form a coherent overview of a subject that is much less complicated than the sum of its most intricate details, then your knowledge of a subject is a mess, or "you don't understand it well enough."

>> No.4802298

>>4802281
Someone asked me to explain "homeomorphisms on topological spaces," not develop the theory of general topology.
I can give you analogies and intuitions that guide the theory, but I'm obviously omitting a whole lot of information, and this layman's explanation is insufficient for any purpose other than motivation.

>> No.4802306

Stupid people not understanding something doesn't mean it isn't simple.

>> No.4802307

>>4802298
That is exactly my point. Its insufficient for any purpose other than motivation. Thus it is not really an explanation. Explanations impart understanding.

You could explain metrics by saying "Well it gives you an idea of some sort of 'distance' between two things", but that doesn't explain metrics to someone. It just tells them what its about.

>> No.4802308

>>4802298
motivation is what we need to start inciting.

we dont teach topics because theyre complex. we dont even give them chances. so none of this interests your average student.

explain it in a way they can easily understand and it piques interest. with interest comes research, study then understanding.

so the moral of the story is stop trying to be complex. explain things simply and you really contribute.

>> No.4802312

>>4802297
I think you miss the point. Understanding is not relative. You say I don't understand something if I can't explain it to a layman, but now you're going back on it and saying "Oh no you don't have to explain it, just wave your hands a little and give them a nice little analogy!" That's not a fucking explanation, that's an analogy.

>> No.4802316

>>4802308
Motivation is not understanding you fuck, whether it leads to it or not. There is not a person alive who can't give an anecdote about something they understand, that is completely fucking different to explaining it.

>> No.4802317

>>4802307

the idea works liek this.

somebody asks you to explain something.
you explain it in the most simplistic way. fuck the details. you have to get the point across.
witht hat basic understanding they can ask questions. with questions, you can supply answers and fill in the details.

this thread isnt about explaining a concept to someone of equal knowledge and undertsanding. the idea is that if you undertsand your field, then you understand the concepts important parts enough to get the main point across to someone alien to the topic.

if you dont understand it, you cant explain it.

>> No.4802327

>>4802324
This.

>> No.4802324

>>4802308
but that's not what the quote is about.
It doesn't say if you can motivate people to study something you don't understand it.
It's good to get people interested in what you've choosen to study but don't lie to them by telling them they have the basis of a field with those few information because they don't.

>> No.4802334

Simply does NOT mean "one sentence analogies" or sum 10000 pages of knowledge into one sentence.

It just means that it can be broken down and transmitted bit by bit to someone of lesser knowledge on the matter!

Feynman was simple, but he broke his explanations into numerous lectures and books.

Einstein's own "layman" explanations of relativity were book, not anecdotes.

>> No.4802344

>>4802324

valid point.

but with true understanding, comes the understanding of whats important and what isnt.

so explanations for different things can be explained simply.

if you dont actually understand the topic, then you dont understand whats important and what can be put on the back burner in regards to explaining an idea.

fuck the mathematics, if you understand the math, then you understand how to get the idea across in a simple way.

1+1. kids dont understand that shit. simple explanation. you have one stick. you add another stick. now you have two. of course, the relaty is, there loads of fractions, interpretations, etc, but you know whats important and what isnt.

theres complex ideas out there, but these complex ideas should be explained in ways easily relatable, and anybody that really understands this knows this.

its about getting the point across.

>> No.4802353

http://www.youtube.com/watch?v=wMFPe-DwULM

This.

>> No.4802358

>>4802344
So you're saying that if you can't publish a high quality textbook then you don't understand the topic?

There's no 'what's important and what isn't' when it comes to maths, its all important, you're dealing in proof, any hole in the proof and its completely wrong. So if you miss things out because they're unimportant, you're simply teaching the person things that are wrong. You need to include all the information, true enough it can be done in more complex or more simple ways, but you can't just drop things because you think they're too hard.

>> No.4802356

Living organisms are just billions of different chemical reactions

>> No.4802359

>>4802356
Not single cell organisms.

>> No.4802382

>>4802358

and thats what im trying to get across. obviously we dont know what eachother knows. we dont what one person knows and what one doesnt.

with actual understanding of a topic comes this knowledge. this board is a piss fest of everyone trying to explain everything all at once. fact of the matter is, we should be going in explaining the important parts in a way that gets enough of the point across that the recipient understands whats being said, and understands what he doesnt know.

so in explaining something simply, you get the main point across, while enticing the listener to ask about what they dont understand. then you can get into the more complicated parts.

this comes with actual understanding.

for example, explain slope

>> No.4802386

>>4802353
Yep, this pretty much sums it up.

>> No.4802394

>>4802382
Slope is the proportionality of change in one variable with the change in another. So that if the second variable changes by an amount y, the first changes by the slope by y. What more is there to say?

>> No.4802410

>>4802394

slope is how much x and y change with eachother.

why couldnt it be explained this way? because youre considering all the irrelevant variables and all the extras involved to make it true.

fact of the matter is, if we stopped for a second and really understood whats important (getting the general idea across), then we'd see real understanding.

math/science right now is so abstract, simply because of the proofs, etc. the proofs are important, and with proofs, you can do all sorts of things, but real with real understanding comes the knowledge of whats important and whats not when explaining something. real understanding isnt about verifying proofs, its about getting the idea across. once we understand that, we'll see real discussion, improvement and progress. right now, people are just regurgitating their classes.

>> No.4802419

>>4802410
lemme rephrase that, with real understanding, you understand how to visualize it, and how to explain it. its like watching binary computing. it looks like character noise to the untrained, but the trained can simply explain it as being patterns.

>> No.4802421

Ah, what an interesting thread!

The funny thing is, it shows how poorly the OP understands the idea he's trying to put across - he wasn't able to explain it simply enough.

>> No.4802428

>>4802421

it was explained pretty straight forward from post one.

then the tryhards came in trying to justify their misunderstandings and inadequacies

>> No.4802434

>>4802428
Ah, bitter, aren't we? Clearly it wasn't well explained, there was even a point where you changed the whole idea for some time to be about motivation, then switched back again. You're just trying to justify your misunderstandings and inadequacies.

>> No.4802441

>>4802434

i guess. now you know what it likes to listen to you all circlejerk about how much you know about math.

dont even understand it enough to contribute anything new to the field.

>> No.4802452

So don't. Get off 4chan as you suggested others do earlier. You come here, to this pile of crap, and start demanding all the crap leave or clean up their acts. All the while you're just shit yourself. Go contribute to your own field.

>> No.4802493
File: 39 KB, 436x434, Recursivethinker.jpg [View same] [iqdb] [saucenao] [google]
4802493

http://en.wikipedia.org/wiki/Principle_of_sufficient_reason

>> No.4802512

>>4802493
But the principle of sufficient reason is in direct disagreement with incompleteness, the latter of which is proved.

>> No.4802527

>>4802512
>on /sci
>talking about proof as though it means something is absolute

Try again.

>> No.4802563

>>4802527
Well it does. If something is proved that's all there is to it. The principle of sufficient reason would have it that every true statement in an axiomatic system has 'sufficient reason' to be true. This is not so, as proved by Godel.

>> No.4802569

>>4802563
Try to google define:proof

It doesn't mean what you think it does.

This is /sci. The manual is stickied.

RTFM.

>> No.4802575

>>4802569
It means exactly what I think it does. The google definition is for common English, not mathematics.

>> No.4802584

>>4802575
And the principle of sufficient reason is in the domain of maths?

>> No.4802589

>>4802584
It enters it. And fails to hold within it. You don't need something to be contradictory everywhere for it to be untrue, it only needs to be contradictory somewhere.

>> No.4802594

>>4802589
Unless you want to redefine the well ordering principle with some sort of 'logic does not hold' axiom. Then its fine.

>> No.4802602
File: 292 KB, 800x600, ein.jpg [View same] [iqdb] [saucenao] [google]
4802602

Einstein said plenty of stupid things.
<----

>> No.4802599

>>4802594
Principle of sufficient reason, rather.

>> No.4802607

>>4802602
agreed

“Killing under the cloak of war is no different than murder.” – Einstein

>> No.4802611

>>4802602
>>4802607
Sure is Schopenhauer in here.

>> No.4802616

Einstein quote principal:

All Einstein quotes on the internet are misattributed.

>> No.4802619

>>4802616
Corollary:

Einstein was a mute.

>> No.4802625

>>4802619
>>4802589
Dropping this line of conversation here? I thought you might actually know something about what you were talking about.

>> No.4802629

>>4802625
Only one of those is mine. You can tell by the pixels.

>> No.4802631

>>4802629
I know, the other was mine.

>> No.4802636

>>4802631
It's hard to follow which one is you because they all say anonymous.

Also, it seems like you are arguing against yourself there, so I reckoned the other person (which I guess is you?) was arguing now, so I let it go to see what would come of it.

Tripcodes, people. They work. I'm proof.

>> No.4802639

>>4802636
How did it seem like I was arguing with myself? The principle fails to hold in any axiomatic system that allows for logic, do you not see this as a problem?

>> No.4802642

>>4802639
Your wording was ambiguous, and so it looked like that post was taking exactly the opposite stance to what you just typed out.

No, it's completely logical to ask why something exists, and to assume that there must be a logical reason that something exists. Even if that reason is that the photon exists in all places all the time, or that infinities are somehow there. We ask how the infinities exist so that we may understand what comes before them, so that we can better qualify them, I think.

>> No.4802644

>>4802642
Then again, I'm completely happy being wrong, so long as you can use logic to show me why.

>> No.4802647

>>4802644
Some of my best debates and discussions have been with me being wrong. I'm not afraid of that which I don't know, because that's what makes me happy, the learning. You and I disagree, but I don't think it's for the reason you think it is.

>> No.4802653

>>4802647
Well I'm sure what you think, because your posts are usually very vague and include phrases like 'read the fucking manual' in place of explanation.

You say its 'logical' to assume that there is a logical reason for something to exist. Perhaps it is, I'd like to see the logic that arrives at that conclusion. Anyway...

Do you accept the incompleteness theorem? If so then you agree that there exist statements within axiomatic systems are true, but not provably so (which is to say, its truth cannot be deduced from the axioms.)

Now the principle of sufficient reason, when applied to an axiomatic system, states that all true statements within the system must be deducible from the axioms. But this is the converse to the incompleteness theorem.

The incompleteness theorem is a theorem (so it has been proven), the well ordering principle is a principle so it is (or was) expected to be true.

What do you make of all this?

>> No.4802655

>>4802653
>Well I'm sure what you think
I'm not sure what you think* rather.

>> No.4802668

>>4802653
Just because we don't understand something, or in this case can't quantify something properly, doesn't mean there isn't a logic behind it. It just means we haven't quite discovered it yet.

Again, proof means evidence, even in math. It doesn't mean something is immutable, it means simply that we show it to work a certain way. Math is not science, but science is based upon math. Both, however, only work through observation. Can you observe, then, the entire scope of both and tell me, at this impasse, that Godel is correct? Do you have, at your disposal, every single axiom that ever will exist? If not, then you are lacking a fair bit of proof.

I would say, however, that such a list will one day exist, and it will exist logically because we formulated it, observing the universe. It will exist for a logical reason, just as your theory of incompleteness exists for a logical reason.

>> No.4802679

>>4802668
Since you are so driven by this point of proofs and things being proven, I'll elaborate further on this point.

If a theorem of any sort is proven, that means only that proofs exist for it. So, Godel had some proofs for his theorem. I can find proofs that cigarettes don't cause cancer, and then I could say that I have proven it. It doesn't mean it is correct, especially since we have since discovered that they probably do.

>> No.4802685

>>4802668
>Again, proof means evidence, even in math.
No, it doesn't at all. To prove a statement mathematically is to deduce from the axioms the truth of that statement, there is no evidence involved and it is indeed immutable.

You don't seem to understand the nature of mathematical proof at all, so this argument has become rather pointless.

By the way, the solution is that the principle of sufficient reason has exceptions. These unprovable statements are such exceptions. I was hoping you might come to this realisation with a little hinting.

>> No.4802688

>>4802679
A statement which is provable is only also disprovable in inconsistent systems.

>> No.4802690

>>4802685
And, as you clearly don't understand, there is a logical reason those statements exist. Or are you saying unproven statements are illogical in their existence?

>> No.4802694

>>4802690
No, I understand that perfectly well. That does nothing to stop it contradicting the principle of sufficient reason (if you were to leave out the exceptions.)

If you try to take a universally applicable version of the principle, it is inconsistent, and useless.

>> No.4802703

>>4802690
>Statements are logical or illogical.
http://en.wikipedia.org/wiki/False_dilemma

Statements can be consistent with other statements, can be inconsistent with other statements, can be proven true from other statements, and/or can be proven false from other statements.

Also, all belief systems are axiomatic, or have non-terminating recursion of justification, or are circular. I prefer the axiomatic belief systems myself.

>> No.4802705

>>4802582
This man has it. This is the point I'm trying to make. I guess I was too roundabout in my positing.

>> No.4802709

>>4802705
You still don't seem to get it...

The principle of sufficient reason says you can prove it using the 'constructs OF that system'. So while that man does 'have it', you still do not.

>> No.4802719

>>4802709
Godel is talking about natural numbers, not the logic of them being there. He also says there will be unprovable truths within the system.

'Not all axiom systems satisfy these hypotheses, even when these systems have models that include the natural numbers as a subset.'

Even Godel's theorems aren't necessarily right when you take other axioms into play.

Not that the sufficient reason theory has anything to do with natural numbers.

Do you still not get this?

>> No.4802724

>>4802719
The point is, just because you can't prove the logic of the precursor, doesn't mean the precursor isn't logical. It just means you can't prove it within its own structure.

>> No.4802725

I know that I know that I know nothing at all.

>> No.4802728

>>4802726
That I know that I know that I know nothing at all.

>> No.4802726

>>4802725
So, you know that?

>> No.4802730

>>4802719
I don't see how you don't get this.

Take a statement A which claims a(x) for all x.

But, there is a b in x such that ~a(b).

Then A is false.

The well ordering principle says, when applied to axiomatic systems, you can always prove the truth of a statement within the system using the axioms of the system.

Incompleteness proves that there are systems for which this is not true

Therefore the well ordering principle is not true (and hence why its not called the well ordering conjecture)

>> No.4802732

>>4802728
Yeah, but you don't know that. You just said so.

Just because one can string words together doesn't mean they hold any meaning.

>> No.4802736

>>4802732
Wouldn't the speech of someone who knew nothing be meaningless?

>> No.4802738

>>4802732
How do you know that?

>> No.4802737

>>4802736
Someone who knew nothing would not speak.

>> No.4802739

>>4802738
Because I don't claim to know nothing.

>> No.4802744

>>4802739
By that logic anyone who doesn't claim to know nothing knows everything. Be less stupid.

>> No.4802749

>>4802739
Apparently you can't claim knowing what double negatives are.

I'm pretty sure that guy meant what he said in a zen manner. A person willing to learn admits he knows nothing. When a person is aware he has much to learn, he shuts up and listens.
Yeah/No?

>> No.4802748

>>4802744
Nothing is not the opposite of everything, it is the opposite of something. It parses differently. Go ask /lit/ if you don't believe me.

>> No.4802772

>>4802748
>opposite of everything
Is this Russel's Paradox I see?

>> No.4802775

>>4802772
wut

>> No.4802797

>>4802748
define nothing

if I have an empty 3+1D space is that nothing?