/sci/ - Science & Math

A lot of people have bad spatial reasoning skills, especially in this day and age, where kids spent a lot of their childhoods sitting in front of two dimensional TVs or playing 2D videogames. Feels bad man.

>>3404111
not sure if troll

>>3404098
I have pretty damn good spatial reasoning skills. I can envision a tesseract, too. But I haven't taken Multivariable yet.

also,
>spacial
>spacial

>>3404118
Good call, my mistake.

Good spacial reasoning? You might want to look into architecture or engineering.

>>3404117
Why would that be troll? Do you think people get spatial reasoning skills if they don't use them at all growing up?

>>3404121
I'm actually studying physics + premed

>>3404126
Because modern video games are mostly 3D, especially the popular ones, and puzzles involving spatial reasoning are extremely common.

their called women, op

and niggers

welcome to real life

>>3404142
Not that I don't appreciate the sentiment, but the mid-tier textbook we use was written by an MIT-grad woman, the god-tier book I use instead was coauthored by a woman, our professor (and the head of the math department) is a woman, and I get all my applicable genes (spatial reasoning, algebraic and logical intuition, mental computation) from my mom.

Professor is lecturing on other coordinate systems
*writes r = 6cos(theta) [0, 2pi) on the board* "What would this look like if I graphed it?"
Class: *silent*
Me: *visualizes* ...a circle with radius three centered at (3,0), but it traces the circle twice?"

Later:
*she draws a sphere and labels rho, phi, and pi*
"Any ideas on how to convert a set of rectangular coordinates to these?"
*silence*
*I look at the components and projections, then answer*
"That's right. Can anybody who didn't already read the material tell me how to convert the other way?"
*I didn't*
*My book is under my chair*

>>3404196

Most people don't learn to visualize stuff because their edumecational backgrounds suck - teachers failing to explain how exactly the equations transfer to graphs or simply content to receive their pay-checks.

Consider yourself lucky, not gifted.

OP, the reason is because a lot of the way mathematics is taught has been dictated by formalists. They prefer to disregard all of the visual representations, insights, analogies, etc... They perceive the mathematics as a purely symbolic text based objective system founded on logic (godel's incompleteness theorems later proved that such a system couldn't be both complete and consistent).

You should stay away from formalist teaching methods, their mathematics aren't bad, but their teaching methods are all rote learning and mindless procedural rule application.

Intuitionists value the insight as much as the proof (deriving proofs from insights and vice versa). They're the best for learning things visually, but there aren't many around and they perceive the mathematics as subjective (something that bothers most people).

Platonists are about as common as formalists, they're a good midpoint on teaching methods.

OP, this is why I hate classes. They have to move at a ridiculously slow pace (even in a condensed summer course). I took Chemistry and Linear Algebra a few summers ago, got As in both and (other than having tons of homework every day for lin. algebra) didn't try or study. The whole point of math and science is to make quantizations of observations predictions easier and more accurate, but it seems that 99% of people just don't understand that, it's like they think someone invented math to make everyone's lives more difficult; so they just subconsciously make everything ridiculously difficult or make no attempt to even understand concepts. All I can say is the obvious statement that the higher up you get in education, the more intelligent your peers will be.

>>3404221
This. Anyone can memorize a bunch of rules, but it's only if you understand what you're doing and why you're doing it that you can begin to see the big picture. Pic related.

>>3404209
Nobody ever taught me how to visualize. I'm not denying I had a great education, but it's always been something that came naturally to me.

And I'm not sure how you can claim that people who learned algebra and calculus were never taught how an equation transfers to a graph. That's half of algebra, and there's not a calculus book out there that doesn't define what a function is, and most of them have pictures of graphs every few pages.

Since when is visualisation even relevant? Ok, so you can picture three dimensional stuff in your mind easily, ok now lets move to five dimensions.

>>3404268
Pic very related. I always figured that being an intuitionist was the reason his writings were so clear to me when other [better] mathematicians had trouble with them.

>>3404221

basically this. i graduated high school a few months ago. i took calculus AB and BC, and both of these courses stressed learning how to solve things "analytically" over any other method. it's a product of the current educational system. they need to be able to assign a number or a grade to you, so it's easier to quantify just how much you're worth. they can't do that if you work things out with your own interpretation of an equation. don't worry about it though, some people are meant to be innovative, others are meant to crunch numbers.

>>3404316

>your own interpretation of an equation

Haha! Ok, sport. You're too intuitive, that's why your equations don't make any goddamn sense.

>>3404285
It's relevant when the professor says that the gradient of f(x1...xn) is normal to the level level curve f(x1...xn) =c. The kid next to me has to be satisfied that the proof in the book is logical, while I spend a few seconds visualizing cross sections of mountains and topographical lines and can see that the statement is obvious.

>>3404285

I'm not OP, but visualization does help avoid some of the pitfalls that basic math people and non math people have in our society.

Basic incorrect arguments like "irrational numbers can't really exist" are commonplace even amongst philosophers and physicists when all you have to do to prove it is to draw a right triangle with the legs measuring 1. The hypotenuse ends up measuring sqrt(2) an irrational number. By reusing that one line you can construct countless other roots.

Similarly the greeks did have division, but they did not have rational numbers. The reason is because they perceived division as a ratio. For example, 3/4 was represented by two lines originating from the same point and being separated by some arbitrary angle (preferably acute, for aesthetics). Then on one line, at a distance of 4 from the origin a point was marked, similarly on the other line at a distance of 3 from the origin. The two points were connected by a new ratio line. Now any other line that is parallel with the ratio line has the exact same ratio between their intersection point's distance from the origin. This helps avoid several pitfals people have with fractions and decimals.

>>3404374
it's not obvious if you don't know the concept of derivation and function variability

and also this
>>3404285
you're kinda newbie in calculus, expect some crazy shit later

>>3404394
This is a vector calculus class, everyone there has some working knowledge of a derivative.

>>3404394
multivariable calculus is the top calculus level course people take, unless you count differential equations as a calculus course.

>>3404407
Not sure if troll

i'm >>3404394

>>3404407, no, it is not, multivariable calculus is 10% of the calculus you need to make something useful.

>>3404390

Here is a visual aid to go with my crappy explanation.

The numbers represent the distance from the origin.

>>3404432
While this is true, ordinary diff eq and on are more specialized branches of calculus and the bulk of it is applications, methods, and techniques.

Besides, the differential is the very first thing someone learns in a calculus course. It's not something a person in multivariable calculus wouldn't know.

Well, it's late, I'm out. A final word of advice, OP. Tutor your classmates. You'll understand it even better, they'll understand it better, and the world is a bit less stupid.

>>3404460
So you can solve diffyqs?
<span class="math">
\frac{d^2x}{dt^2}=-\frac{k}{x^2}
[/spoiler]
This one has been giving me trouble for awhile now.

>>3404460
god, complex calculus man, it's the most important one

OP is a dumbass.

>Yeah, I can visualize in five spatial dimensions!

You can't visualize in more than 3 dimensions, our brain doesn't evolve in more than 3 dimensions. Stop being a pretentious faggot, OP.

>>3404480
I never claimed 5. If it's not a complicated function I can often manage 4 by supposing one of the variables to be time and imagining how the 3D figure changes with time, but that's not terribly useful.

Maybe I was unclear, but by 3+ I meant "3 or more"

>Why am I so much smarter than everyone circle jerk

You're probably not as great as you think you are.

>>3404480
Thank goodness. I was beginning to think /sci/ was filled with asshats that have 3-D retinas.

>>3404394

>you're kinda newbie in calculus, expect some crazy shit later

I have a PhD in pure mathematics. Visualisation is fine for giving you a bit of a feel of what's going on, but deriding rigorous proofs as "formalism" is madness.

In any case, visualisation at higher levels is more about grasping the interaction of different components, not simply trying to see an object floating in space.

>>3404533
Really? I think I'm good enough with numbers that I can satisfy my curiosity about math and physics, but not good enough to make it professionally in either fields. I've met too many people much smarter than myself to think I could.

I'm just talking about one faculty - spatial reasoning - that I thought would be more prevalent among people who learn mid-level math. My apologies if I came across otherwise.

>>3404559

let me guess, you're an engineer

>>3404374

> spend a few seconds visualizing cross sections of mountains and topographical lines and can see that the statement is obvious.
>some other guy saying oh of course that equation in radial coordinates is a double covering of a circle.

Maybe you can see that this is roughly true, but if you can't break things down in the the procedural steps you all disparage so much, you have nothing at all. In particular with the second case, you can tell that it's a cosine wave wrapped around a circle, but you need to examine it properly to see that it's exactly a doubled up circle, and not just same vaguely round thing.

>>3404566
Nope
>>3404128

>>3404567
I have nothing against formalisms, I just don't need them see why, for example, the cross product of two planes' normal vectors is parallel to their line of intersection.

You can see that r=6cos(theta) is vertical at (0,0) and (0,6) and horizontal at (3,3) and (3,-3). But you're right, I hadn't proved it, and I could well have been wrong.

>>3404515

Time isn't always the best way, I use several different methods. Two I suggest you master are using color, and density. Color is very simple, but can be surprisingly powerful. Just imagine the object using hot/cold colors like in thermal imaging with some level of transparency. The other method is a bit more conceptual, but will help you with dealing with integrals referring to moments, center of balance, etc.. Basically visualize your object like normal, but know that certain parts are really dense.

This is still visualizing in 3 spatial dimensions, though mathematically speaking it's visualizing in higher dimensions, I guess.

>>3404307

dude, you have no idea what you're talking about.

Feynman was a putman fellow; his mathematical abilities were world renown.

Your talent is not legendary; half the people on this board can easily visualize just about any graph or relationship they encounter in mathematics from 9th grade through college.

OP, I know just what you mean. I too have a rare ability a math. I can add together any pair of single digit numbers just by looking at them.

Why would you need to visualize anything when doing analysis? Can be useful of course, but it'll never happen that you actually need it

>>3405074

These guys are mostly recent high school graduates who have just realised that the cross product is perpendicular to both input vectors, and think they've discovered something.

>>3405074
Right.

That's exactly why algebra exists in the first place. Geometry is good for analogies and R^3 space physics.

>>3404157
well, I don't. My parents are pretty bad at thinking.

is OP claiming to be able to visualise dimensions above 3?

bullshit.

i can visualize 4... 5 sometimes, if its very simple things
6+ isnt for me...

I can visualize 8- or 9-dimensional objects easily. 10- with some difficulty, and 11 for simple objects.

Also, I can see strings.

Oh my delusional geniuses, more than 3 dimensions without geometric simplifications, yeah, sure.

>>3405186
shut up you shit bag

I have no problem admitting that I can't begin to visualize a fourth spatial dimension.

(Spoiler: you can't do it, either. The best you can do is imagine 3D cross-sections of a 4D object)

>>3405213
QFT motherfuckers

>>3405213 I can't so nobody else can
Hahahahahahaha

>>3405241
Shut up stalin

>>3405241
you're a fucking idiot... your brain can't conceive of it, sorry bro. of course you can claim that you have this ability but there is no way you can prove it or apply it so just shut your fuck.

>>3405249
Yes it can. Pic related.

>>3405257
fag fag fag fag fag fag fag fag thinks he can 4th dimension

noobs, i can visualize objects in non-integer dimensions

I know what you mean OP, the professor was asking if anyone knew about Lagrange multipliers, so I just visualised it and told him "you just parameterise the loop tangent arc and project it down to the extended plane, then just imagine it like a mountain with ski runs on it".

That sure shut him up.

>>3405267
Like 2.5D? I prefer my integer dimensions :D

>>3405267
Fractals?

I can visualize OP's faggotry.
pic related

>mfw other people can't visualise √-1 dimensions.

Your brain can't visualize more than 3 dimensions naturally, however you can use bunch of tricks already mentioned, like moving through time for 4th dimension, or some mix of colors and density (although I never thought of this one).

>>3405480
Your brain can't. Don't assume your restrictions apply to everyone. You are not them.

>>3404488
>implying the brain can't plasticity beyond evolutionary environments

>>3405497
Okay show me what a 4d object looks like

>>3405509
A 3d object with a speed?

>>3405526
>spatial dimensions
>thinks the 4th is time

>>3405509
>can't visualize 4 spatial dimensions
>challenges someone to show a 4D object to his 3D brain
>on a 2D imageboard

Do you ever dream in 4 dimensions, OP? I do, sometimes.

To teach that would require patience, and those who can do it intuitively have no patience. So I guess we'll never know what the fuck you're talking about.

I'm just leaving this shit here:
www.dimensions-math.org/Dim_tour_E.htm

>>3405547
you can't visualize 4 spatial dimensions either faggot. stop pretending.

>>3405570
>M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like.

That was Abbott's flatland. even if escher did it as well, he was clearly copying abbott

Who cares if you can visualise four dimensions, can you visualise infinitely many dimensions? If not, your 'intuition' is basically useless for the majority of modern maths, and large sections of theoretical physics.

And I doubt greatly whether any of you could actually do valid geometric proofs in 4 dimensions without resorting to algebra.

>>3405598
>thinks that if he can't do something no one can do it
>makes claims without evidence

>>3405630
it wasn't me that made the claim. someone else claimed to be able to visualise other dimensions but can't prove it. so even if he can, it doesnt matter because he might as well not.

>>3405526
>i point out that your brain works with 3d object and uses tricks to make them look like they are in higher dimensions
>tells me that i'm inferior to him because my brain cant visualize a 4d object
>somebody asks him how he does it
>liek this:
>visualizing a 3d object
>using a trick to make it look 4d
>trick that I mentioned in my original post as a way to visualize 4d

You aren't very bright, are you?

>>3405638
>tries to defend negative claims
>thinks subjective visualization can be held to objective standards
>thinks he can get a 4D visualization into his 3D brain through a 2D imageboard

>>3405630

>implies they can think beyond the capabilities of the human mind

>>3405653
>implying the capabilities of the human mind are limited to what he's familiar with
>cannot into brain plasticity

>>3405658
>implying brain plasticity is magic

>>3405213 here, nice to come back to see people arguing over how right I am.

>>3405671
>implying magic would be required to do the things he's just too lazy to do

>>3405497
>>3405647
>>3405526
>Implying it's the same guy.

>>3405679
>implying that my statement wasnt about the fag that thinks that brain plasticity is infinite

>>3405679
>magic
>too lazy to do things

hey! Got it!

>>3405685
>implying brain plasticity needs to be infinite to learn to visualize 4D

>>3405658

>implying there aren't objective limits to the human mind

ITT: 'I R speshul. I can into 4D, not you . i win'

>>3405698
>implying 4D visualization isn't within those limits

Let's invent some new dimensions OP can't visualize.

>>3405717
Show that it is.

>>3405730
Imagine <span class="math">S^3[/spoiler]. Oh wait you can't because you're limited by not knowing shit about dimensions.

>>3405730
Tell me how I can show you my qualia.

>>3405738
>think qualia isn't a sensory trick

>>3405738
you can't. therefore for all intents and purposes, you cannot visualise the 4 dimension. i'm glad we cleared that up.

>>3405736
http://www.youtube.com/watch?v=UnURElCzGc0

Are you implying sagan is wrong?

>>3405747
>if you can't make a subjective phenomenon objective, then it isn't even subjectively real

>>3405758
I didn't even say it's not real. I said for intents and purposes, it doesn't even matter if you can't show it.

>>3405738
There is no such thing.

The Poicare conjecture is intuitively easy to understand, yet it took Perelman some years to prove it. Your visualization is worthless if you can't do the math to confirm what you "see".

>>3405774
This

>>3405763
For *your* intents and purposes, perhaps. For *my* intents and purposes, it works just fine. *All* intents and purposes includes mine, though, so you're wrong.

>>3405766
>my lack of understanding, let me show you it

>>3405779
Ah so teh point of this thread is for you to tell us you can see stuff even though it has no bearings on anything outwith your subjective experience? What was the point of tell us? yes, I see now. you are trolling.

>>3405789
>being corrected about an assumed limitation of the human mind is trolling

>>3405779
yours is just yours and no one else's, so I'm right.

>>3405798
Well you admitted that you can't show me that this assumed limitation can be overcome. So you haven't 'corrected' me at all.

>>3405799
>"all" intents and purposes doesn't actually include those of individuals

>>3405811
I didn't say that, nigger. Try again.

>>3405815
>I didn't say what I just said

>>3405810
>I require that everyone else do all my work for me

>>3405826
>>I didn't say what I just said

Saying you're subjective experience is your own is not the same as saying all subjective experiences are not the total sum of experiences.

>>I require that everyone else do all my work for me

haha that is a classic. You're like a theists arguing 'it's your job to find God!!!!"

>>3405835
your

>>3404098
OP you're a fucking cocky american idiot! U think you are so fucking awesome cuz you can visualize a bullshit polar equation. Lemme tell you now, with your cocky bastard attitude you will most likely make it as high up as cashier at mcdonalds, or maybe if youre lucky end up being a chicken catcher . You can then test your awesome visualization skills on imagining the paths chickens will take when you chase them! So stfu and stop being a faggot, and go learn some fucking calculus you moron!!

the rest of you so-called-smart-faggots why are you here. this is exactly why you will never succeed. if you have enough time to be on /sci/ you by default are a fucking moron in your field and will unlikely ever achieve anything of considerable magnitude.

tldr; op is a fag. rest of u gtfo /sci/ and do your resesrah

>think you have good spatial reasoning
>say you can visualize more than 3 dimensions
There's a difference between visualizing and knowing what you're talking about.

The MPC 07/17/11(Sun)02:43 No.3404273
>>3404209
Nobody ever taught me how to visualize. I'm not denying I had a great education, but it's always been something that came naturally to me.

And I'm not sure how you can claim that people who learned algebra and calculus were never taught how an equation transfers to a graph. That's half of algebra, and there's not a calculus book out there that doesn't define what a function is, and most of them have pictures of graphs every few pages.
G

>>3404196

wtf is this shit, all this shit says, is that r is ranging from -6 to +6, nothing more and nothing less, you think you are so great, but you are still in kindergarten

hai guise can I has a 11 dimansional spasial vectuuur quasiun so dat I can shaw u my awsome visulisation skill?????!??!?!?!!

omg i am 12 and i is a geniuuuus

OP's a bullshitting faggot, and a ,ot of supposedly smart people have wasted a lot of time that could have been spent more economically. This thread is the equivalent of spending an hour on the phone listening to a prank call to your own house. Noone is capable of thinking in 4d, so stfu.

>>3405864
naaaaa you are wrungz sirs
i has thugt in 11-d!

>this thread
>implying that 4 dimensions even exist
>mfw your all retarded

>>3405863
>>3405870
You uneducated faggot cats who cannot spell properly! My use of the English language is infinitely more developed and eloquent that yours, similar to my ability to visualize any parametric equation, not only on planes, but on any curved surfaces, including curvatures which approach infinities.... and I don't mean to brag, but 11-d is child's play.. I can do 20-d in my sleep.

Go back to school kitties.

Wassap my motherfuckesr.. Im your neighburhuud frindly nigger.
Wftf is a dimension??? Dat sum new chikan burgurs at KFC or sumtin bro?

>>3405886

I lol'd.

>>3405864
just think about the 4th dimension as going "in" kinda like the tesseract in OP's post
and if its simpler for you then you can shade your stuff for the 4th dimention
or have a little video in your mind with time being the 4th dimension.

so if you can do all these you can do more than 3

i'm not claiming i can do all these, only the first and third options.