this could help

http://nuclearsecrecy.com/nukemap/

Math and psys are awesome, I like thinking of what causes the visual patterns and trying to recognize any thing that is iterating itself. Right after a big linear algebra lecture on vector spaces I was tripping on shrooms thinking that it is very possible that my perception of 3d space is limited. I liked thinking of multiple dimensions and assigning things like time and color to the new spaces to try to conceive extra dimensions. Fun stuff

I've been smoking salvia often and some of the trips help me visualize the fourth and beyond spacial dimensions. This helps a lot because I just finished linear algebra in university and thats all we ever talk about

>>8354
heh, I'm finishing linear algebra right now as well

I'll admit, salvia trips do hint at some extra-dimensional voodoo, but I'm not convinced anyone could leave a trip with an extra understanding of higher-dimensional visualization...

>>8359
I'd say salvia simply obliterates your idea of solidity. Space becomes really weird when floor, ceiling and wall all become sky.

>>8315 lol

>implying Wittgenstein didn't say that the tractacus was flawed

>>8281

Not implying anything of the sort. Just asking a question.

>>8269
If language worked like that, could we have things like poetry or beautiful prose? Obviously, beautiful proofs exist, but it's a different kind of beauty, and I think ithe poetic beauty would be lost in a tractatus-like language.

Think of how flat metaphors would be.

I admit I don't have too firm a grasp on the Tractatus, though. I love Philisophical Investigations.

while(true)
>>8313

The easiest way to think of this is to break it down into two different situations. If you are looking at the odds of getting 6 twice in a row before you have rolled the die the odds are 1/36. This is bcause you have a 1/6 chance of getting a 6 the first time and IF successful you can roll again for another 1/6 chance. To add these odds up you multiply the denominators (bottom numbers) and the nominators (top numbers). 1/6 and 1/6 -- 1x1 / 6x6 -- 1/36.
If you are looking at the second roll after the first the chance is not impacted by the previous roll. While it seems unlikely you will get another 6 the odds are actually exactly the same.

How are all you people getting 1/12?

The chance of getting one six on one dice is 1/6
The chance of getting at least one six on two dice is 1/3
The chance of getting exactly one six on two dice is 5/36
The chance of getting two sixes on two dice is 1/36
The chance of getting a six on the second dice given that you already got a six on the first dice is 1/6

None of these are 1/12.

>>8349
Only 2 people got twelve. And they got it because they didn't think it through. 1/12 is a more intuitive answer (I thought it was 1/12 too tbh, before reading 1/36 and think lol I'm retarded).

Anyway yea,
the odds of rolling a 6 are always 1/6,
the odds of rolling a 6 twice in a row are 1/36.

> 1/12 is a more intuitive answer

Your intuition is broken. When I first read those answers, my intuition spewed its coffee before I even had a chance to think about what it should be.

Could you write that out with more spaces and brackets, because I'm trying to take a crack at it but I wanna make sure I got it down proper

>>8329
Here you go
Made picture of it

>>8337
Made *a picture of it

This is how to put it in.

( ( k ) * ( e ˆ 6 ) ) - k + 1 - ( e ˆ ( 2 k ) ) = 0

>>8339
pic related

>>8201

>If the big bang happened at point a, then all matter is still at point a, and point a is everywhere. Space itself is what expanded.

well yeah. another way of looking at it is that space didn't expand at all, but the matter at point a got much smaller, as it was exploding within the space of point a. when i said everything moves to point b, i'm not talking about an actual point as much as i'm just talking about point a's space expanding (or the matter contracting) and the matter moving away from it's center.

>there's no reason for the universe to contract inwards by gravity, the rate of its expansion is increasing.

but that is what i'm saying. the universe is expanding and currently our explanation is dark energy, right? well what if this dark energy is basically antigravity. as the pieces of the universe separate further from each other and move outward, of course they will begin to move faster, as the force of dark energy or whatever gets stronger.

>At the instant before the big bang - that is, if you could define such a point in time before the natural architecture of time was instantiated - then the universe as we know it would have been of zero dimension. In other words, the universe wouldn't have been "as small as possible" since there would have been no basis for defining such a state of being. That's the problem with using current mathematical thought to analyze a system - or, rather, a singularity - that is not well-behaved in any conceivable sense: reality as we know it breaks down when considering such an idea.

yeah that's why it seems more appropriate to me to consider the point of the big bang to be a point of infinitesimalness. because it doesn't have any dimensions, but there is still something there. my way of thinking about it is that just as .999.. = 1, doesn't .000... = 0?

>Moreover, what are we to say of causality during a time before time? Is not time the underlying force which begets all change? Is not time the quantity upon which all scientific notion is based? This leads us to the logical conclusion that there exist two distinct realms: all things after and including the Big Bang and all things (or, rather, the infinite singularity before - and by "before" I mean "besides") the Big Bang. How do we go from one state of being to the other?

causality seems like a bit of a paradox to me, but the universe seems to do things regardless of whether or not it makes sense to us. in order to get from point a to point b, you must travel through infinitesimalness. it seems impossible but it appears to do it regardless. but what if you are also traveling through infinity at the same time? if that were true, would it make it any less of a paradox? maybe we aren't really moving at all no matter how much it looks like we are. we are only seeing everything from one side, on the other side we are moving the opposite amount.
my theory on time before time is this. point a and point b are both points of complete expansion and complete contraction. in order for all the matter to get to point a, it had to enter a point of timelessness, and when it exploded it left that timelessness. this makes no sense on its own. but from point b's perspective, this moment where everything was all in one place appeared to be the moment where everything was as far from one place as it could be, and in that moment there was still time.

>There are insurmountable technical problems when considering a transition from a finite Universe to an infinitesimal Singularity as you have done. Going from nothing to something is easy: since anything can happen, then something must happen. But going from something to nothing is difficult: if something must happen, then how can nothing happen?

i think what i just said might be an explanation. because when everything was infinitesimal, it was also the size of the universe at its greatest.
>>8204

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>>8215
whoa massive tldr;

Isn't possible that there is matter with a negative mass, that is on the edges of the universe since it is repelled by our mass?

>>8182

> the big bang was a central point at which time all matter was as close as possible.

The Big Bang theory is a model of the expansion of the universe from dense and hot to what we see today and into the future. It breaks down in the earliest moments - it doesn't describe a singularity and it isn't a first event.

>>8202

> the instant before the big bang

This phrase is self-contradictory. If you view the Big Bang as a primordial event, there is no instant before it. However, it's moot because we have no theory of an original event.

> reality as we know it breaks down when considering such an idea.

Reality remains unaffected, it's our theories that break down. A singularity is a gap in a theory.

> there exist two distinct realms: all things after and including the Big Bang and all things (or, rather, the infinite singularity before - and by "before" I mean "besides") the Big Bang.

The ontology of the theory defines only one realm - that which you refer to as "after". The complement of this domain is not defined or implied.

>>8215

Comment too long. Click here to view the full text.

Dr. Thomas Mottingfuck, laddies and gentlemen!

Of course! Thats just what I've been missing this whole time! A cheat-sheet for high school level math, how could I not have thought of that myself? Thank you good sir

STOP THE PRESSES!

What, no calculus formulae or trig identities? >>8300 was wrong, that doesn't even cover high school, let alone anything university level.

I remember 95% of what's on there anyway.

>>8298
DOOD I was just abut to post dis but i trned in myy allgebra 2 book on acident LOL

What no Laplace transforms? How are you going to do anything useful?

>>8316
I'll assume that you've set up the integral properly and just help you with the integration then.
You pretty much want to integrate the three terms separately. Starting with (e^-2x)(x^2); perform integration by parts, giving you another integral which can again be evaluated by parts, which then gives you a trivial integral to evaluate in the last step.
The same can be done for the second term, (2e^-x)(x), but you only need to evaluate by parts once, and the final term, 1, is trivial to integrate.
The answer I got was, (1/4)(e^-2x)(-2x^2 -2x -1) -2e^-x(x +1) +x +c, for you to check against.

I don't think its possible to explain it in better terms than >>8317
Just want to confirm that he hit it on the nose.

Well it's best to just go over how Pascal's triangle works in your head or on paper, the properties of each number propagate out to two numbers when they go down. When an even number is beside another even number, their sum will be even, as with two odd numbers, but when an even and an odd number are side by side they will produce an odd number.
If it so happens that the first few lines set the pattern up right (which they do), then it can only continue along the fractal pattern.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
etc.
The secret is the way that any set of side-by-side of even numbers will be surrounded by odd numbers, which will cause them to reduce in length by one each row, forming downwards pointing triangles.

That was meant to be "The secret is the way that any set of side-by-side even numbers" ... Not that it matters.

The numbers in Pascal's triangle are binomial coefficients, if you want a much more indepth look at how this makes it work, try reading this:
http://ecademy.agnesscott.edu/~lriddle/ifs/siertri/Pascalmath.htm

>>8275
Thanks I see what you mean now.

>>8271

Check out the construction of Cantor's "middle-thirds" set. The triangle is the same thing, just in 2 dimensions.

What is its significance? Not much, really, it's just a funny set, although it might arise in dynamical systems. Or as an example of something with non-integer dimension.

>Lay out Pascal's triangle

Terrible way to do it really. Unless you want to cover a football pitch with Pascal triangle

Behind the abstract definitions there's always a concrete idea. Usually it gets hidden by the language (the way you write math and the way you think about math are usually quite different). When you first encounter a new definition and don't understand it yet, try just rolling with it. Follow the logic of it, and don't worry about it too much. As you work examples involving the ideas, the ideas behind the definitions begin to make sense.

Usually definitions in math are some of the hardest things to understand (when I was an undergraduate I always thought it was the theorems, but I realize now I was mistaken.) For example, take compactness in topology. Why do we define it this way? Because it gives me Heine-Borel theorem, which we'd expect, but it also gives us Tychonoff theorem, which we'd like to be true as well. Usually definitions are motivated by a certain result we want to achieve, and thus they can seem very abstract and obtuse at first glance. After you get at the idea they're meant to capture, it's not so bad, though.

learn2google
site:your.institutes.webserver.edu filetype:pdf intitle:"optimal topic"

>vaguely involving math.

So you study finance?
Good riddance, walk across campus into that tiny building labeled "institute of mathematics" and ask the people hanging around there what they suggest.

Could try here: http://library.nu/