/sci/ - Science & Math

>>1964982
there is a chance
the probability is zero, but it can still happen

umad.

Someone once told me that if you replace the two iron balls used in finding the universal constant of Gravity in the Cavendish experiment, then G would be different.

>>1964986
it will if the balls are made of magnets

Centrifugal force apparently exists to my friend.
"It's in your Physics book, so it must exist!"

>my face when he said that

is there actually any probability if you can calculate and measure everything. and i mean everything.

is there any thing that really happens without you knowing why it happened?

>>1964992
Welcome to string theroy.

>>1964992
2 words
quantum mechanics.

>>1964998

I know a Mathematician that is saying 1/0 falls in a special category, as irrational numbers. He named the group after his own name.

>>1965008

Did you tell him he needs to retake, I don't know, basic arithmetic? Maybe learn what an irrational number is?

>>1965014
he's graduated in math and is crazy about it... I think this is more of a philosophic trip of him... he's a bit crazy, and kinda gifted in the head... he wrote more than 100 books already, composed tons of songs

>>1964982
Op, it is you that is in the wrong; although the probability of any finite string of characters being typed is 1, what this means is that set of samples on which this does NOT occur is a set of measure zero. In particular, the set of samples on which this does not occur need not be empty and, in fact, is not. Long story short, your friend is technically correct. l2measuretheory

op are u me? i had the same argument too.

>>1965025
>>1965025
>>1965025

Oh hi there. You were calling for us?

>>1965027

1/0 is essentially infinity. It's not "irrational". Maybe later on we can have classifications besides "undefinable" for these types of answers, but I can understand his thinking.

>>1965042

That's technically not correct though. It's technically "not defined". But as a number gets smaller and smaller it gets increasingly bigger.

>>1965046

In a division problem. I meant to say as the .00001 gets smaller, the answer gets bigger in 6/.0001

>>1965037
>>1965037
At no point did I say the event had a non-zero probability; in fact, the probability is zero. What I argued was that people do not realize what an event having a probability of 1 or 0 actually means. In particular, an event having a probability of 0 does NOT mean it can not occur; this is a common misconception. I can provide examples if you want.

>>1965052
Not the guy you're talking to, but I would like to hear a few examples. I'm just interested, not being a dick.

>>1965056
random point in [0,1]
the probability that it is 1/2 is zero
but it can still happen

>>1965048
>In particular, an event having a probability of 0 does NOT mean it can not occur

Uh, what? Please give me the examples.

>>1965056
The probability of picking a specific number on the real number line in an interval is 0, even though you will always obviously pick some number.

>>1965042
I wish people would stop repeating this nonsense. 1/0 is NOT essentially infinity, it is essentially a contradiction in terms.

>>1965067

How is it zero though? Are you saying because there are infinite numbers, it's impossible for one to be picked out? I'm not talking about numbers, I'm talking about the characters on a type writer. You know A,B,C, etcetera. There is a limited amount of characters on a typewriter, but there is no limit on an infinite time line.

>>1965083

Or NUMBER line, my mistake.

"Heavy bodies fall quickly than light bodies. See i.e. a feather."

So I showed her a video where a feather and something I don't remember fall where is no air. Both arriving together.

"The video is fake for sure!"

even with infinity theres still a tiny chance it wont happen amirite?

>>1965085
Suppose you wanted the word "dog" to be typed. It is possible that every monkey continues to hit the letter "a" thus failing to ever type the word dog. The probability of the aforementioned event is 0, but as discussed this does not mean it can't happen.

>>1965089

No you are wrong.

Given an infinite string where each character is chosen uniformly at random, any given finite string almost surely occurs as a substring at some position.

>>1965095
>>1965095

There is a possibility that they will keep hitting "a", but eventually one will screw up and hit "q" for example. There is no set line, so eventually one will type out dog.

>>1965095
That's wrong. The probability is not zero, unless you made it physically impossible for it to push the letters d-o-g. Just because it continues to push "a" doesn't mean it cannot push d-o-g. It just doesn't push it, doesn't mean it can't.

This is what you want OP.

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

>>1965111

I did say "almost surely" because I was quoting the theorem.

>>1965083
I don't know what else to say but
http://en.wikipedia.org/wiki/Null_set

science in my /sci/

WE NEED MOAR NERD THREADS GUISE!

>>1965101
No, this is not the case. To see this, let us just consider the case of one monkey.
Let us keep track of each letter typed and label the nth letter by <span class="math"> a_n [/spoiler]. Supposing that each letter is equally likely to be typed the sequence <span class="math"> a_n=a [/spoiler], for all ns is valid. Clearly, there is never a sub-string with the word dog in it.

>>1965110
I meant that the probability of continually typing "a" is 0, not that of typing "dog."

>>1965097
yeah i know it will happen 99.999..% of the time, but there has to be an infinite set of key sequences the monkeys could type and i guess theres an equal chance of the monkeys typing "a" for eternity as there is of them typing anything else.

>>1965131

Not eternity. It can never happen forever if there are other possibilities.

>>1965136
This is wrong. It CAN happen forever, it is just that set on which this happens is a set of measure 0.

may help to get them to understand if you point out that its not going to happen that they just sit there and concentrate
there would be considerable events distracting the monkeys
i dont think it could be expected that the whole of it could be typed in one sitting or without eating or sleeping
also there would be many occurances of near misses where it started with one or two words 'perchance' then failed to continue
or paragraphs, pages, and even entire chapters only too return to random letters without fulfiling the requirements of the theorem

>>1965137
ooops toooo many o's
hate that particular typo; looks retarded

monkeys typing forever is the same as selecting a real number in an interval

the chances of selecting a particular real number in a particular interval is 0

even though *some* real number is selected

>>1965137

The monkeys are a metaphor for random character generation.

A lot of the confusion is stemming from a misunderstanding of what it means for an event to occur with "probability 1 or 0."
To clear this up, please either take a basic course in probability theory or refer to the following posts:
>>1965052
>>1965065
>>1965067

>>1965139

>it can happen forever

The keyword here is "almost surely". If OP did use it like he said he did. Then they're fucking wrong. But if he said "surely" or maybe "will" then he is "technically" wrong.

>>1965158
>>1965158
Tell me, why can it not happen?
To see that you are wrong, suppose there were only 10 symbols and, for the sake of simplicity, suppose they corresponded to the integers 0-9. Then every sample corresponds to a number in [0,1] (not necessarily unique). Note that .(1) can be attained from a sample. In particular, the monkey can continue to hit 1.

The probability of having a substring that is a work of Shakespear is not guaranteed. The number of infinite strings is uncountably infinite. The number of infinite strings containing a work of Shakespear is countably infinite.

>>1965186

See >>1965097

>>1965183

Yes, maybe in a finite time ranger. But in infinity it'll always surely give any number 0-9 that you want.

>>1965199

almost surely*

>>1965199
This is where the misunderstanding is: "almost surely" does NOT mean it WILL occur; it simply means that the set on which it doesn't happen is a set of measure 0. As stated, the infinite sequence .11...=.(1) CAN occur.
This entire question is an example of a question which retards get right (for the wrong reason), people with a little knowledge of the literature get wrong, and people who understand the material get right.

>>1965186
No.

In a given interval, the probability of selecting a normal real number is 1. A normal real number will have some works of shakespeare in it somewhere in its expansion.

So when you have an interval and select a real (infinite monkeys) the odds of you selecting a normal number, and thus eventually shakespeare, is 1....

...but you could pick a rational. The probability is zero, but in dealing with infinite sets like this 0 does not mean impossible any longer.

>>1965215
That is my main point: a probability of 0 is not equivalent with the event being impossible to occur. (I'm not the person you were responding to)

>>1965230

No, that would be me.

>>1965230

Of course, zero and impossible are two different things. Some people confuse them like zero and nothing.

But the thing with an infinite string is, anything that can happen will happen. So if Shakespeare "can" be written, then it will be written.

>>1965215

Yeah, you are right. I was wrong in that the set of things containing Shakespear is countably infinite. However, I have not seen any proof that if you have some ininfite series of characters, it must contain a work of Shakespear. For every instance I get the correct first character, I have 25 incorrect choices for the next character, and the same for each subsequent character of the work.

>>1965268
No, it will not. Stop your faux-philosophy through radio interviews with Brian Greene and just read up on measure theory. With a few hours and some calculus it is easy to grasp the basics well enough to understand the issue here.

>>1965268
That is not the case at all, with regard to your point. It is, indeed, possible to continually type the same letter.

>>1965269
> However, I have not seen any proof that if you have some ininfite series of characters, it must contain a work of Shakespear.
It's a good thing you've not seen it, because it is false.

>>1965275
not op but it is IMPOSSIBLE to type the same letter forever when there are other possibilities. eventually the cycle will be broken.

>>1965284
>>facepalm.jpg
I do hope you are trolling.

>>1965284
Proof?

Say you have the numbers 0-9. You select one number at random. Then another. Then another. If this process is repeated to infinity, is the probability of selecting the number "9" = 1?

I think not.

>>1965295
You are selecting the number and putting them back in the bag.

>>1965307
The fact that the number .(1) can be obtained by ordering the the numbers selected IS the proof. Whether you understand that or not is your problem.

>>1965295
>>1965295

The possibility of this occurring is infinitly small that that at that point it would only make sense to treat it at zero.

hey sciencefags, how long could you shake a garage full of Porsche parts until the Porsche was completely put together and running?

this is how dumb you are

>Everyone in this thread

>>1965333
>hey sciencefags, how long could you shake a garage full of Porsche parts until the Porsche was completely put together and running?this is how dumb you are


It's theoretically possible.

>>1965333
You'd need a garage full of indestructible Porsche parts, but if you had that going for you t<infinity.

>>1965295
It is. L2 infinite series.

That's nothing.

When I was in uni, some of my classmates refused to believe that a feather and a hammer would fall at the same speed if there was no atmosphere to slow them down...
Needless to say, they wouldn't believe me when I told them about Galileo's experiment and how they could recreate it themselves...

>>1965382
Your classmates are stupid fucks.
I typed that while biting/gritting my teeth hard. Fuck sake.

( samefag as >>1965087 )

>>1965382 , I think my sister is more stupid than your mates, since I showed her the proof and still she didn't believed.

The numbers are so large that you would need galaxies filled with monkeys with type writers that were manufactured in different galaxies dedicated to this purpose and the universe would die in the time it would take.

OP is a faggot.

>>1965573
How do you know? All the monkeys could be typing 'a'