Higher than "chance"

[drkitten]

Another interesting point to make is that despite the fact that the probability of the computer generating any specifiable single number is zero, we know that the computer does actually choose one number. This means that in this instance adding up an infinite number of zero probabilities actually equals 1!

[bewildered]
Um, yeah?

We call this process "integration" on this planet.

It's well-studied and a lot of people learn how it works in secondary school.

 

[Dr Adequate]

Another moron...

Again, I have to point out to that saying it won't make it so.

... calling himself a Dr

I don't just "call myself" a doctor. I have a doctorate. It's not like you calling yourself "Interesting".

So, it's possible that an event which has zero probability of occurring to occur anyway?

Yup.

You really want to maintain this?

Yup.

Or are you simply confused between something being possible and something being logically possible??

Nope.

 

[Interesting Ian]

Er... Ian... calling dr k a "moron" won't stop every single detail of his post from being absolutely correct. It just makes you look like a stupid petulant child.

Belittling my intelligence makes him a moron. If I was a sKeptic do you imagine he would do likewise?

If I am incorrect in anything I have said, then it is incumbent upon the him to say what it is. Let him provide an argument. That goes for everyone who says I am wrong.

 

[Interesting Ian]

[bewildered]
Um, yeah?

We call this process "integration" on this planet.

It's well-studied and a lot of people learn how it works in secondary school.

I've never done calculus.

 

[drkitten]

Regarding the statement

--------------------------------------------------------------------------------
It is possible to divide by zero. Any non-zero number divided by zero is infinity.
--------------------------------------------------------------------------------

It does not seem to be incorrect to me, but I shall avoid making definitive statements since Beth says she agrees with everything you say and I respect her judgement somewhat more than your facile proclamations

Well, you could actually think about what I write instead of dismissing them as 'facile proclamations.' Although I admit they are facile, since they're extremely easy both to make and to demonstrate.

To start out with, infinity is not a number. It's a concept, rather like 'truth' or 'justice' or 'love.' So the easy, simple, facile answer of why you can't divide by zero is because there is no 'number' to produce as an answer. A proper handling of infinite quantities requires a limit process.

Another problem is that, as stated, it's incorrect even if treated as a limit process. The limit of any positive non-zero number, when divided by increasingly smaller quantities, of course increases without bound. But the limit of any negative non-zero number decreases without bound, which you would naively express as "negative infinity."

But the real problem is simply that division by zero doesn't make sense. There's a good Dr. Math column on this, which says, among other things

When you divide a number by another number, you can think of splitting it up into groups.

For example, 10/5 (ten divided by five): take the ten and divide it up between five groups so there is nothing left of the ten. You get two in each group, so 10/5 = 2.

This works for numbers that don't divide evenly also: 5/2: take the five and divide it up between two groups so there is nothing left. You can put two in one group and two in the second group, but that leaves a remainder of one. So you can split the one between the two groups and get 2.5 (2 and 1/2) in each group. So 5/2 = 2.5.

However, if you try to do this with zero, it doesn't work. Take any number -- we'll use 10 to make it simple. What happens when you try to split ten up into zero groups with no remainder?? You can't do it! If there aren't any groups, then you can't put the ten anywhere.

Basically, the division concept doesn't make sense when the divisor is zero.


Another way of looking at is is that division is defined as the inverse of multiplication. So an expression like x/y = z is really the same as y + z = x. But if y is zero, then we have the equivalent expression

0 * z = x (for non-zero x)

You would claim that putting the pseudo-number "infinity" in for z makes the equation true. Unfortunately, multiplication of zero by infinity doesn't make sense --- and even if it did, it would have to have several different values at once, which breaks the rules of multiplication, since it would have to be true simultaneously for every non-zero x there is.

So the facile answer is "it's wrong."

The long, but still facile, answer is "it's wrong because....." As you could have found out for yourself in ten minutes with Google-fu.

Wow, just really wish I was a student in one of your classes. I'd really love to take the p*ss out of you.

You'd last about one term.

 

[Interesting Ian]

Again, I have to point out to that saying it won't make it so. I don't just "call myself" a doctor. I have a doctorate. It's not like you calling yourself "Interesting". Yup.Yup.Nope.

If by possible you do not mean logically possible, but something which can actually happen in the real world, then explain how an event with zero proability of occurring can occur anyway.

I await with a great deal of interest.

Although I assure you I won't be holding my breath.

 

[Beth]

Please read my post with more care.

I was not suggesting that the argument about zero probability events occuring was wrong, I was stating that Beth's argument about being close enough to zero that rounding to exactly zero was facetious.

- Timothy

Well, I was giving two different examples of how events with a probability zero can occur. You're right that the argument about rounding is somewhat questionable. Still, I think people do such rounding fairly frequently in real life and I wasn't sure exactly what Ian was referring to with. He has since clarified that it wasn't the rounding case. Sorry if I've offended with such an inexact definition of probability zero.

Beth

 

[Interesting Ian]

You'd last about one term. [/B]

That's a shame. To tell you the truth, I like mathematics -- especially statistics. I enjoy arguing about it on here (contrary to what appearances might suggest).

 

[Interesting Ian]

Well, I was giving two different examples of how events with a probability zero can occur. You're right that the argument about rounding is somewhat questionable. Still, I think people do such rounding fairly frequently in real life and I wasn't sure exactly what Ian was referring to with. He has since clarified that it wasn't the rounding case. Sorry if I've offended with such an inexact definition of probability zero.

Beth

Well I was referring to both in differing parts of the thread. When I said you would not get 4 bridge hands with each hand containing all the cards of each suit, I was referring to the idea that it is so incredibly unlikely that effectively it simply wouldn't happen in the real world.

Like being born; but yet we're here. Which means that I can safely discount the idea that I am simply the product of a sperm and an egg .

 

[TheBoyPaj]

So now we have a better picture of Ian. Someone with no formal training in statistics, but who would heckle the person trying to help them to understand, thus disrupting everyone else's education along the way.

Moron.

 

[Timothy]

Well, I was giving two different examples of how events with a probability zero can occur. You're right that the argument about rounding is somewhat questionable. Still, I think people do such rounding fairly frequently in real life and I wasn't sure exactly what Ian was referring to with. He has since clarified that it wasn't the rounding case. Sorry if I've offended with such an inexact definition of probability zero.

No offense. Simply pointing out that in some cases one gets into trouble by using an informal or lay use of a term, and then using that in an exact formal sense in a "proof". It's a variation of the "fallacy of equivocation" ... using a word to mean one thing in one part of an argument, and another thing in another part of an argument. In this case the difference is slight, but makes all the difference in the world.

- Timothy

 

[Interesting Ian]

So now we have a better picture of Ian. Someone with no formal training in statistics, but who would heckle the person trying to help them to understand, thus disrupting everyone else's education along the way.

Moron.

You mean I disrupt everyones daydreams and they actually prick up their ears and start to listen to the argument, and take an interest

 

[Dr Adequate]

If by possible you do not mean logically possible, but something which can actually happen in the real world, then explain how an event with zero proability of occurring can occur anyway.

If we have an infinite number of equally likely possibilities, and one of them occurs.

(Take your own example of a genuine random number generator. When it produces a number, that number comes up with probability zero.)

 

[Dr Adequate]

Belittling my intelligence makes him a moron.

No.

 

[Dr Adequate]

You mean I disrupt everyones daydreams and they actually prick up their ears and start to listen to the argument, and take an interest

No, that's not what he means. Time to brush up on your comprehension skills.

* sigh *

If you're to dumb to understand simple English sentences, this explains much.

 

[Interesting Ian]

If we have an infinite number of equally likely possibilities, and one of them occurs.

(Take your own example of a genuine random number generator. When it produces a number, that number comes up with probability zero.)

Ummm . .yes. I know this. Let's go back to what I said:

"So, it's possible that an event which has zero probability of occurring to occur anyway"?

To which you answered "yes".

Let me be more precise. What about if I had said:

"So, it's possible that a specifiable event which has zero probability of occurring to occur anyway"?

To which the answer is no.

You pick any number between 0 and 1 with an infinite number of digits after the decimal point, and I say it cannot possibly occur (although it could of course logically possibly occur).

Now the fact that some specific number is generated is neither her nor there. The point is that it is not possible for us to have picked that number beforehand and for it to occur.

Do you see?

 

[Interesting Ian]

No, that's not what he means. Time to brush up on your comprehension skills.

* sigh *

If you're to dumb to understand simple English sentences, this explains much.

It is sad that you feel the need to resort to such rudeness

 

[Interesting Ian]

Ummm . .yes. I know this. Let's go back to what I said:

"So, it's possible that an event which has zero probability of occurring to occur anyway"?

To which you answered "yes".

Let me be more precise. What about if I had said:

"So, it's possible that a specifiable event which has zero probability of occurring to occur anyway"?

To which the answer is no.

You pick any number between 0 and 1 with an infinite number of digits after the decimal point, and I say it cannot possibly occur (although it could of course logically possibly occur).

Now the fact that some specific number is generated is neither her nor there. The point is that it is not possible for us to have picked that number beforehand and for it to occur.

Do you see?

And also it is not of course possible for any special sequence of numbers to have been randomly generated i.e after the number has been generated it would not be possible (although it would be logically possible) for it to exactly equal, say, pi.

Similar reasoning makes the chance of me being born so incredibly close to zero probability, that effectively it could not have occurred. Yet here I am. Therefore I cannot be simply the product of a sperm and egg. You see?

And similar reasoning applies to bridge hands. It is true that any bridge hand is as likely as any other. But this misunderstands the point when I say that each hand consisting of an entire suit is so vanishingly small that effectively it couldn't really happen.

 

[Timothy]

Back to the subject of choosing card color.

I learned and revised a very good card trick that relies on a prepared deck, and when performed properly can be quite amazing.

The patter is that I can quickly riffle through a pack of cards and spot the missing one (chosen and held by the mark).

As I performed this trick with one particularly gullible 18-year-old mark, I was asked to do it a second, third, fourth, fifth, tenth time.

As it became apparent that I could keep her on the hook almost indefinately, I changed the patter that by riffling it by my ear I could *hear* which card was missing.

As time progressed, I eventually was able to let *her* look through the deck, shuffle the deck, and still make it work.

In the end, I was able to do nothing more than hold the deck and tell her which card she'd chosen.

She never figured out how.

While the chance of choosing the correct color 48 out of 52 times is not zero, it is sufficiently close to zero that probablility favors a trick on a nine-year-old.

- Timothy

 

[Gr8wight]

Could you let me know what I have said that you believe to be incorrect? If I'm convinced by your explanation, I'll readily admit it. I don't expect you to respond to this post though

Although I recognise that I can not convince you, regardless of what I say, I will reply nonetheless. I originally replied to your very first post in this thread:

Nonsense, you couldn't achieve that by chance! Get real.

Your response to Bodhi Dharma Zen demonstrated that you don't have even a rudimentary grasp of the concept of chance. After I read several more of your posts in which your comprehension of the world at large slipped farther and farther into the Twilight Zone, I edited my reply.

You still owe PixyMisa a quarter.

I will not post in this thread again.