Are You Sure One And One Makes Two?

[deda]

How much chewing gums you get by adding one to another?

[matt grime]

Not a new thought, in essence. Go and read Whitehead and Russell for a bit of light entertainment.

The simplest refutation/explanation of this is: what do you mean by add? Pick up one stick of chewing gum, now pick up another? How many sticks have you picked up there? That kind of 'addition' is different from putting two pieces in your mouth and chewing. It's not a difficult philosophical argument to have, it just requires you to think about the words you are using.

[Chen]

Two of course.

[Shahil]

Doesn't matt grime's post bring up an interesting topic? Does the chewing gum problem mean that there exists another branch of mathematics hich WILL solve the two pieces uh...riddle?

[matt grime]

In the arithmetic of cardinals aleph-0 + aleph-0 = aleph-0

Or how about a quote from Blackadder II (the one with kate, short for bob)

Edmund Blackadder:So, Baldrick, if I have two beans and I add two more beans, what do I have?
Baldrick: A very small casserole.

[Organic]

First we have to know what is 1 before we add 1 to 1.

For example:

The notation of the empty set is {}, which means that nothing is included between '{' and '}'.

The cardinal of {} is 0 and it is notated like this: |{}|=0

The notation of a non-empty set is {x}, which means that at least some singleton is included between '{' and '}'.

The cardinal of {x} is 1 and it is notated like this: |{x}|=1

Let us say that x=1/2.

Now we have two basic possibilities:


a) The absolute approach:

|{x}|+|{x}|= 2 it means that we ignore the value of singleton x.


b) The relative approach:

If x=1/2 then x+x = 1
If x=1/4 then x+x = 1/2
If x=1/8 then x+x = 1/4
...

But be aware that there is already some 1 in our calculations; otherwise we cannot calculate 1/2, 1/4, 1/8 and so on.

In the case of the chewing gums, the result is 2 by (a) approach,
and can be any other result by (b) approach, if our 1 is already known.

But there is another possibility:

c) 1 property is unknown therefore we cannot write 1+1 = x,

But we can write x+x = 1.

Therefore by (c) x is included in 1.

[matt grime]

Erm, Organic, sorry to start off again, but the cardinality of the set {x} where x is a single element of some kind is independent of what x is.

[Organic]

I know, and I also wrote it in my previous post. See the absolute approach.

[matt grime]

Then what was the point of your post? Apart from to pormote your ignorant postition of mathematics again?

[Michael D. Sewell]

How much chewing gums you get by adding one to another?

It seems vague, but is in fact meaningless.-Dick Van Dyke

[BookWorm]

How much chewing gums you get by adding one to another?


I will awnser that question if you, or anyone, can give me 1/2 of a piece of chalk.

[Michael D. Sewell]

I will awnser that question if you, or anyone, can give me 1/2 of a piece of chalk.

BOOKWORM FOR PRESIDENT!!!!!

[Integral]

Speaking of chalk,

why does a full stick of chalk break into PI pieces when dropped?

[chroot]

ROFLMAO, BookWorm... that sounds like something Feynman would have said. :smile:

- Warren

[BookWorm]

why does a full stick of chalk break into PI pieces when dropped?

What do you mean by a full stick of chalk? They come in so many different sizes.

[Michael D. Sewell]

What do you mean by a full stick of chalk? They come in so many different sizes.

SO DOES CHEWING GUM! THAT'S THE ANSWER!!!

[chroot]

Man, I've never seen Michael quite this excited before!

- Warren

[Michael D. Sewell]

Man, I've never seen Michael quite this excited before!

- Warren

No one ever made it so easy before. This is rich.

[BookWorm]

SO DOES CHEWING GUM! THAT'S THE ANSWER!!!


Ooops, I didn't mean to give it away like that. Hope no one has been trying to figure that one out for to long. They could be a little upset that a kid awnsered it in just a few minutes.




Sorry,
The kid who reads to much.

[Michael D. Sewell]

I got dis idee for a car see, you draw pullusion thru thi exsauhst an blow it out ef the karberator an it manufactures gasoleen. Also it draws heat out of thi atmosfeer wid the radiatur. DON'T even try to tell me it won't work, I seen one.

[Integral]

What do you mean by a full stick of chalk? They come in so many different sizes.
Perhaps, in view of the question which inspired this question, I should have said "new" or "unused".

[Michael D. Sewell]

Sorry, I must have lost it there. OK, I'm back to lamron now. LOL OK Integral, why?
-Mike

[PRodQuanta]

deda said: How much chewing gums you get by adding one to another? Well, let's take a look here...:
If you have 1/3 stick of gum, and you add 2/3 of a stick, you have 3/3, or 1; 1/3 + 2/3 = 3/3 = 1

On the other hand:

If you have .333. . . stick of gum, and you add .666. . . of a stick, you have .999. . ., or....

Wait a tick. What does it equal, .999. . . or 1, because surely they are not the same quantity. :wink:

Paden Roder

[KingNothing]

surely they are!

PS: Good one bookworm. a new quote of mine.

[Michael D. Sewell]

Oh no! not with the .999... again! That's it, I'm outa here. Two clicks and adios...

[deda]

Doesn't matt grime's post bring up an interesting topic? Does the chewing gum problem mean that there exists another branch of mathematics hich WILL solve the two pieces uh...riddle?
There are two ways of doing the addition:

The math one which sums the quantities of the same type:
1 chewg + 1 chewg = 2 chewg
As far as math is concerned chewg cancels the chewg and we have only
1 + 1 = 2

The phylosophical one adds two equal qualities which necessarilly ends with one quality of same type:
chewg + chewg = chewg
and it's true as well.

[Integral]

Sorry, I must have lost it there. OK, I'm back to lamron now. LOL OK Integral, why?
-Mike
Not sure but it may prove that Π =1

[Michael D. Sewell]

Not sure but it may prove that Π =1

uh-oh...

Now THAT'S a thread for Theory Development if I ever saw one.

I'm going to hide now...

[deda]

The point of this tricky question is to practice the difference between

quantity and quality

The question is probably old as phylosophy its self but still few are those that know the corect answer and do physics accordingly. What made me post this thread is Newton's way of equalizing force - mass ratio with angular and linear acceleration at the same time despite the fact that the last have different qualities - units. Newton cannot make a difference between degrees and meters. The only important thing for him is that this ratio divides somthing with time squared.

[BookWorm]

[QUOTE=deda]
The question is probably old as phylosophy its self but still few are those that know the corect answer QUOTE]

What is the correct awnser?

[JasonRox]

The whole chalk talk is from Isaac Asimov.

The book is Asimov on Numbers - Isaac Asimov.

He talk abouts a professor who says Mathematicians are maniacs of some sort, and he goes off to finish his case against the angry professor.

[BookWorm]

The whole chalk talk is from Isaac Asimov.

The book is Asimov on Numbers - Isaac Asimov.

He talk abouts a professor who says Mathematicians are maniacs of some sort, and he goes off to finish his case against the angry professor.

Yes, I have read it.

[Michael D. Sewell]

What made me post this thread is Newton's way of equalizing force - mass ratio with angular and linear acceleration at the same time despite the fact that the last have different qualities - units. Newton cannot make a difference between degrees and meters.

The units for linear acceleration are meters/sec^2
The units for angular acceleration are rad/sec^2

It is a simple matter to see how many meters an object travels along the circumference of a given circle if the radius of the given circle is known. This makes the relationship between radial acceleration and tangential acceleration apparent.

Acceleration is defined as a change in velocity over a time. Since velocity is a vector, there are two ways to produce acceleration: by a change in magnitude or by a change in direction. I don't see any flaws in Newton's laws here. The angular (radial) acceleration is perpendicular to the tangential acceleration.

The total acceleration is equal to the square root of (angular acceleration^2 + tangential acceleration^2)

For some reason, you seem to be intent on discrediting Newton. That's ok; because each time you are proven wrong, the students on this forum get a better understanding of classical physics during the course of the discussion. So in your own way, you are providing a valuable service to many people. If this is your purpose, than I would like to thank you for your contribution.
-Mike