Are You Sure One And One Makes Two?

  • Thread starter Thread starter deda
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the philosophical and mathematical implications of the statement "one and one makes two," using the example of adding chewing gums. Participants explore the nature of addition, cardinality, and the distinction between quantity and quality in mathematical contexts.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants question the meaning of "add" in the context of chewing gums, suggesting that the act of addition can vary based on interpretation.
  • One participant introduces the concept of cardinality, discussing how the cardinal of a set is independent of its elements.
  • Another participant presents different approaches to addition, including absolute and relative methods, leading to various interpretations of the result of 1 + 1.
  • There is a humorous exchange regarding the nature of chalk and chewing gum, with participants making light of the philosophical implications of their sizes and quantities.
  • Some participants reference historical figures and works, such as Newton and Asimov, to illustrate their points about mathematical reasoning and philosophical inquiry.
  • One participant raises the idea that the question of adding chewing gums could indicate a need for a new branch of mathematics to address such philosophical dilemmas.
  • There is a discussion about the relationship between quantity and quality, with references to Newton's equalization of different types of acceleration.

Areas of Agreement / Disagreement

Participants express a range of views on the nature of addition and its implications, with no clear consensus reached. The discussion remains open-ended, with multiple competing interpretations and approaches presented.

Contextual Notes

Participants highlight the ambiguity in definitions and the philosophical underpinnings of mathematical concepts, indicating that the discussion is influenced by varying interpretations of terms like "addition" and "quality." Some mathematical steps and assumptions remain unresolved.

deda
Messages
182
Reaction score
0
How much chewing gums you get by adding one to another?
 
Physics news on Phys.org
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.
 
Last edited:
Two of course.
 
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?
 
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.
 
Last edited:
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.
 
Last edited:
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.
 
I know, and I also wrote it in my previous post. See the absolute approach.
 
Then what was the point of your post? Apart from to pormote your ignorant postition of mathematics again?
 
  • #10
deda said:
How much chewing gums you get by adding one to another?

It seems vague, but is in fact meaningless.-Dick Van Dyke
 
  • #11
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.
 
  • #12
BookWorm said:
I will awnser that question if you, or anyone, can give me 1/2 of a piece of chalk.

BOOKWORM FOR PRESIDENT!
 
  • #13
Speaking of chalk,

why does a full stick of chalk break into PI pieces when dropped?
 
  • #14
ROFLMAO, BookWorm... that sounds like something Feynman would have said. :smile:

- Warren
 
  • #15
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.
 
  • #16
BookWorm said:
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!
 
  • #17
Man, I've never seen Michael quite this excited before!

- Warren
 
  • #18
chroot said:
Man, I've never seen Michael quite this excited before!

- Warren

No one ever made it so easy before. This is rich.
 
  • #19
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.
 
  • #20
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.
 
Last edited by a moderator:
  • #21
BookWorm said:
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".
 
  • #22
Sorry, I must have lost it there. OK, I'm back to lamron now. LOL OK Integral, why?
-Mike
 
  • #23
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
 
  • #24
surely they are!

PS: Good one bookworm. a new quote of mine.
 
  • #25
Oh no! not with the .999... again! That's it, I'm outa here. Two clicks and adios...
 
  • #26
Shahil said:
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.
 
  • #27
Michael D. Sewell said:
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
 
  • #28
Integral said:
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...
 
  • #29
The point of this tricky question is to practice the difference between

quantity and quality

The question is probably old as phylosophy itself 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.
 
  • #30
deda said:
The question is probably old as phylosophy itself but still few are those that know the corect answer QUOTE]

What is the correct awnser?
 

Similar threads

How to teach errors and uncertainty in an undergraduate setting?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Trust me I'm a Photographer -- I have a question
  • · Replies 12 ·
Replies
12
Views
2K
How Can Polyvinyl Acetate Be Separated from Recycled Gum?
  • · Replies 2 ·
Replies
2
Views
2K
Free Body Diagram for a Piece of Gum on the Underside of a Desk
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Is it Valid to Average Two Metrics in Spacetime?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Is a thrusting motion more powerful/deadly than a swinging one?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Measurement Error Analysis in Gaussian distribution
  • · Replies 2 ·
Replies
2
Views
2K
What ONE Physics topic would you choose to study and why?
  • · Replies 18 ·
Replies
18
Views
4K
High School Audio frequency of a humidifier
  • · Replies 12 ·
Replies
12
Views
1K
Graduate Monte Carlo to compute uncertainties, why report the mean and SD?
  • · Replies 2 ·
Replies
2
Views
2K