TexAgs91 said:You're getting into the specifics of what is being added, which is beyond the scope of the mathematical definitions of 2, + and =. 2+2=4 works just fine. It works when you know you have two of something. And another two of something. It adds to 4. If you aren't sure if you have two of something then hold off on adding until you figure it out.ABATTBQ11 said:TexAgs91 said:
The definition of an apple would have seeds built into it. One apple is one apple.
2+2 deals with definitions of mathematical objects, not gravitation. According to their definitions 2+2=4. That's all there is to it.
The definition of an apple having seeds built into it is an assumption and constraint you've added. It goes back to the room and blue versus azul eggshell with off white trim. Every new detail refines the reality you're describing and reduces the set of possibilities that fit the constraints.
Think of it this way: If I point to a woman in front of you, tell you she has a fertilized egg in her uterus, and ask you how many people are standing in front of you, would you say one or two? If your definition of life is that it begins at conception, it is 2 because that fertilized egg has the potential to grow into a fetus, infant, toddler, and so on. If you think life begins at birth, it is 1. Nothing has changed, but how many people are in front of you can be described differently mathematically depending on the assumptions laid out and the question being asked.
Again, in pure math, there is the implicit assumption that all numbers are representative of the same things because the numbers don't represent anything in particular. They're abstract ideas in the same way that some variable like x is an abstract idea or sqrt(-1) is an abstract idea.
Mathematical application is a little different. The specifics and subjects of what are being added, subtracted, or in some other way described in mathematical terms become important. If you are not cognizant of what you are describing and how you're describing it (like sentiment or intelligence), even if the math is right, the description is still wrong. It's like saying, "The sky is green." Grammatically, that sentence is perfectly fine, but it is still incorrect because in reality the sky is blue. 1 half eaten apple + 1 rotten apple = 2 apples. The math is correct (1 of something + 1 of something = 2 of something) because the half eaten and rotten apples have not ceased to be apples, but do you really have two apples? It's still 1+1=2 and in mathematical terms, yes, you technically have 2 apples, but it does not accurately describe the reality of not being able to eat those apples and really having no apples.
Now apply that to something abstract instead of literal and it starts to (hopefully) make more sense. Since it's been mentioned, sentiment score is a decent example. Let's say I have the two statements below and score them in sentiments using a positive and negative lexicon. A "sentiment" s is the difference in the number of matches in each lexicon to score sentiment (2 positive matches - 3 negative matches = -1 sentiments).
"I kind of dislike Joe Biden" - 0 positive matches - 1 negative match (dislike) = -1 sentiments
"I HATE Joe Biden" - 0 positive matches - 1 negative match (hate) = -1 sentiments
These would both have a sentiment score of -1 to indicate mild negativity towards Joe Biden because "dislike" and "hate" are both in the negative lexicon and scored equally. In reality, these two statements, as typed, have vastly different levels of negativity. Despite both expressing negative sentiment, "dislike" and "HATE" are not the same, and there is no measurable distance between them since they're only ordinally related. "HATE" is arguably more negative than "dislike," but by how much? We can average these scores ((-1 + -1)/2) to come up with an average sentiment of -1, but what does that mean if that average could be compared to either of the statements above?
Quote:This is good instruction for the user.Quote:
2+2, or for a more simple example 1+1, comes with it's own assumptions. 1+1 on its face is simple. It's the easiest math problem imaginable. By mathematical rule it is 2, with the implicit understanding that the ones both describe the same thing being added. The last part is important.
In applied math, 1 describes something. It isn't 1 per se, it is, "1 what?" The "what" is a very important part of the application of the objective 1+1 rule because it determines of the 1+1 rule even applies. If you have different, "whats," then it's more of an x+y situation. After all, x+y can be rewritten as 1x+1y=x+y. Still 1+1, but the solution varies depending on the definition of x and y.No. Look at your own caveat right above. A large square is not the same as a small square. You cannot mix object types unless you use the tools we have in math such as 1x+1y=x+y.ABATTBQ11 said:
Now think of the square visual example that Carr presents. If we combine the four squares into one, and ask, "How many squares do we have?" the answer CAN be 5 because the outer perimeter forms a fifth square.
If the question is, "How many squares do we have?" then size is irrelevant. A square by definition is a quadrilateral having straight, equal length sides and 4 right angles. Size is not a part of that, so a square is a square is a square regardless of how big they are. They may not be congruent, but all 5 are still squares.
And as mentioned, a cube created by four squares still produces six squares of the same original size. You have to limit the space to a 2 dimensional plane to invalidate that possible solution to adding the squares together.
Quote:Good advice for users of math. 2+2 still equals 4.ABATTBQ11 said:
The, "whats," you're adding are very important
If anything Kareem should caution people to be careful in how they apply math. No harm in that. But that's nowhere near the same as questioning if 2+2=4.