Does 2+2 always equal 4?

this has absolutely no relevance to your question unless your looking for a philosophical answer, but here ya go:

"I admit that two times two makes four is an excellent thing, but if we are to give everything its due, two times two makes five is sometimes a very charming thing too."

-dostoevsky, "notes from the underground"

I hardly qualify as a math genious, but I think you're talking about bases here. i.e. (and you math folks, please correct me) 2 + 2 = 20 in base 3. Or is it base 2?

I'll shut up now.

Some research reveals...

Hello!
My husband has a physics degree, and he says that basically, 2+2 does always equal 4. But if you want to quibble about it (and I usually like to) a google search revealed this web page:
http://virgil.azwestern.edu/~dag/lol/TwoPlusTwo.html

which seems to examine some cases where it might not.

Happy writing!
~hexseraph

Depends upon the public school, in some it will equal whatever the child wants as to not hurt his/her self esteem

I used to be a college math tutor, so I couldn't keep from checking Haggis's math.

2(base3) + 2(base3) = 4(base10) = 11(base3). So, 2+2=11 in base 3. In base 3, there are the digits: 0,1,2. When your addition results in a total of 3, you "carry" the result to the next place....so a 4 translated in base 3 is a 1 and a carried "3".

About imaginary numbers...they are used in applications where the state of a model at one point in time is dependent on the state of the model at a previous point in time (used in electronics, quantum physics, etc.) An equation might be written like 2 + 2i = 5 where the first "2" is a real number and the "2i" is the imaginary number.

Can someone check my math?***

I like the link hexseraph provided or Haggis's base idea. I am not sure how easy it would be to use imaginary numbers in a story discussion.

Thanks for fixing my math, oarsman. That's why I was an anthro major.

oarsman said:

2(base3) + 2(base3) = 4(base10) = 11(base3). So, 2+2=11 in base 3. In base 3, there are the digits: 0,1,2. When your addition results in a total of 3, you "carry" the result to the next place....so a 4 translated in base 3 is a 1 and a carried "3".

Click to expand...

But Lolly, don't forget, 2+2 still equals 4. The number 11 in base 3 merely reflects a system where the numerical representation of the quantity "4" notates as "11."

My heads hurts now...

Mark Lazer said:

My heads hurts now...

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Get out the heavy drugs...

This is one of those questions I wish I never asked my older Brother. Don is one of those musical geniuses that can pick up any instrument and play like a master within moments. If he hears a piano sonata one time, he can play it. He is a Master Guitarist who cannot tolerate a missed beat, note, string or inflection.

I asked him if 2 + 2 always equals 4 and here is what he told me:

“In music, I would argue that 2 whole notes and 2 half notes equal 3. But I would be more accurate if, in a 4/4 beat, 2 wholes and 2 halves would be 12. But then in a 5/4, 2 wholes and 2 rests would equal 20 unless 1 rest had a quarter following it, then it would be 19 and if both rests were followed by a quarter it would be 18.”

It took me a long time to figure out what the heck he was saying.
Yes, I come from a very strange family.

My brother has a thinkgeek tee shirt that says "2+2=5 (for sufficiently large quantities of two)." That's probably not overwhelmingly helpful, but I thought I'd share.

it depends on the age of the person doing the adding.

Since it's the right time of the year, I have to post my "base" riddle again.

Why is Halloween the same as Christmas?
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Because OCT 31 = DEC 25 (octal 31 = decimal 25)

My good friend Winston Smith says 2 + 2 = 5

"for sufficiently large quantities of two"

LOL

rugcat said:

But Lolly, don't forget, 2+2 still equals 4. The number 11 in base 3 merely reflects a system where the numerical representation of the quantity "4" notates as "11."

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Right. I probably won't express this well; however, I'm going to give an attempt.

When I write "the event {* *}," I mean that there are two things. So, if one holds two golf balls in one's hand, I'll say that the two-ness is the event {* *}. Three golf balls is the event {* * *}.

It is always true that if one has an event {* *} and adds to it a second event {* *}, the result is the event {* * * *}. That is, two plus two always equals four.

The numerals "2" and "4" are part of a system of representing the events above. Because "2" and "4" are arbitrarily defined, they can easily be redefined as we wish. One way we could do that is to change our base. In our usual counting, the numerals go from 0 to 9, and then when we go up one more, we put the digit back to 0 and put a 1 in front of it: "10."

In binary, we do that when we go past 1, so 2(base 10)=10(binary). This change in base doesn't affect the fact that the event {* *} plus the event {* *} equals the event {* * * *}.

Switch gears
There is a type of math called modular arithmetic. The most common way to think of it is this: clock math. If it's 8:00pm and I wait five hours, the new time will be 1:00am. It has its applications, but it's not a counter example to the fact that 2+2=4, because without indicating that one is operating in modular arithmetic, the default is what we're normally used to.

Sorry if that makes no sense. I did my best. ^_^

You probably already know this, but in 1984 they make Winston say/believe that 2+2=5

War is peace, freedom is slavery, ignorance is strength.

I think the lateral concept of thinking is explored in the book by Tony Buzan about Mind Mapping. Other similar equations are involved with an inclination towards relativity.
Working backwards: other things equal four;not only 2 plus 2.

The "for sufficiently large values of 2" is a joke about roundoff errors and significant figures. For example, if you added 2.45 and 2.37, you'd get 2.82 - but if you rounded them all to the nearest integer, it would look as if you had added 2 and 2 and got 5. It's something engineers have to watch out for sometimes when working with imprecise, real world numbers.

"2" would have to be in a number system at least base "3" or larger.

Base 2 would contain only the digits "0" and "1".

So, to get "2" in your number, you'd need at least base 3.

2 (base3) + 2 (base3) = 11 (base3)

where 11(base3) is still good ol' fashioned 4(base-ten) that we usually see.


Speaking of binary, there are 10 kinds of people, those who understand binary, and those who don't.

(where 10 in binary is "2" in base-ten format)

Move along.

Nothing to see here.

greglondon said:

Speaking of binary, there are 10 kinds of people, those who understand binary, and those who don't.

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BRILLIANT!!

BTW, you can tell someone that you can count to four on your fingers using binary, then give them the finger. From either the pinky or the thumb as the first digit (heh), it works. It's the third or fourth joke I've ever made up in my life, and it still cracks me up. ^_^

Ok ok, everyone can relax now because I think I've finally figured out how to make 2+2 equal something other than 4...

If you take two apples, stick them in the freezer for exactly two hours, then take them out and paint them purple, then when they're dry use a black marker and write the numbers one and two on them.
Next take them out into the street and kick them around for approximately 85.35 seconds, then if a bus drives by, pick them up, drop your pants and moon the people on it, then run around the block screaming "I'm a little teapot, short and stout..." until the police show up and haul you away.
Then when you're eventually released or escape, pick up another two apples on the way home and repeat the entire process, then after the second release/escape take all the apples to the top of the Empire State building and line them up on the ledge. Then if a pigeon shows up, put one of those cardboard Burger King crowns on your head, quickly gather everything together and run down to the middle of Central Park. For the next two minutes chew as much bark off the nearest tree as possible, then find a local pet store...

Oh I'm sorry, this is how you learn the alphabet, never mind.



And you will all no doubt be pleased to know that I do really work for a public school.

Tornadoboy said:

Ok ok, everyone can relax now because I think I've got this one figured out...

If you take two apples, stick them in the freezer for exactly two hours, then take them out and paint them purple, then when they're dry use a black marker and write the numbers one and two on them.
Next take them out into the street and kick them around for approximately 85.35 seconds, then if a bus drives by, pick them up, drop your pants and moon the people on it, then run around the block screaming "I'm a little tea cup, short and stout..." until the police show up and cart you away.
Then when you're eventually released or escape, pick up another two apples on the way home and repeat the entire process, then after the second release/escape take all the apples to the top of the Empire State building and line them up on the ledge. Then if a pigeon shows up, put one of those cardboard Burger King crowns on your head, quickly gather everything together and run down to the middle of Central Park. For the next two minutes chew as much bark off the nearest tree as possible, then find a local pet store...

Oh I'm sorry, this is how you learn the alphabet, never mind.

And you will all no doubt be pleased to know that I do really work for a public school.

Click to expand...

WOW!