2 + 2 = 5 And I Can Prove It
When I was in Kindergarten (grade 0 in American school) I asked my teacher why we skip 0 when we count, and if there was anything less than 0. She looked me right in the eyes and said, "There's nothing less than 0 and 0 isn't anything, so we count from 1." Later on I found out that she had lied about numbers less than 0. It sort of got me thinking...
Everyone believes that 2 + 2 = 4 right? But what if I told you that's only because it's how we were taught? What if your teachers told you to count from 0 (like how computers count) instead of counting from 1, then would 2 + 2 still equal 4? Nope. Let's do the math, I'll count a check-mark for each number below to show it:
0 & 1 & 2 + 0 & 1 & 2 = ?
✔ & ✔ & ✔ + ✔ & ✔ & ✔= 6 checks
You can even count it on your fingers, 2 + 2 results in 6 when you start counting from 0. But wait, there's more!
We're counting from 0 here, so technically the 6th digit is the number 5. So let me count that again with check-marks to make it obvious:
0 & 1 & 2 & 3 & 4 & 5
is the same as:
✔ & ✔ & ✔ & ✔ & ✔ & ✔
So there you have it, simple math which you could count on your hands proves that 2 + 2 = 5 but why is that important? Well, it's not just 2+2 it's actually all the math work that humans have ever done. If we've been doing it wrong all this time then don't you think we should start doing it right someday? Eventually we'll have to start counting from 0 out of necessity, like converting to the metric system. The simple math we use today might be okay if it's wrong by a little bit, but in the future we'll need to start doing it right.
All computers (including calculators) count from 0 instead of 1, but when they do math for humans those computer apps and calculators all had to be programmed to adjust their results to give the numbers that humans expect. I know this sounds a little corny, but it's possibly the biggest conspiracy theory of all time.
But you might be saying, "Take it to it's logical conclusion, 0 plus 0 shouldn't equal 1." And you're right, if you put 0 dollars on a table and then add 0 more dollars you wont get 1 magic dollar out of it. But don't forget that we're not done yet, we still need to 'translate' that result of 1 into it's Nth digit. In this case the 1st digit is 0. So 0 + 0 = 0 still, even when you start counting from 0. And 1 + 1 = 3 because 0 & 1 + 0 & 1 = the 4th digit which is 3. I hope that makes sense.
Or maybe you still think 0 isn't even a real number at all? But if we don't count 0 because it represents nothing, then why shouldn't we count 2 twice according to the same logic? Do you think we should start counting from 0? I think we should, and I dare anybody to try and prove me wrong. Let's get a debate started in the comments. Thank you for reading this.
Computers don't count anything. They index which is massively different to counting. Numbers are also just labels. You're whole premise is based on a question with faulty logic due to misunderstanding the mathematics.The Romans never even had a zero, this is a relatively modern symbol. The ancient mathematicians in greece as well as the chinese and japanese and their abacus had no use for the symbol zero as that is simply what it is, a symbol to help us understand counting and labelling systems.
0011010010100 Error Error Error
0 ∈ ℝ
I have 11 fingers... let me count them for you...
Left hand
10
9
8
7
6
Right hand
1
2
3
4
5
See?
6+5 = 11
In modern programming languages, array indices usually begin at zero. This kind of threw me off when I first started coding as I expected the array to start at index 1.
Here is a relevant wiki covering zero-based numbering.
https://en.m.wikipedia.org/wiki/Zero-based_numbering
I'm struggling to see the logic; however, in how this applies to arithmetic operations as you suggest.
Let's suppose the following example in Python:
In this, I instantiate two list variables. If I print index 0 of arr, it will return 'thing1'. If I perform len(arr), it will return a count of 2.
Let's say I create a new list (arr3) and use a couple for loops to add the items in both arr and arr2 to it.
If I perform a len(arr3), the result will be 4 even though the index starts at 0. The last element of arr3 would then be arr3[3] = 'thing4'.
See how that can be confusing? The last index is 3 but the count is 4. However, this does not change the laws of arithmetic. 2+2 still equals 4.
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But what about 'thing0'? In order for counting from 0 to work, you need to begin the count at 0, otherwise you're just converting one counting method to the other.
Indexes aren't counting, they are offsets added to the array's starting memory location. The first object starts at the array's first memory location, the 2nd object's location is after the first object, so we indicate the offset index of 1, move 1 entry away from start of array, 2nd object is here.
You are perfectly entitle to build your own logic.
Thank you :)
Isn’t the number 1 just the value of everything between zero and 1?
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Technically, if you add up all the values between zero and one it'll equal Infinity because there are an infinite number of decimal values that can be defined between 0 and 1.
I'm a math teacher, why didn't I get called to this debate earlier?
Aha! You're finally here :) We could use you're help. What's your opinion about counting from zero? Should zero be counted? And if we do count from zero then is it true that 2 + 2 = 5? I may have been confused about the 2+2 part, but the main point I wanted to make in the article was about counting from zero. So, what's your professional opinion?
The 0 is a real number, even when we count the 0 is part of the natural.
count is the assignment one to one of the objects starting with 1. But why start with 1 if the first number is 0?
We shouldn't take anything for granted. There are recent studies that show that the void is not as empty as we were told. I recommend the works of "nassim haramein".
Finally recently I saw a video where a group was about to check that the decimals of pi were wrong, I saw it in a video in Spanish.
I am running out of fingers while calculating this. Can I have your fingers @anomaly?
You can have as many fingers as you want if you count them this way:
I have seen this before. Lol. Never thought this way, m bad at calculus.
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Okay...
I think in your logic you still get 0 + 0 = 1. Look, we are summing up two zeroes, so we are counting them: 0, 1. Hence, the result is 1, not 0. And if we add one more zero we will get 2.
So, I think this part is not quite correct:
You applied an extra translation step.
Hmm, yeah you might be right about that translation step. The only other thing I can think of is that 0 + 0 isn't really addition because you're not actually adding anything to anything. Thank you for your feedback :)
Taking 2 fingers and adding 2 more fingers does not make 5 fingers. There's only going to be 4 fingers there no matter how you go about counting them. You can imagine a single object is actually 2 objects but in reality it's still only a single object.
Sure you could probably start counting everything at 0 and use your own logic for everything and recreate your own systems for doing things but I fail to see how this would be beneficial at all because one object is not 2 objects or 0 objects, it's one.
I think saying it's the biggest conspiracy theory of all time is a little much. I think maybe you're just counting your thumb as a finger.
When you start the count from 0 then it takes 3 fingers to count to 2, so you might need that thumb. I think most of the confusion comes from what I called the 'translation' part of it, that's when the Nth digit is N-1 at the end. A 6 becomes a 5 for example because 5 is the 6th digit from 0. Technically the result is the same amount, it's just counted differently.
As a programmer I understand that part. Is there something else I'm not understanding correctly?
What I'm saying is that while you can count however you like, one finger is still a single finger. You can change the numbers to whatever words you want or use whatever language you like. However, if the finger is there then it's there. There aren't none of them there. It isn't nothing. It's there. Normally, it's a 1 and not a 0. If it was a 0 then it wouldn't be there because it would be nothing because 0 equals nothing.
You can change the index or the label of that object to whatever you like but it doesn't change reality or the fact that object is there or not. If it wasn't there then there would be 0 of them there and you wouldn't count it. So while you can count however you like or translate numbers however you like, you cannot change reality or how math works. If you take 2 objects and add 2 more objects you have 4 objects. If you are counting from 0 then you'll still have 4 objects, although you may use a different label other than 4 to describe them and count them with different words. You haven't actually changed the number of objects there, you've just given the values different names.
Okay, I understand what you're saying. But what I don't get is this, if we don't count 0 because it represents nothing, then why don't we count 2 twice? Why don't we triple-count 3? And if it was arbitrary to begin with then why didn't we start counting from 2 or some other arbitrary number?
If you're giving the numbers their original values and not using new labels then you can definitely start at any number you like. You could even start at 0 but in that case you won't be referring to a finger that's there, but nothing. If you're starting at 2 then you would be counting 2 fingers that are there, providing there are 2 there to count.
You don't have to count 2 twice because you're counting in whole numbers, which are in increments of 1. You don't use the same logic as 0 because nothing doesn't have to be counted. That doesn't mean you can't or don't have to start counting at 0 but that most people will skip counting nothing because all they care about is the somethings they're counting.
If you count 2 twice then you would have 4 and might be counting by 2s instead of 1s. If you count 3 three times then you'll have 9 and might be counting by 3s instead of 1s. If you counted 2 twice or 3 thrice and so on then you'd be counting more than necessary. Counting something isn't the same as counting nothing because there is something there to count. Although you could count nothing as many times as you like but you'd still have nothing. You could divide those nothings up into multiple nothings but that's not going to make them something, they'll still be nothing. If you start counting spaces where something could be then in that case you are no longer counting nothing, you're counting spaces. 0 represents having no finger there which is why it doesn't have to be counted while 2 or 3 represents 2 or 3 fingers being there and so they can be counted.
I don't think the number you start counting at has to be arbitrary unless maybe you want it to be or maybe if you are giving them different labels or values. It's not going to change how many there actually are no matter how you count them but you you might come up with different results if you aren't counting them properly or if you're using your own labels to describe the numbers.
I still don't understand how we can skip 0 for being 0 if we don't count 2 twice. That's a little bit like saying there's a separate rule for 0 than for any other number. Shouldn't there need to be a mathematical reason for such a rule? And I'm not suggesting that we should count 2 twice, I only mentioned that about 2 to point out the strangeness of skipping 0.
I know how to count the 'normal' way, but I think that way is wrong. When we count a range that spans both positive and negative numbers then we always include the 0. For example:
-3, -2, -1, 0, 1, 2, 3
Notice that when the digits at the end points share the same absolute value then the 0 is at the center of the count. My argument is just that this geometric center at 0 is where we should be counting from. Just like how when we measure the sides of a triangle people tend to count from 0 at the points.
While all those numbers you listed are all integers/whole numbers they do indeed have different rules. 0 would indicate that there are none of whatever you're counting whereas a positive integer would be the sum of those objects and negative would probably be taking that many away from whats already there depending on what you're doing I suppose.
However you can still start counting from 0 or -3 or whatever you like if it suits whatever you're counting. With a triangle maybe some people would start counting the points at 0 because they aren't necessarily interested in the total number of points but the number of lines, although I suppose you will get both in a shape since the start and end point are the same point. Plus if they wanted the total number of points then they would just have to add 1 if the end point and start point aren't the same point as in a triangle or other shape. Although it's pretty obvious there are 3 points and 3 sides in a triangle but in a more complex scenario just adding 1 would give the total number if desired. You could start at -3 if you wanted as long as you know what the numbers represent, however that might be confusing to other people if it's not the standard way of doing it. It also wouldn't necessarily be as simple for you to figure out the total number of points or lines but maybe it would tell you the number you wanted depending on your particular scenario.
Also since positive integers are the sum of the objects being counted, if you are doing an equation like 2 + 2 and since those are integers the result will be an integer because you're likely counting by 1s, so the objects you're counting are actually 1s. If you start counting from 0 then you are starting with nothing, you don't have an object yet or 0 X 1 objects. When you say 1 you now have your first object or 1 X 1 objects. When you say 2 you now have 2 objects or 2 X 1 objects. You aren't adding an additional 2 objects to the existing 1 because they already represent the sum of the objects. Therefore 2 + 2 is likely equal to 1 + 1 + 1 + 1 and not 0 + 1 + 2 + 0 + 1 + 2.
Of course that doesn't stop you from making your own numbering system or counting by 3s if you like.
array indexes aren't count of objects they are values added to first memory location. 0 means no add to starting point so you get 1st object, 1 means add one to the starting point so you get 2nd object from next locatin...