Math Is Wrong
One of the tenets that most people hold is that mathematics is proven, that there is nothing wrong with it, and that is wholly logical. Well, that is the propaganda they teach in school. And you will find few math teachers who can tell you what are the assumptions of mathematics. And further, you will find very few university math professors that will discuss, with the public, where math breaks down.
You remember they told you that a function that goes close to a line, but never quite touches it (asymptotic) doesn't equal the number. y = (1/x) + 4 Sure, as x increases y = 3.9999999999 but, that does not equal 4.
Until you get to calculus, where they ignore that, and just jump to 4.
And then you have ∞ + ∞ = ∞ not 2∞ like every other number. They say that ∞ is special, but that is internally inconsistent.
And, of course
1 = -1 is provable
Math is really messed up. However, most people still think it is perfect, logical, and internally consistent.
1 + 1 = 2 is an assumption
There are a plethora of things in math that are assumptions. Things that are a given, not proved, not derived.
One of those is 1 + 1 = 2.
A mathematician proved (maybe), recently, that 2 + 2 = 4. As long as 1 + 1 = 2 is assumed.
We give children blocks, or beads on a wire to learn to count. Blocks that are all the same size and shape.
And this is good for mathematics, because if you added differences, then the numbers don't make sense.
1 BIG apple and 1 crab apple equals how many apples?
- 1 good eating apple
- 1¼ apples of sufficient size
- 2 apples of differing sizes
The answer to the question is heavily dependent on the conversation, or what the intended use is.
You need 5 apples to make a pie. You need 5 medium sized apples to make a pie.
Mathematics was supposed to be designed for people to use. But the "pure thought" people took it and turned it into a mental abstraction (only). And we just go along with it.
π = 4
This is a weird statement, because anyone who is smart and been good in math class say, no, π = 3.14159265
But, what about this? This proves that the perimeter of a circle is 4 times the diameter.
However, this does not try to get the length of each piece of the circle, it just divides up the horizontal and vertical distances into smaller and smaller pieces. No matter how small, they are still stair steps all the way around.
BUT! Our number system is really messed up. And so, we get π = 3.1415926535.
If we changed to a base 12 numbering system, and used other assumptions, we may find our number system becomes 1, 2, 3, π…
Did you know there is an earth pyramid down in South America that is made of circles 1, 2, π, 4 ? (i may have the order and sizes wrong, it is an old memory, that points to that there were other numbering systems in the long ago.)
When we actually start working on math, we will define the number line, and bring it into alignment with the universe.
This includes ∞. There may be a specific number of atoms in the universe, so talking about any larger number is silly. The universe has a certain start and end, so although the amount of time might be very large, it is a certain number. Not infinity. So, it would be silly to talk about a larger number when discussing time.
In this way, we will avoid silly things like 1 = -1
Even order of operation and symbols are not defined
1 + 1 + 1 + 1( 1 - 1) = ?
-5² ÷ 5 x 5 = ?
Both of these do not have a set answer. Because numerical operators are not defined.
In school, we are first taught an order of operation, left to right.
Later, we start teaching calculus where the order of operation is PEMDAS
So, really, we are taught math completely wrong.
Further ÷ ≠ / and x ≠ *, but we conflate the two. (one belongs to pre-algebra, and the other set belongs to post-algebra)
Even further, we do not have a way to take an equation and put it into a single line on a computer.
In the above math problem is -5² = 25 or -25?
Is the negative sign a modifier of the number, or an operand?
Is it (-5)² or is it 0 - (5²). On X, mathematicians have argued for one side or the other. Both saying that they know what they are talking about, because they teach math.
If we can't even write mathematical equations so that everyone knows and agrees, how solid is mathematics?
In the future, math will be drastically redesigned.
And it will probably be easier for everyone to comprehend.
Ambiguities will be removed.
And calculus will be removed from the curriculum.
Calculus is taught as the first higher math, when we shouldn't waste student's time with it. Most people will NEVER use it. But, it is taught to shut up the smart people from asking embarrassing questions that disprove mathematics.
I have gotten WAY more out of Discreet Math and Fourier Transforms then i have ever used Calculus. Actually, i do not think i have ever used Calculus directly. (I know what it is for, and i can tell that the formulas i am using were derived through Calculus, but i just use the formulas that are already there. Like d = vt (distance = velocity * time), v = at² (velocity = acceleration * time squared, like an item falling from rest) These formulas can be derived/integrated from each other. But why? The physics book gives the formulas.
Unfortunately, to get there, we are going to have to challenge "Mathematics" and there are a lot of ivory tower professors who will resist this change with every fiber of their being. And this is unfortunate, because were we are going is so much better.