@ebuc
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SatanLucy wrote:
So, the men paid $9 each, 3 times $9 is $27, plus the $2 tip is $29, where did the other dollar go?
Boy swallowed it.
Actually, this isn't example of math not making sense.
No, it was actually an example of misdirection.
The men already payed 30$. They got back 5, so they actually payed 25, and now have 5$ left. When they gave boy 2$, they are left with 3$. 25 plus 3 plus 2 is indeed 30.
However, the example makes an error of summing up expenses twice at the end. It completely ignores the 3$ left, and sums up 2$ twice.
Men are left with 3$. They payed 25$ for room and 2$ to boy. That's 27$ expenses. They still have 3$ left. That is 30$.
I added the $2 to $27 to get $29, instead of subtracting it to get the $25.
Good catch.
How about the square root problem, would you call that an example of math that doesn't make sense.
The square root of 4 is 2, it's also negative 2, and 2 does not equal negative 2.
Here's a real example.
Who shaves the barber in a town where the barber shaves everybody that doesn't shave himself.
That's a note that Bertrand Russell sent to Gottlob Frege that destroyed his attempt to make Logicism the foundation of mathematics. There were only three systems in the running, Frege's Logicism, Hilbert's Formalism, and Brouwer.s Intuitionism, and none of them won. Brouwer's Intuitionism didn't stand up to logical analysis, and Kurt Godel demolished Hilbert's Formalism, and Russell demolished Logicism with this simple note.
Mathematicians don't like to talk about it, but today, Mathematics still lacks a foundation that is consistent and complete.
As Eugene Wigner pointed out with his article "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", it is still a tool that works, it's just not clear why.
SatanLucy wrote:
How about the square root problem, would you call that an example of math that doesn't make sense.
The square root of 4 is 2, it's also negative 2, and 2 does not equal negative 2.
Yes, that is an example of math not making sense.
Another example is that -2 is two times smaller than -1, but when you divide -2 by 2, you get -1. Division somehow creates a bigger number instead of smaller one, while multiplication creates a smaller number instead of bigger one.
It's also why 0 is the most problematic number in math. I call him "Troublemaker". This is why my original question was which number is two times greater than zero. There is literally no such number in math.
Any positive number is assumed to be greater than zero, but it is impossible to calculate how many times greater.
How many times is 1 greater than zero?
And why does each number multiplied by zero produce zero?
Multiplication is supposed to produce a number greater than the numbers being multiplied, but this isn't true neither with zero neither with negative number.
And also, what is square root of -4?
There is no square root of -4.
Zero and Infinity are problematic if you think of them as numbers, they represent concepts rather than numbers. Mathematical procedures. aren't really applicable.
They use math to do calculations.
So no number is greater than zero. Math doesn't work.
meow math doesn’t work, stick to the real thing.
SatanLucy wrote:
it is still a tool that works, it's just not clear why.
I mean, math was one of biggest obstacles in AI development. They literally had to introduce non mathematical operations to make AI functional.
I don’t know what you are talking about, can you tell me what a “non mathematical operation” is?
This is because AI depends on non linear math.
Linear math only works with one weight. When you have multiple weights, linear math effectively still turns them into 1 weight.
What are you talking about? Most mathematics is nonlinear, almost all natural processes that science represents with mathematics are nonlinear, linear systems are the rare exception rather than the rule.
They tried to solve a problem with square numbers, to introduce non linearity, but square removes negative numbers and this was a problem.
In the end, they settled for non mathematical function which changes number in an entirely different way.
How does a “non mathematical function” change numbers, numbers are mathematical symbols, it’s reasonable to say numbers don’t even exist outside of mathematics.
I repeat, the regular math cannot make AI functional. AI is a system which turns input into numbers, and then changes those numbers by multiplications to produce output. However, because AI entirely depends on non linear math, and regular math proved itself impossible here, to develop AI they invented math functions which never existed before.
I don’t know anything about the mathematics behind AI, but in science inventing new mathematics is the in thing, we develop mathematical theories that produce unobserved and unobservable realities, with new mathematical dimensions and new laws of physics, they are all inventions that they refer to as "discoveries". I don’t know what that is, but I know what it isn’t, it isn’t science.
I mean, plenty of mathematicians were arguing how math is a complete system, until Godel's incompleteness theorem proved beyond doubt that math cannot form a complete system.
Yep, the great David Hilbert had challenged the mathematics community to develop a proof that mathematics was consistent and complete, most mathematicians of the day saw it as a way to make history, and almost every student was working on it as their doctoral thesis right up to the day Godel came up with a proof that mathematics can’t be consistent and complete.
Who shaves the barber in a town where the barber shaves everybody that doesn't shave himself.
I assume this is problem of circularity in math, as well as a contradiction of any closed math sets. If barber doesnt have himself, he shaves himself, creating a contradiction, and similar is true for math generally. If math does calculations for all areas which cannot do calculations on their own, who does calculations for math?
Yes, it’s the self-referential paradox that puts a bullet through so many mathematical, logical, and philosophical systems. Russell discovered that “the set of all sets that do not contain themselves” was a contradiction that invalidated set theory by introducing a contradictory loop.
SatanLucy wrote:
Most mathematics is nonlinear, almost all natural processes that science represents with mathematics are nonlinear, linear systems are the rare exception rather than the rule
For AI, to make use of multiple weights, you need a non linear activation function which works in AI system.
Let's say you have two weights. One weight is 2. The other is 3.
If you merely multiplied them, it would be linear because result would be same as having just one weight of 6.
Non-linearity is the only way to make AI which has effectively more than one weight.
Non-linearity can be square, but square introduces a problem where -2 and 2 become same.
For this reason, AI functions like Gelu and Relu exist.
Relu basically turns all negative numbers into 0 while keeping positive ones same.
This is non-linearity.
Achieving non-linearity by multiplication, division, addition... is just impossible.
AI works in a way that it turns input into number, multiples that number with all it's weights, and then generates output.
However, without non-linear function, all weights collapse into one effective weight.
For example:
2x3 plus 2x5 plus 2x2 is effectively same as 2x10.
It is only when you add non-linear function that having more than one effective weight in AI model becomes possible.
AI weights are basically just numbers which are multiplied by input. However, to have more than 1 effective weight requires that the math doesn't collapse into linearity.
Functions like Relu are not math functions. They are actually conditional functions.
Relu turns all negative number outputs to 0. It's a very simple function which creates non-linearity. Gelu is more complex.
Non-linear function is mandatory for AI system, and none of the standard math functions could work for AI. Not multiplication, not square, not addition, nothing in math worked to make AI functional.
As I said, they had to invent an entirely new activation functions just to make AI work. Relu is not a mathematical operation, at least not in any standard math.
None of this makes any sense to me, almost all mathematics in nonlinear, almost all processes are nonlinear, ALL interactive processes are nonlinear, you don't need new mathematics because AI needs nonlinear mathematics.
Sidewalker wrote:
SergeantLynch wrote:
Sidewalker wrote:
Why does 1 = .999...
It doesn't actually...It's a bit like comparing English brie with French brie, and will only matter to a Mathematician or an Affineur.
Except it does actually, one divided by 3 is point three repeating, point three repeating times 3 is point nine repeating, therefore one exactly equals .9 repeating.
1/3 = .333...
.333... X 3 = .999...
1=.999...
In simple terms .999... is always .1 and as many relevant 0's as necessary, short of 1.
No, "as many relevant 0's as necessary" implies a finite number, but a repeating decimal is an infinite process, saying "as many relevant 0's as necessary" is like saying the necessary number of times you must traverse the perimeter of a circle to get to the end, there is no end.
The equation exemplifies incompatibility and simply has to make do.
It only demonstrates the incompatibility inherent in representing fractions as decimals because converting some fractions like 1/3 or 1/9 to decimals results in an infinite loop.
Yes, you just exemplified everything I stated...We have to make do with .999...
And the barber visits a gay grooming salon in another town, where his friend Alfonso gives him an a close all over shave, before he dresses up in Alfonso's favourite lingerie...Such is a logical hypothesis Gottlob.