People don’t predict values to determine their answers to questions…

Also, it’s called neural network, not because it works exactly like neurons but because it’s somewhat similar. They don’t “run on neural networks”, they’re called like that because it’s more than one regression model where information is being passed on from one to another, sort of like a chain of neurons, but not exactly. It’s just a different name for a transformer model.

I don’t know enough to properly compare it to actual neurons, but at the very least, they seem to be significantly more deterministic and way way more complex.

Literally, go to chatgpt and try to test its common reasoning. Then try to argue with it. Open a new chat and do the exact same questions and points. You’ll see exactly what I’m talking about.

Alzheimer’s is an entirely different story, and no, it’s not stochastic. Seizures are stochastic, at least they look like that, which they may actually not be.

It’s not. It’s a math formula that predicts an output based on its parameters that it deduced from training data.

Say you have following sets of data.

1. Y = 3, X = 1
2. Y = 4, X = 2
3. Y = 5, X = 3

We can calculate a regression model using those numbers to predict what Y would equal to if X was 4.

I won’t go into much detail, but

Y = 2 + 1x + e

e in an ideal world = 0 (which it is, in this case), that’s our model’s error, which is typically set to be within 5% or 1% (at least in econometrics). b0 = 2, this is our model’s bias. And b1 = 1, this is our parameter that determines how much of an input X does when predicting Y.

If x = 4, then

Y = 2 + 1×4 + 0 = 6

Our model just predicted that if X is 4, then Y is 6.

In a nutshell, that’s what AI does, but instead of numbers, it’s tokens (think symbols, words, pixels), and the formula is much much more complex.

This isn’t intelligence and not deduction. It’s only prediction. This is the reason why AI often fails at common sense. The error builds up, and you end up with nonsense, and since it’s not thinking, it will be just as confidently incorrect as it would be if it was correct.

Companies calling it “AI” is pure marketing.

We teach the fundamentals

Sure. They are, however, not the focus. At least that’s not how I’ve been taught in school. You’re not teaching kids how to prove the quadratic formula, do you? No, you teach them how to use it instead. The goal here is different.

They only teach order of operations.

Again, with the order of operations. It’s not a thing. I’ve given you two examples that don’t follow any.

The constructivist learners…

That’s kinda random, but sure?

And many proofs of other rules…

They all derive from each other. Even those fundamental properties are. For example, commutation is used to prove identity.

But the order you apply operators does matter

2+2-2 = 4-2 = 2+0 = 0

2 operators, no order followed.

If we take your example

2+3×4 then it’s not an order of operation that plays the role here. You have no property that would allow for (2+3)×4 to be equal 2+3×4

Look, 2+3×4 = 1+3×(2+2)+1 = 1+(6+6)+1 = 7+7 = 14

Is that not correct?

Notably you picked…

It literally has subtraction and distribution. I thought you taught math, no?

2-2 is 2 being, hear me out, subtracted from 2

Same with 2×(2-2), I can distribute the value so it becomes 4-4

No addition? Who cares, subtraction literally works the same, but in opposite direction. Same properties apply. Would you feel better if I wrote (2-2) as (1+1-2)? I think not.

Also, can you explain how is that cherry-picking? You only need one equation that is solvable out of order to prove order of operation not existing. One is conclusive enough. If I give you two or more, it doesn’t add anything meaningful.

Yes we are

Yes and no. You teach how to solve equations, but not the fundamentals (and if you do then kudos to you, as it’s not a trivial accomplishment). Fundamentals, most of the time, are taught in universities. It’s so much easier that way, but doesn’t mean it’s right. People call it math, which is fair enough, but it’s not really math in a sense that you don’t understand the underlying principles.

Yes there is!

Nope.

There’s only commutation, association, distribution, and identity. It doesn’t matter in which order you apply any of those properties, the result will stay correct.

2×2×(2-1)/2 = 2×(4-2)/2 = 1×(4-2) = 4-2 = 2

As you can see, I didn’t follow any particular order and still got the correct result. Because no basic principle was broken.

Or I could also go

2×2×(2-1)/2 = 4×(2-1)/2 = 4×(1-0.5) = 4×0.5 = 2

Same result. Completely different order, yet still correct.

My response to the rest goes back to the aforementioned.

Wasn’t it a kickstarter product? I wouldn’t consider venture a pre-order, tbf.

Pre-orders are reservations with pre-payment.

Crowdfunding is, well, funding. You aren’t buying a product. You’re funding it, which comes with additional risks and benefits.

Of course, there’s always a possibility that a product is being funded using pre-orders, which is financially irresponsible (norm varies from industry to industry). But you must be a moron to pre-order a product from a startup you know nothing about and expect not to get scammed. Outright buying their product would be risky enough.

Take housing market. You’re pretty much always either pre-ordering or buying second-hand.

Pre-ordering physical goods is fine, especially if you expect a price hike and supply limitations after launch. I wouldn’t, but I can see how it would make sense.

It’s the digital goods that make no goddamn sense to buy before they’re out. They’re not limited in supply, and their return window is often too small.

That’s because (strictly speaking) they aren’t teaching math. They’re teaching “tricks” to solve equations easier, which can lead to more confusion.

Like the PEMDAS thing that’s being discussed here. There’s no such thing as “order of operations” in math, but it’s easier to teach by assuming that there is.

Edit: To the people downvoting: I want to hear your opinions. Do you think I’m wrong? If so, why?

The “why” goes a little further than that.

In actuality, it’s because of fundamental properties of operations

• Commutation

a + b = b + a

a×b = b×a

• Association

(a + b) + c = a + (b + c)

(a×b)×c = a×(b×c)

• Identity

a + 0 = a

a×1 = a

If you know that, then PEMDAS and such are useless because they’re derived from those properties but do not fully encompass them.

Eg.

3×2×(2+2) = 3×(4+4) = 12+12 = 24

This is a correct solution that is improper if you’re strictly adhering to PEMDAS rule as I’ve done multiplication before parenthesis from right to left.

I could even go completely out of order by doing 3×2×(2+2) = 2×(6+6) and it will still be correct

Oh yeah, that’s a fun one.

Where I live, this would be considered juxtaposition, at least by uni professors and scientific community, so 2(4-2) isn’t the same as 2×(4-2), even though on their own they’re equal.

This way, equations such as 15/2(4-2) end up with a definite solution.

So,

15/2(4-2) = 3.75

While

15/2×(4-2) = 15

Usually, however, it is obvious even without assuming juxtaposition because you can look at previous operations. Not to mention that it’s most common with variables (Eg. “2x/3y”).