There is a difference between what you learn that squares with reality, and what does not.
Yes, which is why I discarded things like Santa Clause and Christianity, because they don't square with reality; while accepting things like the RE, which does square with reality and explains it quite well.
The reason I use order of operations as an example of why learned knowledge can't always be trusted is this.
Which is simply a matter of not understanding and not communicating.
You want to go to that, fine, I have a large collection of apples laid out in grids.
One grid is 2 by 4, one is 8 by 8, one is 4 by 13. How many apples do I have?
2*4+8*8+4*13
And that is the correct way to write it out.
No, wrong. Wrong. Wrong.
And if it is wrong, it is the person who wrote it that is wrong, not the statement itself.
Math is a language which has a meaning.
If someone meant (2+4)/6, then they should have written (2+4)/6.
If they instead write 2+4/6, then they wrote the wrong thing.
Let's make this a word problem.
And then understand how to translate it.
But to understand better, and make a comparison, lets make a slight change, and look at two similar word problems:
Maddie raises apples for a living. Currently, she has two shipments of apples, as a result of her hard work. But this is not enough, so she went to OrderApples.org and bought four more shipments. She has to deliver to two places. How many shipments go to each?
vs
Maddie raises apples for a living. Currently, she has two shipments of apples, as a result of her hard work. She also has a join farm with another person that produces 4 shipments, but this is shared equally between the two people. How many shipments does she have in total?
In the first case you have (2+4)/2
In the second case you have 2+(4/2), which is the same as 2+4/2
It isn't a simple case of those particular words are the only possibility so must be the way.
Instead it is a case of understanding how to translate from the words to the text.
If you would like another example, it is like going from the sentence:
"My dog brought me its lead". into
"Mein Hund brachte mir seine führte"
instead of
"Mein Hund brachte mir seine Leine"
Where instead of interpreting lead as a noun which the dog brought to you, you instead interpret it as the verb lead.
You translating it wrong doesn't make the system wrong. It makes YOU wrong.
Likewise, if someone who natively spoke German was learning English and read that sentence and thought of the wrong lead, that doesn't make English wrong. It means the person trying to understand it is wrong.
For math, we try to remove the ambiguity by defining a specific order of operations.
It is an agreed upon convention, just like the meaning of words.
You not liking that order doesn't make it wrong.
So if you screw up and write it as 2+4/6, when what you really meant was (2+4)/6, the mistake is entirely with you.
Don't blame the calculator for your inability to understand.
But the point of why I didn't include parentheses is that this calculator doesn't even think they are worthy of inclusion in the Basic tab of the calculator.
Because that calculator would assume you do the simple thing:
2+4=
/6=
That then gives the correct answer.
That is how those calculators are meant to be used.
The most basic ones wouldn't even allow the equal sign, instead as soon as you entered any other operator it would put an implicit equal, end the calculation and start the next one.
For example, if I use the calculator in Windows 10 on "Standard" mode, then I type in 2 + 4 / 6 =
and it gives me the answer 1.
And if you pay attention as it does so, I type in 2, and the number appears in the big area.
I press + and I see "2 +" up above in small font.
The 2 is still there in big so I can just hit enter to ad it, but I type in 4 instead, and then 4 appears in the big area.
Then I hit /, and the result of 2+4 gets taken up to the top. Not as 2+4 or anything like that, but as 6, with it literally showing "6 ÷".
That is how simple calculators work.
They don't PEDMAS, because they can only handle one operation at a time.
More sophisticated calculators, which can handle multiple operations at a time, need to be able to unambiguously decide what that order that so that every time it is entered it will get the same result; and ideally this order should be agreed upon between different calculators so they all get the same result.
And other than implicit multiplication, they do.
So which simple calculator were you using?
Or is it more likely that to intentionally show this problem, you are using an advanced calculator which does have parentheses, but you chose not to use them?
If you think I reject everything I'm taught
I don't. I'm pointing out the stupidity of your premise.
The fact that it was taught to me as a child does not make it crap that should be dismissed.
The fact that you don't reject everything you were taught shows how stupid that premise of yours is.
The fact I was taught it as a child is NOT a reason to reject it.
So you asking as if it is is really desperate and pathetic.
I reject theoretical knowledge where the conclusions of the formula don't square with testing
Yet you can't provide a single example of this for the RE.
Instead you reject it because you don't like it.
In fact, you appear to outright reject formulae and do whatever you can to avoid them.
It I make a calculation of height of a tree based on angle, I had better climb that tree, or what I calculated is worthless.
That entirely depends on why you are calculating it.
Are you trying to get an estimate of the route zone to know where to avoid digging without undermining the tree?
Are you trying to see how tall it is to see how far away structures need to be to avoid being hit by it if it falls down?
Are you trying to see if it is long enough to be cut down for planks?
Are you trying to see if it is the right height to be cut down and taken inside as a Christmas tree?
Are you trying to see if it is too tall for the powerlines going overhead?
Are you measuring its height to monitor its growth?
There are plenty of reasons to measure the height, not just to climb it.
So when someone tells me the Earth is round, but they have no "apple" to show me, I tell them to bugger off.
And when someone tells you Earth is round, and they have plenty to show you, you just ignore all that they show, make excuses, outright lie, and then appeal to your tiny balls, when the formulae show what should happen to water on your tiny balls.
If you want water to stick to your tiny balls, you need to be in free fall outside the Roche limit of any more massive object.
But you don't want that.
You instead demand something that shouldn't happen.
You are also told of other experiments to confirm gravity which you ignore.
And plenty of evidence to show Earth is round, which again you ignore, all because water does exactly what is expected for a RE.
A feather and a bowling ball reach terminal velocity
Try it in a vacuum.