I concur with everything you’ve written here.

I concur that a left-to-right interpretation of consecutive explicit multiplication and division is wide spread and how most calculators and computers would interpret:

a / b * c.

But the sources you quote in your blog post and the style guides I’ve read, state that a fraction bar or parenthesis should be used to clarify if it should be interpreted as:

(a / b) * c

or

a / (b * c)

You make the argument in your post that:

a / bc

is ambiguous (which I agree with)

but

a / b * c

is not ambiguous. Which is the part I disagree with, and I think the sources you quoted disagree with you as well. But I’m open to being wrong about that and am interested if you have sources that prove otherwise.

If I’m understanding your response correctly, you believe that

a / b * c

is unambiguous, and always treated like

(a / b) * c

because of a wide spread convention of left-to-right interpretation (a convention that we both agree exists), not because you found a source that states that.

Anyhow… I’m not out to convince you of anything and I appreciate you taking the time to explain your thinking to me.

I would be particularly interested if you found something in a mathematical style guide that recommended an expression like

( a / b ) * c

Should be re-written as

a / b * c

Generally speaking, style guides advise rewriting equations for maximum clarity. Which usually includes a guideline of removing parentheses when their existence isn’t needed to clarify intent.

I believe, and I’m particularly interested to see if you found evidence that my understanding is incorrect, that the LTR convention used by calculators and computer programming languages today exists because a deterministic interpretation is a requirement or the hardware, not because any such convention existed prior to that or has been officially codified one way or the other by any mathematics bodies.

So like, forget division for a sec…

In a mathematics paper, you usually wouldn’t write:

(a + (b + c)) + d

You’d write:

a + b + c + d

(Except perhaps if in your paper the parentheses made it easier to follow how you got to that equation.)

Because in mathematics, it will never matter which order you do additions in, so you should drop the parentheses to improve clarity.

On a computer or a calculator though you might get a different result for those two equations like if a+b overflows your accumulator and c is a negative number, or when these are floating points values with significantly different magnitudes.

I believe english speaking engineers just adopted LTR as the convention for how to interpret it since they had to do something, and the english language is a LTR language. I don’t believe that convention exists outside of the context of computing.

The Wolfram quote and ISO quote in particular that you have in your post imply that an inline division followed by an explicit multiplication is ambiguous as to if it should be interpreted as a compound fraction.

If that’s correct, then it would be the inline division that makes it ambiguous, not the implicit multiplication that makes it ambiguous.

If there’s some source from before computers, or outside of the context of computers forcing a decision. Then your assertion that it is the implicit multiplication causes the ambiguity is correct.

I’m not trying to prove you’re wrong, I’m just genuinely curious which it is. And if you found evidence one way or the other.

My apologies, I wasn’t trying to spar with you friend, just trying to understand why a/b*c wouldn’t also be considered ambiguous, particularly since an author could have written a*c/b and removed any doubt.

In your blog post you also quoted ISO

In such a combination, a solidus (/) shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity.

You seemed to speak rather definitively that it’s only ambiguous when combined with implicit multiplication.

I agree that almost all calculators and programming languages will interpret consecutive explicit multiplications and divisions with left-to-right precedence.

But as far as I’m aware no such LTR rule has global agreement in mathematics, I was curious if you found something in your research that says otherwise.

Will you accept wolfram alpha as credible source?

https://mathworld.wolfram.com/Solidus.html

Special care is needed when interpreting the meaning of a solidus in in-line math because of the notational ambiguity in expressions such as a/bc. Whereas in many textbooks, “a/bc” is intended to denote a/(bc), taken literally or evaluated in a symbolic mathematics languages such as the Wolfram Language, it means (a/b)×c. For clarity, parentheses should therefore always be used when delineating compound denominators.

What is your source for the priority of the / operator?

i.e. why do you say 6 / 2 * 3 is unambiguous?

Every source I’ve seen states that multiplication and division are equal priority operations. And one should clarify, either with a fraction bar (preferably) or parentheses if the order would make a difference.

You state that the ambiguity comes from the implicit multiplication and not the use of the obelus.

I.e. That 6 ÷ 2 x 3 is not ambiguous

What is your source for your statement that there is an accepted convention for the priority of the iinline obelus or solidus symbol?

As far as I’m aware, every style guide states that a fraction bar (preferably) or parentheses should be used to resolve the ambiguity when there are additional operators to the right of a solidus, and that an obelus should never be used.

Which therefore would make it the division expressed with an obelus that creates the ambiguity, and not the implicit multiplication.

(Rest of the post is great)

I’m genuinely not sure which side you think is which.

The exhaust from a typical ICE wouldn’t have enough pressure to inflate a tire, so you’d need a compressor. Of course if you had a compressor you’d just use clean air.

If for some reason you used a compressor to compress exhaust gases to fill a tire, it would mostly be the same as filling with air at first.

Exhaust gas is mostly a mix of carbon dioxide and and water vapour, with small amounts of oil residue, and other organic compounds. The water vapour will condense as it cools likely leaving some liquid water in the tire, which won’t cause immediate issues but will cause vibrations which will accelerate wear not just on the tire but possibly the entire suspension.

The organic compounds will cause the rubber to break down over time and the tire will wear out sooner.

Even if it built with the same disregard as the Chernobyl plant, and there’s “an occasional meltdown”… it’s still actually better than building coal power plant in terms of lives lost per TWh of power generated.

Or something like it controls the lights in the elevator cab (but not the elevator itself).

Total monthly posts exploded after Spez enshitified Reddit, and is still growing steadily month over month.

That suggests that the current decline in monthly active users is primarily because lurkers who only came to lemmy after initially hearing about it on Reddit, went back to lurking Reddit.

The number of users that are contributors is still growing, and that’s what’s important.

It’s ridiculously unusual for a board to actually fire a CEO. Usually if the board thinks a new CEO is needed, even if the CEO doesn’t agree with the decision, there’s a transition plan announced the CEO “stepping down”, or “steps aside”, of the “next phase of growth” or whatever. It has a massive positive spin on it and the departing CEO is paid a ridiculous severance to go along with the plan publicly.

It’s very negative press to have to outright fire a CEO. Especially in a case like this when the CEO saw the company through the kind of growth that every startup has wet dreams about.

Something huge happened, and the world is speculating rampantly about what that was.

We don’t know what Owen’s relationship with Shmi was. Maybe he left home before Cliegg remarried, and was only there when we see him in episode 2 because he came when his dad contacted him in a panic after discovering Tuscan raiders had taken step-mom captive.

I disagree with your interpretation that Cliegg “technically” bought 3PO.

We don’t know the legal rights of slaves in that universe, but presuming this is like slaves in ancient Roman times and they can own property, then 3PO was Shmi’s from the beginning. Buying a slave wouldn’t automatically give you possession of the slave’s property, therefore it was always Shmi’s droid and Cliegg never owned it.

It’s possible that in this universe, slaves can’t own property and Cliegg bought 3PO from Watto in addition to Shmi. But I think it unlikely that Anakin would have built 3PO “to help his mom” if Watto automatically owned it. If Watto owned 3PO he would’ve sold it long before Cliegg bought Shmi.

We also don’t know that Anakin stole 3PO. If it belonged to his mom, he could have simply inherited it when she died.

One could also make the argument that 3PO was always Anakin’s property, and he just left it behind when he left Tattooine.

Owen didn’t pay for C3PO twice.

Anakin built 3PO for his mom Shmi, who was a slave to Watto. Cliegg (not Owen) bought Shmi out of slavery. C3PO was already Shmi’s.

Climate change isn’t caused by just using fossil fuels to make a product, it’s caused by burning fossil fuels releasing greenhouse gasses, (primarily carbon dioxide and methane), into the environment.

Asphalt is a problematic material, but not so much because it’s made from oil. It’s problematic because we burn fossil fuels to harvest the raw crude and to generate the energy needed to refine crude into asphalt. The carbon in the asphalt itself remains sequestered there and doesn’t contribute to the greenhouse effect as long as it isn’t burned later.

If we figured out how to extract crude and generate the vast amount of energy needed to manufacture asphalt without actually burning fossil fuels we’d eliminate the vast majority of asphalt’s impact on climate change.

In fact it’s been shown in a lab that it’s possible to make asphalt from CO2. It’s currently cost prohibitive to do so, but in theory asphalt could be part of the solution to climate change.

Now Asphalt does have other environmental issues, like leaching toxic chemicals into the soil and water table and the fact that it’s usually black which absorbs more the sun’s radiation than almost anything else which would reflect more of the sun’s energy back out into space. But those problems aren’t necessarily solved by using non-petroleum based bioasphault, nor are they unsolvable with bitumen based asphalt.

About 20% of a barrel of oil gets made into products like plastics or foam, that’s not what’s causing climate change. What causing climate change is the 80% that gets refined and burned for cheep energy. So it’s less “Just stop oil” and more “Just stop burning oil”

I also stopped carrying a wallet….

…now I just put it in my pocket instead.