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[WanderingWinder]

"While visiting New York, I met rrenaud, a former circus clown, and my favorite purveyor of fine illicit substances."

"While visiting New York, I met rrenaud, a former circus clown and my favorite purveyor of fine illicit substances."

How many people did you meet?

One - the other people were on their way BACK from St. Ives!
What do I win?

[blueblimp]

Order of operations seems like such a silly thing.  It isn't a property intrinsic to the number system, but just a set of rules for interpreting our chosen method of expressing numbers and operations.  There's no particular reason multiplication has to come before addition, just convention.

It's a convention, but it's the only convention that makes sense. Any convention should be able to write polynomials without parentheses: 2x^3 - x^2 + 1. To do this, you need exponentiation to happen first, then multiplication, then (from left to right) addition and subtraction.

Valid nitpick: this doesn't say anything about division. Nobody really uses the division symbol "÷" in mathematics (instead using fractions), so that's okay. Programmers use a division operator (usually "/"), but programmers are accustomed to memorizing arbitrary conventions, so that's also okay.

Invalid nitpick: what about writing factored polynomials? Like (x - 2)(3x - 1)(x^2 + 4). That requires a lot of parentheses. But the factorization of a polynomial is not a good way to represent it, because it's difficult to add them together. This form is less important.

[DStu]

Invalid nitpick: what about writing factored polynomials? Like (x - 2)(3x - 1)(x^2 + 4). That requires a lot of parentheses. But the factorization of a polynomial is not a good way to represent it, because it's difficult to add them together. This form is less important.

I'm definitely don't want to change the order of operation, but I'm not sure if that is true? How often do you want to add polynomials? Btw it is a good representation to multiply them. And, probably more important, to find its zeros. On the other hand, it's more difficult to differentiate/integrate (Because you would have to add factored polynomials. OK, here we go...).  But it's easier to start factorized and transform into standard than the other way round. Especially for degree >4.
So this form contains more information (for suitable definition of "information").

[Kirian]

It's a convention, but it's the only convention that makes sense. Any convention should be able to write polynomials without parentheses: 2x^3 - x^2 + 1. To do this, you need exponentiation to happen first, then multiplication, then (from left to right) addition and subtraction.

And of course, tetration should precede exponentiation, but I suppose that's a discussion for a different thread.

But the factorization of a polynomial is not a good way to represent it, because it's difficult to add them together. This form is less important.

I disagree that it's less important (finding zeroes), but since the form is written, as a standard, with parentheses, it doesn't worry about order of operations.

Short version:  Standard order of operations is good.  Using them to do arithmetic can be annoying, but properly using parentheses (or RPN if you must) makes things simpler.  Creating a gotcha "puzzle" like this with no parentheses just to mess with people's minds is just plain annoying and tantamount to trolling.

Friends don't let friends abuse mathematical conventions for cheap laughs at the expense of someone who doesn't remember conventions that don't matter if you write the math out properly.

[toaster]

Favorite Oxford comma example:

At the party I danced with the strippers, JFK, and Stalin.

vs.

At the party I danced with the strippers, JFK and Stalin.

[blueblimp]

Invalid nitpick: what about writing factored polynomials? Like (x - 2)(3x - 1)(x^2 + 4). That requires a lot of parentheses. But the factorization of a polynomial is not a good way to represent it, because it's difficult to add them together. This form is less important.

I'm definitely don't want to change the order of operation, but I'm not sure if that is true? How often do you want to add polynomials? Btw it is a good representation to multiply them. And, probably more important, to find its zeros. On the other hand, it's more difficult to differentiate/integrate (Because you would have to add factored polynomials. OK, here we go...).  But it's easier to start factorized and transform into standard than the other way round. Especially for degree >4.
So this form contains more information (for suitable definition of "information").

Adding polynomials is common. For example, off the top of my head, for defining finite fields (which are used for tons of things, such as cryptography). Even doing polynomial division needs polynomial addition.

Maybe I just should have written "less fundamental" instead of "less important". It's simple to define addition and multiplication algorithms for standard form polynomials, and a polynomial you get in any form can (usually) be easily put into standard form.

[Ozle]

7 - 4 + 3 * 2, 4, and 6?

[jonts26]

Favorite Oxford comma example:

At the party I danced with the strippers, JFK, and Stalin.

vs.

At the party I danced with the strippers, JFK and Stalin.

Borderline NSFW

http://www.verbicidemagazine.com/wp-content/uploads/2011/09/Oxford-Comma.jpg

[eHalcyon]

Favorite Oxford comma example:

At the party I danced with the strippers, JFK, and Stalin.

vs.

At the party I danced with the strippers, JFK and Stalin.

At the party I danced with the stripper, JFK, and Stalin.

vs.

At the party I danced with the stripper, JFK and Stalin.

[DStu]

Invalid nitpick: what about writing factored polynomials? Like (x - 2)(3x - 1)(x^2 + 4). That requires a lot of parentheses. But the factorization of a polynomial is not a good way to represent it, because it's difficult to add them together. This form is less important.

I'm definitely don't want to change the order of operation, but I'm not sure if that is true? How often do you want to add polynomials? Btw it is a good representation to multiply them. And, probably more important, to find its zeros. On the other hand, it's more difficult to differentiate/integrate (Because you would have to add factored polynomials. OK, here we go...).  But it's easier to start factorized and transform into standard than the other way round. Especially for degree >4.
So this form contains more information (for suitable definition of "information").

Even doing polynomial division needs polynomial addition.

Not if you write it in factored form...

[blueblimp]

Invalid nitpick: what about writing factored polynomials? Like (x - 2)(3x - 1)(x^2 + 4). That requires a lot of parentheses. But the factorization of a polynomial is not a good way to represent it, because it's difficult to add them together. This form is less important.

I'm definitely don't want to change the order of operation, but I'm not sure if that is true? How often do you want to add polynomials? Btw it is a good representation to multiply them. And, probably more important, to find its zeros. On the other hand, it's more difficult to differentiate/integrate (Because you would have to add factored polynomials. OK, here we go...).  But it's easier to start factorized and transform into standard than the other way round. Especially for degree >4.
So this form contains more information (for suitable definition of "information").

Even doing polynomial division needs polynomial addition.

Not if you write it in factored form...

I might be missing something, but if there's a remainder, I don't think the factorization will help.

[DStu]

Invalid nitpick: what about writing factored polynomials? Like (x - 2)(3x - 1)(x^2 + 4). That requires a lot of parentheses. But the factorization of a polynomial is not a good way to represent it, because it's difficult to add them together. This form is less important.

I'm definitely don't want to change the order of operation, but I'm not sure if that is true? How often do you want to add polynomials? Btw it is a good representation to multiply them. And, probably more important, to find its zeros. On the other hand, it's more difficult to differentiate/integrate (Because you would have to add factored polynomials. OK, here we go...).  But it's easier to start factorized and transform into standard than the other way round. Especially for degree >4.
So this form contains more information (for suitable definition of "information").

Even doing polynomial division needs polynomial addition.

Not if you write it in factored form...

I might be missing something, but if there's a remainder, I don't think the factorization will help.

I think in this case we must first specify in which form we want to write polynomials with remainder, but enough of that now...

[Teproc]

You guys have an acronym for resolving operations in algebra ? Crazy.

And did I seriously read someone suggesting Fahrenheit was better than Celsius ? That's funny.

[WalrusMcFishSr]

Pffff, the metric system only makes sense to humans. Water? Who cares about water? Earthlings, that's who. Everything is in base 10*? Why, because you happened to evolve 10 wiggly appendages for some reason? How arbitrary.

*Yes, I know that every base is base 10 in its own base, so don't even go there pal!

[Archetype]

Pffff, the metric system only makes sense to humans. Water? Who cares about water? Earthlings, that's who. Everything is in base 10*? Why, because you happened to evolve 10 wiggly appendages for some reason? How arbitrary.

Um every base is base 10 in its own base.

[Tables]

Did this thread really need to get bumped?

[Drab Emordnilap]

Did this thread really need to get bumped?

Sure, why not? People talk about things.

[Tables]

Did this thread really need to get bumped?

Sure, why not? People talk about things.

Ehh. I just feel like there's nothing really to discuss that wasn't discussed when the thread was first up.

[AJD]

And did I seriously read someone suggesting Fahrenheit was better than Celsius ? That's funny.

Fahrenheit is awesome! "Rate on a scale of 0 to 100 how hot or cold the weather is, where 0 is 'really cold weather' and 100 is 'really hot weather'"!

[Teproc]

Huh, I don't know why I stumbled upon this thread, I didn't realize it was a few months old. I must have seen someone reading it in the "Who's online" and the title intrigued me. Sorry !

[Awaclus]

Huh, I don't know why I stumbled upon this thread, I didn't realize it was a few months old.

It was from 2012, it's more than just a few months old.

[Kuildeous]

Thread necromancy at work.

[Warfreak2]

Vi Hart already killed this kind of thing.

[SirPeebles]

One of the benefits of the metric system -- versus the imperial system -- is that you have fewer conversions.  Rather than having inches, feet, miles, furlongs, rods, hectares, acres, gallons, fluid ounces, teaspoons, and so forth you have meters.  Then you can have centimeters, kilometers, square meters, cubic centimeters etc., but you can convert amongst them trivially.

The temperature scale didn't have that issue.  These days, the main advantage of the Celsius scale is its near universal ubiquity (which is a significant advantage, by the way!).

[WanderingWinder]

One of the benefits of the metric system -- versus the imperial system -- is that you have fewer conversions.  Rather than having inches, feet, miles, furlongs, rods, hectares, acres, gallons, fluid ounces, teaspoons, and so forth you have meters.  Then you can have centimeters, kilometers, square meters, cubic centimeters etc., but you can convert amongst them trivially.

Well, YOU can, because you're very comfortable with using base 10. But the appendage comment enough points out this is a peculiarity to members of our species, rooted in cultures which use mathematical systems which eventually owe something back to the fact that a recessive trait is near-ubiquitous.

Yes, polydactylism is dominant.

The temperature scale didn't have that issue.  These days, the main advantage of the Celsius scale is its near universal ubiquity (which is a significant advantage, by the way!).

Well, except that your grams, metres, and litres aren't entirely arbitrary in their definitions. I mean, one of them is, but the others are based on having water having a density of 1 and handy conversions between the units (1 ml = 1 cm^3) under "standard atmospheric Earth conditions" (another way that the system is Earth-centric). Celsius scale has this advantage as well - 0 and 100 are special for water in such conditions. Actually, it's somewhat strange to my mind that the figures work out on round degrees in Fahrenheit. Probably if I looked a bit more into the history, I'd find that there is a reason for this (like it got rounded or changed at some point).

And yes, this is another thread ne-ne-ne-ne-necro.