Deep 6 FaWtL

[Tacticslion]

See, that's fascinating - I've never actually seen that before.

That said, I accept the exponential thing as proof of the opposed, but counter it this way:

Consider the problem you posed, that of 2a^3.

That would be (given the parenthesis we've seen) a problem that looks like this: 2(a)^3 -> this would look at PEDMAS, as well.

For the record, you could do it 2(a^3), but that just resolves any perceived problems before they begin by way of PEDMAS.

~ That means parenthetical first: the (a), okay, fine.

~ Then the exponent of that parenthetical. That makes the ^3 the next thing, and taking precedence.

~ Then the 2.

This is still an atomic number, but with a single unknown component, and continues to resolve in said manner.

As an aside, just in case the question arises, 2a^3^3 would most likely be resolved by riots in the streets and anarchy presuming the second ^3 was outside the parenthesis along with the first, making it a modifier of that.

I accept that there is a major view against this, but it also means there are a lot of people I know who continually teach something different from that view: as a for-instance, this was a major problem that someone (whether myself or another student) would get wrong every time, and have to be corrected; hence it's been drilled pretty solidly into my head.

To be fair, I am probably moooooooooostly thinking of physics classes (which often lacks the ability to note unknowns in any other manner, because, you know, reality isn't very tidy). And, you know, I'm willing to accept that there is a hypothetically "proper" way to use these, but I've never seen it done that way in practice - and, to me, when something is never done in practice, across multiple venues the so-called "proper" method seems... not really so proper.

I won't argue that math books are infallible (as a for-instance, on no less than two practice tests I went over with a student of mine, I discovered math problems that were wrong), but this is such a consistent concept it's hard to accept that everyone I've ever known is just "wrong" over two-and-a-half decades, supposedly over something that was "overturned" in the 70s.

I suppose there is irony, there, as I look at practice more often in real life, and hypothetical propriety more often in PF rules debates... XD

In this instance, it feels more like someone changed the meaning of words on me, and are now saying, "Man, how antiquated!" when it's still used in modern books.

Also, non-relevant aside, the modern textbooks are not mine, as a point of technicality. They belong to my students.

EDIT: *dressed*! Naked math... sounds dangerous!

EDIT 2:

Hm. Somehow didn't respond to this.

NH wrote:

Here's another example: 2^3(2+3). Every mathematician I know will do the parentheses first to get 2^3(5). They will then perform the exponent to get 8(5). Then multiply to get 40.

Getting an answer of 2^15 = 32,768 is not something I'd see any mathematician doing.

What's interesting is that I read this as (2^3)(2+3) - because exponents happen before multiplication - but that's a gut reaction, not a logical one; so, in that regard, I see your point is well-taken.

The problem, however, is in the presentation: it's hard to get super-scripts on things like this text program. That's why parenthesis are needed when you're trying to do something that obscure.

But we don'g have that, so let's ignore the (2+3) for a moment by changing out the (2+3) to a, and present it as the following: 2^3a. This problem is, to my reading, incredibly clearly 2^(3a), which, upon substitution, would be -> 2^15 -> 32,768.

I'm going with your answer, and not checking that, 'cause I'm being super-lazy.

The thing is, this is a legitimate reading in physics (and math, I'd suggest) - it's a thing that happens. That makes it normalized, and (relatively speaking) common-use, meaning "proper"... isn't.

Again, the problem is that the parenthesis isn't there - it's lazy notation, as you said.

(I totally agree with the "Use parenthesis!" thing, by-the-by: I keep telling people to do that. Also to SHOW their DAGGUM WORK. That way, even if they get the wrong answer, at least I know why...)

[The Game Hamster]

So, making the first post makes me naked?
That... doesn't feel all that different.
probably because I'm naked anyway. Being furry rocks sometimes.

Edit: AAGH!! Ninja'd

[NobodysHome]

So, you have to understand to whom you are addressing your questions: My undergraduate focus was on logic and set theory. One of my favorite "nighttime reading" books was, "Theorems and Counterexamples in Mathematics", a wonderful book that took all the "great" theorems of mathematics (for example, the Fundamental Theorem of Calculus), dropped each assumption one by one (for example, suppose the function isn't continuous), then provided a counterexample proving the theorem false in that situation.

As I said, a fun, fun read.

So, here's the difference between a "formal" mathematician and an "informal" mathematician (i.e., a physicist): A physicist says, "You can tell from the context what I mean! y/2a obviously means y/(2a), whereas 2a^3 obviously means 2(a^3)! I don't need to be any more formal than that!"

This is anathema to the formal mathematician, who has seen countless counterexamples and exceptions to situations the physicist deems "obvious".

So the formal mathematician says, "No. You may not have anything 'open to interpretation'. You must either formally define 2a = 2*a, in which case y/2a = (y/2)*a, or you must formally define 2a = (2*a), in which case 2a^3 = (2a)^3 = 8*a^3. You don't get to interpret the same symbol in two different ways depending on context."

Needless to say, the formal interpretation is necessary for computer programming, where computers are notoriously bad at interpretation. It is also necessary for mathematical proofs. So those of us who are "purists" insist on such formality. (My Ph.D. is in "pure" mathematics, not "applied" mathematics.) But humans are fantastic at interpretation, so most informally-trained math teachers (in other words, most K12 math teachers) teach the informal method, and teach it as gospel.

[King Yesterday Of Action!Town!]

My Action Force Strike Team.

From left to right: Crazy BaldHead the Fisher-Price caveman, Square Dude (or Evil Square Dude), Sergeant Scoop, Silent Bob, Evil Square Dude (or is that one Square Dude...), and Rolf the Dog.

[captain yesterday]

Pea Bear's "Kawaii" Birthday Cake I'm pretty sure The General invented a whole new level of pink with that cake. :-)

[Freehold DM]

Syrus Terrigan wrote:

Just over 6', but not quite 6'1"; weigh in at 230 lbs or so.

And I hate sunshine. I still have the burn scars (freckles -- lol) from my youth. It hurts the eyes, it burns the skin.

If it can't be winter and after sundown, I only request mostly cloudy and dry, no more than 75 degrees, please.

this guy...this guy gets it.

[Construction Montage C.Y.]

Construction montage! the garden patio all laid out.

Being inspected one last time.

Break time

With the finished border the morning after severe weather

[Freehold DM]

Tacticslion wrote:

See, that's fascinating - I've never actually seen that before.

That said, I accept the exponential thing as proof of the opposed, but counter it this way:

Consider the problem you posed, that of 2a^3.

That would be (given the parenthesis we've seen) a problem that looks like this: 2(a)^3 -> this would look at PEDMAS, as well.

For the record, you could do it 2(a^3), but that just resolves any perceived problems before they begin by way of PEDMAS.

~ That means parenthetical first: the (a), okay, fine.

~ Then the exponent of that parenthetical. That makes the ^3 the next thing, and taking precedence.

~ Then the 2.

This is still an atomic number, but with a single unknown component, and continues to resolve in said manner.

As an aside, just in case the question arises, 2a^3^3 would most likely be resolved by riots in the streets and anarchy presuming the second ^3 was outside the parenthesis along with the first, making it a modifier of that.

I accept that there is a major view against this, but it also means there are a lot of people I know who continually teach something different from that view: as a for-instance, this was a major problem that someone (whether myself or another student) would get wrong every time, and have to be corrected; hence it's been drilled pretty solidly into my head.

To be fair, I am probably moooooooooostly thinking of physics classes (which often lacks the ability to note unknowns in any other manner, because, you know, reality isn't very tidy). And, you know, I'm willing to accept that there is a hypothetically "proper" way to use these, but I've never seen it done that way in practice - and, to me, when something is never done in practice, across multiple venues the so-called "proper" method seems... not really so proper.

I won't argue that math books are infallible (as a for-instance, on no less than two practice tests I went over with a student of mine, I discovered math problems that...

what's pedmas? I know pemdas...

[Tacticslion]

NobodysHome wrote:

So, you have to understand to whom you are addressing your questions: My undergraduate focus was on logic and set theory. One of my favorite "nighttime reading" books was, "Theorems and Counterexamples in Mathematics", a wonderful book that took all the "great" theorems of mathematics (for example, the Fundamental Theorem of Calculus), dropped each assumption one by one (for example, suppose the function isn't continuous), then provided a counterexample proving the theorem false in that situation.

As I said, a fun, fun read.

So, here's the difference between a "formal" mathematician and an "informal" mathematician (i.e., a physicist): A physicist says, "You can tell from the context what I mean! y/2a obviously means y/(2a), whereas 2a^3 obviously means 2(a^3)! I don't need to be any more formal than that!"

This is anathema to the formal mathematician, who has seen countless counterexamples and exceptions to situations the physicist deems "obvious".

So the formal mathematician says, "No. You may not have anything 'open to interpretation'. You must either formally define 2a = 2*a, in which case y/2a = (y/2)*a, or you must formally define 2a = (2*a), in which case 2a^3 = (2a)^3 = 8*a^3. You don't get to interpret the same symbol in two different ways depending on context."

Needless to say, the formal interpretation is necessary for computer programming, where computers are notoriously bad at interpretation. It is also necessary for mathematical proofs. So those of us who are "purists" insist on such formality. (My Ph.D. is in "pure" mathematics, not "applied" mathematics.) But humans are fantastic at interpretation, so most informally-trained math teachers (in other words, most K12 math teachers) teach the informal method, and teach it as gospel.

See, that's awesome!

(Sounds like a fascinating read!)

Sounds legit.

(Though I'd suggest a number of professors are there, too - even math professors! ... though they might be influenced by our proximity to the Cape...)

((Also, this physics dude is totally wrong - I've never seen PEDMAS interpreted so you could end up with five... and he doesn't even actually oppose PEDMAS, in the first place, but rather the incorrect application thereof, and then on "moral" grounds for no functional reason reason, other than "EW"...))

(((Of course, purists are sometimes waaaayyyy off, too, by forsaking PEDMAS, and just applying parenthesis in a random fashion; infinite +/- 1 excluding the first one is simply a different math problem. To me seems like trying to drum up debate over a something that's the rough equivalent of confusing a penguins and a chicken because they both happen to be birds with beaks and feathers that lay eggs and can't fly. Sure, but that's about the end of the similarities... And I mean, sure it's a neat problem, but there is no rational way to get 1/2 as an answer, to me... XD)))

EDIT: had to edit once to add a quote for... lot's of ninja's!

[Freehold DM]

captain yesterday wrote:

Pea Bear's "Kawaii" Birthday Cake I'm pretty sure The General invented a whole new level of pink with that cake. :-)

THAT IS THE MOST AWESOME CAKE EVER

[Tacticslion]

Freehold DM wrote:

what's pedmas? I know pemdas...

They are the same thing - the "d" and the "m" are simply put in different places, which, functionally, doesn't matter (as division is really just multiplying fractions)*, but is secretly because I'm dyslexic and I always pronounce it "pedmas" in my head. XD

* And fractions are secretly division problems, OH MY WORD, MATH HAS BECOME OUROBOROS!

EDIT:

"PEMDAS" actually has its own "proper" set of parenthetical groupings:

0) When two functions have zero weight, go left to right.**

1) P Innermost parenthesis first.

2) E

3) MD or DM though you have to have a grasp on the nature of fractions for this one

4) AS or SA though you have to be really careful with this one, until you get to the point that having negative numbers makes sense.

** The entire debate above is over whether or not two specific functions have equal weight, by way of notation.

[Kjeldorn]

captain yesterday wrote:

Pea Bear's "Kawaii" Birthday Cake I'm pretty sure The General invented a whole new level of pink with that cake. :-)

Am I then only one who finds that cake looking slightly...ominous.

I mean, if it was served by people in robes, with chanting in the background, I would expect the cake to scream and bleed when it was cut.

Might just be the foto-filtering though ^^.

[captain yesterday]

I took those pictures with my phone. :-)

[Tacticslion]

The Game Hamster wrote:

So, making the first post makes me naked?

That... doesn't feel all that different.
probably because I'm naked anyway. Being furry rocks sometimes.

Edit: AAGH!! Ninja'd

Don't worry, I was ninja'd several times, myself, in short order...

[Ninja Cap'n Yesterday]

I have brought great shame on my family.

*smoke bomb* *backflip* *somersault* *jump*

[John Napier 698]

Congrats, Kileanna! I'm very happy for you. Keep up the good work! :)

[Freehold DM]

Tacticslion wrote:

Freehold DM wrote:

what's pedmas? I know pemdas...

They are the same thing - the "d" and the "m" are simply put in different places, which, functionally, doesn't matter (as division is really just multiplying fractions)*, but is secretly because I'm dyslexic and I always pronounce it "pedmas" in my head. XD

* And fractions are secretly division problems, OH MY WORD, MATH HAS BECOME OUROBOROS!

EDIT:

"PEMDAS" actually has its own "proper" set of parenthetical groupings:

0) When two functions have zero weight, go left to right.**

1) P Innermost parenthesis first.

2) E

3) MD or DM though you have to have a grasp on the nature of fractions for this one

4) AS or SA though you have to be really careful with this one, until you get to the point that having negative numbers makes sense.

** The entire debate above is over whether or not two specific functions have equal weight, by way of notation.

mmm.

This sounds math related. Hence, it must burn.

attempts to burn all posts related to this one, cannot reach from top of cabinet, flails ineffectively, adorably

[John Napier 698]

If anyone thinks that PEMDAS is confusing, consider evaluating an expression in a language like C. With all its 15 levels of operators. Some of those operators even evaluate from right to left.

[Freehold DM]

Tacticslion wrote:

(I totally agree with the "Use parenthesis!" thing, by-the-by: I keep telling people to do that. Also to SHOW their DAGGUM WORK. That way, even if they get the wrong answer, at least I know why...)

attempts to start conflagration with this specific part of the post

[NobodysHome]

John Napier 698 wrote:

If anyone thinks that PEMDAS is confusing, consider evaluating an expression in a language like C. With all its 15 levels of operators. Some of those operators even evaluate from right to left.

LOL. I was curious so I posed the y ÷ 2a problem to Shiro's player, one of the most-veteran programmers I know.

His answer? "It depends on which compiler you're using."

[Tacticslion]

And that is what costs you all the points on the test, instead of just a few.

Also, to be clear, I am not bashing either of those guys I linked above. I think they're being on the extreme end, though, by positing things that don't make sense. Sure, math equals freedom, and sure if you put different parenthesis up you'll get a different answer: but each makes a fundamental flaw (the first that pedmas doesn't cover the situation, and the second that those two uses of parenthesis are "the same" problem, rather than just sloppy notation).

[John Napier 698]

NobodysHome wrote:

John Napier 698 wrote:

If anyone thinks that PEMDAS is confusing, consider evaluating an expression in a language like C. With all its 15 levels of operators. Some of those operators even evaluate from right to left.

LOL. I was curious so I posed the y ÷ 2a problem to Shiro's player, one of the most-veteran programmers I know.

His answer? "It depends on which compiler you're using."

Ha-ha-ha. Sad, but true. All kidding aside, this was a problem in the early days of personal computing. Programmers had to try to fit a compiler into a very small, compared to today, amount of memory. So many compiler writers took shortcuts, which lead to the "standard" of the time being thrown out the window in the name of expediency.

[John Napier 698]

Freehold DM wrote:

Tacticslion wrote:

(I totally agree with the "Use parenthesis!" thing, by-the-by: I keep telling people to do that. Also to SHOW their DAGGUM WORK. That way, even if they get the wrong answer, at least I know why...)

attempts to start conflagration with this specific part of the post

Sooo, you're the one that keeps crashing the server. :D

[John Napier 698]

John Napier 698 wrote:

If anyone thinks that PEMDAS is confusing, consider evaluating an expression in a language like C. With all its 15 levels of operators. Some of those operators even evaluate from right to left.

Just to make things clear, this is what I'm talking about. :)

[NobodysHome]

Well, all in all, videos like the ones linked simply offend me. They boil down to, "I did something arcane, and you got the answer wrong, so I'm smarter than you."

It's very much like the videos that surfaced 1-2 years ago "proving" that 1 + 2 + 3 + 4 + 5 + ... = -pi/6 or some such.

The videos always started with, "Oh, this is all very formal, and you can't possibly understand the mathematics, so let me show you poor dumb plebes how this works and why I'm right and why I'm oh-so-much smarter than you."

And in reality, the "formalism" is just, "Well, this evaluates to an infinite series, so I'm going to redefine the measure that I'm using on the integers to make this series converge, and then I'm going to use the same symbols based on a totally-rewritten set of assumptions to come to a finite answer, then I'm going to call all of you stupid for not coming to that answer in the first place."

Exactly the kind of people who make the general public hate math.

I want to beat them all with rubber batons.

EDIT: Yes, there's some bitterness involved. I entered college fully intending to get a Ph.D. in physics. After one too many incidents of, "Well, we end up with six infinities here, but if we ignore all the requirements of the theorems and just drop these four infinities, keep these two, and then combine the terms within the series, then everything works out and we match the observations, so it really doesn't matter that we broke every rule of formality in the meantime," I decided to go the math route.
Mathematicians are Lawful. Physicists are Chaotic.

[thegreenteagamer]

Hi guys.

What did I miss?

[Tacticslion]

NH beating a bunch of (my fellow) math nerds with rubber batons.

[thegreenteagamer]

Fair enough. I noticed that recently, but it's been like...a hundred pages or so. Anything major?

I don't chat around these parts as often as I want to anymore. Job's been keeping me busy.

Did I mention that I'm a mailman now? (That's the government job I got!) I lost 20lbs already!

[John Napier 698]

thegreenteagamer wrote:

Hi guys.

What did I miss?

This thread has temporarily diverted into the realm of Mathematics. Which gives Freehold a serious case of Math-hate. He is currently atop a cabinet ( placed there by Rysky ) and is trying to burn the thread. Which leads to the server crashing, now and then. Anything else I missed?

[John Napier 698]

Congrats on the Postal job! :)

[NobodysHome]

John Napier 698 wrote:

Congrats on the Postal job! :)

Once you go postal, you never go back!

Oh, wait...

[Freehold DM]

NobodysHome wrote:

Well, all in all, videos like the ones linked simply offend me. They boil down to, "I did something arcane, and you got the answer wrong, so I'm smarter than you."

It's very much like the videos that surfaced 1-2 years ago "proving" that 1 + 2 + 3 + 4 + 5 + ... = -pi/6 or some such.

The videos always started with, "Oh, this is all very formal, and you can't possibly understand the mathematics, so let me show you poor dumb plebes how this works and why I'm right and why I'm oh-so-much smarter than you."

And in reality, the "formalism" is just, "Well, this evaluates to an infinite series, so I'm going to redefine the measure that I'm using on the integers to make this series converge, and then I'm going to use the same symbols based on a totally-rewritten set of assumptions to come to a finite answer, then I'm going to call all of you stupid for not coming to that answer in the first place."

Exactly the kind of people who make the general public hate math.

I want to beat them all with rubber batons.

EDIT: Yes, there's some bitterness involved. I entered college fully intending to get a Ph.D. in physics. After one too many incidents of, "Well, we end up with six infinities here, but if we ignore all the requirements of the theorems and just drop these four infinities, keep these two, and then combine the terms within the series, then everything works out and we match the observations, so it really doesn't matter that we broke every rule of formality in the meantime," I decided to go the math route.
Mathematicians are Lawful. Physicists are Chaotic.

strange. This single every mathy I have encountered has explained math to me, not physics.

Ah well.

continues to flail in an attempt to burninate math

[Freehold DM]

John Napier 698 wrote:

thegreenteagamer wrote:

Hi guys.

What did I miss?

This thread has temporarily diverted into the realm of Mathematics. Which gives Freehold a serious case of Math-hate. He is currently atop a cabinet ( placed there by Rysky ) and is trying to burn the thread. Which leads to the server crashing, now and then. Anything else I missed?

not the entire thread, just the math related bits!

flail

[John Napier 698]

Hey, NH. I respectfully disagree, slightly. Theoretical Physicists are Chaotic. Applied Physicists, on the other hand, depend on mathematics, and are therefore, Lawful.

[Freehold DM]

thegreenteagamer wrote:

Fair enough. I noticed that recently, but it's been like...a hundred pages or so. Anything major?

I don't chat around these parts as often as I want to anymore. Job's been keeping me busy.

Did I mention that I'm a mailman now? (That's the government job I got!) I lost 20lbs already!

WOOOOOOOOOOOOOOOOOOOOOOO

[Tacticslion]

Tacticslion wrote:

NH beating a bunch of (my fellow) math nerds with rubber batons.

I wish to clarify.

I am a nerd in that I like math.

That is, by no means, the same as calling me intelligent or highly educated... XD

[Tacticslion]

thegreenteagamer wrote:

Fair enough. I noticed that recently, but it's been like...a hundred pages or so. Anything major?

I don't chat around these parts as often as I want to anymore. Job's been keeping me busy.

Did I mention that I'm a mailman now? (That's the government job I got!) I lost 20lbs already!

That's awesome! Congrats, my dude! Also: so glad to see you (as you e been in my prayers)! And now; to TKD!

[captain yesterday]

thegreenteagamer wrote:

Fair enough. I noticed that recently, but it's been like...a hundred pages or so. Anything major?

I don't chat around these parts as often as I want to anymore. Job's been keeping me busy.

Did I mention that I'm a mailman now? (That's the government job I got!) I lost 20lbs already!

Where's my subscription!!!!

[Freehold DM]

Tacticslion wrote:

Tacticslion wrote:

NH beating a bunch of (my fellow) math nerds with rubber batons.

I wish to clarify.

I am a nerd in that I like math.

That is, by no means, the same as calling me intelligent or highly educated... XD

worry not, you are to be beaten for your love of math, not anything else.

Now find a stepladder, so I can commence with the tenderizing.

[John Napier 698]

Okay, TL. Have fun. Break a leg. ( Or dislocate a shoulder, or grant someone a concussion. Whichever is fine, I'm flexible. :D )

[captain yesterday]

thegreenteagamer wrote:

Hi guys.

What did I miss?

I'm A fire giant (for) now. :-)

Although, not literally.

[captain yesterday]

And apparently my phone is capitalizing random letters and words. >:-(

[Tacticslion]

John Napier 698 wrote:

Okay, TL. Have fun. Break a leg. ( Or dislocate a shoulder, or grant someone a concussion. Whichever is fine, I'm flexible. :D )

Man, considering almost everyone there is (literally) less than half my age, I shall strive to avoid all of those things!

(The exceptions are the black belts, and a small Asian girl - really a college student, but one who weighs, again literally in all likelihood, less than half what I do, and comes up to half way above my shoulder - all of whom can entirely dominate me without trying.)

[Tacticslion]

Also: so tempting to call someone out as being a jerk, and also mentally inept (considering they're crowing about common sense and Occam's razor... incorrectly... while also failing to actually address any of the complaints they are supposedly responding to... sigh...). But that would be mean. So I will passive-agressively post about it here, instead, as a method of venting steam and figuring out a proper response, later. TKD awaits!

[captain yesterday]

thegreenteagamer wrote:

Fair enough. I noticed that recently, but it's been like...a hundred pages or so. Anything major?

I don't chat around these parts as often as I want to anymore. Job's been keeping me busy.

Did I mention that I'm a mailman now? (That's the government job I got!) I lost 20lbs already!

Congrats on the job! and subsequent weight loss. :-)

That sounds like a fun job.

[Freehold DM]

I'm at a webinar.

It is being run by mathematica.

I am not enjoying this webinar.
-_-

[The Game Hamster]

Math is theoretically never more complicated than addition. there are special forms of addition (multiplication - subtraction - and division, ect...), and special times to add different things (The Pemdas formality) Once I realized that, I found math a lot easier. I also still don't really enjoy doing it, but I can do it.

[captain yesterday]

It feels like it should be a Friday, or at the least a Thursday.

[Rantraptor]

[redacted]

[Kajehase]

Only two hours left until Thursday. I'm-a spend them watching an Arcade Fire concert from 2007. Damn, but they can make an awesome-sounding din.