[ARCHIVED THREAD] - Question about Math Theory, PEMDAS (Page 1 of 2)
Posted: 2/20/2013 11:11:20 AM EDT
|
Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something)
What if our system of math as we know it didn't exist? What if math was something totally different? Take the order of operations for example. So let's take the problem 5+10/2. Following PEMDAS, the answer would be 10. BUT, let's say that PEMDAS never existed, and we now follow the "left to right" rule - whereby all equations of this manner were solved left to right. (hereby named L2R) PEMDAS: 5+2/10 = 10 L2R= 5+10/2 = 7.5 My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? |
| This seems like a perfect companion for Are things really as they seem? . |
|
Quoted:
Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) What if our system of math as we know it didn't exist? What if math was something totally different? Take the order of operations for example. So let's take the problem 5+10/2. Following PEMDAS, the answer would be 10. BUT, let's say that PEMDAS never existed, and we now follow the "left to right" rule - whereby all equations of this manner were solved left to right. (hereby named L2R) PEMDAS: 5+2/10 = 10 L2R= 5+2/10 = 7.5 My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? You have a philosophy class right before you have an algebra class, don't you? |
|
The answer is 288, you philistines.
ETA: And neither answer you provide would be correct for the respective system you postulate. PEMDAS answer to 5+2/10=5.2. L2R answer is 0.7. ETA2: Those answers you give are for the original problem of 5+10/2, which you changed when you restated. |
|
Quoted:
Quoted:
Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) What if our system of math as we know it didn't exist? What if math was something totally different? Take the order of operations for example. So let's take the problem 5+10/2. Following PEMDAS, the answer would be 10. BUT, let's say that PEMDAS never existed, and we now follow the "left to right" rule - whereby all equations of this manner were solved left to right. (hereby named L2R) PEMDAS: 5+2/10 = 10 L2R= 5+2/10 = 7.5 My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? You have a philosophy class right before you have an algebra class, don't you? LOL. I'm actually sitting at work right now selling State Farm insurance. This just popped into my head. |
|
Quoted:
Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? Math is logically consistent. The way we express it is a convention; i.e. PEMDAS. |
|
Quoted: Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? When you apply mathematics to the real world it makes more sense. |
|
We use PEMDAS for the same reason we read sentences from left to right. If you could randomly change around the order of words in the sentance, you would alter the meaning. If you could randomly change around the order of operations in an expression, you would alter the meaning. In other styles of mathematical expression, the society would adopt their own convention. The chance of an extraterrestrial using PEMDAS is small, but so is the chance of their using Arabic numerals! |
|
Quoted:
We use PEMDAS for the same reason we read sentences from left to right. If you could randomly change around the order of words in the sentance, you would alter the meaning. If you could randomly change around the order of operations in an expression, you would alter the meaning. So math is not the universal language then? |
|
Quoted:
We use PEMDAS for the same reason we read sentences from left to right. If you could randomly change around the order of words in the sentance, you would alter the meaning. If you could randomly change around the order of operations in an expression, you would alter the meaning. In other styles of mathematical expression, the society would adopt their own convention. The chance of an extraterrestrial using PEMDAS is small, but so is the chance of their using Arabic numerals! In today's environment, I think that's called progress. Forvart! (old rules do not apply). |
|
PEMDAS is a book keeping standard. It is not mathematics. It's a flawed standard that permits nutty solutions due to a weak rule big enough to fly the space station through.
I had never encountered this "rule" until the recent abuse of everything arithmetic. Back in the old days ... Just use parentheses, there are plenty to go around and they cost less than the errors created when they are rationed, or get a zero on your work. L2R= 5+10/2 = 7.5 If everyone agrees that this is the rule, then it's the rule of syntax for solving equations of this format. That's all that matters. It does not alter the fact that 10/2 = 5 when considered in that context, or that 5+5=10. This is nothing but setting down rules of syntax (or book keeping), and PEMDAS with its flaw is the one that is taught, right or wrong. |
|
Quoted:
Quoted:
We use PEMDAS for the same reason we read sentences from left to right. If you could randomly change around the order of words in the sentance, you would alter the meaning. If you could randomly change around the order of operations in an expression, you would alter the meaning. So math is not the universal language then? It is and it isn't. Mathematics itself is absolute, and a universal language. How we express it may not be. I.e. if aliens came to earth they might not see an equation and understand it, because they would have different numerals and symbols for addition and subtraction, etc. However if you take 5 apples there, and you have 5 apples here, and you group them together, you have 10 apples, all day, every day, no matter where you are. the mathematic principle is universal. How you express it might not be. |
|
5 + 10/2 = x
x=10 (PEMDAS) x=7.5 (L2R) If other rules of math still apply, only L2R instead of PEMDAS: Multiply everything by 2. 10+10 = 2x x=10 (PEMDAS) x=10 (L2R) By using algebra to write it differently, you can see how L2R cannot work unless ALL rules of math change as well. |
|
Quoted:
Quoted:
If you did math with poker chips you would find out that numbers work according to PEMDAS. It's all derived through logic. Not theory. It's absolute truth that can be observed in the universe right in front of you. How so? If you don't follow PEMDAS the you won't come up with the correct answer. Your math answer won't match the answer you obtained experimenting with the chips. |
|
Quoted:
Quoted:
PEMDAS is only confusing because people dont use enough parenthesis, they need to do more math with excel.  Ever notice how easy it is to create a 6 deep nested formula in excel, but nearly impossible to decipher one that someone else wrote? That's only due to EXCEL being too stupid to recognize other forms of brackets such as { [ } ], and I'll bet there are some double brackets available in the special characters. |
|
Quoted:
Quoted:
Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? Math is logically consistent. The way we express it is a convention; i.e. PEMDAS. Most accurate and concise response, IMO. PEMDAS is nothing more than a widely accepted standard that makes the expression and interpretation of pre-existing universal mathematical principles easier. PEMDAS and other mathematical conventions are parts of a language, not unlike English or Spanish. A cat, for example, may be called "gato" in some places, but that doesn't change the nature of the thing itself, it is simply a particular way of expressing an idea. |
|
Quoted: Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) What if our system of math as we know it didn't exist? What if math was something totally different? Take the order of operations for example. So let's take the problem 5+10/2. Following PEMDAS, the answer would be 10. BUT, let's say that PEMDAS never existed, and we now follow the "left to right" rule - whereby all equations of this manner were solved left to right. (hereby named L2R) PEMDAS: 5+2/10 = 10 L2R= 5+10/2 = 7.5 My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? The numbers that we pick are just definitions, really. The order we write things down is just semantics. With another system, you would still get the same results, but everything would be written differently.
|
|
Quoted: Quoted: We use PEMDAS for the same reason we read sentences from left to right. If you could randomly change around the order of words in the sentance, you would alter the meaning. If you could randomly change around the order of operations in an expression, you would alter the meaning. So math is not the universal language then? It kind of is. The way we express it isn't. |
|
Quoted: 5 + 10/2 = x x=10 (PEMDAS) x=7.5 (L2R) If other rules of math still apply, only L2R instead of PEMDAS: Multiply everything by 2. 10+10 = 2x x=10 (PEMDAS) x=10 (L2R) By using algebra to write it differently, you can see how L2R cannot work unless ALL rules of math change as well. You're using PEDMAS to disprove L2R. |
|
Quoted: Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) What if our system of math as we know it didn't exist? What if math was something totally different? Take the order of operations for example. So let's take the problem 5+10/2. Following PEMDAS, the answer would be 10. BUT, let's say that PEMDAS never existed, and we now follow the "left to right" rule - whereby all equations of this manner were solved left to right. (hereby named L2R) PEMDAS: 5+2/10 = 10 L2R= 5+10/2 = 7.5 My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? Wonder if C..A..T really spelled Dog?  |
|
Quoted:
Quoted:
PEMDAS is only confusing because people dont use enough parenthesis, they need to do more math with excel. Ever notice how easy it is to create a 6 deep nested formula in excel, but nearly impossible to decipher one that someone else wrote? I never really have an issue. Its just a matter of finding to lowest nest and going tier by tier. I'm an auditor, so I see all kinds of crazy shit done. |
|
Quoted: Quoted: Quoted: If you did math with poker chips you would find out that numbers work according to PEMDAS. It's all derived through logic. Not theory. It's absolute truth that can be observed in the universe right in front of you. How so? If you don't follow PEMDAS the you won't come up with the correct answer. Your math answer won't match the answer you obtained experimenting with the chips. Not true. You would just express mathematics differently, but you would get the same results.
|
|
Quoted: Quoted: We use PEMDAS for the same reason we read sentences from left to right. If you could randomly change around the order of words in the sentance, you would alter the meaning. If you could randomly change around the order of operations in an expression, you would alter the meaning. So math is not the universal language then? No. Math is a universal language for SOME things, but our way of representing math really sucks at times. Witness: 1=.9bar threads Also, when nailing alien chicks, math makes for some god-awful dirty talk. |
|
Quoted:
Quoted:
Quoted:
Quoted:
If you did math with poker chips you would find out that numbers work according to PEMDAS. It's all derived through logic. Not theory. It's absolute truth that can be observed in the universe right in front of you. How so? If you don't follow PEMDAS the you won't come up with the correct answer. Your math answer won't match the answer you obtained experimenting with the chips. Not true. You would just express mathematics differently, but you would get the same results. You may call an apple an orange but the mechanics of the operations will always be the same if you expect answers that match with reality. |
|
Quoted: Quoted: Quoted: If you did math with poker chips you would find out that numbers work according to PEMDAS. It's all derived through logic. Not theory. It's absolute truth that can be observed in the universe right in front of you. How so? If you don't follow PEMDAS the you won't come up with the correct answer. Your math answer won't match the answer you obtained experimenting with the chips. That isn't PEMDAS. PEMDAS is part of the grammar rules for reading and writing mathematical expressions. If you dictated a sequential series of operations with poker chips, PEMDAS wouldn't apply. Maybe I am not understanding what you are saying. |
|
Quoted: Quoted: Quoted: Quoted: Quoted: If you did math with poker chips you would find out that numbers work according to PEMDAS. It's all derived through logic. Not theory. It's absolute truth that can be observed in the universe right in front of you. How so? If you don't follow PEMDAS the you won't come up with the correct answer. Your math answer won't match the answer you obtained experimenting with the chips. Not true. You would just express mathematics differently, but you would get the same results. You may call an apple an orange but the mechanics of the operations will always be the same if you expect answers that match with reality. Exactly. It doesn't matter what you call it, it won't change. If we expressed math differently, the expression would be different, but the thing would still be the same. You would have to structure expressions differently, but it wouldn't change the math.
|
|
Quoted: Quoted: Quoted: PEMDAS is only confusing because people dont use enough parenthesis, they need to do more math with excel. Ever notice how easy it is to create a 6 deep nested formula in excel, but nearly impossible to decipher one that someone else wrote? I never really have an issue. Its just a matter of finding to lowest nest and going tier by tier. I'm an auditor, so I see all kinds of crazy shit done. You have more practice than I. I finally gave up on one formula that spanned about 3 lines in the equation bar. What killed it for me was the way the formula never stayed consistent. If then than that, else if this, then not that, else if this then negative that... |
|
Quoted:
Ok, so this is along the lines of "airplane on a treadmill." (unless I'm missing something) What if our system of math as we know it didn't exist? What if math was something totally different? Take the order of operations for example. So let's take the problem 5+10/2. Following PEMDAS, the answer would be 10. BUT, let's say that PEMDAS never existed, and we now follow the "left to right" rule - whereby all equations of this manner were solved left to right. (hereby named L2R) PEMDAS: 5+2/10 = 10 L2R= 5+10/2 = 7.5 My question is this; is math totally theory based, where in an alternate universe the L2R rule can be accepted and correct - but PEMDAS is not? Is all math only correct because we SAY it is? Or is math a universal truth in which there is only one correct answer and there are a finite number of ways to get that answer? You're using a language to express mathematical concepts. You could change the rules of language, just like you could change the rules of whether adjectives come before or after nouns, so long as the people reading it were aware of the rules change and could understand what you were trying to say. PEMDAS is a language rule that allows the language we use to express mathematics be as flexible as possible. |
|
Quoted: Quoted: Quoted: what about base 8? The Octospiders would approve. 42 is the correct answer for any mathematical problem... it's just figuring out the base that is tricky. What if 0 isn't the base digit? Maybe use 1234 and have a base-4 system, where 42 is usually base-5 or greater... Math really depends on our agreed upon conventions. |
|
Quoted: Quoted: Quoted: Quoted: what about base 8? The Octospiders would approve. 42 is the correct answer for any mathematical problem... it's just figuring out the base that is tricky. What if 0 isn't the base digit? Maybe use 1234 and have a base-4 system, where 42 is usually base-5 or greater... Math really depends on our agreed upon conventions. I'm going with base 3... This is how you count in my system. 2, A, 4 are the numbers. Have fun :) |
|
Quoted:
Quoted:
Quoted:
Quoted:
what about base 8? The Octospiders would approve. 42 is the correct answer for any mathematical problem... it's just figuring out the base that is tricky. What if 0 isn't the base digit? Maybe use 1234 and have a base-4 system, where 42 is usually base-5 or greater... Math really depends on our agreed upon conventions. That doesn't accommodate the theory of zero very handily, but it's doable; Zero = 1234 - 1234. Painful, but doable. |
|
Quoted: Quoted: Quoted: Quoted: Quoted: what about base 8? The Octospiders would approve. 42 is the correct answer for any mathematical problem... it's just figuring out the base that is tricky. What if 0 isn't the base digit? Maybe use 1234 and have a base-4 system, where 42 is usually base-5 or greater... Math really depends on our agreed upon conventions. That doesn't accommodate the theory of zero very handily, but it's doable; Zero = 1234 - 1234. Painful, but doable. Or, 1 would mean nothing.  |
|
Quoted:
Many of the rules we are taught are only true in a certain axiomatic system. That is, in the system designed to model our world... Every model is based on certain definitions and axioms.  True to a certain extent. Some things, like Euclidean geometry or Calculus were invented to solve specific physical problems. Other ideas were developed only as mathematical concepts which were later found useful in describing reality. |
|
Quoted:
Quoted:
Quoted:
Quoted:
Quoted:
Quoted:
what about base 8? The Octospiders would approve. 42 is the correct answer for any mathematical problem... it's just figuring out the base that is tricky. What if 0 isn't the base digit? Maybe use 1234 and have a base-4 system, where 42 is usually base-5 or greater... Math really depends on our agreed upon conventions. That doesn't accommodate the theory of zero very handily, but it's doable; Zero = 1234 - 1234. Painful, but doable. Or, 1 would mean nothing. That was a convenient example. If each symbol is not equal to zero, and we believe we need a zero, the we could substitute any combination wanted to denote zero; 0 = 1 - 1 = 22 - 22 = 41 = 41, and so on. Zero was excluded by Torf. Or maybe not, I think I misread his intent, so one of the other symbols in his system may equal zero. |