Math as a universal language.

[Ikari]

2*2+4 is not 12, it's 8. Learn order of operations.

 

[maquiscat]

2*2+4 is not 12, it's 8. Learn order of operations.

Did you even read the OP or any of my subsequent posts?

 

[Ikari]

Did you even read the OP or any of my subsequent posts?

Not until you learn order of operations.

 

[calamity]

Speaking of math. Appears there are some rather big holes in it.

 

[Ikari]

3 men go into a hotel. The man behind the desk says a room is $30 so each man pays $10 and goes to the room.

A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys' room with $5. On the way the bellboy couldn't figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?

 

[Rexedgar]

3 men go into a hotel. The man behind the desk says a room is $30 so each man pays $10 and goes to the room.

A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys' room with $5. On the way the bellboy couldn't figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?

Man, that’s gonna start some shit......

 

[maquiscat]

Not until you learn order of operations.

Then you are missing the point because the point is that the order of operations is a creation of humans, and the current one recent at that, and thus is not universal. Read it all and you will realize what I am saying.

 

[Ikari]

Then you are missing the point because the point is that the order of operations is a creation of humans, and the current one recent at that, and thus is not universal. Read it all and you will realize what I am saying.

No, order of operations is how it works. Any species that develops math will have to discover the orders of operation as well.

 

[maquiscat]

And given the revival of this thread, and with a nod to @calamity 's post (I'll watch it later when I'm off work), this came across my friends feed.

If Math Is Universal, Why Can’t It Answer a Stupid Facebook Problem?

Perhaps you’ve seen the problem on Facebook or another forum:

slate.com

 

[maquiscat]

No, order of operations is how it works. Any species that develops math will have to discover the orders of operation as well.

You are incorrect. The order of operations has never always been as it is. It is artificial. Thus it is not universal. Go back and read all the points given. Otherwise you don't know what you are arguing against.

 

[Ikari]

You are incorrect. The order of operations has never always been as it is. It is artificial. Thus it is not universal. Go back and read all the points given. Otherwise you don't know what you are arguing against.

It is not incorrect, in fact the joke I posted is an order of operation joke. People on social media not being able to do math doesn't mean that math's not universal. Any species capable of developing math would also need to discover orders of operation.

 

[Rexedgar]

3 men go into a hotel. The man behind the desk says a room is $30 so each man pays $10 and goes to the room.

A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys' room with $5. On the way the bellboy couldn't figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?

• $25 — room
• $3 (3x $1) — back to the men
• $2 — Bellboy

 

[calamity]

• $25 — room
• $3 (3x $1) — back to the men
• $2 — Bellboy

Right, the only way to solve it is:
$27 (3guys *9 dollars each)
-$2 (bellhop's commission)
$25 Room fee

There is no $30 going the other way, even though we clearly see the $30 on the table before the $5 refund.

 

[calamity]

3 men go into a hotel. The man behind the desk says a room is $30 so each man pays $10 and goes to the room.

A while later the man behind the desk realized the room was only $25 so he sent the bellboy to the 3 guys' room with $5. On the way the bellboy couldn't figure out how to split $5 evenly between 3 men, so he gave each man a $1 and kept the other $2 for himself.

This meant that the 3 men each paid $9 for the room, which is a total of $27 add the $2 that the bellboy kept = $29. Where is the other dollar?

One of my favorite math tricks happened a few years ago when several people in a company I worked for took 20% paycuts during the Bush crash. A year later, the boss said, we'll give you all 20% increases now that the economy improved.

More than one person could not figure out why they were still getting less money than they earned before.

 

[maquiscat]

It is not incorrect, in fact the joke I posted is an order of operation joke. People on social media not being able to do math doesn't mean that math's not universal. Any species capable of developing math would also need to discover orders of operation.

They would indeed need to develop an order of operations, but there is nothing requiring that what we currently use is the only possible one for them to develop. Again, go read all the points provided, and then the article I just posted. Then, show me something objective that shows that multiplication and division must naturally come first before addition and subtraction.

 

[Ikari]

They would indeed need to develop an order of operations, but there is nothing requiring that what we currently use is the only possible one for them to develop. Again, go read all the points provided, and then the article I just posted. Then, show me something objective that shows that multiplication and division must naturally come first before addition and subtraction.

Ambiguous PEMDAS

yes, math is a universal language which allows communication among
different cultures. But languages also have been designed by people and
are not always perfect. The PEMDAS ambiguity is actually just an omission
of design. There was no authority which once and for all told that it is
necessary to specify this. The reason is historically clear. One only
realized the problem too late. You say, for you 6/2(1+2) is 1, yes,
almost all humans assume this. If you give it to a computer,
it gives you 9, almost all programming languages do. Yes, like English,
Math has rules. But they are far from perfect. Languages change and
get refined over time. In the PEMDAS discussion it turned out to
be too late to adopt rules. Some have tried and many are fanatic
and think that their way is right. In the 6/2(1+2) case for example,
we can see advocates (i.e. on youtube), who argue,
only 9 is the right answer. But as you say, reading it as 6/2(1+2) is
entrenched and changing that would upset many. The last few slides in
this presentation [PDF] show a bit what linguists say.
It is not really a math problem, it is a linguistic problem. What is good
about the discussion is that all teachers and students now know about
the ambiguity and write down clarified expressions.

 

[maquiscat]

Ambiguous PEMDAS

I'll reply a little more in depth once I am home. I can do more with my laptop than my phone. But this still does nothing to prove that PEMDAS is the only possible order or operations. Did you even read the article that I posted at all? Somehow I doubt it, since you have not referenced it at all.

 

[Ikari]

I'll reply a little more in depth once I am home. I can do more with my laptop than my phone. But this still does nothing to prove that PEMDAS is the only possible order or operations. Did you even read the article that I posted at all? Somehow I doubt it, since you have not referenced it at all.

The entire site that I linked talked about PEMDAS and the various interpretations of mathematical equations.

Despite there being various methods of grouping and operation, Math is still a universal language that leads to communications between cultures. It's not hampered by any specific set orders of operations.

 

[Evilroddy]

I ran across this recently.
View attachment 67326185
So first I am going to ask that if you want to debate any of the other points, start your own thread for that. I want to center on the "math is the universal language."

I'm going to disagree that math is a universal language. When sticking to single operands. This is true. 2+2 will always equal 4, regardless of the number base, label to the digit and such. Going to binary 10+10=100 and 2+2=10 in trinary. But the objects counted are still always the same amount.

But once you get into mixed operands, the order that you perform them is a constructed form, and is in no way natural or universal.

For example: under the current way we do math (PEDMAS or PEMDAS as you prefer) 2*2+4= 8. However, if we reverse the order we perform the operations, 2*2+4=12.

We humans made up that order of operations. So what if another race chose to use a different order? This math is NOT a universal language.

What say you?

Maquiscat:

Mathematics (Maths) is indeed the universal language of humans' for those well trained in this language can communicate with others who are likewise trained regardless of what other languages those other mathematicians are proficient in. Like all languages Maths has its flaws and shortcomings but that does not disqualify it from being a universal language. Now, you're probably thinking he missed the point about mathematical, non-terrestrial aliens and universality. Most of the Maths we use, including the order of operations of arithmetic, is based on demonstrable and provable reality (albeit our reality). In the situation of 2 x 2 + 4 = ?, one can prove it by laying down pebbles in patterns and then counting the total number of pebbles used. Thus the order of operations is verifiable and is not some presupposition dreamed up by some Babylonian or Greek who just came up with it out of the blue. The aliens will see that verifiability too if we show it to them. Now if our aliens are transdemensional ones from an alternate universe where different basic laws apply, then you might have a point, but you used the word "universal" not pan-universal in your OP.

The order of operations is a human construct in the sense that we developed universal laws from counting pebbles but so is our understanding of the known universe. Thus we use synthetic mathematics to describe a synthetic universe of our own creation. What we understand to be the universe is not what the universe actually is. Maths is the universal language of a mathematically understood universe, so Maths is almost by definition a "universal" language.

But Maths does have its limitations and at some very fundamental levels the language/discipline of Maths is on very shaky ground. The Maths of infinities and the maths set theory are just two of the sub disciplines of Maths which have deeply rooted flaws and limitations. These flaws and limitations have introduced profound functional paradoxes into our understanding Maths of the universe it describes as well as the computational models and programmes which we use to understand that universe. The Maths of infinities is notorious for driving mathematicians who look too deeply into the abyss of the infinities insane, ending many prestigious careers and reputations. Modern artificial intelligence wrestles with these slippery concepts too, triggering the need for programmers to "talk down" AIs which become lost in these blackholes of unreasonable reason.

But despite its imperfections, Maths is the best tool we have for studying, understanding and describing the universe to anyone from this universe and so it is indeed a "universal" language.

Cheers and be well.
Evilroddy.

 

[Evilroddy]

Speaking of math. Appears there are some rather big holes in it.

calamity:

That was a very good video. Thanks for posting it.

Cheers and be well.
Evilroddy.

 

[maquiscat]

The entire site that I linked talked about PEMDAS and the various interpretations of mathematical equations.

Despite there being various methods of grouping and operation, Math is still a universal language that leads to communications between cultures. It's not hampered by any specific set orders of operations.

Even as recently as the 1920's math was not consistent as to whether multiplication preceded division or if they were to be performed on the same left to right pass.

In 1907 in High School Algebra, Elementary Course by Slaught and Lennes, it is recommended that multiplications in any order be performed first, then divisions as they occur from left to right.
In A History of Mathematical Notations (1928-1929) Florian Cajori writes (vol. 1, page 274), "If an arithmetical or algebraical term contains ÷ and ×, there is at present no agreement as to which sign shall be used first."
-https://jeff560.tripod.com/operation.html

Now keep in mind that I am not arguing that as an overall race we haven't been working to having a universally accepted set of rules to follow. But that would be no different than if we got linguists together to create a universal language for all to use. It wouldn't be naturally universal.

 

[Mr Person]

Someone still has to prove - and that's mathematically speaking - that you can change the order of operations and translate existing equations in one consistent manner such that they arrive at the exact same conclusion using new-equations plus new-order-of-operations.


Words are not going to do this, people. They can't.

 

[Mr Person]

Even as recently as the 1920's math was not consistent as to whether multiplication preceded division or if they were to be performed on the same left to right pass.

In 1907 in High School Algebra, Elementary Course by Slaught and Lennes, it is recommended that multiplications in any order be performed first, then divisions as they occur from left to right.
In A History of Mathematical Notations (1928-1929) Florian Cajori writes (vol. 1, page 274), "If an arithmetical or algebraical term contains ÷ and ×, there is at present no agreement as to which sign shall be used first."
-https://jeff560.tripod.com/operation.html

Now keep in mind that I am not arguing that as an overall race we haven't been working to having a universally accepted set of rules to follow. But that would be no different than if we got linguists together to create a universal language for all to use. It wouldn't be naturally universal.

Hold on. Hold on. Hold on. Focus on what you quoted. There was (is there now? Why?) no agreement on operation order between division and multiplication. Why. Let's try the basics....

2 x 5 / 3 is the equation. Each case will be marked with parentheses. I could be a complete rube at the moment, but it seems to me that you get the same answer whichever order you choose, as marked.

Case 1. (2 x 5) / 3 = 3.3(repeat)

Case 2. 2 x (5/3) = 3.3(repeat)

And if it was easy to write proper fractions, we should easily show why. They both end up at 10/3. We do not know which should go first because it doesn't matter which goes first.




And this is why I keep beating the same drum. Unless you can show that you can change the order of operations and provide a translation tool that will let you convert equations from what they are now to what they would have to be then to reach the same result in every single case, I don't see much reason to think it's possible. The order of operations seems baked into the way things work.

So maybe that's because of how we talk about it. But maybe that's because it's the only valid way to talk about it.

 

[calamity]

Most of the time, the math is fine. Newton comes to mind. However, not even Sir Isaac knew how to include all the variables.

So, planets sometimes seem to defy the laws of gravity, like when Mercury drifted toward the inner solar system, and tiny things never behave as planned. We simply don't know enough of anything to plug everything that's needed into the equations.

 

[Ikari]

Most of the time, the math is fine. Newton comes to mind. However, not even Sir Isaac knew how to include all the variables.

So, planets sometimes seem to defy the laws of gravity, like when Mercury drifted toward the inner solar system, and tiny things never behave as planned. We simply don't know enough of anything to plug everything that's needed into the equations.

Mercury is the most inner of the inner solar system, it's already there. Jupiter once took an excursion towards the sun during the formation of the solar system, but was ultimately halted by Saturn's birth. In fact, there have been exoplanets found that are gas giants, but orbit close to their sun. This inward spiral into a stable inner orbit isn't unheard of.

It's true that in the time of Newton, he didn't have all the variables, but his work on orbits redefined how understood orbital mechanics and is still the basis to this day on how we calculate planned orbits and such. As more information is found, we can explain more and more of it. For instance, Newton's laws did not properly predict Mercury's perihelion shift, which was faster than expected. And it wasn't until Einstein came along with his theory of relativity that we knew why. Now we can understand it fairly well.