# Math as a universal language.

#### maquiscat

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I ran across this recently.

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?

#### calamity

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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?
Actually your premise in bold above is wrong. If you want 2*2+4 to equal 12, it HAS to be written as 2(4+2)=12.

See, math is a universal language, for those who understand it.

#### maquiscat

DP Veteran
Actually your premise in bold above is wrong. If you want 2*2+4 to equal 12, it HAS to be written as 2(4+2)=12.

See, math is a universal language, for those who understand it.
You missed my point. That order is a construct. Invented by humans. For math to be a universal language, it would have to be consistent even with any theoretical alien race. Alien race is for hypothetical purposes only. But in their development of math they could have decided that addition and subtraction should be done before multiplication and division. This is before we take into account exponents. I think the use of grouping symbols, parentheses in our case, would be pretty universal, in that it isolates a set group of numbers for special consideration.

The individual operations, addition, subtraction, multiplication, division, and exponents, will always render the same results no matter the symbols or number based used. It is only the order of operations when combined that is a construction and thus makes math not a universal language.

#### calamity

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You missed my point. That order is a construct. Invented by humans. For math to be a universal language, it would have to be consistent even with any theoretical alien race. Alien race is for hypothetical purposes only. But in their development of math they could have decided that addition and subtraction should be done before multiplication and division. This is before we take into account exponents. I think the use of grouping symbols, parentheses in our case, would be pretty universal, in that it isolates a set group of numbers for special consideration.

The individual operations, addition, subtraction, multiplication, division, and exponents, will always render the same results no matter the symbols or number based used. It is only the order of operations when combined that is a construction and thus makes math not a universal language.
Since the reality for which the equations are written is universal, the math is universal. Order of operation is intrinsic to the set-up.

Math is not just a series of numbers plastered on a wall. The numbers represent a boundary condition and function.

#### swing_voter

DP Veteran
To put a man on the moon all those mixed operands had to true with the natural world, so the order we put them in is true with the natural world. Otherwise Neil Armstrong would've never made it.

But I did listen to a talk by some mathematician who won a global award and he said that there are made up things about math. I can't remember exactly what he said though.

#### maquiscat

DP Veteran
Since the reality for which the equations are written is universal, the math is universal. Order of operation is intrinsic to the set-up.

Math is not just a series of numbers plastered on a wall. The numbers represent a boundary condition and function.
Again you are simply not comprehending the point. If way back when, when we first started agreeing upon the rules that math follows, we had decided that addition and subtraction were to be done first, instead of multiplication and division, we would still be creating formulas to represent universal forces and such, but they would look different than they do today. Yes that which we are describing would still be universal, but what we are using to describe it is not.

#### maquiscat

DP Veteran
To put a man on the moon all those mixed operands had to true with the natural world, so the order we put them in is true with the natural world. Otherwise Neil Armstrong would've never made it.

But I did listen to a talk by some mathematician who won a global award and he said that there are made up things about math. I can't remember exactly what he said though.

We have to make the math fit the world. The world is is the constant (ignoring that new knowledge can change what we perceive of that constant). It doesn't matter what the order of those operands are. We would have created the formulas to describe them regardless. They would just look different than what we have currently.

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Math is also racist. The "Woke" crybabies said so.

#### calamity

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Again you are simply not comprehending the point. ...
No, I suggest you do not "comprehend" math. Math is not just numbers thrown up on a wall. It's a symbolic language used to represent relationships and patterns. If you have two things and double them and add one more, you have five. That holds true here and on a planet in a galaxy far far away.

Now, misinterpreting the mathematical relationship of 2*2+1=5 to mean the equation 2(2+1)=6, as you suggested in your op, is an error in YOUR formatting, not the math.

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#### calamity

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Math is also racist. The "Woke" crybabies said so.
Actually, since math is entirely objective and not at all subjective, it is the least racist subject taught in schools. So, yeah. The "woke" crowd doesn't understand math. No surprise there--they are mostly liberal arts ninnies after all.

#### maquiscat

DP Veteran
No, I suggest you do not "comprehend" math. Math is not just numbers thrown up on a wall. It's a symbolic language used to represent relationships and patterns. If you have two things and double them and add one more, you have five. That holds true here and on a planet in a galaxy far far away.

Now, misinterpreting the mathematical relationship of 2*2+1=5 to mean the equation 2(2+1)=6, as you suggested in your op, is an error in YOUR formatting, not the math.

You just hit upon the very point I am making. You are correct that if we have two things and double them and add one more, we have five, and that is objectively true universally. It is also universally true and objective that if we have two things and add one and double them we have six. We can show the later as either 2(2+1)=6 or as simply 2*2+1 if our order of operations A/ S first and M/D second. Formatting is the reason that math cannot be a universal language, because it is a symbolic language just like most others. There is nothing in nature that demands that M/D comes first in math. Can you show me anything, outside of human decision over the centuries, that requires that M/D has to come first in our calculations?

My husband also pointed out that I was wrong on the base system premise that base did not matter. And as far as actual calculations go, it doesn't. As noted 2+2 in base 10 gets the same result as 10+10 in binary...once translated between the two. If math was truly universal, we would not need to translate. Two different people using two different base systems would not be able to understand each other's math, until such a problem was overcome. Hence math is not a universal language. It only represents universal constants (including variable processes such as Force, or Voltage) and their interactions, in a variety of potential ways.

#### calamity

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You just hit upon the very point I am making. You are correct that if we have two things and double them and add one more, we have five, and that is objectively true universally. It is also universally true and objective that if we have two things and add one and double them we have six. We can show the later as either 2(2+1)=6 or as simply 2*2+1 if our order of operations A/ S first and M/D second. Formatting is the reason that math cannot be a universal language, because it is a symbolic language just like most others. There is nothing in nature that demands that M/D comes first in math. Can you show me anything, outside of human decision over the centuries, that requires that M/D has to come first in our calculations?

My husband also pointed out that I was wrong on the base system premise that base did not matter. And as far as actual calculations go, it doesn't. As noted 2+2 in base 10 gets the same result as 10+10 in binary...once translated between the two. If math was truly universal, we would not need to translate. Two different people using two different base systems would not be able to understand each other's math, until such a problem was overcome. Hence math is not a universal language. It only represents universal constants (including variable processes such as Force, or Voltage) and their interactions, in a variety of potential ways.
The choice of symbols is always unique--not universal--but the math itself is not dependent on symbols. It is universal. If the math is represented by the wrong symbols, or if the operations are processed in the wrong order, the math is simply wrong.

I believe the disagreement here is nuanced. My position is that math is above the language used to interpret it. You appear to be arguing that the language stands alone.

I see math as only a representation of a physical reality. Your argument ignores the physical reality behind the equations and says, "See, I can write these numbers differently, and they then mean different things." My argument is that the physical reality can only be represented one way; the correct way.

#### maquiscat

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The choice of symbols is always unique--not universal--but the math itself is not dependent on symbols. It is universal. If the math is represented by the wrong symbols, or if the operations are processed in the wrong order, the math is simply wrong.

I believe the disagreement here is nuanced. My position is that math is above the language used to interpret it. You appear to be arguing that the language stands alone.

I see math as only a representation of a physical reality. Your argument ignores the physical reality behind the equations and says, "See, I can write these numbers differently, and they then mean different things." My argument is that the physical reality can only be represented one way; the correct way.
I agree that we are probably more in a nuanced position. Or maybe looking at the same things two different ways. Blind men describing an elephant and all. I fully agree with the bold. My point is that if we had determined long ago that A/S was done before M/D, we would still be able to represent physical reality with equations that worked consistently. Math isn't the physical reality, it is the language. And ultimately no language is actually universal. What I am saying is that "I can write these numbers differently and and they will show the same thing." Much as I can write the letters differently (e.g. red and rojo), and they will mean the same thing.

What I am looking at is the use of the phrase in the context of the OP. They made the statement of "math is a universal language" as if it were something that just is, and is automatic. But it's not, and cannot be. It has to be agreed upon as a language of common use. But common use is not the same as universal.

#### Mr Person

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If you changed the order of operations, your results would have no bearing on reality. You would realize very quickly that you have it wrong because nothing you tried to build or do with this incorrect order of operations would work. You can't just have different math unless you never put it to any practical use, itself an absurd proposition.

Let's assume for the sake of argument that you could have a different set of equations using your incorrect order of operations and they actually did describe reality accurately. Just assume it. Say you tried to communicate with another species using math, say, by showing them a graphic of their planet spinning and orbiting their sun while also showing equations describing how to calculate the amount of time the rotation and the orbit took. And now say they respond similarly, with images of your ship orbiting their planet and equations for calculating how long that takes. Assume that the intended meaning of the graphics are understood by each species.

If each species were using a different order of operations, it would quickly become apparent to each species. Everyone involved would notice something is wrong, and I have little doubt that each species would eventually realize that the other is using a different order of operations, and work out which it is. How? Perhaps trial and error. Provided you know what the infographics are supposed to describe in the first place, it would be easy to rerun the alien equation using different orders of operation until you got the result that accurately describes reality -- the result that lines up with your equation based on your different order of operations.

I suppose the point is that as long as the thing each species is talking about has one fixed value, there has got to be a way to communicate about it. You could run the same hypothetical with species using different units of measurement. Say we use metric and they use blargers per uglags. Communication would be tricky, but you could work it out provided other things about the species are sufficiently similar. (I throw that line in there because there may be alien species so utterly different that communication is fundamentally impossible; some species we might even recognize as life).

Some portion of math has to be universal. Sort of like Chomsky and universal grammar.

But perhaps we should restart at square one: has any mathematician endeavored to prove that you really could rewrite physics equations to produce accurate results using a different order of operation?

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#### Mr Person

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But perhaps we should restart at square one: has any mathematician endeavored to prove that you really could rewrite physics equations to produce accurate results using a different order of operation?

Not being a mathematician, I have no idea how to prove that this is either possible or impossible for all equations. Trying it by trial and error isn't a guarantee. Putting aside the vast number of equations we've discovered, not being able to figure out how to rewrite a particular equation using a different order of operations doesn't necessarily mean it can't be done.

But, if you could prove that you cannot rewrite all equations with a different order of operation such that they still produce the correct result, then you would have proven that the order of operations is universal.

Prove otherwise, and you prove that not all of mathematics is indeed universal.

#### calamity

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I agree that we are probably more in a nuanced position. Or maybe looking at the same things two different ways. Blind men describing an elephant and all. I fully agree with the bold. My point is that if we had determined long ago that A/S was done before M/D, we would still be able to represent physical reality with equations that worked consistently. Math isn't the physical reality, it is the language. And ultimately no language is actually universal. What I am saying is that "I can write these numbers differently and and they will show the same thing." Much as I can write the letters differently (e.g. red and rojo), and they will mean the same thing.

What I am looking at is the use of the phrase in the context of the OP. They made the statement of "math is a universal language" as if it were something that just is, and is automatic. But it's not, and cannot be. It has to be agreed upon as a language of common use. But common use is not the same as universal.
We agree on the bold.

#### calamity

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Not being a mathematician, I have no idea how to prove that this is either possible or impossible for all equations. Trying it by trial and error isn't a guarantee. Putting aside the vast number of equations we've discovered, not being able to figure out how to rewrite a particular equation using a different order of operations doesn't necessarily mean it can't be done.

But, if you could prove that you cannot rewrite all equations with a different order of operation such that they still produce the correct result, then you would have proven that the order of operations is universal.

Prove otherwise, and you prove that not all of mathematics is indeed universal.
Newton invented calculus to describe rates of change and use those relationships in his equations. He could just as well have invented something completely different and, if it worked, it would be just as good. One method I used back in college to double check my work was to solve a given problem using a completely different method. If it checked out, then I knew I was golden.

I guess my point is that there are likely many ways to skin a cat. After all, multiplying 1293 by 781 is really just adding 1293 to itself 781 times. The latter just takes longer is all--well unless you use Excel.

#### maquiscat

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If you changed the order of operations, your results would have no bearing on reality. You would realize very quickly that you have it wrong because nothing you tried to build or do with this incorrect order of operations would work. You can't just have different math unless you never put it to any practical use, itself an absurd proposition.

This seems to assume that we are applying the current formulas and equations using the new order. But such is not what I am suggesting.

I suppose the point is that as long as the thing each species is talking about has one fixed value, there has got to be a way to communicate about it.

This goes right along with what I am claiming. Reality is a universal language, but that which describes reality, be it lingual or mathematical, can never be universal. We would have to translate different order of operands just as much as we would have to translate different number bases.

Some portion of math has to be universal. Sort of like Chomsky and universal grammar.

From Scientific American:
The misconception that Chomsky represents the dominant view comes from the fact that the opposition is divided into many approaches and factions, so there’s no single figure that can be identified with an alternative. Also, he’s famous and charismatic, and people outside the field have heard of him, but haven’t heard of anyone else, and confuse his fame with professional dominance.

But perhaps we should restart at square one: has any mathematician endeavored to prove that you really could rewrite physics equations to produce accurate results using a different order of operation?

I doubt it. Although in my research, I have learned that today's order has not always been. At one point, multiplication was supposed to be done before division, not along side it. That said, and especially with the amount of time invested in the given order, I'm not sure that it could be proven right away. But we might eventually be able to if it were ever a point of import. After all at one time, we assumed that physical objects could not break the speed of sound, and now there are plenty that do. Speed of light is up next!
Not being a mathematician, I have no idea how to prove that this is either possible or impossible for all equations. Trying it by trial and error isn't a guarantee. Putting aside the vast number of equations we've discovered, not being able to figure out how to rewrite a particular equation using a different order of operations doesn't necessarily mean it can't be done.

We would probably have to start from scratch. We write the equations to describe reality. Basically, this would be the equivalent of rewriting the works of Shakespeare into Klingon.

#### AmNat

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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?
Fair point, though the accepted order is a lot more convenient for writing most physical equations and mathematical theorems than the inverted order would be.

In any case, math cannot be a universal language because the language is not universal. There's no inherent significance to Arabic numerals nor to the conventional symbols of mathematics.
I see math as only a representation of a physical reality.
My point is that if we had determined long ago that A/S was done before M/D, we would still be able to represent physical reality with equations that worked consistently. Math isn't the physical reality, it is the language.
The conclusions of mathematics are metaphysical in character. They would hold for any physics.
But perhaps we should restart at square one: has any mathematician endeavored to prove that you really could rewrite physics equations to produce accurate results using a different order of operation?
Not being a mathematician, I have no idea how to prove that this is either possible or impossible for all equations. Trying it by trial and error isn't a guarantee. Putting aside the vast number of equations we've discovered, not being able to figure out how to rewrite a particular equation using a different order of operations doesn't necessarily mean it can't be done.
We would probably have to start from scratch. We write the equations to describe reality. Basically, this would be the equivalent of rewriting the works of Shakespeare into Klingon.
It's only a matter of rearranging parentheses.

#### Cordelier

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We have to make the math fit the world. The world is is the constant (ignoring that new knowledge can change what we perceive of that constant). It doesn't matter what the order of those operands are. We would have created the formulas to describe them regardless. They would just look different than what we have currently.

That brings up a deeper question, though... is math something we created or is it something we've discovered? I suspect whichever side someone falls on that question is going to determine whether they believe it's the "universal language" or not.

#### AliHajiSheik

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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?
Some parts of the earth is flat
Not every vaccine works 100% of the time
12 men have been to the moon, I haven't
Climate has always changed
The universe doesn't care what we think it is doing
I thought the F-word was the universal language
Contrails are water vapor, water is a chemical
Evolution is a theory, but it has a solid foundation
I'm made of star rocks, so I'm an exception
Magic is like science but better than real
Political Science is not a science

#### longview

DP Veteran
You missed my point. That order is a construct. Invented by humans. For math to be a universal language, it would have to be consistent even with any theoretical alien race. Alien race is for hypothetical purposes only. But in their development of math they could have decided that addition and subtraction should be done before multiplication and division. This is before we take into account exponents. I think the use of grouping symbols, parentheses in our case, would be pretty universal, in that it isolates a set group of numbers for special consideration.

The individual operations, addition, subtraction, multiplication, division, and exponents, will always render the same results no matter the symbols or number based used. It is only the order of operations when combined that is a construction and thus makes math not a universal language.
Perhaps not universal, within your context, but safe within the context of the sphere of Human existence.
The idea of the order of operations (generally more complex to less complex) is universal with almost everyone on earth.
The evidence of this is in math scores of people who have trouble with the primary language of where they attend school.
Imagine if a student who speaks some Spanish, got a full ride scholarship in Spain.
They may have trouble grasping the subtleties of the writings of Cervantes, but could do quite well in the math classes.

## ​

#### maquiscat

DP Veteran
The idea of the order of operations (generally more complex to less complex) is universal with almost everyone on earth.

Given the number of people on FB and other media who can't get it right, I find this doubtful. However, even for those who do, it's because it's taught not a natural universal language.

The evidence of this is in math scores of people who have trouble with the primary language of where they attend school.
Imagine if a student who speaks some Spanish, got a full ride scholarship in Spain.
They may have trouble grasping the subtleties of the writings of Cervantes, but could do quite well in the math classes.

That theory works well for countries using the same number symbols, but they would do poorly in countries that use other symbols for numbers, such as many Asian countries do. Granted many now use a combination, but the point still stands.

#### longview

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Given the number of people on FB and other media who can't get it right, I find this doubtful. However, even for those who do, it's because it's taught not a natural universal language.

That theory works well for countries using the same number symbols, but they would do poorly in countries that use other symbols for numbers, such as many Asian countries do. Granted many now use a combination, but the point still stands.
Fair enough, but regardless of the number symbols the algebraic order of operations is still the same.

#### Mircea

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I'm going to disagree that math is a universal language.

Music is math. Can't get any more universal than that.