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.
I ran across this recently.
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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?
Ten plus ten always equals twenty. Did you intend to type an asterisk or x there for multiplication, which would be correct?
Two plus two never equals ten. What in the world does the equation mean? Is this kids are not taught in any math classes?
This entire poster is the type of thing displayed by very insecure neurotic people who need reminders of how they think they’re better than other people anywayI ran across this recently.
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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?
Did you miss the part that 2+2=10 in TRINARY? Are you under the impression that base 10 is the only numeric system in the world?Ten plus ten always equals twenty. Did you intend to type an asterisk or x there for multiplication, which would be correct?
Two plus two never equals ten. What in the world does the equation mean? Is this kids are not taught in any math classes?
Your contention that the order of operations means that math isn't the universal language is the same as pointing out that the Romans wrote VI instead of 6. Math obviously isn't always represented using the same symbols, and that is all the order of operations is; another symbol.
When people say that math is the universal language, they don't mean that an extraterrestrial visitor would see the number 5 written somewhere and magically know what amount that particular squiggle represented.
If you show an extraterrestrial 2 apples, and then 3 apples, and then 5 apples, and then 7 apples, and then 11 apples, a math-savvy E.T. will be able to show you 13 apples to communicate that they understand primes. If you draw a triangle in the dirt, and put two 3 apples along one side, and 4 apples along the other, a math-savvy E.T. will be able to put 5 apples along the hypotenuse.
Binary is a number system that only has 10 digits, 0 and 1. Ternary, by contrast has 10 digits, 0,1, and 2. Hexadecimal has a whopping 10 digits. 0,1,2,3,4,5,6,7,8,9,a,b,c,d,e, and f.
There are 10 types of people in the world. Those who understand binary, and those who don't.
Correction to my own post. 2+2 in base 3 or trinary would actually be 11. 2+2=10 occurs in base 4.Did you miss the part that 2+2=10 in TRINARY? Are you under the impression that base 10 is the only numeric system in the world?
I'm not sure that you read everything because I already noted that the difference in what symbols used did not make a difference.
I covered that as well.
Granted. Not what I addressed at all. Maybe go back and read.
For those that missed this, this typo was supposed to be 16.
NM, I did miss what you did there. No matter the system, there will always be 10 digits IF you are describing them in that same system.That wasn't a typo. It was supposed to be 10.
SO something I ran across that no one has yet to bring up as a point, and that I completely missed in my calculations (Hey I have 9 kids and 12 grandkids. Puns are practically a requirement from me). Multiplication is essentially addition short hand. 2*2 is 2+2+2+2 or 4+4. So in doing multiplication before addition, you are, in effect converting to like units. So there is indeed a mathematical principle for doing multiplication before addition and subtraction. However, division is not subtraction shorthand. 6/2 in no way can be converted in to anything with addition or subtraction. So what is the basis for putting it in any certain order of operation? I've shown the why to multiplication, something none of you did. Can anyone show a why to division?
Not replying to the whole thing, but have to put in....Damn it! The intended equation was supposed to be 2*4, not 2*2. This should teach me not to try math before coffeeOrders of operation are entirely unnecessary. Just put parentheses around everything.
((2*8)+3) = 19
(2*(8+3)) = 22
Prioritizing orders of operations are only useful for avoiding confusion for expressions not contained in parentheses. An extraterrestrial civilization that specified all value groupings with a value grouping symbol in this way would not need an order of operations for their system at all.
Also, thinking of multiplication as essentially shorthand addition is one of the least useful ways to think of multiplication. It's much more useful to think of it in terms of scaling or stretching (or rotating once you get to the complex plane.) But if you do want to think of it as a shorthand addition, then division is also shorthand addition, and also shorthand subtraction, since division is the same process as multiplication and subtraction is the same process as addition.
So for example, if 2*2 is 2+2 (2+2+2+2 or 4+4 doesn't make any sense since 2*2=4, and 2+2+2+2=8) then 2/0.5 is also 2+2. It is also 2-(-2). Multiplication and division both scale a value, with the distinction between the two only vaguely indicating the direction of scaling, since either can be used to scale in either direction. Likewise, addition and subtraction both translate a value in either direction. So for example x+y can be written as x-(-y) and x-y can be written as x+(-y). To take your example, 6/2 is identical to 6*(1/2), so it could easily be converted to (1/2)+(1/2)+(1/2)+(1/2)+(1/2)+(1/2) if you are inclined to convert multiplication in that way.
Did you miss the part that 2+2=10 in TRINARY? Are you under the impression that base 10 is the only numeric system in the world?
Then you have no comprehension of number systems. Computers use both binary and hexadecimal number systems, or base 2 and base 16. In binary, There are only two digits, 0 and 1. Thus 1+1=10 in binary. 9+5=e is in hexadecimal. Trinary would be only three digits, and base 4 would only have four digits. Progression in base 4 would be 0, 1, 2, 3, 10, 11, 12, 13, 20, etc. So 2+2=10 in base 4.I have no idea what that means. All I understand is 2+2=4 and 10+10=20.
Then you have no comprehension of number systems. Computers use both binary and hexadecimal number systems, or base 2 and base 16. In binary, There are only two digits, 0 and 1. Thus 1+1=10 in binary. 9+5=e is in hexadecimal. Trinary would be only three digits, and base 4 would only have four digits. Progression in base 4 would be 0, 1, 2, 3, 10, 11, 12, 13, 20, etc. So 2+2=10 in base 4.
Don't need it to understand basic number systems. A background in computers help, but isn't required either.Did you take calculus in college?
Don't need it to understand basic number systems. A background in computers help, but isn't required either.
The only "basic" number system is counting absolutes forward and backward.
Do you understand the reason why you can express the number 9 with only one digit, but you need two digits to express the number 10?
Because the first single digit number is 0.