Limericks and non-limericks
Mar 31, 2024 06:11:15 #
JD750 wrote:
…The first one the expression on the left is not equal to 81.
The 2nd one checks out. :)
This one:
If (1+x) (real close to 1)
Is raised to the power of 1
Is raised to the power of 1
Over x, you will find
Here's the value defined:
2.718281...
It really depends on the value of x does it not? What if x is 1,000? I think it was supposed to say delta-X.
The 2nd one checks out. :)
This one:
If (1+x) (real close to 1)
Is raised to the power of 1
Is raised to the power of 1
Over x, you will find
Here's the value defined:
2.718281...
It really depends on the value of x does it not? What if x is 1,000? I think it was supposed to say delta-X.
Do the math again on the first one. 12+144+20+6 is 182
Divided by 7 is 26
+55 is 81
On the other one no the limerick implies that x is ‘real close to zero’ although it is true that the wording could be considered ambiguous.
Mar 31, 2024 13:11:19 #
DirtFarmer wrote:
Nope. The cube root of 4 is not = 6. OH it's supposed to be 3 times the square root of 4? For that it needs the * symbol to denote the multiplication (as was done in the next term of the equation, 5*11). As written it's ambiguous and correctly written mathematical equations are not ambiguous. Do the math again on the first one. 12+144+20+6 is 182
Divided by 7 is 26
+55 is 81
On the other one no the limerick implies that x is ‘real close to zero’ although it is true that the wording could be considered ambiguous.
Divided by 7 is 26
+55 is 81
On the other one no the limerick implies that x is ‘real close to zero’ although it is true that the wording could be considered ambiguous.
The other one is supposed to be 1+delta-x, it says "1+X (real close to 1)" which is not correct because x is a variable, it could be 1000 or 1 million or .0001. Again "real close to 1" is ambiguous. Delta-x is by definition a small number and thus 1 + delta-x is close to one, no ambiguity.
For the rhyming grammar they get an A+ but for math they get a D-. But that can easily be fixed so both are correct.
Mar 31, 2024 13:16:06 #
JD750 wrote:
Nope. The cube root of 4 is not = 6. OH it's supp... (show quote)
It’s not the cube root of 4, it’s 3 times the square root of 4. Read the text.
If 1+x is real close to 1, then x is real close to zero.
Mar 31, 2024 14:18:17 #
DirtFarmer wrote:
It’s not the cube root of 4, it’s 3 times the square root of 4. Read the text.
For that it needs the * symbol to denote the multiplication (as was done in the next term of the equation, 5*11). As written it's ambiguous. Correctly written mathematical equations are not ambiguous
DirtFarmer wrote:
If 1+x is real close to 1, then x is real close to zero.
“Real close” is vague, real close compared to what? 0.1 is close 0.01 is close 0.001 is close but the approximation to 2.718281 is not correct for any of those. The term “real close” It is completely ambiguous. Correctly written mathematical equations are not ambiguous.
Apr 2, 2024 18:54:37 #
Apologies for the late reply. Sunday was completely taken up with family activities. Monday was pretty much taken up traveling back home. Tuesday was catchup.
Background: I have been having a discussion with JD750 about a couple of the mathematical limericks. He has opinions about the format of some of the equations. I have other opinions about those formats. This is to continue the discussion. Sacred UHH tradition requires that I present my opinion to all and sundry. Of course JD750 is bound by the same tradition.
The first discussion is about
I maintain that it is not necessarily ambiguous. Algebraic notation equates concatenation of variables with multiplication.
AB=A*B (for variables A and B -- Note that variable names are not limited to single characters so it is possible that AB is a separate variable, in which case some variation of the notation will be required for clarification). When both variables are numbers instead of variables, it will be necessary to use the multiplication operator explicitly since otherwise you will get confusing constructs such as 5*11 being written as 511 or even 5 11. If only one of the variables is a number, the order will be important. 5B could be understood as 5*B if it is known that B is a variable. The same is not true of A11, which looks as if it might be a single variable.
The clarification requirement is important of course. In this case, presents to at least one person a possible alternative interpretation: 
. My opinion is that it is clear as is since the 3 in a cube root is significantly smaller than the 3 as the initial variable and is located within the hook of the radical symbol. Thus the issue may not be the notation, but the font size or the kerning. Since clarification is required I can think of several ways to present this element of the equation.
(1) The original way: () which is clear to me but not clear to JD750
(2) Increasing the font size of the 3 to emphasize that the 3 does not represent the order of the radical: (
). Common usage when the radical does not have the order specified is that it is a square root.
(3) Increase the spacing (kerning) between the 3 and the radical to emphasize that it is not the order of the radical: (
)
(4) Specify that the radical represents a square root by including the order 2 in the radical:
(5) Since the element of the equation is in parentheses, utilize the parentheses to separate the 3 from the radical:
(6) Use the suggestion of JD750 by inserting the multiplication symbol:
The second issue is '1+X (real close to 1)'
Correctly written mathematical equations CAN be ambiguous in that they do not specify the exact value of a variable, which is the case here. Note that there was not a mathematical equation directly involved in this example. It was purely a literary offering. But 'real close to 1' comes from the notation
, where the result of the equation from which the limerick is derived converges as X goes to zero.
Background: I have been having a discussion with JD750 about a couple of the mathematical limericks. He has opinions about the format of some of the equations. I have other opinions about those formats. This is to continue the discussion. Sacred UHH tradition requires that I present my opinion to all and sundry. Of course JD750 is bound by the same tradition.
The first discussion is about
JD750 wrote:
For that it needs the * symbol to denote the multiplication (as was done in the next term of the equation, 5*11). As written it's ambiguous. Correctly written mathematical equations are not ambiguous
I maintain that it is not necessarily ambiguous. Algebraic notation equates concatenation of variables with multiplication.
AB=A*B (for variables A and B -- Note that variable names are not limited to single characters so it is possible that AB is a separate variable, in which case some variation of the notation will be required for clarification). When both variables are numbers instead of variables, it will be necessary to use the multiplication operator explicitly since otherwise you will get confusing constructs such as 5*11 being written as 511 or even 5 11. If only one of the variables is a number, the order will be important. 5B could be understood as 5*B if it is known that B is a variable. The same is not true of A11, which looks as if it might be a single variable.
The clarification requirement is important of course. In this case,
presents to at least one person a possible alternative interpretation: . My opinion is that it is clear as is since the 3 in a cube root is significantly smaller than the 3 as the initial variable and is located within the hook of the radical symbol. Thus the issue may not be the notation, but the font size or the kerning. Since clarification is required I can think of several ways to present this element of the equation.(1) The original way: (
) which is clear to me but not clear to JD750(2) Increasing the font size of the 3 to emphasize that the 3 does not represent the order of the radical: (
). Common usage when the radical does not have the order specified is that it is a square root.(3) Increase the spacing (kerning) between the 3 and the radical to emphasize that it is not the order of the radical: (
)(4) Specify that the radical represents a square root by including the order 2 in the radical:
(5) Since the element of the equation is in parentheses, utilize the parentheses to separate the 3 from the radical:
(6) Use the suggestion of JD750 by inserting the multiplication symbol:
The second issue is '1+X (real close to 1)'
JD750 wrote:
“Real close” is vague, real close compared to what? 0.1 is close 0.01 is close 0.001 is close but the approximation to 2.718281 is not correct for any of those. The term “real close” It is completely ambiguous. Correctly written mathematical equations are not ambiguous.
Correctly written mathematical equations CAN be ambiguous in that they do not specify the exact value of a variable, which is the case here. Note that there was not a mathematical equation directly involved in this example. It was purely a literary offering. But 'real close to 1' comes from the notation
, where the result of the equation from which the limerick is derived converges as X goes to zero.Apr 2, 2024 19:51:16 #
DirtFarmer wrote:
Lots of words to try to deny the reality about the ambiguous equation and vague statement. Apologies for the late reply. Sunday was completel... (show quote)
Like it or not Mathematics is precise language and correctly written statements are NOT ambiguous.
But I did enjoy the limericks. If they were mathematically correct that would be even funnier.
Apr 2, 2024 20:45:56 #
The limericks are mathematically correct if you agree with my interpretation of the notation, even though mathematics and poetry are basically two different languages with different objectives.
Since you disagree with my interpretation of the notation, I challenge you to write (and present to us) a limerick to describe the equations. (Or supply your own equation and write a limerick or other poetic form).
Since you disagree with my interpretation of the notation, I challenge you to write (and present to us) a limerick to describe the equations. (Or supply your own equation and write a limerick or other poetic form).
Apr 3, 2024 02:53:54 #
Mathematics is precise language. Do you realize how much time has been lost sorting this out???
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