Math Semantics's 06 29 2018
You can't multiply fractions because they don't "Multiply" they divide.
So lets that that you have a board 1.5 inches wide by 5 inches. You want to put that on your table saw and adjust the top of your table saw blade flush with the top of the woods, and you want to then angle over one half inch. Effectively you want to cut strips one quarter inch wide with that angle profile on the top and bottom.
So you do that triangle math. x2*y2=z2. You attempt to do that in your head. One half of an inch of wood squared plus 1.5 inches of wood squared equals what amounts to be the length of that new cut face of wood squared.
So you are going about it in your head and you say one half of an inch times one half of an inch should get me more than one half of an inch. But it doesn't it gets you one quarter inch. But you were multiplying!
Now lets scale that up to see why it doesn't make sense. The distances in the scaled up version and the fraction denominated version are both fixed. How long one is with regard to the other is relative.
Now lets say that the dimensions were really 15 inches wide by 5 inches over on the table saw. Equivalent to the same ratio as 1.5 to .5 or three to one. So 15 times 15 + 5*5= z2
15 by 15 equals 225. 5 x5 =25. So you have 250 and you take the square root of that to get z which equals 15.81.
So why is there an inflection point in the math? What terminology can be used to describe what I am articulating?
.5 *.5+1.5*1.5 =z2 z2 =2.5 The square root of 2.5=1.58
But the product of multiplying the fractions isn't a multiplication of them it is s division of them. In effect they are not being "multiplied."
Now lets say you had a different scale where by the it was 15 millimeters and 5 millimeters. Or an entirely different scale equal to 1.5 to 5 but not in inches and fractions. Again reverting back to the above of 15 inches and 5 inches. But in this can 15 inches really doesn't equal 15 inches it really equals 1.5 but you are using 15 instead and you are going to divide the end product by 10 later. So in effect you divide 15.81 by ten to get 1.581.
The question being why the inversion? And how does that inversion equal the positive scale multiplication factor of it? See where I am going?
Now I know all well and good how it works. And I know that is how it works. But I just had to stop and ask why?
So in effect you see the equivalency of a division and a multiplication? What does that equivalency mean?
To me that is a concept that needs to be articulated? Is there something more to it?
Do you see what I am getting at? And again, I know that is how it works. But when you multiply by a fraction you are getting less even though you are multiplying, And because you are getting less you haven't really "multiplied?" Even though if you were to change the scale you would get more.
Which means what? It is relative to what we call more than one and less than one?
A fraction of one.
It doesn't really matter if you have a fraction greater than one involved? As 1.5 times 1.5 is 2.25 and not less than 1.5. Although .5 times .5 =.25.
Now your millimeter scale does away with that issue? Because they are always breaking down the scale to a lesser scale by the factor of 10?
In effect they don't deal in less than one. They just decrease the scale until it is a multiplication of more than one.
Off topic.
I mean it is Friday night have one beer and potentially get 61 types of cancer from it. But if you have less than one beer how many times of cancer to you get? A fraction of less than one beer. So you have half of one beer. You get 30.5 types of cancer. No you still get 61.
And how many beers do you have until you get to zero? Zero. Right. So in effect how is that represented in mathematical terms?
But if you have one half of one beer and then one half of one beer how many times of cancer to you get? 61?
And what happens when you get that cancer? A fraction of you is often removed. What fraction will it be? That is represented by the 61 individual types isn't it.
But back on topic.
Why does the inflection work? You would think that it wouldn't work anymore? The fraction really represents a fixed piece of wood.
Multiply the distance of a fixed pieced of wood times a fixed piece of wood and you always get more! Get it?
So why does the math work? The math says you have less when you really have more?
Okay I am flushing the idea out and almost have it. And it has to do with scale. Which means what?
The math scale remains constant so that the end result is right even though the multiplication divides? But I have to ask metaphysically, why is it true?
In effect it is just a representation in the equation without the product really being meaningful? Because of scale? But yet it works for the end result?
So you get rid of the problem of semantics by decreasing the scale until you are no longer multiplying less than one?
Can you see how it could lead to an engineering error some how? Somewhere deep in some plans somewhere? Someone pulls out that number of 1/4 and goes to work with their saw replicating that one quarter?
© 2018 Thomas Paul Murphy
And can you see the steam coming out of that teachers nostrils if you raise your hand and say "You can't multiply fractions of less than one because the product isn't a multiplication it is a division. "
And here is the real difficult student.
"Okay I get it so what do we call a multiplication of less than ones? We need a new term for it. And it can't be division. Because that is out of context."
:)
Humor: "He no longer has his job at the Chemical plant."
One half milliliter squared is really 2.5 milliliters, if 5 milliliters squared equals 25 milliliters?
It isn't a quarter milliliter.
First you convert it to the lesser scale, then you do the multiplication. Then you convert it to the greater scale? No, somehow it converted itself to the greater scale because you first converted it to the lesser scale?
http://www.answers.com/Q/What_is_a_tenth_of_a_milliliter
The lesser scale being a micro-liter?
So 5 micro-liters times 5 micro-liters equals 25 micro-liters. Or 2.5 liters?
So indeed SAE Math doesn't set up right in life for this? Could you change the scale of standard math to make it conform? You would say a quarter inch really isn't a quarter inch it is 2.5 what? 2.5 tenths of an inch?
But who wants to think of things that way?
So the issue is really about the scale being used in the equation? Is it .5 times .5 or 5 times 5, termed at a lesser scale?
And then why doesn't it matter in terms of Z? Can it ever matter in terms of the value of Z? Under what circumstances if any can it matter in terms of the value of Z?
*****'
A Centimeter being the width of a Chinese Finger and an inch the width of a White Americans?
*****'
Okay I think I have it! Lets convert that half inch into millimeters and then back to inches. (Assuming that the value in the equation represents a true value that can and should be relied on.)
One inch equals 25.4 millimeters. So one half of an inch is 12.7 millimeters.
So 12.7 millimeters squared equals 161.29 millimeters. And then we convert that 161.29 millimeters back to inches and get (/25.4).... 6.35 inches.
So indeed one half inch of wood squared doesn't equal a quarter inch of wood it equals 6.35 inches.
So did that Chemistry teacher of mine who had a shrill voice and a terrible temperament say to always convert everything to metric first? Probably. Off topic, did you ever have a teacher that had a shrill voice and a hot temper that you couldn't learn from because you couldn't or didn't want to become one with a mind like that in learning?
Are there people on Wall Street who work things like that into derivative contracts to screw the American public?
Are there evil sh1t brainiacs who listen to human beings think and derail the product of their results at the opportune time with schemes based on the above concepts? I will assert that is the way of the soulless and that it is true.
How many white Americans lost their jobs and careers because of that? How much waste worldwide was created because of that? How much national debt was created by that beast?
*****'
Since writing this I have proved it untrue. I don't have the time to type that proof for you. But in that proof I learned that there is only one length to a side of a squared number whereby the perimeter sum of those lengths equals the value of the area of that squared number. If you want me to type and publish that send me one dollar!
You can't multiply fractions because they don't "Multiply" they divide.
So lets that that you have a board 1.5 inches wide by 5 inches. You want to put that on your table saw and adjust the top of your table saw blade flush with the top of the woods, and you want to then angle over one half inch. Effectively you want to cut strips one quarter inch wide with that angle profile on the top and bottom.
So you do that triangle math. x2*y2=z2. You attempt to do that in your head. One half of an inch of wood squared plus 1.5 inches of wood squared equals what amounts to be the length of that new cut face of wood squared.
So you are going about it in your head and you say one half of an inch times one half of an inch should get me more than one half of an inch. But it doesn't it gets you one quarter inch. But you were multiplying!
Now lets scale that up to see why it doesn't make sense. The distances in the scaled up version and the fraction denominated version are both fixed. How long one is with regard to the other is relative.
Now lets say that the dimensions were really 15 inches wide by 5 inches over on the table saw. Equivalent to the same ratio as 1.5 to .5 or three to one. So 15 times 15 + 5*5= z2
15 by 15 equals 225. 5 x5 =25. So you have 250 and you take the square root of that to get z which equals 15.81.
So why is there an inflection point in the math? What terminology can be used to describe what I am articulating?
.5 *.5+1.5*1.5 =z2 z2 =2.5 The square root of 2.5=1.58
But the product of multiplying the fractions isn't a multiplication of them it is s division of them. In effect they are not being "multiplied."
Now lets say you had a different scale where by the it was 15 millimeters and 5 millimeters. Or an entirely different scale equal to 1.5 to 5 but not in inches and fractions. Again reverting back to the above of 15 inches and 5 inches. But in this can 15 inches really doesn't equal 15 inches it really equals 1.5 but you are using 15 instead and you are going to divide the end product by 10 later. So in effect you divide 15.81 by ten to get 1.581.
The question being why the inversion? And how does that inversion equal the positive scale multiplication factor of it? See where I am going?
Now I know all well and good how it works. And I know that is how it works. But I just had to stop and ask why?
So in effect you see the equivalency of a division and a multiplication? What does that equivalency mean?
To me that is a concept that needs to be articulated? Is there something more to it?
Do you see what I am getting at? And again, I know that is how it works. But when you multiply by a fraction you are getting less even though you are multiplying, And because you are getting less you haven't really "multiplied?" Even though if you were to change the scale you would get more.
Which means what? It is relative to what we call more than one and less than one?
A fraction of one.
It doesn't really matter if you have a fraction greater than one involved? As 1.5 times 1.5 is 2.25 and not less than 1.5. Although .5 times .5 =.25.
Now your millimeter scale does away with that issue? Because they are always breaking down the scale to a lesser scale by the factor of 10?
In effect they don't deal in less than one. They just decrease the scale until it is a multiplication of more than one.
Off topic.
I mean it is Friday night have one beer and potentially get 61 types of cancer from it. But if you have less than one beer how many times of cancer to you get? A fraction of less than one beer. So you have half of one beer. You get 30.5 types of cancer. No you still get 61.
And how many beers do you have until you get to zero? Zero. Right. So in effect how is that represented in mathematical terms?
But if you have one half of one beer and then one half of one beer how many times of cancer to you get? 61?
And what happens when you get that cancer? A fraction of you is often removed. What fraction will it be? That is represented by the 61 individual types isn't it.
But back on topic.
Why does the inflection work? You would think that it wouldn't work anymore? The fraction really represents a fixed piece of wood.
Multiply the distance of a fixed pieced of wood times a fixed piece of wood and you always get more! Get it?
So why does the math work? The math says you have less when you really have more?
Okay I am flushing the idea out and almost have it. And it has to do with scale. Which means what?
The math scale remains constant so that the end result is right even though the multiplication divides? But I have to ask metaphysically, why is it true?
In effect it is just a representation in the equation without the product really being meaningful? Because of scale? But yet it works for the end result?
So you get rid of the problem of semantics by decreasing the scale until you are no longer multiplying less than one?
Can you see how it could lead to an engineering error some how? Somewhere deep in some plans somewhere? Someone pulls out that number of 1/4 and goes to work with their saw replicating that one quarter?
© 2018 Thomas Paul Murphy
And can you see the steam coming out of that teachers nostrils if you raise your hand and say "You can't multiply fractions of less than one because the product isn't a multiplication it is a division. "
And here is the real difficult student.
"Okay I get it so what do we call a multiplication of less than ones? We need a new term for it. And it can't be division. Because that is out of context."
:)
Humor: "He no longer has his job at the Chemical plant."
One half milliliter squared is really 2.5 milliliters, if 5 milliliters squared equals 25 milliliters?
It isn't a quarter milliliter.
First you convert it to the lesser scale, then you do the multiplication. Then you convert it to the greater scale? No, somehow it converted itself to the greater scale because you first converted it to the lesser scale?
http://www.answers.com/Q/What_is_a_tenth_of_a_milliliter
The lesser scale being a micro-liter?
So 5 micro-liters times 5 micro-liters equals 25 micro-liters. Or 2.5 liters?
So indeed SAE Math doesn't set up right in life for this? Could you change the scale of standard math to make it conform? You would say a quarter inch really isn't a quarter inch it is 2.5 what? 2.5 tenths of an inch?
But who wants to think of things that way?
So the issue is really about the scale being used in the equation? Is it .5 times .5 or 5 times 5, termed at a lesser scale?
And then why doesn't it matter in terms of Z? Can it ever matter in terms of the value of Z? Under what circumstances if any can it matter in terms of the value of Z?
*****'
A Centimeter being the width of a Chinese Finger and an inch the width of a White Americans?
*****'
Okay I think I have it! Lets convert that half inch into millimeters and then back to inches. (Assuming that the value in the equation represents a true value that can and should be relied on.)
One inch equals 25.4 millimeters. So one half of an inch is 12.7 millimeters.
So 12.7 millimeters squared equals 161.29 millimeters. And then we convert that 161.29 millimeters back to inches and get (/25.4).... 6.35 inches.
So indeed one half inch of wood squared doesn't equal a quarter inch of wood it equals 6.35 inches.
So did that Chemistry teacher of mine who had a shrill voice and a terrible temperament say to always convert everything to metric first? Probably. Off topic, did you ever have a teacher that had a shrill voice and a hot temper that you couldn't learn from because you couldn't or didn't want to become one with a mind like that in learning?
Are there people on Wall Street who work things like that into derivative contracts to screw the American public?
Are there evil sh1t brainiacs who listen to human beings think and derail the product of their results at the opportune time with schemes based on the above concepts? I will assert that is the way of the soulless and that it is true.
How many white Americans lost their jobs and careers because of that? How much waste worldwide was created because of that? How much national debt was created by that beast?
*****'
Since writing this I have proved it untrue. I don't have the time to type that proof for you. But in that proof I learned that there is only one length to a side of a squared number whereby the perimeter sum of those lengths equals the value of the area of that squared number. If you want me to type and publish that send me one dollar!
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