Infinite Resistance
- Thread starter physis
- Start date
- Status
charlie
Senior Member
- Location
- Indianapolis
Re: Infinite Resistance
For you Sam, nothing but the best.
For you Sam, nothing but the best.
physis
Senior Member
Re: Infinite Resistance
Rob, I like the way you put that. But the problem with me is that where "the bubble bursts" is exactly what I'm curious about. Something interesting happens there. I think it's partly a language failure and also relates to the fundimental structure of nature. I'm not arguing that 2 plus 2 isn't 4.
Re: Infinite Resistance
now, refer to the plot that paul32 posted above. look at either curve as it approaches an axis. now look even closer. now take out a magnifying glass and look even closer. now take out a microscope and look still closer.
do you see what happens in that region?
not very much...the curve just keeps getting closer & closer to the axis...forever! (i.e to infinity). that is the "something interesting" that happens there. they keep getting closer, but they never touch. ever.
Boy, I'm sure glad I didn't give you that bag filled with cash, or you'd be out buying an electron microscope in order to prove that region of the curve is really filled with thousands of tiny, quivering pixels.
the "bubble bursts" at a mathematical discontinuity. The interesting thing that happens there is that it suddenly becomes undefined. Nothing more and nothing less (in this case, at least). But it is a "language failure" of sorts...you are refusing (or unwilling?) to accept elements of the mathematical language, and/or the thinking that accompanies it. As for the part about the fundamental structure of nature...the math describes it perfectly & completely (again, in this case at least).
now, refer to the plot that paul32 posted above. look at either curve as it approaches an axis. now look even closer. now take out a magnifying glass and look even closer. now take out a microscope and look still closer.
do you see what happens in that region?
not very much...the curve just keeps getting closer & closer to the axis...forever! (i.e to infinity). that is the "something interesting" that happens there. they keep getting closer, but they never touch. ever.
Boy, I'm sure glad I didn't give you that bag filled with cash, or you'd be out buying an electron microscope in order to prove that region of the curve is really filled with thousands of tiny, quivering pixels.
al hildenbrand
Senior Member
- Location
- Minnesota
- Occupation
- Electrical Contractor, Electrical Consultant, Electrical Engineer
Re: Infinite Resistance
Hey Sam,
There are several ways to arrive at this point in the language of math. </font>
IMO, the verbal parallel is in trying to describe God by any name. We can use all kinds of verbal tricks to point in the direction of what is unspeakable, vast beyond knowing. But to quantify. . .?
The language of math doesn't give us the tricks of expression to quantify Infinity.
Now, using math to "point in the direction" of the indeterminate, that's another matter. Calculus has been a major stepping stone. Likening calculus to poetry, maybe the next level in understanding will come in putting the poem to music.
They're coming to take me away. . .ha, ha. . .he, he. . .ho, ho. . .
Hey Sam,
There are two languages in the conversation of this thread. One is verbal and the other is mathematical. In the language of math, as has been said by others in this thread, division by zero is indeterminate.
There are several ways to arrive at this point in the language of math. </font>
- <font size="2" face="Verdana, Helvetica, sans-serif">0 ? 0</font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Infinity ? Infinity</font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Infinity - Infinity</font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Etc.</font>
IMO, the verbal parallel is in trying to describe God by any name. We can use all kinds of verbal tricks to point in the direction of what is unspeakable, vast beyond knowing. But to quantify. . .?
The language of math doesn't give us the tricks of expression to quantify Infinity.
Now, using math to "point in the direction" of the indeterminate, that's another matter. Calculus has been a major stepping stone. Likening calculus to poetry, maybe the next level in understanding will come in putting the poem to music.
They're coming to take me away. . .ha, ha. . .he, he. . .ho, ho. . .
- Location
- Lockport, IL
- Occupation
- Retired Electrical Engineer
Re: Infinite Resistance
With thanks and apologies to Douglas Adams.
"In pace requescat."
If we allow those two expressions as mere conversational representations of actual mathematical concepts, then I can prove (I kid you not), using valid mathematical processes (none of this 2 = 1 stuff), that both are equal to 42!
With thanks and apologies to Douglas Adams.
"In pace requescat."
Re: Infinite Resistance
mathematically speaking, if you were to throw a rock at a window it would never theoretically hit the window. see, if you were to divide the distance between the rock and the window by 1/2 consecutively the distance from the window to the rock would never reach zero(contact)...or something like that!
mathematically speaking, if you were to throw a rock at a window it would never theoretically hit the window. see, if you were to divide the distance between the rock and the window by 1/2 consecutively the distance from the window to the rock would never reach zero(contact)...or something like that!
- Location
- Lockport, IL
- Occupation
- Retired Electrical Engineer
Re: Infinite Resistance
Nice try, justin. An old paradox. I recall discussing it with Pythagoras (or maybe it was his brother).
But if you add up a vast great number of numbers that keep getting smaller, the sum might eventually exceed any number you might chose to name. That particular infinite series, 1/2 plus 1/4 plus 1/8 plus 1/16 on and on to infinity converges to a value of 1.0. The addition of the infinite number of decreasing time intervals (e.g., the time for the rock to move from the 1/8 position to the position that is 1/16 closer to the window) also converges. Math does permit the rock to hit the window.
Nice try, justin. An old paradox. I recall discussing it with Pythagoras (or maybe it was his brother).
But if you add up a vast great number of numbers that keep getting smaller, the sum might eventually exceed any number you might chose to name. That particular infinite series, 1/2 plus 1/4 plus 1/8 plus 1/16 on and on to infinity converges to a value of 1.0. The addition of the infinite number of decreasing time intervals (e.g., the time for the rock to move from the 1/8 position to the position that is 1/16 closer to the window) also converges. Math does permit the rock to hit the window.
al hildenbrand
Senior Member
- Location
- Minnesota
- Occupation
- Electrical Contractor, Electrical Consultant, Electrical Engineer
Re: Infinite Resistance
Charlie B,
I always wondered how Deep Thought arrived at 42.
Charlie B,
I always wondered how Deep Thought arrived at 42.
charlie
Senior Member
- Location
- Indianapolis
Re: Infinite Resistance
You know, I have decided that (after reading all this) my IQ is the cube root of smart. :roll:
You know, I have decided that (after reading all this) my IQ is the cube root of smart. :roll:
Re: Infinite Resistance
O.K.
Forget about everything I said so far. I was lying. Here is the real story about what happens in that region. I'm not supposed to tell anyone, but I'll make an exception just this once. (But don't tell anyone else!!!)
As you enter that mysterious region (I can't call it undefined, right?), billions & billions of tiny aliens jump off the axes & attack you, shrink you down to mini-size, and load you on their mothership. Then they set the autopilot & send you off to their home planet, where you're unloaded and expanded to two times your original size. Once expanded, they use you as an advertising prop in front of car dealership or hamburger stand. Meanwhile, back on Earth, some other chap comes along and looks at that mysterious region and asks "I wonder what goes on in there?". But there's nobody there to warm him to beware. Why? Because you've been captured by those aliens and sent off to their home planet, that's why.
There. Now you know the truth about what happens when you divide by zero. And all of mankind is left to bear the burden of your insatiable curiousity.
are you happy now?
(LOLOL)
LOL! Now how did you guess that? And when was I declared Keeper of The Mathematical Rules? And how do you know if my hands are folded?
O.K.
Forget about everything I said so far. I was lying. Here is the real story about what happens in that region. I'm not supposed to tell anyone, but I'll make an exception just this once. (But don't tell anyone else!!!)
As you enter that mysterious region (I can't call it undefined, right?), billions & billions of tiny aliens jump off the axes & attack you, shrink you down to mini-size, and load you on their mothership. Then they set the autopilot & send you off to their home planet, where you're unloaded and expanded to two times your original size. Once expanded, they use you as an advertising prop in front of car dealership or hamburger stand. Meanwhile, back on Earth, some other chap comes along and looks at that mysterious region and asks "I wonder what goes on in there?". But there's nobody there to warm him to beware. Why? Because you've been captured by those aliens and sent off to their home planet, that's why.
There. Now you know the truth about what happens when you divide by zero. And all of mankind is left to bear the burden of your insatiable curiousity.
are you happy now?
(LOLOL)
physis
Senior Member
Re: Infinite Resistance
----Disclaimer----
THIS IS A GUEST POST (NOT PHYSIS GENERATED)
In discussing the subject here with Sam, I have asked him to please let me comment:
The rules of math can not be changed. If you have nothing, it doesn't matter how many times you want to divide it or multiply it, You still have nothing. If you flip it over,(or as Sam prefers I say, "the inverse of nothing") still leaves you with nothing.
----Disclaimer----
THIS IS A GUEST POST (NOT PHYSIS GENERATED)
In discussing the subject here with Sam, I have asked him to please let me comment:
The rules of math can not be changed. If you have nothing, it doesn't matter how many times you want to divide it or multiply it, You still have nothing. If you flip it over,(or as Sam prefers I say, "the inverse of nothing") still leaves you with nothing.
charlie
Senior Member
- Location
- Indianapolis
Re: Infinite Resistance
Sha-Zam
Sha-Zam
Re: Infinite Resistance
Posted by someone other than Physis:
Sam, since you like this topic, I think you would really like reading about quantum mechanics. Pick up one at the library and give it a whirl. One word of caution though: there are a lot quack "authors" who try to use quantum mechanics to prove everything from religion to aliens and mind reading.
STeve
Posted by someone other than Physis:
Thats exactly why I brought up conductance earlier. The infinity is actually just the inverse of zero current, which is really isn't that mysterious.
Sam, since you like this topic, I think you would really like reading about quantum mechanics. Pick up one at the library and give it a whirl. One word of caution though: there are a lot quack "authors" who try to use quantum mechanics to prove everything from religion to aliens and mind reading.
STeve
- Location
- Lockport, IL
- Occupation
- Retired Electrical Engineer
Re: Infinite Resistance
Was that a typo? Didn?t you mean ?quark authors??
- Location
- Lockport, IL
- Occupation
- Retired Electrical Engineer
Re: Infinite Resistance
</font>
But I still insist that if you divide nothing by nothing, you get a result of 42. Here is the proof:
</font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Take 42, multiply it by the sine of X, and divide the result by X.</font>
- <font size="2" face="Verdana, Helvetica, sans-serif">When X has a value of zero, you will be dividing zero by zero.</font>
- <font size="2" face="Verdana, Helvetica, sans-serif">But the limit, as X approaches zero, of { 42 sin ( X ) / X } is 42!</font>
- Status