Difference between revisions of "Talk:Benderama"
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:Mass is directly proportional to the ''cube'' of length; that is, mass scales directly with volume. If Bender's height is scaled by 60% (and all other linear measures are similarly scaled by 60%), then Bender's volume is 60%^3 = 21.6% of the volume of the original Bender, thus 21.6% of the mass of the original. This has nothing to do with anything in the episode, but is rather a basic result from geometry or physics. Imagine that you have a perfect cube of material that measures 1 m on a side, and weighs 1 kg (thus having a density of 1 kg/m^3). Now make a scale copy of that cube that is 50% smaller. The new cube is half a meter on a side, and still has a density of 1 kg/m^3. Mass is density times volume, thus the new cube has a mass of (1 kg/m^3)*(0.5 m)^3 = 0.125 kg. --[[Special:Contributions/71.83.120.33|71.83.120.33]] 17:19, 25 June 2011 (CEST) | :Mass is directly proportional to the ''cube'' of length; that is, mass scales directly with volume. If Bender's height is scaled by 60% (and all other linear measures are similarly scaled by 60%), then Bender's volume is 60%^3 = 21.6% of the volume of the original Bender, thus 21.6% of the mass of the original. This has nothing to do with anything in the episode, but is rather a basic result from geometry or physics. Imagine that you have a perfect cube of material that measures 1 m on a side, and weighs 1 kg (thus having a density of 1 kg/m^3). Now make a scale copy of that cube that is 50% smaller. The new cube is half a meter on a side, and still has a density of 1 kg/m^3. Mass is density times volume, thus the new cube has a mass of (1 kg/m^3)*(0.5 m)^3 = 0.125 kg. --[[Special:Contributions/71.83.120.33|71.83.120.33]] 17:19, 25 June 2011 (CEST) | ||
::I interpreted it as 60% the volume, which would imply 60% as massive. I'll watch the episode again, but you're probably right that it's a 3/5 scale length ratio. | ::I interpreted it as 60% the volume, which would imply 60% as massive. I'll watch the episode again, but you're probably right that it's a 3/5 scale length ratio. | ||
:::In general, when people talk about scale, they are referring to linear scale. Hence a 1:45 scale model of a train would be a model train that is 1/45th of the length of a full sized train. Thus typical usage would suggest that Bender is scaled by a linear factor of 60% (i.e. all linear measurements are scaled to 60%). If we assume that volume is scaled by 60%, then linear measures would be scaled by about 84% (the cube root of 60%). Visually, it would appear to me that the copies are 60% of the height of the original, rather than 84%. --[[Special:Contributions/71.83.120.33|71.83.120.33]] 19:27, 25 June 2011 (CEST) | |||
Revision as of 19:27, 25 June 2011
God Entity
I believe the voice for the God entity is used in this episode, I'm wondering if it's a purposeful reference to that character. When Bender is defeated in the fight against the ugly giant, light appears on Bender and a voice is heard saying "Walk into the light Bender." and Bender replies saying "Aww, man, do I have to walk?!" Polantaris 07:56, 24 June 2011 (CEST)
- I'm not sure. It sounds more like a general, deep voice to me. I don't see why the Galactic Entity would bother talking to the big Bender. - akitalk 08:08, 24 June 2011 (CEST)
The Formula
The mass of an individual generation is just 60% the mass of a bender in the previous generation. So given the original mass M_0, the mass of a Bender in generation n should be M_0*0.6^(n-1) (assuming n starts at 1). So, given 2^(n-1) Benders per generation, the total mass should be the sum from n=1 to N of M_0*(1.2)^(n-1) = M_0*(1.2^n -1/)0.2 which does not converge as N -> infinity. (1.2 > 1). The article currently says that the mass changes by the cube of the scaling factor. Did I miss something in the episode, or should the mass of a Bender in generation n just be the 60% the mass of a bender in generation n-1 (consider the first duplication: In generation 2, there are 2 Benders, each massing 60% of the original. So, the mass of this generation is M_0*0.6*2; adding this to the original M_0 matches the formula above, 2.2*M_0).
- Mass is directly proportional to the cube of length; that is, mass scales directly with volume. If Bender's height is scaled by 60% (and all other linear measures are similarly scaled by 60%), then Bender's volume is 60%^3 = 21.6% of the volume of the original Bender, thus 21.6% of the mass of the original. This has nothing to do with anything in the episode, but is rather a basic result from geometry or physics. Imagine that you have a perfect cube of material that measures 1 m on a side, and weighs 1 kg (thus having a density of 1 kg/m^3). Now make a scale copy of that cube that is 50% smaller. The new cube is half a meter on a side, and still has a density of 1 kg/m^3. Mass is density times volume, thus the new cube has a mass of (1 kg/m^3)*(0.5 m)^3 = 0.125 kg. --71.83.120.33 17:19, 25 June 2011 (CEST)
- I interpreted it as 60% the volume, which would imply 60% as massive. I'll watch the episode again, but you're probably right that it's a 3/5 scale length ratio.
- In general, when people talk about scale, they are referring to linear scale. Hence a 1:45 scale model of a train would be a model train that is 1/45th of the length of a full sized train. Thus typical usage would suggest that Bender is scaled by a linear factor of 60% (i.e. all linear measurements are scaled to 60%). If we assume that volume is scaled by 60%, then linear measures would be scaled by about 84% (the cube root of 60%). Visually, it would appear to me that the copies are 60% of the height of the original, rather than 84%. --71.83.120.33 19:27, 25 June 2011 (CEST)
- I interpreted it as 60% the volume, which would imply 60% as massive. I'll watch the episode again, but you're probably right that it's a 3/5 scale length ratio.