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/sci/ - Science & Math

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11247041 No.11247041 [Reply] [Original]

A 3 dimensional cube 10cm X 10cm X 10cm of steel, that has a density of 7.8g/cm3 weighs 7800g or 7.8kg.

How much does a 4 dimensional cube with dimensions 10cm X 10cm X 10cm X 10cm weigh?

>> No.11247058

Depends on the density in g/cm^4.

>> No.11247067
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11247067

>>11247041
Nothing, because its not subject to our gravity

>> No.11247071

>>11247067
whats its mass then

>> No.11247086

Assuming you don't include time as a dimension, I think it would weigh infinite grams. Let's ignore mass for a second and take a look at volume and area. How much area does a 10x10x10 cube have from a 2 dimensional perspective? Given that a 2 dimensional object has 0 thickness, the area would be 10*10*10/0. The same concept applies to the first dimension. So if a 4 dimensional object had equal lengths of 10 for all dimensions, its volume would be 10*10*10*10/0. Multiply that by the the density and you get 78000/0 grams. So, basically, it would have infinite 3 dimensional mass.

>> No.11247141

your question is ill posed OP
>>11247086
>psued: the post

>> No.11247155

How ever much one molecule of 4d steel weighs, multiplied by how many 4d molecules fit in your 4d 10cm*10cm*10cm*10cm cube.

>> No.11247167

>>11247155
steel isnt made of molecules, its a crystal lattice

>> No.11247193

>>11247167
Your face is a crystal lattice

>> No.11247369

78kg

>> No.11247374

>>11247041
>>11247058
assuming steel is spherical, we can solve for its radius in 3D to solve for its 4D volume. Assuming most efficient packing, we can then solve for many steel molecules would fit in 10000 cm^4. the mass per molecule would be subject to odd consideration however, and what is meant by "most efficient packing", im unsure in this context given repulsion/attraction dynamics and lattice matrices correspondents in other dimensions

>> No.11247392

>>11247041
everyone here is overthinking it. its just 78kg. you can integrate the 3d cubes over the 4d direction from 0 to 10 and you get 78kg

>> No.11247395

>>11247392
thats not a solid object, its just one 3d steel cube placed once per cm along the 4th axis.

>> No.11247396

>>11247392
Who's to say that the 4D portions of each steel molecule holds as much volume or mass

>> No.11247398

>>11247396
4d is to 3d as 3d is to 2d, litterally nothing is altered when summing infinite 2d planes to 3d, so why would anything change from 3d to 4d?

>> No.11247400

>>11247398
cuz we're not summing space, we're summing an object in space. a 3d object can have varying mass densities, per se, along its 2d sheets

>> No.11247404

>>11247400
I'm going off of the assumption that each cube we sum has the same mass, as the OP did not indicate any possible variation

>> No.11247407

>>11247404
but the question isn't a riddle its about steel which is a real object. Also lets say steels 4d mass density is the same, how will its arrangement/lattice density vary in higher dimensions? perfect sphere packing isnt verified possible in all dimensions, all though i think it is in 4D

>> No.11247412

>>11247407
geometric allignment should be considered effectively negligible, as the minute arrangement of atoms in the real world dont differ greatly from a uniform model. at the scale of 1000cm^4, this is not an issue, however at 1x10^-8cm^4 may arise some issues

>> No.11247414

>>11247396
>>11247398
>>11247400
>>11247404
OP here.

If anyone has any idea how much volume an iron/carbon atom occupies in 4 dimensions, or how 4d lattices pack efficiently then even better, but assuming its the same as 3d, it would be interesting to know what it would weigh even if its not completely accurate

>> No.11247438

>>11247041
the dimension meme was a mistake.

>> No.11247459
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11247459

OP here again
I've worked out the simplest case of a 4d iron cube packed the same as a 3d cube.
The width of a metallic iron atom is 126 picometres, so in an extra spacial dimension, you could fit 793.7 million iron atoms across 10cm assuming it has the same 4d diameter.
This means it would weigh about 6.2 billion kg.

>> No.11247508

>>11247459
thank you for working that out, anon
now I can finally die

>> No.11247520

>>11247508
rest in pepperoni