Question about examples used to visualise higher dimensions

[jamesop]

Hi,
I've been reading quite a few popular science books (Michio Kaku, Stephen Hawking) where the specific example for us to visualise how a 4D creature would interact with us is portrayed through us interacting with 2D "flatlanders".
The specific example is how we would lift a 2D flatlander of its universe and then place him back down in some other location. The problem I have with this is for us to interact with, and pickup something it needs to have 3 dimensions, or else we'd have nothing to grip.
So surely a 4D creature would have the same problem picking us up, as we'd also be lacking a fundamental dimension that they need to manipulate us?
Thanks

 

[reasonmclucus]

Hi,
I've been reading quite a few popular science books (Michio Kaku, Stephen Hawking) where the specific example for us to visualise how a 4D creature would interact with us is portrayed through us interacting with 2D "flatlanders".
The specific example is how we would lift a 2D flatlander of its universe and then place him back down in some other location. The problem I have with this is for us to interact with, and pickup something it needs to have 3 dimensions, or else we'd have nothing to grip.
So surely a 4D creature would have the same problem picking us up, as we'd also be lacking a fundamental dimension that they need to manipulate us?
Thanks

You seem to be making the common mistake of thinking that other dimensions would be like length, width and height in some way. That's because our brains are programmed beginning at an early age to think that those are the only types of things that can be dimensions. The Stephen Hawking of my youth was George Gamow. In one of his books (possibly One, Two Three Infinity) he provided a possible drawing of a 4th dimension super cube in 2 dimensions.

Other dimensions are more likely to be different characteristics. We may already be able to detect other dimensions, but don't recognize them as dimensions. For example, gravity cannot be a function of length, width and height. Although the sun has a greater volume than Earth and greater gravity and Earth is larger than the moon and has greater gravity - a black hole much smaller than the moon could have a gravity of many suns.

The spin of subatomic particles might be a dimension as might be any electrical charge.

 

[JK423]

You seem to be making the common mistake of thinking that other dimensions would be like length, width and height in some way.
...
Other dimensions are more likely to be different characteristics.

...
The spin of subatomic particles might be a dimension as might be any electrical charge.

I didnt quite understand your comment. Since we are talking about space-dimensions, each dimension should have [length] units! It cannot be anything else, a random internal degree of freedom, like spin or electrical charge!
Am i right?
I, also, have a great difficulty in understanding the notion of higher dimensions since there cannot exist more than 3 in this world. The argument "our brain can only see 3" doesn't convince me.. They also say, that these extra dimensions are too small too see. Ok, if we also get small enough in order to see them, how would the look like?

 

[arivero]

Really, except for the confusions induced in #2, this is question of mathematics, isn't it? It is just about training. A good thing is to practice with theorems involving a few dimensions, looking for regular n-gons, etc.

Now, #2 has a point if Kaluza Klein theory happens to be a valid interpretation. In such case, the objects that we usually known as fields are to be interpreted as the "rotations" in the extra dimensions.