The 10th Dimension?

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 BaldFriede wrote:

 Dean wrote:

 BaldFriede wrote:

Actually we can and will appear in several places to a flatlander. Just imagine you only hold the five fingers of a hand into flatland; they will not even seem to be connected for a flatlander; all they will see are five separate circles.
Also imagine flatland to be slightly curved in three-dimensional space.. We could then have part of a foot and part of a thigh in flatland at the same time, provided flatland crossed the leg twice the way it is folded up.

Yes this is correct - except you are still restricted by the limitations of your dimensions and the flatlanders would be able to determine the extent of those limitations - your finger tips can exist in five locations, but not any five locations - repeated observations by the flatlanders would soon discover a pattern and relationship and hence deduce an "other-dimension" connection between them. Of course they would never be able to prove their theories, but the empirical data would support them.

Did you completely think through what you said? Just think what that would mean for our own three dimensions: Any phenomena in which several "seemingly "separated" entities appear close together all the time might be connected in a higher dimension then. Like for example an atom and its electrons (let's notn take quantum interpretations of atoms into account here for simplicity's sake).

Let's not extrapolate things too wildly in the opposite direction.  

I did say that the relationships observed by the Flatlanders could result in them drawing conclusions and theories and we would know whether those theories were true, but they would not. 

They could use their theories to predict things from their findings - for example: if they found four contact points within a given area, they would be able to say that the possible location of the fifth (should it appear) could not be more than a few mm away; If they measured the contact are of each point and compared that to a database they would be able to calculate the relative size of the missing digit and use that data to predict where the contact point could be to a high degree of accuracy. 

What they could not predict would be whether the missing finger tip would make contact or not, they also would not be able to work out what the physical connection between the points would be, whether it were a 3rd dimensional structure, a force or simply magic. They could not deduce a hand from the finger tips alone.

This is very much like what is being proposed by physicists and cosmologists. They gather data, make theories and use those theories to make predictions. What they cannot do is state emphatically that the theories are truths - all they can say is the theory fits the known data.

But yes, if we observed a phenomena in which several "seemingly separated" entities appear close together all the time then we could speculate that they might be connected in a higher dimension. The problem for us is visualising that higher dimension and determining what that connective structure and/or force is, or is likely to be. 

However, the first thing we would do would be to experiment on them, probably by throwing rocks at them. 