## Is it possible for a physical object to be 1-dimensional?

Is it possible for a physical object to be 1-dimensional?

Is it possible for a physical object to be four-dimensional? This depends a bit on what you mean by a "physical object". But it seems plausible to say that the could be a four-dimensional world with four-dimensional objects in it, and why should we not in talking about such a possible world call such objects physical objects? I would address your question in the same way. There could be a one-dimensional world, and there could be objects in it. Again, it seems plausible to say of these one-dimensional objects that they are the physical objects of that one-dimensional world. But then again, if someone where to feel very strongly that the expression "physical object" should be reserved for three-dimensional objects, I for one would not want to get into a long argument over this point.

Now another question you may have in mind is whether there can be one-dimensional objects in our three-dimensional space. We can certainly describe such objects geometrically, so they are possible in this sense (and, again, the question whether we should call such an object a physical object seems to me to be of little interest). Whether the existence of such objects is consistent with the natural laws of our universe and, if so, whether we could detect them, are different questions which, I think, you are not asking.

Is it possible for a physical object to be four-dimensional? This depends a bit on what you mean by a "physical object". But it seems plausible to say that the could be a four-dimensional world with four-dimensional objects in it, and why should we not in talking about such a possible world call such objects physical objects? I would address your question in the same way. There could be a one-dimensional world, and there could be objects in it. Again, it seems plausible to say of these one-dimensional objects that they are the physical objects of that one-dimensional world. But then again, if someone where to feel very strongly that the expression "physical object" should be reserved for three-dimensional objects, I for one would not want to get into a long argument over this point. Now another question you may have in mind is whether there can be one-dimensional objects in our three-dimensional space. We can certainly describe such objects geometrically, so they are possible in this sense (and,...

## A friend and I were discussing our philosophy class a while ago, and somehow we

A friend and I were discussing our philosophy class a while ago, and somehow we got onto the subject of the properties of things and the definition of a place. We began to argue about whether you can be in an object or in a place. I said that you can only be in an object and to be in a place is impossible. But you can be at a place. Example: you are in the building, but you are at the DMV. She said the opposite. That it is possible to be in a place. Who is correct?

The in/at variation is a convention of the English language and has no equivalent in many other languages. It seems to mark no significant underlying distinction, and your question is then one about proper English.

Understood in this spirit, I would say that you are both right. With some places we use "at", with others "in". Consider two buildings, for example, my school and my house. One could say that I am in the first building or at school. And one could say that I am in the second building, or in my house, or in my home, or at home, or at my place.

I assume a grammarian could give you a general rule about when we use "in" and when "at". But, as my example shows, this rule cannot draw on the type of location alone.

The in/at variation is a convention of the English language and has no equivalent in many other languages. It seems to mark no significant underlying distinction, and your question is then one about proper English. Understood in this spirit, I would say that you are both right. With some places we use "at", with others "in". Consider two buildings, for example, my school and my house. One could say that I am in the first building or at school. And one could say that I am in the second building, or in my house, or in my home, or at home, or at my place. I assume a grammarian could give you a general rule about when we use "in" and when "at". But, as my example shows, this rule cannot draw on the type of location alone.

## Is the physical world proportional? What I mean is: is it possible, for instance

Is the physical world proportional? What I mean is: is it possible, for instance, that we find a solar system exactly like ours except for the fact that every object (planets, stones, animals, trees, etc.) is one thousand times longer or less long? What if only twice longer? And what about a different universe where even atoms (and elementary particles, if they have any length at all) were one thousand times "longer"? Is this meaningless?

With regard to both questions, I understand you as imagining that objects are longer or shorter in all dimensions (not merely in one dimension). So spheres would still be spheres, except larger or smaller ones. Right?

On your first question, this is not possible if we hold fixed the laws of nature holding in this universe. To illustrate: In your Twin Solar System, scaled up by a factor of 2, Twin Earth would have eight times as much mass, and gravity near its surface would be roughly twice as great (surface gravity is proportional to the planet's mass divided by the square of it radius). Like the Earth, a scaled-up object would have eight times as much mass, so the gravitational force acting on it (its weight) would be 16 times greater. Now imagine this object suspended by a string. This string would be thicker in two dimensions, hence four times stronger. But the object's weight would be 16 times greater! So, on Earth, the string may be sufficiently strong to support the object even while on Twin Earth the counterpart string would not be strong enough to support the counterpart object. Examples could be multiplied. A Twin-Earth parachutist would also have 16 times as much weight as her counterpart on Earth while her parachute's surface would be only four times as large. Likewise for scaled-up planes, where the wing surface area (creating lift) would not keep up with the increased weight; scaled-up replicas of planes we use here would not be able to fly on Twin Earth. (The examples ignore more subtle differences: Because Twin Earth has higher surface gravity, it would have higher atmospheric pressure and density than our Earth, and it would also be a bit more compressed which would lead to a further increase in its surface gravity.) You see the general point: In many ways, other things would not be the same in a scaled-up (or scaled-down) solar system, because some of its parameters (e.g., forces acting) would vary with the scaling factor, others with the square of the scaling factor, and so on. Interestingly, however, one thing could be the same: Twin Earth could be circling Twin Sun in a stable orbit once a year. Gravitational and centrifugal forces acting on Twin Earth would balance out, both being 16 times what they are in our solar system.

On your second question, yes, I think this would be meaningless for lack of a common benchmark in terms of which lengths could be measured in both universes.

With regard to both questions, I understand you as imagining that objects are longer or shorter in all dimensions (not merely in one dimension). So spheres would still be spheres, except larger or smaller ones. Right? On your first question, this is not possible if we hold fixed the laws of nature holding in this universe. To illustrate: In your Twin Solar System, scaled up by a factor of 2, Twin Earth would have eight times as much mass, and gravity near its surface would be roughly twice as great (surface gravity is proportional to the planet's mass divided by the square of it radius). Like the Earth, a scaled-up object would have eight times as much mass, so the gravitational force acting on it (its weight) would be 16 times greater. Now imagine this object suspended by a string. This string would be thicker in two dimensions, hence four times stronger. But the object's weight would be 16 times greater! So, on Earth, the string may be sufficiently strong to support the object even while on Twin...