The problem as you first present it and the problem that you prove are slightly different. The first allows for the possibility that people point at nobody. This makes it so that it cannot be true that everyone is being pointed at more than they are pointing (the total pointed at score is less than or equal to the total pointing score), but it is possible that everyone is pointing more than they are pointed at (silly example is if everyone points at nobody).
Very interesting remark! I had taken pointing at nobody to mean that the person is not pointing at all. If you eat nothing, have you eaten? If you say nothing, have you spoken? If you give nobody money, are you out any funds? So I don't think I agree with what you say. But I suppose you have in mind that some of us are pointing at the window or some such non-person. It is true that I had in mind from the start only instances of pointing from one person to another. To reply to you, however, let me say it this way: I agree with none of your main objection, since in this case you might be able to take some consolation in that, being that I would agree at least with none of it, which on your interpretation might mean that I could still have some agreement. :-)
The problem as you first present it and the problem that you prove are slightly different. The first allows for the possibility that people point at nobody. This makes it so that it cannot be true that everyone is being pointed at more than they are pointing (the total pointed at score is less than or equal to the total pointing score), but it is possible that everyone is pointing more than they are pointed at (silly example is if everyone points at nobody).
Very interesting remark! I had taken pointing at nobody to mean that the person is not pointing at all. If you eat nothing, have you eaten? If you say nothing, have you spoken? If you give nobody money, are you out any funds? So I don't think I agree with what you say. But I suppose you have in mind that some of us are pointing at the window or some such non-person. It is true that I had in mind from the start only instances of pointing from one person to another. To reply to you, however, let me say it this way: I agree with none of your main objection, since in this case you might be able to take some consolation in that, being that I would agree at least with none of it, which on your interpretation might mean that I could still have some agreement. :-)
Haha yes I interpreted pointing “at nobody at all” to mean pointing at something, but not a person.