There is something about this “thought experiment” that I don’t understand. I’m not even sure about the simplest solution of the simplest case: the case in which one guest-candidate shows up, and the existing guests are all asked to move up one room number, emptying Room One (if I might call it that) for the new guest.This is the only way in which I have been able to understand the “Room One” solution to the Infinite Hotel experiment. The hotel is described as having an infinite number of rooms, each with a guest in it. When all the guests are asked to move to a room of one higher number, it seems to me that nothing has necessarily changed in substance; it is still a hotel with an infinite number of rooms, each with a guest in it--and with an empty twenty-by-thirty-foot box at the near end.
Would the “one extra guest to be accommodated” scenario be satisfied by a person stating that the hotel company could simply construct a minimally-sufficient twenty-by-thirty-foot utility-connected box at the hotel’s near end?I know “making another hotel room” is a rather silly solution, but then so is the notion that one could make an infinite number of people change hotel rooms to accommodate a single person. Moreover, the question at hand is not a matter of real-world practicability, but rather a matter of how the Infinite Hotel experiment could be addressed without arbitrarily changing its conditions. When the standard solution to the “One Extra Guest” scenario is used, Room One--as I stated above--has been changed into as empty a twenty-by-thirty-foot box as my hypothetical constructed one. Each of them functions as a hotel room only insofar as we decide to call them hotel rooms, and place the extra guest in them. Since Room One now has no occupant, yet a description of the condition of the hotel--absent the emptied room--is the same as before, are we not driven to conclude that following the rules of the experiment leads not to its analysis, but to its alteration? How can an ostensible solution to a thought experiment stand, when it is logically indistinguishable from an arbitrary alteration of the experiment’s conditions?
Why not make the thought experiment about filling up an infinite number of infinite hotels? After all, we have decided that there is an infinity of guests, have we not? We have decided that the emptying and filling of hotel rooms can be done instantaneously and for arbitrary reasons. Just because we have to move someone out of one room in order to fill up another doesn’t mean that the first room can’t be immediately occupied by still another guest, a person’s whose absence elsewhere can be filled by yet another. Indeed, why not postulate an infinite number of infinite hotels packed to their limits by a single guest?
The problem, however, is that often we can do nothing about infinities other than wonder about them. As soon as the element of "infinity" has been injected into a consideration (and good luck trying to keep other elements of infinity out) the notion of coming to definite conclusions about the matter is voided. As I was getting at above, the problem is usually one of the conditions of the matter we are considering.
As I will get to in a later post, and as has been dealt with by better minds than mine, the entire notion of "proofs" of God's existence hinge on making the infinite satisfy conditions by which existence might be ascertained--a doomed enterprise.
It is unsurprising that delving into this thought experiment brings another to mind, that of Schrodinger's Cat. (I'm sorry; I don't as yet know how to make umlauts.) The cat has been described as both alive and dead. I will put forth another notion, one having to do with the hotel rooms described above. "Described" is the most salient word I can apply to those rooms, and I suppose that is why my original blog comment was peppered with references I made to the "described" status or character of the rooms and whether or not they were filled. As I tried to say, the Infinite Hotel thought experiment is violated if any of the rooms are empty, and it is unaddressed if the rooms are all filled; violated on the one hand because the conditions of the experiment have been changed arbitrarily, and unaddressed on the other hand in that perpetual filling (even if by a contiguous string of guests forced in at infinite velocity) is only to say without warrant that the infinity of guests can be greater than the infinity of rooms (or is it the other way around? Whichever.)
But what if the room in question is both filled and empty? What if the guest, so to speak, is Schrodinger's cat? Or perhaps it would be better to say, What if we keep--to the extent we might--the question alive in our minds?
I would like to keep the idea of "live" questions in mind as this blog tries to deal with the topic of truth. In so doing I will likely be addressing thoughts like these expressed in a recent article, by David Rothkopf:
We Still Won’t Admit Why So Many People Believe the Big Lie
Many of these lies were created out of necessity. Life is finite. (OK, I’m sorry. It is. Take a deep breath if you need to and then continue reading.) If we don’t come up with a good story about what happens after it ends or why we are here we will all go mad. So we make up preposterous stories about magic people in the sky and then immediately say that we cannot question those stories, that "faith" in them is more important than knowledge of what is real. Why? Because they will not stand up to scrutiny.When challenged, the defenders of these original big lies say the truth is unknowable. Good try. Hard to argue with that. We don’t know there is not an omniscient rule-maker beyond the clouds or a heaven filled with virgins to give pleasure to the faithful so how can you question it? But of course, selling what is unknowable as a truth is one of the most important categories of lies we encounter in life.
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