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Hilberts hotel
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- MarkVitrone
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20 years 8 months ago #8725
by MarkVitrone
Replied by MarkVitrone on topic Reply from Mark Vitrone
I had a reservation but they wouldn't take my Diner's Club so I went to the Holiday Inn where my room was more than finite. In fact, only a skilled Yoga master could sit on the toilet and reach the barely three dimensional toilet paper which was located directly behind and below to the sitter's right hand, as far as possible from useful. 
I made many complaints to the travel agent and she assured me that nothing would be remedied.
I try to separate math truth and reality truth. The questions of infinity and eternity in math and reality are travel agent questions. Meaning that we must visit the number or place to define that number or place. The statement that space and time are infinite is enough. Attempting the quantify infinity especially when mathematics asks us to place that quantity within bounds (like all infinite numbers between 1 and 2 and in essence problems like Zeno, etc). These attempts bring frustration because the solution is unsatisfying. Defining and understanding the relationships of spacial scale is more satisfying because analogy can be made. What comes to mind is the grain of sand encompassing a whole universe type of reasoning. I seem to find that analogy easier to grasp and more fulfilling. Mathematics helps us attempt the approach of reality, its raw pursuit however will lead to unhappiness when debate ensues beyond the point of diminishing returns. Hilbert makes me feel this way because the model doesn't lead to understanding it leads to dissatisfaction similar to greasy roadside diner food when no antacid is present. My question to the panel is WHY? Keeping in mind that my ability to wield the pencil in the world of advanced math is limited, yet my point in questioning the accessibility and utility of this model comes into the realm of its approximation of the reality we know and love. Cheers, MV
I made many complaints to the travel agent and she assured me that nothing would be remedied.I try to separate math truth and reality truth. The questions of infinity and eternity in math and reality are travel agent questions. Meaning that we must visit the number or place to define that number or place. The statement that space and time are infinite is enough. Attempting the quantify infinity especially when mathematics asks us to place that quantity within bounds (like all infinite numbers between 1 and 2 and in essence problems like Zeno, etc). These attempts bring frustration because the solution is unsatisfying. Defining and understanding the relationships of spacial scale is more satisfying because analogy can be made. What comes to mind is the grain of sand encompassing a whole universe type of reasoning. I seem to find that analogy easier to grasp and more fulfilling. Mathematics helps us attempt the approach of reality, its raw pursuit however will lead to unhappiness when debate ensues beyond the point of diminishing returns. Hilbert makes me feel this way because the model doesn't lead to understanding it leads to dissatisfaction similar to greasy roadside diner food when no antacid is present. My question to the panel is WHY? Keeping in mind that my ability to wield the pencil in the world of advanced math is limited, yet my point in questioning the accessibility and utility of this model comes into the realm of its approximation of the reality we know and love. Cheers, MV
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20 years 8 months ago #8621
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<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by MarkVitrone</i>
<br />I had a reservation but they wouldn't take my Diner's Club so I went to the Holiday Inn where my room was more than finite. In fact, only a skilled Yoga master could sit on the toilet and reach the barely three dimensional toilet paper which was located directly behind and below to the sitter's right hand, as far as possible from useful. I made many complaints to the travel agent and she assured me that nothing would be remedied.
I try to separate math truth and reality truth. The questions of infinity and eternity in math and reality are travel agent questions. Meaning that we must visit the number or place to define that number or place. The statement that space and time are infinite is enough. Attempting the quantify infinity especially when mathematics asks us to place that quantity within bounds (like all infinite numbers between 1 and 2 and in essence problems like Zeno, etc). These attempts bring frustration because the solution is unsatisfying. Defining and understanding the relationships of spacial scale is more satisfying because analogy can be made. What comes to mind is the grain of sand encompassing a whole universe type of reasoning. I seem to find that analogy easier to grasp and more fulfilling. Mathematics helps us attempt the approach of reality, its raw pursuit however will lead to unhappiness when debate ensues beyond the point of diminishing returns. Hilbert makes me feel this way because the model doesn't lead to understanding it leads to dissatisfaction similar to greasy roadside diner food when no antacid is present. My question to the panel is WHY? Keeping in mind that my ability to wield the pencil in the world of advanced math is limited, yet my point in questioning the accessibility and utility of this model comes into the realm of its approximation of the reality we know and love. Cheers, MV
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Hilbert's Hotel is a direct consequence of Cantor's treatment of
infinite sets so if Cantor is right then the hotel is an accurate analogy. The two concepts Hilbert was trying to demonstrate was that you can add indefinitely to an infinitely large integer subset without increasing its cardinality and also the fact that the set of reals are so much bigger than the integers that the major domo had to close down the hotel when requested to check in those "types" of guests. These follow from Cantor's proof showing that infinite subsets of the integer set and the set of rationals all have the same size, which he called aleph0, and that real numbers have a larger size he called aleph1.
If Cantor's results give you indigestion, you are in good company.
The large majority of mathematicians today think there should be more sizes for infinite sets (they think the Continuum Hypothesis is false) or don't believe in the notion of completed infinities altogether (though this is more a minority).
My rule of thumb is that if something doesn't make a whole lot of sense for the average educated person, it's probably wrong.
<br />I had a reservation but they wouldn't take my Diner's Club so I went to the Holiday Inn where my room was more than finite. In fact, only a skilled Yoga master could sit on the toilet and reach the barely three dimensional toilet paper which was located directly behind and below to the sitter's right hand, as far as possible from useful.
I made many complaints to the travel agent and she assured me that nothing would be remedied.I try to separate math truth and reality truth. The questions of infinity and eternity in math and reality are travel agent questions. Meaning that we must visit the number or place to define that number or place. The statement that space and time are infinite is enough. Attempting the quantify infinity especially when mathematics asks us to place that quantity within bounds (like all infinite numbers between 1 and 2 and in essence problems like Zeno, etc). These attempts bring frustration because the solution is unsatisfying. Defining and understanding the relationships of spacial scale is more satisfying because analogy can be made. What comes to mind is the grain of sand encompassing a whole universe type of reasoning. I seem to find that analogy easier to grasp and more fulfilling. Mathematics helps us attempt the approach of reality, its raw pursuit however will lead to unhappiness when debate ensues beyond the point of diminishing returns. Hilbert makes me feel this way because the model doesn't lead to understanding it leads to dissatisfaction similar to greasy roadside diner food when no antacid is present. My question to the panel is WHY? Keeping in mind that my ability to wield the pencil in the world of advanced math is limited, yet my point in questioning the accessibility and utility of this model comes into the realm of its approximation of the reality we know and love. Cheers, MV
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Hilbert's Hotel is a direct consequence of Cantor's treatment of
infinite sets so if Cantor is right then the hotel is an accurate analogy. The two concepts Hilbert was trying to demonstrate was that you can add indefinitely to an infinitely large integer subset without increasing its cardinality and also the fact that the set of reals are so much bigger than the integers that the major domo had to close down the hotel when requested to check in those "types" of guests. These follow from Cantor's proof showing that infinite subsets of the integer set and the set of rationals all have the same size, which he called aleph0, and that real numbers have a larger size he called aleph1.
If Cantor's results give you indigestion, you are in good company.
The large majority of mathematicians today think there should be more sizes for infinite sets (they think the Continuum Hypothesis is false) or don't believe in the notion of completed infinities altogether (though this is more a minority).
My rule of thumb is that if something doesn't make a whole lot of sense for the average educated person, it's probably wrong.
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