Michael Egnor talks with podcaster Lucas Skrobot about how we can know we are not zombies

_{Denyse O'Leary

July 5, 2020

Mind, Neuroscience}

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Also: Egnor , a neurosurgeon, told Skrobot: “My wife jokes with me that meeting me is always the worst part of a person’s life.”

Comments

ET: Set subtraction proves that the rationals have a larger cardinality than the naturals. Nope, you can set up a one-to-one correspondence between the natural numbers and the rationals so no element of either set is left out. That only way that can happen is if the sets have the same number of elements. If they don't have the same number of elements then there has to be some element left out. But, just like always, if you follow the scheme linked to above you won't be able to find any left out elements. You have to be desperate to deny that fact. Being right is not being desperate. So order here means any way that makes sense to the person doing it. Anything is fair game. You don't get to rule out orders you don't like. As long as nothing is left out the scheme is good.JVL_{July 24, 2020
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A set is countable if you can count its elements. If the set is infinite, being countable means that you are able to put the elements of the set in order just like natural numbers are in order.
So order here means any way that makes sense to the person doing it.ET_{July 24, 2020
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Set subtraction proves that the rationals have a larger cardinality than the naturals. You have to be desperate to deny that fact.ET_{July 24, 2020
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ET: LoL! @ JVL- still can’t find that obstacle. I take it that none exist. Let's see you do it then. (The primes don't have a pattern by the way.) Still can’t pair the first positive integer with the first positive rational. You don't have to. https://www.homeschoolmath.net/teaching/rational-numbers-countable.php And I said subset which makes the rationals a superset. Higher state means it has a higher cardinality, also. Nope, the rationals have the same cardinality as the natural numbers, the one-to-one scheme is easy to find (see the link above).JVL_{July 24, 2020
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LoL! @ JVL- still can't find that obstacle. I take it that none exist. Still can't pair the first positive integer with the first positive rational. And I said subset which makes the rationals a superset. Higher state means it has a higher cardinality, also.ET_{July 24, 2020
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ET, No problemo. In my reply, I did a similar thing and accidentally started by typing "any rational divided by a rational ...".daveS_{July 24, 2020
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ET: Yes, anyone can find the relative place for primes. Nothing prevents it. That JVL cannot demonstrate an obstacle means none exist. Uh huh. Let's see you do it then. With rationals vs integers no one can pair the first positive integer with the first positive rational. It’s impossible. Cantor came up with a one-to-one correspondence between the integers and the rationals which is how he proved they had the same cardinality. You can look up the scheme. Higher state means it is a superset of the natural subset. Why not just say superset then?JVL_{July 24, 2020
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Thank you for catching that mistake. It was supposed to read any natural divided by a natural is a rational- lost my train of thought. Thanks for the wake-upET_{July 24, 2020
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ET,
OK, so the way to a one-to-one correspondence with naturals and rationals is just to write down the first natural and pair it with any rational (and so on) Because any natural number divided by a natural number will itself be a natural number. The rationals are a set without any rational order. Until you break it down. So it’s basically arbitrary.
There are indeed many ways to pair up the natural numbers with the rational numbers (the bijections are in one-to-one correspondence with the real numbers in fact). There are a lot of different choices you can make, provided you arrange that every single rational number is chosen at some point. It isn't true that any natural number divided by a natural number is always another natural number, however. 1 divided by 2 is 1/2, which is not in N.
To me all of that just means one (the naturals) is a subset of the other.
N is a subset of the rational numbers Q. On the other hand, N is a subset of the real numbers, and you can't find a one-to-one correspondence between N and R.daveS_{July 24, 2020
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Yes, anyone can find the relative place for primes. Nothing prevents it. That JVL cannot demonstrate an obstacle means none exist. With rationals vs integers no one can pair the first positive integer with the first positive rational. It's impossible. Higher state means it is a superset of the natural subset.ET_{July 24, 2020
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JVL Thank you for your answers and for being polite. EugeneEugeneS_{July 24, 2020
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ET: You’re bluffing, again Nope. It can't be done. You don’t even understand what I am saying. If you did you would realize how stupid you sound. Relative cardinalities means you compare similar sets to see how one is relative to another. I know what you're saying, and you won't be able to figure out the specific relative cardinality of any of those sets. You cannot tell me the first positive rational number. You mean just positives after zero? There isn't a 'first' or smallest one. Thank you. So how can you put the rationals in a one-to-one correspondence with the naturals? It's Cantor's diagonal scheme. You can look it up. The rationals would be a higher state of Aleph_null. What does 'higher state' mean?JVL_{July 24, 2020
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OK, so the way to a one-to-one correspondence with naturals and rationals is just to write down the first natural and pair it with any rational (and so on) Because any natural number divided by a natural number will itself be a natural number. The rationals are a set without any rational order. Until you break it down. So it's basically arbitrary. To me all of that just means one (the naturals) is a subset of the other. The continuum remains intact with relative cardinality. It's all scaled based on density. The rationals would be a higher state of Aleph_null.ET_{July 23, 2020
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ET, the answer is what aleph null designates, being able to be matched 1-1 with the naturals. The ellipsis is enormously important, indicating endless, countable continuation. That is a specific recognisable quantity and so it is a number. Going on, the difference is the sparseness with which one gets to endlessness relative to N. I think that is what you are reacting to. Yes, counter-intuitive but that is now commonplace in Math and Physics. KF PS: There are ways to map the rationals to the naturals. Complicated but doable. Rationals are not continuous, though irrationals are power series sums of rationals. They are what bring in the continuum in R. I emphasise in R as R* puts a very dense cloud of infinitesimally altered numbers around any r in R.kairosfocus_{July 23, 2020
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Here's one way to put the positive rationals in one-to-one correspondence with N. You write out the rationals in a table, then traverse the entries as shown by the blue path. Note this results in repeats, for example 1 = 1/1 = 2/2 = 3/3 is hit multiple times. To avoid this problem, ignore any (reduced) fractions that have already been hit. You can include the negative rationals and 0 by interleaving them in the resulting sequence. It's not order-preserving, but that's not a requirement.daveS_{July 23, 2020
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Thank you. So how can you put the rationals in a one-to-one correspondence with the naturals?ET_{July 23, 2020
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No, there is no such number.daveS_{July 23, 2020
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Even a Ford F350 can be lifted, though. Can a machine tell us the first positive rational number?ET_{July 23, 2020
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You cannot tell me the first positive rational number.
This is like "you cannot bench press a Ford F350".daveS_{July 23, 2020
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JVL:
You can’t do it. In fact, no one can do it. You just made that up because you don’t understand the hundreds of years of work done on the primes.
You're bluffing, again
You cannot figure out those relative cardinalities.
You don't even understand what I am saying. If you did you would realize how stupid you sound. Relative cardinalities means you compare similar sets to see how one is relative to another. You cannot tell me the first positive rational number.ET_{July 23, 2020
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ET: It can be done. That is all that matters. Obviously English isn’t your primary language. You can't do it. In fact, no one can do it. You just made that up because you don't understand the hundreds of years of work done on the primes. You're arrogant and assume you know without having learned what has been done. If your examples cannot be done by anyone, you would have a point. But all you are doing is trying to attack me, personally. And all because mere set subtraction upsets Cantor’s foolish idea. You cannot figure out those relative cardinalities. You absolutely cannot do it. This is not personal excepting in that you are making it so.JVL_{July 23, 2020
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JVL:
You CANNOT determine the relative cardinality of the primes.
It can be done. That is all that matters. Obviously English isn't your primary language. If your examples cannot be done by anyone, you would have a point. But all you are doing is trying to attack me, personally. And all because mere set subtraction upsets Cantor's foolish idea.ET_{July 23, 2020
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ET: Parroting is not understanding Denying reality is not winning. I answered that. You just didn’t like the answer. Because you explained nothing. You just said you were right and I was wrong. You didn't address the confict except to pick a side. Nothing prevents anyone from determining the relative cardinalities of countably infinite sets. And all that matters, despite JVL’s whining, is that it can be done. And given that the concept of natural density exists, people have already been doing it. You CANNOT determine the relative cardinality of the primes. Or the perfect numbers. Or the rationaly numbers. Or the set F = {1, 2, 6, 24, 120, 720, 5040 . . . . }. Or the triangular numbers. Or the algebraic numbers. You can't. Again, if you want to make this personal, shut up and let’s get at it. Your inability to think and your inability to comprehend what I post is beyond annoying. I'm sorry you find my continually pointing out that you cannot support your own scheme annoying. Perhaps you should do better. You cannot find the relative cardinality of the primes the rational numbers the perfect numbers the algebraic numbers the triangular numbers the set F = {1, 2, 6, 24, 120, 720, 5040 . . . . }JVL_{July 23, 2020
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then I have to wonder if you are correct.
That is your right. Like I said, I prefer to distinguish between someone's professional opinion and metaphysical views. They are two different things. To Howard Pattee's credit, he does not let his metaphysical stand adversely influence his own scientific opinion, when he acknowledges existing problems, instead of just sweeping the dust under the rug. Eugene Koonin, by the way, is doing the same when he acknowledges that there has not been found a naturalistic solution to information translation. High caliber professionals somehow find courage to acknowledge awkward things. In other things professionals can be blinded just like anybody else...EugeneS_{July 23, 2020
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JVL:
Except that my examples match those given by lots and lots of mathematicians over the last century.
Parroting is not understanding
You’re still not answering the basic question: how is it that I can show you two sets, lined up element to element, one to one, no element left out and yet you say the sets have different number of elements. Explain how that can happen.
I answered that. You just didn't like the answer. Nothing prevents anyone from determining the relative cardinalities of countably infinite sets. And all that matters, despite JVL’s whining, is that it can be done. And given that the concept of natural density exists, people have already been doing it.
Except . .. .you can’t find the relative cardinality of:
So you are proud to be an infant. That isn't helping you. Again, if you want to make this personal, shut up and let's get at it. Your inability to think and your inability to comprehend what I post is beyond annoying.ET_{July 23, 2020
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DaveS: To be fair, no one can calculate the cardinality of the perfect numbers at present. ???? Tell ET that. He hasn't even figured out what I'm asking him to do. He just makes things up because he thinks five minute of thought is enough to understand decades, centuries of mathematical research.JVL_{July 23, 2020
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JVL, To be fair, no one can calculate the cardinality of the perfect numbers at present. :)daveS_{July 23, 2020
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ET: Wow. Just wow. JVL doesn’t understand infinity. And doesn’t know the definition of cardinality. Except that my examples match those given by lots and lots of mathematicians over the last century. The fact remains that anyone can do the math and answer JVL’s infantile challenges. That he wants to put it on me just proves he is nothing t a child. He has already challenged me on other topics- and he doesn’t have nay place to challenge anyone. You're still not answering the basic question: how is it that I can show you two sets, lined up element to element, one to one, no element left out and yet you say the sets have different number of elements. Explain how that can happen. Nothing prevents anyone from determining the relative cardinalities of countably infinite sets. And all that matters, despite JVL’s whining, is that it can be done. And given that the concept of natural density exists, people have already been doing it. Except . .. .you can't find the relative cardinality of: the prime numbers The triangular numbers The rational numbers the algebraic numbers the perfect numbers The set F = {1, 2, 6, 24, 120, 720, 5040 . .. . . } You moan and whine and complain but you fail to apply the system you invented to common, easy to define sets of numbers. You fail and your system fails. It doesn't work.JVL_{July 23, 2020
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ET: I guess that you are a bluffing blowhard. Dr Pattee's own words in one of his papers show he thinks intelligent design has a weak argument. How you missed that I cannot know.JVL_{July 23, 2020
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Wow. Just wow. JVL doesn't understand infinity. And doesn't know the definition of cardinality. The fact remains that anyone can do the math and answer JVL's infantile challenges. That he wants to put it on me just proves he is nothing t a child. He has already challenged me on other topics- and he doesn't have nay place to challenge anyone. Nothing prevents anyone from determining the relative cardinalities of countably infinite sets. And all that matters, despite JVL's whining, is that it can be done. And given that the concept of natural density exists, people have already been doing it.ET_{July 23, 2020
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