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merjet

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merjet last won the day on May 26

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About merjet

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    United States
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    Ohio
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    Married
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    I have several articles published in Objectivity and the Journal of Ayn Rand Studies.
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    University of Illinois
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    actuary (retired)

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  1. 😊 I must confess that my recollection is not as good as it might seem. My last post was copied from something I wrote a few years ago and then edited a little.
  2. A few years ago I purchased and listened to Pat Corvini's two sets of lectures on number:1. Two, Three, Four and All That; and 2. Two, Three, Four and All That: The SequelThe main topic is her view of numbers. A lesser topic is criticism of Cantor's claims about infinite sets, and his method, with she calls postulational and contructive. Corvini does not say so, but the postulational/contructive philosophical view is epitomized by the famous mathematician David Hilbert's opinion that the most reliable way to treat mathematics is to regard it not as factual knowledge, but as a purely formal discipline that is abstract, symbolic, and without reference to meaning.Her method focuses on "the what" of numbers, whereas Cantor's methods focuses on "the how" of numbers. She sharply distinguishes between counting -- which use only the positive integers -- and measuring -- whose domain is the real numbers (integers + rationals + irrationals). Cantor's method of one-to-one correspondence blurs the distinction.She talks about Cantor in the 1st and 3rd lectures of The Sequel. The last 1/3rd or so of Sequel #2 and the first half or so of Sequel #3 elaborate her view of measurement. Then she returns to Cantor and the postulational/constructive view of the rational and irrrational numbers. In her view there are two sorts of infinities -- counting (conceptualized by the positive integers) and measuring (conceptualized by real numbers and attained by subdividing). The postulational/constructive method blurs the distinction and treats open-ended construction like a concrete.I much agree with what she says, but believe there are even stronger criticisms of Cantor's nonsense. At one point in Sequel #1, Corvini talks in terms of 2-to-1 correspondence, but not any wider range of multiple-to-1 correspondences. Nor does she utilize part-whole logic to criticize Cantor's nonsense.
  3. Can you elaborate? Is there an online source for reading more of what she said?
  4. I made the following comment on the Charles Tew thread: “In another video he talks about mathematics. I don't remember which one. He prefaced his remarks with his not being a mathematician, but what he said about math did not sit well with me. As I recall, he said mathematics is about reality. Yes and no. It is also about our concepts. Show me a matrix, differential equation, integral or complex number in reality that wasn't written by some human being, then I will reconsider.” Link. MisterSwig suggested privately that I say more about this in a separate thread. Before I do, what was it that Charles Tew said that did not sit well with me? The video is ‘Sam Harris Doesn't Understand Math‘ (link). Tew launched a tirade on Sam Harris' saying that the Probability{Jesus will come back in Jackson County, Mo.} < Probability{Jesus will come back somewhere}. Defending that claim when the interviewer challenged him, Harris said it is a mathematically precise statement. In addition to the title he gave the video, Tew made several other comments, including the following: - Harris is disastrously wrong about his Jesus claim. - He said that mathematics is about the world. It applies to reality. - He claimed Harris had a Platonic understanding of math. - Mathematicians don’t know what they are talking about, because they aren’t philosophers. Ditto for physicists. Sam Harris was a little imprecise. He should have said, simplifying, Pr{Jesus to Jackson County} <= Pr{Jesus to somewhere}. Not “less than”, but “less than or equal to.” Even holding that both probabilities are zero like Tew said, the “less than or equal to” formulation is true. Also, more generally, Pr{A} <= Pr{B} if A is a proper subset of B. That is the mathematical principle Harris appealed to, even if he didn’t say it wholly correct. In my opinion, Pew’s asserting that Harris doesn’t understand math is a gross exaggeration. Not even arithmetic and some mathematical probability? That’s all I will say about Harris. I move on to some of Tew’s claims. First, his assertion about mathematicians and physicists is pompous and insulting to many people, quite a few I know personally. Next, is mathematics about the world? Maybe Tew took that claim from the title of the book by Robert E. Knapp. Mathematics is About the World. Nevertheless, Tew's understanding of math seems to me pretty shallow. I have been aware of Knapp's book for a while but haven’t read it. Anyway, in my view mathematics is also about the ideas we use to describe the world quantitatively. Let’s start with arithmetic. Is arithmetic about the world? Mostly yes, but not entirely. Consider 5 – 2 = 3. That’s true for all things countable. But what about 3 – 5 = -2? If I begin with 5 dimes in my hand and remove 2 of them, 3 dimes remain in my hand. However, beginning with 3 dimes in my hand and removing 5 of them is impossible. On the other hand, if the temperature is 3 degrees Fahrenheit or Celsius and then falls 5 degrees, saying it’s then - 2 degrees is valid and about the world. Pure math is an abstract discipline, so mathematicians usually ignore exceptions like not being able to remove 5 dimes from my hand when there are only 3 dimes there. By the way, when negative numbers were first considered, they were regarded as fictitious or false. The algebraic equation x^2 + x – 6 = 0 has two solutions (roots), x = +2 and x = -3. Moving on, a parabola (or circle, or ellipse, or hyperbola) is based on a conic section. The algebraic equation for one can be expressed in Cartesian coordinates – invented by Descartes -- or polar coordinates. Similar for volumes such as that of a cone, cylinder, or sphere. Is such mathematics about the world? It surely is. Cartesian and polar coordinates have a direct correspondence to the real world. The axes in both can correspond to distances in the real, external world. On the other hand, there is another coordinate system which has no such direct correspondence to the real, external world. It is often called the complex plane and is pictured here. The horizontal axis is for real numbers, but the vertical axis is for imaginary (or complex) numbers. We can’t use imaginary numbers to express distances in the real world. On the other hand, imaginary numbers are used to describe the real world in physics, more specifically quantum mechanics (link). The same complex plane coordinate system is shown there again. When imaginary or complex numbers were first systematically explored by Euler, Gauss, and Hamilton more than 150 years ago, their practical use was unknown. So one could say that imaginary or complex numbers were not about the world then. Times have changed. A practical use of them was found many years later in quantum mechanics. So one could say that imaginary or complex numbers are about the world now. By the way, I earlier gave an algebraic equation that had two real solutions (roots). Here is an algebraic equation that has no real number solutions (roots): x^2 + 4x + 5 = 0. The two solutions (roots) are -2 + i and -2 – i, where i is the imaginary (complex) number equal to the square root of -1. To be continued in another post(s). I will say something about matrices, calculus, differential equations, maybe more.
  5. Trump’s Health Insurance Changes #2
  6. I observed a few minutes of a few videos here. https://www.youtube.com/channel/UC8iOCGZj09rvCXhXeya4vkw My impressions were not favorable. In one video he called the session with Jordan Peterson at OCON 2018 a disaster. I was there, and the audience surely didn't judge it a disaster. His Why Socialism Fails based an an analogy with computers was poor. Hayek's explanation was far better. In another video he talks about mathematics. I don't remember which one. He prefaced his remarks with his not being a mathematician, but what he said about math did not sit well with me. As I recall, he said mathematics is about reality. Yes and no. It is also about our concepts. Show me a matrix, differential equation, integral or complex number in reality that wasn't written by some human being, then I will reconsider.
  7. I suspect that our differences would diminish if we discussed this more. For now, I will limit myself to the following. I believe that coercion by government should be severely limited. On the other hand, (1) I don't believe it can realistically be eliminated, and (2) coercion comes in degrees. There are guns, incarceration, regulatory prohibitions which have economic effects, court summons, quarantines, etc. Consider settling disputes, familial or business lawsuits or bankruptcy. The parties to such disputes often don't happily and voluntarily submit to remediation. But in order to protect the rights of the wronged in such cases, government must use some degree of coercion -- such as a court summons -- if the dispute is going to be settled rather than do nothing. The latter could possibly make matters worse.
  8. My second try: The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that a description of the properties exhibited by the peculiar panoply of forces and particles of reality may be so accurately depicted by eight-dimensional numbers called “octonions.”
  9. I agree. I think the sentence you partly quoted would be better if it were: The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that the properties of the peculiar panoply of forces and particles that comprise reality spring logically from the properties of eight-dimensional numbers called “octonions.” (my bold).
  10. The Peculiar Math That Could Underlie the Laws of Nature https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/
  11. Spheres of Justice #8 Spheres of Justice #9
  12. Ayn Rand's Legacy of Unifying Social Cruelty https://truthout.org/articles/ayn-rands-legacy-of-unifying-social-cruelty/ I suggest also clicking on the link within "she advocated a cartoon fantasy of economic "freedom"” about half-way through the article. The book is Mean Girl: Ayn Rand and the Culture of Greed. I haven't read the book, but it's likely a screed like the article.
  13. Are you familiar with this? http://www.johnmccaskey.com/induction-and-concepts-in-bacon-and-whewell/
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