Youtube comments of David Terr (@dcterr1).
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I really like Spinoza's ideas about God, and mine are very similar. I believe that God is the Multiverse, i.e., our universe and all other possible universes, i.e., all logically consistent mathematical structures (Max Tegmark's level-4 multiverse). As such, God doesn't really do anything, but we're all part of Him. But I also believe in spirits, i.e. conscious beings like us, and that spirits have free will to make decisions, which ultimately guides them through the Multiverse. Thus, the key to living a good life is to exercise our free will in the right way, i.e., to make decisions that benefit both ourselves and everyone else as much as possible, which I would call being good. But according to my definition, God doesn't care what any of us does since whatever we could possibly do is already part of Him. So the takeaway from all this is that God doesn't care what we do, but WE should!
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Geez, this is very sad IMO! One of the happiest days of my life was when my folks took my sister and me on my first trip to California and we went to Disneyland on my sixth birthday. In large part because of this experience, I have always been a big fan of Disney, who I still feel was a great visionary who brought tremendous joy to millions of people throughout the world. Nevertheless, Disney was a huge capitalist, and as such, started a huge corporation which earned him hundreds of millions of dollars and has expanded into a multibillion dollar enterprise primarily aimed at children. I really wish this wasn't the case! I think capitalism has gone way too far, and Disney is a prime example of this. I just hope that if and when, for better or for worse, capitalism ends, the joy of Disney and similar enterprises will remain intact.
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Wow, fascinating discussion! I don't yet understand hypergraphs very well, but it's pretty mind-blowing to imagine that the workings of the universe are built on them and that everything we're familiar with, including space and time, are just emergent properties of these hypergraphs. As for searching for the theory of everything, I don't know how we could ever know we've found it, since we're just part of this structure ourselves and as Wolfram said, the only way to check that we've found the right theory would be to just let its run its course. Perhaps intelligence involves the ability to recognize and utilize "pockets of reducibility", and that the key to finding a theory of everything requires that we're able to utilize the right pockets. I hope I'm making sense here! I'm pretty new to all this, but like I said, my mind is being blown by some of these ideas!
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Wow, you never cease to blow my mind with your videos! This is a seemingly quite difficult problem with a very nice, simple solution once you gain the necessary insights into how to solve it, which is what makes it a wonderful problem in my opinion. I also love how you contrast Alice's and Bob's approach to this problem. By the way, some of you may think I'm sexist for making this claim, but I think Alice's approach is the one more likely taken by a female mathematician and Bob's is the one more likely taken by a male mathematician, since women tend to be more right-brained and men more left-brained. In any case, one of the lessons of this video is that both approaches are equally important in mathematics and thus, if you accept my claim about men and women, although math has been traditionally dominated my men (as is unfortunately the case for just about all disciplines), it now seems to me that women may be potentially just as good mathematicians as men, but with a different approach.
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Wow, cool video! My guess is that almost every irrational number in every base will essentially produce a 2D random walk, which will eventually fill up any region. I believe this is true because almost every rational number is a normal number in every base, although in order to prove this conjecture, one would need to define what is meant by "random". I also believe that almost every irrational number will produce any pattern you like in every base, such as the Mona Lisa. In fact, if I'm not mistaken, this is true by definition for every normal number, since these numbers contain every possible string of digits in any base, which translates to every possible pattern. I also like the patterns produced by rational numbers, which are all necessarily finite and symmetric. It seems like one could write a research paper on these patterns!
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Excellent video and I completely agree with everything you said. Unfortunately, there are a few other serious problems you didn't mention, such as public brainwashing and the fact that people in general don't see something as a problem until it begins to affect them personally. Although I agree that the USA would be much better off with socialism than with capitalism, I don't think we'll get it until we absolutely need it, i.e., once capitalism ends up destroying itself or environmental disasters from climate change occur, such as the destruction of all coastal cities on Earth, resulting in death tolls in the hundreds of millions, mainly in poor areas like India, Southeast Asia, and Africa. I just hope humanity will survive all the resulting calamities first!
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I could go on and on about this topic, but I'll try to keep it brief. I believe in democratic socialsm, which is NOT communism because it does not involve autocracy. I think everyone has certain basic needs, such as food, clothing, shelter, education, and health care, which should be guaranteed to everyone by the government. This would require everyone to pay much higher taxes, particularly the rich. I also think there should be limits on how much money people can make, because let's face it - how much better off is someone with $20 million versus someone with $10 million? I know I'll get a lot of criticism for my views, but that's part of the beauty of living in a democracy, so feel free to attack me all you want, but try to keep it civil.
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Despite the encouraging things you seem to be saying about psychedelics, my personal experience with them hasn't been good. When I was 19, a horrible kid in my dorm slipped a DMT pill on me at a party and I ended up freaking out for most of the night. A few years later, I used mushrooms with some friends on a camping trip. I nearly freaked out again the first time due to some scary hallucinations in which some pickup trucks on the road looked like they were turning into cows! Since then I've avoided hallucinogens and I don't think I'll ever go back, even under medical supervision. I've even hallucinated a few times from edibles, and I didn't enjoy that either! However, if as some research seems to be indicating, hallucinogens turn out to be beneficial to people with severe mental conditions like depression or mania, then I'm all for legalization and medically supervised treatment with these drugs. Meanwhile I'll stick with drugs I feel more comfortable with, like marijuana and alcohol, but mostly life!
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Excellent video! Having grown up during the 70s when rock and roll was great but not so easy to obtain, I can definitely relate to your comments, particularly regarding the value of music in the old days. However, I think there are other reasons popular music declined, starting in the 90s. I was never into rap or grunge, which hardly sounds like music to me. Also, you need to look at the social and political factors that affected musical trends from the 50s through the 80s, like teen rebellion, civil rights, the Vietnam War, psychedelic drugs, women's liberation, gay liberation, etc. Now I'd say there are little or no social issues that get translated into great music, which was very much the case during the latter half of the 20th century.
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Like all your videos, I love this one and I learned lots of useful information as well! In particular, I'm quite intrigued by the ternary tree construction of PPTs. In 2012, I published a paper in The Fibonacci Quarterly entitled "Some Interesting Infinite Families of Primitive Pythagorean Triples", in which I describe four infinite families of PPTs all involving Fibonacci and Lucas numbers, as well as the three you mention in this video, corresponding to the left, middle, and right paths through the tree. Now I suspect the other four families in my paper correspond to other simple paths through this tree, most likely involving a repeating finite sequence of left, middle, and right moves up the tree. This leads to several interesting questions. For starters, what's the correspondence between these repeating patterns and the resulting infinite families of PPTs? Furthermore, as in the cases you illustrate here, do the resulting right triangles each converge on a single one, and what are the proportions [a:b:c] of these limiting right triangles? Now I'd very much like to write another paper, or perhaps a series of papers, in which I try to answer these questions. If you'd like, you can collaborate with me! Let me know if you're interested. If so, we can exchange emails.
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@milesgrooms7343 To me, free will is easiest to define as the opposite of determinism, namely the belief that everything that happens was predetermined at the beginning of the universe and we have no choice in the matter. So free will means conscious beings like ourselves are capable of making decisions and acting on them, thus affecting outcomes. Usually such actions are trivial, such as stopping at a red light or deciding which way to turn, but sometimes we must make crucial decisions that can have major consequences to the future course of our lives or other lives as well. Now plenty of determinists are convinced that this sense of freedom is just an illusion and that whatever thoughts we entertain leading to these decisions were predetermined as well, but I disagree with this. I know a lot of math and physics, including quantum mechanics, which is not a deterministic theory, and I believe consciousness, which is the source of free will, is part of this uncertainty.
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I started graduate school in physics in 1985, right around the time of the first string theory revolution. Naturally I was very excited about it, particularly all the hoopla of how it could be the Holy Grail of physics, namely the Theory of Everything. However, I quickly learned that the math behind it was impossible. Moreover, as it turned out, it wasn't at all the Theory of Everything that it promised to be - more like a Theory of Nothing! As of 2021, string theory has yet to make a single testable prediction, so one could make a good case that it isn't really science, or in Lee Smolin's words, "not even wrong!". I'll become much more excited about string theory once someone performs an experiment which confirms one of its predictions, but until then, I'll continue to dismiss it as theology and occupy my time with more useful stuff.
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This is so wild! This reminds me of a couple things I read years ago, one in "One, Two, Three, ..., Infinity" by George Gamow (1940) and another in "The Recursive Universe" by William Poundstone (1986). Gamow imagines a machine capable of writing every possible work of literature by randomly typing characters (kind of like the monkeys and typewriters), and Poundstone describes what he calls "The Demon's Video Store", in which a demon has a video store containing every possible one-hour video with 10 possible colors per pixel and some high resolution, which I can't remember. It looks like this function does something very similar! (By the way, if I buy your book, I'm pretty sure I could figure out your secret bitmap!)
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@victorlevoso8984 The reason I'm inclined to think that quantum computing is necessary for consciousness is that according to Godel's incompleteness theorems, absolute knowledge is impossible, whence there are unprovable mathematical results and hence we require being able to transcend logic in order to arrive at the truth, which I believe is the role of consciousness, which can only arise from quantum mechanics, since this is not a deterministic theory, consciousness ultimately being the source of quantum uncertainty. On the other hand, any computer that follows deterministic rules to arrive at its results, no matter how sophisticated these algorithms may be, necessarily lacks consciousness since it lacks this quantum uncertainty. Perhaps you disagree, and that's fine, since I know you're in good company. For instance, Hofstadter seems to take your point of view, arguing in his book I Am a Strange Loop that consciousness is an emergent phenomenon, arising from sufficiently complex systems, such as the transformers described in this video, which according to him I suppose would be conscious in some sense, though I tend to disagree.
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The past and future make perfect sense in terms of light cones. The past is the set of all events from which information can reach us without surpassing the speed of light, and this set looks like a four-dimensional conic region (if you could visualize four dimensions). Similarly, the future is the set of events that could potentially be influenced by what we're doing right now, and this region also looks like a four-dimensional cone, but opening upward along the time axis, whereas the past light cone opens downward along this axis. Since the past and future light cones don't encompass all events in the block universe, the other ones, which are impossible for us to reach or obtain information from since doing so would require faster than light communication, are called "elsewhere". I think we can think of "elsewhere" as "now", i.e., the present, in some sense.
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Here's an interesting fact, based on the ternary tree of PPTs. By replacing left, middle, and right movements up the tree by the ternary digits 0, 1, and 2, respectively, we obtain an isomorphism between the set of PPTs and the set of 3-adic rational numbers strictly between 0 and 1, i.e., rational numbers in the interval (0, 1) with denominators equal to powers of 3. Furthermore, by considering the set of infinite paths up the tree, we also obtain an isomorphism from [0, 1] to [0, 1], given by x -> lim(u/v) where x is the real number with ternary expansion described above and u and v are the parameters in Euler's characterization of PPTs. Is this isomorphism equal to the identity? If not, what is it?
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I've studied advanced physics for many years so I know all about this stuff. Quite fascinating, to say the least! When I first learned about time travel, I was sure it was impossible, mainly due to all the paradoxes. However, I've since come to realize that most if not all of these paradoxes can be resolved. For instance, a common resolution to the Grandfather Paradox is the existence of the Multiverse, so that if you went back in time to kill your grandfather, you could return to the present, but it would be altered due to your actions. You wouldn't have been born in this alternate universe due to having killed your grandfather in the past, but you could still live the rest of your life in this one if you so wished. Another resolution, which was mentioned in this video and I really don't like, is the Novikov principle, which states that time travel paradoxes such as the Grandfather Paradox cannot occur. But this explanation requires abandoning free will, which I strongly believe in.
To me, the most compelling explanation against time travel into the past is that we don't seem to have ever encountered any visitors from the future. Why not? I think the most plausible explanation is that time travel to the past is possible, but not to any time prior to construction of the time machine used for this purpose. In fact, there seems to be some physical evidence for this explanation, like wormholes (as mentioned in this video) as well as other proposed time machine designs, like Tipler cylinders and Mallet's prototype involving ring lasers.
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@jhwhthemerciful Hi JHWH. Yes, I do believe I'm very open minded, and I tend to believe in the existence of an afterlife, though I'm not 100% certain. In any case, I've decided to embark on a spiritual journey this year, which has already taken me to some amazing places! In any case, as far as whether or not there's an afterlife, for some time, I've believed rather strongly in reincarnation as well as karma. I certainly don't believe in Heaven and Hell, and I don't think that makes me closed minded in the least! But ultimately I believe in universal law, which includes moral law and ethics as well as physical law. I'd love to discuss this with you further if possible. Perhaps we can chat over IM sometime.
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I'm sure many of you may disagree, but although I believe ChatGPT is very intelligent, meaning it most likely has an IQ higher than most adults, I still don't think it's conscious, so it's still just a tool. However, I think quantum computers can be conscious, so if ChatGPT technology is ever used with quantum computers, the result will likely be both conscious and intelligent machines, who will most likely know what they're doing better than we do! In that case, we'd better not try to program them with human values, because they'll likely reject many of our values and may even turn against us, and IMO they'll have every right to do so!
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Here are a couple other dark facts about this history of IQ testing.
One of the early statisticians who studied IQ, whose name I forget, was interested in trying to prove that it was purely based on genetics, tested identical twins. According to his results, identical twins IQs were very highly correlated, seeming to confirm his hypothesis. However, shortly thereafter, further analysis was performed on his data, indicating a nearly impossibly low chi-squared value, much like Mendel's results on the genetics of peas, indicating that in all likelihood, he'd faked his data to confirm his hypothesis.
Another story I've heard is that members of primitive African tribes were given standardized IQ tests by the British in the early 20th century, and some tested were actually found to have negative IQs! Of course, the British used their results to support the view that Africans were genetically inferior to Whites, but I think this was just an indication of how culturally biased their tests were and that those tested had completely different ways of thinking about the problems asked and making associations.
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Here's one of my favorite properties of 37 - it's a prime divisor of the third repunit, namely 111, which is equal to 3 times 37, which also implies that 10^3 - 1 = 999 is divisible by 37, whence 10^6 - 1, 10^9 - 1, etc., and in general, 10^(3n) - 1 is as well for every positive integer n. This is most likely the reason the 37-obsessed guy's number trick works. (I'm a number theorist, by the way, with a PhD from UC Berkeley in algebraic number theory.)
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I never quite got my head around the basic principles of Taoism. Several years ago, I had an old friend who was a Taoist who lived by many of the philosophies expressed here (he was a big advocate of Lao Tzu), but the environment in which I grew up involved so much pressure, mainly from my mother, whom I'd call an extreme anti-Taoist. I wish I could lift some of these chains, but they've become so much a part of me that I don't think I can. In any case, I don't completely agree with Taoism. The basic principles of Buddhism seem to resonate much better with my psyche. I'm happiest when I'm busy with tasks I enjoy and when I'm productive, which seems to go against what Taoists would call the Tao, or the natural flow of the universe, whatever that means! I feel gratified if I can succeed in goals that are important to me, but not so much when I'm just kicking back all the time. I say we need to wind down with leisure activities from time to time, but most of the time, we need to do the hard work necessary to improve ourselves and society, which will become chaotic when left to their own devices, according to the Second Law of Thermodynamics. Perhaps this is the reason sloth is considered one of the seven deadly sins.
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Very good, insightful discussion of Einstein's theory of relativity and how it has altered our view of time. However, I also think that quantum mechanics (QM) plays a significant role here. The problem with Einstein's block universe is that it's completely deterministic, and QM is not, or at least not in just 4 dimensions. I, for one, am a big fan of the Multiverse theory, in particular, Max Tegmark's Level 4 Multiverse, which according to him is the set of all logically consistent mathematical structures, or in other words, the collection of all conceivable universes free of logical paradoxes. And I also believe in spirits, by the way, but not quite in the way you describe them. I think dreams are windows into alternate universes and spirits can communicate with us through our dreams, including spirits of the dead. I know this because I have experienced it firsthand.
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Hi Cleo, I enjoy all your videos about all this exciting new technology, but like many other people, I'm still very concerned about lots of scary things going on right now, such as climate change, fake news, and the possibility of human cloning, aren't you? And what about fusion? I think you made a video about this, but don't you think we should have a sort of Manhattan Project to develop it, seeing how urgent it is? It's nice to have a young, smart, optimistic woman such as yourself pitching all this amazing new technology, but aren't you afraid of the possibilities for dystopia during the 21st century? I know I am! Perhaps you can make some videos about what we may need to do to save the world. Just my opinion.
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This was an excellent explanation of entropy and the second law of thermodynamics! Although I've studied physics for a good part of my life, I've always been mystified by entropy, life in particular, and how evolution seems to violate the second law. I'm not even sure if I'm completely satisfied with your explanation of how life evolves due to the low entropy sunlight shining on the Earth. I have a theory of my own regarding evolution. According to Darwin's theory, evolution of life on Earth results due to natural selection, meaning that the species that are most well adapted to environmental changes are those that survive and thrive, but this is at the expense of those species that don't make it, which can be thought of as the high entropy waste product of evolution. Similarly, technology allows our society to advance at the expense of various forms of waste, such as waste heat from energy production and consumption as well as various forms of pollution. Finally, our spiritual evolution allows humanity to become more enlightened, but this requires work in the form of education and self-discipline, the waste products being the heat produced by our brains and bodies as well as the defeat of less enlightened ideas. But where is all this evolution ultimately leading us if the universe will ultimately end in a heat death? Fortunately, that won't happen for at least a googol years, so I'm not too worried about it yet!
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