AlexL Posted June 1 Report Share Posted June 1 Description: Quote Actor Terrence Howard claims that he has invented a theory of everything that improves physics, based on the idea that 1x1=2. After an appearance on the Joe Rogan podcast, his ideas have unfortunately attracted attention. It is, of course, complete bullshit, but I try to say it nicely. (Not quite successfully.) About the author (Wiki): Sabine Hossenfelder (born 18 September 1976) is a German theoretical physicist, philosopher of science, author, science communicator, YouTuber, musician, and singer. Quote Link to comment Share on other sites More sharing options...
tadmjones Posted June 2 Report Share Posted June 2 I like Sabine she's cantankerous. I watched some of the Rogan episode and thought Howard is a little off ,lol. But he did present some , at least on the surface, interesting ideas especially about negative space geometries. I am not familiar with the flower of life or why it is important per Howard to modern theoretical physics, but it had something to do with the geometry of the negative spaces. Not sure what to make of the modelling Howard showed that he claimed 'reproduced' Saturn down to its material distribution and incorporating the rings, I think it was based on 'his' vortices and their interaction with matter and his theory of gravitation as an 'outward in' push from the electromagnetic field as opposed to an attraction between masses. I think she is wrong to characterize Rogan's audience as stupid because they will listen for hours to alternative and perhaps outlandish scientific hypothese, I think she is more butt hurt they are treading in her domain. She isn't very appreciative of Kastrup's critizations of her defense of hidden variables either ,lol. Quote Link to comment Share on other sites More sharing options...
AlexL Posted June 2 Author Report Share Posted June 2 14 minutes ago, tadmjones said: I think she is more butt hurt they are treading in her domain Or that they (Howard) dares to have opinions in areas in which he is - demonstrably - not competent at all. Quote Link to comment Share on other sites More sharing options...
tadmjones Posted June 2 Report Share Posted June 2 (edited) Either way it is still her being butt hurt. Why even comment on non competent opinion? ps maybe because Rogan's audience is so large and her video would get attention and Brilliant will be happy Edited June 2 by tadmjones Quote Link to comment Share on other sites More sharing options...
AlexL Posted June 2 Author Report Share Posted June 2 14 minutes ago, tadmjones said: Either way it is still her being butt hurt. Why even comment on non competent opinion? ps maybe because Rogan's audience is so large and her video would get attention and Brilliant will be happy Mindreading? Maybe she doesn't have the motivations you ascribe to her or suspect her of having... Quote Link to comment Share on other sites More sharing options...
tadmjones Posted June 2 Report Share Posted June 2 (edited) Yeah it could be I have non competent opinions about Sabine's motivations. ps out of curiosity , why did you post a link to her video Edited June 2 by tadmjones Quote Link to comment Share on other sites More sharing options...
DavidOdden Posted June 2 Report Share Posted June 2 4 hours ago, AlexL said: Or that they (Howard) dares to have opinions in areas in which he is - demonstrably - not competent at all. This succinctly summarizes not just this issue, but “the problem” in contemporary socio-epistemology. Everyone is entitled to their own opinion, nobody is entitled to their own facts, and nobody talks about the proper method of evaluating conclusions. Somewhat surprisingly, the video spends 10 minutes on the topic but she provides the killer disproof in her refutation – falsification by definition – within less than 2 minutes. I was startled that she felt that more needed to be said, though there are two substantive questions of fact that could have been addressed in more detail. The first is to provide satisfactory proof of that the claim was made to the effect that Mr. Howard claims 1x1=2. I was recently sent a copy of “Letter from King Leopold II of Belgium to Colonial Missionaries, 1883”, and was curious about the authenticity of the letter (which is in English, not a language of 150 year old Belgium). I harbor a certain level of distrust as to the authenticity of the letter. I am not certain as to Howard’s claim (I haven’t obtained a copy of the book to verify the claim), but there is much more evidence that Howard made some claim than that Leopold II wrote that letter. For the sake of argument I willing to accept this claim (that 1x1=2) as “actually made”. Objectivists are very familiar with the problem of out of context quotes of Ayn Rand’s writing, so I would like to spend a lot more time scrutinizing the original text, though I would probably actually prefer to do something else. The second part, which could stand some improvement, is the much more problematic argument from authority, that 1x1=1 by definition. I understand that it takes more than 10 minutes to prove that by definition 1x1=1, because for one, it requires a very long discussion of self-evident vs. arbitrary definitions (who sets the rules that determine what it “means” to multiply?). Her definition of multiplication is useful to her, Howard’s definition is useful to him, they are both entitled to their opinions. Unfortunately, her exposition of the utility of multiplication kind of fails because we do not multiply 1x7 in computing that there are 7 apples. We are on the boundaries of numeric primitives, that there are cognitively primitive numbers like 1, 2, 3… and not 10, or 9, or any other number. We do indeed use some additive definition of 10 etc by parsing clusters into directly-perceptible subsets of clusters such as “5 and 6”). A less error-prone method and the only one usable for numbers larger than about 12 is actual counting off using naturally-occurring body parts as accumulators. So indeed, she has failed to provide even a shred of evidence that multiplication is useful. After a period of contemplation, I thought of some possibly useful applications of this concept of “multiplication”, for example planning for a party if there will be 19 guests and every guest gets 2 beers, then 5 six-packs will not be enough, to be safe I could get 8 six-packs. Try as I might, I cannot find any useful application of multiplication with 1 as a multiplier (also none with 0 as a multiplier, God forbid that I talk about 1.3 as a multiplier). I say, and I suppose Dr. Howard says, that she is pulling the wool over the eyes of the public. So even though it was initially surprising to me that she spent 10 minutes on the topic, in 2 minutes into the video, I observed an exponential acceleration of the argument, aided with the tool of authority. I do credit her with a small advance in science-education in her proposal of the unit “chopstick-Tesla”, because IMO “units” are or have not been well explained in science-math. Ultimately, I think she is going the right direction, but it is a mistake to rely on apparently arbitrary definitions. It is also a mistake to rely even in the slightest on social convention (anything that smacks of saying “all scientists agree by convention…”), when one is addressing (attacking) wingnut amateur pseudo-scientists, including actual scientists speaking outside their own area of specialization. A well-known problematic example of scientific social convention is the “scientific consensus” on global warming. It is irrational denialism to deny global warming, or any other scientific consensus, however, I am unaware of (and therefore claim the non-existence of) any controlled and objective survey of scientists proving that there is such a consensus on so-called global warming – and that this “consensus” is significantly more-established than some randomly selected unrelated equally politicized factual claim. I see all sorts of wingnut pseudo-science done on language, even by people with PhDs in some field of some sort, and wonder “How can one effectively combat this nonsense?”. Should one even bother? I think one should, provided that (a) one can correctly isolate an target audience (she’s not talking to the crazies but I am not sure who she is talking to – I would say it is more addressed to the scientists who already know the answer) and (b) one can adopt the premises of the intended audience and teach them something new. We can say that by definition the video is a success, and attempt to solve for a: who is she talking to? Quote Link to comment Share on other sites More sharing options...
Doug Morris Posted June 2 Report Share Posted June 2 Multiplication is a widely known operation. If we want to prove that it is worthwhile to talk about multiplication and to prove what 192837465 times 1618152205 is, we may be taking on a very big task. But it is clear that 1 times 1 is 1, and that any operation with the property that 1 operated on by itself is 2 is not multiplication, but something else. If we define multiplication for some pairs of numbers but not others, we make the study of multiplication unnecessarily complicated. Quote Link to comment Share on other sites More sharing options...
AlexL Posted June 2 Author Report Share Posted June 2 6 hours ago, tadmjones said: ps out of curiosity , why did you post a link to her video Good question. I often watch Sabine's videos; I find her mostly rational, though not always. Her videos cover subjects I am interested in and help keep me up to date. Some of her videos discuss the scientific method and pseudoscience. On the other hand, I sometimes debate curious characters who believe that science is merely a game of words, numbers, and formulas. Despite being completely ignorant in specific fields (and often in general), they believe their arbitrary opinions should be considered on the same footing as those of specialists, for example, regarding why relativity or quantum mechanics is wrong. This is why I considered useful to post the link to OO, in Science and Technology section. Quote Link to comment Share on other sites More sharing options...
tadmjones Posted June 2 Report Share Posted June 2 29 minutes ago, AlexL said: Good question. I often watch Sabine's videos; I find her mostly rational, though not always. Her videos cover subjects I am interested in and help keep me up to date. Some of her videos discuss the scientific method and pseudoscience. On the other hand, I sometimes debate curious characters who believe that science is merely a game of words, numbers, and formulas. Despite being completely ignorant in specific fields (and often in general), they believe their arbitrary opinions should be considered on the same footing as those of specialists, for example, regarding why relativity or quantum mechanics is wrong. This is why I considered useful to post the link to OO, in Science and Technology section. I was just wondering why you didn't link the Rogan episode. I do like Sabine so thanks. Quote Link to comment Share on other sites More sharing options...
AlexL Posted June 2 Author Report Share Posted June 2 (edited) 4 hours ago, DavidOdden said: 9 hours ago, AlexL said: Or that they (Howard) dares to have opinions in areas in which he is - demonstrably - not competent at all. Everyone is entitled to their own opinion, nobody is entitled to their own facts I meant it in the sense that a total ignorant on a subject has no moral right to have an opinion and to insist for it to be seriously considered by others. This is similar to the case of someone who never actually read something by Ayn Rand herself and dares to express an opinion. 4 hours ago, DavidOdden said: there are two substantive questions of fact that could have been addressed in more detail. The first is to provide satisfactory proof of that the claim was made to the effect that Mr. Howard claims 1x1=2. At minute 0:59 of Sabine's video is seen some kind of a reference, a title - "Terrence Howard: One Times One Equals Two". Looking it up, I got the place where T. Howard published his research. Unsurprisingly, it was not in the International Journal of Logic and Arithmetic,😁 but on... his Twitter account, under the pompous title "This is the proof to the World of Science and Mathematics that 1x1=2" (See here the tortuous story of publishing this Earth-shattering result). Clicking on the image, one can read T. Howard's "reasoning. He is NOT redefining the operation x, nor is he redefining the symbol 1 - which wouldn't be illegitimate. He means the ordinary arithmetic ! (This takes care of your "Her definition of multiplication is useful to her, Howard’s definition is useful to him, they are both entitled to their opinions") Now: his claim is that 1x1=2 is wrong because it is "unbalanced". This is best explained in one of his comments. Someone asks: "What about what they say that any number multiplied by 1 is itself. In this concept 1 x 1 has to equal 1". Terrence D. Howard answers: "That would contradict the law of action and reaction". 😕This isn't even funny... About 4 hours ago, DavidOdden said: The second part... is the much more problematic argument from authority, that 1x1=1 by definition. ... Unfortunately, her exposition of the utility of multiplication kind of fails because we do not multiply 1x7 in computing that there are 7 apples. If she wanted to illustrate the utility of multiplication, her example is misleading. She should have taken for ex. 3x7 or 7x3 (as you suggest in your own example). However, there is no argument from authority in Sabine's reasoning. As T. Howard is operating within the normal arithmetic, 1x1=1 is, as Sabine says (min 1:30), not an opinion, but the result of the definition(s) - of multiplication x and of the symbol 1. The exact way in which 1 x 1 = 1 (or N x 1 = N) logically (i.e. deductively) results from the definitions depends on what exactly one takes as definition and axioms, IOW how one separates premises from consequences. It seems that there are several approaches at the axiomatization of Arithmetic - see Wiki. It is useful to read for ex. about the Peano axiomatization, to see how a - relatively simple - axiomatization works. Edited June 2 by AlexL format Quote Link to comment Share on other sites More sharing options...
necrovore Posted June 3 Report Share Posted June 3 (edited) There is the old statistician's joke, that 2+2=5 for large values of 2. (This is because of rounding to the nearest integer. 2 could be a rounded version of 2.49, and 2.49 + 2.49 is 4.98, and 4.98 rounds to 5.) So maybe 1 times 1 equals 2 for large values of 1 (such as the square root of 2, which rounds to 1). -- p.s. I am not being serious here Edited June 3 by necrovore Quote Link to comment Share on other sites More sharing options...
Boydstun Posted June 3 Report Share Posted June 3 (edited) “To collapse correctness into propriety is to obliterate the essential character of thought” (Haugeland 1998, 317; further, 325–43; see also Rasmussen 1982; 2014, 337–41; Rand 1966–67, 47–48; Peikoff 1967, 104; 1991, 143–44). ~~~~~~~~~~~~~~~~ Haugeland, John. 1998. Truth and Rule-Following. In Having Thought – Essays in the Metaphysics of Mind. Cambridge, Massachusetts: Harvard University Press. Peikoff, Leonard. 1967. The Analytic-Synthetic Dichotomy. In Rand 1966–67, 88–121. ——. 1991. Objectivism: The Philosophy of Ayn Rand. New York: Dutton. Rand, Ayn. 1966–67. Introduction to Objectivist Epistemology. Expanded 2nd edition. New York: Meridian. Rasmussen, Douglas B. 1982. Necessary Truth, the Game Analogy, and the Meaning-Is-Use Thesis. The Thomist 46(3):423–40. ~~~~~~~~~~~~~~~~ Identity elements for arithmetic There is an identity element in mathematics-venues from sets, groups, vector spaces, Lie algebras, and associative algebras to things less algebraic and more topological, such as uniform spaces and Abelian topological groups. Indeed there is an identity element in any other venue qualifying as a mathematical category (having such an element is one requirement for qualification as such a creature). Under the morphisms of the category, the identity element transforms any element in the category into itself. That is what is going on also, I have noted, when it is ordinarily said that A is A. I mean in the simplest and most usual meaning of A is A, not the fuller meaning such as when we say a thing is the something it is (added by Avicenna, wielded by Rand). Aristotle took the first-figure syllogisms as obviously valid. With assumption of a few other propositions taken as truly valid (they do appear valid), he was able to show that all the other forms of syllogism could be reduced to the first-figure form. Therefore, he concluded, those other forms of syllogism are also valid. Later on, others (e.g. Leibniz) showed that if you used A is A as a premise in a syllogism, you could prove by syllogism those “other propositions taken as truly valid.” So in logic, the identity mapping of A to itself brings, with a little reworking, a streamlining of theory of the syllogism—fewer assumptions. I’d expect those self-mappings (mappings are a kind of morphisms [the morphisms for the category Sets], but people are more comfortable talking of mappings, so that’s why I’m using it) to be useful in streamlining the theory of groups, the theory of the natural or the real numbers, and so forth. That’s not the kind of usefulness most folks are concerned with, but it is a usefulness for adventurers in mathematics and logic. And that usefulness is itself an objective finding within those disciplines, just as I've found that it pays to sharpen an axe for efficient chopping. That the identity element for multiplication takes any number into itself (and, so, takes itself into itself) under the mapping is not chatter on arbitrary stipulations, but a readout of character of a realm. Edited June 3 by Boydstun Quote Link to comment Share on other sites More sharing options...
Boydstun Posted June 3 Report Share Posted June 3 I neglected to list the second reference cited for author Rasmussen. That one is: Rasmussen, D. B. 2014. Grounding Necessary Truth in the Nature of Things. In Shifting the Paradigm: Alternative Perspectives on Induction. P. C. Biondi and L. F. Groarke, editors. Berlin: De Gruyter. Quote Link to comment Share on other sites More sharing options...
Doug Morris Posted June 4 Report Share Posted June 4 On 6/2/2024 at 1:39 PM, DavidOdden said: Try as I might, I cannot find any useful application of multiplication with 1 as a multiplier (also none with 0 as a multiplier, God forbid that I talk about 1.3 as a multiplier). Suppose we state a general principle that if you have n similar containers each of which will hold m eggs, and the containers are all full, there are n times m eggs. A multiplier of 1 would correspond to a case in which there is only 1 container and/or each container holds only one egg. (A one-egg container might be useful if it protects the egg or makes it easier to carry and store eggs.) A multiplier of 0 would correspond to a case in which there are no containers or in which the only "containers" available will not actually hold any eggs. (The latter might be the case if someone is playing games with us or if we only have containers designed to hold pieces of candy.) The cases involving 1 and 0 may not be enough by themselves to justify having such a principle, but why not be thorough and include them? If we are only dealing with counts of discrete objects, there may not really be any need for a multiplier of 1.3. If a rectangle is 1.3 meters long and 0.7 meters wide, what is its area? Quote Link to comment Share on other sites More sharing options...
DavidOdden Posted June 4 Report Share Posted June 4 There are two approaches to mathematical concepts. One is that they are arbitrary conventions, therefore we give arbitrary definitions and deduce consequences of those definitions. Another is that at least some of them correspond to real cognitive methods employed by humans, and we can posit definitions that have some palpable connection to human reasoning. Hostetter’s argument is a bit of a mixed bag, on the one hand saying that Howard is wrong by definition, on the other hand trying to present a cognitive argument for multiplication. Her error is in confusing counting with multiplying (or, speaking in a way that encourages confusion), and implying that the clumsiness of “1+1+1+1+1+1+1 = 7” is eliminated by instead saying “1x7=7”. Multiplication by 1 and 0 are cognitively very different from multiplication by 2, 3 and so on. Multiplication by 1 and 0 are useless, unless they are embedded in more abstract formal methods where we multiply an kinds of number, not just positive integers. At the level of “start from scratch” math, you don’t just arbitrarily assert conventions. Now, I am not claiming that arbitrary multiplication is useless or false, I am saying that engaging in a refutation by a poor retreat to start from scratch math is a mistake, unless one is only talking to fellow believers. Really, the question about this video is the purpose / audience, and not whether Howard has a valid idea (to paraphrase Pauli, it’s not even an idea). Why is n/0 undefined? Why was was division by zero included, to make the system more complete? Quote Link to comment Share on other sites More sharing options...
Doug Morris Posted June 5 Report Share Posted June 5 a/b is the unique number c such that b times c is a. This is not formalistic or arbitrary; it is what division is. The requirement that "a/b times b is a" is clearly what division is. The uniqueness requirement is necessary because using the notation a/b or the wording "the quotient of a divided by b" implies a unique value, and using it when the value is not unique leads to logical fallacies. If we take multiplication by 0 to be undefined, this forces division by 0 to be undefined. If we follow the usual practice of taking multiplication by 0 to be defined, 0 times anything must be 0. (Explanations below.) Thus if a is not 0, there is no number c such that 0 times c is a, so there can not be a quotient. If a is 0, then any number c times 0 is a, so pretending there is a unique quotient leads to fallacies. Explanations of 0 times anything must be 0: If we define multiplication by 0 based on applications, we have the same points I discussed before. If we have no containers, we have no eggs in containers. If our "containers" can't hold any eggs, we have no eggs in containers. Also, if the width or length of a rectangle is 0, the "rectangle" degenerates into a straight line segment with no area. If both are 0, it degenerates into a point with no area. If instead we take a more formal approach, we can prove anything times 0 is 0 as follows: The following holds for any number a. 0 is the additive identity element, i.e. a + 0 = 0 + a = a for any number a. The quantity a times 0 has an additive inverse, -(a times 0). This means -(a times 0) is the unique number such that a times 0 + -(a times 0) = -(a times 0) + a times 0 = 0. The same applies to any number, including a times (a times 0). a times 0 = a times (a times 0 + -(a times 0)) because 0 = a times 0 + -(a times 0). a times (a times 0 + -(a times 0)) = (a times (a times 0)) + (a times -(a times 0)) because multiplication is distributive over addition, i. e. a times (b + c) = (a times b) + (a times c) for any numbers a, b, and c. (a times (a times 0)) + (a times -(a times 0)) = (a times (a times 0)) + -(a times (a times 0)) because b times -c = -(b times c) for any numbers b and c. (a times (a times 0)) + -(a times (a times 0)) = 0 because -(a times (a times 0)) is the additive inverse of (a times (a times 0)). Applying three times the principle that things equal to the same thing are equal to each other, a times 0 = 0. Quote Link to comment Share on other sites More sharing options...
Boydstun Posted June 6 Report Share Posted June 6 (edited) On relations of complex numbers to the physical world, see Ross 1991. If we require that every real number must be applicable to physical length or area as the quantity of the length or the area, then multiplication of a number as quantity of length by itself is area of a square in the Euclidean plane. Then to ask of a number A “What number L multiplied by itself is A?” is to ask “What is the length of any side of a square whose area is the quantity A?”. So if we require that every meaningful real number must be applicable to physical length or area as their quantities, to say as in the headline that 1 times 1 equals 2 is to say the square whose area is 2 has sides of length 1. That contradicts the Pythagorean Theorem, which has the result that the sum of the areas of any two unit squares that can be constructed external a unit square S from two of the latter’s adjacent unit sides equal the area of the square that can be constructed from the hypotenuse of S. An S whose area were 2 and whose sides were each 1 would not have a hypotenuse of correct length, which is to say it would not coincide with actual squares in the Euclidean plane. A square of area 2 cannot have sides of length 1, consistent with the relationship proven in the Pythagorean Theorem; rather it must have sides of length 1.41421356237. . . Then to say that 1 multiplied by 1 equals 2 is to contradict a physical fact about planes in physical space, indeed a fact about the local physical space around us in which there is land or fabric for use and sale. Edited June 6 by Boydstun tadmjones 1 Quote Link to comment Share on other sites More sharing options...
tadmjones Posted June 6 Report Share Posted June 6 I suspect Howard's criticism of method stems from an apprehension of substituting the map for the territory. Quote Link to comment Share on other sites More sharing options...
Boydstun Posted June 6 Report Share Posted June 6 (edited) The Babylonians had tables of squares, square roots, cubes, and cube roots. Their approximation for the square root of 2 was 1.414213 . . . rather than our 1. 414214 . . . . It is unknown whether they knew that the decimals would have to run to infinite places in order reach the exact number that multiplied by itself yields exactly 2. Most Babylonian record of mathematics lies in records of economic problems. I gather it was not until the Alexandrians (BCE 300 to 100 CE – Archimedes, Heron, Nichomachus, Dionphantus) that Greeks thought greatly about numbers themselves. Heron, for example, would write of adding a rectangle to a line, meaning adding the number that is magnitude of area to the number that is magnitude of a line segment. As children, age 3 to 6 these days of ours, we are taught that any sorts of things in a collection can be counted, and that understanding is one requirement for qualifying as knowing how to count. We are heirs of the Alexandrians who skimmed numbers from what they were being used for, such as measuring lengths, areas, or volumes, for counting goods or keeping accounts, or for predicting things in astronomy or in one’s future fortune. Nichomachus’s book on arithmetic was used for 1000 years. Ancient Decimal Multiplication Table from 1 through 9 Using Bamboo Strips – I assume they used 1 as the identity element for the transformation that is multiplication, and that applied to itself, it gives itself as the result. Edited June 6 by Boydstun tadmjones 1 Quote Link to comment Share on other sites More sharing options...
tadmjones Posted June 6 Report Share Posted June 6 Stephen Is it that the question about the Babylonians is based on archaeology only, or is there an argument based on math theory, so to speak , that given the rigor of their computational output suggests a lack of the concept of ‘infinite numbers’? It reminded me of Wolfram’s computational irreducibility. That idea would imply that prior to electronic computation making the calculations humanly feasible , no one can know prior to the completion of the operation the ‘places’ or ‘amount of digits’ of the ‘answer’. But it may be I am misapplying the concept to this particular operation. The thought struck me as interesting anyway. Quote Link to comment Share on other sites More sharing options...
Boydstun Posted June 7 Report Share Posted June 7 @tadmjones – (i) Every irrational in its decimal representation has an infinite train of digits, which does not terminate nor have repeating patterns. (ii) Euclid, for early example, proved that the square root of 2 is irrational. I'm pretty sure that (i) is proven classically and does not require reliance on electronic computing machines. I think the deal with the Babylonians is simply that, unlike Euclid, the clay tablets have not revealed whether they understood irrational numbers and that a decimal representation of them would have digits going on endlessly. I'll try to check further on that tomorrow. Quote Link to comment Share on other sites More sharing options...
Boydstun Posted June 7 Report Share Posted June 7 8 hours ago, Boydstun said: @tadmjones . . . I think the deal with the Babylonians is simply that, unlike Euclid, the clay tablets have not revealed whether they understood irrational numbers and that a decimal representation of them would have digits going on endlessly. I'll try to check further on that tomorrow. Although they had an algorithm yielding a good approximation, there is as yet no evidence they knew it would not yield exactitude in a finite number of iterations, according to this report. tadmjones 1 Quote Link to comment Share on other sites More sharing options...
StrictlyLogical Posted June 7 Report Share Posted June 7 12 hours ago, Boydstun said: @tadmjones – (i) Every irrational in its decimal representation has an infinite train of digits, which does not terminate nor have repeating patterns. (ii) Euclid, for early example, proved that the square root of 2 is irrational. I'm pretty sure that (i) is proven classically and does not require reliance on electronic computing machines. I think the deal with the Babylonians is simply that, unlike Euclid, the clay tablets have not revealed whether they understood irrational numbers and that a decimal representation of them would have digits going on endlessly. I'll try to check further on that tomorrow. @Boydstun I was trying to think of a thought experiment to concretize the "incommensurate" nature of various mathematical quantities as demonstrated by irrational numbers, to better help visualize this sort of thing. I have a concretized example... but as to whether it is intuitive... is another question. So far I have this. Imagine a mathematical circle with a diameter of 1, rolling inside a second mathematical circle with a circumference of 10. Now imagine a moment when the smaller circle is at the very bottom of the larger circle, touching/intersecting at a single point at the bottom of both circles. Imagine "marking" those points on the smaller circle's circumference and the larger circle's circumference (even though the larger circle never moves). Now imagine rolling the smaller circle within the larger one and waiting to see when that smaller circle's dot coincides again with the larger circle's dot... Once you have proven to yourself the answer... ask what this might say about the old (Roman?) idea of infinite loops of time repeating giving rise to every possibility including living again.... Quote Link to comment Share on other sites More sharing options...
Boydstun Posted June 7 Report Share Posted June 7 (edited) SL, I am curious if the Roman idea of infinite loops of time explicitly stated that such gives rise to the possibility of living again. Do they? Much later the possibility of living again being within possibilities in an infinite time was stressed by Nietzsche in the 1880's. He called that the eternal return. He claimed it solved a hefty philosophical conundrum or two, but the solving power was only by contemplation of his construct of eternal return said to be quite a mystery. I put it in the can where metaphysical crystals should be sent along out the house. The idea of the eternal return occurred to me on my own when I was a youth, having never heard of the idea from anyone before. It seemed so simple: if your life did not occur again in a billion years, then consider the possibilities becoming actuals in the 100 billion years beyond that first billion, and so forth. Because there is assumed to be infinite future time, there is time for the infinity of possibilities to become actual. "Every possibility has its day" one might say, and the possibility of same life again and again . . . has its days of actuality. That is all false. For truth on the matter, in moving fiction, I recommend the novel One Hundred Years of Solitude, read entirely to its end. The infinity of time would be only the lowest sort of infinity and that is trite in comparison to the larger sort of infinite possibilities attaching to the unfolding of five minutes of the earth today. The supposed infinity of time does not show that the possibility I shall again live and be typing this note to you will be fulfilled. Indeed, from the nature of the different orders of infinity, we know this will never happen again. I was disappointed in Nietzsche the atheist to be embracing and putting about the idea of the eternal return of the same in the years of his mature, original philosophy. Listening to his own common sense should have prevailed against such a view of the world being correct, even if he was not apprised of the new explorations of infinity by the mathematicians of his day. On the personal psychology side of him, it seemed to me that he, an atheist, had failed to fully own up to the very plain fact that at the end of his life he personally would cease to exist through all future time of the things continuing to exist (just as in the infinity of time before his mind was launched. Now there is something of a circle). Edited June 7 by Boydstun Quote Link to comment Share on other sites More sharing options...
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