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  "map_content": "At the end of the above video, Grant, the host from 3blue1brown, shares this video puzzle he did for Numberphile several years back. \r\n\r\nIn the video, he goes in depth and detail about ways to consider analogies to the concept of the volume of higher-dimensional balls as being similar to the concept of 2-dimensional concentric success cases for the squares of arbitrary complex points. \r\n\r\nThis is a really interesting and helpful way to deconstruct the concept of higher-dimensional modeling, and it somewhat emphasizes the concept of higher-dimensional models being dependent on reflections of lower-dimensional structures.\r\n\r\nYou can watch this video involving an imaginary game of darts and their analogy to higher-dimensional structures here:\r\n\r\nhttps://www.youtube.com/watch?v=6_yU9eJ0NxA",
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  "map_content": "Wow, wasn't aware of that. I have heard many describe Craig as our greatest genius since Turing. That's definitely something interesting that I will have to look into. Thanks!",
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  "map_content": "I can understand that, although I've had some conversations with some brothers that led me to think they may hold that view. I don't think it goes against it per se.",
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  "map_content": "I recently joined Freemasonry on the evening of Feb 17th, an evening with a new moon, a lunar eclipse, a solar fire ring and also representing the start of the new lunar year, the year of the fire horse, in the Chinese Zodiac. AMA",
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  "map_content": "Recently, 3blue1brown shared a video going quite in depth and detail about this exact question and some related equations and concepts. I really like this video, so if the subject interests you, give it a try.\r\n\r\nhttps://www.youtube.com/watch?v=fsLh-NYhOoU",
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  "map_content": "Yes, the dimensions act as memory modules and action modules for the initiating and processing of data relationships. When new modules emerge for collating and extrapolating data, it signals both breakthrough potentials but also increased functionality within greater scopes which were previously undifferentiated categories. I thinkna classic example of what this looks like experientially which most people can relate to is the graphic about the flow from data > information > knowledge > insight > wisdom...\r\n\r\nAt each new stage, a new component of the data becomes highlighted and contextualized which adds invreased meaning and reference to the rest of the content. But no new stage rearranges or changes the stages below them. To be evolved aspects, it is nevessary that they preserve the data layers below. But then add something unique. This confluence of the uniqueness of our own experiences can itself be accessed and it can be arranged and created or manifested such that as individuals, we become stewards if our own lives as opposed to playing out external expectations which we absorb.\r\n\r\nThis process is kind of similar to what Joseph Campbell calls \"the Hero with a thousand faces,\" in the sense that it's our duty and reaponsibility to reject false paradigms which would seek to use us as vessels for carrying out propaganda but instead we actualize the ground of our being. Daniel Krawisz, @CosmosStag, in his description of investor behaviors, highlights that this kind of uniqueness of our own agentic experience forces the market to react to US as opposed to the other way around where we just become a lemming and our views are simply a product of an artificial narrative crafting strategy made by those who would exploit others.\r\n\r\nSo as we become higher cognative lenses through which the universe observes and informs itself, we increasingly become carriers and informational storage  structures for this complex phenomena such that it acts through us and as us and with us... this is also commonly experienced as divinely centered. And its limits are still being explored and scoped by many agentic persons every day.",
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  "map_content": "Exquisite! A looking glass through the window of time and struggle!",
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  "map_content": "5 years ago, I authored my own non-fiction content around the 4th dimension which you can read here: Alpha, Zygote, Omega https://medium.com/@screwluse/alpha-zygote-omega-420310cf458a",
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  "map_content": "Also of note, the pathway to higher dimensionality is the pathway to conjoining wholes if that makes sense. Take an object, mirror it, then conjoin the object with its reflection and you have the new higher dimensional object, i.e. two conjoined lines form a square, two conjoined squares form a cube, two conjoined cubes form a tesseract, etc.\r\nI share some of this content partiallly just as a way to jot the ideas in my head down and to consider them from multiple perspectives. What substantiates the reflection? Perhaps it is the curvature of space which compels cognition and crystalizes into the certitude of dimensionality.",
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  "map_content": "My hypothesis is that these transformations into and out of higher and lower dimensionality are similar to the concept of inward and outward breath inward into fullness and outward to emptiness... \r\n\r\nNassime Haramein shares some insight into thia in his film \"Black Whole.\"\r\n\r\nI took a portion of this video and added my own ideas around the connection to geometry.",
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  "map_content": "My belief which I don't see anyone else talking about...is that the pattern pathways which move through this system of varying degrees of multi-scale competency architecture are self-reflective boundary conditions. \r\n\r\nI use the examples of dimensionality all the time in my explanations for this model because I think they're the most basic and straight-forward examples. So if we consider the concept of a 1-dimensional object, in a way, we can consider it as a \"whole\" object, but we can also consider it as a confluence of multiple objects. Those objects are the 1 dimensionality of the object itself combined with the two zero-dimensional boundary conditions which define it. \r\n\r\nMy argument is that the process of evolution is the process by which this object moves between the conditions of either its self or its boundary. So in other words, the first-person perspective moves between these fluidly. And there's no real signal when you're seeing from the view of the boundary vs. the object. It all feels identical to the first-person view. \r\n\r\nThis is symbolized in many of our phrases, \"when it rains, it pours,\" or \"sometimes you eat the bear, sometimes the bear eats you,\" etc. And what ultimately happens is in this process we tend to accept one orientation and reject another. And what equanimity is and the process of integrating these functionalities is the capacity to release our self-identification with the system such that we have the ability to recognize that the conditions do not define the entirety of the model. In other words, the function which the program calls itself is not the program. And calling a false function doesn't equate with the program itself being false, etc. but that these are deeper components of an integrated system and its various views are simply elements of the terrain that it touches. \r\n\r\nIf you think of this religiously, you could imagine it in the context of God's love. Just because God's love EXTENDS to the depths of those suffering in hellish environment, doesn't mean it is defined by or a product of that Hell.\r\n\r\nThat ultimately it is simply the pathways and patterns of self-awareness that guide upwards and outwards into higher and higher degrees of self-intuition and this includes the views as being both the object of interest and also simultaneously AS its boundaries. \r\n\r\nAnd that this is a tried-and-true process basically for the model of self-liberation... and this system itself follows the very geometry of the evoltuion of dimensionality itself including the conditions for the boundaries, i.e. 1-d is bounded by two 0-d points. 2-d objects bounded by 4 1-d lines, etc.\r\n\r\nUpwards to the point of the orientation and integration with the 4th dimensional framework for the existence and the boundary of Self which extends beyond mere material qualifictions in terms of the orthogonality of X, Y and Z coordinate access, but a 4th dimensional orthogonality which itself is a reflection (hence orthogonal) and this births a new set of boundary conditions which themselves are 3dimensional in nature. \r\n\r\nI believe bitcoin is the first example of this in the real world which is beyond theoretical and is actually implemented in practice.",
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  "map_content": "My belief which I don't see anyone else talking about...is that the pattern pathways which move through this system of varying degrees of multi-scale competency architecture are self-reflective boundary conditions. \r\n\r\nI use the examples of dimensionality all the time in my explanations for this model because I think they're the most basic and straight-forward examples. So if we consider the concept of a 1-dimensional object, in a way, we can consider it as a \"whole\" object, but we can also consider it as a confluence of multiple objects. Those objects are the 1 dimensionality of the object itself combined with the two zero-dimensional boundary conditions which define it. \r\n\r\nMy argument is that the process of evolution is the process by which this object moves between the conditions of either its self or its boundary. So in other words, the first-person perspective moves between these fluidly. And there's no real signal when you're seeing from the view of the boundary vs. the object. It all feels identical to the first-person view. \r\n\r\nThis is symbolized in many of our phrases, \"when it rains, it pours,\" or \"sometimes you eat the bear, sometimes the bear eats you,\" etc. And what ultimately happens is in this process we tend to accept one orientation and reject another. And what equanimity is and the process of integrating these functionalities is the capacity to release our self-identification with the system such that we have the ability to recognize that the conditions do not define the entirety of the model. In other words, the function which the program calls itself is not the program. And calling a false function doesn't equate with the program itself being false, etc. but that these are deeper components of an integrated system and its various views are simply elements of the terrain that it touches. \r\n\r\nIf you think of this religiously, you could imagine it in the context of God's love. Just because God's love EXTENDS to the depths of those suffering in hellish environment, doesn't mean it is defined by or a product of that Hell.\r\n\r\nThat ultimately it is simply the pathways and patterns of self-awareness that guide upwards and outwards into higher and higher degrees of self-intuition and this includes the views as being both the object of interest and also simultaneously AS its boundaries. \r\n\r\nAnd that this is a tried-and-true process basically for the model of self-liberation... and this system itself follows the very geometry of the evoltuion of dimensionality itself including the conditions for the boundaries, i.e. 1-d is bounded by two 0-d points. 2-d objects bounded by 4 1-d lines, etc.\r\n\r\nUpwards to the point of the orientation and integration with the 4th dimensional framework for the existence and the boundary of Self which extends beyond mere material qualifictions in terms of the orthogonality of X, Y and Z coordinate access, but a 4th dimensional orthogonality which itself is a reflection (hence orthogonal) and this births a new set of boundary conditions which themselves are 3dimensional in nature. \r\n\r\nI believe bitcoin is the first example of this in the real world which is beyond theoretical and is actually implemented in practice.",
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  "map_content": "Yes, exactly. You nailed it. I have a series of hypothetical explanations for all this that are hard to discuss with people (even with myself) because they're all so tenuous and loosely held together in my head. \r\n\r\nBut basically, you got it exactly. There are varying degrees of self-reflective boundary conditions. These conditions define our capacity to coordinate what Dr. Michael Levin calls our multi-scale competency architecture. And these boundaries give rise to new modes and models of self-interpretation and directed agentic self-actualization. \r\n\r\nSo for varying people who're at different coordinate points on this integrative self-reflective pattern pathway, the various different information at the junction points communicate different directives and represent different degrees of ordered coordination. \r\n\r\nImportantly, this happens on both the individual but also on the social levels, and you cannot conflate these or assume that one stands in for the other. And this is a primary point of emphasis, especially in respect to the application to bitcoin technologies and big vs small block value structures because effectively, the small-block narrative (in my humble estimation) is trying to implement a philosophical framework that depends on the virtues of collectivism being the natural progression of the extension of self. In other words... when we become agentic enough and self-directed enough, we evolve to a form of collectivism.\r\n\r\nIn this example, collectivism is like the butterfly.. self-direction and agentic activity is like the caterpillar. \r\n\r\nAnd to be totally honest, it is very hard not to assume this as the logical conclusion of the maturity and manifestation of Self.\r\n\r\nI believe this is the remnants of a post-modern philosophy, perhaps even a deconstructionist philosophy, which rightfully sees the flaws in a purely centralized model of something and says the best way to evolve out of a reliance on centralized structures is for \"all structures to be equal.\" The classic example of this is the participation trophy meme where we flatten the meritocracy of our subjective and often biased value judgement mechanisms as a direct counter-point to the inherent flaws in the centralized model. But ultimately, I think big blockers see that this might be a model which correctly identifies the flaws in a centralized model, and therefore represents at least some progress, ultimately, it throws the baby with the bathwater because it assumes that the only just counteraction to such a model is to homogenize the space of participation (raspberry pis) because this egalitarian model assures that the threats to decentralzied modeling are mmitigated by ensuring that no threat can ever emerge over and above any other network participant. \r\n\r\nThe big block model I think argues correctly that the point is not to eliminate the dependency on wholescale large service providers who prove value through the meritocracy of their efforts, i.e. dynamic robust capitalism empowered at the micropayment scale, but actually, the key innovation in to structure such a system so that the health of the whole is incentivized by the self-directed coordination of these distributed external service providers in such a way as they're economically incentivized to provide value to the system (which depends and relies on scale, hence the big blocker's being correct.)\r\n\r\nSo what this repesents within the context of my interpretive modeling is the shift from the idea that the homogenization of the individuals to fit a collective ideal which allows for the propogation of information nimbly by virtue of the fact that we're all acting as substrates within the higher collective self (which is an instinct to become subservient to higher-order effects just like there is an evolutionay impulse in cellular biology to allow for coordinated neural pathways to broaden the scope of a cell's goals from its own limited nature into a deeper nature via coordination through the multi-scale competency architecture of a coordinated bodily system being directed via the emergence of a central nervous system, a limbic system, a vascular system, muscular and skeletal systems, etc. where now instead of me existing is a Ho-Hum single cell wondering how to acquire enough metabolic substantive wherewithal to justify my own consumption strategies, now I get to say, Ok, I'll stop thinking about my own metabolic patterns and pathways, I'll assume the neural network to which I'm connected is appropriately managing this, and instead, I'll become a specialized cell (like a liver cell) that just gets really really good a tthe thing that livers do, i.e. cleaning blood. And I'll assume if I'm good at cleaning blood as a part of this higher-tier multi-scale competency architecture, I'll just naturally find balance and accord in terms of my metabolic demands and requirements because otherwise, I represent a threat to the higher-level goals of the system to which I am participating....)\r\n\r\nAnd so partially, we, as modern, agentic, self-sovereign, cognitive systems, we have this instinct within us to simply become a \"part of the ship, part of the crew\" that is a drive and has existed within us and supported our growth to this point for literally millions if not billions of years going back to our emergence as eukaryotes or prokaryote systems and our need to continually preserve and manage the evolutionarily significant information whcih can lead to our achieveing this higher and higher degrees of cognition, agency, self-direction, etc.\r\n\r\nSo when we're standing on the shoulders of giants in terms of our evolutionary biological instincts and we're saying, NO, our instinct is not to join the collective in hopes that we'll form some deeper model of coordination, but now, having accessed this deeper realm of abstract symbol-logic and self-directed agentic capacity, we say, actually the best pathway is for us to REMAIN distinct, but to get better at the ways in which we share and communicate and exchange peer to peer private information such that some portions of the network don't have access to the entire history of data from which to make decisions (the entire point of building a solution that replaces a centralized model to begin with) then we see that we come to this evolutionary threshold point beyond which very few have ever ventured and for which we stand and represent possibly the entire purpose and potentiality of life in the very first place.",
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  "map_content": "I like this video also. The model remains consistent up until the fraction 1/15th which I connect to the vector equilibrium. Buckminster Fuller called the V.E. the greatest possible volume for a field of unity. I connect this description to the Egyptian myth of Isis and Thoth whose body was cut into 14 pieces. This relates to the vector equilibrium which has 13 vertexes and 14 faces... once a unit is divided into beyond 14 pieces, it loses the unity principle which depends in part on this interplay between the integral described in this video. Another way to think of it is as a \"copy of a copy\" whereby some of the integrity of the original becomes lost.\r\nhttps://youtu.be/851U557j6HE?si=ruBGRCWa4a4Z9fTN",
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  "map_content": "A cool video about how pi shows up in odd places.\r\nhttps://youtu.be/6dTyOl1fmDo?si=m5nHlBqfXQNs4vBK",
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  "map_content": "The radius of the unit circle is 1. Its diameter is 2. It's bounded by a triangle whose side lengths are 3, 4 and 5. The area of the unit circle within the boundary is \u03c0 and the area of the entire triangle is 6.",
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  "map_content": "Wanted to come back to this post to share a few additional pieces of content that I think are interesting to consider in this context. \r\n\r\nRecently, I noticed a paper which argued that rotations in physical space for dynamic systems can return to their origin by doubling the walk and uniformly scaling all rotation angles. I believe this is connected to the argument that all motion is vector reflection which I included in the sub comments of this original post. You can read this new paper here: \r\n\r\nWalks in Rotation Spaces Return Home when Doubled and Scaled\r\nhttps://arxiv.org/abs/2502.14367",
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  "map_content": "One of the ideas that I've been considering has to do with this concept of boundaries and connecting them to this idea of multi-scale competency architecture which is being described by Dr Michael Levin.. and combining these ideas with this concept of motion being hyperplane reflection... \r\n\r\nSo I guess if I can create an analogy, we could imagine a system of coordinated symbol-logic... imagine it is the logical boundary of a rational young adult... the arrival at the boundary such as 2+2 = 4 affords a reflection opportunity. On the one hand, a \"katoptron\" reflection of the individual... depending on the individual, this reflection can either be integrated or it's discarded. \r\n\r\nThis relates somewhat to Dr. Levin's competency archiecture model... for example, a non-rational being may encounter the rationality boundary, and discard or otherwise reject its reflection in the same way that as young children, we often reject hard truths about the world because we are not yet mature enough to acknowledge and embrace them.",
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  "map_content": "John Baez talks about many of these topics in the video I shared in this thread. You can see it here: https://app.treechat.com/p/060591cb-14f9-492b-96bd-ee44b129b7a4\r\n\r\nHe talks about the \"Clifford Algebras\" which describe something called the Double Cover of the Orthogonal Group.. and they represent a capacity to use matrices to produce algebras that allow for this kind of manipulation. https://en.wikipedia.org/wiki/Spin_group\r\n\r\nI think that computer graphics famously use this kind of math to make very easily manipulatable 3d graphics such as avatars for video games or 3d structures inside the game that need to move and pivot while retaining their orthogonality such as moving towards a tree while also spinning and looking up.. Using this kind of vector relationships for the object allows for all three actions being produced simultaneously to produce a visualization that matches what our own eye would see if we were doing the same but in the physical world instead of a virtual one. In other words, this Clifford algebra, the spin groups, the vectors, the matrices, etc. help produce a visually consistent experience between physical and virtual worlds. This allows for the virtual world to be experienced in some ways as an extension of the physical world, and in some ways helps us to accept the world as \"real\" or \"authentic.\"",
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  "map_content": "This you could argue is somewhat supported by the idea of a curvature to space-time whereby, beyond some hypothetical event horizon, what we think of as the separations of our identity and the distinctions between our concepts of self vs. other, we become re-fused or a better term may be re-integrated into a single form. Piaget describes a bit of this process but in reverse where children begin with a fused perspective of their surroundings and themselves being intertwined, but they lack the capacity to take the perspective of others and so this process of whats sometimes called \"spiritual involution\" followed by \"spiritual evolution\"is necessary such that the \"fused\" or re-integrated consciousness is not unified in an oblivious sense (like a childs) but in what might be described as a trans-rational sense where it carries the capacity for rationality and interchange between self-and-other but also reincorporates the sense of a oneness.",
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  "map_content": "So there's some direct symbolism here between the relationship between both 12 and 13, along with the number of days in the year using both tetrahedral and triangular numbers. \r\n91 which is part of the symbolism in the Mayan complex at Chichen Itza is the 13th triangular number..\r\n\r\nSo there's again some symbolism here between the 12 and the 13, or the 12 and the one, not only in the formation of the vector equilibrium itself, but also in their connection to both triangular and tetrahedral numbers which themselves each connect to our solar cycle.",
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  "map_content": "The form is unique in the sense that it acts as an expanded and non-valent version of a univalent icosahedron structure, bivalent octahedron, and quadrivalent tetrahedron to borrow Buckminster Fuller's descriptions. So in a way, it represents a full expansion and contraction of these forms. But also, you can form the vector equilibrium by organizing 12 spheres around a central sphere into \"spheres of closest packing.\" This carries some obvious symbolism to both things like the twelve apostles around the anointed one, but also things like the 12 zodiacal cycles around a common geocentric design.",
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  "map_content": "A famous example of the tetrahedral numbering system, you have the song, the \"twelve days of Christmas\" which combines the varying days and gifts to produce a model of what a tetrahedral model with a base of twelve would look like. There's some symbolism between this model for the tetrahedral number for base 12 with the number of days in the year...364 with the final day representing Christmas Day itself (the 365th.)",
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  "map_content": "In addition, there's also connection to this symbolism in the pyramid of Chichen Itza in Yucatan in which the pyramid itself has 91 steps along each of its 4 sides which when multiplied by 4, you get 91x4=364 and these steps each lead to a platform at the top which itself represents the 365th step.",
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  "map_content": "Our ability to choose our future means the ability to invent a world of our making. Choice returns us to our deepest reverence. This is the key insight in the culmination of the Matrix. Agent Smith thinks he's finally defeated Neo, reprogramming Neo as a copy of himself, but this has the opposite of its intended effect. This reboots the matrix, undoing the mechanism of central controls and gives rise to the individuating power of agency and choice. \r\n\r\nThanks for tuning in! Let me know if you have any questions. Cheers!\r\n\r\nhttps://www.youtube.com/watch?v=C5JVFCouXIU",
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  "map_content": "He argued that Leonardo Da Vinci's use of the vanishing point in his frescos as being the \"origin\" of the third dimension within man's mental modeling, and only after this point do we see the emergence of things like rationality, the scientific method, western liberalism, separation of church and state, etc. He links these to the transformation from a two-dimensional model to a three-dimensional model of interpreting the world. He also points out that this model introduces the concept of \"dialectical opposites\" to our understanding. Prior to this shift, there was a polarity but the polarity implied in a way a uniformity of substance. For example, the yin yang represents both the light and the dark, but these are not opposed but instead are complimenting forces which help to carve out and define each other and on whom each other depend. With the introduction of the third-dimension, you have for the first time, according to Gebser, the concept of the dialectical opposites.",
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  "map_content": "And this is what I believe bitcoin is poised to demonstrate to the world. I believe when Jean Gebser is describing a future signified by \"aperspectival\" mutation in consciousness such that we are not \"bound to a singular, fixed vantage point,\" I believe he is prophetically envisioning a future driven on distributed consensus and proof-of-work. I believe bitcoin is the closest thing to a working model of 4th-dimensional structures for the re-orientation of human life away from centralized models like Facebook and Google and back into peer-to-peer exchanges of valuable information and small-world network effects.",
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  "map_content": "I'll try to wrap this up in only a few more posts and I'll relate this all to bitcoin, but first I'll just share some of my own story. I started a martial arts discipline at age 18, and this profoundly altered my perspective on life. My teacher was a student of a program called Landmark Forum, and this program is an extension of the EST program that Erhard led. I became deeply involved in supporting individuals working through this leadership training as a volunteer. \r\n\r\nMy initial training was led by a dynamic and visionary influencer named Jeff Willmore. \r\nPic related.",
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  "map_content": "And the other one was named Jean Gebser. \r\n\r\nGebser wrote a book called The Ever Present Origin and in it, he argued that mankind has gone through several developmental leaps in its conscious-capacity both on the individual and on the cultural and social levels. He analogized these leaps in consciousness as being symbolically related to dimensional shifts in the complexity of spatial form. \r\n\r\nhttps://www.youtube.com/shorts/PKAQaxKffnw",
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  "map_content": "But then one day, I was on a long bus ride, and I read a full book by him called Integral Psychology. And this truly changed my entire life. When I arrived on the bus, it was like my hair was on fire. I had never read anyone who could articulate and speak to the things I'd experienced during my year of silence, but this book could. So I began to explore less about Ken's guests and more about his own models and ideas. \r\nEventually this led me to two Swiss Psychologists named Jean!... One was named Jean Piaget, https://www.youtube.com/watch?v=IhcgYgx7aAA",
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  "map_content": "Truly dumbfounded by what I was learning on multiple fronts, my martial arts discipline, the Zen and Eastern undertones of kung fu as well as this leadership training which engendered new models for thinking, I found myself on a journey of voluntary silence for one year. During this year, I encountered many indescribeable elements to both myself and the world around me. When I started speaking again, I found very little capacity with my peers to relate with anything I was describing. Eventually, I found this relatability with an individual named Ken Wilber. Here he is in one of my favorite discussions describing the nature of the subject and the object.\r\n\r\nhttps://www.youtube.com/watch?v=NQ_HsQkBkJA",
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  "map_content": "Buckminster Fuller's description of the vector equilibrium is something to really spend time on and consider. He makes bold claims. He says that this form, the V.E., represents the highest field for a form of unity. In other words, beyond this form, you cannot hold more in a single field, and instead you'd necessitate to divide. So you could imagine that this form represents the Zygote, the fertilized egg, which initiates the cellular division process of embryogenesis. \r\n\r\nhttps://www.youtube.com/watch?v=jcq_Hzo8PC8",
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  "map_content": "Neil's description is useful because it doesn't just go into what the object is, but how we could define it by what it's bounded by. This in part introduces the concept of something called Nets, and this video gives a detailed explanation about what \"nets\" are with respect to higher-dimensional objects, and shows some examples in both three dimensions as well as four dimensions for the concept of \"nets.\" https://www.youtube.com/watch?v=Yq3P-LhlcQo",
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  "map_content": "He shares a lot of powerful information about cycles of time and the platonic solids and ways that these overlap or intersect. \r\n\r\nThese \"platonic solids\" are also called regular polyhedrons meaning that all of their faces, vertexes and angles are identical. These shapes also appear in the 4th dimension, albeit, there is a unique difference in how they show up. In the 4th dimension, these are called \"Polychorons\" or polytopes. https://en.wikipedia.org/wiki/4-polytope",
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  "map_content": "I'll take a second to unwind from higher-dimensional modeling and instead turn attention to the third dimension. There are a lot of magical and wonderful things about this third dimension and they relate in ways to things we encounter in the 4th, so let's look at them for a second. One of my favorite lectures is this one by Randall Carlson talking about Sacred Numbers in both time and space. This is worth an entire watch: https://www.youtube.com/watch?v=R7oyZGW99os",
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  "map_content": "The above video about Spheres in Higher Dimensions helps to illustrate this concept of hyperplane reflection representing \"motion.\" In the above video, math influencer, Matt Parker, author of a book of fun things to do in the 4th dimension, describes the Pythagorean Theorem generalizes to any number of dimensions. So regardless of which dimension you're in, add up all the orthogonal directions and take the square root of them, and that's the length of the new unit.",
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  "map_content": "You need to watch the video described above to understand what he's talking about in this analysis, but what's interesting is that when you arrive at 4 dimensions, the space between the \"padding spheres\" becomes equal to the size of an additional padding sphere. This is because the when you take the square root of four orthogonal directions, aka, 1+1+1+1=4 and take its square root, you get 2, and then subtracting the original length of 1 from the original padding sphere, you get 1. If you think about this, that is a conceptual model for the argument in the above video that \"all motion is hyperplane reflection.\" And it could be argued that the new \"void space\" of the original sphere is just the same sphere itself but having \"moved\" its location via reflection.\r\n\r\nDoes that make sense? I'm not claiming this is true, I'm just saying there is an argument for that using this math.",
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  "map_content": "One of the reasons why a 4th dimensional object is impossible to behold in our traditional material world is because each plane would need to be orthogonal to every other plane. We run out of orthogonal space after 3-dimensions, i.e. X-axis, Y-axis and Z-axis. \r\n\r\nBut one thing that the above video started me to consider is what if the 4th orthogonal direction IS a reflection of another dimension. In other words, you could have X\u2081, Y\u2081, Z\u2081 and you could have the reflection of X\u2081 which we could call X\u2082. This would satisfy the need to have a 4th orthogonal plane without the need to bend it beyond our traditional space/time.\r\n\r\nhttps://www.youtube.com/watch?v=mceaM2_zQd8",
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  "map_content": "This story was originally published in 1941, and it ultimately inspired Carl Sagan who described it as a beautiful example of science fiction presenting new conceptual models to a mainstream audience in a way that oriented them to deep truths about the universe which they were nevertheless unaware of...\r\n\r\nCarl Sagan goes on to describe a conceptual model for this 4th dimension here: https://www.youtube.com/watch?v=UnURElCzGc0",
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  "map_content": "The 4th dimension, in the context that I'm using it, doesn't have to do with \"time.\" This is the most common way it gets described. How I'm using the context is that this is a 4th spatial dimension. \r\n\r\nThis dimension exists mathematically, although not physically. \r\n\r\nThe 4th dimension was used as a plot device in a story called, \"He Built a Crooked House.\" You can read that story here: https://homepages.math.uic.edu/~kauffman/CrookedHouse.pdf",
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  "map_content": "In addition to Carl Sagan's useful description above, Neil DeGrasse Tyson also provides some context around the structure of some of the 4th dimensions models using an analogy not only to what the object is, but by that which it is bounded by. Rather than me repeat Neil's comments, you can watch them yourself here: https://www.youtube.com/watch?v=veXBK2Mfujk",
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  "map_content": "Hello everyone, wanted to share a bit about my interest in the 4th dimension. Let me know if there's anything specific you want to know. \r\n\r\nHere's a little bit of an overview, why I'm interested, why I think it's related to bitcoin and how it intersects with our every day lives.",
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