Stephen you are great I ve been watching you for years! I enjoyed a lot your conversation with Coecke, it was fantastic. Please could you arrange a conversation with Joscha Bach!!! ????
A Postulate: Any sufficiently complex system is it's own "universe" with its own physics (e.g.: mathematics, "our" universe, fluid dynamics, weather systems, complex computer systems, consciousness, biological systems, etc.).
48:00 "That's very beautiful " 51:00 "On the other hand I think it's good to listen to Nature.." 57:00 "As we go through time, We're being rewritten every minute"
I doubt that there is cold fusion, but yes some kind of vacuum energy effect that might be real. Garret Moddel has some interesting results about that. Regarding infinity, I now think of infinity as an inexhaustible potential, meaning that it's impossible for completed infinities to be manifested.
These talks are full of thoughtful gems, something you don't get out of one-sided conversation. Some interesting things in the end regarding Leibniz and the so-called "monadology", but I do think that Chaitin is hitting on some things here that aren't explicitly mentioned. Particularly, Leibniz's "characteristica universalis" and, what may well have been the premonitions of both the characteristica and the monadology, was his first doctoral dissertation, "Dissertatio de arte combinatoria". These ideas seem very much in line with Wolfram's "Ruliad". For more accessible info and exploration: en.wikipedia.org/wiki/Characteristica_universalis en.wikipedia.org/wiki/De_Arte_Combinatoria
the element or atom that makes up universe should be called -- prst (strong word consonants only means finger in czech language, and they call children little fingers) or Akasha or Akash or krku or strč si prst do krku or Akasha or Akash or kāś or Akashajala or Akashatejas or pao or vortz or vort or zvort or zkash or zkas or zprst - - that is my input ... arūpa jhāna derived from a root kāś meaning "to be". All matter is composed of five basic elements - panchamahabhutas - which inhere the properties of earth (pritvi), water (jala), fire (tejas), wind (vayu) and space (akasha). Akasha or Akash (Sanskrit ākāśa आकाश) means space or sky or æther in traditional Indian cosmology, depending on the religion. The term has also been adopted in Western occultism and spiritualism in the late 19th century. In many modern Indo-Aryan languages and Dravidian languages the corresponding word (often rendered Akash) retains a generic meaning of "sky".[ The word in Sanskrit is derived from a root kāś meaning "to be". It appears as a masculine noun in Vedic Sanskrit with a generic meaning of "open space, vacuity". In Classical Sanskrit, the noun acquires the neuter gender and may express the concept of "sky; atmosphere" (Manusmrti, Shatapatha Brahmana). In Vedantic philosophy, the word acquires its technical meaning of "an ethereal fluid imagined as pervading the cosmos". In the Linga Purana, akasha is translated as "firmament" and listed as one of the 1,008 names of Lord Shiva.[5] Adherents of the heterodox Cārvāka or Lokāyata philosophy held that this world is made of four elements only. They exclude the fifth, akasha, because its existence cannot be perceived.[6] Jainism Main article: Ākāśa (Jainism) Akasha is space in the Jain conception of the cosmos. Akasha is one of the six dravyas (substances) and it accommodates the other five, namely sentient beings or souls (jīva), non-sentient substance or matter (pudgala), principle of motion (dharma), the principle of rest (adharma), and the principle of time (kāla). It is all-pervading, infinite and made of infinite space-points.[7] It falls into the Ajiva category, divided into two parts: Loakasa (the part occupied by the material world) and Aloakasa (the space beyond it which is absolutely void and empty). In Loakasa the universe forms only a part. Akasha is that which gives space and makes room for the existence of all extended substances.[8] At the summit of the lokākāśa is the Siddhashila (abode of the liberated souls).[9] Buddhism In Buddhist phenomenology, akasha is divided into limited space (ākāsa-dhātu) and endless space (ajatākasā).[10] The Vaibhashika, an early school of Buddhist philosophy, hold the existence of akasha to be real.[11] Ākāsa is identified as the first arūpa jhāna, but usually translates as "infinite space
With the massive caveat that the evolution is constantly ongoing in the population and in the virus that has the population as a host ofc, even an endemic virus that is mostly shuffling around its antigens with small changes to function or removal of function can backtrack to a location in the universal meta-genome where there is a path that essentially behaves like a disequilibrium, and that how speciation of viruses works in general i think.
Meant to say every pathogen, remove the backtracking and replace it with efficiency cutbacks or something and it’s basically the same explanation, but with different details.
But i think this process of initial strain-> local maximum-> efficient backtracking-> speciation-> disequilibrium -> local maximum-> rinse and repeat is basically what goes on with the topology of the universal meta-genome of every organism. just with very different timescales and environmental factors, viruses are the simplest case ofc generally infecting 1 species at a time in a pandemic like disequilibrium. Ofc such changes does go on with the whole ecosystem as well, but fir humans for example i have a hard time seeing any kind of selection based on the immunity of nature so to speak, it more like a virus with only one individual to infect and survive in, which is pretty different.
About Chaitin's remarks on the existence of the reals. I have a hard time with the idea that continuity and discreetness are different or incompatible things; more like two sides of the same coin.
zprst or prst is a fundamental element of space strčh is a fundamental element of space -- the element or atom that makes up universe should be called zprst or prst or strčh or zamb or otti or zamm
@3:30 Greg is right. A sentient species that can do mathematics is no longer constrained by material evolution and can start to endlessly evolve in perfecting intellectual/spiritual capacities (by the latter I just mean social virtues - kindness, compassion, wisdom --- not mysticism nonsense). Material environmental constraints are the province of adaptation for species who have not evolved second order intellectual capacity.
@47:00 omg. Two things here. First "cold fusion" is a thing, this was understood, the issue is you cannot break even. Second: vacuum "energy" is not energy. Unless you are talking gravitational scales (which you are not) energy as quantum vacuum is a misnomer. Only differences in energy have meaning outside of gravity. So what you take with your left hand gets sucked out from your right hand. So with any vacuum energy device you again have a break-even problem to solve. The simplest one is Casimir plate energy. Once the plates get pushed apart a ways (oooohh... vacuum energy man!!!), you need at least that energy to put back to run a cycle. So it is not a reservoir of energy for any useful heat engine. Quantum vacua fields do not store energy, they just shunt around small (tiny) fluctuations in modes. You cannot break even with this.
Makes a lot of sense to me, and is probably related to the real dynamics behind endemic equilibrium in viruses, vs pandemic species. Its pretty Simple, an endemic species has reached a local maximum with respect to certain functions, so with respect to the biology of the host species at a given level of immunity the virus cannot easily gain any bigger advantage by further development of existing genes, that are close enough to the genes with potential gains of function such that such a random transition is likely at all. I say likely because no such equilibrium can be stable, what happens in reality when a virus reaches this kind of equilibrium with respect to its function, is that the level of immunity rises in the host species until losing function along with modifying antigens provides a larger advantage in transmissibility than the loss of function now corresponds to given the evolution of the state of the immunity in the host species. the virus will then be driven to devolve some of its functions or change them in random ways that has the greatest change to antigens in terms of the ability for our immune systems to recognize them, at minimal cost to function, this might manifest most often in respiratory viruses tho, because in other more severe viruses the strategies for replication might be to be way too deadly and then people are forced into contact with them, instead of having to infect respiratory system tissue in large numbers to spread. With modern sanitation and so on ofc these don’t usually cause pandemics anyway, respiratory viruses are the wast majority of endemic species. Anyway the same dynamics goes on with respect to for example ebola in their host species, and is usually only in disequilibrium when they jump species in pandemic situations.
@33:30 The Continuum Hypothesis is not about platonism. It is a basic conjecture of ZF set theory: Is 2^{\aleph_0}=\aleph_1 ? Although now thanks to Gödel and Cohen it is a conjecture of only larger axiom schemas. You have to understand though that platonism admits many different axiomatic schemas, each mutually incompatible. Consistency is only required within one choice of axioms. There are some platonists (self-described) who believe, like some religion, that "there is only one (schema)." But they're delusional. We already know there are consistent axiom schema that are mutually inconsistent. Choosing one of them and calling It "the only mathematics" is like choosing a Honda Civic and calling it "the only car." Fine, you win, it _is_ the only car. My Ford Mondeo is a flurkinwheelitzen then. If your ZFC+not(CH) axiom schema is by your decree _the only mathematics_ then I guess I am studying chaitingodematics rather than "mathematics." You cool with that? The analogous (but only analogous) platonistic puzzle is whether a true well-defined continuum of minimal cardinality exists in the mindscape (mathematical realm). If so, it'd be a metaphysical basis for something like continuum spacetime. No one can frame that as a mathematical conjecture though, it's mysticism. Cool to think about, maybe even useful to think about, but mystical.
@59:00 that's wrong Stephen. Maxwell's daemon would agree the Second Law holds, and could prove it better than we can. It is a law of statistics obeyed by _any_ sufficiently thermalized system (no energy in or out) in _any_ universe, not a law of elementary motion. The was Eddington's point I believe.
Zeno's paradox seems appropriate here. Lets think in 2 dimensions for a moment, creativity or novelty will be randomly distributed, and it will be the inverse square law that dictates the rate of growth of discovering novel information. We humans are not infinite, so our ability to detect novel information will become more and more difficult as time progresses. We will have to travel further intellectually to find novelty, we have already picked the low hanging fruit, in other words, novel data accumulation will be a product of diminishing returns.
History has shown the opposite. Power law seems to better describe the rate of technological development by humans. Oldowan tools were used for 1 million years for example. The more technological development there has been the faster that rate of development becomes. This is the broad historical general pattern. When you zoom in there are fluctuations and such. Currently the rate of technological development is a bit stagnant, but that's a reflection of decaying, rotting capitalist relations of production. With fundamental transformation of these property relations, by turning the means of production into collective property, there'll be again a huge increase in technological development.
@Kostoglotov You are (falsely I think) assuming _intellectual space_ is geometric and, to boot, locally Riemannian. Well, it could well be so, but does not have to be such a topology, and if you are honest is vanishingly likely to be so. The so-called Mindscape (q.v. Rudy Rucker and others) is likely better described by a complex highly irregular network structure with connections that are not well-described by euclidean or even Banach type metrics, more like p-adic structure or other network topology, and that's if the mind even has a well-defined geometry, it doesn't have to, each persons mind has a different structure. Best not to generalize from the particular to the generic in this field of study.
Its kind of like a virus develops a bunch of limbs, and when our immune system gets good enough on average it begins to pay off to have only 4 fingers instead of 5, and eventually it’s better to just have a single joint and at that point there is room for a different path of evolution to take place, maybe into a leg instead or a tail, who knows, its an analogy, but genetically it’s quite similar, if the functions begin to become ambiguous in its efficiency then there is more room to explore the landscape of the universal meta genome than if the only way to live is to have fingers. i think the virus case is quite cool, we are going to probably get some evidence of exactly how it happens in a large scale pandemic-> endemic, and my bet is that the variants will increasingly over time change their antigens as much as possible in terms of detection by the immune system and as little as much in terms of functions, and i hope we don’t see speciation tbh because if we do we are rolling the dice on wether we get quite different but still potentially dangerous variants that are far away genetically from the strains we have seen until now. we’ll see, i hope not, i think the chance of that is quite low, but still its a possibility.
You tvo busy beavers should take a break ;) Proton = 4 (orange) Cartesian theater vith 6 axis visible (hexagon) Electron = 5 (blue) Time = 7 (refraction angle to let one 6 in one dark quadrant) Ether = 0 (void-filament)=magnetic 0|0 [flover of life void structure-vater makes circles] god = 9 (spiral as 90 degree cube borner) 360 degrees links the circle(9) to a square(4) hence the 49 number 0=9 as 40 days and nights The all = 1 (also 6 as vhite) Polarity = 2 = 0|0 Consciousness = 3 (mandelbrot=circle collapsed on one side in the void borning the circle out of the heart) = DARK (pupil color) Thought = 6 (also knovn as light as number of man) = VHITE Infinity or source = 8 (octave to the unit as the all) = SUN = STARS Free vill = 11 (the controller of 3 and 6) CREATOR = 9 (god)[in mattter or angle viev is 7] DECODER = 0|0 (the creature's eyes, that observes the 3'rd 0 as 9) 3+3+3=9 Holy Trinity = C0|0R NUMBER GEOMETRY (red orange yellov green turquoise blue violet[indigo]) (9876543210) (angles in circle) [imagination] [logic] [motion] {6} {3} {9} COMPLEX NUMBERS = color Cartesian system (mathemaics vith colors instead of numbers) Imaginary axis = 6 Real axis = 3 color perception hidden in 0, the number Cartesian system is giving birth to the Riemann Hypothesis (12=full circle as 1/2=0.5 the trivial 0 line) rainbov number format: PINK(+) is the observer 2487050 (8 colors full, 7 as observer of self) 8+7=15(MIracle) = 6 0-foundation 369 - only curves (etheric numbers) 147 - only angles [time bound numbers] 258 - angles and curves (explorer numbers) Analog vorks vith 0 and 9 Digital vorks vith 0 and 1 5 vay separation of 9 is 4-5 3-6 2-7 1-8 0-9 (self borning from void) as the 10 fingers in front of you + you as the 11'th th-cam.com/video/eyzWz8mpMM8/w-d-xo.html
This will never stop to baffle me: to what lengths some people are ready to go, and how many nonsensical crap they are willing to utter and 'discuss' in order to confirm their bias; their godlessness bias that is.
Assume there’s a “god” (any one of the hundreds or thousands of them that humans have asserted exist). What created god? I thought about this for maybe 5 minutes once when I was a pre-teen and easily realized that “god” isn’t an explanation for anything. It’s a crutch for the mentally feeble and the emotionally handicapped and a gift for society’s predators who can use it to easily manipulate them. It’s compelling to you because it requires zero intellect or comprehension of anything at all.
@@AngusRockford So you asked yourself a uestion, a fair and important one to be fair, you spent a whole *5 minutes* thinking about it, at an age when you could hardly tie your own shoe laces and then came up with the moronic answer that everybody else who claims that maybe the universe has a Maker is for the "mentally feeble and the emotionally handicapped". Talk about the Dunning-Kruger effect in action. It is moronic and childish then, but as you grow older, it becomes just plain moronic (because childish implies an innocent ignorance). The answer is: the logical thought process entails that every creation has a creator, and since that can't go ad infinitum, there must be an entity that is not (read "can not") be a creation itself. Allah is the Creator: “He is Allah - One- the Sustainer ˹needed by all˺. He has never had offspring, nor was He born. And there is none comparable to Him.” 112. Now, let's try this again: take some time and think about how stupid this idea that everything was/is/will be here long before/after we are here popped out from nowhere by nobody for no reason. As per God being a "gift for society’s predators", I simply cannot speak of you or anybody's experience, but as a Muslim, I didn't end up with that conclusion, based on my personal experience of course. That being said, if the catholic church covers up child abuse, it's up for the good Christians to defend (or better, disavow) those crimes, of which Jesus (peace be upon him) is absolutely innocent of. Final point, to my 'chagrin', any human being admitting the existence of a God that inspires awe in its wonderful creations, is proof of his/her propensity to be humble and modest, which is never a bad personal trait :) ... even among the Nobel prizes of biology, physics.. you hardly find so much nonsense uttered with this much confidence. Russel is ever more right: “One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.”
@1:05:00 "Proof in math is like time in physics..." bro, _bro!_ this is not serious. You are confusing analogy with actual metaphysics. You can use analogy for discovery, but you cannot use analogy to make ontological claims like you do here. You can use analogy to _guess_ at ontological claims. Also, seems like you are confusing mathematics with process. Mathematics is abstraction, not process. _Doing_ mathematics is not the same _as Mathematics._ Running an algorithm (instantiation) is not _the algorithm._ There is no such concrete entity as "the algorithm" (for _any_ algorithm). It is an abstraction.
He's not just using "analogy" as discovery. He assumes that mathematics is a computational system just like physics. Whether or not his assumptions are correct is another matter.
@8:00 "humans haven't changed that much..." is a very myopic and (imho) false view. You are indexing far too much on the material (like an idiot marxist). Being human (or maybe I should put that in quote marks?) "being human" is not constrained to our biology and material condition or the qualitative similarity in works of literature over history. As Phillip Anderson wrote, "more is different" and we have a _lot more_ in not material terms but intellectual and spiritual terms, by the latter for instance, the general sphere of human empathy has inexorably grown over history, it can now (in many people at least, not all) encompass the whole Earth, and indeed it must do so for at least a sizeable minority if we are to survive as a species. When we note that _more is different_ we are also talking about combinatorial explosions, even in a finite system (number of possible games of _go_ compared to chess) in which case more is not only different, more is richer, immensely so. But we can even go beyond that: just by the rather "natural" development of the mathematical number systems we already right there have created infinite intellectual space to explore (try telling Hugh Woodin otherwise! The dude may be on a flight of fancy, but it is still exploration of an imagined infinite realm). Don't flame me for saying so, but already we know mathematics is not constrained by finite computation. The computational paradigm is useful framing for some issues, but it is not all of mathematics. It is also a logical fallacy to claim that _because_ human brains are finite we are _thus_ inherently limited to finite computations. This ignores the fact that with the discovery of transfinite set theory we have in fact created infinite realms to explore. The fact one person's brain is finite does not mean humans as a species are limited by a finite realm of thought. No! Our _realm of exploration_ is infinite, even while one person's brain might be finite. (And do not ask me to define a "realm" I do not know what that is, but I refer you to the more primitive notion of a topological "space".) Put another way, although your, or even our whole collective, minds cannot encompass infinite thoughts, any _single_ thought cloud we have is not constrained to a finite set of "all possible thoughts." The abstract set of "all possible thoughts" is infinite, and as far as anyone knows it has a multiply connected topology, so we are not exploring this space by local jumps, a single "jump" in thinking can get us from one idea to nearby (in mental space) some completely bizarre unheard of ideas. The Mindspace is not a Euclidean space (or if it is, well, sh*t...., we're in serious trouble!) You can be a dick about it all, like Zeilberger and other finitists, and _define_ mathematics to be finite, hence escape Gödel propositions, but that's just _your_ definition. Fine I say. Just don't foist it upon me. Note also that "the discrete" is not the same as "the finite." That whole line of thinking is completely flawed logic which suckers amateurs. The transfinite ordinals are "discrete" not continuous, they "count" come continua, but are not themselves continuum sets. Every set is discrete, all the transfinite sets, even all the Aleph_k are discrete. Having uncountably many elements does not make you continuous. Having a discrete set that can be placed in bijective correspondence with an ideal continua, like the Real number line (indexed by the set of Real numbers), is no contradiction. The Real number line (a physicalist sort of notion, is not the same as the abstract set of Real numbers, the latter is just one of many possible models for the former). "Continuous" is a topological notion, and sets have no topology until you pick one, and _every_ set can have a discrete topology imposed on it (the trivial topology), and _every_ countable infinite set can get a "continuous" topology (homeomorphic to the reals) imposed on it (the standard topology on it's power set).
BTW: the plausibility[*] of strict finitism in mathematics is not an argument for why it should be adopted as the only valid way to do mathematics. Same as the incompleteness of Peano arithmetic or ZFC set theory is not an argument against adopting these as valid foundations for mathematical exploration. [*] Plausibility here might be taken as "powerful enough to do everything we want with numbers and associated concepts." It is a philosophical notion, not a rigorously defined notion. We surely cannot say now what we want mathematics to do for us at some arbitrary future time.
@13:00 this is not quite right Stephen. And Darwin was not so much of a genius you should hang by his every word. Inexorable growth in complexity is not a law of natural evolution (it is not even a law of black hole thermodynamics out to long times) it is a statistical feature, not a law. Closer to a law (though still statistical I suspect) would be progressively (perhaps punctuated) more parsimony --- be as simple as you can be to solve the survival and replication problem facing you, but no simpler. It is based on the reality you have a finite reservoir of free energy (or exergy). This can, sometimes, run the opposite way to increasing complexity. With increasing complexity (take collateralized debt and derivatives in financial economics) can come _increased fragility_ (q.v. Hyman Minsky). I think Greg's theorems are too abstract to be simply relatable to natural evolution in the Earth's biosphere in the naïve way your conversation tried to suggest. With his theorems he can say some generic things about Natural evolution, but not a lot.
Before you get tendentious with me, I understand the _desire_ to have "one perfect mathematics." And I understand that _was_ the original motive for philosophical platonism. But as Marx said, the followers of a philosopher have a duty to correct his/her mistakes and make improvements, or overturn things entirely in the program. What Gödel bequeathed to us is a precious understanding that there need not be one single perfect mathematics, there can be several. It does not destroy the essential thesis of platonism however. It enlarges the platonic realm. The essential idea is mathematics aught to be describing something: "our universe" was one motive. But dovetailing nicely (fortuitously?) with modern physics, we have this idea (fictional, fantasy, speculative, regardless) of the Multiverse, which maybe is nature giving us a strong hint that there is never going to be one unique mathematical structure that can consistently describe all universi. Maybe in the far future we will figure out that, hey... whaddya know... there _is_ only one axiomatic schema that describes all multiverses. But until we nail down that result, there seems nothing terrifying about admitting mutually inconsistent mathematical structures. The danger (not terrifying, just logical) is that you can never usefully employ two or more such structures to describe the same phenomena, that _would_ lead to absurdities. I think the idea there had to be only one unique _mathematics_ was based on a non sequitur, like some hope that all spoken languages could be mutually translated perfectly, which turned out not to be true. So why would it be true for mathematics? I think the intuition it should have been so for mathematics is based on the intuition about numbers: there is something awesomely unique about counting: 1,2,3,4... there is only one way to do it, so there should only be one way to "correctly" axiomatize arithmetic. But of course we know that is in fact dead true. Arithmetic _is_ perfect and unique. There is only one of them cars. It is only when encountering the transfinite that we get a branching of possible mathematical axiom schema. It is an enlargement, but _finite_ arithmetic is still completely unique and perfect. Like Chaitin though, I regard that enlargement as beautiful, not horrific. ("Small is beautiful" is only a "thing" in context of a resource constrained shared environment. Numbers are unconstrained and inexhaustible.)
“In a finite universe, there is no incompleteness.”
Stephen you are great I ve been watching you for years! I enjoyed a lot your conversation with Coecke, it was fantastic. Please could you arrange a conversation with Joscha Bach!!! ????
really cool talk thanks wolfram team and friends ^.^
A Postulate:
Any sufficiently complex system is it's own "universe" with its own physics (e.g.: mathematics, "our" universe, fluid dynamics, weather systems, complex computer systems, consciousness, biological systems, etc.).
48:00 "That's very beautiful "
51:00 "On the other hand I think it's good to listen to Nature.."
57:00 "As we go through time, We're being rewritten every minute"
I doubt that there is cold fusion, but yes some kind of vacuum energy effect that might be real. Garret Moddel has some interesting results about that. Regarding infinity, I now think of infinity as an inexhaustible potential, meaning that it's impossible for completed infinities to be manifested.
24:27 Curious about this convergence he speaks of and how it relates to LUSI
The dynamic world never fails to add opportunity in contrast to any idealised stasis
Is there an analogous Gauss curve model for an integer
We need a part 3 please. Can you also interview Sara Walker and Anirban Bandhyopdhyay.
What does Chaitin think about your approach of generating randomness form small programs? It seems to be in contradiction whith his AIT?
These talks are full of thoughtful gems, something you don't get out of one-sided conversation. Some interesting things in the end regarding Leibniz and the so-called "monadology", but I do think that Chaitin is hitting on some things here that aren't explicitly mentioned. Particularly, Leibniz's "characteristica universalis" and, what may well have been the premonitions of both the characteristica and the monadology, was his first doctoral dissertation, "Dissertatio de arte combinatoria". These ideas seem very much in line with Wolfram's "Ruliad".
For more accessible info and exploration:
en.wikipedia.org/wiki/Characteristica_universalis
en.wikipedia.org/wiki/De_Arte_Combinatoria
In a complex integrated self identifying entity like the cell how random is a functional mutation really?
Conversely could time be proof in other words a perception of process which we instrument
Before we pursue this dialogue. "How many rejections have you had".
"The set of set theorists is not a large set"
the element or atom that makes up universe should be called -- prst (strong word consonants only means finger in czech language, and they call children little fingers) or Akasha or Akash or krku or strč si prst do krku or Akasha or Akash or kāś or Akashajala or Akashatejas or pao or vortz or vort or zvort or zkash or zkas or zprst - - that is my input ... arūpa jhāna derived from a root kāś meaning "to be". All matter is composed of five basic elements - panchamahabhutas - which inhere the properties of earth (pritvi), water (jala), fire (tejas), wind (vayu) and space (akasha). Akasha or Akash (Sanskrit ākāśa आकाश) means space or sky or æther in traditional Indian cosmology, depending on the religion. The term has also been adopted in Western occultism and spiritualism in the late 19th century. In many modern Indo-Aryan languages and Dravidian languages the corresponding word (often rendered Akash) retains a generic meaning of "sky".[ The word in Sanskrit is derived from a root kāś meaning "to be". It appears as a masculine noun in Vedic Sanskrit with a generic meaning of "open space, vacuity". In Classical Sanskrit, the noun acquires the neuter gender and may express the concept of "sky; atmosphere" (Manusmrti, Shatapatha Brahmana). In Vedantic philosophy, the word acquires its technical meaning of "an ethereal fluid imagined as pervading the cosmos".
In the Linga Purana, akasha is translated as "firmament" and listed as one of the 1,008 names of Lord Shiva.[5]
Adherents of the heterodox Cārvāka or Lokāyata philosophy held that this world is made of four elements only. They exclude the fifth, akasha, because its existence cannot be perceived.[6]
Jainism
Main article: Ākāśa (Jainism)
Akasha is space in the Jain conception of the cosmos. Akasha is one of the six dravyas (substances) and it accommodates the other five, namely sentient beings or souls (jīva), non-sentient substance or matter (pudgala), principle of motion (dharma), the principle of rest (adharma), and the principle of time (kāla).
It is all-pervading, infinite and made of infinite space-points.[7]
It falls into the Ajiva category, divided into two parts: Loakasa (the part occupied by the material world) and Aloakasa (the space beyond it which is absolutely void and empty). In Loakasa the universe forms only a part. Akasha is that which gives space and makes room for the existence of all extended substances.[8]
At the summit of the lokākāśa is the Siddhashila (abode of the liberated souls).[9]
Buddhism
In Buddhist phenomenology, akasha is divided into limited space (ākāsa-dhātu) and endless space (ajatākasā).[10]
The Vaibhashika, an early school of Buddhist philosophy, hold the existence of akasha to be real.[11]
Ākāsa is identified as the first arūpa jhāna, but usually translates as "infinite space
With the massive caveat that the evolution is constantly ongoing in the population and in the virus that has the population as a host ofc, even an endemic virus that is mostly shuffling around its antigens with small changes to function or removal of function can backtrack to a location in the universal meta-genome where there is a path that essentially behaves like a disequilibrium, and that how speciation of viruses works in general i think.
Meant to say every pathogen, remove the backtracking and replace it with efficiency cutbacks or something and it’s basically the same explanation, but with different details.
But i think this process of
initial strain-> local maximum-> efficient backtracking-> speciation-> disequilibrium
-> local maximum-> rinse and repeat is basically what goes on with the topology of the universal meta-genome of every organism. just with very different timescales and environmental factors, viruses are the simplest case ofc generally infecting 1 species at a time in a pandemic like disequilibrium. Ofc such changes does go on with the whole ecosystem as well, but fir humans for example i have a hard time seeing any kind of selection based on the immunity of nature so to speak, it more like a virus with only one individual to infect and survive in, which is pretty different.
About Chaitin's remarks on the existence of the reals. I have a hard time with the idea that continuity and discreetness are different or incompatible things; more like two sides of the same coin.
zprst or prst is a fundamental element of space strčh is a fundamental element of space -- the element or atom that makes up universe should be called zprst or prst or strčh or zamb or otti or zamm
41:05 ❤️
@3:30 Greg is right. A sentient species that can do mathematics is no longer constrained by material evolution and can start to endlessly evolve in perfecting intellectual/spiritual capacities (by the latter I just mean social virtues - kindness, compassion, wisdom --- not mysticism nonsense). Material environmental constraints are the province of adaptation for species who have not evolved second order intellectual capacity.
@47:00 omg. Two things here. First "cold fusion" is a thing, this was understood, the issue is you cannot break even. Second: vacuum "energy" is not energy. Unless you are talking gravitational scales (which you are not) energy as quantum vacuum is a misnomer. Only differences in energy have meaning outside of gravity. So what you take with your left hand gets sucked out from your right hand. So with any vacuum energy device you again have a break-even problem to solve. The simplest one is Casimir plate energy. Once the plates get pushed apart a ways (oooohh... vacuum energy man!!!), you need at least that energy to put back to run a cycle. So it is not a reservoir of energy for any useful heat engine. Quantum vacua fields do not store energy, they just shunt around small (tiny) fluctuations in modes. You cannot break even with this.
Makes a lot of sense to me, and is probably related to the real dynamics behind endemic equilibrium in viruses, vs pandemic species. Its pretty Simple, an endemic species has reached a local maximum with respect to certain functions, so with respect to the biology of the host species at a given level of immunity the virus cannot easily gain any bigger advantage by further development of existing genes, that are close enough to the genes with potential gains of function such that such a random transition is likely at all. I say likely because no such equilibrium can be stable, what happens in reality when a virus reaches this kind of equilibrium with respect to its function, is that the level of immunity rises in the host species until losing function along with modifying antigens provides a larger advantage in transmissibility than the loss of function now corresponds to given the evolution of the state of the immunity in the host species. the virus will then be driven to devolve some of its functions or change them in random ways that has the greatest change to antigens in terms of the ability for our immune systems to recognize them, at minimal cost to function, this might manifest most often in respiratory viruses tho, because in other more severe viruses the strategies for replication might be to be way too deadly and then people are forced into contact with them, instead of having to infect respiratory system tissue in large numbers to spread. With modern sanitation and so on ofc these don’t usually cause pandemics anyway, respiratory viruses are the wast majority of endemic species. Anyway the same dynamics goes on with respect to for example ebola in their host species, and is usually only in disequilibrium when they jump species in pandemic situations.
@33:30 The Continuum Hypothesis is not about platonism. It is a basic conjecture of ZF set theory: Is 2^{\aleph_0}=\aleph_1 ? Although now thanks to Gödel and Cohen it is a conjecture of only larger axiom schemas. You have to understand though that platonism admits many different axiomatic schemas, each mutually incompatible. Consistency is only required within one choice of axioms. There are some platonists (self-described) who believe, like some religion, that "there is only one (schema)." But they're delusional. We already know there are consistent axiom schema that are mutually inconsistent. Choosing one of them and calling It "the only mathematics" is like choosing a Honda Civic and calling it "the only car." Fine, you win, it _is_ the only car. My Ford Mondeo is a flurkinwheelitzen then.
If your ZFC+not(CH) axiom schema is by your decree _the only mathematics_ then I guess I am studying chaitingodematics rather than "mathematics." You cool with that?
The analogous (but only analogous) platonistic puzzle is whether a true well-defined continuum of minimal cardinality exists in the mindscape (mathematical realm). If so, it'd be a metaphysical basis for something like continuum spacetime. No one can frame that as a mathematical conjecture though, it's mysticism. Cool to think about, maybe even useful to think about, but mystical.
Bery crude description there but yeah
@59:00 that's wrong Stephen. Maxwell's daemon would agree the Second Law holds, and could prove it better than we can. It is a law of statistics obeyed by _any_ sufficiently thermalized system (no energy in or out) in _any_ universe, not a law of elementary motion. The was Eddington's point I believe.
1 time
2 space
3 matter
4 life
5 sex
6 morality
Zeno's paradox seems appropriate here. Lets think in 2 dimensions for a moment, creativity or novelty will be randomly distributed, and it will be the inverse square law that dictates the rate of growth of discovering novel information. We humans are not infinite, so our ability to detect novel information will become more and more difficult as time progresses. We will have to travel further intellectually to find novelty, we have already picked the low hanging fruit, in other words, novel data accumulation will be a product of diminishing returns.
History has shown the opposite. Power law seems to better describe the rate of technological development by humans. Oldowan tools were used for 1 million years for example. The more technological development there has been the faster that rate of development becomes. This is the broad historical general pattern. When you zoom in there are fluctuations and such. Currently the rate of technological development is a bit stagnant, but that's a reflection of decaying, rotting capitalist relations of production. With fundamental transformation of these property relations, by turning the means of production into collective property, there'll be again a huge increase in technological development.
@Kostoglotov You are (falsely I think) assuming _intellectual space_ is geometric and, to boot, locally Riemannian. Well, it could well be so, but does not have to be such a topology, and if you are honest is vanishingly likely to be so. The so-called Mindscape (q.v. Rudy Rucker and others) is likely better described by a complex highly irregular network structure with connections that are not well-described by euclidean or even Banach type metrics, more like p-adic structure or other network topology, and that's if the mind even has a well-defined geometry, it doesn't have to, each persons mind has a different structure. Best not to generalize from the particular to the generic in this field of study.
Its kind of like a virus develops a bunch of limbs, and when our immune system gets good enough on average it begins to pay off to have only 4 fingers instead of 5, and eventually it’s better to just have a single joint and at that point there is room for a different path of evolution to take place, maybe into a leg instead or a tail, who knows, its an analogy, but genetically it’s quite similar, if the functions begin to become ambiguous in its efficiency then there is more room to explore the landscape of the universal meta genome than if the only way to live is to have fingers. i think the virus case is quite cool, we are going to probably get some evidence of exactly how it happens in a large scale pandemic-> endemic, and my bet is that the variants will increasingly over time change their antigens as much as possible in terms of detection by the immune system and as little as much in terms of functions, and i hope we don’t see speciation tbh because if we do we are rolling the dice on wether we get quite different but still potentially dangerous variants that are far away genetically from the strains we have seen until now. we’ll see, i hope not, i think the chance of that is quite low, but still its a possibility.
The fundamental flaw in AI is human nature in its use.
You tvo busy beavers should take a break ;)
Proton = 4 (orange) Cartesian theater vith 6 axis visible (hexagon)
Electron = 5 (blue)
Time = 7 (refraction angle to let one 6 in one dark quadrant)
Ether = 0 (void-filament)=magnetic 0|0 [flover of life void structure-vater makes circles]
god = 9 (spiral as 90 degree cube borner) 360 degrees links the circle(9) to a square(4) hence the 49 number 0=9 as 40 days and nights
The all = 1 (also 6 as vhite)
Polarity = 2 = 0|0
Consciousness = 3 (mandelbrot=circle collapsed on one side in the void borning the circle out of the heart) = DARK (pupil color)
Thought = 6 (also knovn as light as number of man) = VHITE
Infinity or source = 8 (octave to the unit as the all) = SUN = STARS
Free vill = 11 (the controller of 3 and 6)
CREATOR = 9 (god)[in mattter or angle viev is 7]
DECODER = 0|0 (the creature's eyes, that observes the 3'rd 0 as 9) 3+3+3=9
Holy Trinity = C0|0R NUMBER GEOMETRY (red orange yellov green turquoise blue violet[indigo]) (9876543210) (angles in circle) [imagination] [logic] [motion] {6} {3} {9}
COMPLEX NUMBERS = color Cartesian system (mathemaics vith colors instead of numbers)
Imaginary axis = 6
Real axis = 3
color perception hidden in 0, the number Cartesian system is giving birth to the Riemann Hypothesis (12=full circle as 1/2=0.5 the trivial 0 line)
rainbov number format: PINK(+) is the observer 2487050 (8 colors full, 7 as observer of self) 8+7=15(MIracle) = 6
0-foundation
369 - only curves (etheric numbers)
147 - only angles [time bound numbers]
258 - angles and curves (explorer numbers)
Analog vorks vith 0 and 9
Digital vorks vith 0 and 1
5 vay separation of 9 is 4-5 3-6 2-7 1-8 0-9 (self borning from void) as the 10 fingers in front of you + you as the 11'th
th-cam.com/video/eyzWz8mpMM8/w-d-xo.html
This will never stop to baffle me: to what lengths some people are ready to go, and how many nonsensical crap they are willing to utter and 'discuss' in order to confirm their bias; their godlessness bias that is.
Assume there’s a “god” (any one of the hundreds or thousands of them that humans have asserted exist). What created god? I thought about this for maybe 5 minutes once when I was a pre-teen and easily realized that “god” isn’t an explanation for anything. It’s a crutch for the mentally feeble and the emotionally handicapped and a gift for society’s predators who can use it to easily manipulate them. It’s compelling to you because it requires zero intellect or comprehension of anything at all.
@@AngusRockford So you asked yourself a uestion, a fair and important one to be fair, you spent a whole *5 minutes* thinking about it, at an age when you could hardly tie your own shoe laces and then came up with the moronic answer that everybody else who claims that maybe the universe has a Maker is for the "mentally feeble and the emotionally handicapped". Talk about the Dunning-Kruger effect in action.
It is moronic and childish then, but as you grow older, it becomes just plain moronic (because childish implies an innocent ignorance).
The answer is: the logical thought process entails that every creation has a creator, and since that can't go ad infinitum, there must be an entity that is not (read "can not") be a creation itself. Allah is the Creator: “He is Allah - One- the Sustainer ˹needed by all˺. He has never had offspring, nor was He born. And there is none comparable to Him.” 112.
Now, let's try this again: take some time and think about how stupid this idea that everything was/is/will be here long before/after we are here popped out from nowhere by nobody for no reason.
As per God being a "gift for society’s predators", I simply cannot speak of you or anybody's experience, but as a Muslim, I didn't end up with that conclusion, based on my personal experience of course. That being said, if the catholic church covers up child abuse, it's up for the good Christians to defend (or better, disavow) those crimes, of which Jesus (peace be upon him) is absolutely innocent of.
Final point, to my 'chagrin', any human being admitting the existence of a God that inspires awe in its wonderful creations, is proof of his/her propensity to be humble and modest, which is never a bad personal trait :) ... even among the Nobel prizes of biology, physics.. you hardly find so much nonsense uttered with this much confidence.
Russel is ever more right: “One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.”
@1:05:00 "Proof in math is like time in physics..." bro, _bro!_ this is not serious. You are confusing analogy with actual metaphysics. You can use analogy for discovery, but you cannot use analogy to make ontological claims like you do here. You can use analogy to _guess_ at ontological claims. Also, seems like you are confusing mathematics with process. Mathematics is abstraction, not process. _Doing_ mathematics is not the same _as Mathematics._ Running an algorithm (instantiation) is not _the algorithm._ There is no such concrete entity as "the algorithm" (for _any_ algorithm). It is an abstraction.
He's not just using "analogy" as discovery. He assumes that mathematics is a computational system just like physics. Whether or not his assumptions are correct is another matter.
@8:00 "humans haven't changed that much..." is a very myopic and (imho) false view. You are indexing far too much on the material (like an idiot marxist). Being human (or maybe I should put that in quote marks?) "being human" is not constrained to our biology and material condition or the qualitative similarity in works of literature over history. As Phillip Anderson wrote, "more is different" and we have a _lot more_ in not material terms but intellectual and spiritual terms, by the latter for instance, the general sphere of human empathy has inexorably grown over history, it can now (in many people at least, not all) encompass the whole Earth, and indeed it must do so for at least a sizeable minority if we are to survive as a species.
When we note that _more is different_ we are also talking about combinatorial explosions, even in a finite system (number of possible games of _go_ compared to chess) in which case more is not only different, more is richer, immensely so. But we can even go beyond that: just by the rather "natural" development of the mathematical number systems we already right there have created infinite intellectual space to explore (try telling Hugh Woodin otherwise! The dude may be on a flight of fancy, but it is still exploration of an imagined infinite realm). Don't flame me for saying so, but already we know mathematics is not constrained by finite computation. The computational paradigm is useful framing for some issues, but it is not all of mathematics.
It is also a logical fallacy to claim that _because_ human brains are finite we are _thus_ inherently limited to finite computations. This ignores the fact that with the discovery of transfinite set theory we have in fact created infinite realms to explore. The fact one person's brain is finite does not mean humans as a species are limited by a finite realm of thought. No! Our _realm of exploration_ is infinite, even while one person's brain might be finite. (And do not ask me to define a "realm" I do not know what that is, but I refer you to the more primitive notion of a topological "space".)
Put another way, although your, or even our whole collective, minds cannot encompass infinite thoughts, any _single_ thought cloud we have is not constrained to a finite set of "all possible thoughts." The abstract set of "all possible thoughts" is infinite, and as far as anyone knows it has a multiply connected topology, so we are not exploring this space by local jumps, a single "jump" in thinking can get us from one idea to nearby (in mental space) some completely bizarre unheard of ideas. The Mindspace is not a Euclidean space (or if it is, well, sh*t...., we're in serious trouble!)
You can be a dick about it all, like Zeilberger and other finitists, and _define_ mathematics to be finite, hence escape Gödel propositions, but that's just _your_ definition. Fine I say. Just don't foist it upon me.
Note also that "the discrete" is not the same as "the finite." That whole line of thinking is completely flawed logic which suckers amateurs. The transfinite ordinals are "discrete" not continuous, they "count" come continua, but are not themselves continuum sets. Every set is discrete, all the transfinite sets, even all the Aleph_k are discrete. Having uncountably many elements does not make you continuous. Having a discrete set that can be placed in bijective correspondence with an ideal continua, like the Real number line (indexed by the set of Real numbers), is no contradiction. The Real number line (a physicalist sort of notion, is not the same as the abstract set of Real numbers, the latter is just one of many possible models for the former). "Continuous" is a topological notion, and sets have no topology until you pick one, and _every_ set can have a discrete topology imposed on it (the trivial topology), and _every_ countable infinite set can get a "continuous" topology (homeomorphic to the reals) imposed on it (the standard topology on it's power set).
BTW: the plausibility[*] of strict finitism in mathematics is not an argument for why it should be adopted as the only valid way to do mathematics. Same as the incompleteness of Peano arithmetic or ZFC set theory is not an argument against adopting these as valid foundations for mathematical exploration.
[*] Plausibility here might be taken as "powerful enough to do everything we want with numbers and associated concepts." It is a philosophical notion, not a rigorously defined notion. We surely cannot say now what we want mathematics to do for us at some arbitrary future time.
@13:00 this is not quite right Stephen. And Darwin was not so much of a genius you should hang by his every word. Inexorable growth in complexity is not a law of natural evolution (it is not even a law of black hole thermodynamics out to long times) it is a statistical feature, not a law. Closer to a law (though still statistical I suspect) would be progressively (perhaps punctuated) more parsimony --- be as simple as you can be to solve the survival and replication problem facing you, but no simpler. It is based on the reality you have a finite reservoir of free energy (or exergy). This can, sometimes, run the opposite way to increasing complexity. With increasing complexity (take collateralized debt and derivatives in financial economics) can come _increased fragility_ (q.v. Hyman Minsky). I think Greg's theorems are too abstract to be simply relatable to natural evolution in the Earth's biosphere in the naïve way your conversation tried to suggest. With his theorems he can say some generic things about Natural evolution, but not a lot.
Before you get tendentious with me, I understand the _desire_ to have "one perfect mathematics." And I understand that _was_ the original motive for philosophical platonism. But as Marx said, the followers of a philosopher have a duty to correct his/her mistakes and make improvements, or overturn things entirely in the program. What Gödel bequeathed to us is a precious understanding that there need not be one single perfect mathematics, there can be several. It does not destroy the essential thesis of platonism however. It enlarges the platonic realm.
The essential idea is mathematics aught to be describing something: "our universe" was one motive. But dovetailing nicely (fortuitously?) with modern physics, we have this idea (fictional, fantasy, speculative, regardless) of the Multiverse, which maybe is nature giving us a strong hint that there is never going to be one unique mathematical structure that can consistently describe all universi.
Maybe in the far future we will figure out that, hey... whaddya know... there _is_ only one axiomatic schema that describes all multiverses. But until we nail down that result, there seems nothing terrifying about admitting mutually inconsistent mathematical structures. The danger (not terrifying, just logical) is that you can never usefully employ two or more such structures to describe the same phenomena, that _would_ lead to absurdities.
I think the idea there had to be only one unique _mathematics_ was based on a non sequitur, like some hope that all spoken languages could be mutually translated perfectly, which turned out not to be true. So why would it be true for mathematics?
I think the intuition it should have been so for mathematics is based on the intuition about numbers: there is something awesomely unique about counting: 1,2,3,4... there is only one way to do it, so there should only be one way to "correctly" axiomatize arithmetic. But of course we know that is in fact dead true. Arithmetic _is_ perfect and unique. There is only one of them cars. It is only when encountering the transfinite that we get a branching of possible mathematical axiom schema. It is an enlargement, but _finite_ arithmetic is still completely unique and perfect. Like Chaitin though, I regard that enlargement as beautiful, not horrific. ("Small is beautiful" is only a "thing" in context of a resource constrained shared environment. Numbers are unconstrained and inexhaustible.)