KJW

Nobody has suggested that genetic patterns are random. If they were random, cells would not function. The point that I (and others) have been making is that genetic patterns exist within a context governed by chemistry and biology, and that mathematical patterns that might exist do not provide sufficient context to explain such patterns. I am a believer of the idea that the laws of physics exist for purely mathematical reasons. But going up to the next tier of physical organisation called "chemistry", though completely dependent on the laws of physics, has a much reduced reliance on mathematics. Biochemistry depends on chemistry but is its own tier of organisation because there is much more to biochemistry than just chemistry (sometimes, I wonder if it's possible to study biochemistry without knowing any chemistry, but having studied both, I'm not in a position to answer that question). And note that I mentioned "chemistry" and "biology" separately above. That's because the impact that chemistry and biology have on genetics is entirely separate. Thus, although ultimately mathematics is (I believe) responsible for everything, the nature of emergent behaviour is such that higher tiers of organisation contain fundamentally additional notions than the tiers below them. For example, consider the following polypeptide amino-acid sequence: Tyr-Gly-Gly-Phe-Met-Thr-Ser-Glu-Lys-Ser-Gln-Thr-Pro-Leu-Val-Thr-Leu-Phe-Lys-Asn-Ala-Ile-Ile-Lys-Asn-Ala-Tyr-Lys-Lys-Gly-Glu Considering only the sequence itself, perhaps also including anything about the amino acids that form the sequence, but without searching for the sequence on the internet or elsewhere (that would be cheating), try to work out what function this polypeptide performs. Yes, I know what the polypeptide is and what it does, but I don't believe that such knowledge can be obtained from the sequence itself without any physiological context. That is, the amino-acid sequence only makes sense within a larger context that has not been provided. Note that one might be able to determine the three-dimensional shape of the polypeptide from the sequence. But I maintain that even the three-dimensional shape of the polypeptide would not be sufficient to determine its function outside the larger context. Even the entire human genome is not entirely self-contained. We need nutrients from the external environment without which parts of our genome may not make sense. We interact in other ways with our environment that probably affects parts of our genome also. Each lifeform has a genome that allows it to survive in the environment, but those genomes are different, representing different solutions to essentially the same problem. But the details of any particular solution to the problem of survival depend on the specific environment, not all genomes admit survival in all environments. Again, this is beyond anything mathematics could determine.

When I was a teenager, I had a few aquariums, and the water filtration would operate on this principle. Also, the aquarium bubbler would help circulate the water, presumably also by this principle.

Sir Patrick Stewart was also Avery Bullock in American Dad!.

Cryptography is about hiding communication and messages from eavesdroppers. I don't see the analogue of an eavesdropper in genetics. I don't think those scientists that genetically engineered food were thinking in terms of information theory. I think it more likely they were thinking about the biological function of the genetic material being added or removed (as well as the technical procedures).

If multiple ontologies are attached to the same mathematics, then this would indicate that the mathematics does not have an ontology. However, this doesn't mean that the mathematics doesn't suggest a preferred ontology. I believe the mathematics does suggest the Many Worlds Interpretation as the preferred ontology. No. The Many Worlds Interpretation is actually the logically simplest interpretation. It is simpler to have all possible worlds than to select one of those worlds. Selection adds complexity to an interpretation that is unnecessary in accordance with Occam's razor. And if there are multiple possible outcomes to a physical interaction, it is simpler for all of those outcomes to happen than to randomly choose one of those outcomes. Mechanistic randomness adds complexity, perhaps even impossibility, to an interpretation that is unnecessary in accordance with Occam's razor. I find it strange that people think that the many worlds conflict with parsimony as if there is an unaffordable cost to having many worlds. The crucial issue is whether or not a single world is deterministic. If it is deterministic, then the many worlds is ontologically unnecessary. Otherwise, I see it as necessary. And if it is necessary, then the parsimony principle and Occam's razor doesn't enter into consideration. It should be noted that determinism is the result of the mathematics that describes the laws of physics being sufficient to constrain the possible futures for a given past to just one. There is no reason at the outset to believe that the laws of physics are sufficiently constraining. A natural objection to the Many Worlds Interpretation is the unobservable other worlds. We see only one outcome, not all of them. However, being unobservable does not imply non-existence. Of course, care is needed to avoid Russell's teapot. It can be said that if the other worlds were inconsequential, then the Many Worlds Interpretation would be unnecessary. But the other worlds are not inconsequential. Although they are unobservable, their existence is logical. They provide what I believe is the explanation for the randomness of quantum outcomes. Other interpretations seem to either lack an explanation or invoke an unobserved mechanism for selection of quantum outcomes. Interestingly, the Many Worlds Interpretation provides a mathematical basis for the unobservability of the other worlds: classical states are orthogonal. This weakens the unobservability objection. As far as I'm aware, there is no experiment that has revealed quantum mechanics to be anything but complete. When one actually has some understanding of the true nature of quantum mechanics, it becomes clear why there is intrinsic randomness and in particular, why the information that would otherwise select a particular outcome doesn't exist. For example, the Heisenberg uncertainty principle is a mathematical consequence of the relationship between conjugate variables. It's been a while since I looked at that. I would like to work out gravitational deflection of timelike and lightlike trajectories from infinity, non-circular orbital precession, and orbital decay of mutually orbiting equal mass black holes along with the concomitant emission of gravitation. Unlike the previous problems, none of these involve the simplicity of stationary frames of reference, although I'll attempt solving these in a rotating coordinate system nevertheless. One can measure the mass of the sun in metres, and one can measure the mass of a bowling ball in kilograms. But unless the value of G is measured (eg Cavendish experiment), one will not be able to calculate how many bowling balls has the same mass as the sun. IIRC, the Cavendish experiment has been described as "weighing the earth". Physicists have identified seven base dimensions of measurement from which all other quantities can be defined. One can invoke dimensioned fundamental constants to reduce the number of base dimensions, for example expressing mass in metres instead of kilograms, and indeed it is something I have enthusiastically done. But I see two problems: 1, from a practical perspective, the seven base dimensions are all different, requiring different types of measurement. For example, measuring length using a clock is different to measuring length using a ruler. That is, time and length are different even though c connects them. And 2, when one uses all seven dimensioned fundamental constants to reduce the number of base dimensions, one instead obtains the Planck units. In itself, this is a benefit rather than a problem, but it does seem to indicate that invoking dimensioned fundamental constants to reduce the number of base dimensions is misguided.

This is handwaving. You say that "When B decodes these signals, the relational math of the information transfer perfectly reproduces the standard relativistic result: B measures C's clock as running slower than their own." but do not say how much slower or give any indication beyond a mere assertion that it perfectly reproduces the standard relativistic result. For example, what is the Doppler effect observed by B of C's clock? Also, what is the Doppler effect observed by B of A's clock? Is the Doppler effect observed by B of A's clock the same as the Doppler effect observed by A of B's clock? I don't see how they can be same if B's clock rate is throttled by Lorentz factor γ relative to A's clock. Special relativity is based on the principle that all inertial frames are equivalent. This has implications that I fail to see as fully implementable in a model with a preferred rest frame.

Hmmm, @Time Traveler, it appears to me that you haven't responded to @swansont's three clock scenario. The glaring problem I see with your theory is that it has an absolute rest frame, contrary to relativity. The way you appear to explain time dilation seems to indicate a misunderstanding of how time dilation arises in relativity. Anyway, suppose one observer is at rest and consider two other observers, one moving at β with respect to the observer at rest, and the other moving at –β with respect to the observer at rest. The question @swansont posed is how the two moving observers observe each other's clocks with regards to time dilation.

https://en.wikipedia.org/wiki/QI

I recall an episode of QI in which it was said that humans do not sense "wetness". What we perceive as "wetness" is really changes in temperature due to the heat conductivity of water compared to air. However, it was also said that there are creatures that do genuinely sense "wetness", and therefore it is not simply a matter of semantics to say that humans do or do not sense "wetness". Not necessarily. For example, different interpretations of quantum mechanics use the same equations to describe the physics being observed. However, the different interpretations represent different ontologies, so the mathematics in this case does not indicate the ontology of quantum mechanics. Specifically, both the Copenhagen Interpretation and the Many Worlds Interpretation are described by the Born Rule, but they are ontologically quite different unless one accepts the ontology of the Many Worlds Interpretation and regards the Copenhagen Interpretation as the solipsistically subjective perception of the Many Worlds Interpretation, which I do. One thing to note is that the mathematics of the Born Rule does not actually contain wavefunction collapse, and it is my belief that mathematics cannot explicitly model intrinsic randomness.

Isn't the scientific principle of falsifiability a philosophical notion?

A differential equation is considered solved if it is reduced to a problem of integration. That's no consolation if the difficulty is with the integration. For example: [math]\displaystyle \dfrac{d^2y}{dx^2} = ky^2[/math] [math]\displaystyle \dfrac{dy}{dx} \dfrac{d^2y}{dx^2} = ky^2 \dfrac{dy}{dx}[/math] [math]\displaystyle \int \dfrac{dy}{dx} \dfrac{d}{dx}\left(\dfrac{dy}{dx}\right)\ dx = \int ky^2 \dfrac{dy}{dx}\ dx[/math] [math]\displaystyle \int \dfrac{dy}{dx}\ d\left(\dfrac{dy}{dx}\right) = \int ky^2\ dy[/math] [math]\displaystyle \dfrac{1}{2} \left(\dfrac{dy}{dx}\right)^2 = \dfrac{k}{3} y^3 + C[/math] [math]\displaystyle \dfrac{dy}{dx} = \sqrt{\dfrac{2k}{3} y^3 + 2C} = \sqrt{\dfrac{2k}{3}} \sqrt{y^3 + A}[/math] [math]\displaystyle \dfrac{1}{\sqrt{y^3 + A}} \dfrac{dy}{dx} = \sqrt{\dfrac{2k}{3}}[/math] [math]\displaystyle \int \dfrac{dy}{\sqrt{y^3 + A}} = \sqrt{\dfrac{2k}{3}}\ x + B[/math] In this case, the original differential equation has been reduced to a problem of integration. However, the integration appears to be some form of elliptic integral. Actually, one could argue that a second-order differential equation be considered solved if it is reduced to a first-order differential equation. For the above equation, that is indeed straightforward. Interestingly, it is the arbitrary constant from the first integration that creates the difficulty for the second integration.

That reminds me of this meme:

I wonder if Trump will demand that Zelenskyy stop attacking Russian data centres.

Hmmm, one thing I don't think you grasp is that although DNA is a store of information, the manifestation of that information in living organisms is largely chemistry. Among other things, DNA encodes information that is used to produce proteins called enzymes that catalyse chemical reactions necessary for life. That is, understanding the patterns that occur in a base sequence of DNA ultimately requires an understanding of the chemical reactions being catalysed by the corresponding enzymes. And while there is a connection between the base sequences of DNA and the chemical reactions being catalysed, this connection contains an arbitrary element that prevents the connection being pure in a mathematical sense. This arbitrary element is the genetic code, the correspondence between the triplet codons of the DNA and the amino acids of the proteins. This correspondence is the result of a set of aminoacyl-tRNA synthetases that attach specific amino acids to specific tRNAs. Actually, the genetic code is not entirely arbitrary because it also relies on chemistry and evolved optimisations. The following is a representation of the genetic code that allows direct inspection of the relationship between the triplet codons (of mRNA) and chemical structure of the corresponding amino acids:

From the article: Trump resumed the federal death penalty after an informal moratorium during previous administrations. The federal government executed 13 people between 2020 and early 2021, contributing to making Trump the most prolific execution president in over 130 years.

Do rings obey a type of "shell theorem"?

I knew I shoulda taken that left turn at Albuquerque! 😉

The central concept of DNA, I think even more significant than the genetic code, is that each DNA-base hydrogen-bonds to its complementary DNA-base. Adenine (A) hydrogen-bonds to thymine (T), cytosine (C) hydrogen-bonds to guanine (G). Adenine and guanine are purine bases, thymine and cytosine are pyrimidine bases. Note that in each case a purine base hydrogen-bonds to a pyrimidine base to maintain the correct separation between the two strands of the double-helix. Thus, the two strands of the double-helix have complementary DNA-base sequences (actually also reversed because the two strands are opposite in direction). This is the basis of DNA replication. The hydrogen-bonding between complementary DNA-base pairs is also the basis of transcription. DNA replication:

I think if biology does connect to the prime number sequence, it would be due to the sieve of Eratosthenes. I understand that cicadas actually do this.

I am opposed to capital punishment and am glad I live in a country where it doesn't happen. However, if capital punishment is to be accepted, then there should only be ONE attempt, no more. If that attempt fails, it should be considered as a "pardon from God¹". Actually, I think Christa Pike should be freed from prison as a result of this "pardon from God". This implies that the amount of time on death row should be long enough that the "pardon from God" does not constitute an injustice to the victims. ¹ In the same sense that insurance companies use "act of God".

Why the Rest of the World Thinks Americans Are Brainwashed From the YouTube webpage: What if the most effective propaganda isn't on a poster or a state-run news channel, but in the songs you sang as a kid, the history class you sat through, and the pledge you recited before you could even spell it? How much of what Americans believe about their own country is actually true, and how much of it was carefully engineered to keep you from asking that question? As someone who's lived in over a dozen countries and spent a decade studying cults, dogma, and thought control, I started noticing patterns in American culture that people overseas find absolutely bizarre, but most Americans never question because they've been marinating in it since birth. From an America-centric education system that barely acknowledges the rest of the world, to Cold War binary thinking that still shuts down policy debates today, to the "Land of the Free" myth that crumbles under even a casual glance at the data, we're breaking down seven forms of propaganda most Americans don't even realize they grew up with. We'll explore CIA-backed coups against democratically elected leaders like Mohammad Mosaddegh in Iran, Jacobo Árbenz in Guatemala, and Salvador Allende in Chile. We'll look at why the U.S. ranks 57th in press freedom, how "Under God" and "In God We Trust" were Cold War marketing decisions (not founding principles), and why the Treaty of Tripoli explicitly stated America was not founded as a Christian nation. We'll examine a military budget larger than the next ten countries combined, the Princeton study showing average Americans have "near-zero" impact on policy, and why the concept of American exceptionalism functions less as a belief and more as a social enforcement mechanism designed to silence dissent. Chapters: 0:00 - Introduction 1:26 - US-Centric Education 2:43 - The Cold War Binary 5:47 - The Land of the Free Myth 9:05 - The Military Budget 10:40 - The Pledge of Allegiance 12:24 - The Christian Nation Myth 14:25 - American Exceptionalism

I was focusing on “construct” which may indeed be beside the point you intended to make, but not (IMO) the way you made it. The density calculation of a BH is made up of the singularity and then a huge volume of nothing. It’s an average, not a description of a physically realizable object. To physically “construct” it requires a collapse at some point. I think with regards to the point I'm making that "bricks" should be regarded as a metaphor for something that is strong and won't collapse under its own weight. Although it is not a realistic view of bricks, the whole idea of building a black hole with bricks is hardly realistic, and given that a realistic material that won't collapse under its own weight doesn't exist, it is reasonable for me to take licence with the use of "bricks". Furthermore, the idea of building a black hole with bricks does suggest a gentle cumulative process that will eventually form a black hole without the application of matter-crushing forces. But ultimately, the point I'm making is not about the absence of matter-crushing forces, but about the formation of black holes.

Why are eukaryotes so limited compared to prokaryotes?

If you constructed a structure out of bricks, how would it become a BH without matter-crushing forces? The structure would always have a radius larger than the Schwarzschild radius. No, the Schwarzschild radius of a black hole is proportional to the mass, and the mass of a ball of uniform density is proportional to the cube of the radius. Therefore: [math]r_s = \dfrac{2 G M}{c^2}[/math] [math]M = \dfrac{4 \pi \rho r^3}{3}[/math] [math]r_s = \dfrac{8 \pi G \rho r^3}{3 c^2}[/math] [math]r_s \geqslant r \implies \dfrac{8 \pi G \rho r^3}{3 c^2} \geqslant r[/math] [math]\implies r \geqslant \sqrt{\dfrac{3 c^2}{8 \pi G \rho}}[/math] That is, even for a material of low density, if the ball of material has a large enough radius, the Schwarzschild radius of the ball will exceed that radius. Whether or not the ball of bricks can support its own weight under its own gravity is irrelevant to the point I'm making. Even if the ball of bricks can support its own weight, the mere size of the ball if large enough is sufficient to produce a black hole. That is, it is not necessary for the ball of bricks to collapse under its own weight to produce a black hole.