joigus

This is an interesting twist. Denominator expansions should make sense and therefore provide a basis to partition the sample space into significant exclusive propositions. Otherwise, one could end up saying things like, eg, P(outcome of coin flip = heads) = P(outcome of coin flip = heads| angels have wings) + P(outcome of coin flip = heads| angels do not have wings) Pretty soon we can get confused by the "logical span" of common language. Angels neither have wings, nor haven't, simply because angels do not exist. We simply cannot assign probabilities to any of both.

I agree. But OP seemed to understand the numerator and be only concerned/confused/curious, as the case may be, about the denominator. And the denominator is P(B)=P(B|A1)+P(B|A2)+P(B|A3)+... for every which Ai in the sample space of the A's. Feel free to correct my English anytime, by the way. Conscience is every bit as important as consciousness.

P(B) is P(B) no matter what A, so it's P(B) = P(B|anything) rather than everything. Language can be a naughty little helper.

I've been reading the arguments back and forth and I'm still missing something here. I have to confess I need more reading. Carnot's argument about the efficiency of heat engines is, from a logical POV, based on two assumptions --correct me anybody if I'm wrong: 1) Conservation of energy 2) Existence, to a reasonable degree of approximation, of heat reservoirs, ie, systems so big and thermodynamically static* that they can exchange any amount of thermal energy necessary --or irreversible work-- for the engine to work between the higher-temperature reservoir and the lower-temperature one. As one famous argument by Sagan goes, extraordinary claims require extraordinary proof. Because for Carnot's argument to be flawed it would require either 1) or 2) to be wrong, extraordinary evidence that either one of them is the case is required. It seems that the OP leans on the side that heat reservoirs are nothing but monumental abstractions with no basis on real physics. A claim that seems ludicrous to me. A further qualification could be necessary, which is the distinction between reversible work and irreversible work. Carnot's argument, AFAIR, relies only on the concept of reversible work. Irreversible work is, to all intents and purposes concerning thermodynamic arguments, pretty much indistinguishable from heat losses or gains, and can only be detected by means of precise calorimetric measurements, in principle. After a short time, any irreversible work will have leaked into the "worked upon" system in the form of heat. But --and it's a big 'but' implied, I think, by other members too--, the more a system resembles a heat reservoir, the more difficult it becomes to make precise measurements of heat loss --never mind it coming from irreversible work done. If a system can absorb or release any sizeable amount of heat --or irreversible work, like eg the motion of a blender-- without significantly changing its temperature, how can you be sure of the amount of energy it has received or released by means of calorimetric measurements based on known heat capacity/specific heat of such reservoir? What's more, how can you be sure that the conclusion to be drawn is that Carnot's efficiency formula is not correct? Wouldn't it be reasonable to demand from you that you design an engine that improves that? I mean, build a heat engine that delivers an efficiency better than that provided by Carnot's argument --kitchen availability pending. Also --and no minor point: I apologise if I've misunderstood any of the points under discussion. I need more time to get up to speed. * Both as compared to the engine.

Can a part of something map the totality of that something? Can a code-key pair decode the whole message it's a part of? Think about it. Maybe the answer is "yes." If so, it would have to be an exceptionally clever code-key pair. So I suppose my answer is "I don't know."

Right off the top of my head, using bacteriophages by means of suitable biotechnology is by no means a crazy idea. After all they're --what-- a couple thousand bases in their nucleic acid sequence? I'm guessing the reason why it hasn't been proven efficient might be related to the human body's immune response to pieces of alien DNA/RNA set loose in the body fluids. But I don't know. Maybe @CharonY --who is the resident expert in bio-- might find some time to answer the questions I'm just able to guess at right now. I do remember reading that people were considering this option again.

Viruses that target bacteria are known as bacteriophages. Bacteriophages have been tried as possible medicine. The idea is at least a century old or more. It is my understanding that the level of success was very limited. Experts can give you a more complete account. Google for "bacteriophages as antibiotics" and you will find many entries.

This all seems to belong in the decades-old ongoing mindless hullabaloo about quantum mechanics and consciousness. If there's something that's clear about quantum mechanics and the process of measurement is that it's nothing to do with consciousness necessarily, but with quantum mechanics of open systems and dissipative processes. Conscious processes sure involve dissipation and quantum mechanics of open systems.

How would the human eye destroy quantum mechanics? And if so, in what way is a human eye essentially different from any other photo-detecting device? --Never mind entanglement.

I must have missed it. I made a mistake. The SG experiment is not about charged particles. It's about particles with a permanent magnetic moment. They'd better be non-charged if you want to show just the beam-splitting effect without any qE Lorentz dragging term. Anyway, the force (classically) is a vector gradient of the effective potential energy term. You can do quantum mechanical calculations to show that --quantum mechanically--the beams split into 2S+1 levels. No purely classical calculation can give you that. The essence of this calculation is that (1) There is an inhomogeneous magnetic field in the window of the Stern-Gerlach device, and (2) the states of the particles can be described with a quantum-mechanical function that has 2S+1 distinct basis states. Use of vector identity, ∇(A⋅B)=A⋅∇B+B⋅∇A+A×∇×B+B×∇A allows you to expand, \[ \nabla\left(-\boldsymbol{\mu}\cdot\boldsymbol{B}\right)=-\left(\boldsymbol{\mu}\cdot\nabla\right)\boldsymbol{B}-\boldsymbol{\mu}\times\nabla\times\boldsymbol{B} \] where μ is the magnetic moment of the particles --you can think of gaseous paramagnetic Ag atoms as an example-- and B(z) is the z-dependent magnetic field inside the window. Because the window is very small, you can do a Taylor expansion, \[ \boldsymbol{B}\left(z\right)\simeq\left[\boldsymbol{B}\left(0\right)+z\boldsymbol{B}'\left(0\right)\right] \] Because quantum mechanics of spin introduces a discrete set of states --e.g., S=1/2 has 2 states--, you can expand the incoming states with, \[ \boldsymbol{\mu}=g\frac{\hbar q}{2mc}\left(\begin{array}{cc} 1 & 0\\ 0 & -1 \end{array}\right) \] Use of the quantum mechanical evolution operator with, \[ e^{-iHt/\hbar}\simeq e^{\left(\boldsymbol{\mu}\cdot\nabla\right)\boldsymbol{B}\tau/\hbar} \] (valid only for the small time τ the particles spend inside the window), you can show that the salient states are waves deflected in momenta by amounts --S=1/2--, \[ \triangle p_{z}\simeq\pm g\frac{\hbar q}{2mc}\boldsymbol{B}'\left(0\right) \] So part of the beam goes up, and the other goes down. You can see a more detailed discussion of this in David Bohm's Quantum Theory. No part of your calculation shows this. Instead, as @exchemist said, a classical situation would have the beams deflect in every other intermediate direction, as I said too.

Yes, that's true. My comments were really meant about the prevailing direction. But, as you said, this is a huge subject, with many exceptions and several levels of "turbulence" around the average tendencies.

I apologise for mistake when I said, It should've been "westward migrations throught the steppe." That's apparently the prevailing direction of migrations through the steppe. And it is no accident. Sometimes geography introduces an element of predictability to migrations, if not complete predictability. There's very intesting material by Oxford archaeologist Barry Cunliffe pointing out how the landscape there kind of invites you to go westward. I seem to suffer from some kind of mild --I hope-- directional dyslexia. I promise to get up to speed as to present discussion too ASAP. The latest arguments about Australia and Polynesia I find fascinating. Apparently there is a paleoanthropological mystery/gap in our knowledge as to populations of South Asia during the Middle Paleolithic[?]. There's also the quite puzzling presence of Denisovan genes in people from Melanesia and parts of South-East Asia[?]. Sorry for imprecision. The take-home lesson is --I think-- we still do not completely understand what happened in South Asia for too long a time to be sure about any kind of big picture of what happened there. There are far more uncertainties about this than there are answers or any kind of big picture. @studiot was indeed right when he said this is a huge subject.

As pointed out above, there are many factors, depending on time and place. People follow herds, rivers change their course, lakes dry out, advance of ice sheets force populations southwards, etc. The dynamics of population change are, I think, as varied as can be. Some migrations take place in one generation --example: eastward migrations through the steppe--, others take many generations to advance significantly.

It only does that if you assume quantum mechanics is valid for the charged particles and classical field theory is valid for the EM field. If you combine quantum and classical attributes, it's possible to obtain relatively satisfactory models for some quantum behaviours. You have to put in QM by hand at some point. If charged particles can adopt any orientation --they are classical too--, it's obvious that you would get the continuous range of deflections I was talking about.

The whole point of the Stern-Gerlach experiment is to disprove the classical theory of radiation. You get two or more (2S+1), separated, clearly defined spots where the charged particles end up, corresponding to the different values of spin. If the phenomenon could be interpreted classically, you would get a continuous range of arrival positions, which is never the case. That's why the SG experiment is considered to be one --among many-- confimation of quantum dynamics, as opposed to the expectations of classical-field dynamics.

No. If AI were able to "create" a herd of antelope or a coral reef, plus the long-term incremental changes in the fossil record that led to them, I may change my mind. Then we would have gone full circle in the generation of intelligence by intelligence, which is only the first step that it would take to convince me. IOW: Evolution is obvious once you understand its principles and let the facts sink in. And it is impossible to grasp if you have a very concrete, atavistic prejudice that obstructs your understanding, by ignoring the facts and misunderstanding its principles.

I'm rather confused by your use of the term "a number's territory." You obviously mean something you're finding difficult to define --I infer that from your repeated use of quote marks. Can you be more precise? It's obvious there are numbers so big that you would be hard pressed to find anything physical that makes them relevant. Or so I think. Is something like that what you mean?

My pleasure. I don't know how Graham's number is constructed either. A good principle to organise (integer, counting) numbers by scale (in physics) could be perhaps considering this: Small numbers: Number of people in a room (somewhere between 10 and 102=100) Moderately big numbers: Number of atoms in a typical piece of matter (1023) Big numbers: Number of photons in the universe (1090) Really big numbers: Permutations of big numbers or number of ways to re-arrange big numbers: (close to NN/eN) The last one is called Stirling's approximation. It's a way of "taming" really big numbers by avoiding them directly (knowing all their digits) and using instead a ballpark way of dealing with them.

You might be interested in this: https://en.wikipedia.org/wiki/Graham's_number https://en.wikipedia.org/wiki/Large_numbers The thing about these large numbers is not just, of course, how big they are. You could always talk about Graham's number +1, and that would be bigger. It's rather about humongously big numbers that somehow are significant in one part or another of mathematics. Graham's number is really really big in the sense that people seem to be quite uncertain about most of its digits. So in that sense it's very peculiar. Not at all like powers of ten. It's kind of unwieldy in the extreme.

My feelings exactly.

I don't think it's a coincidence. It's obvious that our anatomy seems to favour use of 10-base number system. The Babylonians had a preference for 60-based number system. And the reason is the high number of divisors that 60 has: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30. One problem is that you need sixty symbols or digits, which becomes cumbersome. But still, there are traces of the Babylonian system in our 12-based hour system, as well as in measuring angles.

A good starting point could be, Can you explain in terms as simple as possible how information compression could be relevant to QM?

Yes, but that's on another level. I thought you meant freedom for investors. A regular job is not the market.

I'm afraid 100 % free and 100 % ethical is impossible. The moment you introduce freedom, you also introduce the potential for non-ethical behaviour. It's the law of unintended consequences at work. 100 % free would be like the savanna. 100 % ethical --by regulation-- would stall most enterprising iniciatives. So it's a compromise we must reach. It's always been like that. Would an algorithm be possible to limit the potential damage of guaranteed unethical behaviour? Sure. But I'm afraid people wouldn't like it, plus there's no money in it for algorithm designers. When I say "people wouldn't like it" I mean rather the tens who hold billions than the billions who hold tens.

I'm assuming you're made of matter, so no. I reckon you would have to make an antimatter copy of yourself and send it to an antimatter version of the past environment you would like to be in. Here's the answer, in the form of a well-known poem by physicist Harold P. Furth, A.E.C. stands for "Atomic Energy Comission, and the poem refers to the certainty that any close interaction between matter and anti-matter would end up in a burst of gamma rays. You touch any sizeable amount of antimatter, and you're done.