For sure I hope it will reach $300 in a few days !

I think the past is essential if you are considering PoS schemes with PoS-style governance.  How can you obtain decentralization, if the initial distribution is highly centralized (near 100% in the beginning), and if the PoS schemes are such that this ratio is decreasing much slower than if there was distributed PoW at a certain point ?  Moreover, if a majority of this initially centralized PoS system is also deciding upon everything else (hard forks, protocol modifications ; who knows, unmixing and revealing former anonymisation, reverting former transactions, everything you can think off) ?
In what way is this different from a central bank ?

In other words, fiat works better.

You are losing me here.  I can read that 10 times, and still not know what it might mean.  I try to wrap my mind around what you mean with "microstates superinposed".  If the system is isolated and in a pure state, it is of course in one single state (which may be a superposition of "base states" in which I like to express this state, but it is still just one single quantum state).  If the system is entangled (which it most certainly is) with the rest of the universe, it is entangled, which means exactly what I wrote earlier: several individual quantum states of the cup are, well, entangled, with states of the environment.  And that is exactly the entropy we are talking about: the number of those states that is involved.  If there were only state, the entropy would be 0, and if there are many, the logarithm of 2 of that number of states is the entropy of my cup (I'm assuming uniform distribution, which is not necessarily true, but which would diminish the entropy if not uniform).

There's no such thing as "cumulative entropy over time".  I think that is the error you are making, by thinking that the entropy is about the *entire history - and future* of a system.  No, entropy is the ignorance of the *current state*, not about its entire past and future.  That doesn't make sense, because if that were the case, entropy wouldn't be a time-dependent concept, and the second law could not even be formulated !

It is as if you were saying that the "velocity of an object is the whole of movement that an object did and will do in the future" or something.  But if that is the case, you couldn't talk about the acceleration (the *change* in velocity) and not write down Newton's second law !  Velocity is instantaneous, now, and doesn't care about the state of motion yesterday or tomorrow.  If it did, velocity would be an a-temporal notion, and you couldn't ask how velocity changes over time.

In the same way, entropy is an "instantaneous" notion, because the second law of thermodynamics tells us how entropy needs to CHANGE over time.  If all our past and future ignorance were already included, the entropy tomorrow would be the same one as today, as all ignorance would already been included, as well today as tomorrow.

I think you are confusing the notion of entropy itself, with the notion of dynamics.  If I know the dynamics of an isolated system perfectly well (which is very rare), then there's a kind of Liouville's theorem that tells me that my knowledge of the microstate (even if imperfect) is conserved.  When I know something about the microstate today, that knowledge is still pertinent tomorrow, and my entropy about that micro state didn't grow.
If however, my knowledge of the dynamics of the system is not perfectly accurate, OR the system interacts with the environment (of which, by definition, I don't consider the dynamics), then my knowledge of the microstate today will probably get lost gradually over time: my entropy of the system grows, until it reaches its full value of my total ignorance of it, given by one or another canonical statistical ensemble, constrained only by a few macroscopic parameters.

This "loss of knowledge over time" is intimately related to the second law.  It is always related to "the environment" of which the unknown microstate is much more entropy-rich than my system, and is an infinite source (for all practical purposes) of ignorance (= entropy).

This is also why the notion of "entropy of the universe" is problematic.  The universe cannot be entirely observed from the outside, and cannot connect to "its environment" ; as such, this notion breaks down.

No, of course not, and that is not necessary.

In order for a perception to be consistent, only those things that are *observed* from the secondary observer need to be consistent.  The rest doesn't matter.  If I can't observe it, ever, I don't care, it doesn't exist in a certain way.

Take the following case:

There is me, Joe, and a light bulb (in my reality).

I see the lightbulb glowing green.  (direct observation).
I see Joe saying "the light is green" (my observation of Joe)

This is a consistent world view, a consistent history of observations.

Nothing stops one, however, from considering now Joe's point of view (in Joe's reality).

Joe sees the lightbulb glowing red (direct observation)
Joe sees me saying "the light is red" (Joe's observation of me)

This is (another) consistent world view, a(nother) consistent history of observations.

In the consistent history view of things, both are not in contradiction.  My observing a green light, and observing Joe say "green light" is not in contradiction with Joe observing a red light and observing me say "red light".  Joe, as primary observer, simply has a different consistent history than me.

What would be inconsistent, is that I see a green light, and I see Joe saying "red light".  Or Joe seeing a red light, and seeing me say "green light".

Joe only exists for me to the extend that I can observe him, and that I can observe other things that might observe Joe and so on.  If all these observations are consistent, then that's my consistent view of reality.  Which may be entirely different for another primary observer, but to which I have no access.

Crypto trustlessness at its best.  Love it

Well, I don't very often use bitcoin to buy stuff, and it is a while ago.  But this thread inspired me to have a look at current fees, and if what is written here is right:

https://bitcoinfees.21.co/

then things are getting expensive.  If 50 000 satoshis are the average price to get your transaction through "normally", that is about $0.6 right now, or am I wrong ?  That is not a negligible amount any more as compared to fiat.

Well, you seem to be right.  A few months ago, only 6% of transactions used the anonymous feature, and now it reached already 29%.  

Ok, if you really want to get into this: physics is a relationship between an observer and "the rest of the universe".  That "rest of the universe" contains entities which the first observer might identify as observers (I will call them "secondary observers"), and in order for his physics to be consistent, whatever the first observer observes from those secondary observers, must be coherent with what the first observer observes, and what he would observe if he were in the place of those secondary observers.   In other words, the only consistency must come from what the first observer observes "directly" and what he observes when observing those secondary observers.   This is the "consistent history" view of physics.  At no point, an observer "needs to prove" anything to a secondary observer.  He simply needs a consistent view between his "direct observations of nature" and his "observations of other observer entities".

The idea that there is a single objective reality out there goes out of the window with that view, but for an observer, the consistent view of his observations of nature, and his observation of secondary observers, is what comes closest to his best guess of what his objective reality might look like.

This kind of consistent history approach (first formulated if I remember correctly by Gell Mann in the 1960ies) explains very easily a lot of quantum "paradoxes", like the EPR "paradox", and also explains apparent paradoxes like Maxwell's demon.

In as much as those "secondary observers" are actual observers of their own, what is needed for everything to be consistent is that they too, in THEIR view of reality, see the first observer as consistent with that.

The simplest solution to this is that all observers observe the same objective reality, which is a classical viewpoint, but difficult to reconcile with quantum mechanics.  But it is not the only solution to this, and "consistent histories" is another, much more complicated, but quantum mechanically compatible, view of things.  If you want to stick to the classical "objective world" view, you have to introduce many strange things in order to explain quantum mechanical effects, such as "spooky action at a distance", "non-causal effects going back in time" and other weird things, while consistent histories don't need all that stuff.

In the same vein, entropy is a relationship between an observer and a system: it is his ignorance about the system's micro state.  In as much as another observer DOES know this micro state (like Maxswell's demon), then that system has no entropy wrt to that secondary observer, but that secondary observer now has entropy wrt to the primary one.

However, in most all cases, "human observers" don't know microstates and hence, they all agree more or less on the physical entropy of most objects, give or take a few bytes.

A secret key has no entropy with respect to its owner, and has (hopefully) full entropy wrt to an attacker.  Maxwell's demon is like the guy with his secret key: he known the micro state of the gas ; but as such, the demon has as much entropy wrt us, than the gas itself.

It really is ill-defined, and in as much as you'd like to estimate it, you'll probably end up with 0.  Yes, zero.  Like the total energy content of the universe is also most probably zero, in as much as that even could have a meaning.

Most people talking about the "entropy of the universe" talk about the "entropy of the REST OF THE UNIVERSE with respect to an observer inside that universe".  But there's a subtle difference between what one would call the entropy of the universe (with respect to an "outside observer" hence ill defined) and the "entropy of the rest of the universe".



That really doesn't matter.  My cup of hot water is also entangled with the rest of the universe, but that doesn't increase its entropy with respect to me.
The "states of the internet" is the number of different states the internet can be in, and that is limited to the technical capacity of that system.  If we limit ourselves to the *digital states* (and not to, say, the heat in a micro processor - like I'm not taking into account the nuclear states when accounting for the entropy of my cup of coffee) of the devices that make up the internet: the nodes, the network devices and so on, their digital state is entirely determined by all bi-stable digital components, essentially memory bits (and a few register bits in processor units and FPGA).  If you know every single state of every single bi-stable circuitry of every device that makes up the internet, then you know the entire state of the internet.   That's equivalent to me knowing the quantum state of the entire set of molecules making up my hot cup of water: i'd know the microstate of my hot water.  The IGNORANCE of that microstate is what makes up the entropy I have about that cup of hot water, and the IGNORANCE I have of the state of every bistable state of every component of the internet is what makes up the entropy I have about the internet.

My rather secure guess is that the internet doesn't have 10^25 bistable circuits.  It would mean about 10 billion devices with each a Petabit memory state.  We aren't there yet (in a few years we will maybe).


No, of course not, not any more than the swimming of a whale, which is entangled with every molecule in my cup of hot water for historical reasons, increases the entropy of my cup of coffee.  Because that's exactly what entropy is about: my ignorance of *just the cup of water*, and NOT its environment.  

The posts only contain at most the amount of bits that are needed to download the page (in compressed format).  And they were already taken into account by counting the empty bits on the page's server's hard disks.  So someone posting some stuff on the internet doesn't really increase its entropy.  A technician adding a few more disk units in a data center, does.


Ah, if you call "the internet" all of physical spacetime between here and Andromeda, of course we're talking about different stuff.  I'm talking about all the data that is available to be transferred and stored by all nodes with an internet connection.
Now, of course, you can say, there are sensors connected to the internet, so they bring in an "unbounded amount of entropy".  No, not really.  When that camera takes a picture, say, of 8MB, then these 8 MB are available and are entropy to you if you didn't know the picture.  But if at the next instant, the camera takes a new picture, the previous one is gone.  There's still 8 MB of entropy because of that camera.  If the previous picture wasn't STORED, and made available for download, the new pictures don't add entropy.  If you are looking at each picture, you get 8 MB of information THROUGH the internet.  But each time that picture gets refreshed, and not stored (nor on the camera side, nor at a cache site, nor at your side) on an internet-connected device, the internet's entropy doesn't increase.  In fact, when the camera takes the picture, its entropy rises (for you) with 8 MB.  When you look at it, you receive 8 MB of information, and hence the internet's entropy LOWERS with 8 MB wrt you.  When the camera takes a new picture you haven't seen yet, the internet's entropy rises again with 8 MB.  When you look at it, it lowers again with 8 MB.  Etc.

This is like a telephone wire.  The (digital) state of the wire is 1 bit at a time.  Whole conversations can go through a telephone wire.  But the state of the wire is at most 1 bit.  When you haven't received the bit yet, it has 1 bit of entropy.  When you read it out, it has 0 bit of entropy, until the transmitter puts another bit on it. Etc...

The internet, as defined by all the devices connected to it and their digital states, has less entropy than my cup of hot water.

A sensor, looking at the entire universe, has only the entropy of the data it has at a certain point in time, while you didn't look at it.  From the moment you know the data, its entropy falls back to zero, until the next (unknown) data are taken.

I entirely agree.  This is always the same law: predictions are difficult if they concern the future.  It is the crypto equivalent of Malkiel's thesis, that there's no "smart investor" that *systematically* can outsmart the market, and that in the long run, monkeys playing on the stock market do just as well as hedge fund managers.
 
But of course, on every time slice, there are lottery winners, who think they have something special.

Maybe a few bitcoin whales made enough profit with the existing bitcoin rally, that they can afford to pump another coin ?  I have no idea, but someone decided that it was time for DASH to rally, and that someone needed to have sufficient money to pump it.

To be honest, I liked DASH, but I don't like it too much at the moment.  However, I'm very happy with the current rally and I hope, even though I think it is somewhat ambitious, that DASH overtakes ethereum.  Overtaking bitcoin will be a bit hard *at the moment*, but one never knows.   I'm not entirely without hope, and if it is true that the current rally is due to trading an infinitesimal part of the entire amount of DASH around, with all the rest locked up in master nodes, then this lever arm is sufficiently big that relatively small whales can pump this to unknown heights.  If they can keep it there for a while, people will get used to these high prices.

I think such rallies are in general bad for a currency: they attract speculators like bullshit attracts flies, and once a currency is in the hands of speculators, there's no relationship any more between its fundamentals (essentially Fisher's formula for a currency) and its market cap.  But as this is screwed up with DASH in any case, it is a great thing that DASH rallies, because it can then demonstrate that "established orders" need not to be permanent.

I like DASH for its historical origin which was anonymity.  Even though its technology (mixers) is depreciated as of now, it is important that anon tech becomes visible.  What I don't like about DASH is that it is pseudo-distributed, but essentially centralized.  This is what allows DASH to do VISA-like processing (its "instant transactions") which are simply approved by the equivalent of a banker network (the master nodes) instead of having to undergo distributed cryptographic consensus-processing.  But this is also exactly what I don't like about DASH: it is a new kind of "bankers network".  Like with fiat banking, the bankers take most of the seigniorage and they have their say in the "central bank", which determines the rules of the system (the code).  DASH's system really is too much like a copy of our current fiat system: a "central bank" that sets the rules (that writes the code, can augment, diminish, can decide about everything) and is financed (10%) ; a set of "first line commercial banks" (the master nodes) that most probably collude concerning their interest, and have their say in the central bank (voting system of the "community") and reap in almost half of the freshly printed money so that the interest keeps flowing, and moreover, know all the "anonymous details" of their customers (the master nodes know the mixing origins of course), so that anonymity is relative with respect to your banker.  On the other hand, this centralized system is almost as efficient as the actual fiat system, and can indeed offer instant payments.
In as much as the fiat system works well, DASH will work almost just as well, contrary to bitcoin for instance, who suffers the full weight of decentralisation and all the crypto hassle that comes with it.
And in as much as DASH's central bank and commercial bank system is abroad, it is maybe still a better option for small illegal stuff than using fiat with a domestic bank.

So DASH has indeed a potentially great future, in the sense that it is a central bank system that can sell itself to the crowd as a distributed crypto, with optional anonymity, and the speed of VISA.  Why not, after all.  If it can show that the "established order" can be overthrown, that would be great.

Of course DASH is a better alternative (technologically-wise) than bitcoin.  Almost any altcoin is better than bitcoin.  Bitcoin is the most primitive version of crypto, so there's no doubt that most altcoins are better.  There are a few that are worse, true.

Crypto is based upon the idea of trustlessness.  That is, the development of protocols where y there *is no central authority imposing the rules*, but the *rules themselves* and the *respect of the rules* results from a hypothetical dynamics of a consensus algorithm.  That is what distributed trustlessness means.  It is the hypothesis that a given *published rule set* will lead to a system dynamics where a derived hypothetical rule set will result from the natural antagonist dynamics, and that derived hypothetical rule set is considered "honest enough" to induce a monetary belief system.

With bitcoin, the hypothesis is that the consensus mechanism of PoW will enforce the monetary rules of bitcoin, and that the PoW mechanism is a kind of "fair distribution system" of coins.   The belief is that the bitcoin software implements this correctly.

But you could just as well take the hypothesis that bitcoin was a huge ninjamine between just a few people in the knowing, which colluded or not, and there's no way to know if you weren't part of them.  However, you can also see that a lot of the mined coins the first few months are still in their coinbase address.  It is impossible to know whether the secret keys of these addresses are still in the hands of some or not.  It is impossible to know whether there was a kind of collusion between the first people that mined bitcoin in 2009.  You should study the source code of the bitcoin core software to see whether this code does what it says it does.

Nevertheless, there's a lot that you CAN verify with bitcoin "after the fact", and you can believe that the consensus mechanism did function.  If you understand enough about cryptography, you can assume that it works more or less as announced.  However, that's entirely YOUR OWN belief.  Nobody came to you to invite you to believe that.  If ever it turns out that 90% of what happens on bitcoin is the work of a small group who has in fact cracked the PoW function of bitcoin, and can churn out a block in 5 minutes, no matter what difficulty with a secret algorithm, or that the digital signatures on bitcoin are totally fake and you're the only dude really sending money to an exchange to buy bitcoins while they are lauching their ass off, that's entirely your silly belief that is wrong.  Because that's the essence of the whole concept of trustlessness: that the data are there for you to verify, but that that verification is entirely your affair.

Ideally, you should write your own "bitcoin core" software to check the block chain, and you still have to believe that nobody has a simple way to crack the cryptography of bitcoin.  It is still your belief that the block chain hasn't been done over a few times by a single centralized authority.  It is still your belief that the consensus mechanism works as you read it should work.  All this is your verification work, and your fundamental beliefs.

If this is not the case, you're the only one to blame that you accepted a "trustless system" on trust.  


Yes, but saying so is exactly what is to be expected in a trustless scheme.   In the same way that someone propagating a rewound block in an attempt of a 51% attack is not going to announce that he's performing a 51% attack, and in the same way that someone trying to do a double spend attempt before inclusion in a block is not going to tell you that he did so ; and you believe the system is *supposed to be designed* to prevent this dynamically, and not by "calling the police".

As these facts are known now, the players that accept it, well, accept it consciously,  and those that didn't inform themselves are trusting entities in a trustless system and are hence asking to be ripped off.


My point is: "no", because the whole point of crypto is that you don't believe anything, and that you verify everything yourself.  If you do place trust somewhere, you're placing yourself outside of the fundamental paradigm of trustlessness.  


Many people will say they were, because they didn't realize what fundamental postulate they were subscribing to: trustlessness.  If they got scammed, it means that:
1) they trusted some entity (which is a no-go in trustlessness)
2) they didn't verify everything themselves
3) they made wrong assumptions about the emerging dynamics (maybe they BELIEVED some claims, which brings them back to 1) ).

This question is similar to "which is better: punch cards or hard disks"

Cryptonote is simply technically superior.  This is not so shill any coin out there, but DASH anon tech is based upon bitcoin crypto technology, which is not exactly suited for it.  Cryptonote uses more advanced cryptographic tech which solves automatically the problem DASH tried to implement with a complicated system of masternodes and all that.

Spot on.  That said, he often generates great posts

My point is rather that people don't measure the depth of the notion of "trustlessness".  They are so used to trusted relationships, that they have a very hard time imagining what it really means, trustlessness.  My idea is that trustlessness is an illusion, which is why crypto is an ill-defined notion.  It is essentially impossible to adhere to trustlessness and not come to a grinding halt, simply because true trustnessless implies also that you have to verify EVERYTHING yourself, which you can't.  Trustlessness implies the end of the division of labor in a sense.

What is a scam ?  A scam is a violation of invited trust.  I invite you to trust me (that is, I promise you something), you trust me on that, and I do what I promised you not to do, or I don't do what I promised you to do.
Both conditions are necessary in order to be able to talk about a scam.  If I don't invite you to something (if I don't promise anything), and you GUESS that I will act in a certain way, while I act differently, that's not a scam, I didn't promise you anything.  You were just guessing (wrongly) about my behaviour.  Even if you asked me, I'm not obliged to tell you the truth.  You wanted to obtain something from me (information), I simply didn't want to give it to you.
If you don't believe me, and you don't trust me, then I cannot scam you either, even if I promised you something and I didn't keep my engagements.
A scam has as necessary and sufficient conditions: I invite you to trust me, and you trust me ; then I act differently.

The funny thing is that we are using "trustlessness in a sand box": we assume trusted entities (devs, exchanges, miners, users, github....) to play a "confined game of trustlessness" inside this trusted environment.   This is silly.  This is the same silliness of wanting "the law to regulate crypto".  "Trustlessness in a sandbox" is stupid.  If there IS a trusted environment, then there's no need to play a confined game of trustlessness: ground the trust in the system in the trusted environment.   And if there isn't such a trusted environment, don't pretend it exists, and if it doesn't behave as you GUESS it should, cry "SCAM".

Trustlessness is a notion in the same basket as "anonymity".  In its absolute form, it is an illusion.  However, you can make systems that do incorporate sufficient "protection in a more or less trustless environment" that they make it "too difficult to bother scamming" in certain cases ; in the same way that there are anon technologies that make it "too difficult to de-anonymize" in certain cases, if these cases aren't worth to bother.  But there are no absolutes in this domain.

At a certain point, there's no point in putting a lot of work in "protocol trustlessness" when the rest of the system needs more trust.  For instance, the PoW that goes in the bitcoin network is WAAAAAY too high as compared to all the trust needed for the rest of bitcoin to function.   There's more chance of someone compromising the core devs, or github, or whatever, rather than compromising the block chain itself "following its rules". 

Imagine that the core devs collude to bring out a new version of bitcoin core that allows to "crack" Satoshi's stash (by simply *accepting* bad signatures of it) ; imagine that this code is already in the bitcoin core code, but not activated yet.   People reading the code and discovering this (how many people do this ?) might want to keep it secret, and use it themselves.  By the time this code is running about everywhere, they activate this part of the code, nobody really notices directly, it seems that Satoshi's stash moves finally, they cash out part of it on exchanges, and by the time people realize (you only need a few hours for this), the deed is done.
They won't do this, but NOT BECAUSE OF bitcoin's protocol, but rather because there are too many trusted relationships that will go after them, including probably the law and so on.  One will finally count on trusted entities for this not to happen and not count on a fully trustless system.

So at a certain point, one has to stop the silliness of trustlessness.  In the same way that there's no absolute anonymity, there's no absolute trustlessness.  Some protection against "easy identity theft" helps.  And some measures in trustlessness can help.  But forget about systematic trustlessness.

I'm very much aware of Penrose's work, and he's right about almost everything.  But this has not much to do with what I'm trying to make you see.  You are confusing the "entropy of the universe" (which is an ill-defined concept) with the entropy of a sub-system in relation to an "observer", which is entirely well-defined, and to which almost all of what is scientifically claimed about entropy, is about.  
This entropy is defined as a function of the possible cases that the observer needs/wants to consider, and hence limited to the sub-system under study.

The (quantum) entanglement you are talking about is in fact exactly the generator of entropy in a system state: it is the fact of limiting one's attention to a sub-system, while this subsystem entangles with the rest of the universe, that changes the quantum state of the subsystem from a pure state into a mixed state, and while the entropy of a pure state (which implies it is also a *known* state) is zero, a mixed state has a (well-defined) entropy.

I don't know how much you're acquainted with this, I can hardly write out a three-year course on quantum physics and statistical physics here, but essentially:

If you have a sub-system A that is a priori isolated from the environment B ("the rest of the universe"), and you happen to know the exact quantum state of A, then the whole universe is in a special product state |a> |b> ; where |a> is the quantum state of A.  The entropy of A as such, with respect to you, is zero, because you know its micro state perfectly, it is |a>.

Once A interacts unavoidably with the rest of the universe, A gets entangled with it, and there's no specific quantum state of A any more.  However, you can still limit your attention to system A.
The quantum state of the whole universe is now a sum of |a1>|b1> + |a2>|b2> + .... |an> |bn> where we have been running over all possible micro states of A: there are n of them.
The quantum description of just system A now reduces to a density operator, which takes on the form:

| a1 > < a1 | (<b1 | b1>) + |a2 > < a2 | (<b2|b2>) + ... |an > <an | (<bn | bn > ).

Here, ( <bi | bi > ) are positive real numbers, the norms of the quantum states of "the rest of the universe" that are entangled with our system's quantum state ai.  There are only n such states of the universe that MATTER even though there are infinitely more of course, but they are not solicited by the entanglement with our system.

As such, our density operator consists of n quantum states, with statistical weights given by ( <bi | bi> ).  In the worst case, these weights are all equal, which means that our density operator corresponds to "total ignorance of the micro state of A".  Usually, we take extra conditions on the interaction with the rest of the universe, like "energy conserving" or "thermal equilibrium".  This changes the values of ( <bi | bi >), and leads to things like micro-canonical ensemble, canonical ensemble and so on.

In the worst case, we don't know which of the n micro states our system is in (due to entanglement with the rest of the universe), and then its entropy is log_2 (n) in bits, or 1/K_b ln(n) in thermodynamic units.

From an information perspective, if a system can be in N possible states, its entropy is (at most) log_2 (N).

Now, let us compare.  A cup of hot water, at 80 centigrade, 100 grams, say, will contain MORE than the entropy increase from freezing to 80 degrees, right ?

Now, the heat delivered to 100 grams of water to go from 0 to 80 centigrade is 418.6 J/K x 80 = 33488 J.
This heat is transferred at a temperature of less than 80 centigrade, so less than 360 K.   As such, the entropy *increase* is at least 93J/K.

Now, this corresponds to a number of states N equal to e^(6.739 10^24), or to a number of bits equal to 9.7 x 10^24.

Note that I didn't even consider the entropy of icy water, which is not zero.

So my cup of hot water has already an entropy of 10^25 bits.  No computing system on earth masters a memory capacity (*) of 10^25 bits, not even the whole internet.

(*) I take memory capacity as "state space" proxy.

This is where you are simply wrong concerning the concept of entropy, and where you deify it.
I think that as long as you haven't cleared that up, you will use the concept in a "magical" way and be misled by otherwise correct claims about it, like the second law of thermodynamics.

It is this kind of erroneous handling of the concept that also leads creationists to claim that evolution is not possible because of the second law of thermodynamics, for instance.   This is because they use the notion of entropy outside of its established, well-defined domain, but hope to use results that are only valid from within that well-established domain.

No offence, you are a brilliant guy, but don't fall in the trap of using precise mathematical/physical notions outside of their domain of definition in a hand-waving way, and hope that their rigorous properties from within the well-defined logical system still mean something.