Calculating Information Entropy

[shernren]

Derail from http://www.christianforums.com/t3315965-teach-me-why-i-should-believe-in-evolution.html&page=8

How does one count information entropy? It's really simple:

H(x) = -sum for all i [ p(i) log2 p(i) ]
http://en.wikipedia.org/wiki/Information_entropy

H is entropy.
x is the message.
i is all possible "events". For example, DNA has four "i"s: A, T, C, and G.
p(i) is the "probability" of an event, in this case the number of occurrences of a particular event over the total number of events. For example, in the message "aabc", p("a") = 0.5 and p("b") = p("c") = 0.25.
log2 is the logarithm to base two.

Example 1:
aaaa -> aaab
For "aaaa", there is only one possible event. Therefore
p("a") = 1, log2 p("a") = 0, and p("a") log2 p("a") = 0. A nonsense message consisting of a single letter has zero entropy!
For "aaab":
p("a") = 3/4; log2 p("a") = -0.415; p ("a") log2 p("a") = -0.3113 (hereafter abbreviated as plp("a"))
Similarly, plp("b") = -.5
plp("a") + plp("b") = -0.915; H(x) = 0.915.

Example 2:
aabb -> aaab

For "aabb":
p("a") = 1/2 -> plp("a") = -.5
Similarly, plp("b") = -.5
plp("a") + plp("b") = -1; H(x) = 1.
For "aaab":
H("aaab") = 0.915, by Ex. 1
Notice a negative entropy change of -0.085. Random mutations can cause information entropy to decrease!

Example 3:
kissed -> kisses

For "kissed":
p("s") = 1/3
plp("s") = -0.5283
p("k") = 1/6
plp("k") = -0.4308
similarly, for "i", "d" and "e", plp = -0.4308
Sum of all plp = -2.252; H("kissed") = 2.252
For "kisses":
p("s") = 1/2 -> plp("s") = -.5
p("k") = 1/6
plp("k") = -0.4308
similarly, for "i" and "e", plp = -0.4308
Sum of all plp = -1.792; H("kisses") = 1.792

Again, a negative entropy change brought about by a mutation which could very well be random. I think "kissed -> kissee", "kissed -> kidded", and "kissed ->iissee" all yield negative entropy changes as well. The entropy change seems to be irrelevant to the meaning of the message, doesn't it?

Example 4:
"argument" - > "rgument" -> "gument"
I will not prove these results, which are perfectly repeatable, for the sake of brevity of working. (If Fermat could do it, so can I.)
H("argument") = log2(8) = 3
H("rgument") = log2(7) = 2.807
H("gument") = log2(6) = 2.585

Now even deletions decrease entropy! Not just that, nonsense strings have less entropy than sense strings.

Example 5: (DNA)
ATCAGC -> ATCATC
H("ATCAGC") = 1.918
H("ATCATC") = log2(3) = 1.585

Even when dealing with DNA, random mutations can decrease entropy.

This should put to rest any notion of a Second Law of Thermodynamics for information content.

 

[rmwilliamsll]

p(i) is the "probability" of an event, in this case the number of occurrences of a particular event over the total number of events. For example, in the message "aabc", p("a") = 0.5 and p("b") = p("c") = 0.25.


there is something here i don't understand.

p(i) is the probability of the ith event

but you are taking the letter set to be those letters actually seen. when it appears to be over the whole potential set.

H(aaaaa) is different if:
{a} or {a,b} are the set of possible symbols.
for the {a} H(aaaa)=0
as in:
Example 1:
aaaa -> aaab
For "aaaa", there is only one possible event. Therefore
p("a") = 1, log2 p("a") = 0, and p("a") log2 p("a") = 0. A nonsense message consisting of a single letter has zero entropy!

but if the set is {a,b}
p(i)=.5, p(i)* log2 (.5)=.5 * (-1), summation for all i=-.5*4=-2


ok...what did i miss?


notes:
http://www.ccrnp.ncifcrf.gov/~toms/pitfalls.html for a general discussion of relating H() and S() and the problems of doing it.

 

[shernren]

To be honest, I have no idea what I'm supposed to do when creationists talk about the "entropy of a signal". Apparently mutation increases the entropy of a signal, a DNA code in particular. The more I read, the more that claim strikes me as being nonsensical. You're right, entropy is defined for sources of information.

The only way I could think of defining it meaningfully for a signal is to treat the signal as a source of information itself. In other words, the entropy of signal "aaab" is really the entropy of an information source which outputs "a" 3/4 of the time and "b" 1/4 of the time. The entropy of signal "kisses" is the entropy of an information source which outputs "s" 1/2 of the time and "k", "i", "e" 1/6 of the time.

That's the closest thing I can think of if someone were to ask me what the "entropy of a particular DNA sequence" is (assuming of course that informational entropy is meant, and not the physical molecules-bonds-ions-etc. entropy). After a night's sleep I'm quite sure even that is nonsense.

Are there any people here who actually know what they're talking about when it comes to information theory?? XD

 

[random_guy]

To be honest, I have no idea what I'm supposed to do when creationists talk about the "entropy of a signal". Apparently mutation increases the entropy of a signal, a DNA code in particular. The more I read, the more that claim strikes me as being nonsensical. You're right, entropy is defined for sources of information.

The only way I could think of defining it meaningfully for a signal is to treat the signal as a source of information itself. In other words, the entropy of signal "aaab" is really the entropy of an information source which outputs "a" 3/4 of the time and "b" 1/4 of the time. The entropy of signal "kisses" is the entropy of an information source which outputs "s" 1/2 of the time and "k", "i", "e" 1/6 of the time.

That's the closest thing I can think of if someone were to ask me what the "entropy of a particular DNA sequence" is (assuming of course that informational entropy is meant, and not the physical molecules-bonds-ions-etc. entropy). After a night's sleep I'm quite sure even that is nonsense.

Are there any people here who actually know what they're talking about when it comes to information theory?? XD

If we're talking about strings and the information content in strings, then the Creationists application of information theory to DNA is wrong.

I briefly studied measuring information in building decision trees for my machine learning class, and it seems that Creationists have it backwards. They think that the more random a string is, the more information it has, when in reality, the more random a string is, the more information it has because it takes more bits to describe it. That's what I gather from information theory. Therefore, random mutations are more likely to increase information.

 

[Deamiter]

I think this argument is totally bogus. The whole concept of "information entropy" has NOTHING to do with entropy in thermodynamics. The concepts cannot be related like this!

It's like saying, "since gravity pulls down, heat must flow down." You're applying a concept in one specific area of physics (the flow of heat or energy) to something totally unrelated (information theory). I agree with the conclusion, but the argument is crap.

The laws of thermodynamics have nothing to do with "information." There is no law that says that information must decay over time. There is nothing that prevents an open system (like the Earth) from becoming more complex. NOTHING. And applying entropy to the "information" contained in DNA is a complete perversion of a theory where it does not apply.

 

[shernren]

Yes, my bad. The moral of the story is that DNA has no "informational" entropy, and therefore any idea of a 2nd Law generalization forbidding evolution in information-theoretic terms is bogus.

But I took too much time on the OP to want to delete it.

 

[shernren]

.

 

[cubanito]

At some point, information must decrease as physical entropy decreases. A completely regular repetition of a single element (such as aaaaaaa) to maximum, in a setting where only a single element is possible, has the lowest possible entropy. It carries no information. Similarly the complete absence of anything (the null set) also has 0 entropy, and no information.

However, a completely random occurence of an infinity of elements, which has maximal entropy, also carries no information either.

Information is a NON-PHYSICAL entity which can be carried only in physical states between extremes of physical entropy.

At this we have an immediate revulsion: what is meant by non-physical? What is meant is something that scientists have come to grudgingly accept, that some aspects of reality are not strictly matter or energy. Information is one such real, mathematically quantifiable reality, which is neither matter nor energy. Information can be represented by a particular ordering of matter, but it is not in itself that matter. Your computer's software is clearly qualitatively different than hardware. The SAME software can be represented in various physical media, but it is not that media.

Therefore, calculations of physical entropy have little relation to information. It is true that at the extremes of total or zero physical entropy information can not be represented. This does not exclude (or include) what happens to information in the vast middle, where physical entropy is sufficient to allow the representation of information.

The fact that reality is not describable by naive materialism is very disconcerting for many. Yet physicists working in quantum mechanics have found that reality is far more interesting, and does not fit within the framework of philosophic materialism. Information is one such aspect of reality which, while quantifiable and interactive with matter and energy, is not in fact matter nor energy.

JR

 

[Deamiter]

At some point, information must decrease as physical entropy decreases.

Indeed, I'll concede the point. However, on Earth, this will not be a significant factor until the Sun burns itself out. I think most of us expect Jesus to make a stop back here SOMETIME in the next few million years (let alone the billions it would take for the universe to succomb to heat death). On human time scales, there is no barrier to an increase in information provided that the Sun's still pumping energy onto the Earth.

Information is a NON-PHYSICAL entity which can be carried only in physical states between extremes of physical entropy.

Quite right.

Therefore, calculations of physical entropy have little relation to information.

My point exactly.

The fact that reality is not describable by naive materialism is very disconcerting for many. Yet physicists working in quantum mechanics have found that reality is far more interesting, and does not fit within the framework of philosophic materialism. Information is one such aspect of reality which, while quantifiable and interactive with matter and energy, is not in fact matter nor energy.

JR

Here you lose me. Materialism is perfectly capable of describing information... though certainly not as some physical entity. Information is a philosophical construct -- like mathematics, the idea of information is a concept that helps us to make sense of the universe. We've defined information so as to be able to use the patterns created by nature.

So in essence, the laws of nature creates patterns. We use our philosophical construct of information to be able to make use of these patterns.

It's not inexplicable -- it's just our way of describing what was already there in nature.

 

[cubanito]

Please note my use of the term "NAIVE materialism." By this I mean the kind of materialist thinking that prevailed among scientists from about the time of Newton to the 1930's. Starting 1925 with Einsteinian relativity, rapidly worsening as Quantum Mechanics became increasingly bizarre, continuing with Godell's 2 incompleteness theorems, and spreading through multiple disciplines, such as Piaget's utter destruction of behaviorism as an explanation for language aquisition; "modernism" hit a wall and was irretrievably destroyed. Modernism, which consisted of a simple belief in materialism, together with an optimistic view that everything could be known, explained and predicted by the scientific method died very suddenly. Currently there is much angst about how to replace it, with post-modernism's assertion that there is NO objective Truth, or if such Truth exists we are incapable of ever knowing it leaving most unsatisfied.

Thus materialism has had to grapple with the obvious fact that there is more in this world than matter and energy, such as information. Now, while information can be represented by the arrangement of physical elements, as we agree, it is something other than mattr/energy. Use whatever terms you like, non-physical realities (in the past called metaphysics, a term shunned because, while accurate, is imprecise). In fact, I'd prefer if you come up with a term.

The thing is, information has it's OWN entropy, which can not be calculated given the formula you used. As you've agreed, that formula gives incorrect results. Input a string of 1 million a's into that formula, and make the informational content where a single a is replaced by a single b. For all but one such string you get the incorrect message, yet the formula yields identical entropy values. Better yet, take any single english word. For example "word". This string has the identical entropy to "owdr" yet it is obvious tha "word" carries information and "owrd" does not.

Informational entropy is calculated as the CHANGE from an ideal message, not as the arrangement of physical bits. Thus "word" has 0 informational entropy, "wzrd" higher entropy, "azrd" higher still and so on. How this is calculated is beyond my understanding, and in fact, some parts of the physical arrangement (namely the first & last letters plus the length of the word) are more important than others. Thus "wzfd" is more recognizable as "word" than "zorchs". I am not well versed in this field at all, but can clearly see the formula you cite is either incorrect or (more likely) misapllied.

But in fact things are much worse for materialists these days, even materialists that have grudgingly expanded their philosophy to account for such real non-physical phenomena as information and aesthetics.

In fact, there is conclusive proof from experimental evidence that CONCIOUSNESS alters the behaviour of matter (principally the alteration of behaviour of single particles to being observed as they encounter a double slit). Now this is even more disturbing to materialist because it demands there be an actual difference between inanimate and animate observers. It amuzes me greatly to read modern physicists as they grapple with quantum mechanics. Many quickly start talking about Eastern religions (for example, read "The Dance of the Wu-Li Masters"). When materialist philosophy has to be so expanded as to admit the concept of "conciousness" as a variable in physical experiments, it is materialism in name only.

Information decays over time, just as physical entropy increases over time. Not all the magic homunculi can increase useful information as a totality of the system. This is a simple fact we all see every day. Messages do not become clearer to understand with cellular static. While great discoveries do occur because of accidents, it is only by the intervention of an intelligence.

If you truly believe in the random increase of information, you would respond by hitting your keyboard randomly. You do not because the scientific method you have employed since you were knee high has taught you that information requires an intelligent effort to aquire and disseminate. As an agnostic, I did not have the faith required to believe the myths in my textbooks about self-ordering matter, and chose rather to believe my own eyes. It never seemed my room ever got neater by my throwing things around, nor my book reports more convincing by randomly smudging ink on a page. Perhaps had I an appreciation of modern art I could believe in macroevolution and the powers of randomness, but to me, even before belief in Christ, both modern art and macroevolution seemed like a scam. The fact that very, very intelligent people spend millions of dollars and gawk appreciatevely, (dare I say with religious awe?) at both modern art and macroevolution dosen't impress me. I have always chosen to believe my own reason than the madding crowd.

JR

 

[jereth]

I think this argument is totally bogus. The whole concept of "information entropy" has NOTHING to do with entropy in thermodynamics. The concepts cannot be related like this!

But when preaching to the scientifically naive masses, the use of scientific sounding concepts, even if grossly misapplied, gives the appearance of correctness. The masses don't know any better and are easily duped.

The more I look at AiG material, the more I approach the conclusion that they are liars and deceivers.

 

[Deamiter]

Informational entropy is calculated as the CHANGE from an ideal message, not as the arrangement of physical bits.

This is quite true, but again, does not apply to DNA. Quite simply there is no string of DNA that is defined as "ideal." Creationists might start with the assumption that there was an ideal string which has since decayed, but such an assumption is worthless since it is not backed up by evidence or predictions. Quite simply, there is no scientific or evidencial basis for applying this sort of information theory to genetics. It is solely an assumption based on a theological interpretation of the Bible.

In fact, there is conclusive proof from experimental evidence that CONCIOUSNESS alters the behaviour of matter (principally the alteration of behaviour of single particles to being observed as they encounter a double slit). Now this is even more disturbing to materialist because it demands there be an actual difference between inanimate and animate observers.

Surely you are not suggesting that the double slit experiment does works ONLY when a conscious observer is present!

This claim is a load of hogwash. A single particle passes through both slits due to its wave nature, not due to any influence by the observer! In most cases, the observer IS inanimate (a camera)!

You've either severely misunderstood the wave nature of particles (a quick class or even a textbook on Quantum Mechanics should clear that up) or you've read the metaphysical musings of somebody who does not understand this material.

I don't know if I can be clearer -- the effects seen in a double slit experiment are NOT dependent on the oberver (much less the consciousness of said obersver). If this is the basis of your rejection of Agnosticism, while I rejoice that you have found Christ, I fear that your conversion may have been unfounded.

If you truly believe in the random increase of information, you would respond by hitting your keyboard randomly.

In fact, evolutionists do NOT believe in a random increase in information. As we've gone over and over in this thread, the application of information theory (as used in computers) is absolutely incompatable with genetics. Your definition of information and of an increase in information has nothing to do with mutations.

By the same definition of information, snowflakes represent a HUGE "random increase in information" as do every other crystal on the planet. The growth and increase in apparent order is quite common in the natural world -- all it requires is energy. It is perhaps fortunate (or as I believe, a result of good planning on God's part) that we have the sun to give us a constant source of energy.

 

[cubanito]

But when preaching to the scientifically naive masses, the use of scientific sounding concepts, even if grossly misapplied, gives the appearance of correctness. The masses don't know any better and are easily duped.

The more I look at AiG material, the more I approach the conclusion that they are liars and deceivers.

Excuse my newbiness, but what is AiG?

JR

 

[rmwilliamsll]

Excuse my newbiness, but what is AiG?

JR

answers in genesis, the quintessential YECist site at:
http://answersingenesis.org/

 

[cubanito]

This is quite true, but again, does not apply to DNA. Quite simply there is no string of DNA that is defined as "ideal." Creationists might start with the assumption that there was an ideal string which has since decayed,

but such an assumption is worthless since it is not backed up by evidence or predictions. Quite simply, there is no scientific or evidencial basis for applying this sort of information theory to genetics. It is solely an assumption based on a theological interpretation of the Bible.

If OK with you, the discussion is branching out into various areas, so I will respond to chunks in separate posts. I am very much liking this discussion in both tone (respectful but direct) and content. Thank you for intelligent responses. I will attempt to do as well.

You are quite correct that the Creationist assumption of an "ideal" DNA string is unwaranted when creationism is itself under question. It would only be useful in testing for internal consistency of creationism. So allow me to get to the same point by a different (longer) route.

Rather than approaching the total DNA sequence, for which even creationist does not claim a single ideal (genetically, the first bear is postulated as perfect as the first man), allow me to look at single genes. I agree that no gene acts independently (indeed, not even the total gene pool of all living beings). All information must be taken within a context, in the case of single genes that includes a functional cell within an appropiate exterior enviornment. Nevertheless, it is impossible to gain much useful knowledge beyond an aethetic appreciation to try and understand the totality. Thus we must dissect and control out multiple variables to gain understanding.

So take a single gene, in fact I'll pick one well studied and rather favorable to macroevolutionary ideas: human hemoglobin. Various different genes code for what is essentially an oxygen carrier. Some of these genes are found in most humans, at different times. Hemoglobin F in the fetus binds oxygen more tighly than the normal adult hemoglobin A. This allows the fetus to survive within the mother, as it can avidly pull oxygen out of her HgA. However, because HgbF does not give up it's ox as easily, it is not as well suited for the adult, whose tissues at times require more rapid delivery of oxygen. Both those genes are well suited to human life, first fetal and then adult (HgbF expression falls off rapidly after birth).

But there are many other Hgb types out there. The most common of these "alternatives" is HgbS, which differes from Hgb A by a single amino acid (a single DNA base pair alteration). When deprived of oxygen and subjected to a slightly acidic enviorment, it becomes and remains a gigid rod, rather than a globular protein. The effect on the red blood cell is a deformation known as "sickling" because the typical doughtnuty shape transforms into a permanent sickle. That has disastrous consequences, as these cells quickly hang together and block off capillaries. Heterozygotes suffer minor problems, and have a modestly decreased lifespan. Homozygotes without extensive medical help die in childhood, and even with help die young and suffer many disabilities. There are other Hgbs, all of them cause similar results.

Now there is a marked benefit to the HETEROZYGOTE who lives in a malaria endemic area. The mild propensity for sickling is immediately triggered by the parasite, and thus someone with sickle cell trait (HgbA/HgbS) is highly resistant to malaria. Other variant hgb also for the most part serve to confer either partial or total malarial resistance. All manner of interesting combinations occur when, for example, someone has HgbC/HgbS, but these are not germane. The evolution of these alternate adult Hgb has been put forth as one of the strongest cases favoring macroevolution by many textbooks. It was so to me when I was in school.

HOWEVER please not that for an adult human living within the biodomes available on earth, only HgbA is physiologically best fit. The many other mutations, which are in fact kept in the gene pool primarily by malaria, are all quite deleterious in their homozygous state, and in the abscense of malaria, confer clear disadvantage to the heterozygote vs the homozygote.

Now, if you prefer I use the word "best fit" than ideal, fine. It's still a rose, it still shows there is only one best fit hemoglobin in the adult. Thanks to malaria, we clearly see a process of mutation resulting in genes that are uniformly LESS fit than the original. We see that without malaria, and in the presence of natural selection, all these alternate genes would eventually disappear in favor of a single "best fit" Hgb A.

The same situation can be found in most other genes. For most biologic proteins (outside the immune system) I know of, there is a SINGLE "best fit" molecule, and a host of mutations which confers selective disadvantage to the individual, ESPECIALLY is a homozygote. The exception to this almost always involves the immune system. For example, there are individuals who lack certain T-cell receptors that are virtually immune to HIV. However, because of the lack of these receptors, their immune system does not function as well as that of others who avoid HIV.

Again, please note there exist in the population many proteins, and almost all have a single "best fit" composition. Except for disease, I know of no example where a mutation confers a selective advantage.

Thus, there is in fact a very long list of "best fit" (ie IDEAL) genes, from which variance always comes at a selective cost.

JR

 

[cubanito]

Double slit experiments with a camera that whose output no one looks at are undoable. If no one looks at the data the camera records, then how does anyone know what the data is? The reason why individual particles change their behaviour depending on wether their trajectory is followed or not are not understood. In fact, there are various schools of thought on how to interpret quantum mechanics, as I'm sure you are well aware. The fact remains, the actions of fundamental particles are not in keeping with straight materialism. When the probable trajectory of a fundamental particle is altered by the presence of an observation, conciousness has entered the discussion.

JR

 

[rmwilliamsll]

Double slit experiments with a camera that whose output no one looks at are undoable. If no one looks at the data the camera records, then how does anyone know what the data is? The reason why individual particles change their behaviour depending on wether their trajectory is followed or not are not understood. In fact, there are various schools of thought on how to interpret quantum mechanics, as I'm sure you are well aware. The fact remains, the actions of fundamental particles are not in keeping with straight materialism. When the probable trajectory of a fundamental particle is altered by the presence of an observation, conciousness has entered the discussion.

JR

1. Schrodinger's cat is alive and well.

2. does a tree that falls in the forest where no one hears it really make a sound?


3. so a little boy goes up to the rabbi with a little alive bird hidden in his hand, intending to trick the rabbi with the question:

is the bird in my hand dead or alive?

if he said alive he would squeeze and kill it.
if he said dead he would open his hand and free the living bird.

the rabbi merely answered:
whatever you desire it to be.

 

[Deamiter]

If OK with you, the discussion is branching out into various areas, so I will respond to chunks in separate posts. I am very much liking this discussion in both tone (respectful but direct) and content. Thank you for intelligent responses. I will attempt to do as well.

You are quite correct that the Creationist assumption of an "ideal" DNA string is unwaranted when creationism is itself under question. It would only be useful in testing for internal consistency of creationism. So allow me to get to the same point by a different (longer) route.

Rather than approaching the total DNA sequence, for which even creationist does not claim a single ideal (genetically, the first bear is postulated as perfect as the first man), allow me to look at single genes.

Note that you have not chosen to look at single genes as you claim, but at single proteins. It is true that the defective protein is generated by a single mutation, but it is NOT true that you can define a genome that is "best fit" for that protein. It's a small point, but quite important. For example, there are people like Lance Armstrong who have extremely high lung capacity. It's not simply training but a mutation for a larger and more efficient lung that has given him this high lung capacity.

Second, and perhaps more importantly, you have utterly failed to define information. You've picked a protein that is best for a particular task... That's great. My neurons are best for making up my brain. If the neurons are corrupted, I won't survive. But looking at lungs again, is it a gain or loss of information if a mutation causes the lung cells to divide a few more times inside a fetus? The main difference between our brains and a chimp's brain is that growth in our frontal lobe is extended a few more days in humans. Is such an extension an increase or a loss of information? Why?

Double slit experiments with a camera that whose output no one looks at are undoable.

Nonsense. I am perfectly capable of taking a picture that nobody will ever view.

First off, what's with throwing around the word "materialistic?" Nobody in science ever performs an experiment using "materialistic" methods... it just doesn't make any sense. Usually when Christians throw around the term they're talking about a person's love of objects. It's useful in philosophy when talking about major differences in worldviews. It has got NOTHING to do with quantum mechanics -- if you try to use it in that context, you'll just end up confusing everybody! If you're talking about pre-quantum mechanics, you might call it Newtonian mechanics. And yes, Newtonian mechanics are incapable of predicting the wave nature of particles. Pre-quantum mechanics is NOT equivilant to "materialistic."

It seems that you're conflating two different issues -- the uncertainty principle and the wave nature of matter. We can show that the pattern on the screen is the sum of all possible paths between the source and the screen (and the probability of the particle taking that path). The wave nature of particles has also been well documented in particle accellerators.

Now you seem to claim that my consciousness has altered the double slit experiment. Again I say nonsense. What you're thinking of is the observation of a single particle. In order to observe the particle, we must bounce something off it. The act of bouncing something off it changes its momentum and position unpredictably.

However, if you shoot a single photon (or electron for that matter) through a double slit, the interference pattern will always be present. There is no collision involved. To quote you, the probable trajectory of the particle has NOT been affected by its observation, thus no consciousness is involved.

Now you can always go post-modernist and say that NOTHING is real until it's observed... but that's not science. It's a purely philosophical position. You're welcome to it, but do realize that as it's unsupportable (and impossible to disprove) it is useless for anything but as an interesting exercise in logic.

 

[Deamiter]

Forgive me, but I just have to ask. Do you have any formal training in physics? Quite simply, you remind me of many of my peers who took tons of theology and philosophy classes, and LOVED to argue about the nature of the universe... But who really didn't care much about what Heisenberg's uncertainty was built on (or what it predicted) much less how light can be both a particle and a wave simultaneously.

Do you agree that all particles have a wave nature? If not, is there some background or references you have that would refute the last few decades of work in quantum mechanics? If so, why is a consciousness necessary for a particle's wave nature to produce interference patterns after passing through a set of slits?

 

[Smidlee]

D

Even when dealing with DNA, random mutations can decrease entropy.

This should put to rest any notion of a Second Law of Thermodynamics for information content.

Yes mutations can in few cases decrease entropy yet over all , random mutation cause entropy of information to increase. This is the same with a factory that entropy decease to build a product but over all (the big picture) entropy increase is greater than the decease in entropy ... thus this is the whole point of 2nd LoT. 2nd Lot doesn't state that entropy can't decrease in an area but there is a greater cost elsewhere. So information applies the same as heat.