Information = Entropy

(George Brooks) #16

@Jon_Garvey, that’s a pretty powerful statement from @Swamidass, wouldn’t you agree?

Can I have a witness here? Maybe @grog ?!? It doesn’t get any more God-centered than that!.. not realistically speaking anyway!

(Nonlin Org) #17

Skimming through Shannon’s, I don’t see the equality.
Are you saying that a random noise generator creates information? I think not. Information always requires a deciphering key and some redundancy, both of which reduce entropy.

(Chris Falter) #18

I think it’s on page 11 of Shannon’s landmark paper, which Joshua @Swamidass cited in his original post.

Joshua, please correct me if I am wrong. Thanks!

(George Brooks) #19


If a random number generator can eventually pick any lock with a finite number of numbers… I think it’s pretty clear that information can be generated unintentionally … and probably with amazing consequences.

@Swamidass’s career is in the area of computation and artificial intelligence… I think you are kidding yourself if think you can refute anything he tells you is the God’s truth.

(Nonlin Org) #20

Don’t see it, but the graph on that page that peaks perfectly at (0.5, 1) does not account for the key and for redundancy. Shannon takes the ideal case there.

By itself and without other inputs? Not happening.

(Peaceful Science) #21

Well I am not the source of God’s truth. So I am sure he can refute me on that. =)

Exactly right. It is on page 11.

“Creates” is too strong a term. Rather, randomness is a source of information.

True random generators are a source of information, because they are high entropy and are not compressible. True random generators (e.g. from cosmic background radiation, quantum noise, brownian motion, radioactive decay geiger counts) all produce pure information.

Pseudorandom generators in a precise technical sense are not high information, because the stream is compressible to the seed and the random algorithm. However, in practice they do produce strings indistinguishable from high information. If it is a good pseudorandom generator, the key and algorithm are secret, and we keep a secret that it is a pseudorandom string, it is effectively impossible to distinguish a pseudorandom string from information. It will be incompressible and (nearly infinite) information to anyone who does not know the compression.

This is the surprising feature about information, it is exactly equal to entropy, which is highest in random streams.


(Nonlin Org) #22

How so? Information is meaningful only to the sender and receiver (and the spy). To all others it’s noise. Also, once again don’t forget the deciphering key and the mandatory redundancy.

The Infinite Monkeys theorem affirms that randomness could create Hamlet or The Odyssey (but the argument is really about life forms, not about literature). Indeed, a random process could theoretically generate these masterpieces. And if we allow for many alternative targets (like any document ever created), the probability of success goes up substantially. Quite likely, the “monkeys” would have duplicated many other information (like chemical formulas) way before typing Hamlet. But monkeys care about bananas, not Hamlet, so the random output remains meaningless until an educated reader assigns meaning based on his/her prior knowledge. Hamlet and Odyssey are important precisely because we recognize them as non-random. They fit in our history and culture and have been preceded and followed by other non-random creations. Creators, not Randomness, provide meanings. More:

No! Absolutely not.

(Peaceful Science) #23

How so? By logic clearly laid out in this foundational paper. Since 1954, the definition of information has not changed. Information = Entropy. Without this paper, information theory may not have come to be.

And I have no idea what this mandatory redundancy is of which you speak. Nor is a deciphering key relevant all. Who enforces these rules? Information equals entropy independent of these concerns.

You seem to be confusing information and meaning. Information does not .deal directly with semantics. And as I have explained, semantic information is extremely low information content.

Which then raises the question, why in the world we use information content of data (like DNA and genomes) as a measure of “meaning” and semantics? Information is entropy, not meaning. And DNA does not convey meaning. It just holds information, and much of this information records history, like bread crumbs marking a trail through time.

(Peaceful Science) #24

Is equivalent to…

Except, most combination locks are much much much easier to pick than writing the odyssey. Cool huh?

(George Brooks) #25


I recommend that you don’t spend too much time repeating your absolute rejection of a career researcher on a topic from which he makes a living.

Sure… reject his position as a matter of due course. Because then you can discuss your different ideas. But if it looks like all you are doing is rejecting everything he says, over and over, I’ll be flagging your postings accordingly. And then it will be up to the Administrators…

(Greg Rogers) #26

I won’t pretend to know a fraction of the science you guys know. I became a Christian not because I am smart. I became a Christian because I chose to have faith in God and His gospel. And where did that faith come from? It came from the Word of God- “Faith comes from hearing.” And this faith has absolutely transformed my life from the inside out! I once was selfish and mean spirited and now when I see someone in a position of need or weakness such as some of the mentally handicapped folks bagging groceries at Kroger or those poor helpless girls mistreated in the sex trade, I just want to pray out to God on their behalf and do something to help them! The idea of racial discrimination I must say takes the cake as one of the most foolish things mankind has come up with! I love all people…and I don’t want accolades for saying any of this. I actually feel uncomfortable saying any of this in a way…but making much of God and less of me brings much joy anyway and I cannot help but to say it. How was this faith generated? Not my intelligence. Not much of that here…It was generated again by having faith in the God of the Bible that was generated and given by the God of the Bible and the gospel of His Son dying in my place! It has turned me upside down, inside out, and upright from a place of being hunched over in disobedience and unbelief.

My faith also comes from another place that is God ordained. I love nature! I love its beauty, its colors, its functional balance. I am amazed at the complexity of the brain and how God created sexual beings for reproduction and symbiotic relationships between plants and animals and all of the creative designs in animals and flowers and colors in fish (#1 favorite vacation endeavor has been snorkeling reefs although it has been awhile) Then you have the dynamics needed to even make earth habitable for life to exist…things like the position and size of the earth’s moon, the earth’s magnetic field, its atmosphere, the presence of water, the fact that water in its frozen state is unusually less dense than its liquid state thus able to float…and all those other planets floating in space and rotating about stars in a universe stretching billions of light years etc. God calls these things a basis for faith in Him as well. In Romans 1:20 it says “God’s invisible qualities-his eternal power and divine nature-have been clearly seen, being understood from what has been made, so that men are without excuse.”

Have very little understanding of the specific scientific arguments back and forth between ID and theistic evolutionists. At face value the idea of chance causing complexity like we see it today no matter how much God lipstick you put on it does not sit well with me at all…I still must sit back (in my simpleton way) and suggest that if folks still want to argue the details of two views, maybe consider laying down the argument and put our energies as Christians towards a unified effort that finds a priority of grounds for worshipping Him as our Creator and Designer who has indeed clearly revealed Himself in creation. And we must stop pretending that our intellectual pride and the potential profitability from a book deal or in an occupation does not affect our propensity for stiff arming unity for arguing over some semantics for attention sake. I am still a sinner who can only understand this temptation from ongoing personal experience thankfully occurring less and less in me! .

And His Gospel that frees me from this tendency creates a paradigm that eliminates both sniveling and swaggering (thank you Dr. Keller) “so that no man may boast” which also declares GOD! He is coming back soon and for one don’t want to have my pants down if He does in my lifetime.

Sometimes I want to sense that we become so obsessed with the trees in these scientific details arguing chance vs design (amongst Christians nonetheless who are called to have faith in an Intelligent Designer) that this blinds us from the forest where that God does indeed dominate, rule and always longs for men to bask in his loving presence to find blessing in worshipping Him!

You guys are so smart! I am blessed more than you will know reading a lot of these items on this website. I was led by another to check out a quote from this segment I thought so pertinent and likeminded to the sentiment here and wanted to add another two cents. Anyone here and otherwise who is offering their genius towards the proclamation of the God who describes himself in His word as an Intelligent Creator and an all wise Designer -I honor you! Thanks for listening to this incredibly less smart country boy ramble!

(Jon Garvey) #27

Absolutely - that’s why Joshua and I generally get on so well even when we disagree, both here and elsewhere.

Sadly not everyone sees things his way, either in the EC camp or the ID camp - and certainly in the metaphysical naturalism camp that prevails within the biological “guild”. There’s a tendency to see the “unexplained information” as “chance” and therefore quite possibly or probably undesigned and undirected.

And as for the “explained” information, that is, whatever lends itself to explanation by the laws of nature, that is often seen as secondary causation running autonomously from God, rather than as a channel of divine providence in its “general”, predictable, aspect.

The classical doctrine of providence is exactly as Joshua has stated it: the governance of all things towards their intended ends. The"novel" component in Joshua’s statement is the agnosticism of information theory - which of course threatens equally both “this shows the marks of design” and “this shows signs of randomness”. That leaves one back with having to make a choice based on metaphysical and theological commitments, rather than science.

To be fair, universal providence is recognised by all the main Intelligent Design people too, such as Michael Behe, Douglas Axe, William Dembski, Steve Meyer. The claim (right or wrong) that there are instances where design can be detected in some scientific way is emphatically not a belief that only those things come under God’s designing providence - that seems rather to be a straw-man criticism by their detractors.

(Peaceful Science) #29

Amen. With your focus here, it does not matter what you think of the details of our origins. I share of information theory because it is fun for me revel in God’s work in our world. I am glad you have enjoyed it.

Though I would point to Jesus. He is the clearest revealing of the Creator. If you have seen Him, you have seen the Father.

(Peaceful Science) #30

That is exactly right.

Though the novelty here is only marginal. It does not take a lot of math to realize that unexplained patterns in data are not evidence of anything other than noise and finite understanding. And in the case of ASC, neither is the opposite true; explained patterns in the data are not evidence of intelligence either, because a lot of processes impart patterns on data. Therefore, we cannot presume to prove or disprove God with an equation.

Besides, I find the Word in the flesh, Jesus, is much more compelling than any equation could ever be. And I say this even though I love equations.

Do you know how correct you are here?

His arguments, to the extent I understand them, persuade me, and actually reinforce the point above that chance and design cannot be formally distinguished. Since that is counterintuitive, it leads again to the possibility that the explanation for this indistinguishability of opposites is that “chance” is only and always, in reality, God’s choice. Chance looks the same as choice simply because chance always is choice, the providential choices of the logos of God.

You are echoing Shannon’s language precisely in the original paper (see page 10 right before the information = entropy equation on page 11).

From his point of view, he is not actually formulating this in terms of “chance,” but in terms of “choice.” Of course, the parallel derivation in thermodynamics is rather about “chance”. Both,ultimately derivations are encoding uncertainty from a particular point of view, but end up with exactly the same equation.

One could even say that the foundation insight of information theory is that “choice = chance”, at in a mathematical case.

Someone theological needs to connect this to the “scandal of particularity” and God’s autonomy…

(George Brooks) #31


My apologies for only now seeing your response.
My dear sir, you are completely wrong about this.
My original statement said, Any lock with a finite series of numbers.

You apparently do not understand how easy this is. As a young father, I was faced with my son’s friend who had a 4 position bicycle lock. You know… 4 wheels with digits from 1 to 9. And he didn’t remember the combination.

So I sat down, and while talking to him began to rotate each disk, one position at a time, then one disk at a time. Starting at 0000, going from 1111 to 1199, and continuing. Somewhere around 32xx the lock opened.

That is how a random number generator can eventually pick any finite series lock. But it could take a while.

Do you understand my assertion now? Or do you still want to dispute it?

(Antoine Bret) #32

Many thanks Joshua, this is very clear and useful.
I’m a physicist, and I have a question on entropy. I hope it won’t be too technical. Here it is:
Take a system with total energy E. It has an Hamiltonian H, a E is an eigenvalue of H. If I remember well, you can also define its entropy S, like S = k Ln N, where N is the degree of degeneracy of the eigenvalue E (or the dimension of the Eigenspace associated with E).
Here’s my question: if the system is isolated, its energy E won’t change with time. So N shouldn’t change either, so S. You would then conclude that S won’t increase, which contradicts the 2nd law.
Where’s the mistake?
Many thanks!

(Steve Schaffner) #33

If the system is in an eigenstate, then it is a in a stationary state and doesn’t change at all. There is no requirement that S increase in a system that undergoes no change.

(Peaceful Science) #34

There are several caveats/qualifier to the 2nd law. It is not a universal rule. Perhaps it should not even be called a “law.”

Here comes the first caveat. At equilibrium dS will approximately = 0. So if the system hits equilibrium, S well remain essentially constant. The second law is really more like dS >= 0 than a dS > 0. In simplified idealized simulations (like those we are discussing), it is common for the system to stabilize and S to stabilize at a specific value.

The second caveat is that the second law does not hold in small systems. Interestingly enough, in molecular systems it is well known however, that there can be fluctuations where dS < 0. So the 2nd law is not an inviolable law It is better to think of it like the Central Limit theorem for gaussian distributions. The larger the system the stronger it will hold

The reason why this is really important. As Maxwell correctly puts it…

The truth of the second law is … a statistical, not a mathematical, truth, for it depends on the fact that the bodies we deal with consist of millions of molecules… Hence the second law of thermodynamics is continually being violated, and that to a considerable extent, in any sufficiently small group of molecules belonging to a real body.

This, once again, is a surprising fact. What we understand about macroscopic bodies does not hold when we go down to small numbers of particles. We have to rework our understanding of these things substantially. Of course, is in this realm too, and can see its entropy increase and decrease by natural processes alone.


(Greg Rogers) #35

We all have gifts. some have mercy, others have strengths related to intelligence. We can use these things to glorify God.

We must be careful however. the weakness found in those with mercy might be the fear of man. The weakness found in those who are intelligent might be to stiff arm wisdom from God for reliance on personal intelligence.

I have indeed changed Mr. Brooks! I came into biologos searching for answers and it seems that I have come out the back end finding hope in God as Creator who could have created in any fashion He would choose more than I did coming into the forums. I have found really smart folks here but find myself trusting wisdom from God more…this is not to say that I am insincere in complementing those who are brilliant! Ravi Zacharius is one of the most brilliant people I have ever encountered yet his gaze seems to be well placed on God’s Word and heavenly wisdom and not earthly.

(Nonlin Org) #36

You can look it up. DNA base pairing, 3’-5’ ends, and telomeres are all examples of mandatory redundancy.
The key is absolutely essential. Remember Rosetta Stone? Even assuming the random generator creates information, you do not have a key for it.

facts provided or learned about something or someone.
"a vital piece of information"
synonyms: details, particulars, facts, figures, statistics, data; More
what is conveyed or represented by a particular arrangement or sequence of things.
“genetically transmitted information”

I do not.

He already told you not to make him into an idol. It seems you didn’t get that message.

Sorry, but your explanation is childish and wrong. You opened the lock, not a random number generator. You, the human, can use a random number generator to help you, the human, reach your willful goal.

The hammer doesn’t build a house. Instead the human can use a hammer to build a house of his/her desire. Get the difference?

Aside from this, “any lock with a finite series of numbers” is a gross exaggeration. Just try three times with your bank account and you will find your IP address locked out of this scheme.