Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century

In 1931, Kurt Gödel delivered a devastating blow to the mathematicians of his time

In 1931, Kurt Gödel delivered a devastating blow to the mathematicians of his time

In 1931, the young mathematician Kurt Gödel made a landmark discovery, as powerful as anything Albert Einstein developed.

In one salvo, he completely demolished an entire class of scientific theories.

Gödel’s discovery not only applies to mathematics but literally all branches of science, logic and human knowledge. It has earth-shattering implications.

Oddly, few people know anything about it.

Allow me to tell you the story.

Mathematicians love proofs. They were hot and bothered for centuries, because they were unable to PROVE some of the things they knew were true.

So for example if you studied high school Geometry, you’ve done the exercises where you prove all kinds of things about triangles based on a set of theorems.

That high school geometry book is built on Euclid’s five postulates. Everyone knows the postulates are true, but in 2500 years nobody’s figured out a way to prove them.

Yes, it does seem perfectly “obvious” that a line can be extended infinitely in both directions, but no one has been able to PROVE that. We can only demonstrate that Euclid’s postulates are a reasonable, and in fact necessary, set of 5 assumptions.

Towering mathematical geniuses were frustrated for 2000+ years because they couldn’t prove all their theorems. There were so many things that were “obviously true,” but nobody could find a way to prove them.

In the early 1900’s, however, a tremendous wave of optimism swept through mathematical circles. The most brilliant mathematicians in the world (like Bertrand Russell, David Hilbert and Ludwig Wittgenstein) became convinced that they were rapidly closing in on a final synthesis.

A unifying “Theory of Everything” that would finally nail down all the loose ends. Mathematics would be complete, bulletproof, airtight, triumphant.

In 1931 this young Austrian mathematician, Kurt Gödel, published a paper that once and for all PROVED that a single Theory Of Everything is actually impossible. He proved they would never prove everything. (Yeah I know, it sounds a little odd, doesn’t it?)

Gödel’s discovery was called “The Incompleteness Theorem.”

If you’ll give me just a few minutes, I’ll explain what it says, how Gödel proved it, and what it means – in plain, simple English that anyone can understand.

Gödel’s Incompleteness Theorem says:

“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”

You can draw a circle around all of the concepts in your high school geometry book. But they’re all built on Euclid’s 5 postulates which we know are true but cannot be proven. Those 5 postulates are outside the book, outside the circle.

Stated in Formal Language:

Gödel’s theorem says: “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”

The Church-Turing thesis says that a physical system can express elementary arithmetic just as a human can, and that the arithmetic of a Turing Machine (computer) is not provable within the system and is likewise subject to incompleteness.

Any physical system subjected to measurement is capable of expressing elementary arithmetic. (In other words, children can do math by counting their fingers, water flowing into a bucket does integration, and physical systems always give the right answer.)

Therefore the universe is capable of expressing elementary arithmetic and like both mathematics itself and a Turing machine, is incomplete.

Syllogism:

1. All non-trivial computational systems are incomplete

2. The universe is a non-trivial computational system

3. Therefore the universe is incomplete

You can draw a circle around a bicycle. But the existence of that bicycle relies on a factory that is outside that circle. The bicycle cannot explain itself.

You can draw the circle around a bicycle factory. But that factory likewise relies on other things outside the factory.

Gödel proved that there are ALWAYS more things that are true than you can prove. Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few unprovable assumptions.

Gödel’s Incompleteness Theorem applies not just to math, but to everything that is subject to the laws of logic. Everything that you can count or calculate. Incompleteness is true in math; it’s equally true in science or language and philosophy.

Gödel created his proof by starting with “The Liar’s Paradox” — which is the statement

“I am lying.”

“I am lying” is self-contradictory, since if it’s true, I’m not a liar, and it’s false; and if it’s false, I am a liar, so it’s true.

Gödel, in one of the most ingenious moves in the history of math, converted this Liar’s Paradox into a mathematical formula. He proved that no statement can prove its own truth.

You always need an outside reference point.

The Incompleteness Theorem was a devastating blow to the “positivists” of the time. They insisted that literally anything you could not measure or prove was nonsense. He showed that their positivism was nonsense.

Gödel proved his theorem in black and white and nobody could argue with his logic. Yet some of his fellow mathematicians went to their graves in denial, believing that somehow or another Gödel must surely be wrong.

He wasn’t wrong. It was really true. There are more things that are true than you can prove.

A “theory of everything” – whether in math, or physics, or philosophy – will never be found.  Because it is mathematically impossible.

OK, so what does this really mean? Why is this super-important, and not just an interesting geek factoid?

Here’s what it means:

  • Faith and Reason are not enemies. In fact, the exact opposite is true! One is absolutely necessary for the other to exist. All reasoning ultimately traces back to faith in something that you cannot prove.
  • All closed systems depend on something outside the system.
  • You can always draw a bigger circle but there will still be something outside the circle.

Reasoning inward from a larger circle to a smaller circle (from “all things” to “some things”) is deductive reasoning.

Example of a deductive reasoning:

1.    All men are mortal
2.    Socrates is a man
3.    Therefore Socrates is mortal

Reasoning outward from a smaller circle to a larger circle (from “some things” to “all things”) is inductive reasoning.

Examples of inductive reasoning:

1. All the men I know are mortal
2. Therefore all men are mortal

1. When I let go of objects, they fall
2. Therefore there is a law of gravity that governs all falling objects

Notice than when you move from the smaller circle to the larger circle, you have to make assumptions that you cannot 100% prove.

For example you cannot PROVE gravity will always be consistent at all times. You can only observe that it’s consistently true every time.

Nearly all scientific laws are based on inductive reasoning. All of science rests on an assumption that the universe is orderly, logical and mathematical based on fixed discoverable laws.

You cannot PROVE this. (You can’t prove that the sun will come up tomorrow morning either.) You literally have to take it on faith. In fact most people don’t know that outside the science circle is a philosophy circle. Science is based on philosophical assumptions that you cannot scientifically prove. Actually, the scientific method cannot prove, it can only infer.

(Science originally came from the idea that God made an orderly universe which obeys fixed, discoverable laws – and because of those laws, He would not have to constantly tinker with it in order for it to operate.)

Now please consider what happens when we draw the biggest circle possibly can – around the whole universe.
(If there are multiple universes, we’re drawing a circle around all of them too):

  • There has to be something outside that circle. Something which we have to assume but cannot prove
  • The universe as we know it is finite – finite matter, finite energy, finite space and 13.8 billion years time
  • The universe (all matter, energy, space and time) cannot explain itself
  • Whatever is outside the biggest circle is boundless. So by definition it is not possible to draw a circle around it.
  • If we draw a circle around all matter, energy, space and time and apply Gödel’s theorem, then we know what is outside that circle is not matter, is not energy, is not space and is not time. Because all the matter and energy are inside the circle. It’s immaterial.
  • Whatever is outside the biggest circle is not a system – i.e. is not an assemblage of parts. Otherwise we could draw a circle around them. The thing outside the biggest circle is indivisible.
  • Whatever is outside the biggest circle is an uncaused cause, because you can always draw a circle around an effect.

We can apply the same inductive reasoning to the origin of information:

  • In the history of the universe we also see the introduction of information, some 3.8 billion years ago. It came in the form of the Genetic code, which is symbolic and immaterial.
  • The information had to come from the outside, since information is not known to be an inherent property of matter, energy, space or time.
  • All codes we know the origin of are designed by conscious beings.
  • Therefore whatever is outside the largest circle is a conscious being.

When we add information to the equation, we conclude that not only is the thing outside the biggest circle infinite and immaterial, it is also self-aware.

Isn’t it interesting how all these conclusions sound suspiciously similar to how theologians have described God for thousands of years?

Maybe that’s why it’s hardly surprising that 80-90% of the people in the world believe in some concept of God. Yes, it’s intuitive to most folks. But Gödel’s theorem indicates it’s also supremely logical. In fact it’s the only position one can take and stay in the realm of reason and logic.

The person who proudly proclaims, “You’re a man of faith, but I’m a man of science” doesn’t understand the roots of science or the nature of knowledge!

Interesting aside…

If you visit the world’s largest atheist website, Infidels, on the home page you will find the following statement:

“Naturalism is the hypothesis that the natural world is a closed system, which means that nothing that is not part of the natural world affects it.”

If you know Gödel’s theorem, you know all systems rely on something outside the system. So according to Gödel’s Incompleteness theorem, the folks at Infidels cannot be correct. Because the universe is a system, it has to have an outside cause.

Therefore Atheism violates the laws mathematics.

The Incompleteness of the universe isn’t proof that God exists. But… it IS proof that in order to construct a consistent model of the universe, belief in God is not just 100% logical… it’s necessary.

Euclid’s 5 postulates aren’t formally provable and God is not formally provable either. But… just as you cannot build a coherent system of geometry without Euclid’s 5 postulates, neither can you build a coherent description of the universe without a First Cause and a Source of order.

Thus faith and science are not enemies, but allies. They are two sides of the same coin. It had been true for hundreds of years, but in 1931 this skinny young Austrian mathematician named Kurt Gödel proved it.

No time in the history of mankind has faith in God been more reasonable, more logical, or more thoroughly supported by rational thought, science and mathematics.

Perry Marshall

“Math is the language God wrote the universe in.” –Galileo Galile, 1623

Further reading:

Incompleteness: The Proof and Paradox of Kurt Gödel” by Rebecca Goldstein – fantastic biography and a great read

A collection of quotes and notes about Gödel’s proof from Miskatonic University Press

Formal description of Gödel’s Incompleteness Theorem and links to his original papers on Wikipedia

Science vs. Faith on CoffeehouseTheology.com

238 Responses

  1. benito-san says:

    alright just delete my other “awaiting moderation” posts from a month or two ago, your entire argument across all of these blogs boils down to this:

    “Show me a code that’s not designed. All you need is one.”

    positively charged ion (encoder) -> photon (message) -> negatively charged ion (decoder)

    either I’m right or I’m wrong about this, given your expertise it should take all of 1 minute for you to respond to this please

    • Perry Marshall says:

      Go to www.cosmicfingerprints.com/blog/solve. There is a PDF form where you can attempt to formally demonstrate that the system you have just described is a formal communication system, with encoding / decoding tables, symbolic characters etc. It’s essentially fill-in-the-blanks, based on Bernard Sklar’s textbook on engineering communication theory.

      Fill in the form and submit it and I’ll post it. Then everyone here can see whether what you have just said makes sense or not.

  2. benito-san says:

    well thank you for responding so promptly, but you didn’t even say whether you thought my idea had any merit! it follows Shannon’s model, that’s gotta count for something right? 🙂

    I’ve looked at that “/blog/solve” challenge before and I’d be up for giving it a shot (eventually hehehe) but I have a few questions about it that I think are kind of important:

    1) did you assemble this list yourself, or is this a standardized form in your field of work?

    2) is it safe to assume that all man-made codes should (or must) be able to follow this list of criteria?

    3) Criterion 8 defines the term “character” but doesn’t apply it to anything, and the term doesn’t appear in the rest of the list, which is confusing… and it’s not very difficult to imagine a simple code in which this step would be unnecessary…

    obviously I’m just a layperson when it comes to your area(s) of expertise…. in the context of these blogs, the word “code” to me means simply ANY method of communication or information exchange, even stuff like bee waggles which you’ve acknowledged but understandably disqualified from the challenge as being products of an underlying code (DNA)… so my final question is, when Perry Marshall uses the word “code,” am I misinterpreting it? 🙂

    thanks for your time,
    Ben

    • Perry Marshall says:

      Your idea has a superficial resemblance to Shannon’s model. It’s a nice try.

      1) This format is taken straight out of a standard digital engineering communications textbook, in the first chapter where codes are universally defined.

      2) Yes, ALL man-made codes follow this criteria. As does DNA.

      3) #8 refers to the fact that real codes have more than one symbolic layer, in this case two. Most codes and languages have far more than 2 layers. Even Morse Code has 2 layers. It has dots and dashes (layer 1) and combinations of dots or dashes that form letters (layer 2).

      A code with only one layer is too simple to be of much use to anyone. You could define a code where you map greek letters to english letters, ie a = alpha, b = beta and so on but all you did was substitute one letter for another.

      I am using an extremely precise definition of code so that there is zero ambiguity about anything I say. Common everyday usage of the word code might be slightly less formal than mine but 95% of the time the word code in normal English usage is identical to my definition.

      • benito-san says:

        just wanted to make sure about those 3 points, thanks, but I can’t really tell whether you were agreeing with my definition of code as any method of info exchange… do you consider traffic lights to be a type of code? smoke signals? how about “tap once for yes, twice for no?” for the sake of this comment I’ll assume the answer is yes, in which case my question is: how would you fill out the “/blog/solve” form for traffic signals? wouldn’t that be a one-layer code (3 symbols in total) which is of great use to many people, or am I missing something (which is very likely)? 🙂

        actually if you wanted to be sporting about that challenge, maybe you could post (or link) an example of that list being correctly filled out for something simple like Morse Code

        also, could you explain why my ion/photon idea is wrong? when a negatively charged ion interacts with a positively charged ion to attract one another, isn’t that simply a set of instructions being carried out? we don’t know why these instructions (laws of physics) are the way they are, but they DO exist, so I honestly don’t understand how this is not code… one ion emits a photon, another receives it.. information is exchanged, and action is taken accordingly…. where did I go wrong? 🙂

        thanks again,
        Ben

        • Perry Marshall says:

          I have offered a formal definition from communication theory and it’s the only one I’m willing to accept. I do not necessarily agree with your definition. Many systems that are codes by your definition would fit and some would not.

          Traffic lights- yes that does count as a very simple code. Red = Stop, Green = Go, Yellow = Caution. It’s a code but not a language. It’s too trivially simple to count for the /blog/solve page because there is no alphabet. It’s one degree simpler than a = alpha, b = beta. Note my #6: “The message passed between encoder and decoder must be a sequence of symbols from a finite alphabet.”

          Smoke signals – probably a 2 layer code. I don’t really know because I never learned smoke signals.

          On the /blog/solve page I already show an example for ASCII. Morse code would be almost identical.

          The reason why your ion photon idea is wrong is that there is no freely chosen convention of symbols and no instructions. There is only linear physical cause and effect. This is no different than gravity. It’s just attraction. There is no alphabet involved. Fill out the coding table for ions and you’ll see exactly what the problem is.

          • benito-san says:

            all you have to do is take a look at the Periodic Table and the Standard Model and you have your symbols

            as for no instructions, I completely disagree, the instructions are the laws of physics themselves (including gravity)… if you were to create a computer model of the interactions of subatomic particles and molecules, you would obviously have to program a set of very specific instructions to produce an accurate model, right? doesn’t the presence of a law or a rule imply some sort of instructions by definition? dismissing this as “just attraction” does not seem very scientific to me I’m sorry to say, it’s not enough to stop at cause-and-effect as just-the-way-things-are, especially if you believe in the idea of an uncaused cause 🙂

            now, on to the statement “It’s a code but not a language.” I fear that you may be trying to change the rules on the fly here, because the word “language” does NOT appear in the instructions of the challenge… furthermore, in criterion 7 you equate the term “alphabet” with the term “symbol set”.. what is wrong with an alphabet of only three symbols: Red/Yellow/Green? sure it’s not a language but it gets the job done, it performs a function as a code, shouldn’t that be the ultimate criterion? if we were to find a mysterious device on the moon with a simple, one-layer code (possibly resembling a traffic light), would you disqualify this as evidence for alien intelligence because the code wasn’t complex enough?

            finally, I forgot to address this in my last comment, but earlier you said “#8 refers to the fact that real codes have more than one symbolic layer”… what do you mean “real codes”? this sounds completely arbitrary to me, and since you’ve acknowledged that traffic lights DO count as a simple code it also sounds contradictory… I’m sure that in the context of your field of work, traffic lights are a laughably simplistic system to really think of as “code,” but it’s code all the same… maybe a better example of one-layer code would be order tickets at a restaurant: you write down numbers (from a set of dozens or maybe over a hundred different symbols), hand the chef an order slip, and get a variety of different dishes a few minutes later that you never had to mention by name… this is a real code, a real form of communication, that real people use all the time to improve efficiency.. the fact that it doesn’t have the complexity to warrant a Step 8 sounds more like an indictment of your Step 8 than the simplicity of one-layer code… I think perhaps you either need to eliminate Step 8, or else change the nature of the challenge (e.g. give an example of a naturally occurring 2+ layer code)

            okay I’ll shut up now, I hope you can take the time to fully address this, I’ll be looking forward to it 🙂

            thanks
            Ben

            • Perry Marshall says:

              Ben,

              It’s interesting that as you sit here and try to argue with me you have not yet filled out the table I gave you at /blog/solve. Fill out the table.

              The laws of physics are inviolable. There is only one outcome that is possible. If you wish to call them instructions you are welcome to think of them that way, but they do not exist in the form of symbols and they cannot be disobeyed.

              The laws of codes are symbolic and the convention of symbols in any code is freely chosen. It is possible for encoding / decoding to be done incorrectly. It is possible for the table to not be followed. And that is the vast difference between codes and non-codes.

              I am not trying to change the rules on the fly, you are. I gave you a criteria and a standard, universal format you can use to describe the behavior of any code.

              I completely agree, a traffic light is a real code. But you can’t formulate a set of instructions for building anything with a code that simple. You need more than one layer to do that. You can build things with ASCII and DNA and computer languages. Thus the set of definitions that the engineering profession has chosen.

              The periodic table is a man-made legend, or code, for describing and classifying atoms. The names we give to atoms are codes, but atoms are not codes. If you made a computer model of the laws of physics then you would have a symbolic representation of the physical world. But the physical world is not symbolic.

              If you don’t like the formal definition of a digital communication system then you are welcome write to Dr. Sklar or the publisher of the engineering textbook and complain. The criteria I have chosen here is universal.

              If you think that the laws of gravitational attraction or physics are codes then fill in the table and demonstrate that they are.

              • benito-san says:

                Perry,

                I doubt this will come as much of a shock, but a lot of this material is pretty much new to me… I haven’t filled out the table yet because I’m still trying to fully grasp some new concepts and new vocabulary first, hence the questions (and forgive me if they sound like arguments)… which I have more of 🙂

                1) I’m not trying to change any rules, I’m honestly just trying to understand them, and when you bring up the concept of a “language” that can “formulate a set of instructions,” which doesn’t appear at all on the challenge page, it is confusing… or is that why I’m having a problem with step 8? is step 8 meant to be interpreted as such? I can accept that if that’s the case, but that just brings me back to my one-layer code question… why isn’t it enough for a code to successfully perform a function for it to qualify as “real code?” I wasn’t trying to be flippant with my alien device analogy, it just seems to me that the discovery of even a simple code (exclusive from our DNA) should be important… furthermore, and fundamentally, if you’re seriously open to the possibility of a code that isn’t the product of a mind, wouldn’t it actually make More sense to look for a simple, one-layer code that might be (perhaps of necessity) a precursor to anything more complicated than that?

                2) I’m having trouble reconciling the 4th and 5th paragraphs of your last comment…. “I gave you a criteria and a standard, universal format you can use to describe the behavior of any code” followed by “I completely agree, a traffic light is a real code.” but this is confusing, because if a traffic light is a real code, then how could you fill out that form without skipping step 8?

                3) could you please define “freely chosen convention of symbols?” my google skills are poor, I seriously can’t find an actual definition of that phrase…

                4) is it accurate to say that DNA can ultimately be expressed in purely chemical terms, which are based on the Periodic Table?

                that’s all I got for now, I truly am hesitant to fill out the challenge form until I understand exactly what we’re talking about, I hope you can bear with me.. thanks,
                Ben

                • Perry Marshall says:

                  Ben,

                  One of the most important concepts in information technology is that codes exist in layers. The OSI 7 Layer Model is the most popular embodiment of this idea. Real world languages consist of a code within a code within a code. In binary, 1= on and 0 = off. If you have nothing more than that, you can’t do much. That’s why in ASCII, 1000001 = A. Therefore ASCII, one of the simplest codes there is, is a 2 layer code.

                  Then after it’s decoded from ASCII, letters also form words and those words have grammar rules that form meaning and this is true whether we’re talking about English or HTML pages or spreadsheets.

                  Just for this blog comment to be seen by you on your computer, the information was probably encoded then decoded in at least 10 layers. And that doesn’t include you understanding the text. That’s just on the level of the computers between me and you.

                  A 1 layer code does qualify as a real code. But all you’ve done is attach a couple of symbols to something (like 1=on, 0=off) and you can hardly do anything with it.

                  Freely chosen means 1 could have meant off and 0 could have meant on. We were free to choose it either way and we chose 1=on. A could have been 0111110 but it’s 1000001. Freely chosen.

                  The free choice all by itself is why you can’t derive the laws of any code from the laws of physics or chemistry. Because those laws by definition cannot make that choice for you. When you invent the code you have to make the choice.

                  By the way this is the most rudimentary example of the fact that conscious beings have free will.

                  And it is a fact that there is not even any such thing as a naturally occurring 1 layer code, much less a multi-layer code.

                  The engineering definition of a code as 2 layers allows for the possibility of creating as many layers as you want, just by adding more.

                  In engineering, things start getting interesting once you have more than one layer. You have 1’s and 0’s and you have ASCII, now you can create a simple language like HTML or a complex language like C++. But you have to have a basic structure first.

                  What DNA is made of can be expressed in purely chemical terms but the operation of the genetic code cannot. Why? Same reason that what your computer is made of can be expressed in purely chemical terms but the operation of programs inside it cannot. You cannot understand a computer without understanding things like ASCII and the BIOS and the data format of the hard drive and USB and all those things are codes and none of those things can be derived from the rules of physics and chemistry. They are freely chosen.

                  And by the way the layered nature of DNA and all other codes is why evolution through random mutation is impossible. Evolution MUST obey the rules of the code or it will only destroy the information.

                  Or to put it another way, EYolutixn MUST obey coe rules7of Hhe codH or Vt will only dPstroy rhe information.

  3. benito-san says:

    Perry,

    well thank you for confirming 3 and 4 for me, but you didn’t actually directly address either 1 or 2… I do understand that languages are far more complex than simple codes, but if a code can be a code without being a language, then your step 8 seems completely arbitrary… if it’s not, then how do you fill it out for a traffic light, or a system of numbered dishes in a restaurant?

    my only other question at the moment is this: where is the freely chosen convention of symbols for describing DNA if the Periodic Table doesn’t count?

    • Perry Marshall says:

      If you want to fill out the table for a traffic light, then n=1 and C=k. It becomes a “trivial case.”

      ASCII needs 2 layers because you need 1 and 0 (“on” and “off” or “5 volts” and “0 volts”) in order to have a signal in the first place, and combinations of 1’s and 0’s to represent letters of the alphabet. Step 8 isn’t completely arbitrary, it’s absolutely necessary in order to communicate instructions.

      If you disagree, then show me how to communicate instructions with just “on” and “off” with no 2nd layer of code.

      Ben, DNA is a language. The genetic code operates with 2 layers of symbols. For all those who say that DNA can occur naturally, I’m asking for one other example of a code with 2 layers of symbols that occurs naturally.

      In the genetic code, 4 letters map to 64 triplets which form 20 amino acids which form proteins. GGG = Glycine. AAA = Lycine.

      It could be theoretically possible for GGG to code for Lycine and AAA to code for Glycine instead. There are in fact a few organisms where the genetic code table is slightly different. That is the freely chosen convention of symbols. You cannot derive the genetic code from the periodic table.

  4. benito-san says:

    “I’m asking for one other example of a code with 2 layers of symbols that occurs naturally.”

    if it’s possible to fill out step 8 for a 1-layer code with n=1 and C=k, then you are most certainly changing the rules with that statement

    I’ve already given examples of how to communicate instructions with just one layer of code, where the instructions are inherent (agreed upon) in the symbols, e.g., order up a 101 and you get a burger and fries… this is clearly a system of “digital communication between an encoder and a decoder, using agreed upon symbols,” to quote your definition of Information on the challenge page… do information theory and communication engineering have anything to say about the use of 1-layer codes in everyday human life? do these theories address the natural world or the laws of physics in any way?

    one of the first things I asked you earlier, regarding the criteria on your challenge page (and obviously ignoring 1-2), was “is it safe to assume that all man-made codes should (or must) be able to follow this list of criteria?” which you answered with an unambiguous Yes… I don’t know if you were assuming that when I said “code” I meant “2-or-more-layer code,” or if you were just allowing for “trivial cases,” but I’ve been operating under the assumption that 1-layer codes should be perfectly applicable because they WORK… and if there is such a thing as 1-layer codes that perform functions (which I’ve demonstrated), then shouldn’t that be the starting point for looking for a naturally occurring code? wouldn’t the simplest possible kind of code be the most likely to occur naturally? or more to the point, if any multi-layer codes do occur naturally, wouldn’t there be, by definition, a simpler 1-layer precursor of sorts that would’ve had to come first? is it possible to devise a multi-layer code without starting with the first layer?

    anyway, I’m still having trouble with “freely chosen,” and with the difference between labeling elements on the periodic table and labeling amino acids and proteins (combinations of elements)… I’m not claiming that you can derive the instructions for the genetic code from the Periodic Table, but you can describe all of the symbols involved in DNA in those terms, so how can one be freely chosen while the other isn’t? also, what would be an actual example of a non-freely chosen convention of symbols?

    that’s a lot of questions sorry, but every single one of them is being asked in all seriousness, thanks again for your time,
    Ben

    • Perry Marshall says:

      Ben,

      101 = burger and fries is still a 2 layer code. Because you not only have the relationship between 101 and the burger and fries, you also have 1 and you have 0. And you have some way that 1 and 0 are each transmitted.

      Yes, you are right, red = stop and green = go is a man made 1-layer code. You do have to have a first layer before you can have a second layer. In terms of the 7 layer OSI data model, the first layer of symbols has to be mapped to some physical phenomena. Yes, 1 layer codes have a place in the world, obviously. But it’s pretty trivial. Most computer programs and languages have at least a half dozen layers.

      There is no such thing as a non-freely chosen convention of symbols. Symbols are by definition freely chosen. 1 can mean off and 0 can mean on. Red can mean go and green can mean stop.

      The genetic code is freely chosen because there is no law of physics that says it has to have 4 letters. It could have 6 or 8 or 2 or any other number.

      There is no law of physics that says GGG has to code for Glycine. You can make Glycine plenty of other ways. Some other set of letters could have coded for Glycine.

      There is no law of physics that says codons have to be triplets. In some other scheme it could be quadruplets and GGGG could code for Glycine.

      All of these relationships – the 4 letter alphabet, the triplet structure, the 64 positions on the genetic code table – are completely freely chosen. Just like human codes being 1/0 could be trinary (0 1 2) instead of binary. There’s no law that says ASCII has to be a 7 digit code and have 2^7=128 letters. It could be an 8 digit code and have 2^8=256 letters. It could be an 8 digit code with 3 states per digit and have 3^8 = 6561 letters.

      All of these coding schemes are theoretically possible. Those choices are entirely independent of the periodic table. It doesn’t matter what your hard drive is made of, or whether your data is stored on a cd (pits etched in aluminum and read by a laser) or if you use a hard drive (North/South magnetic domains read by a sensor), it’s the same data. Or it could be the same medium and different data.

      This is why Information is a fundamentally different entity than matter and energy with different properties and you cannot derive the rules of any information system from the laws of physics. They have to be determined in advance by a conscious agent. There are no known exceptions to this.

      This is why the atheist/materialist worldview has no explanation for the origin of information.

      • benito-san says:

        Perry you continue to diss the 1-layer codes and I have to keep sticking up for the little guy 🙂

        so okay, 101 = burger + fries is a 2-layer code, how about ordering a #1 at McDonalds? all I’m trying to say is that 1-layer codes clearly have their uses, and it’s curious to me that information theory and communication engineering don’t seem to address this? or even allow for it? in fact now I have a new question..

        what is the first layer of the genetic code? is it the symbols of the periodic table? I can’t get away from the idea that if the “language” of the genetic code actually arose from natural processes (which is the argument you are inviting with these blogs), it would obviously have had to start from simplicity, therefore we should look for naturally occurring 1-layer codes, but you have only dismissed this idea out of hand based on your all-codes-are-products-of-a-mind syllogism.. as an analogy, wouldn’t it be reasonable to postulate that simple human communication likely began as a 1-layer code, one sound = one idea? anyway I don’t have my mind made up either way on DNA, I’m just trying to get to the bottom of things as best I can

        as for an explanation of the origin of information, well.. I’ve tried to tackle this one before and never got my comment posted, but I think I’ll risk it again anyways: the fundamental particles of nature contain information in and of themselves, e.g. mass/charge/wavelength/etc… asking what the origin of Information is, is the same question as asking what the origin of Matter and Energy and Spacetime are, is it not?

        now here is my final major question, and it’s pretty straightforward: why does the fact that the laws of physics are inviolable disqualify them from being a code?

        thanks again,
        Ben

        • Perry Marshall says:

          Information theory and communication engineering need to perform complex tasks with a single stream of data, ie 111010100110101010101101010010100011010

          In order for DNA (or computer data) to easily copy it has to be in a linear string like this.

          The only way to accomplish this is with multiple layers of coding – maybe 20+ layers of symbology.

          The PHYSICAL layer of the genetic code is adenine, guanine, thymine, cytosine.

          1 layer codes do not exist either in nature, because nature does not contain symbolic relationships. This goes to your final question – why does the inviolability of the laws of physics disqualify them as code? Because codes are by definition freely chosen. In a computer, 0 could be ON and 1 could be OFF. But the normal convention is 0 is OFF and 1 is ON. Free choice. There is no free choice in the laws of physics.

          Free choice is only an aspect of conscious beings, not physical objects. Thus there is a definitional infinite chasm between information and non-information.

          The particles contain information question, I addressed in a recent reply I just made an hour ago.

  5. vYzion says:

    It’s like for every confusion I clear up, you go out and find 5 more buckets of mud…

    I tell you about incompleteness, you respond with undecidability. These two are not the same. Undecidability means there are no effective methods to determine, in a finite amount of time, whether a given statement (A) is true or false in a given system. Incompleteness (oF Goedel’s kind), means that there is some statement such that either itself (A) or it’s negation (~A) is not provable in that system. These are not saying the same thing. Undecideability is like saying “I’ll let you know when I reach the end of the rainbow if there is a pot of gold or not…too bad it’s impossible to reach the end. Incompleteness is saying; “Yes, there is definitely a pot of gold at the end of the rainbow, but you can’t ever get to it.”

    So, I’m still not sure how you’ve acquisitioned this to Turing Machines…If you give a Turing Machine and undecidable problem, then it “halts” in the sense that it never reaches an output. But the undecidability has nothing to do with the Turing Machine…Undecideability is a relatioinship between a statemetn and a system to which the statement belongs. Turing machines are used to determine whether or not that relationship holds. If I say a nail is 3 inches long, what have I said about the ruler? Incompleteness is a property of systems of statements. Calling a Turing Machine ‘Incomplete” in this sense, is like calling a sound red. IT’s just not the type of thing that can be incomplete in this sense.

    Perry…can you please go out and actually read something about the foundations of mathematics, logic, meta-logic…basically something other than Shannon’s book (which actually has a pretty narrow scope…I mean seriously, if Shannon were taken to be THE paradigm of information, then there was a time, not to distant, where the transmission of information would have been impossible by humans). I guess I should explain…on this model, the speaker would be encoder, and the hearer would be decoder. So, speaker says something (“encodes” his thoughts in an auditory-format), auditory symbols are transferred, the hearer’s brain then “decodes” these sound waves into “meaningful words.” And this is all well and good, until we get to the obvious question: How do speaker and hearer know that they they have sent and received the “correct” information?

    You answer – “It can only be judged by an outside observer who is capable of inductive and deductive reasoning. ”

    Couple things.

    First, this seem factually false. Aren’t there scores of protocols and fail safes etc. that ensure the uncorrupted transmission of data? Further, transmitted information is checked for corruption upon receipt. I have seen, more than once, the little pop up box that says my file has been corrupted, or didn’t download correctly, or whatever. But, as we all know, computers can’t reason inductively. Thus, computers shouldn’t be able to judge whether or not it has received an uncorrupted version of some data.

    Seriously though, what work does “who is capable of inductive and deductive reasoning” actually doing? It looks like a feeble attempt to bring unity into your project. I mean, 2 year-olds understand language, yet I doubt we’d say they make any use of deductive or inductive abilities to do so. I tell my cat “NO!!” and it stops. Is my cat using deduction or induction? I tell my dog “Sit,” and he inductively establishes that every previous time he heard that sound and performed a particular action that he got a reward. Thus, this time he will get a reward…and probably next time as well.

    Even if I go along with this, the consequences are pretty ridiculous. This would mean that I have to wait for external confirmation before I’m able to know that I understand what you’ve said to me. That some deductive/inductive using something or other must monitor our conversation and make little check-marks whenever I heard you correctly. Of course, hearing correctly and understanding aren’t anywhere close to the same thing. I can hear Chinese correctly all the day long and not understand any of it. So, our outside observer must not only ensure that the raw data got transported correctly (that you heard right) but also that the interpretations are identical. So that when someone tells me “I’m going to the bank,” I understand them to mean a riverside, not a financial institution. And the problems this causes with metaphors and Sarcasm is fairly obvious.

    Maybe it’s different for you, but I’m not aware of any data corruption scans occurring during my conversation with people. I’m not aware of any voice in the back of my mind saying “Yes, you understood that correctly.” And, even if I did, I”m not sure what to make of it. It seems I’d need an external observer to make sure I understood the little voice correctly…

    In short, 99.9%of the time, when I’m having a normal conversation, I do so without an external observer. No one, or no thing, tells me what the other persons is saying or means to be saying. In fact, most everyone with a native command of a language needs no one to confirm anything for them. When you say to me “Please get me some water.” I go get you water…I don’t take the time to consult with an external entity about whether or not mine and your maps of the English language are isomorphic.

    What Shannon has done, what you seem to have trouble grasping, is circumscribed the use of the word “information” for a fairly narrow field. However, it’s obvious there has been information long before computers and networking. When you try to juxtapose it with elements that are clearly not in its domain (natural language, for starters), then absurdity results…like what we saw above.

    And as for a 1 layer code used to communicate, look up Wittgenstein’s Builders.

    Too much to write…I need to take a break…

    • Perry Marshall says:

      Scott,

      Undecidable propositions are intrinsic to the definition of incompleteness. That is why Gödel’s original paper was called “On Formally Undecidable Propositions Of Principia Mathematica And Related Systems.”

      An incomplete system is one that cannot decide the truth of a proposition without reference to something outside of the system.

      You are mis-stating what a Turing machine does and what an undecidable problem causes to happen. A Turing machine does NOT halt on an undecidable problem, it keeps running infinitely.

      And you’re forgetting what the original question was. You said, “What does it mean for a physical system to be incomplete?”

      I said it meant that it can’t converge on an answer in a finite period of time. Go back and read what I said.

      Here’s an even simpler example of the incompleteness of a physical system: Ask a physical system to determine its own weight.

      It cannot do so without interacting with something external.

      I never said that Shannon was THE paradigm of information. There is far more to information than Shannon’s paper. Shannon is the lowest common denominator. It’s the simplest description of communication that doesn’t leave out something vital. And based on the minimal set of components in Shannon’s system, all such systems that we know the origin of are designed.

      How do speaker and hearer know that they have sent and received the correct information? Well stop misquoting me because my answer is not “It can only be judged by an outside observer.” When I said this I was referring to mechanical systems. In this example, both speaker and listener are conscious observers.

      So each of them can observe by what actions get taken and what effects result from the conversation whether they understood the speaker correctly.

      Yes, there are scores of protocols and fail safes. Which are all secondary or tertiary encoding/decoding systems which make logical checks against the first system.

      Yes, computers can judge but computers are always programmed to do what they do by conscious minds.

      Do you know of any computers that perform checksum operations etc etc that you know the origin of that are not designed?

      I have kids, do you? 2 year olds do inductive reasoning as follows:

      1. Last week a dog bit me
      2. I see a dog
      3. I’m afraid that dog will bite me, therefore I start crying

      2 year olds do deductive reasoning as follows:

      1. Every time I turn my cup upside down the milk spills out
      2. Today if I turn my cup upside down the milk will spill out

      They also use deductive and inductive reasoning to learn how to speak language in the first place.

      When we do any kind of cryptography we use both inductive and deductive tests to develop a level of certainty that we understand the language we are studying.

      We do data corruption scans all the time in conversation. We miss bits of conversation because of noise and we fill in the blanks from context. Everyone who speaks any language, native or not, has to use a variety of means to make sure they received the message properly AND that they actually understood the intent.

      Language itself has redundancy. In print you can delete about 30% of the letters at random and people can still figure out what the original message said.

      One of us may be having difficulty understanding what Shannon said but I don’t think it’s me. I am well aware of what his model is capable of and what it’s not. It doesn’t deal with pragmatics at all. But it does deal with encoding and decoding of digital codes; with syntax, statistics and semantics. Which is quite enough. All systems isomorphic with Shannon’s, that we know the origin of, are designed.

      Thus Hume’s argument is definitively overturned.

  6. vYzion says:

    LOL @ Perry.

    I really don’t know why I bother…too much time on my hands.

    Perry says:
    –2 year olds do deductive reasoning as follows:

    1. Every time I turn my cup upside down the milk spills out
    2. Today if I turn my cup upside down the milk will spill out–

    Perry, this is not deductive reasoning…this is inductive reasoning. This is exactly the kind of reasoning that science uses. “Well, the experiment turned out this way last time, I have the same set up, so the experiment will probably turn out the same way.” Don’t see how it could be any more obvious that this is inductive. You have a set of base cases (i.e., all the time I’ve turned my glass upside down) and then you extrapolate to a specific case of interest (i.e., THIS particular instance of turning my glass upside down) and then you draw an inference based upon the base cases (i.e., the milk will fall out).

    Be that s it may, it is extremely doubtful that 2 year-olds (excepting prodigies and geniuses) actually do this. If they did, we wouldn’t need to tell them things over and over again, we’d just tell them to think about it. No, the child’s avoidance of the dog (in your properly labeled inductive argument) is much closer to conditioning than reasoning. As if a system of logical inference were needed to determine if one was afraid. “Well, I was afraid of heights yesterday. I’m presently on top of the Empire State Building looking down. So, I should be afraid right now.” And then I’m afraid…right? Sorry Perry, but it doesn’t seem as if the reasoning process has anything to do with emotions…I don’t “decide” to be a afraid of heights or dogs. (Now, I CAN decide to avoid them based upon a prior incident, but that’s not the same as being afraid…maybe I’m just allergic.) Now, perhaps it’s the case that reasoning and the “emotional response” lead to the same outcome (i.e., avoiding a dog), but that doesn’t mean that they are the same process.

    Is loving my family really the end result of a process of reasoning? Do I really need to determine if certain necessary and sufficient conditions are present before I love my family? “I loved my family yesterday, I love them today, so I’ll probably love them tomorrow.” This is absurd. As if the REASON I love my family today is BECAUSE I’ve loved them on days prior and the reason I’ll love them tomorrow is because of the same? I’m sure your family will take comfort in the fact that your love for them is the logical outcome of certain processes of reasoning that you’ve engaged in. Psychologism at it’s pinnacle. LOL @ Perry.

    You also say another curious thing, that I don’t quite understand:

    –Here’s an even simpler example of the incompleteness of a physical system: Ask a physical system to determine its own weight.–

    (For the sake of argument, I’ll use your own convoluted version of incompleteness.)

    One interpretation is pretty silly. Like I’m supposed to go up to a toaster and say: “Toaster, determine your weight!” Most people would think that I’m incomplete in the head if I were to do such things.The toaster can’t determine anything, it’s a toaster. It seems strange to say it’s “incomplete” because it can’t do something it was never designed to do (i.e., determine it’s own weight).

    Actually, your problem is even worse than this. The above is just silly sounding, but it does make sense, that is, it is meaningful, we can imagine fairy tales with anthropomorphic kitchen appliances. What you say, literally makes no sense, it has no meaning. The point you are getting at, is that the “physical system” needs a scale in addition to itself in order for its weight to be determined. And this is absolutely correct. But, what you fail top realize, and have been failing to realize for quite some time now, is that the use of the concept “weight” IMPORTS scales into the system. It makes zero sense whatsoever to talk about weight in absence of scales…it makes zero sense to talk about “temperature” in absence of thermometers. (When I say “in absence of,” I don’t mean “I presently don’t have one on hand.” I mean that such things do not exist.)

    Now, I can still say thing are “hot” or “cold,” I can say they are “heavy” or “light.” But hot/cold and heavy/light (and comparatives in general) are not scientific. True, they form the basis of something that could become a scientific quantity, but they themselves are not. This is obvious because what’s heavy to one person, may not be heavy to another, but what weighs 20 pounds for one person weighs 20 pounds for everyone.

    Scientific quantities are defined by their methods of determination. What does it mean to say that the toaster weighs such and such…It MEANS taht when i put it on a scale, the scale will give THIS reading, give or take some margin of error. So, if there are no such things as scales, there is no meaning to the concept of weight. Hence, to speak of a “determination of weight” either implicitly assumes scales or it’s meaningless.

    Hence, your “even simpler example” doesn’t work either. Simply using the concept of “weight” assumes a system which includes a method of determination…for weight, that method is a scale. Hence, by even talking about “weight” you are talking about scales ans thus, in your “even simpler example,” scales ARE a part of the system in question (i.e., a system where the concept of “weight” makes sense) and thus has not illustrated anything to do with incompleteness. Since scales are required for “weight” to have meaning, the scale (i.e., the thing you mistakenly believe to be outside the system) you were leading me towards actually ends up being inextricable from the system itself.

    Now, I can think of a toaster without thinking of weighing it and then I would have a system with no scale. But once I entetrtain the thought of weight, the scale mcome p[art and parcel. The method of determinatino is boundc up with the concept. You use one, you use the other. So when you ask me to determine the weight of something, you more or less force a scale into the system.

    I don’t really see the benefit of continuing to correct your misunderstandings about Goedel and what he did. I didn’t study Goedel’s, in depth, work until my second Graduate level logic course (yes, my degree required graduate level logic courses) and you, Perry, are still somewhat confused about Freshman Undergradaute level logic stuff (e.g., the difference between deductive and inductive arguments, a slew of fallacies, etc.)…I ‘ve been correcting you for some months now, but you never seem to learn any of it. You can reference wikipedia all the day long, but you clearly don’t understand what it is your referencing. People have spent their entire careers working on this stuff trying to understand it. Yet, you, Perry, are on par with them after reading a couple wikipedia articles and posting your thoughts to an internet blog for a couple years? That’s somewhat vain.

    LOL @ Perry

    • Perry Marshall says:

      Scott,

      From wikipedia, example of Deductive reasoning:

      1. All men are mortal
      2. Socrates is a man
      3. Therefore, Socrates is mortal

      You’re right, when I said
      1. Every time I turn my cup upside down the milk spills out
      2. Today if I turn my cup upside down the milk will spill out–

      that was inductive but if I had said

      1. Milk always spills out of upside down cups
      2. Today if I turn my cup upside down the milk will spill out–

      That would be deductive.

      I could have worded it better. In any case, children can both reason from the general to the specific (deduction) as well as from the specific to the general (induction). They are capable of both.

      And both are necessary in the process of cracking codes. Which, as you’ll recall, was my original point.

      Yes, loving your family and believing that they love you is to some extent a process of reason.

      A toaster cannot measure its own weight for the benefit of an outside observer without also having an outside object to rest on. There are statements that are not provable in the system.

      Of course I understand that it makes no sense to speak of weight without referring to scales. Remember, I said that any system subjected to measurement performs computation.

      A toaster could have a scale built in but it still couldn’t weigh itself without an object to rest on. It’s incomplete.

    • battleblazer says:

      I just want to comment on a huge hole in vYzion’s theory. I refer to a comment he made regarding a nail:

      “If I say a nail is 3 inches long, what have I said about the ruler? Incompleteness is a property of systems of statements.”

      What is an inch? We KNOW what an inch is because it has been defined as a certain length. What would happen if we do not know what an inch is? Then it would be meaningless. But because we have learned that an inch is 25.4 mm (the same thing applies to millimeters, or metres or any other term in ANY field you choose), we can say that a nail is 3 inches long.

      But by referring to a length, one automatically refers to the instrument to measure it, that is an instrument that can tell us the length of the nail is 3 inches long (eg a ruler). Here we take things for granted: that an instrumant can accurately measure 3 inches.

      That tells us a few things about the nail and the inferred measurement tool (be it a ruler, another nail of known length, etc).

      Sorry, but the same principal can be used in any of the statements he makes which I find does not hold up.

      • vYzion says:

        @ battleblazer

        I don’t see the rebuttal. You say is:

        “That tells us a few things about the nail and the inferred measurement tool (be it a ruler, another nail of known length, etc).”

        My question is WHAT does it tell us! If I say that a nail is 3 inches long, then absolutely I’m making reference to a ruler (that was my point against Perry, which he conceded). But what have I said about the ruler!?

        1) That the ruler is at least 3 inches–No. Maybe the ruler is only one inch and I put 3 of them together.

        2) That the ruler can accurately measure 3 inches.–No. Any scientist reading this will be abashed at your ignorance of significant figures and various types of measurement error and error bounds etc. Suppose our ruler had only marks for 1″, 2″ etc. and no subdivisions. In this case, some convention will have been established that determined whether we say it’s 2 inches, 3 inches or whatever (remember, anything beyond one sig fig is meaningless). Now, what does “accuracy” mean in this situation. Maybe it’s the case that we need a different ruler for each sig fig in order to measure any given object. Simply saying the nail is 3 inches long doesn’t differentiate between these and thousands of other examples that can easily be contrived. “It’s either raining or it’s not raining” doesn’t tell me anything about the weather or any other meteorological phenomena.

        3) That there is a ruler–Maybe, but existence isn’t a property. To say a thing exists doesn’t really say anything about the thing. It says that something “answers the call” so to speak. Names are not properties of things anymore than name tags are properties of people. Besides, it need not indicate the existence of rulers at all. In fact, the claim functions much closer to a conditional than an observation. “This nail is 3 inches” means that IF I choose to take a measurement, THEN that measurement will be 3 inches. But I can also say “IF you see a unicorn, THEN it will have a horn on its head.” Of course, this doesn’t mean that anything “answers the call” of unicorn.

        If you have a hard time understanding that existence isn’t a property, then think of it this way. If someone asks you describe e.g., a table, you will say things like “It’s such and such color. It’s XX feet tall by YY feet long. It’s made out of wood, (it’s in my kitchen??) etc.” Do you also say, “Oh yeah, by the way, it also exists.” If you were to make a list of all the things that there are, the list would may include things like: tables, chairs, colors, sounds etc. Are we also going to put “existence” on that list? And how would you point (that is, ostensibly define, or infuse meaning into it) to it? I can point and say “That’s red” or “That’s round.” And after a while, process of elimination can pinpoint which feature you call red and which you call round. Clearly, this doesn’t work for existence. Everything you point to gets the existence tag. There is no property to be picked out. Imagine someone who ended all of sentences with a sound, e.g., “Eh” or maybe a cough etc. I think we’ll agree the “Eh” doesn’t mean anything…it’s sort of like a verbal period (and periods don’t carry any semantic weight). Now, if he only used “Eh” in particular circumstances, then it may very well have meaning…but not if it’s after every sentence…then it’s just grammar.

        And no, you can’t point to pictures of things that do (tigers) and don’t exist and say “That doesn’t exist and that doesn’t.” Suppose you point to a a painting and say “There’s a unicorn.” I would be perfectly justified in saying “No, that’s a picture of a unicorn and that pictures has just as much existence as the picture of the tiger.” In fact, I’m perfectly justified in saying that “Unicorns don’t have horns (since they don’t exist), pictures depict unicorns as having horns.”

        So, I ask again, what is the “principle” you speak of and how has it rebutted anything I’ve said? What does a 3 inch nail tell me about rulers (either a particular one or rulers in general)?

        You seem to share many of Perry’s misconceptions about language. Both you and Perry would benefit from doing a lot more reading on this subject.

        • battleblazer says:

          Hi vYzion

          Actually you have described it very well –

          “…is that the use of the concept “weight” IMPORTS scales into the system. It makes zero sense whatsoever to talk about weight in absence of scales…it makes zero sense to talk about “temperature” in absence of thermometers. ”

          Same thing about the length of an object and rulers. So by inferring to it you HAVE made subjective infererence TO the ruler. What you picture a ruler to be may not be the same way I picture a ruler (rulers are not the same throughout the world) and as you pointed out – maybe there isn’t a ruler that is 3″ long – and that is subjective. The same thing can be said about scales and weight.

          Rereading the post, I still say this, there are a few things that you do not grasp. And there, in itself, is where the problem is. You KNOW you understand it, but what happens if you don’t?

  7. vYzion says:

    –1. Milk always spills out of upside down cups
    2. Today if I turn my cup upside down the milk will spill out––

    Yes Perry, this is deductive. Of course, let’s not fail to notice that the justification for premise 1 is inductive. We don’t know that milk ALWAYS spills, it always HAS, so we assume that (or get into a habit of expecting that) it always will (I mean, children without a sufficient amount of experience in the world, would not be all that surprised should the milk not fall out of the glass).

    Now, since an argument can be no more certain than the premises it’s founded upon, the first premise, for all practical purposes, cause you to lose the deductive rigor you set out to show. It’s just that this argument is obviously weaker than the Socrates being mortal and dying argument. However, deductive arguments don’t differ in degree…only inductive ones do.

    So yes, if milk falls out of glasses BY DEFINITION, then this is deductive. But seriously, why should we expect that part of milk’s “essence” is that it fall out of glasses. Were it not for experience to teach us, there’s really no reason to think that milk, or anything, ought fall.

    In any case, what I find interesting is this:

    “A toaster could have a scale built in but it couldn’t weigh itself without an object to sit on. It’s incomplete.”

    I really don’t know what to think. It seems like all your saying is that toasters (or scales, I suppose) don’t float in mid-air. I think we all agree with you there. So, if you really want to think of the table-top as “completing the toaster/scale combo” in some sense, then go ahead, but I doubt you’ll to many people willing to adopt this way of speaking…and I really don’t see what the connection between it and Goedel could be.

    It’s really strange what’s happened here. You’ve somehow gone from

    “Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century” helping to PROVE to us that God (or some entity vastly superior to ourselves) was NECESSARY in order for the universe to exist

    and now we’ve both finally settled on:

    “Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century” telling us that toasters (and scales) don’t float in mid-air.

    In my humble opinion, something has gone awry for you.

    But, I guess you still win. You have provided a consistent way of talking about incompleteness outside of the domain for which it was was intended (I guess you could say you’ve broadened it’s domain). Don’t see the benefits of speaking this way about things (I guess other than somehow toaster-scales not floating proves the existence of said super-cool entity) but I find no principled objection to it.

    These seem like a Pyrrhic victories, but victories nonetheless.

    Touche.

  8. vYzion says:

    I’m embarrassed.

    Perry said that in order determine the weight of a toaster, with a built in scale, you’d still be need a surface to set the toaster upon…he then further claims that this is a consequence of Goedel’s incompleteness theorems (he has still yet to address the fact that Goedel had 2 of them and that they don’t say the same thing…but, his exposition seems to run the two together…I pointed this out to him earlier but he’s made no response.)

    In any case, I somewhat facetiously replied that if he want to think of tables as “completing” toaster/scales, then that’s his business. But, the fact still remains that this take on incompleteness is not at all obviously related to Goedel’s.

    Whereas my above rebuttal is fine and need to be addressed (that is, the connection needs to be made explicitly..that is, a PROOF must be written), there is an even better, more obvious, rebuttal that, embarrassingly, escaped me earlier.

    Perry, that fact that the toaster/scale needs a surface can, and should, be attributed to Newton’s 3rd Law. Now, if you wish to say that Goedel’s Theorems somehow “ground” Newtonian physics, then that would be a much more revolutionary and interesting discovery than whatever it is you think you have here with Intelligent Design Theory 2.0. (If you could do this, your name would be etched in history…of course no one will rememeber your re-vamped Intelligent Design as anything special, but showing that Goedel’s Theorems ground Newtonian physics (not just that the mathematical representation conforms…at best you may get that there are truths that science can’t teach us, but I don’t think that’s in dispute here…of course, if that’s the case, and God is one of those things, then you lose the right to say that what you have here is “scientific.” Ex hypothesi, this is something that science can’t teach us, ergo it’s not scientific.), that would be one of the greatest discoveries of human intellectual history.)

    So, in order for your toaster example to be an example of what you claim (incompleteness of physical systems), then you need to show a logico-mathematically rigorous proof that takes you from Goedel to 3rd Law. Of course, given that the 3rd Law is based on observation, as opposed to logico-mathematical consequence, this seems, in principle, impossible.

    I suspect what you will respond is something like “Well, Scott, Goedel’s theorem applies to all mathematical systems (passing certain requirements)…Newtonian Physics is such a system, so it applies to Newtonian Physics.”

    This is wrong for a number of reasons..

    1) Your entire site relies upon physical systems being subject to Goedel as well linguistic ones. So, as far as your argument goes, that Newtonian Physics has a mathematical representation is irrelevant.

    2) Quantum Mechanics does not adhere to Newtons 3rd Law, yet it too is a mathematical system that represents physical systems. So, you owe an explanation of why Goedel leads to the 3rd Law in one case, but not the other.

    3) It show a confusion about what Goedel’s Theorem is. Goedel’s Theorems are NOT explanatory…they are purely descriptive. It says systems with these properties ALSO have this property. Thus, it must be established that the system in question passes the pre-conditions…you have failed to show that physical system pass such pre-conditions. And as my rebuttals have focused on bringing to light, physical systems aren’t even, ontologically, the type of thing that CAN have said pre-conditions as a property. It’s like calling a sound “red.” This response show a clear type confusion (read some Bertrand Russel if you don’t know what type confusion is).

    If you have another reasons why I should attribute the inability of toasters to float in mid-air to Goedel’s Theorems rather than Newton’s Laws, I’d be happy to hear it.

  9. Oldstyle says:

    I want to start by saying that Perry Marshall is providing an excellent service to all people that place logic as our highest order of intelligence. It offers all of us a chance to see something of life that goes beyond logical explanation. And this is good because we so think that life and meaning can be discovered from a logical understanding of all things – and that eventually our logic will get there. This is something I seriously doubt.

    I doubt that logic is an answer because out logical brain is a better servant than a master, and the state of the world today is evidence to support that statement. We do things because we can – not because it is wise, healthy, or just.

    Nowhere is it stated as a fact, a law or even a theory that the universe ultimately makes logical sense.

    So our logical arguments have more entertainment value than anything else, and I love the arguments for the hours of joy that I give and receive while trying to logically justify something that does not need to be justified. Does a blade of grass need to justify itself? – Make logical sense to the world? – Can grass survive without logic?

    That which is really important about life gets lost in the analysis of what existence is all about. And, Ironically, it’s not all about logical analysis. But, for many people that use their awareness to focus on brainy logic more than any other focus of awareness then Perry provides a wholesome camp to hang around and enjoy the arguments.

    What about love?

    We could live in nature without logic (free of pollution and overpopulation) but can we live without love? Not that I want to go back in time to primitive days before the Internet, but love is what makes our living worthwhile. You would toil in the fields without complaint if you were loved.

    Medical science has discovered that the heart is made up of over 60% of neuron cells, and the heart is the first organ to be formed following conception. I suspect that it is the heart’s intelligence that decodes the DNA as the foetus develops.

    The heart’s intelligence is described very well with the story of King Solomon being presented with a baby and two women both claiming to be the mother. If King Solomon were to apply logic he would be asking for witnesses, documents and verifiable proof of motherhood. But no, wisdom dictates that the true mother (not necessarily the real mother) would save her child’s life. Thus, he puts forth the suggestion to share the baby by cutting it in half.

    The wisdom of the heart is no better or worse than the intelligence of the mind – they are both intelligent, but the heart makes a better master than a servant when the power of love motivates decisions.

    Love is a power, but not a force. Propulsion is a force that pushes against something to move away from, whereas love is the power of attraction and it unites us with what we love. Propulsion is limited because it needs something to push against and in the open spaces of our universe propulsion cannot take us very far. Love, on the other hand, is without limit and therefore the power of attraction is without limit. Just maybe we want to take a look at the power of attraction as a new science in addition to, or to replace, propulsion science.

    What do you think it means when Christ said, “Love God with all your heart, with all your mind and with all your soul” Do you really think that the statement was about loving God? It would seem so, yet the experience is one with “love”, and love grows within and connects us with the greater love for all things, including ourselves, without ever looking for personal gain. I believe that Christ’s message was to start loving something because it all comes back to us, and because the world cries out for love.

    The wisdom and intelligence of heart is with us always. I find joy in solving analytical problems, but I find that love opens a different world of awareness that logic does not – and vice versa. My conclusion is that neither is better than the other, they are just different. And I also suspect that both are required for a balanced perspective that can take humanity further than either heart or mind could do on their own.

    Perhaps the following brief story will suffice to illustrate.

    Farmer John is the owner of some of the best farmland in the valley and his farm was praised by all that had seen the fields, the fences, the crops and animals. One day the Reverend of John’s church stopped by and was admiring the farm as he got out of his car. Farmer John saw the minister and came over to greet the Reverend.

    The Reverend said, “You know John, God sure has blessed you with this wonderful farm of yours.”

    Farmer John replied, “You know, Reverend, there’s not a day goes by that I don’t thank God for this land, but you should have seen it when he had it all to himself.”

  10. RDWallace says:

    Perry, If the universe is as you say finite, with a finite amount of space, time, energy and matter, what is on the other side of this finite universe? Are you saying there is nothing beyond the boundaries of your finite universe? It is logical and reasonable to assume there is more universe. Perhaps infinite multiverses that each have finite properties. If you were to say that the other side of this finite universe is the domain of God, then that is yet something. If you were to say nothing is beyond this finite universe, again “nothing” is still yet something beyond it, because the word “nothing” represents an aspect and property of what lies beyond it. What are you defining as a universe? The finite part of a multiverse that we live in or the totality of all existence?

    As far as my imaginative speculation is concerned about other civilizations existing in the universe and their relationship to Jesus, I think we can agree that the following is reasonable and logical:

    1. Even if you are right in your speculation that the universe is finite, the amount of space and matter in your presumable finite observable universe is so vast that mathematically it would be extremely improbable for intelligent life not to exist. Just in our own galaxy alone there is estimated to be 5000 civilizations as illustrated by the Drake equation. Therefore, statistically ET exists.

    2. God could be master creator for them as well as us.

    However, Jesus cannot be their deity because Jesus is human. Jesus represents theologically a part of God for humans because he is in their likeness. What further confuses things is that Jesus and God are considered one in the same. However, I will shed some of my speculative imagination on behalf of Jesus instead of ET as you commented I lacked. Perhaps, God has a different representative of himself for each of these civilizations in their likeness and these beings are the same entity for them as well as humans, only differering in form. In addition, these representatives of God are the same being existing in all places at the same time. Aside from angels and Satan, the Bible speaks nothing of any other intelligent beings or civilizations outside of Earth existing in Gods creation. This is all of course imaginative speculation, just like many of your so called proofs that God created the universe. I have not seen any convincing mathematical equation or theory that supports the universe being finite if we are talking about the totality of existence. What I have found quite often is many contradictions in Biblical explanation. For example:

    1. Why did God create anything in the first place? The theological answer is: “To glorify himself.” However, that explanation is contradictory because that implies that a God that encompassess everything and has everything, needs something. God would need nothing. The word “Glorification” is a human attribute that we are assigning to God. God, by definition is above any human attribute of desire or need.

    2. The Bible speaks of Gods love, jealousy, anger and wrath. Again, assigning human emotions to God. Is God, God, or a human? These feelings emanate from the human brain for various reasons; communication, coping and survival to name a few. Is the Bible saying the mind of God is like a human mind?

    3. “Free Will”…My favorite contradiction. As I mentioned in my last post this notion creates a paradox in that God would know what we decide to do before we do it. God would know the outcome beforehand. To disagree with that would be saying that there are things that God does not know. “Free Will” cannot be a test of human obedience for God because he would know exactly what we will do. Therefore, all that we do is what God wanted and intended or it would not be.

    I could go one, but I leave that for another post.

    Perry, Lastly I would like to commend you on starting this forum whether we agree or disagree. You have opened a world of powerful thinking and debate that I have been longing to participate in. I think some comments here cross the line of debate over to being impolite and abasing. I’m impressed that you post them anyway. There is no need for people to get angry and rude about your comments. Much of what you say is very thought provoking and inspires profound ideas that we all can learn from. In the end, it is the sum total of all our comments that will lead us closer to truth and knowledge with I presume is your prime directive and mission. Thank you Perry.

    • Perry Marshall says:

      I’m content with Wikipedia’s definition of universe: The universe is commonly defined as the totality of everything that exists,[1] including all physical matter and energy, the planets, stars, galaxies, and the contents of intergalactic space

      Your #1: You’re assuming that “God” includes everything, or that everything would already be in God. The Judeo Christian position is that God is separate from the created order. If that is true then your #1 makes no sense. No Christian theologian would accept your #1. Every Christian theologian I know would strenuously object to your statement that God is above desire or need.

      2. I think in some sense, yes, God is a being who in some respects is similar to a human. Emotions and will are innate to consciousness.

      3. Knowing what someone will do is not the same as determining for them what they will do. It’s also not the same as wanting them to do it. Free will is real, not an illusion and thus is not a contradiction.

      Thanks for participating in this discussion!

      I encourage you to read John 1.

      • GMEstes1 says:

        God is many different things to many different people. The Bible devotes a lot of time and gives a lot of information about the Judeo-Christian God. God explains
        He is the only God yet manifest Himself in three distint persons. Many see themselves through characters of God. Either the Father, Son, or Holy Ghost.
        Other religions make the same exact claims as Christianity. Many explain where their God came from…Budha, Mohammid, Ra, Isies, and Horrace had a beginning. Christianity has shrouded Jesus in divinity, claiming he didn’t have an earthly father…yet He did and was born out of wed lock as far as I can determine. His mother had been a prostitute and Joseph, I have no clue but most likely particpated in pre-maritial sex.
        When our last day comes…we will know all the answers for we will have the answer book??

  11. RDWallace says:

    Hello again Perry. I found this web site that appears to combine a scientific explanation supporting many of your view points through quantum theory and a metaphysical explanation through conscious particles. For example, It points out the fact that particles such as electrons can exist in different places at the same time and have a memory. The article appears to infer that these properties give rise to the notion that residual conscious energy may continue to exist after a person is dead, which gives rise to the notion of ghosts or spirits. In fact it gives credibilty to an underlying consciousness that permeates sub atomic particles thus considering it the ultimate consciousness. Perhaps the conscious of God. The article is quite profound and fascinating.
    Must read. It may give you plenty ammunition for some of your arguments.

    http://www.dapla.org/conscious_particles.htm

    • Perry Marshall says:

      Fascinating stuff. There’s an interesting book called “Biocentrism” by Robert Lanza, a very good read, which explores related ideas. The world is much stranger than we realize. I’ve been wading into quantum mechanics lately and it is quite fascinating.

  12. RDWallace says:

    Well Perry,
    Its been months since anyone has made a post here since my last one. Did I leave a cliff hanger? You said in your last post that God is separate from his creation. Therefore his creation…The universe… Is finite. Correct? However, in the same breath you said God has attributes like humans. Dispite the contradiction, I must repectively point out that your theist account of how things are and came to be do not require proof. Just faith that it is true. Since this forum began with the logic of Godel, how about focus on just that, LOGIC. Logic requires proof to some degree in its determinations. Logic and science will never say “This is true because it is written in a book” Instead, science is subject to change, correction, addition, contribution or modification. Facts are always evolving in science. We can agree that one of the staples of understanding the universe is that it is in constant change. However, biblical account never changes. It is always the same story from writers who understood the world and spoke in the tradition of their time. Science appears in order and in accordance with the means to the natural progression of human understanding. Conversely, science will never be absolute. Nor does it make such a claim. However, one of the foundations of Christianity and Islam is to absolutely believe and accept without the basis of any proof. I mentioned in my last post that I would save some discussion on this. Here you go. Here is logic at its best. Give me some answers to these contradictions and paradoxes to biblical account of creation:

    GIVEN:

    1. God is without mistake, all knowing, encompasses everything and created everything.

    Therefore:

    a. Man cannot be fallen or God made a mistake in his creation.
    b. Nothing can happen without God knowing it is going to happen c, Nothing exists without God wanting it to exist, to include evil.

    Therefore:

    All is exactly as it should be

    Again, logically, to say differently, is to say a perfect God did something he did not want to do.

    The typical theist response when face with this is the usual “No one can know the mind of God” in the same breath giving God human attributes like jealousy, wrath and love.

    After all that, you will be surprised that I believe in God. However, not like most theists. I believe in God on a metaphysical level that weds science and theism. There is no reason for theism and science to be contrary. Instead, they are blissfully compatable if the mind is open to both logic and spiritualism.
    The problem with spiritualism is that there is no language; only faith, feeling, intuition and emotion. The problem with science is the lack of the previous. However, neither science or theism can stand alone. Instead they should support each other in understanding beyond scientific facts. I pray for the day when humanity will adopt both as a unified religion.

  13. kenkoskinen says:

    Perry I have said I would comment on your use of Gödel’s Principle of Incompleteness and here it is.

    Gödel did not think his principles were applicable to the areas outside of mathematics that you & some others claim. Initially, for example, people noticed it had a similarity to Heisenberg’s Principle of Uncertainty in quantum mechanics. Some further reasoned since mathematics cannot discover all truths and science is based on math therefore science cannot discover all truths. Gödel eschewed its use to these other areas. His work was of one of logic specifically applicable to the understanding of mathematical systems. He showed the limitations of verifiability of some mathematical systems; not all of them as you incorrectly assert.

    Perry you wrote: “Any system of logic or numbers that mathematicians ever came up with will always rest on at least a few improvable assumptions.” Gödel’s principle does apply to all mathematical systems. It does not apply to Euclidian geometry or even non Euclidian geometry such as the system Einstein used while developing General Relativity. Nor does it apply to systems of arithmetic that are without the multiplication operation such as Presburger arithmetic. It only goes to what Gödel defined as “formal systems” but for the sake of brevity I will not go into the details but will provide references at the end.

    Clearly Gödel’s work does not apply to anything you can draw a circle around. I do not know where you got the circle idea but it needs to be deleted. You unfortunately used the term “Theory of Everything” in your discussion. David Hilbert had earlier postulated completeness in mathematics was possible and Gödel set out to test it. After working his logic systems he came back with a negative answer but only in Hilbert’s context. It does not have anything do with “Everything.” The same misnomer is also unfortunately used in the physics in light of the search for “the unified field theory” (a much better label that TOE). This also has a very specific meaning and is different than the aims in the logistics of mathematics. Also, there is no such thing as a literal “Theory of Everything” as no one theory will literally explain everything. Unfortunately you have mixed the misnomer you misused in the logistics of mathematics, with physics/science and even taken it for a ride into theology.

    Perry your claims about the laws of mathematics negating atheism and the so-called “Incompleteness of the universe … IS proof that in order to construct a consistent model of the universe, belief in God is not just 100% logical… it’s necessary” are not true. You started off misfiring and your applications are incorrect. You are not alone in the misuse of Gödel, as some very bright people have done the same. However, I think you have taken it to extremes.

    Barrow, John D., New Theories of Everything: The Quest for the Ultimate Explanation, Oxford University Press, New York, 2007, pp. 51 – 61.

    Download “Physics and Gödel” by John Barrow http://arxiv.org/abs/physics/0612253

  14. kenkoskinen says:

    Since I posted my last comment I have ceased to receive email alerts to any new comments on subscribed blogs/threads on this site. I checked “Manage your subscriptions” and all seems in order. Has anyone else noticed anything unusual? Moderator please check into this and alter if any reason is found.

  15. mindless says:

    By itself, Godel’s Incompleteness Theorem does not imply the existence of “some infinite metaphysical entity” or para-logical postulate. There are at least two possibilities: 1) That there is indeed a Theory of Everything, for which Godel’s Incompleteness Theorem requires the existence of some “infinite metaphysical entity’ or para-logical postulate, or 2) Reality is not axiomatizable, and not every statement is falsifiable, nor every event in nature computable (i.e., there is no Theory of Everything). Please keep in mind that one of Godel’s Incompleteness Theorem corollaries is that arithmetic (along with logic, physics, and language) is not axiomatizable.

    Now, someone previously stated that Naturalism is “the hypotheses that the natural world is a closed system, which means that nothing that is not part of the natural world affects it.” According to Godel’s Incompleteness Theorem, Naturalism cannot explain (falsify) all truths in nature, so it cannot be a Theory of Everything. But the same thing could be argued about any theory that introduces God as an axiom, albeit the idea of God being a very special axiom since it can be made to be para-logical, infinite, eternal etc. I think this is partly what Derek and Perry were discussing about.

    But regardless of whether it is legitimate or not to introduce the existence of such ultimate postulate (e.g. God), Godel’s Incompleteness Theorem does not imply its existence, since there is always the possibility that reality may not be completely axiomatizible. I don’t believe it is possible to know this by either inference or deduction.

    As Pascal said: “The God of Abraham, Isaac and Jacob, not the God of the philosophers and scholars.”

  16. Reflections on Truth | Get Real Post says:

    […] (Source: Link) […]

  17. Mateus says:

    Hello, Mr. Marshall!

    I LOVE this article and I’m very interested on translating it to Portuguese.

    Do I have your permission? And would you publish it here as well?

    Thank you so much for your reply!

    Mateus

    • Perry Marshall says:

      Yes go ahead. This one’s slightly better:

      http://www.perrymarshall.com/articles/religion/godels-incompleteness-theorem/

      • Mateus says:

        Okie-dokie, Mr. Marshall, I’m gonna do it ASAP. Thank you very!

      • Mateus says:

        OK, I’ve just finished the translation.

        Would you please tell me what email address I can send it in order to be published?

        Thank you very much once again!

        • kenkoskinen says:

          Mateus, if you translate this into Portuguese you will be repeating Perry’s mistakes. He does not understand Godel and comes to sweepingly inaccurate statements. Let me share the comment I sent him on June 4, 2012.

          “Perry, Godel’s theorems only go to the completeness of formal systems of mathematics. He showed that in such systems there will always be an axiom that cannot be proven within such a system. It does not mean that a formal system cannot be accurate but only incomplete in the above sense.
          He did not apply it to physics. This was done by others and particularly to Heisenberg’s Uncertainty Principle in quantum mechanics. Godel did not agree with the comparison.
          Godel theorems do NOT apply to geometry as it is not a formal system and is complete. It does NOT mean it applies to anything you can draw a circle around. Please read “A World Without Time: The Forgotten Legacy of Godel and Einstein.”
          You are misleading people.”

          Perry has yet to respond but please do not translate and/or publish this inaccurate stuff into Portuguese or any other language. Why deceive others?

  18. kenkoskinen says:

    Perry, Godel’s theorems only go to the completeness of formal systems of mathematics. He showed that in such systems there will always be an axiom that cannot be proven within such a system. It does not mean that a formal system cannot be accurate but only incomplete in the above sense.

    He did not apply it to physics. This was done by others and particularly to Heisenberg’s Uncertainty Principle in quantum mechanics. Godel did not agree with the comparison.

    Godel theorems do NOT apply to geometry as it is not a formal system and is complete. It does NOT mean it applies to anything you can draw a circle around. Please read “A World Without Time: The Forgotten Legacy of Godel and Einstein.”

    You are misleading people.

  19. Kurt Gödel e o Teorema da Incompletude: A descoberta Matemática Nº 1 do Século XX e suas relações com fé e razão - Blog do Yuri says:

    […] artigo de Perry Marshall (traduzido ao português por Mateus Scherer Cardoso) me causou um deslumbramento tão grande que […]

  20. Podzak says:

    To me, this is logic, not mathematics.
    If it is maths, please show your working out.

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