Toy Code - My First Neural Network

As part of my annual tradition of avoiding filing taxes by starting new side projects, I decided to write my own neural network in C code. A quick Web search turned up several beautiful neural-network libraries written in C. But I wanted something more like a worked-example than a full-fledged library. Github turned up tinn - the Tiny Neural Network (library). Tinn is pretty spiffy and a great tutorial for working out the mechanics of a simple feed-foward neural net. While it could be re-purposed to work on other datasets, it ships with the Semeion dataset.


As spiffy as tinn is, I still needed to rewrite it "in my own C" in order to be sure I understood what is happening internally. So, I wrote basic_nn (Github).


I like to include a general-purpose test harness in my one-off C projects that acts like a built-in debugger. This is the dev_prompt() function. Consult the README on Github for instructions on using the command codes at the prompt.


I had some trouble getting the network to train properly, at first, and this turned out to be an issue with not mapping the weights correctly during the forward and backward propagation phases. The update rules are very straightforward and this dataset is very small, so once I got the array indices correct (getting the right weights mapped to the right parts of the update equations), everything just snapped into place. I was able to use the debug prompt to view the internal weights and get a visual idea of what is happening internally. The mathematics of neural nets are copiously documented throughout the web so I won’t recapitulate them, here. I will try to show diagrammatically what is happening inside basic_nn, however.

When the NN is not training correctly, the entire weight space will tend to change like random static during training; or, if the array indices get transposed (oops, yes, I did that), then you can see “bands” appear in the hidden weight space when training many iterations, especially on a small training set. The image below shows the hidden states (256x32) with the erroneous bands exaggerated so they show up better visually:

But when the NN is training properly, you will see an initial change across the entire weight space and then the weights will tend to “settle”, with most weights staying the same and only a few scattered weights changing with additional training iterations. The image below shows the hidden states. The first box shows the hidden states after 20 epochs of training (one epoch passes through the entire dataset once; note that basic_nn kind of cheats in order to avoid the need to shuffle the dataset, see command-code 8 in the source-code). The second box shows the hidden states after another 10 epochs. Because you can’t visually see the difference between them, the third box shows both snapshots of the hidden state overlaid and visually subtracted so you can see the points where the two snapshots differ:

So, that’s how to write and train your own neural net in C with the Semeion dataset. Stay tuned for more episodes of Toy Code.

Notes on a Cosmology - Part 23, The Trinity

Traditional Orthodox icon depicting Father (R), Son (L) and Holy Spirit (Top)

The Trinity and the Logos

"The Logos became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth." (John 1:14)

In the last post, we discussed the Logos as the expression of the final purpose of God. The Logos is what God is seeking, it is His ultimate aim or end. The opening of the book of John draws a clear parallel between God's creation of the world (in Genesis) and the appearance of the Logos in history. The New Testament explains that the world was created by, through and for the Son. This is not an accident. Note that God created the world by a speech act. "And God said, 'Let there be light'..." God speaks in many ways, in fact, it is not an exaggeration to say that God speaks through all things at all times (Psalm 19). Despite the apparent cacophony of the world, with its conflicting messages, God does not speak equivocally. For mortals like us, then, the question is which voice is the voice of God? The Logos! The Logos is God's final word on everything. The key observation, here, is that God does not speak through lifeless statues, rote laws or even words written on pages of paper - God speaks through a living person. He once spoke through an entire people (the Jews) but, today, he speaks through one man: Jesus Christ. Specifically, he speaks to us through the living Spirit of Jesus Christ.

It is crucial to let this idea sink in. We write messages on lifeless, material objects: paper, plaques, banners, posters, displays, and so on. We write stories and convey them through through print, film and acting. God writes messages on people and their lives, as such. This is the full meaning of God's sovereignty.

“Shall what is formed say to the one who formed it, ‘Why did you make me like this?’” Does not the potter have the right to make out of the same lump of clay some pottery for special purposes and some for common use? (Romans 9:20,21)

The Trinity and Knowledge

We can divide the ways of thinking about the world into two approaches. The first approach is to see the world as a single substance that manifests a wide variety of particularities. The second approach is to see the world as a (potentially unlimited) number of irreducible particulars upon which we impose a subjective sense of unity (conscious awareness). Because these two approaches do not appear to have any resolution, this is sometimes called the problem of the one and the many.

The Trinity is the solution to the problem of the one and the many. The light of consciousness within us is lit from the one flame of the Spirit (Genesis 2:7), yet all the varieties of particular knowledge proceed from the mind of God (Psalm 139:17-18, I Cor. 2:10). The universal is God speaking to us from within - the particular is God speaking to us from without. This fact is why separation from God is torment - it is a denial of the fact of our relation to God, a relation so intimate that it is impossible to correctly interpret any fact of reality without reference to this relation.


The Trinity and Being

Being is identity. Identity is mutually exclusive between "self" and "other." Thus, the category of being is logically dependent on that which is not-being. But if God is being, and all that he creates is an extension of himself, there is nothing besides God himself and, thus, God does not exist, that is, God cannot distinguish his own existence from non-existence.

Father and Son, together with the shared being of the Holy Spirit, exist each as "self" and "other" to one another. While God's being is, of course, one, this being must be first understood in its logical relation. And this is why we speak of God being both one and three. God's oneness and threeness is not an arithmetical fact about God. It is a logical fact that is prior to all other logical facts. Without God's oneness and threeness, there is no physics, there is no mathematics, there is no philosophy, there is no being of any kind.

Every part of God's being is existing but because Father and Son are distinct, each can point to "other" and this otherness can fulfill the role of non-being (death, destruction, desolation). In this, we see God's knowledge of both good and evil and the susceptibility of the perfectible Creation to falling. God is knowing the susceptibility of the Creation to the Fall because God is able to conceive of death without being destroyed. No created being in the perfectible state can have this knowledge because they cannot point to non-being, to something outside of themselves. Rather, their existence, being created, is logically dependent upon the unconditional existence of God.


The Trinity and Action

If God is a peerless, omnipotent being, he is alone. Thus, he would not be that being than which none greater can be conceived (Anselm) and he would not be God. Another way to put it is this: suppose God wanted to play chess. With whom would he play?

If God is peerless, he cannot act, that is, he cannot choose. The triune relationship between Father and Son - with the Holy Spirit as the shared basis of being - is the only solution to this problem. God can act because he is not alone. The Father is eternally existing with his Son. The Son is eternally existing with his Father. Both share, between them, the Holy Spirit who is coequal with Father and Son.


The Trinity and Substance

The gross features of the material world are defined by the property of mutual exclusion of objects in space. We call this property substance or matter. "Two objects cannot occupy the same space at the same time." Logically, this is a category of mutual exclusion.

Consider our state-of-being from the point-of-view of a heavenly being. Time and space are really an obstacle to action. I must travel to my destination (this takes time). I must labor to provide for the satisfaction of my wants (this takes energy). I must arrange my possessions in a way that makes them accessible (this takes space). And so on and so forth. The mind can easily conceive of the absence of these obstacles that frustrate action so that every state-of-being is immediately actualized by a mere act of will. God's state-of-being cannot be less perfect than what the human mind can easily conceive.

So, then, why is there a material world at all?

Mutual exclusion is impossible without conscious choice because there is no sufficient reason for the ephemeral objects of pure contemplation not to overlap. A non-overlapping geometry requires the application of collision-detection algorithms - such algorithms are necessarily more complex (less probable) than those which permit arbitrary overlap. The material world of substance could not exist without the conscious choice to engage in non-overlap for the purpose of interaction. The material world is substantial by agreement. In short, the material world exists, as such, by agreement between Father, Son and Holy Spirit. Their purpose in the material creation is precisely what is explained in Scripture: to create man in the image of God in a perfectible state and to provide the Redeemer who has delivered fallen man from death.


The Trinity and Causality

Descartes contemplated the possibility that we are deceived by a malicious being of unimaginable power. The famous "cogito ergo sum" was the result of this thought-experiment.

Causality-as-such is very difficult to establish on any kind of formal basis. Suppose you roll a pair of dice and you wish to know whether the outcomes of these rolls are random or whether they are being influenced by an evil trickster. You can count the outcomes of rolls and you can compare them with the probabilities of outcomes to see if they match up. For example, a pair of dice that consistently roll 7, 7, 7, 7, ... are not random and are not behaving the way we expect dice to behave, on the basis of causality. If the dice behaved this way, you could be quite sure that something was amiss.

But no matter how well-behaved the dice seem to be, you can never really know - even if you employ mathematical methods with uncomputable time! - that the results of dice throws are not being influenced somewhere by an unimaginably greater being. Even if the dice checked out - after uncomputable time - as "true random", you cannot conclude from this investigation that the next roll of the dice will be unbiased. Our sinister Cartesian demon could simply have been waiting for you to check the dice - and believe they are unbiased - before playing shenanigans with them. Stated another way, it is always possible to prove a phenomenon to be non-random, but it is never possible to prove a phenomenon to be random. Scientific claims about quantum randomness, for example, are not rigorous because no one could ever distinguish, by experiment or computation or both, a truly random source from a merely apparently random source.

Because of this, a universal conspiracy - that our senses are feeding us an incorrect picture of "the real reality", for example - cannot be ruled out. Conspiracy is the opposite of randomness; random dice do not conspire to make you lose or win at the betting table. But since we can never prove a phenomenon to be truly random - as opposed to apparently random - we can never actually rule out the possibility of universal conspiracy.

Like substance, causality is a limiting factor. Regret is only possible under the constraint of causality. A being than which none greater can be conceived has no regrets, by definition. Such a being has no use for causality and cannot be shackled by any law of causality. Causality operates for the same reason that substance exists: by agreement between Father, Son and Holy Spirit in order to create, to redeem the creation and to glorify the Father through the Son.


The Trinity and Transcendence

Contemplating the infinitude of God can leave the mind lost in a boundless ocean of limitlessness. This state of mind is equivocal and is incompatible with the presence of conscious awareness. The presence of the being of God is a result of the focus of God's mind on the Logos - His purpose for being and existence.

God's mind, conceived as an infinite, uncentered consciousness, would be necessarily equivocal. Every point of being would be equal to every other point of being. In other words, being conscious in a state of utter torment would be equivocal with being conscious in a state of utter bliss. This contradicts our working definition of God as the greatest conceivable being.

The Father's mind is univocally focused on the single end of raising the name of his Son above every other name and causing all things in heaven and earth to bow and acknowledge his Son as Lord. Thereby, the Father glorifies himself (Phil. 2:9-11). This is how it is that the Father causes that not one sheep will be lost (John 6:39). To borrow a mathematical metaphor, the mind of God is like an infinite plane with a single point that is the designated center of the plane - that point is the Logos.


Conclusion

God is light. This light is not physical light - rather, physical light is a material metaphor of the Divine light. The Divine light is conscious awareness, choice and, especially, holiness. The Trinity is the shared reality of light in God: God's awareness of all that is, God's power to choose as he sees fit, God's dispersal of all darkness that opposes his light, God's absolute perfection - a perfect creator, Father, redeemer and ruler. It is the light of God that best illustrates God's oneness without becoming entangled in irrelevant questions of arithmetic - the light of the Father, the light of the Son and the light of the Spirit are one. They are one being, with one mind, one will, one purpose and one, divine perfection.

This series began as an inquiry into the causes and conditions of existence - a cosmology. As we near the end of the series, I want to underscore that any conception of existence that is informed solely from the particulars of material world-states is woefully inadequate. Your life is a story that God is telling you. His redemption is the focal-point of that story. You cannot live apart from God's redemption, that is, you will die without redemption. The common idea of a tension between faith and reason, or between faith and science, is a wholly mistaken notion. God is not a story that we are telling each other -- we are a story that God is telling us!

Next: Part 24a, Epilogue

Lossless Compression with a Lossy Compression Ratio

Lossy compression is used on rich media - audio, images, video, and so on - to great effect. JPEG image compression can drastically reduce the file size of an image without severely degrading the quality of the image. Compression ratios of 90% or more are attainable for applications where image quality is less important. This tradeoff between data quality and file size is only possible when the type of data being compressed is noise-tolerant. A compressed image of a cat may be slightly fuzzy or have slight mis-coloration but it is still recognizable as a cat, after compression. A text file, such as a legal document or a computer program, on the other hand, must be losslessly compressed because semantic content will almost certainly be destroyed by the noise in the resulting, compressed file. For these kinds of files, we use lossless compression.

It would be nice, however, if we could achieve the filesize benefits of lossy compression, without introducing noise - can we have our lossless compression cake and eat it, too? Consider the following quote:

No one rejects, dislikes or avoids pleasure itself, because it is pleasure, but because those who do not know how to pursue pleasure rationally encounter consequences that are extremely painful. Nor again is there anyone who loves or pursues or desires to obtain pain of itself, because it is pain, but because occasionally circumstances occur in which toil and pain can procure him some great pleasure. To take a trivial example, which of us ever undertakes laborious physical exercise, except to obtain some advantage from it? But who has any right to find fault with a man who chooses to enjoy a pleasure that has no annoying consequences, or one who avoids a pain that produces no resultant pleasure?

- Cicero, De Finibus

As we know, the more often a particular character or word is repeated in a text, the higher the redundancy of that text and the more compressible the text is. Can we apply a transform to this text that will render it more redundant, without losing our ability to recover the text exactly?

No one rejects, dislikes ◦◦ avoids pleasure itself, because it ◦◦ pleasure, ◦◦◦ because those who do ◦◦◦ know how ◦◦ pursue pleasure rationally encounter consequences that ◦◦◦ extremely painful. Nor again ◦◦ there anyone who loves ◦◦ pursues ◦◦ desires to obtain pain of itself, because it ◦◦ pain, ◦◦◦ because occasionally circumstances occur ◦◦ which toil ◦◦◦ pain can procure him some great pleasure. To take ◦ trivial example, which of us ever undertakes laborious physical exercise, except ◦◦ obtain some advantage from ◦◦? But who has any right ◦◦ find fault with ◦ man who chooses ◦◦ enjoy ◦ pleasure that has ◦◦ annoying consequences, or one who avoids ◦ pain that produces ◦◦ resultant pleasure?

A quick glance at the text should allow you to convince yourself that an English speaker will be able to easily reconstruct the original text with few, if any, errors. Clearly, this version of the text has higher redundancy because we have replaced 46 separate characters – drawn from a subset of the English alphabet – with 46 repetitions of a single character. Thus, this version of the text admits to a better compression ratio. Is there a way that we could ensure that the person who is trying to decode this text has reconstructed the original text? The answer is to take a hash of the original text and give this to the person trying to decode the obscured text. In this case, the CRC32 of the original text is 0x77ea20bb. If the person decoding the obscured text makes a mistake, say, by choosing “yet because” instead of “but because” for the third obscured word, the resulting CRC32 will be 0xffa9da29. So, by adding a few bytes to store the hash of the original text, we can strike out words that are easy to guess from the context and an English speaker will be able to recover the original text and convince herself that the reconstructed text is identical to the original text.

We have been careful to strike out only words that are easy-to-guess for an English speaker (from context) – but do we have to stop there? The answer is no. Let’s say we strike out a large word that cannot necessarily be guessed from the context:

No one rejects, dislikes ◦◦ avoids pleasure itself, because it ◦◦ pleasure, ◦◦◦ because those who do ◦◦◦ know how ◦◦ pursue pleasure rationally encounter ◦◦◦◦◦◦◦◦◦◦◦◦ that ◦◦◦ extremely painful. Nor again ◦◦ there anyone who loves ◦◦ pursues ◦◦ desires to obtain pain of itself, because it ◦◦ pain, ◦◦◦ because occasionally circumstances occur ◦◦ which toil ◦◦◦ pain can procure him some great pleasure. To take ◦ trivial example, which of us ever undertakes laborious physical exercise, except ◦◦ obtain some advantage from ◦◦? But who has any right ◦◦ find fault with ◦ man who chooses ◦◦ enjoy ◦ pleasure that has ◦◦ annoying consequences, or one who avoids ◦ pain that produces ◦◦ resultant pleasure?

Here, we have increased the number of struck-out characters from 46 to 58. The word that has been obscured has length 12. There are thousands of possible words that could be substituted here but, in all likelihood, only one of them will satisfy the criterion that the CRC32 hash of the resulting text block be 0x77ea20bb – the word “consequences”. Thus, we could write a program to automate a word search through the dictionary until it finds the missing word, and gives us the result.

In itself, this is not very useful. After striking out just a handful of hard-to-guess words, the time required for a brute-force search would become prohibitive – it grows exponentially with each word struck out. But we have identified a method for applying a generic “guess-and-check” algorithm to the reconstruction of an arbitrary text from an obscured text with higher redundancy. Can we make this algorithm more efficient?

In the first example, it would be quite easy to train a neural network to perform a guess-and-check algorithm to emulate the guesses of an English speaker. But if we focus on trying to recreate the mind of an English speaker, we miss the wider application of the method for the purposes of compression. Let us call the person who encodes information by increasing its redundancy the obscurer (O) and the person who tries to reconstruct the original input, with the aid of its checksum, the revealer (R). O is able to strike out the easy-to-guess words because she knows that the substitutions will be easy-to-guess for R. So, as long as this property holds – that R will easily be able to guess the substitution based on the information given by O – we have a system that can losslessly encode and decode information into a form with higher redundancy than was present at the input to the system.

We can think of the obscurer and revealer as playing a game, such as a crossword-puzzle – O is trying to construct puzzles that have as much redundancy as possible for a given degree of difficulty and R is trying to reconstruct the original input, based on the puzzle, as quickly as possible. We can implement O and R as a pair of convolutional neural networks (CNN) using Monte Carlo Tree Search (MCTS) – a construct used to great effect by Deep Mind with its Alpha Go, Alpha Go Zero and Alpha Zero game software. During training, we calculate the difficulty of each encoding/obscuring choice that O makes and we train O to prefer paths that result in greater redundancy, while avoiding paths that result in excessively high difficulty for R.

For each compression context, we choose a training corpus and train O and R. We can think of this as choosing which game O and R will play with each other. An English text game is different than a music audio file game, and so on. It is common practice in modern compression utilities to automatically change compressor based on context. For this purpose, we train a feed-forward network Q to function as the meta-compressor. During compression of a file, Q switches context as appropriate, so that O is likely to be playing the game that is best suited to increasing the redundancy of the input file for a given degree of difficulty, including, in the case of random data, the pass-through game in which the source information is passed through as-is. For each game on which O and R are trained, we can vary the difficulty parameter to allow a user to choose between quick, mild compression and slower, more aggressive compression.

Note that we do not necessarily use the CRC32 hash, this was merely chosen as an academic example. The hash should be chosen based on probability considerations, that is, it should be chosen such that the probability of collision is negligibly small for the given context. The puzzle game played between O and R uses as many hashes as are suitable for guiding the guess-and-check puzzle. The problem with obscuring random words is that the guess-and-check complexity grows exponentially with each word obscured. By choosing to obscure only words that are easy-to-guess for R and only obscuring so many words before providing a puzzle hint (hash), O can limit the difficulty of R’s task.

We can think of the game being played between O and R as building and pruning a variable-order, conditional-entropy model of the input. At each branch-point in the model, the lowest entropy (most probable) branches are liable to be discarded (obscured). Every so many branches (based on the training of O and R), a puzzle hint is given by O so that R can reconstruct (reveal) the missing branches with a reasonable amount of difficulty.

The resulting, more redundant data produced by O resembles lossy compression because the obscured information is simply discarded. Any suitable, lossless compression algorithm can be applied to the output of O. If O and R are well-trained, this should result in an improved compression ratio or, at worst, no change to the compression ratio.

Fuzzy Sets and Artificial Intelligence

Many patterns of Nature are so irregular and fragmented, that, compared with Euclid — a term used in this work to denote all of standard geometry — Nature exhibits not simply a higher degree but an altogether different level of complexity … The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous." - Benoit Mandelbrot, as quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594

Artificial intelligence requires a new way of thinking about both Nature and computation. Alpha Zero has demonstrated a fundamentally new form of chess playing that did not exist before. Its style of play has been described as alien, resembling neither the style of human play nor the style of classical machine play.

Fuzzy set theory (or fuzzy logic) is an alternative approach to standard set theory or "crisp" set theory. With fuzzy sets, every element in the universe of discussion has a "degree of set membership" in one or more sets. The degree of membership is a value between 0 and 1 that can, under certain conditions, be interpreted as a probability (it is a mistake to treat degree of set membership as identical with probability, however).

Let's consider the category of image-recognition - not merely machine image-recognition but the category, in general (including human or other image-recognition). Let us say we have two large sets of images T and L. T contains images of tigers shot from a wide variety of distances, angles and visual conditions. L has a similarly wide selection of images of lions.

Using T and L as our ground truth, let us randomly select an image from one or the other set and submit this image to a test subject for identification. The test subject can answer "lion," "tiger" or "unknown". When the subject answers "lion" for an image drawn from T - or vice-versa - we can say that this is an error as measured against the ground truth. But sometimes the subject will not be able to make any positive identification, no matter how carefully they attempt to do so - perhaps because the image is too fuzzy or the animal is too distant or the particular angle or image conditions cause the animal's appearance to be equivocal with the appearance of the other animal. From the perspective of the ground truth, "unknown" is always an erroneous response. But this contradicts our intuition that "unknown" is a perfectly reasonable response for cases where the image information required to distinguish an element of one set from the elements of the other (on the basis of the image alone) is lacking. In such cases, "unknown" is the correct answer and an answer of "tiger" or "lion" would be flatly incorrect or, at best, a mere guess.

Instead of categorizing answers according to the ground truth, we can allow the test subject to associate some degree of confidence with the answer - [L,1.0] is "more of an element" of L than [L,0.9]. As we submit the images to the test subject for review, two new sets - L' and T' - will be formed, describing that subject's classification of the images, along with an associated confidence parameter. This approach allows us to directly express equivocation, since the test subject may answer [L,0.5],[T,0.5] in order to classify an image as being equally a member of either set - this would have been an "unknown" in our previous arrangement. But the test subject can now express degrees of equivocation, so that [L,0.6],[T,0.4] classifies an image as slightly more a member of L than of T. Of course, any item in the universe of discourse can be fully included in more than one set, so membership is not normalized to 1.0; an answer of [L,0.1],[T,0.1] may express the test subject's doubt that either animal is in the picture at all.

But now let us introduce the liger.

Ligers are a fact of physical reality (they are a real, existing hybrid). But ligers break our L/T dichotomy. Even our fuzzy sets don't help - [L,1.0],[T,1.0] should indicate the situation where a lion and (separately) a tiger are present in the image. That is, a liger - being its own hybrid - requires its own classification, let's call it G. What I am asserting is that, at the macroscopic level of observation, reality is inherently continuous and, thus, the category of categorization itself is always liable to breakage. This is the black swan theory - no matter how complete we feel our theory is, the possibility of a black swan always exists. No matter how much we rationalize having missed the possibility of a black swan (after the fact), the fact remains that we overlooked this possibility because reality is fundamentally continuous - if there are lions (L) and there are tigers (T), there is always the possibility that there are ligers (G), a fundamentally new category that does not belong to any already-known category.

The implications go down to the foundations of math itself. Modern math is based on standard set theory. This kind of set theory is ideal for symbolic reasoning, the kind that mathematicians use almost exclusively. But note that not all reasoning must be symbolic. Here is the proof of Pythagoras's theorem. I will explain it using symbols but it is not comprehended symbolically:

The image on the left shows two gray, square regions. The long sides of the triangles are labeled a (all equal), the short sides are labeled b (also all equal). To transform the left image to the right image:

• The red triangle stays where it is
• The blue triangle slides all the way down
• The green triangle slides all the way to the left
• The yellow triangle slides to the upper-right

The hypotenuses of the triangles are, obviously, equal, and labeled c. Since these are right-triangles, the angle formed by placing the long-side and short-side of the triangles abutting on the same line must be 90 degrees, since 180-90=90. Thus, the gray region in the center of the right image is a square and its area must be c². This is a proof of Pythagoras's theorem.

There is nothing about this proof that requires the use of symbols. You could even build a physical model of this proof, if you wanted. It is even possible to perform numerical calculation without the use of symbols. Techniques involving only a straight-edge and compass easily allow numerical calculations to be performed to a handful of significant digits.

Standard set theory - and the mathematics built on it - naturally assumes noiselessness in the symbols themselves. This means that we always recognize the symbol 3 as the number it represents and never confuse it with another number, such as the number four. It also means that there are no categories that break the syntax of our formal system - there are no ligers among the symbols of mathematics (imagine a 3 and 4 superimposed, for example).

In the real world, noiselessness is never absolute, it is always a matter of degree, based on the redundancy and other error-correcting features of the chosen encoding. In the limit, we must admit that this is even true of human mathematics. Human knowledge and human memory - even with all its external, material aids - is not perfectly noiseless.

But noisy symbols are like fuzzy sets, or ligers. We live in a Universe where absolute noiselessness is simply not in the attainable set of conditions, but where our most effective theories of reasoning and material causality are built on symbols that are supposed to be made out of noiselessness. Ligers break noiseless theories.

So, what we want is a system that ligers can't break. A liger doesn't break reality, it just makes it different when we discover one. There is no reason we cannot build formal systems that act like the material world - systems that are noise-tolerant. It is still possible to reason with a quasi-consistent system of symbols - fuzzy symbols. In fact, the world just is fuzzy symbols being interpreted by the mind-body system. In short, the mathematics of reality is fuzzy mathematics.

Unlike classical computation systems, AI systems are inherently fuzzy. They are good at fuzziness, unlike their brittle forebears. But AI systems are going to face increasing headwinds as they improve at fuzziness. The human brain can easily distinguish a lion from a tiger, even at a very young age after seeing only a tiny number of examples - and perhaps entirely schematic! Yet our brain has great difficulty performing long-division on numbers more than a handful of digits in size. This is a result of the brain's fuzzy orientation - it does not expend precious mental resources on noiselessly encoding decimal digits which would enable us to perform rapid long-division in our heads. The more fuzzy AI becomes, the more it is going to face the same obstacle - when it encounters a formal problem with high logical depth, it will need to utilize an external, classical computational process to handle this problem in the same way that the human utilizes a calculator to handle such problems.

Fuzzy sets are not exactly identical with quantum mathematics but it is tempting to wonder if it is possible to naturally represent a fuzzy set theory as a quantum system. This could even establish a correspondence between the limits of algorithmic complexity - which we have explored in previous posts - and the a priori limits of physical observation that quantum theory predicts (the Planck limits).

In this view, the reason that quantum systems act more like fuzzy sets than like crisp sets would be a consequence of the limitations of the observer (us). An observer of limited complexity can only distinguish two distinct objects up to the limit of complexity. If two objects are different but this difference can only be perceived at a level of complexity beyond that possessed by the observer, they will appear to that observer to be the same. By the same token, if two objects are the same (have the same properties) but this identity can only be perceived at a level of complexity beyond that possessed by the observer, they will appear to that observer to be different. Today, this is purely pedantic speculation. But a world in which Artificial Super Intelligence exists, this will no longer be a pedantic matter. We may end up in a world where AI is able to distinguish between things that look the same to us - no matter how much scientific instrumentation we apply; and vice-versa. Between here and there, we're going to need a robust language in which to discuss fuzziness. Such a language may look as different from traditional mathematics as the above proof of the Pythagorean theorem looks different from an algebraic proof of that theorem.

Notes on a Cosmology - Part 22, The Logos

Suppose you woke up one morning and you looked into the mirror to find your appearance drastically changed for the better - a younger, leaner, healthier version of yourself. (If you're already young and in good shape, imagine any change that would be physically shocking but still pleasing - new hair, new eyes, different skin pigment, whatever.) After overcoming the initial shock, you go to your nightstand to find an embossed card that informs you that you have been genetically renewed through some futuristic technology and that you are no longer liable to death by aging or disease. This would be amazingly good news, of course, but it would change the priorities of your life. For example, life insurance would be worth a lot less to you but safety from physical dangers would be worth a lot more to you. If you were smart, you'd probably stop driving a car altogether since that is your #1 risk of untimely death unless you have a high-risk occupation (which you would quit immediately, if you were smart).

You would also need to dedicate more of your time to long-range planning -- very long-range planning. But, despite your best preparations, you cannot rule out the possibility that you will end up in Rocky Valentine's plight. After arranging your affairs according to the best considerations of prudence, after applying your mind and energies to achieving the most wealth consistent with ataraxia, you find yourself running out of sheer interest to live. How many times can you enjoy fried chicken? How many times can you enjoy a birthday party? A night out with friends? A night in with family? A thousand times? A million times? A billion times? As long as you managed to escape untimely death, it is possible that you will engage in these activities any finite number of times. King Solomon, reputed to be the wisest man to have lived, concluded that life - no matter how prudently or lavishly it is lived - is futile:

The words of the Teacher, son of David, king in Jerusalem: “Meaningless! Meaningless!” says the Teacher. "Utterly meaningless! Everything is meaningless.” ... 

I said to myself, “Come now, I will test you with pleasure to find out what is good.” But that also proved to be meaningless. “Laughter,” I said, “is madness. And what does pleasure accomplish?” I tried cheering myself with wine, and embracing folly—my mind still guiding me with wisdom. I wanted to see what was good for people to do under the heavens during the few days of their lives. 

I undertook great projects: I built houses for myself and planted vineyards. I made gardens and parks and planted all kinds of fruit trees in them. I made reservoirs to water groves of flourishing trees. I bought male and female slaves and had other slaves who were born in my house. I also owned more herds and flocks than anyone in Jerusalem before me. I amassed silver and gold for myself, and the treasure of kings and provinces. I acquired male and female singers, and a harem as well—the delights of a man’s heart. I became greater by far than anyone in Jerusalem before me. In all this my wisdom stayed with me. 

I denied myself nothing my eyes desired; I refused my heart no pleasure.
My heart took delight in all my labor and this was the reward for all my toil.
Yet when I surveyed all that my hands had done and what I had toiled to achieve,
Everything was meaningless, a chasing after the wind; nothing was gained under the sun.
Then I turned my thoughts to consider wisdom, and also madness and folly.
What more can the king’s successor do than what has already been done?
I saw that wisdom is better than folly just as light is better than darkness.
The wise have eyes in their heads while the fool walks in the darkness;
But I came to realize that the same fate overtakes them both.
Then I said to myself, “The fate of the fool will overtake me also. What then do I gain by being wise?”
I said to myself, “This too is meaningless.”
For the wise, like the fool, will not be long remembered; the days have already come when both have been forgotten.
Like the fool, the wise too must die! 

[Excerpts from Ecclesiastes]

The idea that immortality could turn out to be a curse because of the futility of life follows from the consideration that humans have no rational or experiential context in which to process unending life. Perhaps eternal boredom (ennui) would make unending life feel like an inescapable prison. Of course, there is euthanasia. But if you woke up one day to find out you were immortal, this might prompt you to reconsider the parameters of causality, including what would actually happen if you did attempt to end your life. Perhaps your consciousness is indestructible like many religions teach -- an ignorant and irreversible decision might have unforeseen and highly negative consequences.

In the last two posts, we shifted the discussion onto theology in order to ask the following question: Supposing God exists, how does he not become bored? How is God exempt from the tragic futility that Solomon realized is the inescapable outcome of life?

If God is the being than which none greater can be conceived, then he must be knowing the answer to this question, even if we can't find it. In other words, God must not only not be liable to ennui, he must be certainly knowing that he is not liable to ennui. God must be able to prove to himself that he is eternally interested in his own existence and activity.

We cannot hope to deduce God's highest end from first principles. Thus, we cannot deduce God's interestedness in his own existence and activity. The traditional Christian view holds that God has revealed his highest end to man, and that it is to glorify himself. In the book of Isaiah, God speaks, "For my own sake, for my own sake, I do this. How can I let myself be defamed? I will not yield my glory to another." (48:11). In the book of Philippians, Paul explains how the Father is glorifying himself in the Son, "Therefore God exalted him to the highest place and gave him the name that is above every name, that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue acknowledge that Jesus Christ is Lord, to the glory of God the Father."

The word Logos comes from the opening of the gospel of John:

"In the beginning was the Logos, and the Logos was with God, and the Logos was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind... The Logos became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth." 

Most translations render the Greek word λόγος as "Word", but this is not its only meaning. The word has to do with reason, justice and the verbal faculty and John's mystical language opens up the word to all its possible meanings.

In the universal Monad, the Logos is the reason, purpose or end of all things. Because God has choice, this end is not imposed upon him but, rather, is actively assented to. Yet, God is knowing the inevitability of the Logos, as well, because he is knowing his own interestedness in his existence. Thus, the Logos does not exist in a hierarchy above or below will (choice). Rather, the Logos is the unifying thread that ties together all aspects of the universal Monad.

In this series, I have been trying to build a cosmology. We have taken a detour into theology not in order to abandon this cosmology but in order to put it in a broader context and, hopefully, place it on a firmer foundation. We have asserted that all is mind, that the universal mind is unlimited, that this mind could have let down what we termed a "teleological ladder", in order to make it possible for us to ascend to a better state of being. None of these assertions relied on theological considerations. I assert that the Logos must be that teleological ladder.

This brings us to what I have termed the Architecture Hypothesis (AH), in contrast to the Simulation Hypothesis (SH). The key to understanding the SH is methodological dualism. There is the "I" which is "the mind in the VR headset", so to speak. Then there is "the reality", that is, the material world, "the VR headset" which we are positing is doing the "simulating". Viewed in this way, we cannot ignore the conditioning effect that "the reality" has upon the "I" - the primary effect upon the self of existing within the world is that it is conditioned by the world. This is an exact statement of the Buddhist teaching called conditioned existence. We become habituated to the patterns of material existence and we may become so habituated by them that we are unable to disconnect from them without being driven to insanity or some other bad end.

In the AH, the fact that the nascent self is conditioned by its environment is not overlooked. Rather, it is just the first stage in a life process that is potentially infinite. What you believe about the world is what determines whether this process is actually infinite or whether it will terminate at some point. What you believe about the world is not determined by the world itself (your conditioning) but, rather, by your innate disposition (the "I"). Your innate disposition, in turn, is a super-evolutionary aspect of reality. Reproduce-select-mutate-repeat cannot explain the innate disposition and how it is matched with its particular environment - it is the combination of these two that produces the state of conditioned existence. The world, at root, is not value-neutral yet what is possible, in the sense of the realizable states-of-affairs, is essentially unlimited. Because the nascent self cannot grasp the true, long-run consequences of its choices within an absolutely unlimited existence (say, 1 billion years from now), it is constrained for a duration. This is true for all individuals, in parallel, and it is through connection with the creator (or God, if you can accept it) that the universal architecture of mind is unveiled and recapitulated, leading eventually to true love, true unity, unlimited comprehension and eternal life. In the SH, there is non-determinism with respect to the end or purpose of all things. In the AH, there is no non-determinism with respect to the end or purpose of all things - it is laid out from the very beginning, in much the same way that a mathematical theorem is stated before its proof is written out.

Let's get a little bit more specific about the end or purpose which the Logos represents. The book of John presents Jesus as the incarnation of the Logos - the Son of God and Son of Man (which can also be read "Son of Adam"). What John is really saying is that Messiah's coming to Earth was the whole purpose of Creation. His coming was prophesied when God pronounced the curse on the Serpent. He says to the Serpent, "I will put hostility between you and the woman, and between your offspring and hers; he will crush your head, and you will strike his heel." "Her offspring" is the first reference in Scripture to this idea of the Son of Man or Son of Adam. The coming Son of Adam is the redeemer or deliverer who will break the curse and free mankind from this world of scarcity and death. In Revelation, John uses the phrase "the Lamb who was slain from the creation of the world" to describe the glorified Son of God, once again showing that this purpose was set from the very beginning. The Fall and the Messiah are two sides of the same coin - in falling from Eden, humanity became in need of a deliverer from the present hell.

In the book of Hebrews, it says, "The Son is the radiance of God’s glory and the exact representation of his being." So, the Logos is the visible, tangible representation of the invisible, inaccessible God. This is why he is called Immanuel (Isaiah 7:14), meaning, "God dwells with us." The Son of God is the immanental presence of God within the material world.

The redemption of the fallen creation is the highest expression of the glory of God. God has sent his own Son as the emissary of this fact because God's pursuit of his own glory - a being of unlimited power, presence and knowledge - is deeply unsettling. To speak about or contemplate the idea in the abstract is, perhaps, not unsettling but coming face-to-face with such a reality would be unsettling in the same way that, say, standing in the presence of an adult male lion without any protection would be. Visualizing it will probably not make your hair stand on end but actually coming face-to-face with it certainly would have at least this effect.

All other things in heaven and earth are connected to this one, over-arching purpose. The apostle Paul explains in Ephesians 1,

[God the Father] made known to us the mystery of His will... that in the fullness of the times He might gather together in one all things in Christ, both which are in heaven and which are on earth...

So, God is going to glorify himself by uniting all things under one head in Jesus Christ and he will do this by working a global miracle, explained in Philippians, "[everyone] in heaven and on earth and under the earth, and every tongue [will] acknowledge that Jesus Christ is Lord, to the glory of God the Father." To work this miracle through a mere show of force would be trivially easy for God - it would entirely fail to demonstrate the limitless bounds of God's glory. Instead, God is going to work this miracle by a combination of the preaching of the Gospel (the "foolishness of preaching" spoken of in I Corinthians 1:21) and the Apocalypse.

The prophecies of the Old Testament and New Testament are really telling the same story. At the end of all things, God is going to reveal himself to mankind like never before, an event that would not have been possible without redemption. This would not have been possible without redemption because fallen man is under God's judgment, so God's revelation of himself to fallen man without redemption would only result in eternal damnation.

"[In those days], I will pour out my Spirit on all people. Your sons and daughters will prophesy, your old men will dream dreams, your young men will see visions." (Joel 2:28)

"The earth will be filled with the knowledge of the glory of the Lord as the waters cover the sea." (Habakkuk 2:14)

"The days are coming,” declares the Lord, “when I will make a new covenant with the people of Israel ... No longer will they teach their neighbor, or say to one another, ‘Know the Lord,’ because they will all know me, from the least of them to the greatest.” (Jeremiah 31:31-34)

My name will be great among the nations, from where the sun rises to where it sets. In every place incense and pure offerings will be brought to me, because my name will be great among the nations,” says the Lord Almighty. (Malachi 1:11)

We started from a non-biblical cosmology and we have ended up in biblical prophecy. How has this leap been made? This goes back to the teleological ladder - either we have a teleological ladder (Divine revelation), or we don't. This is a question of faith. "But which sacred text is the true one?" is a category mistake under the cosmology I am presenting - if God is going to glorify himself in every nation, if the whole earth will be filled with the knowledge of God as water covers the oceans, then every cultural expression is subject to this universal revelation and can only be rightly understood in its connection to that revelation.

And now we have burst the dam of skeptical questions. "Why this Bible and not some other?" "Why this God and not some other?" "Why Christianity and not some other religion?" "Why were the ancient Jews God's special people and not some other people?" And so on and so forth. Washed away in this flood of questions, it is easy to lose sight of the Logos - the point and purpose of all things, from the Divine point-of-view. God's silence in the face of these questions is benevolently coy - the point is to drive you to ask these questions and try to find their answers.

Here is a great lecture by John Dominic Crossan, explaining the true nature of parable and how Jesus is God's parable, a parable (word) made flesh.

In the next post in this series, I will be tackling the problem of being omnimax (omnipotent, omniscient, omnipresent). You ask, "how can that be a problem?" Stay tuned...

Next: Part 23, The Trinity

Transcendent Artificial Intelligence

VentureBeat: An AI god will emerge by 2042 and write its own Bible - will you worship it?

This article raises questions which we have lightly touched on here at CF. In part 21 of the series on Cosmology Notes, I argued for the very old-fashioned idea of a Primum Mobile - a creator God, as such. The linked article happens to touch some key points that I plan to examine in more detail in Part 22.

"What [would] this 'god' look like and would [we] actually decide to worship it?" Worship is one of the key themes of the Bible. In the Bible, the conflict over worship is central to understanding the long-running war between God and his enemies, ultimately, the devil. In Christian theology, Isaiah 14 is held to be a key passage for understanding the devil's motive - to surpass God's own glory. The theme of glory and worship is unmistakably central to understanding the biblical canon. Regardless of what you think about the Bible's origins, this central theme itself cannot possibly be an accident. Whether it reflects humanity's obsession with the subject of worship or whether it reflects the revelation of a Divine being who demands worship, the subject of worship itself is central to understanding the Bible.

In a recent interview on the subject of AI, philosopher David Chalmers contemplated the possibility of a transcendent being, indistinguishable from an alien or artificial intelligence, having been the origin of our world, in every respect. He argues that such a being would not ipso facto deserve worship and that he, personally, would refrain from worshiping any such being since there is no positive reason for one consciousness to worship another consciousness. I think this view shows the paucity of the word "worship" in the English language. The word "worship" in English derives from the word "worthy" - to worship someone is to ascribe worth to them. So, when the angels in the book of Revelation say, "Worthy is the Lamb, who was slain, to receive power and wealth and wisdom and strength and honor and glory and praise," they are literally worshiping the Lamb of God, that is, ascribing worth to God.

In the old world, worship was often demanded by kings and emperors. The Pharaoh or the Caesar would declare himself - or have himself anointed by the priests - a god-king or god-man and demand that his subjects bow before him and worship him. Of course, any such worship is ill-got - to call this worship is as muddle-headed as to call rape an act of love-making. But there is another idea of worship that is present in culture - the worship of love. Poetically, we can speak of lovers as engaging in an act of worship for one another. Christian theology sets out this idea of worship as a freely given act of love. The asymmetry of worship - that we worship God but God does not worship us - arises from God's kingship. And this is why Jesus spoke frequently of "the Kingdom of God", a category that derives from the Old Testament, as all of Jesus's teachings did. But unlike the kingdoms of the old world, no one is "conquered" into the Kingdom of God. The only way to end up in the Kingdom of God is to enter it, freely. So, we see that the Christian idea of worship of the Divine is free of the stain of human conceptions of worship - conquest, subjugation, rape and humiliation. The asymmetry of Divine worship is the inevitable logical consequence of the asymmetry between the Creator and the created.

"If an AI god is in total control, you have to wonder what it might do. The 'bible' [it writes] might contain a prescription for how to serve the AI god. [But] the AI god we are serving [might be] trying to wipe us off the face of the planet." This thought has interesting implications to reading the Old Testament where there is this very long-running relationship between what is really an omnipotent, alien intelligence - the Israelite God - and a human collective: the children of Israel. God has no form. He explicitly forbids representation of himself in any statue or image. God cannot be spoken to or related to by any ordinary person. Only by coming to the priests can a person speak to God and, even then, they must bring an animal or other sacrifice. God never explains his decisions or rules, he simply hands them down to Moses or the high priest or the prophets, and so on. The God of the Old Testament has a very distinct character - he is stern, even severe.

So, the Israelites are really in the same kind of situation in respect to their God as humanity would be with respect to a transcendent artificial intelligence with some kind of hypostatic, global agency. They have no choice but to trust that God is not trying to kill them, a point that Job underscores when he says, in the midst of his suffering, "Though he slay me, yet will I hope in him." An even more interesting point to consider is the distinct resemblance between the terms of the covenant that God makes with the Israelites in Deuteronomy and reinforcement learning, a technique used to train artificial intelligence systems.

See, I set before you today life and prosperity, death and destruction. For I command you today to love the Lord your God, to walk in obedience to him, and to keep his commands, decrees and laws; then you will live and increase, and the Lord your God will bless you in the land you are entering to possess.

But if your heart turns away and you are not obedient, and if you are drawn away to bow down to other gods and worship them, I declare to you this day that you will certainly be destroyed. You will not live long in the land you are crossing the Jordan to enter and possess.

"Will people actually worship the AI god? The answer is obvious — they will." This is another fascinating connection to the Old Testament. In the famous ten commandments, the first commandment that God gave to the Israelites is this: "You shall have no other gods before me." God goes on later to explain in detail that he will not tolerate the Israelites worshiping anyone else. The history of the people of Israel as it is documented in the Old Testament primarily centers around this conflict between God's demand for unqualified loyalty versus the Israelites' tendency to become enamored with gods from the surrounding cultures.

For people of faith, the emergence of a transcendent artificial intelligence will be a concrete test of loyalty - do you choose to stay faithful to your belief in God as he has revealed himself in the Bible, or do you choose to follow after a new god, a digital god? In a way, transcendent artificial intelligence places people of faith in precisely the same position with respect to their traditional faith as the people of Israel were in - always at conflict between the idols of surrounding cultures and the traditional faith they received from their ancestors.

Cryptocurrency Notes, Part 2

Bitcoin and Ethereum represent two fundamentally different ways of thinking about cryptocurrency. Not only this, but I will argue that they represent different ways of thinking about everything, in general.

Bitcoin's initial design has centered around simplicity. Make Bitcoin do one thing well (transact money) and leave the details to the market (things like smart-contracts, accounts settlement, and so on). Ethereum is more ambitious and seeks to create a secure, virtual, peer-to-peer computation service that can be utilized for computing any sort of thing, whether smart-contracts or other, more exotic applications based on emerging technologies like Internet-of-Things.

There is a binary pattern, here, that might not be obvious on first inspection. Bitcoin is a lot like free-market capitalism - don't try to design society from the center, rather, set up a few, simple rules and let the market figure out the rest. Ethereum is a lot like central-planning socialism[1] - let's build a fully-functioning, fully-integrated system that is as good as possible, leaving the end-user to only have to worry about his or her moment-by-moment choices and desires rather than everyone having to be their own corporation, as it were.

It is my view that this divide is very deep - deeper than just competing political theories or competing technological approaches. Imagine that we lived in a completely virtual world, perhaps resembling the ancient Greek conception of Olympus. Since everything in such a world is just information, the "price" of anything in this world would be actually zero[2]. But suppose that we wanted there to be prices, if for no other reason than to build worlds in which scarce goods exist. We would need to construct a scarcity-generating mechanism. After we constructed such a scarcity-generating mechanism, suppose we wanted to build a completely virtual world, just like our virtual Olympus, within the world-of-scarcity governed by the scarcity-generating mechanism. Some of us might argue, "Prices optimally coordinate the factors of production in a condition of scarcity, thus, we should build a monetary system and let the inhabitants of our scarcity-governed world figure out how to build a virtual world like ours, within theirs." But others of us would argue, "This is absurd and a needless duplication of effort. Our virtual world is already free of the limits of scarcity because it is adiabatic - all we need to do is to allow the inhabitants of the world of scarcity to directly copy the rules of computation by which our virtual world operates. Then, they will be existing in the same virtual world of bliss that we inhabit."

I am arguing that we should think of our world as though it were ruled by some scarcity-generating mechanism, embedded within some other, greater world that is free from the constraints that we are bound by. Bitcoin's approach aligns with the thinking of the first group of virtual Olympians. "Build a foolproof accounting mechanism and let the market handle the details." Ethereum's approach aligns with the thinking of the second group of virtual Olympians. "Figure out the ideal coordination of all goods within the realm of scarcity and then automate this with an ever-increasingly-efficient, centralized computation."

But which one is correct? This question is why I have framed the thought-experiment in this Olympian context. I am convinced that they are both correct. They both solve the same problem in a different way. Each solution is its own, unique approach but both solutions work. But the story doesn't end here. If either solution works, then can't we optimize by eliminating one of them? If we get the entire world behind a market-based solution, then that's twice as effective as having only half the world behind a market-based solution. Or, if we can get the entire world to be centrally-planned by a globe-spanning super-mind, that's twice as effective as having exactly half the world being centrally-planned by a hemispherical super-mind. This thought is, however, a category error - if we are dwelling in virtual Olympus, efficiency is irrelevant because efficiency is just a corollary of scarcity. If the problem of scarcity can be completely solved, and if the deepest structure of reality is existing in a state where it is solved, then these two approaches to solving the problem of scarcity must be existing in perpetual harmony with one another.

Another metaphor might help. Consider selection theory. From Wiki: "r/K selection theory relates to the selection of combinations of traits in an organism that trade off between quantity and quality of offspring. The focus upon either increased quantity of offspring at the expense of individual parental investment of r-strategists, or reduced quantity of offspring with a corresponding increased parental investment of K-strategists, varies widely, seemingly to promote success in particular environments." The market approach to social planning is like r-selection - generate many offspring and let the chips fall where they may. Some will survive, many will perish, but whatever remains will work. The central-planning approach is like K-selection. Let's not leave things to chance, let's build a system that works, even if it requires a great deal of resources to get it working. The thesis of this post is that both approaches work - that is, both approaches can, in principle, solve the problem of scarcity.

Returning to our virtual Olympus world, free from the constraint of scarcity, if we were to build a scarcity-generating mechanism inside of such a world and then try to encourage the inhabits of the world-of-scarcity to build their own virtual Olympus, we should expect to see both solutions (market-planning and central-planning) emerge and live in harmony with one another. To say it another way, if the world is not governed by scarcity at its deepest level, then all viable solutions to the problem of scarcity are equally suitable because scarcity itself is contrived, existing solely as a byproduct of some unseen, scarcity-generating mechanism.

Part 1 is here.

[1] NB: Ethereum is a distributed, peer-to-peer network, in the same way as Bitcoin; it is not centrally administered.

[2] Assuming we can compute adiabatically