Ontological Mathematics for Engineers: Blockchain and Bitcoin.
In which we use the language of Ontological Mathematics to help us understand Blockchain and Bitcoin technologies.
- "Mathematics is where essence and existence are identical."
- "Time is the coin of your life. It is the only coin you have, and only you can determine how it will be spent. Be careful lest other people spend it for you.
--- Carl Sandburg"
- "Time is the coin of your life. It is the only coin you have, and only you can determine how it will be spent. Be careful lest other people spend it for you.
--- Carl Sandburg"
- "Blockchain is the original God, Bitcoin its prophet, and the Altcoins are the disciples."
- "Immutability changes everything."
Introduction
In this post, another entry in the Ontological Mathematics for Engineers series (or its implicit co-series Engineering for Ontological Mathematicians), we primarily focus on the Blockchain and, to a lesser extent, its more widely known cousin Bitcoin. What makes this write-up unique is that we will be using the language of Ontological Mathematics (OM) to help us achieve our objectives (although "OM-like" or "OM-inspired" is probably a more accurate description).Once again, as in the case with computer science monads for ontological mathematicians, we use the powerful yet nuanced expressiveness of OM to give us deeper insights into the technology at hand, and in turn we symbiotically use the language of Blockchain to concurrently deepen our understanding of OM.
I just about guarantee you won't hear this comparison made anywhere else (*1).
(*1) Mostly because the OM community is tiny, and although the Blockchain/Bitcoin community is rather sizable, the intersectionality with OM is also tiny. In short, Bitcoiners don't know OM, and OM'ers don't know Bitcoin (and, quite frankly, most engineering/Computer Science topics either)
Blockchain
The more fundamental, and thus more interesting, technology is Blockchain. Bitcoin is built on top of Blockchain, so most, but not all of the "magic" of Bitcoin comes from Blockchain, which is why we will concentrate on it.Intent vs Implementation
There are two perspectives from which to understand Blockchain: the intentional and the implementational (*2).The intentional perspective, or the efficient cause, is the why -- the high-level understanding of the potential applications of Blockchain. Things like how trust is built into the substrate itself, and that it doesn't require a third party to impart trust (something known as disintermediation). These are intentional characteristics. You can think of the intentional perspective as the semantics of Blockchain.
the implementational perspective, or material and formal causes, is the how -- the low-level structures and technology that Blockchain is actually built with. Things like SHA-256 numbers, and how it uses a distributed network of nodes with a 51% voting algorithm. These are implementational characteristics. You can think of this perspective as the syntax of Blockchain.
Most people will find the high-level intentional aspect most interesting. However, in this post we will concentrate on the implementational aspects. This is for several reasons. The main reason is the OM perspective most congruently applies to concepts at the implementational level. The other reason is that there are other much better sources to get the high-level intentional characteristics than this post. Indeed there are hundreds of books written on the subject, as well as countless YouTube videos talking about this perspective (*3).
(*2) Intent vs Implementation:
When arguing with someone, something I like to say is "I like your intent but not your implementation" (or vice-versa). It's kind of a polite, back-handed way to say you disagree with somebody, but it's just nerdy and over-the-top enough that most people don't get defensive.
Another variant is "I like your topology but not your geometry".
(*3): The three books I read in research are:
Life After Google: The Fall of Big Data and the Rise of the Blockchain Economy, George Gilder, 2018 (highly recommended and very approachable)
Blockchain Basics: A Non-Technical Introduction in 25 Steps, Daniel Drescher, 2017 (definitely more technical).
Double Entry: How the Merchants of Venice Created Modern Finance, Gleeson-White, Jane; 2011
Fortunately, learning Blockchain at the implementational level, while challenging, is more fruitful than the intentional level because it's at this level that you can, ironically, more easily understand the why of Blockchain: it's potential and limitations, much better than you can with the traditional "why" of intentional analysis. And there's less of a feeling that you're simply drinking the Kool-Aid that the traditional high-level perspective provides.
However, the implementational level is normally hard to grasp unless you have a background in Computer Science. But we can circumvent this by using the language of OM which is a powerful fit for describing Blockchain (for instance in seeing it as a being database composed of dimensionless numbers as we will soon see)
What is Blockchain
However, before we can really get into the implementational level, I have to at least provide some sort of brief high level overview of what the Blockchain is. Wikipedia provides some technical aspects..... a growing list of records, called blocks, that are linked using cryptography...An intuitive series of descriptions that I would like to offer foreshadows some of the OM terminology we will be using:
... an open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent way
... a decentralized, distributed, and oftentimes public, digital ledger that is used to record transactions across many computers so that any involved record cannot be altered retroactively, without the alteration of all subsequent blocks
... A linked list that uses dimensionless "natural" numbers as addresses.The main importance of Blockchain is that it provides a secure and trusted way to represent data such that it can be made publicly available in a secure fashion, yet still allowing for reliable controlled change. One of the big potential cultural level changes it can provide is that it obviates the need for a third-party intermediary to verify trust -- trust is architected into the system, baked into the substrate itself, and thus you no longer need credit card companies or governments to mediate or enforce transactions. Transactions can now be fully peer-to-peer.
... A database of pure being, as opposed to a database of becoming as is typical.
... A noumeal database reified into the phenomenal domain.
... A transcendent-(like) database made immanent.
Blockchain is a natural outgrowth of early mp3 Napster-era file sharing protocols like Freenet and Limewire. Also important is that it is one of the few technologies that "tilts right". A lot of other technologies like aerial drones, facial recognition, nuclear fusion etc. "lean left", that is to say favor big institutions, big governments, and authoritarianism. Blockchain, by tilting right, favors empowering individuals, so it is generally considered a very "libertarian" form of technology.
Once you learn about this technology and begin to really appreciate it, you can see why some people are proclaiming Blockchain as a revolutionary advance: a next-generation technology that will take us into a financial golden age, fundamentally restructuring our economy and financial systems. I used to think this was just hyperbole from newly minted Bitcoin millionaires and their self-serving agendas, but while the cynic in me says this is still largely true (there's nothing like making millions of dollars to make a "true believer" out of you), most of the "Bitcoin Illuminati" profess that Blockchain is the revolution, not Bitcoin, partially contradicting the premise that that it's entirely self-serving.
However, while Blockchain certainly has the potential to live up to this hype, that doesn't necessarily mean that it will. For instance, there are some serious performance issues that need to be overcome, as well as hostility from incumbent financial entities esp. governments issuing fiat currencies. Blockchain is not in the best interest of many large institutions, and their legions of elite bureaucratic Mandarins. Indeed, cultural blockage is probably more of a serious impediment than technical blockage.
On Double Book Accounting
The rise and metamorphosis of double-entry bookkeeping is one of history’s best-kept secrets and most important untold tales. Why? First, because it arguably made possible the wealth and cultural efflorescence that was the Renaissance. Second, because it enabled capitalism to flourish, so changing the economies of the world forever. Third, because over several centuries it grew into a sophisticated system of numbers which in the twenty-first century governs the global economy. This medieval artifact is still in daily use around the world.
Gleeson-White, Jane. Double Entry: How the Merchants of Venice Created Modern Finance (p. 8). W. W. Norton & Company. Kindle Edition.There is however one intentional aspect that is not widely noted that I'd like to discuss: the realization that Blockchain is the logical successor to Double-entry bookkeeping.
In order for the magnitude of this statement to sink in, one needs to have the proper appreciation for how important a technology double-book accounting actually is.
At its core, Double-entry bookkeeping is basically calculating liabilities and assets as two separate processes. Without getting into too much detail, this confers the ability to have separate people working on each section, which greatly reduces the risk of fraudulent activity.
Double Book Accounting allowed businesses for the first time to be run by people other than close family members. It allowed public corporations to exist for the first time, and led to things like public stock markets. In other words, it allowed business entities to go from the individual level to the cultural level. Likewise, I would assert that Blockchain allows us to go from the cultural level to the inter-cultural level, or maybe even the universal level. The ironic thing is Blockchain does this by empowering the individual (allowing for disintermediated peer-to-peer transactions). So by restoring the proper balance and authority to the individual, it enables further cultural/collective integration.
Technologies do not have to always be complicated like computer chips. Some of the most impactful technologies are the most basic. Double-book Accounting is almost hidden in plain sight -- it was almost like a discovery not an invention. It's such an easy variant over simply redundantly calculating things twice, but the impact is huge.
Dimensional vs Dimensionless Numbers
So finally we can now get down to some Ontological Mathematics (OM) concepts.At its most fundamental level a Blockchain is, well, a chain of blocks. Where a block is just some data structure, be it a representation of a bitcoin, an Employee object (i.e. a model of an employee in a business app), or just a string of some sort. Another name for a chain in Computer Science is a linked list. It's basically just one unit of data with a pointer to the next:
(data 1)[pointer to next block] -> (data 2)[pointer to next block] -> (data 3)[pointer to next block]..etc
Or more visually:
These pointers will be the memory address within the computer where the data resides. Those addresses will vary from computer to computer, and even over time as the app is run on the same machine, thus you can say the pointer is substrate dependent. It's a relative offset, and a dimensioned number. In other words, if the pointer has a value of 5000, it means either the address is 5000 bytes greater than "here" or it means absolute memory location 5000, either way it's a relative number -- relative to the computer it's running on. It doesn't make sense to say the address of the data block is "5000": you have to supply some unit and a context. So 5000 implies 5000 bytes.
Just think of that 5000 as an observable/empirical number that determines where the next data block resides in space and time. That's basically what I mean by a dimensional (or dimensioned) number. If I talk about the "document at memory location 5000", we had both better be on the same page if we are trying to synchronize. You also have to trust that what I put at memory location, is what's actually still there when you look at memory location 5000.
Dimensionless Numbers
Then there's the concept of dimensionless numbers. These are essentially pure numbers that have no units. There are very few things in the real world that can be described by dimensionless numbers -- they are typically only appropriate for concepts in the Noumea (or "math" domain). For instance, imagine I said that I was "five". Of course most people would assume I'm talking about age in years. But what if said I was talking about length. Then you would have to know if I meant feet, meters, or inches. If I told you "feet", you would have know what part of my body I was referring to. In short, simply saying you have "five" of something has no meaning unless there's a unit and context. And the percept of the concept "five" will have a different relative meaning depending on the unit and the context. However, as a pure number "five" (or "5") has an absolute meaning independent of unit and context. For instance, I know that 5 is half as much as 10 and this is true always, anywhere or anytime: 5 feet is half as long as ten feet, 5 hours is half the time as 10 hours etc.. As a matter of fact you can think of a dimensionless number as being completely outside of space and time in pure "being".So dimensioned numbers are phenomenal, relative, contextual, substrate-dependent, in space-time and represent becoming. Dimensionless numbers are noumenal, absolute, context-free, substrate-independent, outside space-time and represent being.
SHA-256 numbers
To me, the single most important technology of Blockchain is the fact that it uses SHA-256 numbers for addresses (A blockchain will still use relative addresses as a physical necessity, but the SHA-256 now becomes the primary logical address used for identification). A SHA-256 number (pronounced "shaw 256") is a 256-bit "digest" of a text document. That it to say, every document can be mapped to a unique SHA-256 number. A SHA-256 is 256 bits and that means there a 2^256 or 1.1 x 10^77 possible values. As a point of reference there are 10^80 number of atoms in the visible universe, and 7.5 x 10^18 grains of sand on the earth.While this is a large number, it's obviously less the number of possible documents, which is infinite of course, but practically speaking the odds of you ever finding two documents that have the same SHA-256 number are astronomically small (*4), thus you can think of the SHA-256 number for a document as being its "document number" in document space. So let's say the SHA-256 number for the string "Hello World" is 42. Then you can think of there being a large library of pre-existing documents, such that if I gave you "42" you could then look into the library and determine that I'm referring to the document that has "Hello World" in it. One other document that would also be in there would be "War and Peace" by Tolstoy, but the vast majority of documents would be complete gibberish.
(*4): This is not true for SHA-1 numbers, which are "only" 160 bits. In 2017 someone actually discovered two different documents that generated the same SHA-1 number, known as a "hash collision". Of course, doing this required a massive computational effort as well as using a newly discovered algorithm that was 100,000 times more efficient at finding duplicates than simple guessing.
Note, the beauty about SHA-256 numbers is they are always 256 bits, whether the document it is applied to is 8 bytes or 20 terabytes. Another way to assign a unique number to a document would be to just simply consider it's binary representation to be it's "number" (this is essentially what Gödel numbering is). Thus the string "abc" would be (in ASCII) "616263" since a=61, b=62, c=63. The drawback with this scheme is the document number for a 20 tb document would itself be 20Tb long -- not very practical to consider as pointer or proxy for the thing itself.
Now, if you can think of SHA-256 numbers as being addresses in "total document space", when the data I'm pointing to is the string "hello world" I append to the physical memory location the SHA-256 number is as well. Then when I look at what is actually at memory location 5000 (as previously mentioned, you still need physical pointer) I can verify that the SHA-256 number for the data at this location is the same as the SHA-256 number in the pointer, thus allowing for disintermediation -- I can verify for myself the data has not been altered without having to rely on someone else. (*5).
(*5) How can you verify that the program that calculates the SHA-256 number has not itself been corrupted? Easy, you take it's SHA-256 number using another version of a SHA-256 program and verify it has the correct SHA-256 number. Of course you have now introduced a recursion: how do you verify that this other SHA-256 program is not corrupt? You verify it with yet another SHA-256 program. Eventually, you would get back to the first SHA-256 program ever written, which of course could not have been verified by another SHA-256 program. You have take it as an axiom this root program is not corrupt. Thus, at the very base of the chain of trust is a small amount of faith -- that the first SHA-256 program was indeed correct. It's funny how in any rational based system, you need at least one axiom, basically something that you just have to take on faith, to anchor the whole system. This is the role the PSR (Principle of Sufficient Reason) serves in OM. It's basically a small bit of "faith" in an otherwise faithless system. It's like the small seed of the "yin in the yang", or the male in the female, in the yin-yang symbol AKA the great monad. Thus every rational system is "tainted" in a small way by faith, which is what I call a "controlled paradox".
The ultimate "controlled paradox" is how zero actually contains a totality -- that is to say nothing is something. A very special type of something -- a controlled nothing (one that adds up to zero globally , but not locally, or a something that is a tautology of nothing). True controlled paradoxes are not actually paradoxes (to the left of "doxa" on the [Plato's] divided line), but are arguably super-rational or trans-rational, that is to say to the right of "ratio" on the divided line. To understand a super-rational system require intuition not language -- it's beyond the ability of math to capture it's essence.
But now we're getting way off topic.
So let's say the sha-256 number for "abc" is 1 (it's real SHA-256 is 03cfd743661f07975fa2f1220c5194cbaff48451) and the sha-256 for "hello world" is 42 (it's really 22596363b3de40b06f981fb85d82312e8c0ed511). Now I can think of my linked list as being:
("abc" 42) -> ("hello world" 1) -> ("abc" 42)
That is document node 1 ("abc") points to document node 42 ("hello world") , points back to document node 1 ("abc").
At any point in time I can easily verify that the data block "hello world" in fact equals the expected SHA-256 number of "42" (SHA-256 numbers calculate in milliseconds for small files, but I just did a test on a 500 MB file on my laptop and even that only took about 3s). In other words, "trust" is built into, or architected into, the substrate.
This is very similar to the way "trust" was built into double-book accounting. With double-book this trust allowed for the transition from family to publicly-owned businesses. With Blockchain it allows for disintermediation, or the removal of third-parties from a transaction. So now you can have trusted peer-peer transactions between two strangers without a middle-man such as a credit card company. That's a big deal. It may not seem like it at first, since we're so used to everything being mediated, but if you think it through and all the ramifications of what this now enables, it's a revolution.
Your linked list can now use "natural" address space numbers. SHA-256 are basically dimensionless, pure numbers outside of spacetime. They pass the litmus test for being a dimensionless number in that they don't require any units: "abc" is "1", and "hello world" is "42" (or more technically "abc" is isomorphic to 1 and "hello world" to 42). You don't need units such as "bytes" or "feet".
Being vs Becoming
Another property of blockchains is that they are immutable. Note: they are only physically immutable. Logically, they are mutable. Here's what I mean. Let's say you have a variable "a" and it's set to a value of 5. Let's say you want to alter this to be 6. If you were to update a, it would allow this to happen by creating a new variable, also called "a" (but maybe more appropriately named a-prime since it's a different "a"). The original a would remain unchanged since it's immutable. That's what I mean by physically immutable. But you could also think of the new "a" as being an updated "a". That's what I mean by logically mutable. It's just like you as a person over time. Are you the same person you were a second ago? What about the same person when you were first born? What about when "you" were just an ova and a sperm? Every second of the day, you are physically a slightly different person than you were before. However, there is the persistent illusion that "you" span all these different states. It's an illusion, but a very powerful one.The Clojure programming language has spent a lot of time working out the properties of an immutable memory model and they have an interesting article on identity, entity, state, and values here.
Anyway, these all get into the OM concepts of being vs. becoming. Being is eternal and outside time, but it doesn't necessarily have to be static. It can accommodate variation by have new being states. Becoming is a space-time concept. It is about change and erasure. Most computer databases are mutable, which represents the concept of "becoming". An immutable database, on the other hand, is associated with "being".
Blockchain OM concepts.
So those are two big OM(-ish) concepts of Blockchain. The fact that they use dimensionless numbers from the Noumenal or Math domain, instead of dimensional numbers from the Phenomenal or Scientific domain, and the fact that the DB is "being" not "becoming" e.g. "controlled" immutable vs mutable.We'll talk more about what insights this gives us at the end of this post.
DNA vs RNA
I would like to briefly mention two more perspectives that were edifying to me when learning about Blockchain. However, they come from science not OM.The first is an analogy with DNA (to a normal DB's RNA). DNA is essentially double-stranded RNA. RNA was the precursor to DNA (see RNA world). RNA is good for storing information, but the problem it's not stable enough. It's too easy to change. DNA is the next version of RNA, the double-book accounting or the blockchain version of RNA, if you will (Actually I would say DNA is double-book accounting version and the brain, in relation to memes instead of genes, is the blockchain version). Blockchain is very robust and stable. But it still allows for change. The primary way it can safely assure safe change is through the concept of having many distributed copies and then having a 51% voting algorithm before updates are accepted.
This concept of stability becomes evident when you consider the Bitcoin blockchain. As of this writing, all bitcoins have a net worth of approximately 120 billion USD. Think about that. There is a publicly available "account" (or database), that anyone can download and indeed anyone can alter, at least locally. However, no one has ever been able to hack this DB to covertly re-assign bit-coins (most bitcoin-related crimes involve stealing people's crypto-keys which allows them to indirectly re-assign coins).
Let's pretend Bill Gates had all his money in a single account, say on Charles Schwab, and that he publicly released this account number and made all the information publicly available. How long do think it would be until it got hacked? The money would disappear in short order, even with all the tacked-on security of Schwab. That is because the substrate in a traditional database is itself not secure -- i.e. it's not secure by design. Security and controlled changed is baked into Blockchain in the substrate itself. It has an almost mathematical level of security baked into the substrate or architecture itself.
In other words, Blockchain is DNA to a standard DB's RNA.
Quantum Entanglement and Superposition
The last analogies that helped me were to think of the nodes in a blockchain as being quantumlly entangled particles, and the various copies, running on different servers as being quantumly superimposed particles. I'm not going to belabor these analogies too strongly here, in the interest of length and the fact that my target audience is OM's. But suffice it to say, a blockchain is sort of like an un-collapsed quantum wave, that is to say very delicate where one bad quantum input or observation can collapse and corrupt the entire structure, not just an individual node. This is a rough metaphor of course, but it's another way Blockchain maintains its integrity. This feature makes it obvious when the global "wave structure" has been collapsed, and thus corrupted.Practical Consequences
So what do we gain by looking at Blockchain from an OM point of view? First of all, it gives us a more expressive language for understanding Blockchain concepts at a deep level.For example, which do you think is a deeper description of Blockchain?
- A decentralized, distributed, and oftentimes public, digital ledger that is used to record transactions across many computers.
- A dimensionless numbered, being database, that is DNA-like and quantum wave like: the transcendent made immanent.
(*6) Blockchains: "Being" databases in a "becoming" world, reminds me of the Metallica song "The Thing That Should Not Be". Blockchains are syntactical and coherent compared to a traditional database that is semantic and correspondent. They are a fish out of water in the material world -- the transcendent made immanent (of course, this is also what gives them their power), just as "becoming" is out of place in the "being" world -- the immanent made transcendent. The thing that should not be indeed.
It's the Questions, Stupid.
One concept I've gained an appreciation of from studying OM, and philosophy in general, is that questions are first-class peers of answers: getting good answers is only useful if you ask good questions. It's GIGO (garbage in garbage out) otherwise i.e. getting "good" answers to bad questions is not useful, maybe even counter-productive.This may seem obvious, but I didn't figure this out until just a few years ago, after realizing I'd spent about 25 years in various jobs I really shouldn't have been in (while they may have been close, they really weren't my true passion). Throughout my career I asked the "good" question "How can I get ahead in my career?" and was getting "good" answers such as "work hard", "study x,y,z" etc, but I de-emphasized the more important questions "What do I really want to do?" "What do I like?", "What am I good at" etc. By not asking the right questions, what I ended up doing was a lot more accidental and less intentional than I would have liked. Using the proper model, will help you ask the right questions.
One point of view gained from employing the OM perspective is that Blockchain is qualitatively different than a traditional database. Blockchain is being-centric, traditional dbs are becoming-centric. The difference is not one of quantity but quality. For example, blockchains are notoriously slow -- transaction update times are measured in minutes, whereas traditional database transaction times are measured in milliseconds if not nanoseconds. In other words, Blockchain is 9 or 12 orders of magnitude slower. I think the common perception is that Blockchain is slower simply because of a quantitative difference i.e. that if you just have to write the code a little faster or throw a bunch of hardware at it you could rectify this problem (*7). So a common question to ask is "How can you make Blockchain faster, or as fast as a traditional db?", but by understanding and appreciating the slowdown due to the impedance mismatch of running a "being" database in a "becoming" (space-time) context, you realize you need to ask the more appropriate question "Can Blockchain actually replace all traditional (becoming) dbs?", "Where is it appropriate to use Blockchain vs a traditional dbs?". The answers to these questions makes you realize that perhaps only a certain class of low-activity transactions, such as escrow transactions when buying a house, is practical with Blockchain.
(*7) Note: Visa does 1700 transaction/second or 150 million transaction per day. It's hard to see Blockchain ever scaling up to this level even with massive hardware improvements.
So thinking of Blockchain in OM terms makes you ask the appropriate questions, and thus get better answers. I think this is a subtle but very important point.
On the topic of scaling, could Blockchain technologies ever replace credit cards? This is very important because right now everything you buy with a credit card is recorded by a third-party (the credit-card company). This is unlike cash where only the two parties are aware of the transaction. Let's face it, eventually any data collected by large entities will be used against you. You may find someday you're unable to get health insurance, or it will be very expensive because you eat too much fast food, or drink too much etc.
One possible solution is to have a traditional db with some money in it, say $1000 to front-end the transactions in real time, and to subsequently be replenished (minutes later) once the Bitcoin transaction settles. However, does the introduction of a traditional mediated transaction on the front-end "taint" the entire process?
On the other hand, is having a mediated transaction all that bad, anyway? After all the credit card companies pay for any fraudulent activity (of course the argument with bitcoin would be you would have much less fraudulent activity in the first place). My goal here is not answer these questions, just to mention that they are difficult problems, in a subtle kind of way, that requires a powerful nuanced language to disentangle them, which, as we previously discussed, is where OM plays an important role.
Conclusion
So maybe it was a little ambitious to attempt, in a single blog post, to explain some of the deeper insights I gained from looking at Blockchain from an OM perspective (as well as a scientific perspective with the DNA and quantum mechanical analogies).But I have three meta-goals that I hoped to achieve.
First and foremost, is to show that Ontological Mathematics is useful for describing everyday "ordinary" technologies, and not just useful for the universe as whole or at the "Theory of Everything Grand Unification" level. As above, so below: the syntax and rules used by the universe above echo below.
Second, is the reverse of meta-goal one: using the language of Blockchain to help reify certain concepts in OM -- Blockchain is basically a noumenal concept made actual in the phenomenal world (transcendent made immanent), and thus takes some of the "mystery" out of the Noumena.
Third, is to simply make people interested in further learning about Blockchain and Bitcoin, and to realize that they are very powerful, potentially cultural and financial altering technologies, and not just the latest buzzword-de-jour as hyped by newly minted Bitcoin millionaires.
I can testify that time and time again OM has greatly increased my understanding of Engineering and Technology systems, and I want to share OM with world, and motivate others to learn it. Then hopefully there will be more people using this wonderful shared language from which I can then in turn further learn from them.
Update History:
2020-07-06: Minor grammatical edits.
2020-09-21: Yet more grammatical edits.
I briefly touched on the difference between paradoxical and super-rational in this post on Blockchain.
ReplyDeleteIn the comment after this coment (unfortunately, I'm maxing out on the 4096 char. limit) I include a more detailed discussion from a post I originally made to the Illuminatus Pythagoras YouTube channel (https://www.youtube.com/watch?v=IBLuy3MJ0xQ&t=4s) on this topic, which I think some readers might find interesting:
There were a couple of things you said I would like to offer some feedback on, though. The comments have to do with your usage of the word "paradox":
ReplyDelete@7:30: "logic ends in paradox"
"People are drawn to videos like this because they've arrived at some of the fundamental paradoxes of existence. People who haven't' embraced paradox will be disturbed"
@12:35: "Ultimate reality is fundamentally paradoxical."
"And I think this is true because, paradoxically, only a paradoxical reality, which can't logically exist, can logically exist"
comment: I think it's important to distinguish between "paradox" and "supra-rational". Note: I learned about this from systems researcher Kent D. Palmer at schematheory.net. In his tutorial from June 3, 2014, he gives a great analysis of Plato's divided line that I've never seen anywhere else. Basically, there are two main sections to understanding: doxa, and ratio. Doxa is opinion: grounded and ungrounded, and ratio is about reason: representable and non-representable. Naturally, doxa is considered to be a lower form of understanding, and is the domain of faith. Ratio is considered higher and is where math and philosophy reside. But there are two implied regions that are not officially part of the divided line: the part to the left of doxa (paradox) and the part to the right of ratio (suprarational). When you say "para-dox" what you're literally saying is below Doxa, or lower than the lowest. Doxa is the realm of contradiction, absurdity, and inconsistency. Not "fake" absurdity, but true absurdity -- like saying something is true and false. Suprarational, on the other hand, is even higher than rational. It's the highest and best form of understanding. It's like infinite intuition, for things that can't be understood rationally. Paradox and suprarational are inverse duals, and often conflated and/or confused with each other. Things, when expressed in the wrong or limiting language that are paradoxical, can become suprarational when expressed in the right language, or when looked at in the right way. Koans are a perfect example. Westerners interpret them literally and thus consider them paradoxical. But it you interpret them the right they become suprarational: deep truths. Think of a quantum wave. When the wave is not collapsed, we accept that the photon can be in two places at the same time -- it's suprarational. But when you collapse the wave and try to claim the particle is in two places at the same time, we say that's absurd, a paradox. Either the particle is one place, or it's two particles.
So while it may be true that the universe is paradoxical at one level, I think it's really ultimately suprarational, and it only seems paradoxical because you're using the wrong language. I'm not trying to come across as a nitpicker -- I realize you're probably using "paradox" in the vernacular, or are trying to emphasize the actual paradoxical aspect. But by only using paradox you don't emphasize the suprarrational aspect. Indeed, I think you might be saying "pardoxical" when you really mean "suprarational". Saying the universe is paradoxical is the same as saying it's chaotic. Basically, I think the comments you make about "paradox" would be more precise if you used "suprarational" instead.
"So, to realize when opposite things can be true at the
same time, without conflicting, that’s the super-rational. In
our tradition, we don’t understand the super rational very
well, but there’s other traditions like Zen Buddhism that is
rooted in the understanding of the super-rational. When we
interpret them based on the idea of that they’re just
paradox or absurdity then that just shows our ignorance
because we don’t understand the super-rational in our
tradition very well."
-Kent Palmer