You'll find these in reverse chronological order because I'm not insane
Sup people. Ex fizz, back at it again, trying to understand reality. So as I mentioned a couple posts ago, I’ve been working a bit more on Orchid, because I’m pretty sure it’s the only way. However, in bathing myself repeatedly in the hot, soupy stew that is fundamental mathematics, I’ve been forced to think a bit harder about certain things than I normally would. Like, for instance, “what is information?” Now all you information theory nerds can go wallop some cows for all I care, because typically discussions pertaining to information theory disintegrate into nonsense about entropy and other such jazz. And, allow me to be vulnerable for a sec, I don’t care enough about entropy to have studied it enough to know what the frack information theorists even care about. So maybe I’m just dealing with the same problems as them.
So let’s cast information theorists aside for a moment and return to first principles in these matters. Let me first ask a question: what is information? And now, let me answer it. As best as I can tell, information is a correspondence between the configurations of several (sometimes unrelated) stable systems. I realize that’s not super helpful, so let me give you an example from cave man days, because those are my favorite examples.
Let’s say we have two cave men, Dave and Thnead. Dave and Thnead enjoy being alive, and are therefore wary whenever they are approached by a saber-tooth tiger or an allosaurus. Both of those animals are big red flags to Dave and Thnead and typically spell out a gruesome bloody demise. Let’s say Dave and Thnead keep their best weapons at the back of their cave to protect them from the weather. Now then, Dave and Thnead take turns keeping watch during the night to minimize the chance of gruesome death by wandering saber-tooth tiger or allosaurus.
You know what, Dave and Thnead might as well be gay. How’s that for character building? That helps the analogy because now they have a good reason for wanting each other to stay alive.
This is an egregiously drawn out analogy, but let’s say Dave and Thnead come up with a system. If the boi that is keeping watch during the night sees a mean beasty, then that boi will throw small rocks (the type that float) at the back of the cave to wake the other boi up. Now then, everyone knows that rocks are better than sharp sticks for attacking saber-tooth tigers, and sharp sticks are better than rocks for attacking allosauruses. Because of that, our bois agree to throw one rock to the back of the cave if a long toothed tiger is spotted, and two rocks if a large reptilian fang-lord (allosaurus) is spotted, simply so that our bois are best equipped to fight whichever beasty they may encounter.
Dang that example was way shorter in my head. It’s literally equivalent to “one if by land, two if by sea” but we’ll ignore that for now.
Anyway the whole point of that written charade is to emphasize the correspondence between the number of rocks thrown and the type of beasty strolling by in the night. Even though there doesn’t seem to be any inherent tying the type of beasty to the number of rocks thrown, this system allows information to be passed between our lads.
So then, we get to the question that be-titles this post: what the flip-shack frack is a definition?? You may be wondering why this is important. Well, intellectually endowed reader, the notion of a “definition” is the only reason why the number of rocks thrown to the back of a cave has any correspondence to the nature of the animal that lurks in the darkness. Otherwise, those two systems have absolutely no meaningful connection.
The reason why I care about this is because I’m attempting to determine the extent to which information is fundamental to the universe, and the extent to which information is a human construct. It has become crystal clear to me that in any system within which there exists some notion of forward progressing time, the most fundamental entity is a stable system. The question, then, is whether information as we know it exists on a fundamental level or on the level which is only meaningful to the entities known as humans. And the answer to that question rests on the true nature of a definition.
While I’ve been writing this, I think I’ve stumbled upon something major. A definition is only meaningful if the source of the definition is itself well-defined and perceivable. Ah yes. That’s it. Well I just wrote three pages to answer my own question. I suppose before I wrap this up, I should explain my realization. Definitions are themselves merely characteristics of stable systems. Why does the character sequence “r-e-d” mean anything to you? Because you know that whenever I’m trying to describe an object that’s giving off electromagnetic radiation around 700nm in wavelength, then I will use the character sequence “r-e-d.” Thus even if you aren’t in the room, you now have a clear idea of the nature of the light coming off the object and entering my eyeballs.
So basically definitions and information are just “if, thens.” For example, in the case of our cave men, the following statement describes the stable behavior of one cave man “if [boi] sees allosarus, he will throw two rocks. If [boi] sees tiger, he will throw one rock.” Therefore the presence of a thrown rock immediately yields the other boi information on the nature of the beast outside the cave. Cool!
If you’re wondering why any of this is actually interesting, email me and I’ll do a better job of explaining it. Otherwise, bye bye now!
What is poppin, boys and girls?? It’s your boi, Daniel frikin P. finally back from the dead yet again to give you some sweet, sweet content. Well, I suppose that’s a bit of a lofty claim. If web app forging, or general software corralling falls into your category of sweet, sweet content, then, well…I’m your man.
Let me immediately address the beluga in the room (I feel that the particular topic at hand is more egregious than what is typically correlated with your standard “elephant in the room” cliché, so I have appropriately replaced elephant with a more egregious entity to find in your room, namely the beluga). I, Lord Ex Fizz, have not posted any content in what feels like a decade. I am not sorry, and I don’t repent. If at any point you were invested enough in my postings to care about when I put something new on the ol’ site-erino, then perhaps you feel as though some sort of fizzy apology is in order. I love you dearly, should you find yourself in this category, but frankly, my lack of posting is none of any of our concerns.
As you may have guessed, I haven’t been writing ex-fizzicle content simply because I have been coding. Somewhat non-stop. What have I been coding, you ask? Well that’s the point of this new project, so tighten your belts and shoelaces, and settle on in.
Let me weave you a tale. At the beginning of human existence, before any notion of a social contract, humans essentially existed in a state of anarchy. If I looked over and saw you holding a really cool looking rock, then by golly, I’d go over, smash you in the head with another worse rock, and take that beautiful orb you’re holding right out of your hands.
Smashing other humans in the head is all fine and good, but what happens when a bigger boi comes along and wants my rock? Well, friends, I’m finna get smashed, and that’s a fact, jack. Now, brethren and sisthren, ya boi ex fizz is not in the business of getting smashed, so what do I do to prevent that? Well, I form a social contract with the bois around me. I may not be able to steal whatever I want from weaker human, but there’s a much lower chance of me getting smooshed, and that’s just really fantastic.
If you extend this notion more, you end up with a government. Healthy governments are pretty fantastic because even though not everyone has a perfect moral system that would perpetuate a healthy society, the blessed government provides a series of incredibly potent incentives for acting as though you do. To put it in a less overtly verbose way, if I smash someone in the head, I’m probably going to jail for a long time, so basically, I’m not about to go out on the street and start smashing people.
Now let me weave you another tale about the human experience. Around the turn of the century, humanity was reborn, not of flesh, but of ones and zeros, binary. With the advent of social media, humanity was able to assume a new digital form of being that afforded a set of experiences and abilities previously impossible.
However, much like the early stages humanity, we see in typical social media settings that there are no systems in place (like governments) that incentivize good behaviors. Sure Facebook and Twitter are desperately trying with their moderators and censorship, but that is mostly causing a whole lot of outrages, and the solutions they are implementing typically in no way scale with the size of the user base.
The effect of this, as especially seen on Twitter, is a huge population of humanity that essentially exists in a state of unregulated anarchy. And while the consequences of negative behavior may not threaten a person’s physical well-being (except in some cases – I’m looking at you, cyberbullying) they certainly take a non-trivial toll of people’s emotional well-being.
AT THE SAME FRIKIN TIME, the blessed, blessed internet is simply one of the most fascinating and impactful technologies ever developed. The level and speed of connection it provides is simply staggering. The fact that I can host an API in Ohio that I can access in milliseconds from Colorado, well, it’s simply breathtaking. Put in a more relatable sense, I, Danny boi G, can talk to someone in Singapore with millisecond latency. We take that for granted, but I mean, that’s literal insanity.
Anyway, why do I care, aside from my natural inclination towards juicy, juicy tech? Well, despite the extreme toxicity that something like twitter propagates, my hypothesis is that the absolutely insane level of connection afforded by the internet should be able to be used in a manner that benefits humanity and brings us together, rather than tearing us apart.
Now then, let’s get down and dirty with the Parleya experiment. I’ve identified three fundamental processes that are integral to the continued development of humanity.
Connection – human beings need to be able to cooperate in order to accomplish anything. If you live in America, you’ll notice we’re being torn apart by political and social issues, which introduces a wide variety of barriers to continued progress.
Accessibility, Integrity, and Quantity of Information Transfer – In order for human beings to effectively utilize stable subsystems to build stable and sustainable solutions to problems, they must attain the best possible understanding of both the problems they face and the tools at their disposal to solve said problems. Right now many news and media have strong incentivizes to mischaracterize problems due to political agendas, the desire to produce interesting content, and other things of that nature. In order to move forward, we must create systems that incentivize the propagation of accessible information that accurately characterizes the true nature of the information in question.
Analysis of Information – As previously mentioned, forward progress necessitates the use of stable systems to build solutions to problems. In order to build sustainable solutions to problems, we must understand the tools at our disposal, which necessitates a clear understanding of the relevant systems that can be utilized for our benefit.
Yikes that was long winded. Anyway, Parleya aims to address topic number one, ie connecting people. Specifically, the goal of Parleya is to build a platform that incentivizes healthy conversation about traditionally polarizing or controversial topics. If we’re actually good friends in real life, then you’ve heard me talk about Parleya for sure. I just haven’t blogged about it yet because for some reason I didn’t want to.
It has become apparent, however, that I should be providing some level of log to this project, because it’s essentially a scientific experiment. Well, I suppose any startup can be classified as an experiment, but especially this one, because the goal is clear, and the solution is not. Anyway, the purpose of this project is to log my hypotheses, observations, and conclusions with regards to the solutions I try for Parleya.
If you’re wondering what I’ve been coding, it’s Parleya. I’ve been working on it since the end of June, and I just finished the MVP. Shoot me an email if you’re interested in testing out the MVP.
Anyway, as previously mentioned, I’m going to write out my initial hypothesis for the first iteration of the project. Here goes.
As I mentioned, one major problem that I’ve identified with most major social media platforms is the fact that there are essentially no incentives against poor, unproductive behavior. If Kylie Jenner tweets something about her dog, there’s basically nothing stopping me from calling her a selfish whore, just because I’m feeling cranky.
Now, as is somewhat evident, this sort of name-calling behavior, and the ease with which twitter users can mock and dunk on each other does not in any way produce particularly meaningful discussions. Thus the principle goal of Parleya is to find a conversational structure that disincentivizes negative behaviors. Here is my first hypothesis for such a solution.
In a hopefully scientific fashion, I shall lay out the central assumptions I’m making about internet users.
If people are on Parleya, they want to interact with other people. The internet is boring even for trolls if nobody interacts with them.
People typically do not enjoy interacting with people that are obviously extremely aggressive or quick to post personal attacks against other users.
People typically do not enjoy interacting with people who are obviously over-sensitive and unwilling to engage with opinions other than their own. These are the assumptions I’m making. Now let me tell you how Parleya v1 works.
User one posts a conversation about a controversial topic. User two does not agree with user one’s point of view, and therefore posts a mean message with an emotional attack against user one. User one doesn’t like this one bit and decides to block user two’s message. Ok, Danny, I hear you saying. You’re describing social media. What about this is any different from anything else? Well, blessed reader, sit down, hush up, and let me frikin tell you.
The reason why Parleya is different is that conversations and messages are largely anonymous, but three numbers are associated with every message or conversation someone posts on Parleya. Here they are:
The number of times the user has had a message blocked
The number of times the user has blocked someone else’s message
The number of successful conversations of which this user has been a part
You may immediately see why this is useful. If your first number is high, then perhaps you have posted a lot of overly aggressive or offensives messages that people have blocked, which implies you’re not a good conversationalist. If your second number is high, then you have blocked a ton of other people’s messages, which implies you are overly sensitive or triggerable, and therefore not a good conversationalist. Finally, if your last number is high, that implies that you have obviously been a part of many good conversations, and thus are a good conversationalist.
Therefore according to assumptions 1, 2, and 3, people will want to keep their first two number down, and their third number up. Also let me say that explaining this by means of text is probably the worst way to do it, and if you’d like a better demonstration, shoot me an email, and I can demonstrate this app over zoom.
Anyway, as you might be able to see, if assumptions 1, 2, and 3 hold true, then there is a strong incentive to not post offensive messages on this platform, which is essentially what makes the platform different from other existing platforms.
The last part about the app that is cool is that after a successful conversation, you can send friend requests to other users who posted good insightful responses. Thus, even though Parleya conversations are anonymous, after a good conversation, you are able to connect with people from entirely different backgrounds and hear more about them and what informs their opinions.
Ugh, I’m on page frikin 9. Aint nobody got time for a post this long. I’ll add one last thing because it’s important. I got about 20 people who were interested in the testing the app, and what I quickly found is that I can’t approach user beta testing with a laissez-faire methodology, and I need to ensure users understand the platform and the flow of conversations before using it. So that’s where I’m at. I think you’re probably as tired reading this as I am writing this. See ya.
Sup readers. Prepare yourselves for another disjointed post. I’m basically using my blog as a repo for and log of my thought processes.
K, so basically a big thing that I’ve learned about myself is that even though I really enjoy learning about pretty much anything technical (math, physics, CS, etc) it’s immensely hard for me to stay motivated to continue working on a project unless I can very easily discern why the project benefits humanity. That’s part of the reason why I’m really enjoying my current project.
Oh wait. I forgot that I haven’t written a single blog post about my current project yet. RIP. I’ll do that soon. Basically, I’m trying to build a social media platform that psychologically incentivizes healthy, non-violent conversations about traditionally controversial and polarizing topics. I’m bringing this up simply because I perceive the goal of this project as being of upmost importance for the future health of the purportedly self-healing super graph that is humanity.
Anyway, back to Orchid. The reason I bring all this up is because in past months, I haven’t really been able to come up with a compelling reason why building Orchid would be beneficial to humanity, which has meant that it’s somewhat difficult to remain motivated to work on it, which in turn means I haven’t prioritized working on it, which means I haven’t worked on it all that much.
Orchid, however, has been dancing around the back of my head for the past couple of months simply because I think it would be super cool if it worked. If nothing else, it would give me a way to work on learning things like QFT without the overwhelming frustration of working with ginormous equations with pencil and paper. While I personally don’t see learning QFT as a particularly meaningful pursuit at this juncture of my life, the equations that govern quantum fields are super, super juicy, and it’s fun to play around with them.
Anyway, in trying to come up with ways that Orchid could benefit the humanity graph, I’ve had a couple ideas. This first one kinda showed its head in my last post, but I’ll flesh it out a bit more here. Basically, if Orchid works as I intend, it will essentially create a method for storing mathematical entities of all varieties in well-defined computer data structures. Neat. Additionally, the rules governing mathematical manipulations of these particular mathematical entities will also be stored in similarly well-defined computer data structures. The reason why this is compelling is because computers would then have the ability to work with and manipulate these structures on their own, without human interference. Obviously, the algorithmic approach the computers would take in manipulating the mathematical structures would be defined by humans, but it would essentially allow computers to perform the same sorts of computations humans do all by themselves.
Why is this potentially cool? Because up until this point, most mathematical software is essentially super-powered calculators. Mathematica, for example, has been built over the last 30 years, and during that time, human beings have translated all varieties of mathematical processes into code. There’s a reason it takes up like 20 GB. It’s gigantic. But if you want to numerically solve erf, like I did back in high school, well then boy is Mathematica for you. How is orchid different? Instead of having a bunch of hard-coded algorithms for solving and manipulating previously defined mathematical expressions, Orchid allows you to define entirely new mathematical entities and the rules that govern them. This, furthermore, allows users to have a central location for creating a manipulating all varieties of mathematical entities.
Not only that, but the computer itself would have a way of creating and manipulating exotic mathematical structures. This means that computers would be able to do what previously could only be done with pencil and paper, or on a blackboard. Instead of slaving away doing a bunch of predefined calculations, computers could actually be “doing the math” in the same way that humans have for the last several centuries.
I imagine it might not be immediately clear why computers doing pencil and paper mathematics would be beneficial to humanity. Let me explain as clearly as I can. Mathematics has provided humanity with perhaps the most robust and effective method for quantitatively understanding the world around us. And when humans better understand the world, they can make better predications about the state of the world. As I’ve discussed in previous posts, whenever a structure exhibits stable characteristics and behaviors, that structure can be effectively utilized in the creation of another, larger stable structure. In this context, that means that whenever humans are able to understand the stable characteristics and behaviors of a system, they are frequently able to use that system in a manner that increases humanity’s overall fitness.
Theoretical physics, as a field of study, is perhaps the best and most well-established example of what I’m describing. The phone in your pocket, the missile defense system that keeps you safe, and the lightbulb that illuminates your house are each examples of the staggering amount of technologies that fundamentally would not exist without developments in theoretical physics.
And what is theoretical physics? It is the practice of modelling physical systems in terms of well-defined mathematical structures, and then making predictions about the systems themselves using well-defined mathematical manipulations on those structures. In case you are wondering, experimental physics is the practice of designing and carrying out experiments to gather data on physical systems. Analyzing these data sets is what allows theoretical physicists to determine the degree to which their models accurately describe reality. So, if you’ve ever wondered what those nerds up in national labs, universities, or particle accelerators are doing, it’s that.
Physics is all fine and good, but I’ve found that much of what goes on in modern day physics doesn’t actually seem to affect many people. Some of it certainly does, but a good deal of it is documented in papers that 99.99% of humanity can’t understand and don’t really do people any good.
However, there are plenty of other real-world systems that could be analyzed using the aforementioned methodology. Data scientists are basically the people attempt to understand large data sets using machine learning or other statistical methods. From what I understand of current practices in data sciences, there really isn’t a large amount of coming up with novel mathematical models for understanding data sets in a manner similar to theoretical physics. There certainly is some, but nothing compared to physics.
And there’s a very good reason for this: coming up with appropriate mathematical models for different systems requires a huge amount creativity and intellectual capacity. In other words, it’s really, really hard. Ever wonder why everyone thinks Einstein was so smart? It’s because he came up with extremely precise mathematical frameworks for describing relativistic systems. He did a bunch of other stuff too, but he’s celebrated mainly for his ability to create compelling mathematical models for physical systems. And let me tell you, General Relativity is no small pill to swallow. There are a ton of moving parts and different mathematical structures at play, but my gosh, the resulting theory is objectively gorgeous.
Anyway, I could fawn on about GR all day long, but that’s not why we’re here. The reason Orchid is compelling is because it would drastically simplify the process of coming up with mathematical models to describe different systems. Not only that, with the right set of algorithms, the computer could by itself create mathematical models to describe data sets.
That last sentence probably didn’t have the desired effect on you, so let me rephrase. Orchid could potentially allow a computer to do the same thing Einstein did that made him famous as one of the smartest people in history.
IMHO, that’s pretty dank. But even if that last bit doesn’t happen, Orchid would still provide humanity with a framework for easily constructing and manipulating mathematical entities, which could in turn be used to understand the world around it with a degree of precision previously unattainable.
Well, maybe that’s being overly optimistic. We’ll see.
Anyway, when I started this post, I wasn’t going to talk about Orchid, I was going to give the recipe for consistently and efficiently modelling a system mathematically. Here goes.
Just hit page 7, which is about 5 pages longer than I thought this post was going to be, so I’m going to wrap this sucker up. I guess as one last thing, if this stuff interests you, shoot me an email. After leaving Berkeley, I haven’t talked to a lot of people interested in this stuff.
May your socks always come bedecked with cool designs. Peace.
Sup readers. Prepare yourself for a post that will make absolutely no sense. Or it might. I’m not really sure yet. Basically, I’m revisiting Orchid, and I’m attempting to determine how to make it fundamentally useful.
The fundamental shift in my thinking that I just recognized is that in order for a mathematical model to be useful, it must be defined within a particular context. I realized two nights ago that if the entire game of complexity comes down to stable structures with well-defined behaviors, and humans are good at categorizing such structures, then in order to replicate it, you need a machine that is able to meaningfully describe the set of characteristics and structures of a particular stable structure it encounters by means of data. So the goal is basically three steps. One: Develop a universal method for describing the characteristics and behavior of stable structures in terms of computer data structures. This is and has been the entire purpose of Orchid, as mathematical entities are essentially perfected abstractions of perfectly stable structures. Two: Develop a method for extracting a set of characteristics and behaviors about a particular stable structure encountered in a data set into the data structures discussed in step one. Three: Develop an algorithm by which computers can meaningfully interact with these data structures in order to make meaningful and increasingly refined predictions about the structures in question.
I’ve already worked out a good deal of the difficulties of step one during my previous efforts with Orchid, but it’s really step two that’s giving me trouble. I presume step three will be the most difficult, but I’ve logically decided not to even consider that yet as to preserve the amount of unpolluted thinking space that currently exists in my brain. Anyway, step two. How do we possibly do this? My first goal is to essentially translate simple statements into mathematical structures that are meaningful. So take this, “If I stack blocks on top of each other, I end up with a taller structure.” Incredibly simple statement, right? Well, how do I translate that statement into a working mathematical entity? That’s a pretty tough question.
I think my mistake for the past day of thinking about this is that I was attempting to match any object or stable structure with a corresponding mathematical entity. Ideally this mathematical entity would be sufficiently robust to fully describe the object in question, including the object’s behaviors. But that’s really tricky. Take me for example. If I jumped off a cliff, a meaningful question might be, “How long is it going to take this boi to hit the ground?” Good question, reader. I certainly would like to know how many seconds of life I have remaining. However, imagine I insulted a friend of mine, causing them to be angry (purely hypothetical, (hehe)). Based on my previous method of description, I would have come up with a mathematical entity that described Danny Geisz and used that object to model the two previous situations I described. But what sort of object would I be? Like, for real? Should I be modelled as a mapping from my environment to a particular phrase, which would in turn be modelled as a mapping from my friend’s previous emotional state to his/her final emotional state? What about the first situation? Should I simply be approximated as massive object as traditionally used in kinematics? If that were the case, then I would be a simple scalar: mass.
I’d like to think that there’s a bit more to me than my mass, so that’s clearly not the way to go. Maybe a slightly better method for modelling myself would be as a cartesian product of a variety of sets that together describe my characteristics and interaction with reality. Still, though, that seems insufficient and highly disorganized.
What I’m realizing even as I write this is the importance of context. The context of me jumping off a cliff ought to be modelled differently than the context of insulting a friend. Specifically, (and now I’m really going stream of consciousness) a particular question should be posed, and a particular quantity studied. More specifically, the characteristics and behavior of the entity being studied should be described in as great a depth as reasonable by mathematical language, and everything else ought to center around that main model. For the example of me jumping off a cliff, the two important quantities are time and my height off the ground. When my height reaches 0, we measured the time elapsed, and wala! We found an accurate prediction of the time I have left to live. (Congrats, Danny, you’ve done basic kinematics).
The situation of the emotional state is a bit less traditional. I think in this situation, the important quantity is the friend’s emotional state. Then we can regard my insult as a mathematical mapping of the previous emotional state to the final emotional state. Furthermore, we could model me, Danny Geisz, as a mapping from my current emotional state, to the words I said to my friend, which affected his/her emotional state.
In Quantum Mechanics, a particle is described as a wave vector. Why? Because simple mathematical manipulations on a wave vector yield interesting quantities like a particles position or momentum (specifically the probability that a particle will have a specific position or momentum). So basically, the interesting quantities of a particle (within the context of QM) are modelled as a wavevector, and any other entities that interact with the particle are modelled as transformations on the wavevector. Neato.
I suppose my goal, however, is to build a computational system that’s capable of analyzing a set of data and generating mathematical models that describe the data. These mathematical models could then be used to make a more cohesive and robust set of predictions about the world than the models traditionally associated with machine learning. If I’m trying to build a computer that beats a human, I need it to be able to replicate the human experience and do it in a manner superior to humans. Humans are really quite good at classifying objects and using logic to make predictions based on their “modelled” view of particular stable structures. So I want Orchid to do this, but better.
After writing this, I’m realizing that simply regressively generating mathematical models isn’t sufficient for the level of classification I require. I think I need to do some more thinking about the relationship between a structure and a mathematical context, because that’s the space where computers could excel relative to humans. Ok, that’s all for now.
Aight lads and lasses. Let’s get technical. I want to code more than anything right now, but a certain thought process has been coursing through my veins for the last twelve or so hours, and I need to get it down. If my language gets too technical, it’s your fault for not understanding me. Haha, take that. Nothing like purposefully trying to push my readers away. Here we go!
I’ve written several posts about this, most recently the post about love, but I think the part of physics that is topically most interesting at this moment is the process of analyzing the stability of different systems. I’ll lay out the reason why this is interesting.
One central law in physics is the second law of thermodynamics, which roughly states that the disorder in a global system increases over time (that statement is a shade of the mathematical glory that is a proper study of entropy, but my readers don’t got no time for equations). The simple (and painfully cliché) analogy that is given for this statement is to imagine a new deck of cards. The cards are nicely in order. But the second you start shuffling, the cards quickly become scrambled and disorderly. If you hunker down and examine the probabilities in question, a randomly shuffled deck of cards is far more likely to be “disorderly” than “orderly.”
By applying similarly simple probabilistic theory to physical systems, you basically get the basics of statistical mechanics, which concerns itself with average quantities of systems with a large number of constituents (usually at or above 1023. Gotta love my boi Avogadro). To make a long story painfully short, you can essentially think of a thermodynamic system as a deck of cards that’s constantly “reshuffling” itself, and like a deck of cards, “disorderly” configurations of the system are generally significantly more probable than “orderly” configurations.
Great. So why should you care, inquisitive reader? Well, look at human beings. Human beings are incredibly well-ordered systems of incomprehensible complexity. To perhaps make the point clearer, if you took all the subatomic particles that make up your body and threw them into a box at random, the probability that the particles would end up in the configuration of a human being is disgustingly small. Outrageously small. If you think along this line of reasoning, the probability of humanity existing in our universe is so unthinkably small, it’s a miracle we even happened.
I simply refuse to believe that what I’m about to discuss hasn’t been rigorously treated by smarter minds than my own, but I’m going proceed as though these are original thoughts because I enjoy feeling like I’m scientifically innovative.
The fundamental question of this post is the following: Are highly ordered and complex systems probable given the configuration of our universe?
Given what I’ve already stated, your gut reaction to this question is probably: “No, Danny! Stop being dumb.” Hey, reader, watch your mouth. No one’s forcing you to read this, so go shuck a duck.
In order to continue, we ought to have a civil conversation regarding stability, because it’s ever so important. In fact, I think it’s the key.
In the previous example with the deck of cards, let’s change things up a little bit. Imagine that every single time the deck is in new deck order, small magnets engage that keep the deck from being reshuffled. So even though new deck order is statistically unlikely, if you continue shuffling the deck for eternity, the average configuration of the deck of cards is new deck order because once it reaches that state, it can’t be reshuffled.
To get a bit more rigorous, I’ll define a stable configuration of a system to be a configuration that is resistant to change (not super rigorous definition, but it’ll do). As we’ve seen with the “sticky” deck of cards, even is an “orderly” configuration of a system is statistically improbable in terms of possible random configurations of the system, over a large swath of time, the “orderly” configuration is actually probabilistically likely because it’s most stable.
The question now is, what would make any one system any more stable than another? Well, take a helium atom, for example. What makes a helium atom any more stable than a hydrogen atom? Those of you chemistry nerds are probably kerfuffling about orbitals and valence electrons. Hey, chemistry nerds? Y’all can also go shuck some ducks, then go take a proper class on Quantum Mechanics. Or, even better, just read R. Shankar’s The Principles of Quantum Mechanics. What a truly divine textbook. A mathematical masterpiece at the very least. Anyway, I’m not going to even try to explain humanity’s best understanding of the physics of stable orbits, but I can give you a much more abstract answer.
The reason why the helium is a stable configuration of protons, neutrons, and electrons is because these particular particles exhibit a rich set of behaviors when near one another. You probably remember that protons and electrons have opposite electric charges and therefore attract. Our understanding of quantum electrodynamics actually gives a more compelling explanation than that of simple electric fields. In QED, electromagnetic effects are described by an exchange of photons between different particles. Fun fact, QED was the first theory with full agreement between quantum mechanics and special relativity (got that straight from the wiki).
I went down rabbit hole. Regardless of how fascinating QED is, the important thing to keep in mind is that subatomic particles exhibit a rich set of behaviors when interacting with one another. The reason why helium is stable is because of the underlying rules governing the interactions between protons, neutrons, and electrons. If these particles didn’t interact with one another (much like cards in a deck) then there would be no notion of stability, and in those systems, disorder would be statistically likely, even throughout a broad swath of time.
So then, if you want any notion of stability in a system, you want there to exist a rich set of behaviors between the underlying constituents of the system.
Ok, I’m going to go in a slightly different direction now. I want to talk about what constitutes an “orderly” system. I tend to think of a human being as a highly ordered system. Amazon (as in the company) is a highly ordered system. Quartz is a highly ordered crystalline structure.
I think the big thing here is that an ordered system has a fixed set of stable characteristics. Two examples of this: 1) Human beings have arms. On average, a human being will keep both arms all throughout their life. I can reasonably predict that tomorrow morning I will have both arms attached to my body. 2) If someone punches me, I’ll get angry. For the average human being, if you punch them, they’ll probably get angry. I can reasonably predict that if I were punched tomorrow morning, I would get angry.
Ok, so to get a bit more rigorous, (also do know that I’m basically making this up on the fly), the degree to which a system is orderly is proportional to the number and stability of each of the systems characteristics. Cool. One thing to note here is that under this definition, in order for a system to be orderly, it must also necessarily be stable.
Actually, wait. Now that I’m thinking about it more, I think stability and orderliness might be two sides of the same coin. Remember my definition of stability? A system that is resistant to change. Cool, but how do you quantify whether a system is resistant to change? Well, a good first step is to describe the characteristics of a system, and if those characteristics remain the same as time progresses, then your system is stable. But what I just described was my definition of orderliness. Ha! Geisz’s first law: Stability = Order.
Ok, let’s move along. Remember, the big question of this post is whether highly ordered and complex systems (like humans) are probable given the configuration of our universe. What we should talk about next is how stable systems are able to build themselves into bigger stable systems.
What I’m going to talk about next is probably going to be markedly similar to my post about love.
Remember, the recipe for stability is a rich set of behaviors between the constituents of the system. So, an electron and a proton are able to organize themselves into the “stable” and “orderly” configuration of hydrogen because of the underlying interaction between two particles of opposite electric charge.
Hydrogen is all well and good, but I want human beings, I don’t just want hydrogen. How do we get from hydrogen to human beings? In other words, how does one stable system bring forth another stable system.
Remember the recipe. For stability to occur, we need a rich set of behaviors between the constituents of the system. So, if we want hydrogen (and perhaps some other atoms) to build themselves into systems of increased complexity, we need them to be able to interact with one another. Because of the whole business of stable orbitals, certain atoms do interact with one another, and therefore are able to form stable configurations, which we call molecules. On the other hand, helium, while incredibly stable, isn’t able to “help” other atoms create systems of greater complexity (molecules) because it doesn’t interact with any such atoms.
As an interesting side note, even though helium is pretty tame from the perspective of chemistry, it does still interact with other particles in an entirely different context. Because helium is light and stable, in the presence of a dense, gravitationally dominant object, a mixture of helium and other heavier gases will push helium to the top due to helium’s low density. This is a perfect example of a stable characteristic of a system, which means that an atmosphere could be considered a stable and orderly system. So again, any time the constituents of a system exhibit a rich set of stable interactions, there is potential for the system to be stable and orderly.
I think you probably get the idea. I’m at seven pages, so I should probably wrap this sucker up, but I think there should be a big takeaway here. If you want to propagate complexity and order, you want stable systems that exhibit stable behaviors. That’s all for now.