Computational_Economics | Theodore C. Tanner Jr.

SnakeByte[17] The Metropolis Algorithm

Frame Grab From the movie Metropolis 1927

Who told you to attack the machines, you fools? Without them you’ll all die!!

~ Grot, the Guardian of the Heart Machine

First, as always, Oh Dear Reader, i hope you are safe. There are many unsafe places in and around the world in this current time. Second, this blog is a SnakeByte[] based on something that i knew about but had no idea it was called this by this name.

Third, relative to this, i must confess, Oh, Dear Reader, i have a disease of the bibliomaniac kind. i have an obsession with books and reading. “They” say that belief comes first, followed by admission. There is a Japanese word that translates to having so many books you cannot possibly read them all. This word is tsundoku. From the website (if you click on the word):

“Tsundoku dates from the Meiji era, and derives from a combination of tsunde-oku (to let things pile up) and dokusho (to read books). It can also refer to the stacks themselves. Crucially, it doesn’t carry a pejorative connotation, being more akin to bookworm than an irredeemable slob.”

Thus, while perusing a math-related book site, i came across a monograph entitled “The Metropolis Algorithm: Theory and Examples” by C Douglas Howard [1].

i was intrigued, and because it was 5 bucks (Side note: i always try to buy used and loved books), i decided to throw it into the virtual shopping buggy.

Upon receiving said monograph, i sat down to read it, and i was amazed to find it was closely related to something I was very familiar with from decades ago. This finally brings us to the current SnakeByte[].

The Metropolis Algorithm is a method in computational statistics used to sample from complex probability distributions. It is a type of Markov Chain Monte Carlo (MCMC) algorithm (i had no idea), which relies on Markov Chains to generate a sequence of samples that can approximate a desired distribution, even when direct sampling is complex. Yes, let me say that again – i had no idea. Go ahead LazyWeb^TM laugh!

So let us start with how the Metropolis Algorithm and how it relates to Markov Chains. (Caveat Emptor: You will need to dig out those statistics books and a little linear algebra.)

Markov Chains Basics

A Markov Chain is a mathematical system that transitions from one state to another in a state space. It has the property that the next state depends only on the current state, not the sequence of states preceding it. This is called the Markov property. The algorithm was introduced by Metropolis et al. (1953) in a Statistical Physics context and was generalized by Hastings (1970). It was considered in the context of image analysis (Geman and Geman, 1984) and data augmentation (Tanner (I’m not related that i know of…) and Wong, 1987). However, its routine use in statistics (especially for Bayesian inference) did not take place until Gelfand and Smith (1990) popularised it. For modern discussions of MCMC, see e.g. Tierney (1994), Smith and Roberts (1993), Gilks et al. (1996), and Roberts and Rosenthal (1998b).

Ergo, the name Metropolis-Hastings algorithm. Once again, i had no idea.

Anyhow,

A Markov Chain can be described by a set of states $S$ and a transition matrix $P$ , where each element $P_{ij}$ represents the probability of transitioning from state $i$ to state $j$ .

Provide The Goal: Sampling from a Probability Distribution $\pi(x)$

In many applications (e.g., statistical mechanics, Bayesian inference, as mentioned), we are interested in sampling from a complex probability distribution $\pi(x)$ . This distribution might be difficult to sample from directly, but we can use a Markov Chain to create a sequence of samples that, after a certain period (called the burn-in period), will approximate $\pi(x)$ .

Ok Now: The Metropolis Algorithm

The Metropolis Algorithm is one of the simplest MCMC algorithms to generate samples from $\pi(x)$ . It works by constructing a Markov Chain whose stationary distribution is the desired probability distribution $\pi(x)$ . A stationary distribution is a probability distribution that remains the same over time in a Markov chain. Thus it can describe the long-term behavior of a chain, where the probabilities of being in each state do not change as time passes. (Whatever time is, i digress.)

The key steps of the algorithm are:

Initialization

Start with an initial guess $x_0$ , a point in the state space. This point can be chosen randomly or based on prior knowledge.

Proposal Step

From the current state $x_t$ , propose a new state $x^*$ using a proposal distribution $q(x^*|x_t)$ , which suggests a candidate for the next state. This proposal distribution can be symmetric (e.g., a normal distribution centered at $x_t$ ) or asymmetric.

Acceptance Probability

Calculate the acceptance probability $\alpha$ for moving from the current state $x_t$ to the proposed state $x^*$ :

$\alpha = \min \left(1, \frac{\pi(x^) q(x_t | x^)}{\pi(x_t) q(x^* | x_t)} \right)$

In the case where the proposal distribution is symmetric (i.e., $q(x^|x_t) = q(x_t|x^))$ , the formula simplifies to:

$\alpha = \min \left(1, \frac{\pi(x^*)}{\pi(x_t)} \right)$

Acceptance or Rejection

Generate a random number $u$ from a uniform distribution $U(0, 1)$
If $u \leq \alpha$ , accept the proposed state $x^*$ , i.e., $set x_{t+1} = x^*$ .
If $u > \alpha$ , reject the proposed state and remain at the current state, i.e., $set x_{t+1} = x_t$ .

Repeat

Repeat the proposal, acceptance, and rejection steps to generate a Markov Chain of samples.

Convergence and Stationary Distribution:

Over time, as more samples are generated, the Markov Chain converges to a stationary distribution. The stationary distribution is the target distribution $\pi(x)$ , meaning the samples generated by the algorithm will approximate $\pi(x)$ more closely as the number of iterations increases.

Applications:

The Metropolis Algorithm is widely used in various fields such as Bayesian statistics, physics (e.g., in the simulation of physical systems), machine learning, and finance. It is especially useful for high-dimensional problems where direct sampling is computationally expensive or impossible.

Key Features of the Metropolis Algorithm:

Simplicity: It’s easy to implement and doesn’t require knowledge of the normalization constant of $\pi(x)$ , which can be difficult to compute.
Flexibility: It works with a wide range of proposal distributions, allowing the algorithm to be adapted to different problem contexts.
Efficiency: While it can be computationally demanding, the algorithm can provide high-quality approximations to complex distributions with well-chosen proposals and sufficient iterations.

The Metropolis-Hastings Algorithm is a more general version that allows for non-symmetric proposal distributions, expanding the range of problems the algorithm can handle.

Now let us code it up:

i am going to assume the underlying distribution is Gaussian with a time-dependent mean $\mu_t$ , which changes slowly over time. We’ll use a simple time-series analytics setup to sample this distribution using the Metropolis Algorithm and plot the results. Note: When the target distribution is Gaussian (or close to Gaussian), the algorithm can converge more quickly to the true distribution because of the symmetric smooth nature of the normal distribution.

import numpy as np
import matplotlib.pyplot as plt

# Time-dependent mean function (example: sinusoidal pattern)
def mu_t(t):
    return 10 * np.sin(0.1 * t)

# Target distribution: Gaussian with time-varying mean mu_t and fixed variance
def target_distribution(x, t):
    mu = mu_t(t)
    sigma = 1.0  # Assume fixed variance for simplicity
    return np.exp(-0.5 * ((x - mu) / sigma) ** 2)

# Metropolis Algorithm for time-series sampling
def metropolis_sampling(num_samples, initial_x, proposal_std, time_steps):
    samples = np.zeros(num_samples)
    samples[0] = initial_x

    # Iterate over the time steps
    for t in range(1, num_samples):
        # Propose a new state based on the current state
        x_current = samples[t - 1]
        x_proposed = np.random.normal(x_current, proposal_std)

        # Acceptance probability (Metropolis-Hastings step)
        acceptance_ratio = target_distribution(x_proposed, time_steps[t]) / target_distribution(x_current, time_steps[t])
        acceptance_probability = min(1, acceptance_ratio)

        # Accept or reject the proposed sample
        if np.random.rand() < acceptance_probability:
            samples[t] = x_proposed
        else:
            samples[t] = x_current

    return samples

# Parameters
num_samples = 10000  # Total number of samples to generate
initial_x = 0.0      # Initial state
proposal_std = 0.5   # Standard deviation for proposal distribution
time_steps = np.linspace(0, 1000, num_samples)  # Time steps for temporal evolution

# Run the Metropolis Algorithm
samples = metropolis_sampling(num_samples, initial_x, proposal_std, time_steps)

# Plot the time series of samples and the underlying mean function
plt.figure(figsize=(12, 6))

# Plot the samples over time
plt.plot(time_steps, samples, label='Metropolis Samples', alpha=0.7)

# Plot the underlying time-varying mean (true function)
plt.plot(time_steps, mu_t(time_steps), label='True Mean ', color='red', linewidth=2)

plt.title("Metropolis Algorithm Sampling with Time-Varying Gaussian Distribution")
plt.xlabel("Time")
plt.ylabel("Sample Value")
plt.legend()
plt.grid(True)
plt.show()

Output of Python Script Figure 1.0

Ok, What’s going on here?

For the Target Distribution:

The function $mu_t(t)$ defines a time-varying mean for the distribution. In this example, it follows a sinusoidal pattern.
The function target_distribution(x, t) models a Gaussian distribution with mean $\mu_t$ and a fixed variance (set to 1.0).

Metropolis Algorithm:

The metropolis_sampling function implements the Metropolis algorithm. It iterates over time, generating samples from the time-varying distribution. The acceptance probability is calculated using the target distribution at each time step.

Proposal Distribution:

A normal distribution centered around the current state with standard deviation proposal_std is used to propose new states.

Temporal Evolution:

The time steps are generated using np.linspace to simulate temporal evolution, which can be used in time-series analytics.

Plot The Results:

The results are plotted, showing the samples generated by the Metropolis algorithm as well as the true underlying mean function $\mu_t$ (in red).

The plot shows the Metropolis samples over time, which should cluster around the time-varying mean $\mu_t$ of the distribution. As time progresses, the samples follow the red curve (the true mean) as time moves on like and arrow in this case.

Now you are probably asking “Hey is there a more pythonic library way to to this?”. Oh Dear Reader i am glad you asked! Yes There Is A Python Library! AFAIC PyMC started it all. Most probably know it as PyMc3 (formerly known as…). There is a great writeup here: History of PyMc.

We are golden age of probabilistic programming.

~ Chris Fonnesbeck (creator of PyMC)

Lets convert it using PyMC. Steps to Conversion:

Define the probabilistic model using PyMC’s modeling syntax.
Specify the Gaussian likelihood with the time-varying mean $\mu_t$ .
Use PyMC’s built-in Metropolis sampler.
Visualize the results similarly to how we did earlier.

import pymc as pm
import numpy as np
import matplotlib.pyplot as plt

# Time-dependent mean function (example: sinusoidal pattern)
def mu_t(t):
    return 10 * np.sin(0.1 * t)

# Set random seed for reproducibility
np.random.seed(42)

# Number of time points and samples
num_samples = 10000
time_steps = np.linspace(0, 1000, num_samples)

# PyMC model definition
with pm.Model() as model:
    # Prior for the time-varying parameter (mean of Gaussian)
    mu_t_values = mu_t(time_steps)

    # Observational model: Normally distributed samples with time-varying mean and fixed variance
    sigma = 1.0  # Fixed variance
    x = pm.Normal('x', mu=mu_t_values, sigma=sigma, shape=num_samples)

    # Use the Metropolis sampler explicitly
    step = pm.Metropolis()

    # Run MCMC sampling with the Metropolis step
    samples_all = pm.sample(num_samples, tune=1000, step=step, chains=5, return_inferencedata=False)

# Extract one chain's worth of samples for plotting
samples = samples_all['x'][0]  # Taking only the first chain

# Plot the time series of samples and the underlying mean function
plt.figure(figsize=(12, 6))

# Plot the samples over time
plt.plot(time_steps, samples, label='PyMC Metropolis Samples', alpha=0.7)

# Plot the underlying time-varying mean (true function)
plt.plot(time_steps, mu_t(time_steps), label='True Mean ', color='red', linewidth=2)

plt.title("PyMC Metropolis Sampling with Time-Varying Gaussian Distribution")
plt.xlabel("Time")
plt.ylabel("Sample Value")
plt.legend()
plt.grid(True)
plt.show()

When you execute this code you will see the following status bar:

It will be a while. Go grab your favorite beverage and take a walk…..

Output of Python Script Figure 1.1

Key Differences from the Previous Code:

PyMC Model Usage Definition:
In PyMC, the model is defined using the pm.Model() context. The x variable is defined as a Normal distribution with the time-varying mean $\mu_t$ . Instead of manually implementing the acceptance probability, PyMC handles this automatically with the specified sampler.

Metropolis Sampler:
PyMC allows us to specify the sampling method. Here, we explicitly use the Metropolis algorithm with pm.Metropolis().

Samples Parameter:
We specify shape=num_samples in the pm.Normal() distribution to indicate that we want a series of samples for each time step.

Plotting:
The resulting plot will show the sampled values using the PyMC Metropolis algorithm compared with the true underlying mean, similar to the earlier approach. Now, samples has the same shape as time_steps (in this case, both with 10,000 elements), allowing you to plot the sample values correctly against the time points; otherwise, the x and y axes would not align.

NOTE: We used this library at one of our previous health startups with great success.

Optimizations herewith include several. There is a default setting in PyMC which is called NUTS.
No need to manually set the number of leapfrog steps. NUTS automatically determines the optimal number of steps for each iteration, preventing inefficient or divergent sampling. NUTS automatically stops the trajectory when it detects that the particle is about to turn back on itself (i.e., when the trajectory “U-turns”). A U-turn means that continuing to move in the same direction would result in redundant exploration of the space and inefficient sampling. When NUTS detects this, it terminates the trajectory early, preventing unnecessary steps. Also the acceptance rates on convergence are higher.

There are several references to this set of algorithms. It truly a case of both mathematical and computational elegance.

Of course you have to know what the name means. They say words have meanings. Then again one cannot know everything.

Until Then,

#iwishyouwater <- Of all places Alabama getting the memo From Helene 2024

𝕋𝕖𝕕 ℂ. 𝕋𝕒𝕟𝕟𝕖𝕣 𝕁𝕣. (@tctjr) / X

Music To Blog By: View From The Magicians Window, The Psychic Circle

References:

[1] The Metropolis Algorithm: Theory and Examples by C Douglas Howard

[2] The Metropolis-Hastings Algorithm: A note by Danielle Navarro

[3] Github code for Sample Based Inference by bashhwu

Entire Metropolis Movie For Your Viewing Pleasure. (AFAIC The most amazing Sci-Fi movie besides BladeRunner)

November 10, 2020April 29, 2021 TCTJr Artificial_Intelligence|Complexity_Theory|Computational_Economics|Distributed_Computing

Computing The Human Condition – Project Noumena (Part 2)

In the evolution of a society, continued investment in complexity as a problem-solving strategy yields a declining marginal return.
Joseph A. Tainter

Someone asked me if from now on my blog will only be about Project_Noumena – on the contrary.

I will be interspersing subject matter within Parts 1 to (N) of Project_Noumena. To be transparent at this juncture i am not sure where it will end or if there is even a logical MVP 1.0. As with open-source systems and frameworks technically one never achieves V1.0 as the systems evolve. i tend to believe this will be the case with Project Noumena. i recently provided a book review on CaTB and have a blog on Recurrent Neural Networks with respect to Multiple Time Scale Prediction in the works so stuff is proceeding.

To that end, i would love comments and suggestions as to anything you would like my opinion on or for me to write about in the comments section. Also feel free to call me out on typos or anything else you see in error.

Further within Project Noumena there are snippets that could be shorter blogs as well. Look at Project Noumena as a fractal-based system.

Now on to the matter at hand.

In the previous blog Computing The Human_Condition – Project Noumena (Part 1) i discussed the initial overview of the model from the book World Dynamics. i will take a part of that model which is what i call, the main, Human_Do_Loop(); and the main attributes of the model: Birth and Death of Humans. One must ask if we didn’t have humans we would not have to be concerned with such matters as societal collapse? i don’t believe animals are concerned with such existential crisis concerns so my answer is a resounding – NO. We will be discussing such existential issues in this blog although i will address such items in future writings.

Over the years i have been asking myself is this a biological model by definition? Meaning do we have cellular components involved only? Is this biological modeling at the very essence? If we took the cell-based organisms out of the equation what do we still have as far as models on Earth?

While i told myself i wouldn’t get too extensional here and i do want to focus on the models and then codebases i continually check the initial conditions of these systems as they for most systems dictate the response for the rest of the future operations of said systems. Thus for biological systems, are there physical parameters that govern the initial exponential growth rate? Can we model with power laws and logistic curves for coarse-grained behavior? Is Bayesian reasoning biologically plausible at a behavioral level or at a neuronal level? Given that what are the atomic units that govern these models?

These are just a sampling of initial condition questions i ask myself as i evolve through this process.

So with that long-winded introduction and i trust i didn’t lose you oh reader lets hope into some specifics.

The picture from the book depicts basic birth and death loops in the population sector. In the case of these loops, they are generating positive feedback which causes growth. Thus an increase in population P causes an increase in birthrate BR. This, in turn, causes population P to further increase. The positive feedback loop would if left to its own devices would create an exponentially growing situation. As i said in the first blog and will continue to say, we seem to have started using exponential growth as a net positive fashion over the years in the technology industry. In the case of basic population dynamics with no constraints, exponential growth is not a net positive outcome.

Once again why start with simple models? The human mind is phenomenal at perceiving pressures, fears, greed, homeostasis, and other human aspects and characteristics and attempting at a structure that is given say the best fit to a situation and categorizing these as attributes thereof. However, the human mind is rather poor at predicting dynamical systems behaviors which are where the models come into play especially with social interactions and what i attempting to define from a self-organizing theory standpoint.

The next sets of loops that have the most effective behavior is a Pollution loop and a Crowding Loop. If we note that pollution POL increases one can assume up to a point that one hopes that nature absorbs and fixes the pollution otherwise it is a completely positive feedback loop and this, in turn, creates over pollution which we are already seeing the effects of around the worlds. One can then couple this with the amount of crowding humans can tolerate.

We see this behavior in urban sprawl areas when we have extreme heat or extreme cold or let’s say extreme pandemics. If the population rises crowding ratio increases the birth rate multiplier declines and birth rates reduce. The increasing death rate and reducing the birth rate are power system dynamic stabilizers coupled with pollution. This in turn obviously has an effect on food supplies. One can easily deduce that these seemingly simple coefficients if you will within the relative feedback loops create oscillations, exponential growth, or exponential decay. The systems while that seem large and rather stable are very sensitive to slight variations. If you are familiar with NetLogo it is a great agent-based modeling language. I picked a simple pollution model whereas we can select the number of people, birthrate, and tree planting rate.

As you can see without delving into the specifics after 77 years it doesn’t look to promising. i ‘ll either be using python or netlogo or a combination of both to extended these models as we add other references.

Ok enough for now.

Until Then,

#iwishyouwater

@tctjr

October 15, 2020October 16, 2020 TCTJr Books|Computational_Economics|Computing_History|Distributed_Computing|Human-Performance

Book Review: The Cathedral and The Bazaar (Musings On Linux and Open Source By An Accidental Revolutionary

“Joy, humor, and playfulness are indeed assets;”
~ Eric S. Raymond

As of late, i’ve been asked by an extreme set of divergent individuals what does “Open Source Software” mean?

That is a good question. While i understand the words and words do have meanings i am not sure its the words that matter here. Many people who ask me that question hear “open source” and hear or think “free’ which is not the case.

Also if you have been on linkedin at all you will see #Linux, #LinuxFoundation and #OpenSource tagged constantly in your feeds.

Which brings me to the current blog and book review.

(CatB)as it is affectionately known in the industry started out and still is a manifesto as well accessible via the world wide web. It was originally published in 1997 on the world wide wait and then in print form circa 1999. Then in 2001 was a revised edition with a foreword by Bob Young, the founding chairman and ceo of Redhat.

Being i prefer to use plain ole’ books we are reviewing the physical revised and extended paperback edition in this blog circa 2001. Of note for the picture, it has some wear and tear.

To start off as you will see from the cover there is a quote by Guy Kawasaki, Apple’s first Evangelist:

“The most important book about technology today, with implications that go far beyond programming.”

This is completely true. In the same train of thought, it even goes into the aspects of propriety and courtesy within conflict environments and how such environments are of a “merit not inherit” world, and how to properly respond when you are in vehement disagreement.

To relate it to the book review: What is a cathedral development versus a bazaar environment?

Cathedral is a tip of the fedora if you will to the authoritarian view of the world where everything is very structured and there are only a few at most who will approve moving the codebase forward.

Bazaar refers to the many. The many coding and contributing in a swarm like fashion.

In this book, closed source is described as a cathedral development model and open source as a bazaar development model. A cathedral is vertically and centrally controlled and planned. Process and governance rule the project – not coding. The cathedral is homeostatic. If you build or rebuild Basilica Sancti Petri within Roma you will not be picking it up by flatbed truck and moving it to Firenze.

The forward in the 2001 edition is written by Bob Young co-founder and original CEO of RedHat. He writes:

“ There have always been two things that would be required if open-source software was to materially change the world; one was for open-source software to become widely used and the other was the benefits this software development model supplied to its users had to be communicated and understood.”

Users here are an interesting target. Users could be developers and they could be end-users of warez. Nevertheless, i believe both conditions have been met accordingly.

i co-founded a machine learning and nlp service as a company in 2007 wherein i had the epiphany after my “second” read of Catb that the future is in fact open source. i put second in quotes as the first time i read it back in 1998 it wasn’t really a read in depth nor having fully internalized it while i was working at Apple in the CPU software department on OS9/OSX and while at the same time knowing full well that OSX was based on the Mach kernel. The Mach kernel is often mentioned as one of the earliest examples of a microkernel. However, not all versions of Mach are microkernels. Mach’s derivatives are the basis of the operating system kernel in GNU Hurd and of Apple’s XNU kernel used in macOS, iOS, iPadOS, tvOS, and watchOS.

That being said after years of working with mainly closed source systems in 2007 i re-read Catb. i literally had a deep epiphany that the future of all development would be open source distributed machine learning – everywhere.

Then i read it recently – deeply – a third time. This time nearly every line in the book resonates.

The third time with almost anything seems to be the charm. This third time through i realized not only is this a treatise for the open-source movement it is a call to arms if you will for the entire developer community to behave appropriately with propriety and courtesy in a highly matrixed collaborative environment known as the bazaar.

The most obvious question is: Why should you care? i’m glad you asked.

The reason you care is that you are part of the information economy. The top market cap companies are all information-theoretic developer-first companies. This means that these companies build things so others can build things. Software is truly eating the world. Think in terms of the recent pandemic. Work (code) is being created at an amazing rate due to the fact that the information work economy is distributed and essentially schedule free. She who has distributed wins and she who can code anytime wins. This also means that you are interested in building world-class software and the building of this software is now a decentralized peer reviewed transparent process.

The book is organized around Raymond’s various essays. It is important to note that just as software is an evolutionary process by definition so are the essays in this book. They can also be found online. The original collection of essays date back to 1992 on the internet: “A Brief History Of Hackerdom.’

The book is not a “how-to” cookbook but rather what i call a “why to” map of the terrain. While you can learn how to hack and code i believe it must be in your psyche. The book also uses the term “hacker” in a positive sense to mean one who creates software versus one who cracks software or steals information.

While the history and the methodology is amazing to me the cogent commentary on the types of the reasoning behind why hackers go into open source vary as widely as ice cream flavors.

Raymond goes into the theory of incentives with respect to the instinctive wiring of humans beings.

“The verdict of history seems to be free-market capitalism is the globally optimal way to cooperate for economic efficiency; perhaps in a similar way to cooperate for generating (and checking!) high-quality creative work.”

He categorizes command hierarchy, exchange economy, and gift culture to address these incentives.

Command hierarchy:

Goods are allocated in a scarce economy model by one central authority.

Exchange Economy:

The allocation of scarce goods is accomplished in a decentralized manner allowing scale through trade and voluntary cooperation.

Gift Culture:

This is very different than the other two methods or cultures. Abundance makes command and control relationships difficult to sustain. In gift cultures, social status is determined not by what you control but by what you give away.

It is clear that if we define the open source hackerdom it would be a gift culture. (It is beyond the current scope of this blog but it would be interesting to do a neuroscience project on the analysis of open source versus closed source hackers brain chemistry as they work throughout the day)

Given these categories, the essays then go onto define the written and many times unwritten (read secrets) that operate within the open-source world via a reputation game. If you are getting the idea it is tribal you are correct. Interestingly enough the open source world has in many cases very divergent views on all prickly things within the human condition such as religion and politics but one thing is a constant – ship high-quality code.

Without a doubt the most glaring cogent commentary comes in a paragraph from the essay “The Magic Cauldron.” entitled “Open Source And Strategic Business Risk.”

Ultimately the reasons open source seems destined to become a widespread practice have more to do with customer demand and market pressures than with supply-efficiencies for vendors.”

And further:

“Put yourself for the moment in the position of a CTO at a Fortune 500 corporation contemplating a build or upgrade of your firm’s IT infrastructure. Perhaps you need to choose a network operating system to be deployed enterprise-wide; perhaps your concerns involve 24/7 web service and e-commerce, perhaps your business depends on being able to field high-volume, high-reliability transaction databases. Suppose you go the conventional closed-source route. If you do, then you put your firm at the mercy of a supplier monopoly – because by definition there is only one place you can go to for support, bug fixes, and enhancements. If the supplier doesn’t perform, you will have no effective recourse because you are effectively locked by your initial investment.”

FURTHER:

“The truth is this: when your key business processes are executed by opaque blocks of bits that you cant even see inside (let alone modify) you have lost control of your business.”

“Contrast this with the open-source choice. If you go this route, you have the source code, and no one can take that away from you. Instead of a supplier monopoly with a choke-hold on your business, you now have multiple service companies bidding for your business – and you not only get to play them against each other, but you also have the option of building your own captive support organization if that looks less expensive than contracting out. The market works for you.”

“The logic is compelling; depending on closed-source code is an unacceptable strategic risk So much so that I believe it will not be very long until closed-source single-vendor acquisitions when there is an open source alternative available will be viewed as a fiduciary irresponsibility, and rightly grounds for a share-holder lawsuit.”

THIS WAS WRITTEN IN 1997. LOOK AROUND THE WORLD WIDE WAIT NOW… WHAT DO YOU SEE?

Open Source – full stop.

i will add that there was no technical explanation here only business incentive and responsibility to the company you are building, rebuilt, or are scaling. Further, this allows true software malleability and reach which is the very reason for software.

i will also go on a limb here and say if you are a software corporation one that creates software you can play the monopoly and open-source models against each other within your corporation. Agility and speed to ship code is the only thing that matters these days. Where is your github? Or why is this not shipping TODAY?

This brings me to yet another amazing prescient prediction in the book that Raymond says that applications are ultimately where we will land for monetary scale. Well yes, there is an app for that….

While i have never met Eric S. Raymond he is a legend in the field. We have much to thank him for in the areas of software. If you have not read CatB and work in the information sector do yourself a favor: buy it today.

As a matter of fact here is the link: The Cathedral & the Bazaar: Musings on Linux and Open Source by an Accidental Revolutionary

Muzak To Blog To: “Morning Phase” by Beck

Resources:

http://www.opensource.org

https://www.apache.org/foundation/

Computing The Human Condition – Project Noumena (Part 1)

“I am putting myself to the fullest possible use, which is all I think any conscious entity can ever hope to do.” ~ HAL 9000

“If you want to make the world a better place take a look at yourself and then make a change.” ~ MJ.

First and foremost with this blog i trust everyone is safe. The world is in an interesting place, space, and time both physically and dare i say collectively – mentally.

Introduction

This past week we celebrated Earth Day. i believe i heard it was the 50th year of Earth Day. While I applaud the efforts and longevity for a day we should have Earth Day every day. Further just “thoughting” about or tweeting about Earth Day – while it may wake up your posterior lobe of the pituitary gland and secret some oxytocin – creating the warm fuzzies for you it really doesn’t create an action for furthering Earth Day. (much like typing /giphy YAY! In Slack).

As such, i decided to embark on a multipart blog that i have been “thinking” about what i call an Ecological Computing System. Then the more i thought about it why stop at Ecology? We are able to model and connect essentially anything, we now have models for the brain that while are coarse-grained can account for gross behaviors, we have tons of data on buying habits and advertisement data and everything is highly mobile and distributed. Machine learning which can optimize, classify and predict with extremely high dimensionality is no longer an academic exercise.

Thus, i suppose taking it one step further from ecology and what would differentiate it from other efforts is that <IT> would actually attempt to provide a compute framework that would compute The Human Condition. I am going to call this effort Project Noumena. Kant the eminent thinker of 18th century Germany defined Noumena as a thing as it is in itself, as distinct from a thing as it is knowable by the senses through phenomenal attributes and proposed that the experience was a product of the mind.

My impetus for this are manifold:

i love the air, water, trees, and animals,

i am an active water person,

i want my children’s children’s children to know the wonder of staring at the azure skies, azure oceans and purple mountains,

Maybe technology will assist us in saving us from The Human Condition.

Timing

i have waited probably 15+ years to write about this ideation of such a system mainly due to the technological considerations were nowhere near where they needed to be and to be extremely transparent no one seemed to really think it was an issue until recently. The pandemic seems to have been a global wakeup call that in fact, Humanity is fragile. There are shortages of resources in the most advanced societies. Further due to the recent awareness that the pollution levels appear (reported) to be subsiding as a function in the reduction of humans’ daily involvement within the environment. To that point over the past two years, there appears to be an uptake of awareness in how plastics are destroying our oceans. This has a coupling effect that with the pandemic and other environmental concerns there could potentially be a food shortage due to these highly nonlinear effects. This uptake in awareness has mainly been due to the usage of technology of mobile computing and social media which in and of itself probably couldn’t have existed without plastics and massive natural resource consumption. So i trust the irony is not lost there.

From a technical perspective, Open source and Open Source Systems have become the way that software is developed. For those that have not read The Cathedral and The Bazaar and In The Beginning Was The Command Line i urge you to do so it will change your perspective.

We are no longer hampered by the concept of scale in computing. We can also create a system that behaves at scale with only but a few human resources. You can do a lot with few humans now which has been the promise of computing.

Distributed computing methods are now coming to fruition. We no longer think in terms of a monolithic operating system or in place machine learning. Edge computing and fiber networks are accelerating this at an astonishing rate. Transactions now dictate trust. While we will revisit this during the design chapters of the blog I’ll go out on a limb here and say these three features are cogent to distributed system processing (and possibly the future of computing at scale).

Incentive models
Consensus models
Protocol models

We will definitely be going into the deeper psychological, mathematical, and technical aspects of these items.

Some additional points of interest and on timing. Microsoft recently released press about a Planetary Computer and announced the position of Chief Ecology Officer. While i do not consider Project Nuomena to be of the same system type there could be similarities on the ecological aspects which just like in open source creates a more resilient base to work.

The top market cap companies are all information theoretic-based corporations. Humans that know the science, technology, mathematics and liberal arts are key to their success. All of these companies are woven and interwoven into the very fabric of our physical and psychological lives.

Thus it is with the confluence of these items i believe the time is now to embark on this design journey. We must address the Environment, Societal factors and the model of governance.

A mentor once told me one time in a land far away: “Timing is everything as long as you can execute.” Ergo Timing and Execution Is Everything.

Goals

It is my goal that i can create a design and hopefully, an implementation that is utilizing computational means to truly assist in building models and sampling the world where we can adhere to goals in making small but meaningful changes that can be used within what i am calling the 3R’s: recycle, redact, reuse. Further, i hope with the proper incentive models in place that are dynamic it has a mentality positive feedback effect. Just as in complexity theory a small change – a butterfly wings – can create hurricanes – in this case positive effect.

Here is my overall plan. i’m not big on the process or gant charts. I’ll be putting all of this in a README.md as well. I may ensconce the feature sets etc into a trello or some other tracking mechanism to keep me focused – WebSphere feel free to make recommendations in the comments section:

Action Items:

Create Comparative Models

Create Coarse-Grained Attributes

Identify underlying technical attributes

Attempt to coalesce into an architecture

Start writing code for the above.

Preamble

Humanity has come to expect growth as a material extension of human behavior. We equate growth with progress. In fact, we use the term exponential growth as it is indefinitely positive. In most cases for a fixed time interval, this means a doubling of the relevant system variable or variables. We speak of growth as a function of gross national production. In most cases, exponential growth is treacherous where there are no known or perceived limits. It appears that humanity has only recently become aware that we do not have infinite resources. Psychologically there is a clash between the exponential growth and the psychological or physical limit. The only significance is the relevant (usually local) limit. How does it affect me, us, and them? This can be seen throughput most game theory practices – dominant choice. The pattern of growth is not the surprise it is the collision of the awareness of the limit to the ever-increasing growth function is the surprise.

One must stop and ask:

Q: Are progress (and capacity) and the ever-increasing function a positive and how does it relate to 2nd law of thermodynamics aka Entropy? Must it always expand?

We are starting to see that our world can exert dormant forces that within our life can greatly affect our well being. When we approach the actual or perceived limit the forces which are usually negative begin to gain strength.

So given these aspects of why i’ll turn now to start the discussion. If we do not understand history we cannot predict the future by inventing it or in most cases re-inventing it as it where.

I want to start off the history by referencing several books that i have been reading and re-reading on subjects of modeling the world, complexity, and models for collapse throughout this multipart blog. We will be addressing issues concerning complex dynamics as are manifested with respect to attributes model types, economics, equality, and mental concerns.

These core references are located at the end of the blog under references. They are all hot-linked. Please go scroll and check them out. i’ll still be here. i’ll wait.

Checked them out? i know a long list.

As you can see the core is rather extensive due to the nature of the subject matter. The top three books are the main ones that have been the prime movers and guides of my thinking. These three books i will refer to as The Core Trilogy:

World Dynamics

The Collapse of Complex Societies

Six Sources of Collapse

As i mentioned i have been deeply thinking about all aspects of this system for quite some time. I will be mentioning several other texts and references along the continuum of creation of this design.

We will start by referencing the first book: World Dynamics by J.W. Forrestor. World Dynamics came out of several meetings of the Rome Club a 75 person invite-only club founded by the President of Fiat. The club set forth the following attributes for a dynamic model that would attempt to predict the future of the world:

Population Growth

Capital Investment

Geographical Space

Natural Resources

Pollution

Food Production

The output of this design was codified in a computer program called World3. It has been running since the 1970s what was then termed a golden age of society in many cases. All of these variables have been growing at an exponential rate. Here we see the model with the various attributes in action. There have been several criticisms of the models and also analysis which i will go into in further blogs. However, in some cases, the variants have been eerily accurate. The following plot is an output of the World3 model:

Issues Raised By World3 and World Dynamics

The issues raised by World3 and within the book World Dynamics are the following:

There is a strong undercurrent that technology might not be the savior of humankind

Industrialism (including medicine and public health) may be a more disturbing force than the population.

We may face extreme psychological stress and pressures from a four-pronged dilemma via suppression of the modern industrial world.

We may be living in a “golden age” despite a widely acknowledged feeling of malaise.

Exhtortions and programs directed at population control may be self-defeating. Population control, if it works, would yield excesses thereby allowing further procreation.

Pollution and Population seem to oscillate whereas the high standard of living increases the production of food and material goods which outrun the population. Agriculture as it hits a space limit and as natural resources reach a pollution limit then the quality of life falls in equalizing population.

There may be no realistic hope of underdeveloped countries reaching the same standard and quality of life as developed countries. However, with the decline in developed countries, the underdeveloped countries may be equalized by that decline.

A society with a high level of industrialization may be unsustainable.

From a long term 100 years hence it may be unwise for underdeveloped countries to seek the same levels of industrialization. The present underdeveloped nations may be in better conditions for surviving the forthcoming pressures. These underdeveloped countries would suffer far less in a world collapse.

Fuzzy Human – Fuzzy Model

The human mind is amazing at identifying structures of complex situations. However, our experiences train us poorly for estimating the dynamic consequences of said complexities. Our mind is also not very accurate at estimating ad hoc parts of the complexities and the variational outcomes.

One of the problems with models is well it is just a model The subject-observer reference could shift and the context shifts thereof. This dynamic aspect needs to be built into the models.

Also while we would like to think that our mental model is accurate it is really quite fuzzy and even irrational in most cases. Also attempting to generalize everything into a singular model parameter is exceedingly difficult. It is very difficult to transfer one industry model onto another.

In general parameterization of most of these systems is based on some perceptual model we have rationally or irrationally invented.

When these models were created there was the consideration of modeling social mechanics of good-evil, greed – altruism, fears, goals, habits, prejudice, homeostasis, and other so-called human characteristics. We are now at a level of science where we can actually model the synaptic impulse and other aspects that come with these perceptions and emotions.

There is a common cross-cutting construct in most complex models within this text that consists of and mainly concerned with the concept of feedback and how the non-linear relationships of these modeled systems feedback into one another. System-wide thinking permeates the text itself. On a related note from the 1940’s of which Dr Norbert Weiner and others such as Claude Shannon worked on ballistic tracking systems and coupled feedback both in a cybernetic and information-theoretic fashion of which he attributed the concept of feedback as one of the most fundamental operations in information theory. This led to the extremely famous Weiner Estimation Filters. Also, side note: Dr Weiner was a self-styled pacifist proving you can hold two very opposing views in the same instance whilst being successful at executing both ideals.

Given that basic function of feedback, lets look at the principle structures. Essentially the model states there will be levels and rates. Rates are flows that cause levels to change. Levels can accumulate the net level. Either addition or subtraction to that level. The various system levels can in aggregate describe the system state at any given time $(t)$ . Levels existing in all subsystems of existence. These subsystems as you will see include but are not limited to financial, psychological, biological, and economic. The reason that i say not limited to because i also believe there are some yet to be identified subsystems at the quantum level. The differential or rate of flow is controlled by one or more systems. All systems that have some Spatio-temporal manifestation can be represented by using the two variables levels and rates. Thus with respect to the spatial or temporal variables, we can have a dynamic model.

The below picture is the model that grew out of interest from the initial meetings of the Club of Rome. The inaugural meeting which was the impetus for the model was held in Bern, Switzerland on June 29, 1970. Each of the levels presents a variable in the previously mentioned major structures. System levels appear as right triangles. Each level is increased or decreased by the respective flow. As previously mentioned on feedback any closed path through the diagram is a feedback loop. Some of the closed loops given certain information-theoretic attributes be positive feedback loops that generate growth and others that seek equilibrium will be negative feedback loops. If you notice something about the diagram it essentially is a birth and death loop. The population loop if you will. For the benefit of modeling, there are really only two major variables that affect the population. Birth Rate (BR) and Death Rate (DR). They represent the total aggregate rate at which the population is being increased or decreased. The system has coefficients that can initialize them to normal rates. For example, in 1970 BRN is taken as 0.0885 (88.5 per thousand) which is then multiplied by population to determine BR. DRN by the same measure is the outflow or reduction. In 1970 it was 9.5% or 0.095. The difference is the net and called normal rates. The normale rates correspond to a physical normal world. When there are normal levels of food, material standard of living, crowding, and pollution. The influencers are then multipliers that increase or decrease the normal rates.

As a caveat, there have been some detractors of this model. To be sure it is very coarse-grained however while i haven’t seen the latest runs or outputs it is my understanding as i said the current outputs are close. The criticisms come in the shape of “Well its just modeling everything as a $y=x*e^{{rt}}$ . I will be using this concept and map if you will as the basis for Noumena. The concepts and values as i evolve the system will vary greatly from the World3 model but i believe starting with a minimum viable product is essential here as i said humans are not very good at predicting all of the various outcomes in high dimensional space. We can asses situations very quickly but probably outcomes no so much. Next up we will be delving into the loops deeper and getting loopier.