Author Archives: Cameron
“We are the Universe experiencing Itself.”Neil deGrasse Tyson
Dr Tyson wasn’t the first to express this sentiment; in fact, philosophers and prophets have been saying it for thousands of years. It’s similar to the statement in Genesis that man was given dominion over the Earth (Genesis 1:28). Humanity is placed within the universe, but at the intellectual apex of it. It’s as if all the components of the cosmos were the base and walls of a pyramid, with thinking human beings were at the top. At the same time, those human beings are constantly looking outward, to absorb and comprehend all that is.
It’s a statement of what it is be a human. To be human is to be an unerasable piece of the vast and mysterious cosmos. Learning, discovering, analyzing, imagining–all these things change us, and in changing ourselves we change the universe of which we are part. Beliefs form the basis of knowledge, and by extension, conscious choice. In the modern world, we’re presented with an array of beliefs–a buffet of thoughts and paradigms to select from. It’s bewildering and requires us to choose with imperfect knowledge. Many delay those choices until deep into adulthood. But beliefs become the basis from which one’s intellect is built, so an initial set of beliefs must be chosen. Trees need roots to become anything more than a thin twigs jutting from the ground. In the same way, a person needs a set of beliefs to grow from. Then, through experience and experimentation, our beliefs evolve.
Many books that are about an area of science–whether it’s cosmology, medicine, or chemistry–tell a narrative of the development of knowledge in that area. I think it’s not just because narrative is so important to people, but also because learning about the world around us changes us. And by changing ourselves, we change our world. We change the universe. Stories about the growth of knowledge become stories about the growth of the universe itself.
The first people to develop cities were the Sumerians. They dug canals in Mesopotamia, between the Tigris and Euphrates rivers, growing wheat and barley. In their fallow fields they herded sheep, goats, and cattle. They built cities and towers from clay brick and pitch. They invented writing, mathematics, and constructed the first wheels. They created the first piece of written literature, the Epic of Gilgamesh, a tale of a bad king who tries to defeat death. As Paul Cooper points out, their civilization had begun, reached its zenith, and collapsed before the last woolly mammoth died.
For the Sumerians the world was a round plate of land floating atop a vast ocean of bitter water, the sea. The sea surrounded the land, while sweet water filled the heavens. The sky was a dome that held the waters in the heavens high above the land. Clouds and rain were courses of water that passed through the ephemeral fabric of the sky. Sweet water from the mountains filled the rivers that nourished the people and their crops. In the Babylonian mythos, which was adapted from the Sumerian, the universe was not created from nothing. Instead, it sprang into existence when the god Marduk slayed Tiamat, the chaotic dragon-goddess of the sea. The Sumerian model spread throughout the old world, and is the basis of many religious texts.
Our understanding of the universe has changed, but many of those changes are more superficial than they appear at first glance. Untamable Tiamat has been replaced with a hot, roiling instanton. The god Marduk has been replaced with the unfractured pressure of the four fundamental forces. The symbolism of myth has been replaced with the abstract language of mathematics. The death-defying hero, Gilgamesh, has been replaced with millions of researchers, students, writers, and spectators. In short, all of us.
To discover, learn, and grow, is to change the universe. We are beings looking outward, searching the heavens. And there among the galaxies, we discover ourselves.
I bring fresh showers for the thirsting flowers,
From the seas and the streams;
I bear light shade for the leaves when laid
In their noonday dreams.
From my wings are shaken the dews that waken
The sweet buds every one,
When rocked to rest on their mother’s breast,
As she dances about the sun.
I wield the flail of the lashing hail,
And whiten the green plains under,
And then again I dissolve it in rain,
And laugh as I pass in thunder.
The Cloud, Percy Bysshe Shelley
As a child I spent what seemed like hours at a time watching clouds move across the sky, shifting shapes as they went. Seeing dragons, devils, ships, and castles moving and morphing across a blue canvas. I can’t be the only one. Rain clouds rolled in this morning and I found myself watching as a few low-lying, dark gray ones trundled along beneath the overcast sky.
Lower clouds appear to be moving faster than higher ones, but this is an illusion. In reality, wind speed increases with altitude. But when a low cloud bears down in its dark and shadow and immensity, it’s nearly impossible not to tremble at one’s own insignificance.
So, what creates the illusion of faster movement? The answer lies in the changing angle of an observer’s eye as it tracks a cloud. The observation angle changes faster when a cloud moves faster or when it’s closer to the observer. Closer can mean altitude–the cloud is lower in the sky, or it can mean distance over the ground–the cloud is closer to being directly above the observer.
So how much difference does it make?
Start with the sky, and a cloud, and it’s a sunny day, and there’s a guy standing on the ground looking at the cloud. The cloud’s altitude is a, and the distance over ground is d. Take a line straight into the sky and another that goes from the guy’s eyes to the cloud. Those two lines make an angle, θ. A breeze blows on the cloud, pushing it horizontally with velocity H, and vertically with velocity V.
So now for the nerdy stuff. When the cloud’s to the right of the dude, d and θ are positive, and to the left they’re negative. a is always positive. H is positive when going right and negative when going left. V is positive when the cloud moves up and negative when it moves down. The tangent of θ is d divided by a, and can be calculated if their lengths are known.
The total change of the angle θ with time is found by adding the change in angle due to horizontal movement to the change due to vertical movement:
Gad, that’s ugly to work with. It basically says when the cloud flies left, the angle changes in the negative direction. When the cloud is to the right of the observer, the angle changes in the positive direction when the cloud moves down, and in the negative direction when it moves up. And when the cloud is to the left, vertical movement causes changes in the opposite direction. How does it look when calculated?
I started with altitude and horizontal distances of 200 feet, and since they’re equal, the angle is 45 degrees. The cloud flies by at 10 feet per second, and the observers eyes track it across the sky. Here’s what the angle, θ looks like over time. It starts out at postive 45 degrees, reaches zero when the cloud is directly overhead, and goes negative as it flies to the right of our guy on the ground.
So what happens if the cloud is now 20 feet off the ground instead of 200, and still whizzing by at 10 feet per second? Well, at first it’s just a cloud on the horizon, getting bigger and bigger, and our guy’s head doesn’t even have to move. It takes 15 seconds for the angle of observation to go from 85 to 70 degrees. Then the cloud flies over in a tear, going to an angle of -70 degrees in only 13 seconds, before shrinking into the horizon.
This reminds me of something:
“How did you go bankrupt,” Bill asked.
“Two ways,” Mike said. “Gradually and then suddenly.”
—Ernest Hemingway, The Sun Also Rises
A shot of the excel sheet and the formulas are below. Happy cloud watching.
B3 = A2 + E2 and copy down
C3 = C2 + D2 and copy down
F2 = DEGREES(ATAN(C2/B2)) and copy down
G2 = F2 – F3
Got a secret
Can you keep it?
Swear this one you’ll save
Better lock it in your pocket
Taking this one to the grave
If I show you then I know you
Won’t tell what I said
‘Cause two can keep a secret
If one of them is dead?
— The Pierces
Like most folks I enjoy a good conspiracy theory, and sometimes even a bad one. They allow the listener to suspend disbelief and consider for a moment that the social world in which he or she resides is an illusion. This is somewhat similar to the ability to slip into the fictional world of a story or novel, and bears similarity to the Gnostic assertion that the material realm is an entrapping illusion. In fact many very good films are based on the idea that conspiracies are afoot–the Bourne, Mission Impossible, Star Wars, and of course the Matrix series.
In modern societies, however, there are many conspiracy theories peddled as truth that cause real harm to their believers. One recent example from my country is PizzaGate–a ridiculous story based on the notion that a major Presidential candidate was operating a pederasty ring through a Washington DC pizza place–that led to a believer carrying out an armed raid. Another example is the belief that childhood vaccination is a cause of autism, an assertion founded on falsified data. Failure to vaccinate has led to numerous outbreaks of dangerous epidemic diseases in just the last few years. I should note that the longest running conspiracy theories I know of aren’t theories at all because in the minds of their believers they aren’t disprovable. In that sense they are fictitious certainties,
In his 2016 paper “On the Viability of Conspiratorial Beliefs” Dr David Grimes of Oxford University applied probability models to four popular conspiracy theories–NASA moon landing hoax, climate change fakery, vaccination-autism link, and cancer cure conspiracy. His model simulates the probability of a conspiracy being leaked using a Poisson distribution with conspiracy population parameters based on exponential decay, the Gompertz function, and no change. In order to understand Dr Grimes work a little better, I coded his equations in Octave and simulated his parameters, replicating the generalized results displayed in Figure 1 of the paper.
In examining the work I found one point where I wanted to test a variation. The population parameters and probability distribution used in the paper are continuous–the growth models allow for fractions of a conspirator to leak information. I added an integer rounding function to the population parameters. I also decided on a binomial discrete probability function, where the probability of a leak is treated similarly to the probability of a defective part rolling off an assembly line. I also added a parameter that allows for a leak, presumably to the press, to require verification from additional defectors.
To test this formula I decided to test the fake job numbers conspiracy. The idea is that the US Bureau of Labor Statistics was cooking up job numbers in 2012 to assist the reelection campaign of President Obama. A few problems with this are:
- The BLS employs more than 2500 individuals with a broad range of political preferences
- Job figures are also measured by private firms, such as Gallup and ADP, which show different raw numbers but similar trends
- There really isn’t any evidence that the average American voter pays close attention to economic releases
The down side to the discrete formula is that it uses factorial numbers to calculate the binomial coefficient. Numbers greater than 170! are treated as infinite by Octave. To mitigate this, I used a conspiracy population of 100, with an individual chance of leaking at 0.1% per year, and a press requirement of 2 defectors to publish the leak. While it looks like it would be possible to carry out such a conspiracy one time, the chance of the conspiracy being broken in 80 years is 91.49%. If one assumes a single leaker is sufficient, the chance of discovery rises to more than 99.99%. The chance of carrying it out with the involvement of 2500 must be slim indeed.
The m file code for the discrete distribution is below:
function conspViaDisc(decayType, p, N0, numIt)
x = [1:numIt]; % fill x-vector for x-axis values
alpha = 10^-4;
beta = 0.085; % alpha & beta for gompretzian function
te = 40; % mean age of conspirators
lifeExp = 78; % mean life expectancy of conspirators
lambda = log(2)/(lifeExp-te);
N(1) = N0;
a = 1; % Number of leakers needed to break the conspiracy
if decayType == “G”
for n = 2:numIt
N(n) = int16(N0*exp(0-lambda*n)); % Gompretzian decay
elseif decayType == “E”
for n = 2:numIt
N(n) = int16(N0*exp((alpha/beta)*(1-exp(beta*(te+n))))); % Exponential Decay
for n = 2:numIt
N(n) = N0; % No Decay
L(1) = 0.001; % Estimated probability of discovery in timestep 1
cumL(1) = L(1);
for n = 2:numIt
if N(n) >= a
summ = 0;
for m = 1:a
s = m-1;
binCoef = factorial(N(n))/(factorial(s)*factorial(N(n)-s));
summ += binCoef*(p^s)*((1-p)^(N(1)-s));
L(n) = (1-summ)*(1-cumL(n-1));
cumL(n) = cumL(n-1) + L(n);
L(n) = 0;
cumL(n) = cumL(n-1) + L(n);