Science is a tool that mankind uses to expand our technical knowledge of the world and universe around us.
People use the term “science” broadly, but it has a specific meaning:
Performing an experiment to determine the outcome of a closed system when an independent variable within that system is modified.
You don’t have to have a degree to be a scientist. A scientist is anyone who follows a rigorous scientific process, called the scientific method:
Observe, Analyze, Hypothesize, Experiment, Conclude, Repeat
Please enjoy these science-related posts.
If you have a set of things, a permutation is a specific way that you can list those things. Although algorithms exist to list every permutation, most of them rely on recursion – the calling of a function from within itself – which is horribly inefficient.
If you want a non-recursive algorithm that lists every permutation, keep reading…
This question came up in the context of another topic, and I immediately envisioned an excellent interview question:
Explain the difference between simulation and emulation
As someone who has written thousands of simulations, this is how I would answer that question…
Simulation is a closed system where the state “S” contains all relevant variables and their values, and S(i) describes those values at a specific iteration within the simulation.
S = { V0..Vk }
S(i) = {V0,i; V1,i; .. Vk,i}
Based on the variable values in S(i) and a system of rules A{R0… Rm}, the simulation calculates a new state, S(i+1).
In the simulation, we have a starting state, S(0) and an eventual end-state S(n), which is created after n iterations of the simulation. We start with S(0) and apply the rules of A{} in order to obtain S(1), and this continues until we reach S(n).
So explicitly, a simulation requires feedback from the current state in order to create a subsequent state, given a specific set of variable values and a specific set of rules that operate on those values.
Emulation is a simulation whose rules are copied from another system.
Given a set of rules that describe system B: {R0..Rm}, if system A is an emulation of B then it simply contains the same rules:
A = B = {R0..Rm}
Given any state S(i) and a set of rules A{}, if we apply those rules to the current state, we get a new state S(i+1):
S(i+1) = A{} -> S(i)
Given the same state S(i) and another set of rules B{}, if we apply the rules in B{} to the current state S(i), we get S'(i+1), which is an “alternate-reality copy” of S(i+1):
S'(i+1) = B{} -> S(i)
If two different sets of rules A{} and B{} applied to any possible state S(i) produce the same next state, then:
S'(i+1) = S(i+1)
And therefore:
A is an emulation of B or vice-versa.
The important detail is that both systems A and B are equivalent, but they might not be implemented the same way – for example, the rules of B might be implemented in hardware, while A might be a software emulation of B.
Emulation is a specific simulation that answers the question: “how would some other specific system respond, given a state of S”.
Conversely, in a simulation, you can have a set of independent rules that aren’t tied to any other system – the simulation is simply answering the question: “what would happen, if…”
I’ve seen definitions of both simulation and emulation that tie to copying something from the real world, but I disagree. For example, I could easily write a simulation of a 4D solid traversing 3D space, which is a completely hypothetical model that has no tie to the real world.
Likewise, if you copy the rules of some arbitrary simulation over to another system, then you’ve emulated the original simulation, with no ties to the real world – for example, you could emulate our clearly-contrived 4D solid simulation by copying its rules from a state diagram or a set of software commands to some other equivalent logical system – for example, the logical rules within a game simulation.
Which brings us to a final point: Simulations (and by extension, emulations) can contain other simulations. For example, you could have a simulation of a digital pet within a simulation of a digital world. The state logic and iteration of the digital pet could be driven inside the world simulation, or it could be driven externally and simply rendered based on its current state. If the digital pet is driven inside the world simulation, it could be driven within the code of the simulation (created at compile time), or it could be implemented as part of the logical rules of the world – for example, as a script or state machine that’s created using in-world tools during runtime.
We were brought up learning “the sun rises in the east, and sets in the west”, which is absolutely true.
Anyone with experience in the outdoors, including scouting, will probably have been told:
In the morning, follow your shadow to travel west.
In the afternoon, follow your shadow to travel east.
And… moss grows on the north sides of trees, etc…
HOWEVER….
That’s not always EXACTLY true…
About a year ago, I had a discussion about a road that runs north-south, and why the sun doesn’t track east-west.
It went like this:
Him: East is THAT way (points southwest)
Me: Um… No. The road there runs north-south, so east is perpendicular to that road.
Him: Well, I was always taught that the sun points east-west.
Me: That’s not exactly true, because the Earth is tilted on its access, causing certain parts of the Earth’s surface to be closer to the sun…
Him: I don’t believe all that…
Me: It’s spring. Go stand at the fence pole and walk from the fence to the house, following the sun’s path. Then, do it again, same time of day, 6 months from now.
(To this day, we disagree on due east)
When I instinctively mentioned the Earth’s orbit, and the 23 degree tilt of Earth’s axis, I knew that to be correct, but I ended up dwelling on the actual mechanics.
So, here we go…
The Earth is tilted on its rotational axis by 23 degrees, relative to its orbital orientation around the sun.
As a result, over the course of a year, which is the Earth’s orbital period, that tilt causes the Earth’s orientation relative to its orbital plane to change.
In the winter and summer, if you were to slice through the center of the sun with a big knife, along the axis of the Earth’s rotation, the sun would be sliced vertically – perpendicular to the orbital plane, which is the path that the Earth follows as it orbits the sun.
However, in the spring and fall (and all other times), the Earth is canted with respect to the orbital plane, and thus if you were to slice through the sun’s center with a knife aligned with the Earth’s rotational axis, the sun would be cut at an angle with respect to the orbital plane.
In the summer, the Earth’s north pole is canted toward the sun. From the sun’s perspective, its track is perfectly parallel to the Earth’s equator, which is perpendicular to the Earth’s rotational axis.
Likewise, in the winter, although the Earth’s north pole is canted away from the sun, the sun’s track is still parallel to the Earth’s equator.
In the spring and fall, the plane of the Earth’s rotational axis is tilted from the sun’s perspective.
In the spring, from the sun’s perspective, the Earth appears tilted to the right, causing the sun’s track to pass along a path that’s rotated counter-clockwise relative to the Earth’s equator and rotational axis.
Likewise, in the fall, the Earth is tilted in the opposite direction due to its orbit, and the sun’s track appears rotated clockwise relative to the Earth’s equator and rotational axis.
Thus, in winter or summer, the sun’s track follows a true east-west path. At every other time, the Earth appears slightly tilted to the sun, causing the sun’s track to follow a northeast-southwest track in the spring, or a southwest-northeast track in the fall.
So, to all of you scouts out there…
Or, why floating point operations are slow, and how to avoid them.
Using a color scale to visualize output makes it easy to understand data, and see patterns that aren’t intuitive.
A simple 1 or 2-color scale is really simple to implement, but what if you want to use the whole spectrum?
Download the PDF:
Creating Mazes Using Cellular Automata_v2.pdf
Download the Windows EXE:
mazegen_v6.exe
In 1984, there was an annular solar eclipse visible from Texas, and every school-aged student made a pinhole projector, that allowed you to view a representation of the sun and the shadow of the moon as it passed in front.
Now, everyone has a smart phone, so in honor of the upcoming August eclipse event, why not make “an app for that”?
Update: Now takes time-lapse photos
Or as I call it:
First, let me present the app and how it works.
Later, a rant about Google Play
From time to time, I run across a vendor who says:
We have over 40 years of combined experience…
What does that really mean?
The intended meaning is that, if there are 4 people in the room, they each have about 10 years of experience.
But, it could also mean that one of them has 39 years of experience, and the other three have been in the business for only 4 months!
Further, let’s say that this particular vendor is an AI (Artificial Intelligence) consultant – why would I want 40-year-old advice from the mid 1970’s, when the largest computers of that era didn’t have as much computing power as my smart phone?
Essentially, we have a set of scalars that are supposed to represent the respective sizes of each individual’s experience base within the group.
Let’s say we have 4 people:
This gives us a set of 4 scalars: {12, 15, 8, 10}
Although there are many valid ways to compare and combine these numbers, there are also very many ways to combine them, that don’t make sense.
At the end of the meeting, Stacy proudly proclaims, “we have 45 years of combined experience“, because she added all of these scalars, but what does that really mean?
It’s not like the team are simply ONE person who becomes eminently more qualified with combined magnitude. Take the case of our most junior member – in theory, if we give Johnny another year of experience, he still sits within the footprints of all three of his other team members. The team’s range of experience is really based on it’s most senior member (Stacy).
It’s not like there is some kind of historical significance, as if getting to some magic number of combined experience qualifies the team for an historical marker. If they make it to 100 years of combined experience, they can’t proclaim “experience since 1917!”.
Talking about a set of numbers that each represents a constant value is just like combining height: Unless you plan to have them stand on each others’ shoulders, or make them lay on the ground end-to-end, the “combined height” would be completely pointless. The statement, “we have 22 feet of consultants visiting us today…” just doesn’t make any sense. Nor would it make sense to say, “it took 600 pounds of consultants to fix this problem”.
Instead, if we understand that we have a set of 4 people, and each scalar in the set represents ONE of the four people, we can come up with some meaningful metrics by comparing rather than combining:
Likewise, if we’re talking about numbers that reflect a rate, such as salary or billable rate, it might make sense to say, we had four consultants come in for a meeting. Their combined billable rate was $800/hr, and the meeting lasted two hours, so the cost of the meeting was $1,600.
When you use math to compare or combine a set of numbers, ultimately, you have to maintain perspective about what those numbers really mean.
If you combine numbers in ways that don’t make sense, you might create a meaningless metric.
More to come, later. I just posted this video showing a time-lapse execution of a simple algorithm to use the digits of Pi as a source of drawing instructions.