SIMulation vs EMulation

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

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

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.

Comparison

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.

Why the Sun does NOT track East-West

(Most of the time)

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…

• In the winter or summer, your shadow points east-west.
• In the fall, put the sun over your right shoulder to follow an east-west path.
• Likewise, in the spring, put the sun over your left shoulder to follow an east-west path
• When a map shows that a road runs north-south or east-west, it runs north-south or east-west, regardless of where the sun points.