As for considering this a "new platform" of sorts, I have a question: Is there a way to verify the authenticity of the file? Is it possible to tamper with the file to make it do things that are impossible in actual gameplay? If it is possible, does this mean that we simply have to trust the submitter that the recording has been genuine?
Is my life-long dream of seeing a Doom TAS finally coming into fruition?
That being said, the rules say that the hardest difficulty should always be chosen unless there's a very good reason not to. In this case I don't see what that reason could be. On the contrary, choosing the nightmare difficulty would showcase the prowess of TASing. This run looks perhaps a bit too much like a regular segmented speedrun of the game...
I usually end up TASing games that I realize have already been submitted to the site, but to avoid breaking rules I just upload them to Youtube for reference.
Hmm? There is no rule that says you can't submit a TAS for a game that already has one published. (Of course yours needs to improve on it if you want it to have a chance of being published, but no rule stops you from submitting in either case.)
Let's hope they get over that stupid castle in the premiere double-episode and forget it for the rest of the season. Although it will inevitably be there in every single episode as an eyesore, just to remind us how ugly and unbefitting it is.
Man, I already miss the cozy tree library, even though I have yet to see a single episode where it doesn't exist anymore.
Unless you actually give me something to work with, like a definition of what you consider to be a "simple" description of a number, I can't respond to your questions and arguments in any satisfactory way. I myself find the description for Graham's number fairly basic: the arrow notation isn't hard to understand and neither is the recursion it's defined with. Sure, I can't grasp the resulting number, but that goes for a googol too.
Actually I think you are demonstrating my point quite well. You can't come up with a simple, intuitive description of the number, which is what makes it so inconceivable.
yet the definition of Graham's number does not count, we can't understand these reasons or argue against them. After all, all are just definitions of numbers in arbitrary systems, so where do you draw the line? What is "a simple manner"?
Well, try to explain the magnitude of Graham's number in a simple manner that's easy to understand.
Your capacity to write down the definition of a number in a system of choice is a metric you yourself dismiss: after all, if it were one, the possibility of defining Graham's number would make it conceivable.
I think you are being intentionally obtuse.
The size of googol is trivial to explain to the average person. Even the average person has some grasp of a concept like "a 1 followed by a hundred zeros". As I have said several times, it's not a question of the average person understanding the exact size of the number, but a notion of how large it is, in common terms that can be related to common concepts.
And of course there are myriads of other ways you could describe the size of a googol (such as describing the diameter of a sphere of water made up of that many molecules, for instance.)
Googol is very easy to describe, and it's very easy to compare it to other numbers of similar magnitude. Its magnitude can be grasped. Conceived.
Googolplex is admittedly a bit harder to describe, but there nevertheless are relatively simple descriptions of it, like the several examples I quoted from wikipedia.
However, Graham's number is so immensely large that it defies any such description. You just can't describe it as "a 1 followed by n zeros" (because you can't express n in a simple manner), or "n times the atoms in the universe" (again, because n can't be easily described) or anything like that. You simply can't compare Graham's number to anything, which means you can't get a grasp of how big it really is, compared to anything.
You understand perfectly what I mean, yet you still argue against it. Why?
in which case it's pointless arguing with you.
How exactly did my semi-humorous post become a flamewar?
The size of googol is trivial to demonstrate. After all, it's 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.
No, a million is easy to conceive because you can say, for example, "10x10x10 meters of water weights a million kilograms".
The thing is, even if you consider those verbal descriptions of googolplex highly abstract, my point is that there just is no such description for Graham's number. You can't just say, for example, "writing down Graham's number would take 1010000000000 books", because that would be way too little.
Wikipedia itself gives examples of how you can describe the magnitude of googolplex:
"Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes."
"A typical book can be printed with 106 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore it requires 1094 such books to print all zeros of googolplex."
"if a person can write two digits per second, then writing a googolplex would take around about 1.51×1092 years, which is about 1.1×1082 times the accepted age of the universe."
Graham's number, however, has no such easily understood description because of its sheer magnitude.
First, as a simple example, the vast majority of numbers are literally inconceivable because they are not computable or definable.
I'm talking about magnitudes, not about exact numbers. The magnitude of something like pi is easy to describe by comparing it to a real thing, even though you could never know its exact representation. Exact representations are not the point.
Sure, there are infinitely many uncomputable and undefinable numbers between 0 and 1, but their magnitude is trivial to grasp. After all, they are between 0 and 1.
Second, I mostly agree with you on Graham's number. However, it can be defined rather succinctly. If you accept some notion of chained arrow notation, then it's not all that hard to "conceive" of a number greater than Graham's number.
To the average person the arrow notation says absolutely nothing. It's just an abstract notation. It doesn't give them a notion of the magnitude of the number because it can't be compared to anything else that's more tangible.
But there are numbers that stretch beyond inconceivability. For a simple and familiar example, consider a googolplex, which is 10^10^100.
The magnitude of googolplex can be more easily understood because it uses familiar notions, namely exponentiation, and only two levels of it. I'm sure one can come up with a visualization of the magnitude that can give even a vague idea of its size. It's not inconceivable.
Graham's number, however, uses too many levels of exponentiation to be describable by comparing it to anything. It just escalates way too quickly and defies all comparison. It defies all description.
Are less people signing up and actively participating in the tasvideos forums? The vast majority of avatars are way too familiar... Really rarely do I see an avatar I have never seen before (even more rarely from someone I don't remember seeing before, and whose post count is really low.)
(This is not really a math question, but given that it's about math, I thought it would be appropriate here.)
The memetic phrase "you keep using that word; I do not think it means what you think it means" is a quote from the movie The Princess Bride.
The word in question being referred to is "inconceivable". The character (who is using it "incorrectly") is using it to mean "incredible" or "hard to believe". Yet, as the other character says, there may be a subtle difference.
"Inconceivable" means "difficult or impossible to be conceived" (rather than difficult or impossible to believe.) But what could be a concrete example of something that's inconceivable?
The human mind perceives the "size" of numbers mostly by comparing them to real things, or multiples of the size of real things. We compare very large numbers to things like "the number of atoms on Earth" (or even "the number of atoms in the universe"), or things like "the size of our galaxy/universe".
Even if we don't really have a good grasp of how large that amount is, it nevertheless anchors it to something real that we can compare to. Although the exact size may be more intangible to our brains, it nevertheless allows us to compare bug numbers between themselves. For example if something is "as big as Earth" and something else is "as big as the solar system", we get a concept of which one is significantly larger than the other.
We often also use multiples of these real things to get a picture of the quantity, by saying things like "a trillion times the number of atoms in the universe", or "a trillion times the mass of the Sun". Again, while the actual quantity remains pretty abstract, it nevertheless gives us a comparison point, so we can compare the large numbers between themselves, and know which one is clearly larger than the other. Something that's "a trillion times the size of our galaxy" is much larger than something that's "the size of our solar system".
Graham's Number, however, defies all visualizations and comparisons to real things, even if using multipliers. There exists no way to adequately compare it to anything. You can't say something like "Graham's number is as big as a trillion trillion trillion times the number of subatomic particles in our universe", because that would still be way, way too small of a number. Graham's number is so immensely large, that there is no simple sentence, comparing it to the size of anything real, that can be used to describe its size. It is basically impossible for our brains to have even a vague concept of how large it is.
In other words, the size of Graham's number is truly inconceivable.
There is no necessity for the simulation to run in real-time or slower. It can also run faster, exactly like an emulator can run the game slower, in real-time or faster than the original console.
(This is assuming that the "meta-universe" where this simulation is running even has the same concept of "time" as we do. It's not completely out of the realm of conceptuality that what we perceive as "time" is also an artificial simulation, and there is no such thing in the simulating universe.)
This video shows how much it takes for light to travel from the Sun to Jupiter... but of course from a completely Newtonian point of view. Relativity is not taken into account in any way.
Never mind what it would look like. I'm, however, interested in the actual times.
Light takes approximately 8 minutes 20 seconds to travel from the Sun to Earth... from our point of view. From the photon's own point of view it takes 0 seconds.
So I was thinking: At what speed would you need to travel so that, from your own point of view, it takes you 8 minutes 20 seconds to travel from the Sun to the Earth? (To simplify the calculations, let's just assume special relativity, unless someone is really willing to go to GR.)
131. It really helps if you understand the xor operation (which most programmers do).
I think this is one of the problems with most IQ tests: Your experience affects the result a lot. A person with the exact same IQ but with less experience on such things would score less.
It's common to use the term "non-euclidean geometry" in video games where the level geometry does not follow logical physics. For example you are seemingly inside a close room with a column at its center, but if you walk around the column you end up in a completely different place (typically there's some kind of "portal" surface at one side of the column that connects the level to another completely different level.) For example the game Antichamber is based on this.
Is "non-euclidean geometry" a misnomer in this case? It doesn't sound like a case of hyperbolic or elliptic geometry.
It turned out that DOSBox wasn't "a 100% emulated environment so it's completely independent of the system that's running it."
What I mean is that the environment is emulated 100%, just like eg. a NES emulator does. It's not just a thin compatibility layer over the underlying OS (which means that DOSBox works on a multitude of platforms and OSes.)
What I'm getting at here is that in principle this ought to allow making it as deterministic as any other emulator.
DOSBox has tons of settings that can be fine-tuned. I'm wondering if Bisqwit's case wasn't simply a question of those settings being different.
Euclidean, hyperbolic and elliptic geometries are the only three alternatives in this context? Is a spherical coordinate system an elliptic geometry?
Why isn't it possible to circumscribe every possible triangle in hyperbolic geometry?
Please remind me again why DOSBox can't be used for TASing. (DOSBox is a 100% emulated environment so it's completely independent of the system that's running it.)
Is it simply because TAS tools haven't been implemented in DOSBox?
(Not that DOSBox would help with Binding of Isaac, because it only emulates DOS games, but still... The question was if there are any other PC emulators.)
Wikipedia asserts that Euclid's parallel postulate is equivalent to Pythagoras' theorem. It also asserts that it's equivalent to the postulates "every triangle can be circumscribed" and "there is no upper limit to the area of a triangle" (Wallis axiom).
The equivalence between those postulates seems extremely non-self-evident and unintuitive. Could someone explain why they are equivalent?
