If you tried to represent all of your integers using only three digits, you would need an infinite selection of characters
I didn't say that you can represent all integers with three digits. I said you can represent all integers (and rational numbers) with three symbols.
If you place a limit on the number of characters, then you will need a potentially infinite number of digits to represent all of your numbers.
So what? That's not the point. The point is that any integer (or rational number) can be represented with a finite sequence of symbols (from a finite set of them). There's no integer that would require an infinite amount of them. (Also, this representation is not dependent on ancillary things like the size or shape of those symbols.)
The same cannot be said of real numbers. You cannot represent every single real number with a finite sequence of symbols (from a finite set).
So far there are only 10 numbers, 26 letters of upper and lower case and however many other special symbols you want to add to your alphabet. If you want to represent all the integers with only three symbols, you're going to have a bad time.
You would need the aleph-naught members in your alphabet in order to represent all the integers if you only wanted to use 3 letters/numbers/characters.
Or are you talking about how many unique symbols you need? In which case, you can use one symbol to represent all rational numbers.
I don't even understand what you are talking about there. There's some kind of miscommunication issue at play here.
"If you want to represent all the integers with only three symbols, you're going to have a bad time." "you can use one symbol to represent all rational numbers." This seems to be saying that you can't represent all integers with three symbols, but you can represent all rational numbers with one symbol. Pardon me if I find this highly contradictory.
If you are talking about referring to rational numbers of the form a/b, and saying that requires only two symbols, you are mistaken
Ok, it requires three: Two digits and a way to separate the numerator from the denominator. (Although you can use a sequence of digits to first tell how many digits are in the numerator, and end it with a unique sequence. It's simpler if you just use three symbols.)
(unless you have an infinite alphabet).
Where's that coming from?
It only requires one integer to represent all rational numbers anyway, since the number of rational numbers is countable.
But you still need (at least) two digits (ie. symbols) to represent the integer.
If we eschew the requirement that it be representable in the universe then we can simply represent each number by a line segment with a length in any sufficiently well defined unit system.
I hope you understand why that sounds so unsatisfactory as an answer, even though it's difficult to define "representation" in this context.
A small amount of symbols (in fact, two) is enough to represent all integers and even rational numbers, and the representation is trivial to define and to interpret. It does not require supernatural accuracy. (Even though such a representation is arbitrarily large, any given integer or rational number has a finite representation that could in principle be trivially interpreted, simply by reading the sequence of two symbols.)
Your suggestion is extremely non-trivial, requires an infinite amount of symbols and, basically, requires infinite accuracy in order to be interpreted correctly (which is quite unlike the representation of integers, which is always finite and trivial to interpret, no matter which integer you choose.) It's also dependent on the physical shape of the symbol (something that integers/rationals do not require at all.) Can it be called a "symbol" at all?
As for rating a movie when it is a submission, I thought of that back in 2008. Seemed like a great idea, all those votes would turn into ratings and improve the rating system and give judges more information for judging. But it clearly failed. Instead people rated 10 on movies, to see them published, and ratings were heavily inflated. We reverted back.
The idea of having more than two categories (well, three) in the submission voting may indeed sound like a great idea at first. However, as you say, it's prone to abuse and to skew up results (someone may vote 10 just to see something published, while someone might vote 0 for a stupid reason, eg. because they don't like the console or improvements to an existing run). A "yes/no" voting system avoids abuse because everybody's vote weights as much as everybody else's, so no one person can skew up the results.
This run does indeed have known improvements. For example, I'm ashamed to admit that in the last level I didn't know that you can go inside some of the doors, thus avoiding some of the required barrel jumping and potentially saving time (although whether it actually saves time is impossible to say without testing.) I would have actually understood if this had been rejected again for the reason "suboptimal, has known improvements".
And yes, a bit after submitting this I tried finding glitches and found the one I mentioned in an earlier post: In some places you can fall through the floor on the lower left corner of the screen and you will appear on the upper right corner, falling to the ground again. Then you can continue as normal, but with the playable character on the right edge of the screen, which avoids many of the obstacles requiring back-and-forth jumping.
However, manipulating the randomness and enemies in this game is a real b**ch and a pain in the a**. In that second attempt I got so stuck in one place where I just couldn't manipulate enemies that I got completely frustrated.
I think I still have the movie file somewhere if someone is interested. (It goes about half-way through the game, IIRC.)
CoolKirby wrote:
Wouldn't taking damage in the last level be faster though, or is there no invincibility time?
Whenever you take damage you are thrown towards the left (regardless of which way you were facing). I doubt that taking damage would save any time.
Can I assume that "moon" is just a temporary name until a better name is devised? Because the moon has been traditionally used (and is still used) for publications that are somehow notable (regardless of what kind of runs they are.)
Yes, there needs to be a better name for that...
What happened to this?
It seems to me that the meaning of both stars and moons have been changed radically, without changing their symbols/names. I'm not sure that's such a good idea. Better rename the tiers to something else, and retain original meaning and purpose of the star and moon symbols, IMO.
Declare each real number to be its own symbol, distinct from the symbol of any other real number.
Real numbers cannot be symbols because they cannot be all represented.
What you did is just a tautology: "I represent each real number with itself." That leads us nowhere. Of course the set of real numbers is uncountable. I already said that.
I know Cantor's diagonal argument, and your post answered the question "can you prove that there are uncountable sets?"
But that was not the question I asked.
but have yet to explicitly name the resulting quadrants before we talk about them.
<nitpick> "Quadrant" would refer to a four-way partition. If you are talking about a division into 8 parts in a three-axis system, the proper name would be "octant"... :P </nitpick>
If your set of symbols is uncountable you can represent the reals just fine.
Could you explain how a set of distinct individual symbols (that can be used to represent numerical values) can be uncountable? Because I cannot even fathom how. (Granted, I'm not that good at math and grasping things like infinite sets, but still...)
Once upon a time, TASvideos was all about entertaining movies. Now with the Vault tier, it's all about world records. Causual viewers will consider almost all of the movies boring.
A good chunk of people already consider 99% of the runs boring. Not much would change if we start accepting more runs than previously.
I think it's more important that people who are searching for a run of a certain game can find it, if possible. After all, there always are those people who played that one crappy game as a kid and want to see it utterly destroyed now. The entertainment value of a TAS skyrockets when you have actually played the game, no matter what kind of game it is.
I was under the impression that people are allowed to have their own opinions
As I said, you are entitled to your opinions, and you can freely express them, but please do not vandalize the voting and rating systems just out of principle as some kind of useless "protest". Protest with words, not by vandalizing someone's submission.
For example, the technical rating of a movie should be based on its technical qualities, not on whether you find it "boring" or not. (Also, "technical rating" refers to the TAS itself. It does not refer to the technical quality of the console.)
The author of the TAS does not deserve your empty "protest".
Do you mean that there is a difference between the idea that we could write down two (possibly preposterously large, but finite) natural numbers to express any given rational, but "most" reals do not have a finite number of digits?
Having an infinite number of digits is not a problem per se. For example the majority of rational numbers have an infinite number of digits, yet can be represented with a finite expression (namely, two integer numbers).
Any representation of a number uses a countable amount of symbols. Therefore such representation can only be used to represent countable sets (even if those sets are infinite). The set of real numbers is uncountable, which means that there's no one-to-one mapping between all the real numbers and a set of countable representations. Therefore it's not possible to represent all possible real numbers, no matter what kind of notation you use.
It's not so much about infinity (after all, there's an infinite amount of natural numbers, yet every single one can be represented using eg. the decimal notation) but about countability.
So we are talking about as many as 100 stars based on current publication numbers; more than doubling the number of starred movies.
I fear that if starred runs are too numerous, they will somewhat lose the original intent of stars, ie. to act as a guide to the newcomer, like "if you don't know what TASing is all about, watch these first."
Of course if we go to having different categories of "stars", it might be a bit too much and make things even more confusing. (I'm all about categorizing things into hierarchies, I'm a bit of a perfectionist like that, but I also try to be pragmatic.)
Warp, I don't think you reading the proposal, because your questions I think are CLEARLY answered, please make an attempt to find your answers there.
I must admit that I just cannot find anything that would even remotely hint at an answer to whether a new "gruefood revival" event will be held or not. If you would be so kind to redirect me or quote the relevant part, I would be grateful.
The "must match or beat existing records" rule wouldn't be relaxed for vault movies.
It's just that not nearly every old console game has a normal speedrun either...
Btw, I'm still wondering about my question on whether there will be another "gruefood revival" round or not, if publications become more acceptable after this change.
I'm not sure I understand your question. We already have a system to represent any natural number. We have had such systems since antiquity.
Assuming you mean "writing it down", that system fails horribly very soon.
I didn't say "writing it down". The OP says "express", which is quite an ill-defined and ambiguous term. What did he mean by "express"?
We can "express" all natural numbers. We have a system for that. As I said, for example with decimal digits. We can also "express" all rational numbers likewise. We cannot express all real numbers.
If he meant "physically write it down" then the answer is trivial: No. Obviously there's an infinite amount of natural numbers and a finite amount of space. This question wouldn't make much sense.
If it ever got published, I'd automatically rate it 0/0.
That (especially the "automatically" part) sounds like you are boycotting it on principle with no rational reason whatsoever. (For example, you haven't explained why this TAS deserves a technical rating of 0. Other than "I don't like it", that is.)
I'd say that your boycott is not appreciated nor needed. If you don't like the system then don't watch. You can write your civilized opinions why the system should be removed from the list of acceptable consoles for TASing, but please do not vandalize the voting and rating system just because you have a personal issue with the console. The author of the TAS doesn't deserve it.
But my question was more about pitting human ingenuity in mathematics and naming conventions against the fact that numbers can get infinitely large. Who would win? Like I mentioned (and as Scepheo and andymac mentioned) I feel as though we can get as clever as we want with the most advanced computers, but there are always numbers that are just not able to be represented in any meaningful way due to their magnitude.
I'm not sure I understand your question. We already have a system to represent any natural number. We have had such systems since antiquity.
Question: If "bad game choice" is removed as a justifiable reason to reject a submission, will current gruefood fodder that has been rejected for that reason be opened up to a new round of voting (like the similar event that took place a year or two ago)?
There are many games with submissions but no published TASes, and the verdict has often been bad game choice. Should they all get a new chance and a new round at the workbench? Should this be automatic, or should there be a nomination thread (like with that revoting event)?
Another question: Even if "bad game choice" is thusly removed as a reason for rejection, does that mean that any submission for a game that has no published TAS would be automatically accepted, or would there still be a minimum standards of quality that the TAS must surpass? For instance, if the run looks sloppy or seems to have suboptimal parts that could be improved, would that still be grounds for rejection (even if it's the first submission ever made for that particular game)?
If the answer to both questions is yes, then I assume that at least some of the previously rejected submissions could still remain rejected even after the re-evaluation...
