>>580995843 even if the number of ants was the amount of marines multiplied by the weight of all the marines the ants would still loose, even if they were some genetically engeneered evil fucking hitler ant they would still loose. imagine on this infinite plane the marines are shoulder to shoulder in a massive line, no second row of men, thats it. then the ants are facing them off, their the same length front, but their forces stretch back 100km into the distance, and their stacked twice as tall as a marine. the flamethrowers still burn them like fucking crazy man, have you ever burnt insects, they last 0.00002/10s of a second.
I'm so drunk right now it's not even funny. My point still stands. Graham's number is too big. Fuck ants, the marines would lose by default if normal physics applied and that many atoms existed in the universe.
>>580995843 The sheere mass of bodies would create a gravitational pull pulling both sides into the center of mass creating a mass of Marants given enough time the would be compressed into a ball of pure oil 2 weeks later the U.S decide they need to "liberate" the ball of pure oil
you niggas dont even understand that if you took every atom in our universe and made each atom the size of our universe and then made those atoms into lead it still wouldnt weigh as much as grahms number
The ratio of their masses would be far greater than the ratio of a galaxy's mass to an electron's mass.
Forget the flamethrowers. You could give the Marines advanced weapons technology that kills trillions of ants for every picojoule of energy expended -- but even then the Marines would only succeed in killing such a tiny proportion of the ants that it would take special mathematical notation even to represent such a tiny number.
the number of atoms in the universe is approx 10^78. now, googolplex ALONE is 10^10^100, which makes it already impossible to exist in a phyiscal form. now apply this to an infinitely larger number than googolplex such as graham's, but instead of counting it as atoms, turn it into ants.
>>581001938 Yeah that's the issue. G1 is something you can get your head around, despite being very large already. G2 just takes it too far and fuck G64 sideways with a rake.
I get more scared by this shit than anything else. It's like the minds of men have conjured an unfathomable universe immune to any inspection bar those with the mental fortitude to weather its storms. God damn. We have no business dealing with numbers that large.
A good point, and one worth exploring. It would depend on the ants' density. I think if the ants' density was what you normally find in an ant colony, I wouldn't worry about the gravitational attraction creating a black hole.
I think a more serious issue is that the mass of the ants would exceed the mass of the known universe. The mass of the known universe is quite a small number -- certainly less than 10^1000000 kg. That's not nearly enough mass to create a Graham number of ants.
So I just read what grahams number actually is, and googolplex is a ridiculous fart in comparison, its a grain of sand compared to the entire known universe times a thousand. googolplex marines couldn't incinerate a grahams number amount of ants before the heat death of the universe, which would be so stuffed with ants that it's essentially just one massive black hole
>>580998948 >>580998975 Imagine a Planck unit. You can't, but try. It's a measurement so ridiculously small, it's really only useful for theoretics, or for measuring shit like the things that make up the things that make up the things that make up the things that atoms are made of.
Now, imagine that each Planck volume, that could fit only a few of these things that make up the things, et cetera, represents a single digit of a number.
If you then tried to write out Graham's number, using these mathematically miniscule-ass fucking digits, you wouldn't be able to fit it inside the fucking UNIVERSE. Not even CLOSE. Even when EACH DIGIT is a fucking million times smaller than an ATOM.
THAT's how absurdly, monolithically fucking GARGANTUAN Graham's number is.
>>581002590 It was an upper bound, I think. The solution was proven to be smaller than that number. Oddly that's sort of useful for mathematicians but I can't even make a simile for it. If I was to say 'it's like me describing an atom as smaller than the universe' I'm still too many orders of magnitude out.
>>581002913 Yes, but it's much, much bigger than that too. That's the easiest way to understand Graham's number. If you can conceive of something, it's bigger. By so much more that you weren't even close.
>>580995843 haha are you retarded the ants will win easy. This is literally over a universe FULL of ants. If you assume a flat infinite plain (assuming the ants can choose their starting configuration) you could just have the ants stacked up GOOGLEPLEXES OF MILES HIGH. The motherfuckers could just FALL on the marines and they would kill them all.
I really think everyone in this thread is underestimating the sheer vastness of the ant borg
>>581003221 Well, technicallt, my explanation didn't include an upper bound, so it describes anything up to and including practical infinity, But, you I know what you mean. It really doesn't even bear thinking about, except you're into some pretty high-level fucking mathematics, and even then it... Well, thinking bout it is rarely justified, is what I'm saying.
>>581004567 Graham's number is so large that it would take more atoms than in the observable universe to create a digital (numerical) representation of it (meaning to write out every single number, it would take up more space than the entire universe allots for)
So, as you said, 9/10 /b/ros here don't realize how large the number is.
Ok, I'm not a retard but I am definitely in no way a mathematician. I've read the wikipedia page but without any understanding of the esoteric language I still have absolutely no idea what this number IS. Assuming, philosophically, that every number, real or imaginary, relates to something at least theoretical in the universe, what does Graham's number refer to?? If it is bigger than the universe, what the fuck is it? Answers in English for us "uneducated faggots" please.
Can't Graham's number be computed by a processor and represented on a screen? Yeah it might take a lifetime or several to scroll from top to bottom but it seems like that can be done. Jupiter didn't fit on earth but it's image fits on my screen.
>>581005479 Useful in as much as it proves that the solution for that problem is lower than it. If you try to solve the problem but find a solution larger than G, either your solution is wrong or G is wrong. Most likely your solution is wrong.
You may question the use of such a large number as an upper bound but the difference between 'finite but fucking huge' and 'infinite' is very important in mathematics and gives you a lot of power. It's useful enough to exist in its own right, and interesting enough in just how large it is.
>>581005715 There might be now. To be honest G blew so many people's minds that it probably doesn't matter. I wonder how much bigger it is.
Depends what you mean by "represented". If you mean represented by writing it in digits 0-9, then no, because there are so many digits in the number, the number of the digits themselves is greater than the number of atoms in the universe, let alone the number of atoms in any physical storage/memory device.
It can be represented by any number of special notations pretty easily, even on a small slip of paper, if you can devise them.
>>581005046 It's like imagining the impossible, so think about it like this. We take a googolplex of marines. Then we fit the googolplex of marines inside one atom. Then we fill the entire universe with those atoms filled with googolplex of marines. Then we take a googolplex of those universes, and Graham's number is about googolplex times bigger than the number of marines in total. That's still not a Graham's number, but it should get to the ball park of how badly the marines would get their asses kicked by the ants.
>>580995843 You fucking retards can't even comprehend how big a Googolplex is, let alone how big Grahams number is. The ants win, even single atoms slowly eroding away the marines would STILL win.. Fuck do some research guys
>>580995843 The marines would win because If they first lit up the ants into a blazing inferno, the fire would spread to all the other ants, faster and faster like a forest fire, the marines just had to run away and watch it at a distance But 1000 years is not enough to burn them all though
>>581007135 As I said, you can represent it in a single character if you call it G and people know what you mean. As stated before, there aren't enough atoms in the universe to represent it as a base 10 number and, worse, the number of digits in G can't be represented in base 10 with the number of atoms in the universe).
>>581007843 You don't understand. If every atom in the universe powered the screen and the rest was literally just the screen you still couldn't get near reading anywhere near how many digits are in G.
This goes for anyone talking about computers or calculations or representation. The universe is not big enough to contain G in base 10, or even the number of digits in it (and probably the number of digits in the number of digits, but I don't know for certain; I'd assume so).
>>581007713 So how much memory? Like if we had a storage chip the size of a house? Cleveland? Norway? Antarctica? The Pacific Ocean? The moon? Earth? You can fit a few TB in something the size of a small box.
Ants would win. I can't even fathom how big graham's number actually is. But I work really well w/ large numbers. So here we go.
Each Marine could cover 150 sq yards per second max w/ a flame thrower (an extremely liberal estimate). They would have 31,557,600,000 seconds to kill the ants. So that's 4,733,640,000,000 sq yards each marine can cover. This all assumes that the Marine is 100% efficient for the entire 1000 years (no sleep, no eat, no reloading the flamethrower, no re-positioning or placement fuckups).
Assuming that 1,000 ants would fit in a square yard that means 1 marine could kill 150,000 ants per second, or 710,046,000,000,000,000 ants total.
Multiply this by a googolplex, and you have the maximum amount of ants the marines could kill. I didn't write it the total because I don't really have room, but it's a fathomable number smaller than graham's number.
Ask 1 marine to kill the entire earth population of ants. now multiply the number of ants with a googolplex ^ googolplex ^ googolplex. he has a planck (10 ^ -44) second to do it. that comparison isn't even near what would happen with a graham number of ants, therefore ants win, marines are absolutely nothing to it.
>>580995843 the winner would be the marines. the winner is at whatever side theres less fatalities. once the 2 sides decide to like in harmony, the loser would then be the ants due to their astronomical loss of lives.
>>581008773 the fight doesnt end untill 1 side is wiped out and the ants wont stop untill they are all dead or marines are all dead. Also, 0.00000000000000(insert googolplex of zeroes here)...1% of the ants is plenty to kill all the marines.
now I want to know what would Graham's number look like in a base of 10^10000000000000000. how many digits and would it fit on earths base covered with paper (i don't know how to say 2r*pi in english so i said base)
Everyone knows about Graham's number. You're not smart because you heard of Graham's number, faggot.
But you are an idiot of you think, with OP's provisions of no sleep and 1000 years of FLAMETHROWER fuel (not counting other forms of ammo or improvised combat techniques, that is) that the ants stand any chance.
They are not even smart enough to wipe out 10 of the marines. They do not have the hardware to kill any at all. And crushing them is out of the fucking question, don't tell me that's what you were thinking, retard.
I watched a really bad old movie once called Panic at Lakewood Manor where ppl got attacked by rampaging hordes of killer ants or at least I think it was ants it might have been bees or mice or something
Graham's number is so large, that it's just absurd to even consider it, even talking about a graham's number of sub-atomic particles.
The fight would likely last for t roughly equal to infinity years, but considering the fact that ants don't possess the ability to kill, neither can they e.g. suffocate the marines by outnumbering them (because they're fighting on an infinite plain), then the marines would eventually win. Given the infinite plain, I don't think any number of ants could overpower that many marines with flamethrowers, because ants are non-aggressive.
>>581006059 Yes it can be computed and u can witness this process, however there is no memory sufficiently large to store the result. However, you could theoretically start to "stream" the calculation. In this case the increasing entrophy of the would sooner or later become a problem before you can watch a fraction of this stream...
>>581008801 Here's an analogy for you. Cotton is pretty harmless. But if you put enough of it on a tank, it will still crush it. Numbers don't matter, graham's number is to big for anything else in the universe. If the marines are close enough to burn the ants, they should be already dead, crushed by a wave of infinite ants
a notepad document with one digit in it is 1 byte, two digits is 2 bytes, and so on.
The volume of the observable universe is 3.4 x 10^80 meters cubed. One planck volume is 4.22419 ×10^−105 meters cubed. Therefore the volume of the observable universe is roughly 8.29 x 10^184 planck volumes.
THE DIGITS IN GRAHAM'S NUMBER WOULD OCCUPY MORE PLANCK VOLUMES THAN THE OBSERVABLE UNIVERSE, BUT FOR THIS, LET'S PRETEND IT TAKES UP EXACTLY THE SPACE OF THE UNIVERSE.
So for argument's sake, we'll say graham's number has 8.29 x 10^184 digits, so on a notepad document, that would 8.29 x 10^184 bytes. That, friends, is 8.29 x 10^160 yottabytes.
8.29 x 10^160 yottabytes. THAT IS 8.29 X 10^160 TRILLION TERABYTES
DO YOU GET IT YET
ALMOST EVERY ATOM IN THE UNIVERSE WOULD HAVE TO BE A TERABYTE HARD DRIVE TO BE ABLE TO WRITE IT IN A NOTEPAD DOCUMENT
AND GRAHAM'S NUMBER HAS MORE DIGITS THAN WHAT I JUST CALCULATED FOR ARGUMENT'S SAKE
>>581006059 Some guys in Germany invented a storage unit that stores one bit on 12 atoms. The ratio of bits per base10 digits converge at around 3.322, so you'd need to multiply Grahams number by 3.322 then multiply by 12 again in order to get the amount of atoms needed to store it.
Note that in normal harddrives it takes one million atoms to store one bit.
>>581011392 i think what he meant was: make a program in c program SOMEHOW calculates Graham's number it takes him almost infinite years to calculate printf("%d",Graham); it takes another almost infinite years to print that shit out but i think it could be possible if only we had 8.29 X 10^160 TRILLION TERABYTES of RAM memory so the calculating be done in one second ;_;
This whole thread is just regurgitating shit they've read on the wiki, the truth is we don't know how large the universe is, we don't know how large grahams number is. It's just.... very big.
However to the topic, if there were the amount of ants equal to grahms number it would create a super massive black hole that basically destroyed the universe. you can forget breeding, or lifespan, everything would just die instantly.
It's like trying to summon too many units in WC3 the game just crashes.
"A" Graham's number of ants, should they wish to destroy the Marines, would simply crush them under their enormous weight. No biting, stinging, or shooting necessary, anything of that magnitude would win against anything less than it.
>>580995843 I don't think anyone in this thread understand just how big a number graham's number is. It's so large that in super exponential notation (ie 10^10^10^...^10^n) we can't use exponential notation to describe the number of powers of 10 we'd need.
Here's a video on just how large graham's number is: https://www.youtube.com/watch?v=GuigptwlVHo
Anyway, the bottom line is that the marines would stand NO chance. Zero.
>>581017143 It doesn't really matter. Graham's number is too big for this universe. The number of digits in Graham's number is too big for this universe. The number of digits in the number of digits of Graham's number is too big for the universe. The number of "number of digits" required to get something that could be written in the universe is too big for the universe.
There isn't even a Grahams number of atoms in the observable universe so a Grahams number of ants would be many many observable universes worth of ants. Against a Googleplex of Marines, who could fit into an area the size of our own galaxy, they would fuck them. No doubt they'd fight a good fight but they would be fucked. Fuckidy fucked fuct fucked.
The ants would win you dolts. Once the marines run out of fuel the ants could literally become a giant mass and roll over them. The humans would be trapped and crushed under the sheer weight of the ants.
>>581017143 I just made a notepad file with a 1 in it, saved it, it's one byte. Then i wrote a 2 in it (so the file reads "12") and saved it, and now it is two bytes. I did this before I posted originally, as to not be an idiot, like you.
Now, to check myself, I just made it read "1234567" and it is - get this - 7 bytes.
>>581020407 I think you underestimate the size of a googolplex. One googol is greater than the number of atoms in the observable universe. The observable universe has approximately 10^78 atoms that we can observe.
A googol is 10^100 A googolplex is 10^(10^100)
A typical human has 7*10^27 atoms. For simplicity we will take 1/7 of a human as 10^27 to be the number of atoms in a human.
In one googol of marines you would have 10^27 * 10^100 that's already WAY FUCKING MORE than 10^27 times the obserable universe. I dont feel like explaining in meticulous detail, so as metaphorically speaking,
to say that you can fit a googolplex of marines in an area the size of our own galaxy would be like saying "you can fit our solar system into an area the size of an atom."
What do I mean by a perfect killer? I mean the most effective killer that can exist without violating the laws of relativity. Specifically, after one second of a perfect killer's time, everything within one light-second of the perfect killer's position has been killed. Within one year, everything with light-year, etc.
By laws of relativity, nothing can possibly kill more effectively than this.
Okay, so, the marines have 1000 years of fuel, meaning each of them kills everything within a 1000-lightyear sphere. Let's give them 1000000 years each instead. They're on an "infinite plain" so it might make sense to only use hemi-spheres, but let's assume the ants also burrow under the ground.
1000000 light-years is 9.460 × 10^21 meters.
A sphere with that radius has a volume of about 3.547 x 10^64 cubic meters.
Let's also assume the ants are incredibly tightly packed, such that they're approximately Planck length in size. As such a single cubic meter contains about 10^104 ants.
There are a googolplex of these marines. As such the marines as a whole kill about 10^64 googolplex cubic meters of ants, which is about 10^168 googolplex ants.
...This is such a breathtakingly small number compared to Graham's number that I can't even come up with a suitable analogy to describe how insignificant it is. Even with perfect killer marines and quantum-packed ants, the marines will never make a dent in the ants. If the ball of ants is the size of the observable universe, in a million years the perfect killer marines will kill so few ants that it's impossible to measure the space containing how few they killed because it's smaller than the smallest possible unit of measurement.
im going to assume they are fire ants. fire ants ae known to crawl over each other. all ants touching then fire spreads. marines out run fire somehow. bullets travel through a lot of ants. ants are slow. obviously marines would win.
OP needed to add 1 more thing to allow the marines to win: "No getting tired/exhausted." If that is a variable, and the ants are not spawned in a circle around the marines (meaning there is 1 graham's number of ants on one side, 1 googolplex of marines on the other, and infinite running space behind the marines where no ants exist) then the marines win. They could indefinitely retreat into the infinite plane where no ants exist and while doing this could use their flamethrowers (which have run out of flame) to smash the ants running toward them. This would take a near-infinite amount of time but they would eventually win.
>>581022625 Yo totally, I was running on a googol not a googolplex. I may of been wrong on that for years. Eh. And when I say within our galaxy I mean as a mass condensed into an area the size of our galaxy, not on planets and such. Maybe two. But, yeah, a googolplex is far vaster .
>>580995843 >never once hear of Graham's number >gain mild interest >wiki >holy what the fuck reading shit like this that is over my head actually makes me angry. it truly brings out primal instincts and makes me want to throw things
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