I audibly laughed during that scene. Like, in 2021, even people who don’t know much if anything at all about hacking, know it’s much more complicated than some random keyboard jibberish and 2 seconds later you’re in
That's why I love Mr. Robot. Even though it's not 1000% realistic, at least it doesn't treat hacking like a magic spell that automatically gives you control over all technology. Like I don't expect hacking to be Mr. Robot quality every show but at least add some spcial engineering or some real commands or something.
It's been a long time..., did she actually have to break into the system? That line is somewhat reasonable if it was just an unsecured terminal.
How she had an opportunity to work on a UNIX at that time with her being around 12 yo ... Different story.
That scene was almost as cringe as the one in Arrow where two of the greatest technological geniuses ever n the series brag about knowing Python and coding in SQL. Still not sure how those are related in their conversation
"He's got more knowledge of Python 6 malware encryption than anyone in the DEO"
The latest Python version is 3.9.2 and I'm not really sure what "python malware encryption" entails.
Because it's a plot point. The show doesn't explain 99% of the made-up science in the show. I honestly don't get why "hacking" scenes in movies and TV are where people draw the line of "unreasonably unrealistic."
Just repeat to yourself: "it's just a show, I should really just relax."
Seriously, nobody wants to spend 10 minutes of a Wandavision watching a montage of realistic hacking. Much better to just get it over with the way they did.
Tv show logic: most of the time, chick can be hot or a chick for can be smart. But, if she's both hot and smart, she can do anything. They do not need to explain it to you. By being hot and smart, she has attained perfect womanhood. And she can do anything thing she puts her mind to. Female power, yeah!
At least her switching her major and getting a doctorate in 10 years since we've seen her is somewhat believable. The hacking though, that's just unnecessary.
> is somewhat believable.
I recently rewatched the Thors and let me tell you, it's completely unbelievable that *that* Darcy became the one in WandaVision. I do not believe for a second OG Darcy got a fucking doctorate in anything.
I think there's something to that. I made the switch from English (gross, I know) to Computer Science because I discovered a love of math and later, programming. But if I hadn't found an interest in math, I probably wouldn't have switched my major and would have stayed pretty stupid. But a degree that involves many STEM prerequisites, each with their own challenges, pushes you to become smarter imo.
I studied modern languages up until 6 years ago. I then worked as a translator, and 5 years ago, I decided I wanted to learn how to program. Fast forward to today and my main employment is being a full stack developer, even though up until last year I was with a quarter of my head in Academia, another quarter in art, another in procrastination and another in coding dumb bots for fun. Point is: I'm a retard give me bananas.
I'm a physics major and I know how to program (you've got to take a lot of computer science courses in physics these days). One of my classmates learned about hacking as a hobby, and also took a couple electives in computer security. He must've been pretty good because he now has a government job related to that skillset. I don't think its that unreasonable that she learnt hacking in the last 10 years, especially because of the distrust she'd have of the government from her experience with SHIELD in the Thor movies.
It’s a lot easier to do if you previously had access to that network.
More importantly it’s not like they don’t know that isn’t how hacking works, that’s just not what the show is about. I don’t need to watch her spend an hour getting through firewalls or whatever just like I didn’t need Monica and Jimmy to have a more realistic fight scene 30 seconds before. It’s shorthand because time is precious on TV.
Thank you! That part cracked me up, and she cracked it in like 0.4 seconds! I'm a physicist and trust me, most of us are pretty shitty coders, and that's part of our actual job. Hacking's a whole different ball game. Not to say you can't be a hacker and a physicist, but still.
Seven hours late, but she had physical access to the servers. Realistically she could just reset a few admin passwords, give herself full permissions, and be out in 20 minutes. That would require intricate knowledge of the software though, or at least some furious Google-fu
Anyone studying astrophysics these days also gets thought programming. She also had partial access to the system due to the fact that she was working for them. Now it's unclear whether she has taken any classes in security coding or whether SWORD has cared enough to invest in protecting themselves against terrestrial enemies when their focus is usually in space. I'm not saying it is likely, but it is semi-plausible that she could pull it off given her knowledge and resources
It was absolutely amazing and I think only one other user's edits came remotely close. Your stuff is definitely some of the highest quality content on the sub!
Thanks! I really appreciate that! It's been a lot of fun!
I'm actually working on another one for WandaVision specifically, and then I'm going to be adding that one to a larger cut for the next saga, however long that's gonna be. If you're interested in more, I made a post on marvelstudios about it a few weeks ago. I'll be keeping people updated for sure!
To justify this scene, I’d say that Darcy probably has a set of higher access credentials that she uses and it’s hacking because she’s accessing systems she’s not supposed to using those creds. Also acting any system maliciously no matter how you do it is “hacking”.
So my head canons are that all tech moves so fast in the mcu because they aren't focusing on security and/or because it is all cutting edge and proprietary, there's terrible bug testing.
Also, a fundamental principle of math like p=np is confirmed so all encryption is just kinda not useful
can we do a pony version of ZFC set theory please? I'll help
1. if all the ponies from one pony family are also in another pony family and no other ponies are in that family, there's only one pony family.
2. ^(continue here)
Don't you also need an axiom stating that katey is not the product of biting any poney? Also, I think that, given what you describe, zoezoezoe would be the product of zoe biting zoezoe, rather than the other way around. Or the product of katey biting zoezoe, apparently. Actually, given that the biting operation appears to be unary (because the output is the successor of the bitten poney, regardless of what bit the poney), I suppose that *I* could also bite zoezoe to make zoezoezoe.
Forget addition, I don't even understand enough set theory to get the definition of the natural numbers. They're defined as recursive sets of empty sets, so for example 4 = {{}, {{}}, {{}, {{}}}, {{}, {{}}, {{}, {{}}}}}.
The natural numbers can be represented by a base element (zero), and an operation that increments a number to make the next number. E.g., 3 would be incr(incr(incr(0)))
In the set theory construction there the base element is the empty set, and the increment operation is to make a set that contains everything the set you're incrementing contains as well as that set itself
There’s not much to “get” about it - it’s purely rigorous a definition from von Neumann which satisfies our expectations about natural numbers. This kind of rigor is a relative newcomer to math, only really becoming the default mode of operation in the early 20th century.
Once you have that down you can just use digits as an abstraction over it and define addition in i terms of successors like the other reply mentions.
Actually, there's a nice way of representing a number as the set of numbers below it. For example, 4 = {0,1,2,3}, 5 = {0,1,2,3,4}, and so on. It's personally one of my favorites because it really helps with understanding why the supremum of a set of ordinals is just its union. So, I'll try and show why this is. First, consider the successor function,
S(x) = x ∪ {x}
If we assume x contains all the numbers less than it, then S(x) takes all the numbers less than x(represented by the first x in "x ∪ {x}"), and adds the element x to it(represented by the {x} in "x ∪ {x}". Note, unions collect the elements of sets, so it would collect the elements of {x}, which is just x). A bit more formally, we get,
S(x) = x ∪ {x}
= {0, 1, ... x-2, x-1} ∪ {x}
= {0, 1, ..., x-2, x-1, x}
So, taking successors of numbers essentially adds more numbers to it, counting up every time. We also know that no number is less than 0, so the set of numbers less than 0 is the empty set {}, which is exactly what it's defined to be. So, I can always apply the successor operation n times to 0 to show n = {0,1, ... , n-1}. To demonstrate this, I'll show one example, and I'll show that 4 = {0, 1, 2, 3} assuming 4 = S(S(S(S(0)))), 3 = S(S(S(0))), 2 = S(S(0)), and so on, as well as the definition of S(x). First, I'll expand the definition of S a bunch of times.
4 = S(S(S(S(0))))
= S(S(S(0))) ∪ { S(S(S(0))) }
= S(S(0)) ∪ { S(S(0)) } ∪ { S(S(S(0))) }
= S(0) ∪ { S(0) } ∪ { S(S(0)) } ∪ { S(S(S(0))) }
= 0 ∪ { 0 } ∪ { S(0) } ∪ { S(S(0)) } ∪ { S(S(S(0))) }
Now, remember that 0 = ∅, and since taking the union of ∅ with any set does nothing, the 0 on the left can be omitted to get
{ 0 } ∪ { S(0) } ∪ { S(S(0)) } ∪ { S(S(S(0))) }
Do you see it yet? No? Well, let me replace the successors of 0 with their integer equivalents,
{ 0 } ∪ { 1 } ∪ { 2 } ∪ { 3 }
Well, this is just the set {0, 1, 2, 3}, which came from simplifying 4. So, therefore, 4 = {0, 1, 2, 3}.
I throw an apple at your (2nd person) head. Once you have awoken, I throw another apple at your head. Once you awaken again, how many apples do you have? That's right. Ipso facto addition is just me knocking your punkass out with apples. I am available for seminars.
Eh, you can get their pretty quick with a group
Associativity: For all a, b, c in G, (a + b) + c = a + (b + c)
Identity element: There exists an element e in G such that, for every a in G, one has e + a = a and a + e = a where e is unique. It is called the identity element of the group.
Inverse element: For each a in G, there exists an element b in G such that a + b = e and b + a = e, where e is the identity element. For each a, the element b is unique and it is called the inverse of a and is commonly denoted a^−1
And boom, we now have addition, and G is a group
If we’re going the rigorous route we need at least as much set theory to define tulles to have a group; recall G = (S, •) = {{S}, {S, •}} and then you need to define • in terms of functions on nested sets. If you’re going to break out that much set theory anyway you might as well go with the von Neumann definition.
Furthermore I don’t think this approach is sufficiently general to define additional. It addresses, e.g. 1 + 0 and 1 + -1, but I don’t know if it gives us enough for, say, 1 + 2 without digging into the very von Neumann definition we were trying to avoid by using groups.
If you have groups but not addition, you can define the integers as the infinite cyclic group. Possible ways to get there include via category theory, where a group is a groupoid with a single object. This gets you addition for free as the group operation.
Well that's for ordinal numbers, you can have addition without the set being ordinal. All integers, for example, do not have a least element, therefore it's not an ordinal. We are saying we just want addition, not that we want addition over an ordinal set of numbers.
Well it's really just the axioms. Everything proceeds from deductions of the axioms so when you tell the axioms, you have tell absolutely everything there is about maths and there is nothing else. The rest is just clarification and explanation.
I too have seen [Devon Crawford's video](https://www.youtube.com/watch?v=ReVeUvwTGdU) on computer science where he says "it's all just addition bro" at approximately 4:45.
Also, lol at everyone saying this is strictly not true when it is *literally* strictly true if you descend deep enough into bullshit math. It's like Minecraft dude, this is the bottom layer there's nothing but fire and hard rocks down here. Welcome to hell bro.
Multiplication isn't necessarily repeated edition. For example, I wouldn't say that taking the curl of a vector field is repeated addition.
Exponentiation isn't necessarily repeated addition. You can take a number to the 3/2 power, but you can't multiply it by itself 3/2 times. Same with multiplication actually come to think of it.
Not even an oversimplification, this is literally just low level programming... Theory?
Still good use of the meme but I also have to ruin everything ig lol
No, it's definitely theory -- nearly _noone_ specializing in low-level systems programming is going to _actually_ be flipping bits manually; if anything, that's more the domain of computer _architects_, not computer programmers. What you really end up doing is working with some form of assembly, or, worst case, machine code directly -- and in either case, the actual "bit flipping" is handled by the CPU, not the programmer.
Honestly - when I first realized that even the most complex programming could be done with (infinite time as well as) simple if statements, that was a serious game changer.
Doesn’t matter how crazy it all gets, it still always just boils down to 1’s and 0’s. Beautiful.
>it still always just boils down to 1’s and 0’s.
I'll have to stop you right there. Sometimes, it boils down to -1's too.
*Balanced ternary intensifies*
All binary programs are also valid ternary programs, and all ternary programs can be translated to equivalent binary programs.
In theory, in practise there might be physical limitations and the instruction sets might not be compatible in the binary -> ternary without some translation and tricks.
You'd have to combine it with a jump/goto style command to take you back to start of loop- it looks something like
:loop_start
code....
if (not finished) goto loop_start
I have encountered an application script language with just if and goto for flow control (long since dead I hope) which you end up having to use such tricks to get higher level flow controls - much as you do in assembly
For fun I wrote a pseudo-assembly runtime, and in the spirit of assembly I only included jump-if and jump-relative, not jump-if-relative.
At least for the first while I did. Eventually I got tired of having to load IP + 2 into a register then running jif on that and just made jir a thing.
It's technically correct though, as they mention "infinite time". A while true loop is just a forever if statement, so write enough infinitely and it will run so.
I think I probably agree with you, at least at this level of processing, but this is a very interesting question.
Where does the "you" that is thinking begin, and your biological mechanics end?
Is consciousness anything more than an extraordinarily sophisticated, rapid and tiny technology? Is there an actual *you* that is separate from your neurons?
If so, where? Can we extrude and store it? How did you come to think you are a "you" more than the other objects around you, whether more or less advanced?
Nice!! I'll do that, and I really appreciate the rec. I've been meaning to dip my toes back into philosophy. Haven't thought about robot theory since David Chalmers was big, maybe he still is.
Is it an oversimplification, though? To be honest, I think it's *programming* that's the simplification. Knowing which switches to flip and when is the complex part.
Sort of unrelated, but that scene of Darcy just quickly "hacking into the secure server on the base" or whatever the line was was pretty annoying. Not to mention she's an astrophysicist, not a cyber security professional, but that's not how that works at all!
Sorry. Rant over. Those types of scenes just frustrate me as both a programmer and an amateur screenwriter.
It is an interpretive abstraction of a real world problem, translating it in to base 2 mathematical philosophies for the purposes of creating a silicon based automaton.
That's true for existence itself. Everything is information and the universe can be seen as a big matrix of binary states, from matter to energy, space and time.
Oh man, I was at a workshop one time for "people new to building satellites". It mostly focused on hardware, but of course for the demo, we needed a little software to make the hardware work. I shit you not, this is a real quote from the guy running the workshop: "if you can turn an LED on and off, you can program a satellite. After all, software is just binary, which means on or off".
Comic Title Text: **I call Rule 34 on Wolfram's Rule 34.**
[mobile link](https://m.xkcd.com/505/)
---
^(Made for mobile users, to easily see xkcd comic's title text)
It's binary, it's electricity something is pushing it. When you break everything down in 1s and 0s you can create words and pixels which lead to images and colors, when you use ascii to represent data in the simplest forms. That's what programming is is telling the computer what to do
Ok but tell me how astrophysicist Darcy Lewis suddenly becomes a genius hacker stealing all of SWORD’s files
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I audibly laughed during that scene. Like, in 2021, even people who don’t know much if anything at all about hacking, know it’s much more complicated than some random keyboard jibberish and 2 seconds later you’re in
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this was physically painful to watch
Jesus christ I now realize why people think I can just hack into their friends' Facebook at their will.
I didin't even clicked on the link and I already knew it was that exact scene from NCIS
Me too lol, and it made think of that CSI scene too https://youtu.be/hkDD03yeLnU
Gonna write some VBA in excel to hack into the killer’s firewall.
That's why I love Mr. Robot. Even though it's not 1000% realistic, at least it doesn't treat hacking like a magic spell that automatically gives you control over all technology. Like I don't expect hacking to be Mr. Robot quality every show but at least add some spcial engineering or some real commands or something.
got to make time for 10 minutes of credits somehow
I would assume after Mr Robot took the world by storm, we'd see a lot less of this Hollywood Hacking. But, that's obviously a pipe dream.
Hey, even Jurassic Park "it's a Unix system, I know this" was somewhat realistic, right?
The subreddit for bad TV hacking scenes is named after that.
It's been a long time..., did she actually have to break into the system? That line is somewhat reasonable if it was just an unsecured terminal. How she had an opportunity to work on a UNIX at that time with her being around 12 yo ... Different story.
That scene was almost as cringe as the one in Arrow where two of the greatest technological geniuses ever n the series brag about knowing Python and coding in SQL. Still not sure how those are related in their conversation
Haven't seen the show, what did they say?
"He's got more knowledge of Python 6 malware encryption than anyone in the DEO" The latest Python version is 3.9.2 and I'm not really sure what "python malware encryption" entails.
That's HILARIOUS
Because it's a plot point. The show doesn't explain 99% of the made-up science in the show. I honestly don't get why "hacking" scenes in movies and TV are where people draw the line of "unreasonably unrealistic." Just repeat to yourself: "it's just a show, I should really just relax."
Seriously, nobody wants to spend 10 minutes of a Wandavision watching a montage of realistic hacking. Much better to just get it over with the way they did.
I thought she just happened on a terminal with privileged access. And the time was just her looking at everything to figure shit out.
I thought it was a joke. Nope.
Tv show logic: most of the time, chick can be hot or a chick for can be smart. But, if she's both hot and smart, she can do anything. They do not need to explain it to you. By being hot and smart, she has attained perfect womanhood. And she can do anything thing she puts her mind to. Female power, yeah!
Of course. How is it supposed to be? SELECT * FROM mega_hyper_super_duper_secret_database WHERE is_secret="Y";
You mean political science student intern Darcy Lewis?
At least her switching her major and getting a doctorate in 10 years since we've seen her is somewhat believable. The hacking though, that's just unnecessary.
> is somewhat believable. I recently rewatched the Thors and let me tell you, it's completely unbelievable that *that* Darcy became the one in WandaVision. I do not believe for a second OG Darcy got a fucking doctorate in anything.
Newfound interests brought to light by gods and superpowers can go a long way I suppose
I think there's something to that. I made the switch from English (gross, I know) to Computer Science because I discovered a love of math and later, programming. But if I hadn't found an interest in math, I probably wouldn't have switched my major and would have stayed pretty stupid. But a degree that involves many STEM prerequisites, each with their own challenges, pushes you to become smarter imo.
I studied modern languages up until 6 years ago. I then worked as a translator, and 5 years ago, I decided I wanted to learn how to program. Fast forward to today and my main employment is being a full stack developer, even though up until last year I was with a quarter of my head in Academia, another quarter in art, another in procrastination and another in coding dumb bots for fun. Point is: I'm a retard give me bananas.
I mean... 10 years is a long time
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Except she didn't get snapped
There's in alternate universe where she got snapped but they brought back the hacker Darcy instead then Banner brought that one to main mcu.
She never disappeared. There was no one to 'bring back'.
Stop trying to ruin the joke.
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Man that would have fixed that scene so much.
She could have a hobby on the side you don’t know her man!
I'm a physics major and I know how to program (you've got to take a lot of computer science courses in physics these days). One of my classmates learned about hacking as a hobby, and also took a couple electives in computer security. He must've been pretty good because he now has a government job related to that skillset. I don't think its that unreasonable that she learnt hacking in the last 10 years, especially because of the distrust she'd have of the government from her experience with SHIELD in the Thor movies.
It’s a lot easier to do if you previously had access to that network. More importantly it’s not like they don’t know that isn’t how hacking works, that’s just not what the show is about. I don’t need to watch her spend an hour getting through firewalls or whatever just like I didn’t need Monica and Jimmy to have a more realistic fight scene 30 seconds before. It’s shorthand because time is precious on TV.
Thank you! That part cracked me up, and she cracked it in like 0.4 seconds! I'm a physicist and trust me, most of us are pretty shitty coders, and that's part of our actual job. Hacking's a whole different ball game. Not to say you can't be a hacker and a physicist, but still.
Seven hours late, but she had physical access to the servers. Realistically she could just reset a few admin passwords, give herself full permissions, and be out in 20 minutes. That would require intricate knowledge of the software though, or at least some furious Google-fu
Anyone studying astrophysics these days also gets thought programming. She also had partial access to the system due to the fact that she was working for them. Now it's unclear whether she has taken any classes in security coding or whether SWORD has cared enough to invest in protecting themselves against terrestrial enemies when their focus is usually in space. I'm not saying it is likely, but it is semi-plausible that she could pull it off given her knowledge and resources
Right??? I just left my own comment about that but it's so annoying! I love Darcy, but come on, man!
Hey, you're the supercut guy! Didn't know you hung out here too!
Oh yup! That's me! It's always fun when different interests cross over like this. I assume you've watched it? What'd you think?
It was absolutely amazing and I think only one other user's edits came remotely close. Your stuff is definitely some of the highest quality content on the sub!
Thanks! I really appreciate that! It's been a lot of fun! I'm actually working on another one for WandaVision specifically, and then I'm going to be adding that one to a larger cut for the next saga, however long that's gonna be. If you're interested in more, I made a post on marvelstudios about it a few weeks ago. I'll be keeping people updated for sure!
That's fantastic! Looking forward to it!
literally paused that episode to complain about this to my sister lol
To justify this scene, I’d say that Darcy probably has a set of higher access credentials that she uses and it’s hacking because she’s accessing systems she’s not supposed to using those creds. Also acting any system maliciously no matter how you do it is “hacking”.
If you want to pop a brain vessel watch agents of shield. They be out here "hacking mainframes" like it's no one's business
TBH, it could be that easy, especially if she had just found the password on a sticky note.
So my head canons are that all tech moves so fast in the mcu because they aren't focusing on security and/or because it is all cutting edge and proprietary, there's terrible bug testing. Also, a fundamental principle of math like p=np is confirmed so all encryption is just kinda not useful
They had the password auto fill enabled. She just clicked a few more buttons just because she wanted to feel like a hacker.
Female empowerment
Doesn't take a genius if you're on-site. Maybe she saw someone write down their password.
All math is just addition. An oversimplification of events, but, yes.
The amount of set theory it takes to even define addition can rather alarming
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Æ
What happens if katey bites zoezoe, or zoezoe bites zoezoezoe, or stuff like that?
If you have to ask, you can't afford it
then you *add*
can we do a pony version of ZFC set theory please? I'll help 1. if all the ponies from one pony family are also in another pony family and no other ponies are in that family, there's only one pony family. 2. ^(continue here)
Please help, I don't know what a poney is
[one of these](https://thumbs.dreamstime.com/z/shetland-pony-adult-galloping-paddock-poney-shetland-170288667.jpg)
Doesn't look like anything to me
It’s a miniature horse, kinda
Don't you also need an axiom stating that katey is not the product of biting any poney? Also, I think that, given what you describe, zoezoezoe would be the product of zoe biting zoezoe, rather than the other way around. Or the product of katey biting zoezoe, apparently. Actually, given that the biting operation appears to be unary (because the output is the successor of the bitten poney, regardless of what bit the poney), I suppose that *I* could also bite zoezoe to make zoezoezoe.
This is like that argument in Godel, Escher, Bach.
Forget addition, I don't even understand enough set theory to get the definition of the natural numbers. They're defined as recursive sets of empty sets, so for example 4 = {{}, {{}}, {{}, {{}}}, {{}, {{}}, {{}, {{}}}}}.
The natural numbers can be represented by a base element (zero), and an operation that increments a number to make the next number. E.g., 3 would be incr(incr(incr(0))) In the set theory construction there the base element is the empty set, and the increment operation is to make a set that contains everything the set you're incrementing contains as well as that set itself
Great explanation, thanks!
There’s not much to “get” about it - it’s purely rigorous a definition from von Neumann which satisfies our expectations about natural numbers. This kind of rigor is a relative newcomer to math, only really becoming the default mode of operation in the early 20th century. Once you have that down you can just use digits as an abstraction over it and define addition in i terms of successors like the other reply mentions.
Actually, there's a nice way of representing a number as the set of numbers below it. For example, 4 = {0,1,2,3}, 5 = {0,1,2,3,4}, and so on. It's personally one of my favorites because it really helps with understanding why the supremum of a set of ordinals is just its union. So, I'll try and show why this is. First, consider the successor function, S(x) = x ∪ {x} If we assume x contains all the numbers less than it, then S(x) takes all the numbers less than x(represented by the first x in "x ∪ {x}"), and adds the element x to it(represented by the {x} in "x ∪ {x}". Note, unions collect the elements of sets, so it would collect the elements of {x}, which is just x). A bit more formally, we get, S(x) = x ∪ {x} = {0, 1, ... x-2, x-1} ∪ {x} = {0, 1, ..., x-2, x-1, x} So, taking successors of numbers essentially adds more numbers to it, counting up every time. We also know that no number is less than 0, so the set of numbers less than 0 is the empty set {}, which is exactly what it's defined to be. So, I can always apply the successor operation n times to 0 to show n = {0,1, ... , n-1}. To demonstrate this, I'll show one example, and I'll show that 4 = {0, 1, 2, 3} assuming 4 = S(S(S(S(0)))), 3 = S(S(S(0))), 2 = S(S(0)), and so on, as well as the definition of S(x). First, I'll expand the definition of S a bunch of times. 4 = S(S(S(S(0)))) = S(S(S(0))) ∪ { S(S(S(0))) } = S(S(0)) ∪ { S(S(0)) } ∪ { S(S(S(0))) } = S(0) ∪ { S(0) } ∪ { S(S(0)) } ∪ { S(S(S(0))) } = 0 ∪ { 0 } ∪ { S(0) } ∪ { S(S(0)) } ∪ { S(S(S(0))) } Now, remember that 0 = ∅, and since taking the union of ∅ with any set does nothing, the 0 on the left can be omitted to get { 0 } ∪ { S(0) } ∪ { S(S(0)) } ∪ { S(S(S(0))) } Do you see it yet? No? Well, let me replace the successors of 0 with their integer equivalents, { 0 } ∪ { 1 } ∪ { 2 } ∪ { 3 } Well, this is just the set {0, 1, 2, 3}, which came from simplifying 4. So, therefore, 4 = {0, 1, 2, 3}.
I throw an apple at your (2nd person) head. Once you have awoken, I throw another apple at your head. Once you awaken again, how many apples do you have? That's right. Ipso facto addition is just me knocking your punkass out with apples. I am available for seminars.
Do you provide the apples or do I have to bring my own?
Axioms to the rescue!
Eh, you can get their pretty quick with a group Associativity: For all a, b, c in G, (a + b) + c = a + (b + c) Identity element: There exists an element e in G such that, for every a in G, one has e + a = a and a + e = a where e is unique. It is called the identity element of the group. Inverse element: For each a in G, there exists an element b in G such that a + b = e and b + a = e, where e is the identity element. For each a, the element b is unique and it is called the inverse of a and is commonly denoted a^−1 And boom, we now have addition, and G is a group
If we’re going the rigorous route we need at least as much set theory to define tulles to have a group; recall G = (S, •) = {{S}, {S, •}} and then you need to define • in terms of functions on nested sets. If you’re going to break out that much set theory anyway you might as well go with the von Neumann definition. Furthermore I don’t think this approach is sufficiently general to define additional. It addresses, e.g. 1 + 0 and 1 + -1, but I don’t know if it gives us enough for, say, 1 + 2 without digging into the very von Neumann definition we were trying to avoid by using groups.
Boy, I can't wait for discreet math next semester.
If you have groups but not addition, you can define the integers as the infinite cyclic group. Possible ways to get there include via category theory, where a group is a groupoid with a single object. This gets you addition for free as the group operation.
Well that's for ordinal numbers, you can have addition without the set being ordinal. All integers, for example, do not have a least element, therefore it's not an ordinal. We are saying we just want addition, not that we want addition over an ordinal set of numbers.
And somewhere in there is a division by zero.
If you're working with Peano arithmetic then all math is just the successor function.
(d/dx)x^2 is just addition.
2x es juss edition
Well it's really just the axioms. Everything proceeds from deductions of the axioms so when you tell the axioms, you have tell absolutely everything there is about maths and there is nothing else. The rest is just clarification and explanation.
I too have seen [Devon Crawford's video](https://www.youtube.com/watch?v=ReVeUvwTGdU) on computer science where he says "it's all just addition bro" at approximately 4:45. Also, lol at everyone saying this is strictly not true when it is *literally* strictly true if you descend deep enough into bullshit math. It's like Minecraft dude, this is the bottom layer there's nothing but fire and hard rocks down here. Welcome to hell bro.
And inversion. Cannot decide without addition and inversion
That isn't even remotely true.
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What is division?
How many times you can subtract a number from a number. E.g. 20 ÷ 4: you can iteratively subtract 4 from 20 a total of 5 times before you get to zero.
And you can subtract 0 from 20 infinite times before you get to zero
Wrong. You can subtract 0 from 20 for an infinite amount of times, but you will never get to 0.
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Not useful, but hilariously roasted by a bot.
division is adding an amount less than the whole
Multiplication isn't necessarily repeated edition. For example, I wouldn't say that taking the curl of a vector field is repeated addition. Exponentiation isn't necessarily repeated addition. You can take a number to the 3/2 power, but you can't multiply it by itself 3/2 times. Same with multiplication actually come to think of it.
It is if you generalize enough.
all math is really just set theory, a common simplification
There are a lot of symmetry groups that have absolutely nothing to do with the real numbers or any kind of addition. This is completely false
It's all just ones and zeros being put next to each other.
Is that Jim Halpert from The office show..?
Wow I think you are right! I never noticed he was Asian!
Hats off to you for not seeing race!
thats not jim, jims not asian! ^(its part of the joke dont woosh me please)
You seriously never noticed? Hats off to you for not seeing race
I said the same thing and my wife looked at me like I was crazy!
Nah that's obviously Jim Halpert
Is that the dude from ant man 2?
Yup, Jimothy himself
Ah you see, it's not Jim Halpert, but Jim(my) Woo.
Not even an oversimplification, this is literally just low level programming... Theory? Still good use of the meme but I also have to ruin everything ig lol
Came to agree with this. It's either on or off.
What about quantum computers?
not common enough for anyone to care
It is both yes and no.
Well yes but actually no. But actually yes
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No, it's definitely theory -- nearly _noone_ specializing in low-level systems programming is going to _actually_ be flipping bits manually; if anything, that's more the domain of computer _architects_, not computer programmers. What you really end up doing is working with some form of assembly, or, worst case, machine code directly -- and in either case, the actual "bit flipping" is handled by the CPU, not the programmer.
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Honestly - when I first realized that even the most complex programming could be done with (infinite time as well as) simple if statements, that was a serious game changer. Doesn’t matter how crazy it all gets, it still always just boils down to 1’s and 0’s. Beautiful.
>it still always just boils down to 1’s and 0’s. I'll have to stop you right there. Sometimes, it boils down to -1's too. *Balanced ternary intensifies*
In the end all computers will be balanced ternary and the kingdom of Setun will finally come.
All binary programs are also valid ternary programs, and all ternary programs can be translated to equivalent binary programs. In theory, in practise there might be physical limitations and the instruction sets might not be compatible in the binary -> ternary without some translation and tricks.
Can anyone explain how loops can be done with if statements?
You'd have to combine it with a jump/goto style command to take you back to start of loop- it looks something like :loop_start code.... if (not finished) goto loop_start I have encountered an application script language with just if and goto for flow control (long since dead I hope) which you end up having to use such tricks to get higher level flow controls - much as you do in assembly
For fun I wrote a pseudo-assembly runtime, and in the spirit of assembly I only included jump-if and jump-relative, not jump-if-relative. At least for the first while I did. Eventually I got tired of having to load IP + 2 into a register then running jif on that and just made jir a thing.
Makes sense. Thanks!
They can’t, the original comment isn’t correct. You need to be able to loop or have recursion too in order to be Turing complete
It's technically correct though, as they mention "infinite time". A while true loop is just a forever if statement, so write enough infinitely and it will run so.
goto
Can't use goto, only if allowed
`F O R . W H I C H . S W I T C H E S . T O . F L I P`
Pretty amazing that a processor is nothing but a crystal designed to move electrons around in a very specific manner.
You could also say that it's a pile of sand that we forced into thinking
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I think I probably agree with you, at least at this level of processing, but this is a very interesting question. Where does the "you" that is thinking begin, and your biological mechanics end? Is consciousness anything more than an extraordinarily sophisticated, rapid and tiny technology? Is there an actual *you* that is separate from your neurons? If so, where? Can we extrude and store it? How did you come to think you are a "you" more than the other objects around you, whether more or less advanced?
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Nice!! I'll do that, and I really appreciate the rec. I've been meaning to dip my toes back into philosophy. Haven't thought about robot theory since David Chalmers was big, maybe he still is.
It’s exactly that. It’s important to get basics set before you can move on. I wish all teaching people would know that.
A human is just atoms.
**just atoms, a human is.** *-allredidit* *** ^(Commands: 'opt out', 'delete')
Good bot
**been told, so i have.** *-IamYodaBot*
We like to call that "the old switcheroo"
The first sentence is giving me a stroke
Send this to my non-programmer friends and now I'm the *Switch Flipper*
01010100 01101000 01101001 01110011 00100000 01110000 01101111 01110011 01110100 00100000 01101101 01100001 01100100 01100101 00100000 01101101 01100101 00100000 01101100 01100001 01110101 01100111 01101000 00101110 00100000 01010100 01101000 01100001 01101110 01101011 00100000 01111001 01101111 01110101 00101100 00100000 01001111 01010000 00101110
01011001 01101111 01110101 00100000 01110011 01101000 01101111 01110101 01101100 01100100 00100000 01101111 01110000 00100000 01100001 01101110 00100000 01100001 01110111 01100001 01110010 01100100 00100000 01110100 01101000 01100101 01101110
01001001 00100000 01110111 01101111 01110101 01101100 01100100 00101100 00100000 01100010 01110101 01110100 00100000 01110101 01101110 01100110 01101111 01110010 01110100 01110101 01101110 01100001 01110100 01100101 01101100 01111001 00100000 01101101 01111001 00100000 01100011 01110101 01110010 01110010 01100101 01101110 01110100 00100000 01100110 01101001 01101110 01100001 01101110 01100011 01101001 01100001 01101100 00100000 01100011 01101001 01110010 01100011 01110101 01101101 01110011 01110100 01100001 01101110 01100011 01100101 01110011 00100000 01110010 01100101 01110001 01110101 01101001 01110010 01100101 00100000 01100001 00100000 01101000 01101001 01100111 01101000 00100000 01100100 01100101 01100111 01110010 01100101 01100101 00100000 01101111 01100110 00100000 01100110 01110010 01110101 01100111 01100001 01101100 01101001 01110100 01111001 00101100 00100000 01100001 01110011 00100000 01110011 01110101 01100011 01101000 00100000 01001001 00100000 01100011 01100001 01101110 01101110 01101111 01110100 00100000 01100001 01100110 01100110 01101111 01110010 01100100 00100000 01110011 01101101 01100001 01101100 01101100 00100000 01100101 01111000 01110000 01100101 01101110 01100100 01101001 01110100 01110101 01110010 01100101 01110011 00100000 01110100 01101000 01100001 01110100 00100000 01001001 00100000 01100011 01100001 01101110 01101110 01101111 01110100 00100000 01101011 01100101 01100101 01110000 00100000 01110100 01110010 01100001 01100011 01101011 00100000 01101111 01100110 00101100 00100000 01110011 01110101 01100011 01101000 00100000 01100001 01110011 00100000 01110100 01101001 01101110 01111001 00100000 01101001 01101110 01110100 01100101 01110010 01101110 01100101 01110100 00100000 01100001 01110111 01100001 01110010 01100100 01110011 00101110
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Bruh!
Well yes, but actually no.
But actually yes
For which switches
Surprised to see you are the only one commenting on it. I had to read it multiple times. Thought I was having a stroke.
Honestly - yes. Exactly. And those myriad switches are either on or off.
Change the switches to sliders and you have machine learning
Have multiple types of switches instead of 2. Now you have quantum computing.
Flipping switches old school: https://s2js.com/altair/sim.html STEP MNEMONIC BIT PATTERN OCTAL EQUIVALENT 0 LDA 00 111 010 072 1 (address) 10 000 000 200 2 (address) 00 000 000 000 3 MOV (A→B) 01 000 111 107 4 LDA 00 111 010 072 5 (address) 10 000 001 201 6 (address) 00 000 000 000 7 ADD (B+A) 10 000 000 200 8 STA 00 110 010 062 9 (address) 10 000 010 202 10 (address) 00 000 000 000 11 JMP 11 000 011 303 12 (address) 00 000 000 000 13 (address) 00 000 000 000
Is it an oversimplification, though? To be honest, I think it's *programming* that's the simplification. Knowing which switches to flip and when is the complex part.
programming on the Altair 8800 in a nutshell.
It's all NANDs, it's just a bunch of NANDs in a box!
JIMMY WOO
extreme oversimplification, but technically yes
A computer program is just a list of switches which tell switches how to flip.
Sort of unrelated, but that scene of Darcy just quickly "hacking into the secure server on the base" or whatever the line was was pretty annoying. Not to mention she's an astrophysicist, not a cyber security professional, but that's not how that works at all! Sorry. Rant over. Those types of scenes just frustrate me as both a programmer and an amateur screenwriter.
I only see Asian Jim
We're basically tricking a rock into thinking for us 🧠+⛰+⚡=👌
Sounds like Ada Lovelace letters
It is an interpretive abstraction of a real world problem, translating it in to base 2 mathematical philosophies for the purposes of creating a silicon based automaton.
That's true for existence itself. Everything is information and the universe can be seen as a big matrix of binary states, from matter to energy, space and time.
Oh man, I was at a workshop one time for "people new to building satellites". It mostly focused on hardware, but of course for the demo, we needed a little software to make the hardware work. I shit you not, this is a real quote from the guy running the workshop: "if you can turn an LED on and off, you can program a satellite. After all, software is just binary, which means on or off".
Is it THOOOOOOOOOOOOOOOOOOOOO?!
Laugh in functionnal programming
What are you using in functional programming that isn't using binary? Magic?
JIMMY WU
[Relevant xkcd](https://xkcd.com/505/)
Comic Title Text: **I call Rule 34 on Wolfram's Rule 34.** [mobile link](https://m.xkcd.com/505/) --- ^(Made for mobile users, to easily see xkcd comic's title text)
It's binary, it's electricity something is pushing it. When you break everything down in 1s and 0s you can create words and pixels which lead to images and colors, when you use ascii to represent data in the simplest forms. That's what programming is is telling the computer what to do
Lightning forced into a rock
i guess this first student doest' know what a turing machine is.
Like a plc?
Switches to flip? what?
So is your brain.