- There it goes.
- Yay! I made a 2D version of a
greedy cup siphon recently, and Matt Parker suggested that I might be able to build a water computer by chaining together a
number of these siphons. For example, maybe I
could use these siphons to add numbers together. Computers add numbers by chaining together a series of logic gates. For example, these logic gates add two digit binary numbers together. I'll get into the details
of that diagram later, but what are the logic gates made out of? Well, in a computer, they're
made out of transistors, but they don't have to be. If you're familiar with
Matt Parker's channel, you'll know that logic gates can be made out of dominoes, for example. But what about using the
flow of water instead? This was my first attempt. If both inputs are turned on, they collide in the middle,
filling up this central bucket, and water flows out of
the middle hole there. If only one input is turned
on, there's no collision, and water flows into one
of the two side buckets. In other words, water only
pours out of this output if both inputs are turned on. In a computer, you call that an AND gate, a logic gate where the
output only turns on when both inputs are on. If I combine these two outer holes into a single tube like this, then water only flows out of this tube if one or the other of
the inputs are turned on but not both. In a computer, that's
called an exclusive or gate. So this should work as
an AND gate or an OR gate or both at the same time. Actually, this arrangement
fails immediately because water is too sticky. It sticks to these outer faces, and you can't get a jet strong enough to pass across the gap. But if you can separate
the water from the glass, you can get it to work. - What I did like about that one is you can very easily see why it works. - [Steve] Yeah. - And that's why I love these
ridiculous physical computers, because there's no magic to computing. - One slight issue is flow rates. So for example, you know, if the flow in is slower
than the flow out, this is gonna build up and
then it's gonna spill over. In the end, this mechanism
had too many issues. Also, I really wanted to use the greedy cup siphon mechanism, which this doesn't have. Actually, the reason Matt Parker thought of water computers while watching my video was because of a mistake that I made. I put the siphon in the
middle of the container. That actually split the container into two independent areas. - I did enjoy your video,
watching you having to pour both very
carefully to synchronize. It had that sense of an AND. - There really is an
AND-ness to it, isn't there? The problem is you have to
really worry about timing. Both those bits from each side have to come in at the same time, they have to meet at the
same time at the top there. Actually, you can get much
more reliable AND gate from this thing. What you do is you define a one
as a certain volume of water that gets just above halfway on here. So if you put two ones in, the volume of water gets
all the way to the top, the greedy cup siphon is activated, and your AND response comes out there. An exclusive or is a little bit trickier. - I sent you a sketch where I had a dual-height greedy cup siphon, with one on each side
but different heights, which I thought would work, but I wasn't sure if it would be reliable. - So in the end, the solution was to drill a small hole here. It's a slow leak, and what that means is if you put a one in
there and only a one, you're not gonna get a greedy cup siphon, but you are eventually gonna get it to all come out of that slow leak. If you put two ones in for your input, then the siphon is activated
and the chamber empties. It doesn't empty instantaneously, so there will be a small amount of leak through the exclusive or channel. So when you look at the chamber that's catching the exclusive or output, if there's just a little
bit of the bottom, you read that as a zero, but if the chamber is full up to here, then you read it as a one. One thing that's nice is that this single device houses two gates. You've got two inputs and two outputs. One output gives you the exclusive or, the other output gives you the AND. - Conceptually, we had to switch from thinking about
something you would turn on and it would just keep flowing and settle into some kind of state to now you've got packets
of water representing bits. - Why don't I show you? I can't change cameras, so why don't I do a WhatsApp
video call with you? I know, I know. Oh, you've just, why
did you reject my call? That's very rude. Are you screening my calls? - Hey, all right. - Hey. - So I'm gonna mute you.
- So I'm gonna mute you here. - [Steve] There it is. - [Matt] Oh my goodness. I have no sense of the scale of what I, well, I know the scale of the achievement. - It's pretty cool, isn't it? But what on earth is it doing? Well, it's implementing
this logic gate diagram that I showed you before. Actually, if I turn it on its side, you can start to see they
have a similar shape. But what exactly is this
logic gate diagram doing? Well, at this point, it's helpful to switch up the language that we use. Instead of talking
about inputs and outputs being turned on or turned off, let's talk about ones and zeros. So for example, in the
case of an AND gate, you would say if both
the inputs are a one, then the output is a one. Thinking about the
logic gates in that way, we'll be able to show that
this particular arrangement is actually going through a process of long addition of binary numbers. You'll know from doing
long addition at school that if you add two digits
together and it goes above 10, then you carry the one. So for example, here,
nine plus four is 13, you put the three down there, and you put the one up
there into the next column. The same thing happens with
long addition of binary numbers. If there's a one and
a zero in this column, then you put a one down here. But if there's a one and a one, well, one plus one is two, and
two in binary is written 10. So you put the zero down
here, and you carry the one. You might already be
noticing some logic gates hidden in these operations. For example, the number
that you put down here, if you think about that as the output, what we have is an exclusive or operation. You only put a one here in the output if one or the other of
the inputs is a one. If they're both one, then
you actually put a zero. What about the carry? Well, the carry is related to those two inputs like an AND gate. In other words, you only carry a one if both of the inputs are a one. So let's put that together in a diagram. This is called a half adder. Moving to the next column
in this long addition, there are actually three inputs. So the logic diagram is a
little more complicated. Here it is. I'm not gonna explain it all, but feel free to pause the video if you want to ponder it for yourself. But this is called a full adder. And if you want to add, say, two four-digit binary numbers together, you just chain three full
adders together like this with a half adder at the start because the first column
doesn't have a carry coming in. Because now our devices are an AND gate and an OR gate in one, we can simplify this logic diagram to look like this. Some aspects of this water computer aren't completely obvious. Like this bit here, for
example, it's a splitter. The reason you need a splitter is because, well, if this siphon activates, it's because you've put two ones in. You've got a volume of water
that represents actually a two. So you have a two coming out of here. But I only want a one to go in here. So I need to split it in half. A one goes this way and
another one goes this way. This is just a drain. I originally had one
continuous tube for the drain, but that was acting like a siphon and preventing any water
going into this one. That's why you've got this funnel here. It just breaks that siphon effect. This bundling is also a bit confusing. Honestly, that's just for tube management. If you look closely, it is
just two separate inputs, this one and this one. Really, I should have an
XOR tube coming out of here into a readout bucket like this one, but it's a lot easier just to not bother drilling a hole in here, and then this doubles up
as the readout bucket. You might be thinking, "Well, hold on, "this has got three inputs. "How can that work?" And actually, these two
inputs should really go through an exclusive or
before going into here. But it doesn't really matter, because you would never actually get both of those on at the same time if you consider the logic
prior to these two tubes. So it's fine to just have
them both go straight in. Do you want to give me two numbers to add? - I kind of want to see 11 plus five. The reason I think that'd be interesting is you're gonna have different
types of cascading rollovers. - [Steve] So let's put a one in there. A one is 10 milliliters, by the way, in case you were wondering.
- Oh, that's good to know. I've always wondered what
the volume of a one is. - So these are the two
numbers we're adding, 11 and five, written in binary. You take the two digits
from the ones column, put them in these syringes; the two digits from the twos column, put them in these syringes; the two digits from the fours column, put them in these syringes; and the two digits from the eights column, and put them in these syringes. We're then gonna watch
these five readout buckets. You've got the ones
bucket, the twos bucket, the fours bucket, the eights bucket, and the sixteens bucket. 11 plus five is 16, so we want a one in that final bucket and nowhere else. - There it goes!
- Hey, there you go. It worked. So now, and then that one should rollover. - [Matt] And then the next one? - [Steve] Oh, come on. Ah, balls. Part of it is getting the
right amount in the syringe. You don't want too much so that there's too much
dribble left over, and so on. - [Matt] Maybe a one is 11 milliliters. - [Steve] I also think we've
got a bit of an issue here where some of the water's
dribbling down the backboard - You've got a memory leak, Steve. I've never been so proud
of such an easy joke. Could be a security issue, if I'm honest. - [Steve] Yeah, I think
someone is using this to mine Bitcoin, and it's
slowing everything down. - What if we generate two random numbers, and we'll give the
computer a good clean-out, and we'll add the two random numbers so we have no way to influence this, and if that works, we
declare it a raging success? - [Steve] Yeah, sounds good. - Got it, so four plus nine. And that's pretty close
to the nine plus five that we were thinking
would be a good idea. That's gonna be pretty boring, 'cause it's all just gonna plonk through. Tell you what-
- Or do you want to? - Oh, I just had a closer look, Steve. It was a five. Huh. - Oh, right. - I'm sorry. - The reset is like, I lift this up, I go like that, and then I go like that. - Oh, yeah, the Etch A Sketch
approach to researching. Underused in modern computing. Although the undo on the
iPhone is a shake, so. So the dominoes reset was a day if you have a team of like tens of people. I got two three digit numbers working on the domino computer. If you get this to work, this would be a substantial increase in computing power. - [Steve] All right, here we go. - [Matt] Okay, bam, we've had our AND, 'cause that still could have gone wrong. Like, I know we're saying
it's a trivial calculation, but that split had to work. And now we just need two slow leaks. - [Steve] Which is what we've got. It's 01110, which is eight plus
four plus two, which is 14. What were we adding together again? - [Matt] Nine plus five. - [Steve] Is 14, yay! - In my experience, the more facetious of the commenters on this video will point out that you
just went to a lot of effort to show that nine plus five
equals eight plus four plus two. - Of course, that's really a fair comment because you only do the
eight plus four plus two bit at the end when you're converting back to decimal in your head. If you stay in binary like a computer, then we've actually done
something really useful. We've shown that 0101
plus 1001 equals 01110. You know, maybe I could build something that converts it to a decimal readout. - Your water computer, my domino computer, there's discrete states
that it ends up in. So it probably can't say it analog. But there are actual analog computers. So famously, there was a
guy called Bill Phillips who was an economist and worked on dams, and realized the equations for water flow matched the equations that
are used to model the economy, and they built a actual
analog water computer to model the economy, like with taps for like government
spending and interest rates. This is kind of before you could just numerical solution
your way out of the problem. In other news, Steve, I've just looked up. You are on 877,000 subscribers. I am on also 800 and something. We're gonna keep collabing
until we get to a million. - [Steve] You challenged
me to the water computer. I want to see a video on the game Dobble. - That is one of the most
requested video topics. - [Steve] Is it? - And there's no accessible videos on it. - That's gonna be a
really interesting video, so make sure you subscribe
to Matt in advance. Link in the card and the description. He's approaching a million subscribers, so let's get him there as quick as we can. I'm also approaching
a million subscribers. So if you're not subscribed and you've watched a few of my videos, I'd love you to consider whether I've earned your subscription. Should we do one more calculation, maybe slightly higher numbers or something so we get down to that final bucket? - Yeah, what about like seven plus 15? - Yeah, here we go. - [Matt] Okay, units are
in, units are overflowing. We've got an AND. - [Steve] Yep. - [Matt] Oh, yep, twos have overflowed. We've got an AND. - [Steve] There it goes. - [Matt] Okay, the waste
seems to be working. Just dump that one. - [Steve] There it goes. - [Matt] Now we just need one more AND. - Come on.
- Come on. - [Matt] There's enough, surely
there's enough coming in. There it goes! - [Steve] Yay! - [Matt] You've done it. Seven plus 15 equals 22. - For completeness, here's
that original calculation, 11 plus five, actually
working instead of failing. And just for fun, here's 15 plus 15, in other words, all the ones. I didn't go into detail about how binary numbers work in this video. If you want to brush up on that, I can heartily recommend the sponsor of this video, Brilliant. The best way to learn something is by doing it for yourself. Like, if you want a really
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If you found this interesting you might like a game where it progresses towards building a computer using gates.
https://nandgame.com/
I'm the guy in the video. AMA
This is really fascinating! I am not a Comp-Sci guy but it kind of made sense, thanks!