Excellent. Alright, guys... Routing! So, now that we've got Sentinel, actually Routing becomes... much, much simpler.

The... One of the hard things about Routing, I think, is that XOR, this XOR thing... the XOR... distance, and whatnot, is... very, very difficult to get your head around, and to try and... reason with. Especially, it seems... the more mathematical we are, the more difficult that is. Uh, so I find it easier! But, um...

One good thing about Routing is, all that XOR information is in the Routing table. So, when we... when we want to do something, in Routing, like work out, "What is the distance between A and B?" Or... uh, "Is... A closer, than C?" The Routing table does that. Now, you can't have, "Is A closer than C," because you've got to do "with respect to," whatever, some target. So, one of the main things to... know about Routing is, this Routing table handles the XOR relationship. Same thing to do with distance, or measurements, or, any of that sort of stuff: that information is in the Routing table.

And, initially the Routing table, when the Routing table was written, in, this sort of previous version of Routing, there was actually an [??] in it, that said: "Don't ever change this." "Don't ever touch this." Because... the Routing table's got stuff in it, that you look and think, "That's not correct!" Like, "You should be able to sort something, without having a 'with respect to.'" And... any time you do, any time you touch this Routing table, you should be sweating blood. Because, you should be in a position where maths doesn't make sense anymore; and your head's got to be in a... a place, that can cope with XOR stuff.

So... just, the Routing table on its own, we could probably spend... days and days, going over, in how that works. But, Erik has done some pretty good, uh... presentations, and videos, about the Routing table, and the whole XOR Networking thing—and things like: distance, and closeness; all these... all these relationships, are, not obvious. But, Erik's covered all of that. So, I figured, today, just to say that: anything to do with distance, closeness, or whatever is in this XOR space, and the Routing table... handles, that, for us. And... and the main....

The Routing table... is critical, in Routing. And, in a previous version of Routing, we totally screwed up. Uh... The version of Routing, that, we had, in C++, has got, enormously screwed up logic; it's completely insecure, because of enormously screwed up logic.

And... here's the fundamental thing, about Kademlia-based networks. If you take... the Routing table, it splits in two. So that's... eh, bucket. I think we've called this bucket 0. Then it splits in two again. So: bucket 1. And it splits in two again: bucket 2. Splits in two: bucket 3... all the way to 511. ...Now, if you, imagine, that the whole XOR address range: from "you" to "!you" (the complete opposite of you). So, you may think 0-FFFF. But you can't think 0-FFFF; you've got to think from "you", to the complete opposite.

The way... the way that the system works, is, and it's got to work like this: you know... you know some information, about this part of the network; so bucket 0, you know some information. So let's call, that, information, that you know... 1,000. So you know 1,000 of, this piece of information. Your knowledge, if we could measure knowledge... ranks 1,000: there, *tap tap tap*. This bucket here: the knowledge that you would have over this bucket, would be 2,000. ...You would have double the amount of knowledge you do of this bucket, than you do of this bucket. This bucket here: 4,000; ... 8,000. So: as, you... send, a message, across... an XOR network... every bucket that you send the message to... so, every bucket you send a message to: if it's just one [??], we'll have 2x the info.