Hello, and welcome back to the craft box. My name is Brandon today. We are doing Another episode if it's a number two of the storm walkthrough Today's challenge. No heels because you guys voted for that and discord if you want to vote on the challenge of the episode go and Click the link to my discord in the description below. That was um really great. I'm plugging right there Um, but yeah, we are doing it. No no heels today So I've already taken out all of the heels that I had not that we had any in because We've only really just finished the item card only challenge So we are allowed to use lightning bats and thunder snake today if we want to Which is fun if you haven't checked out last episode you should probably do that because it kind of Kind of describes what what this walkthrough is all about So that's fun Let's see how long it takes us to get the rune skull because this could take a while did not collect Wow One already nice So yeah, currently the poll for the next episode of the storm walkthrough for the challenge is up on my discord as well I didn't think I said that at the start, but yeah I'd try and put it up just before I start recording the next episode So yeah, if in the future I have to record like a whole bunch of once I'll just put up a whole bunch of them all at once so you can like vote on Like say I need to record five episodes. I'm away for like five weeks. That will never happen But if I'm away for like a long time or a time that and I can't record a couple of episodes Then I'll put up all of the all of the All of the polls for those episodes Generally, I like to do a week beforehand read a week before I record slash they come out because I basically Generally record this on the day before it comes out. Okay. We are getting so bad luck like what is this seriously? This has taken forever already. This is what fight number five I think yikes Big yikes, at least we one shot that guy. That's always good always. Oh still not did not collect. Okay Sometimes the clues as well. There's a lot of defeating collect quest here that I just take forever. There we go We got it nice amazing I honestly cannot wait until this area is all updated graphics wise like it's gonna look so cool I really didn't want to record as soon as as soon as I heard that they're updating the graphics here in the next Test run, which will probably be dropping sometime really soon. I didn't actually want to record anymore until they finished it But like I need to unfortunately Because this is gonna be a heck of a long Walkthrough like if we only do one episode a week, which I'm still debating having a couple more extra ones We will see It will probably take about two years at this with the current amount of Episodes that have planned which is up until the end of the barrier part to so basically the end of the game now in 2019 I was about to say 2018 Wow 2019 it's gonna take about two years. So that's fun We'll see if we can increase the episode Count per week. I don't know if I can too much because these do generally take quite a long time to record mainly because That's just like a like I'm last episode was like 33 minutes of just playing the game Which is kind of weird because I don't usually play anymore that much like all in a row Like I mean I did that for the death walkthrough, but not like constantly recording and like not having a break Because in the death walkthrough between like Cuts I would like stop the recording software and I would like go and watch YouTube while I was finishing off the rest of the stuff But um now nope can't do that. I just record the whole way through Which is kind of it provides something different for me and it's not the same which is nice, but also It means for me at least it feels like it takes longer to record because I'm just sitting there forever Playing the game and talking And then have to go through and edit it all which it takes a lot longer because it's not as simple as just cutting Where with the video ends and stuff? Which is what people called assembly, but you know, I'm lazy. I'm lazy. Whoa level right level. Yeah level look at that Look at us go level six amazing We're actually I actually forget that Cyclops Lane is actually kind of quick like if you can do it really quick And get the drops really quick. It's actually not too long I think when we recorded the a team it took us about 20 minutes to do Yeah, but I mean the whole of Wizard City itself the free-to-play area takes about an hour I would say is my estimation will find out when when we get to Try an avenue which is gonna be the last street spoiler alerts Fun fact all of the areas Like the episode numbers for the areas are laid out in the um the opening the first postcard of the Like the main like the world postcard because obviously in the intro for this series There's like two postcards well two main postcards one for the one for the world and then one for the um episode Um, and I'm not sure if there's gonna be if the others are gonna be floating around that we've already done I'm still having You'll see because if it was at the start then you know it obviously is going to be like that But if it isn't then it may not be um, so yeah, it's completely up for debate really Um, and I don't know yet depends how much I want to edit it I guess but yeah, basically in the world thing is all of the episodes in order So just so you know what episodes coming up next All of the areas are in order and then there's also especially for the Wizard City one I know there's also the faces of like Merlin bros. I think Halston belstrom and Malastir because you know those are kind of important characters. Hi Nolan Hi Nolan. Oh look the war horn pass. We are nearly done already Um, we need to leave a mark because otherwise I'm gonna be walking for ages. I honestly do forget how quick um Like Cyclops lane goes Like I don't actually know how long I've been recording. I don't really time these episodes I do I did time the death walkthrough fun fact you're getting like all the behind the scenes I don't know if this is going to be cut out, but um Yeah, they I do actually time the death walkthrough because I kind of try and make it about 15 minutes We're definitely not longer than 15 minutes simply because I don't think it makes a good video if it's longer than 15 minutes Especially for like a standard like let's listen to all of the dialogue And only do like one boss fight episode sort of stuff. I don't think it makes a particularly good episode if um if it's like 50 minutes of just me doing the questing like I If I'm doing that it has to be kind of all cut up like this episode These walkthroughs are like all cut up into parts of just the best bits But saying that wow two fizzles in a row. What is this? What is this witchcraft? Saying that we can't you can actually see the full uncut videos If you go to my discord channel again, just say shameless self promotion really And you go into the boogal channel once you've typed slash agree to enter the server Basically just agreeing to the rules You can um you can type exclamation point storm And you can get a list of all of the commands that you can go to to see all of the behind the scenes videos So that's just like the full uncut videos So if you want to see what I cut out of this episode, which I don't know yet because I'm still recording it Obviously and haven't edited it yet. There's probably a lot of stuff that I cut out I know last time there was a lot of good stuff that I had to cut out to try and keep it like 20 minutes ish So yeah, if you want to see that you can go to my discord and find find them all They're private it on my do not private it there unlisted on my channel So you can't actually like search to find them because I mean, I don't think I don't think it's right like having that is just another video It's kind of a cop out But if you want to see what I can't or just watch that instead of the actual thing you can They are generally really ready technically the day before the day before they um The episode comes out. So like today later today this episode like this uncut video that I'm recording right now Is technically already ready and up on the channel and the command would already work um That's a wee little cheeky bit But you know if you want to watch the full bit or you just want to watch the cut out But if you don't have enough time because these could be a long a lot longer in the future Like I'm talking hours Because I know chrysalis has got to be a pain a big pain Um, well that wasn't too bad. That wasn't too bad. We didn't even get it anyway Um, definitely didn't fizzle like five million times like we did the previous fight, which is always nice I really don't like them this this always takes me forever like no matter what no matter how well I've done with all of the previous quests. This fight always takes so long Also, I'm really proud that we haven't needed to heal yet. I'm really proud of that I'm just worried about the final boss fight really with general archelius. He's usually quite a challenging foe Me and him go back a long way from him destroying me on the death walk through like multiple times um But yeah, we also do have an advantage because we are storm So we want to do a lot of damage and two we also boost on them. So as long as they don't shield We're like really good. Um Yeah, which is also why I tried an avenue last because then hopefully by then I have the prism Also, if you have any other things that you'd like to see my storm do Um, obviously I'm trying to do all of the side quests. I don't know about badges yet still to decide on that. Um Mainly because my death is doing that currently. So I don't know if I want to Grind out for the same badges again, um all over again. Um But if there's anything else you want to see my storm wizard do eventually, um, let me know in the down in the comments I'm always open to suggestions Um about what you would love to see my characters do same with my myth or my We don't talk about my balance or my death really if you have anything else you would want to see those two characters Do you should let me know in the comments as well because I'm always I always love to hear what you want to see. Can we please get the warhorn pass like seriously? Like what is this? What is this luck? We have been out here more longer. We've spent at least half our time Fighting things for defeating collect quests Like what is this? What is this? No fizzle. Yay, so good Blum Okay 117 Bad. You're bad mate. You're bad. You're done bad. Okay thunder snake again because the only spell we use is thunder snake apparently Um, okay Okay, doki 88 damage nice And thunder snake That did max good 139 not too bad Just need to hit him off with a uh a minus spark and all should be good I am trying to save mana because Mana is the one thing that you seem to run out of really really quickly Especially in the early game, um, you more likely to run out of mana than you are how Especially in these quests because there's just an abundance of health wisps, but not an abundance of mana Can we seriously get this like what the heck? Why is this taking so long?  That only took five million years Okay Here we go general archel is let's go boy. No heals No heals limited mana. We can do this. I believe I believe in us, uh, we're not going to use this. He has so much health though 470 what the heck what though? Um, I'm going to try and get out the cyclops legion here first probably the best idea This legion here should be dead. We are nearly at a quarter health down. Which is not the best We probably will with this be at a quarter health down. We just need to then Go hardcore on what's his face here? General archel is we fizzled unlucky? Of course we did. Yep, that happens I could go for a minus spark on him um into a tempest I think that's probably what we're gonna have to do that'll be the move I think just because I don't really want to die. Okay. We're at 64 health. This could be bad Hopefully they both fizzle Like hopefully they both fizzle. We're also going second, which is not cool. Really not cool. Please fizzle. Please fizzle Please fizzle No, we're dead This does so much damage Yeah, we did. Oh no. No said reacts only. Well, we died once to rattle bones. We died once to this guy We'll try and get out the legion here the minion first. Wow. Okay already a fizzle at least we're going first this time At least we're going first. That's always a good start Always a good thing when you're going first. They haven't hit me yet, which is also great. So we didn't hit them.  We fizzled again. Damn it. Damn it. Why do we fizzle so much storm? Why are you bad? He fizzled can he fizzle? No, he's not gonna fizzle. That's unfortunate. Firecat isn't too bad though Firecat isn't too bad. It did 98. That's the minimum the minimum it could do Um, I really actually should have taken off my pet because it can heal. I didn't actually think about that Let's just hope it doesn't luckily it's behaved this um Luckily it's behaved so far and has not healed. I know I said I wouldn't use this but this is just to get them down at least the minion out because we've tried three times now to get the minion out so I mean Might as well. We can always go for like a thundersnake into The thundersnake because that's what we know how to spam these days thundersnake Um, okay, that did so much. Holy moly just as well. I got the minion out. Jeez Yeah, thundersnake into a thundersnake We'll probably kill unless this kills and does max if it does max it might kill if not, then that's unfortunate Did not did not kill 117 weak Super weak, okay fizzle. Good job. Good job bud. Good job. Good job. Um, what goes around comes around 71 We need another thundersnake If we fizzle this could be game over We didn't it's gg. We did it gg boys Hopefully this goes. Yeah, he did. Yeah, cool. Nice work. We did it only died once which is great You have defeated me. Um accuracy. Yeah, I think we need that one accuracy It's better than one damage or two damage or something. Um, Nolan.  Even though that's not his name And then we will talk to um, mr. Mr. Ambrose of Merle, um, but yeah, let us talk to Merle and then end off the episode here With a level See we did it. We leveled up. Look at last go level six Level seven actually we can learn a new spell amazing We will be doing all of the spell quest with dialogue Just so you know just like we did with the um death walkthrough just because I like doing the spell quests um So yeah, if it's got if it's a spell quest with dialogue, we will Do it otherwise if it's just a normal spell, which I don't think it is No, it is actually a normal thing. So we'll be doing that next time. Thank you for watching Um, remember to like and subscribe before we got brazil about us We don't exactly whenever some other storm walkthrough and room in the craft outside the box


What we've covered so far is block ciphers and stream ciphers. Both of them are using symmetric key cryptography, in that when we saw desks, when you saw it in your homework, same with AES, the Advanced Encryption Standard, even RC4, which is a stream cipher. In all of them, the sender has a key and the receiver to decrypt must have the same key. So by symmetric ciphers, we mean that the key is the same at both sides. There's one key and it must be kept secret. That's the most common form of cipher. It's been around for a long time. All the classical ciphers use that approach where you need to have some secret and decrypt, you need to know that secret. In the last 30 or 40 years, and maybe a bit older than that, but not so publicized, people come up with a new form of cryptography that avoided the need for both sides to have the same secret. The problem with requiring the same secret, that is at the encryptor and decryptor, is that somehow that secret, that key, needs to be distributed. So if I want to encrypt something and send to you using desks, I choose, for example, my desks key and somehow I need to get that desk key to the destination so that they'll be able to decrypt. How do I do that? How do I send my key to someone else? Assuming they're on the other side of the world. Okay, you know, we want to communicate across the internet. I want to encrypt a file using desks. I choose some random 64-bit key and encrypt. I can send the ciphertext, the encrypted file, to the destination via the internet, but for them to decrypt, they need to have the key. How do they get the key? Any ideas? A voice call over the internet, but the problem with that is that we're assuming that the internet is not secure. That's why I'm encrypting the information in the first place. So when I send, let's say, my email message, I want to encrypt it. Why would I want to encrypt an email message? Because I don't trust the internet service providers or someone in between my computer and the destination because possibly they can read my message. So picking up the phone or Skype or a online application to make a voice call, still we have to send that key via the internet. So that doesn't help because if someone listens in, listens into my Skype call or my message that I send and sees the key, then of course they can decrypt my file. Any other ways to send the key to someone? Okay, some physical device that generates some key, let's say based upon some timestamp or current time it generates the key. How do I get that device? I want it, with the internet we want to communicate instantly. I want to send an email to someone. For that approach to work that person I want to communicate with must have this same device that I have, not so convenient. Maybe I can post it to them, so maybe in a week's time they can read my email, but not so useful for real-time communications or at least normal internet communications. In the same way that maybe I could write on a piece of paper my key, put it inside an envelope and use the old snail mail, the post to send it. So long as I trust the post, maybe if it's very secret, maybe someone just read the letter at the receiver and see the key. So what else can I do? Fly there, expensive. Not very convenient. Anything else that I can do to send someone the key? If I send it across the internet, someone may be able to see the key. What could it be? Hidden message. Okay. Stegonography. There's one way. Hide that key inside some other message. Okay, there's one option. But I have to tell, for that to work, for the person to find the key from the hidden message, they must know the algorithm for how I hid it. So how do I tell them the algorithm for how to hide messages or how to unhide messages? It's the same problem. So it's getting this initial information to the receiver is possible, but quite inconvenient with the normal approaches we have. What about if we encrypt the key? Then how do we, if I encrypt the key, then I need another key to encrypt it, then how do I get that other key to the other person? It's the same problem. So using symmetric key encryption works, except there's a problem of key distribution. Asymmetric cryptography tries to overcome that problem. It provides encryption by using two different keys. Not the one same secret key, but a secret key and also a public key. A key that everyone can know, including the attacker or malicious user. And what we'll see, and we'll see it after the midterm, what we'll see is with asymmetric cryptography, what you do is you encrypt using your algorithm using a public key and you send the ciphertext to someone and only the person who has the corresponding private key can decrypt. So the idea is I want to send to someone, I encrypt, so every user has two keys, a public and a private key. So the destination has their own public and private key. If I want to send something to them, I encrypt it with their public key and the algorithms are designed such that only the person who has that corresponding private key can decrypt. And that's a way to avoid having to distribute the keys. We still need to distribute a public key, but by definition a public key we can just tell everyone. We don't have to keep it secret. Now we're not going to cover how that works until after the midterm, but some of the mathematics that it depends upon, the example algorithms we'll look at, requires some different or some things that you may not know, and that's what we're going to cover today. It's a very simple number theory. Some of it you'll already know and we'll just quickly go through to refresh your memories. Some of it will be new. So this topic on number theory is going to support the next topic on public key cryptography. Start simple and we'll go through some examples as we go if I have some. You know that a number has a number of divisors or sometimes we call the factors, a factors of any number we can find. Let me get organized here. So just some definitions of terminology. So you know this or at least most of this, but you may not have used the terminology. We can say some number, some b divides a. We're both b and a integers. If a is equal to some other integer m multiplied by b, that is two divides ten. The way we write it, two divides ten, for example, because ten equals five times two. So we can work out what the divisors are of some integer. So what are the divisors of the number ten? What divides ten? Ten, two, five, one. So they're the divisors of ten. So we're dealing with integers here. So that's simple. So sometimes you may see the notation written as, for example, a divisor b or ten, b is a divisor of a, so two divides ten, for example. That's nothing new, just some terminology. So the other way you think of it is a factor. So what are the integer factors of ten, one, two, five and ten? The numbers that can divide ten and give us an integer as an answer. And the other thing you probably know is that we can look at two numbers and find the greatest common divisor. So what's the greatest common divisor of ten and fifteen? Five. So we just look at the divisors of ten, one, two, five, ten. The divisors of fifteen, one, three, five, fifteen. And what's the greatest common number? Five in that case. So the greatest common divisor is something that we see sometimes. There are algorithms to find that. That is when we have large numbers to more efficiently determine the greatest common divisor of two integers. We're not going to cover the Euclidean algorithm, but there are ways to implement that. Something that you may not have heard of. We mentioned it in a previous topic, but we didn't really explain it. We can say that two integers are relatively prime if their greatest common divisor is one. So it's a concept which I think is new to most of you, relatively prime. So we compare two numbers. If their greatest common divisor is one, then we say they are relatively prime. So don't confuse it's a prime number, it's slightly different. The two integers are relatively prime if the divisor is one. Are ten and fifteen relatively prime? The integers ten and fifteen, are they relatively prime? No, the greatest common divisor of ten and fifteen is five. So those two numbers are not relatively prime. What is a number that is relatively prime with ten? So given the number ten, find another number which is relatively prime with it. And there may be multiple answers. Some people have said an answer, some have said a wrong answer. Again, a number which is relatively prime with ten. One, three, five is not because five and ten have a greatest common divisor greater than one. Two is not. So there are many, okay. So we look at the divisors of ten, one, two, five and ten. They cannot be relatively prime with ten and any numbers which are multiples of ten or of the divisors. So one is relatively prime with ten. Three is relatively prime with ten. Is four? Four is not because four and ten have a greatest common divisor of two. Six is not because since ten is an even number, it has a divisor of two. So any other even number will also have a divisor of two. So we can work out which integers are relatively prime with each other. We'll use that as we go through. Another thing that you know about, I'm sure you've seen, is prime numbers. So a prime number or an integer, an integer greater than one is a prime number if and only if its divisors are one in itself. So the definition of a prime number. And we can often, we can always factor any integer into divisors which are primes. Before we go into that definition, some example of prime numbers and you would have seen them is on the next slide. So this is a list of the prime numbers which are under 2,000. So all of these, for example the number 97 is a prime number because the divisors of 97 are one and 97. And that's it, there are no other divisors. So our prime numbers, prime numbers are used in a number of the ciphers that we look at with asymmetric cryptography. Any integer, doesn't have to be prime, any integer can be factored into prime numbers. So choose any number and we can find its factors or its divisors which are all combined of prime numbers. And sometimes we may write that, and let's give an example to show that. Note that there's a mistake in this equation here. Where a equals p2, p is a prime number. Instead of 2 it should be 1 here, this first p2 should be p1. So you can fix that in your notes. If we have prime numbers p, like the first prime number, the second prime number, the third prime number, p1, p2, p3, then any integer a, we can write as the multiplication of those prime numbers raised to some exponent. Let's give some examples. Let's write it on the board for these simple ones. Let's do it on the screen. What's the, write the number 18, for example, as, find the prime divisors of 18. The prime factors of 18, okay, 18. So 18, and we'll write them in a moment, you'll try another one, is 2 times 9, or 2 times 3 to the power of 3. 2 and 3 are prime numbers. So we can break 18 into the multiplication of multiple prime numbers. What about 22? Find the prime factors. And 24, okay, so we can write them. Let's see if I can write that, so it's a bit clearer. So some examples, what have we got? We can write 18 as 2 to the power of 1 multiplied by 3 to the power of 2, where 2 and 3 are prime numbers, p1 and p2, and some exponent. And similar, we can consider any integer. Another example is 22. What are the prime factors of 22? Remember, 2 is a prime number. It's, we can write it in as 2 to the power of 1 times by 3 to the power of 0. Let's list all the prime numbers up until the maximum one, sometimes useful. What else do we have? 7 and 11 to the power of 1. So one way to be complete is to look at the prime numbers in sequence. So the first five prime numbers are 2, 3, 5, 7 and 11. 22 is any integer is made up by multiplying prime numbers together, the prime factors. In this case, it's 2 to the power of 1. Well, we don't have a 3 in here. We can say 3 to the power of 0, which is just 1, multiplied by 1 by 1 by 1, multiplied by 11 to the power of 1. Or we could have, in shorthand, write 2 to the power of 1 times 11 to the power of 1. Sometimes we look at the exponents. And 22 is simply, if we write the prime numbers in order, 1, 0, 0, 0, 1, that's used in some forms. I don't think we'll see it in any other examples. So just a characteristic of all integers can be factored into prime numbers or have prime factors. And that will become important later. One more example, what is it? 24. What is 2 to the power of 3, which is 8, times by 3 to the power of 1, which is 3. So again, the exponents here are 3 and 1. So in theory, any integer can be broken into its prime factors. In practice, with large integers, finding the prime factors is very time consuming. That is, for very large integers, when we're talking about hundreds of digits, hundreds of digits long, finding the prime factors of a very large number is effectively impossible with the compute power we have. There are no known algorithms that can do it in reasonable time. We'll see that that's an important part of some security algorithms later. So simple stuff so far. We have prime numbers, we have divisors, we have a greatest common divisor, and maybe the only new thing to use two integers are relatively prime if their greatest common divisor is 1. Any questions? Nothing complex yet. Next thing. What are, when we do normal arithmetic, ignore modular arithmetic, when we do normal arithmetic, what are the operations that we know and we use all the time? Arithmetic, when you learn in primary school, what are the operations, the first operation you learn? Addition, second, subtraction, multiplication, division. Anymore? Anymore? Mod. Before mod, you probably learned some, maybe you learned exponentiation and logarithms, raise to the power of, and a logarithm, which is the inverse effectively. So how would I write it, but sometimes exponentiation, you see the hat character two to the power of three, like we saw in our prime numbers. And the other operation we sometimes see is logarithm. Note that they are related in some way, that in that is, for example, exponentiation raising a number to the power is just multiplying multiple times. So there's a relation between multiplication. So that's the operation that we have in normal arithmetic, and we can see that they go together, that is, we could think that subtraction is the opposite of addition. Three plus two equals five, five minus two equals three. So we can say that subtraction is the inverse operation of addition, inverse of addition. And similar division is the inverse of multiplication. Five times two is 10, 10 divided by two is five. Okay. And similar logarithm is the inverse of exponentiation. So those operations are related. You know them, your experts on them. What we're dealing with in a lot of the security algorithms is modular arithmetic. When we introduce in all of these operations the mod operation, sometimes written as percent, that is, we find the remainder. So let's look at modular arithmetic. So some definitions first. So what do we mean by mod? If we have some integer a and some positive integer n, then a mod n is the remainder when a is divided by n. That's what we know as mod. n is called the modulus. So a mod n, n we call the modulus. And the answer is the remainder. What we're going to deal with is modular arithmetic. We can say that two integers a and b are equivalent or more precisely congruent modulo n. If a mod n is the same as b mod n. So if a mod n equals b mod n, then we say that a and b are congruent modulo n. And we often write that is simply a is equivalent to b when we use mod n. So we often write now a is equivalent to b and then in brackets mod n. For example, 12 mod 10 is equivalent to 2 mod 10. Okay, so 12 is equivalent to 2 or congruent modulo in mod 10, they are equivalent. So 12 mod 10 equals 2 mod 10 or 12 equals 2 in mod 10 is another way to think of that. Note that the mod n operator mod by something, it takes the set of integers or possible integers and maps them into a finite set. From 0 up to n minus 1 and we often denote that set as z n. So when we mod by 10, any integer, the answer is always going to be between 0 and 9. Modular arithmetic performs our operations that we have for normal arithmetic but all in mod n. And within the confines of the set z n. So the answers will always be in z n when we use our modulate arithmetic. And in fact, effectively the inputs are all within the set as well. So we'll define that we can, when we do modulate arithmetic, we'll go through the six operations and see how they work when we use the mod form. Some are obvious, some are not so obvious. Because this form of arithmetic is used in some of the ciphers that we'll cover later. In fact, we've already seen it in some of our ciphers. We've seen it in the Caesar cipher. So the properties of modular arithmetic, some of them are similar to the properties of our normal high school primary school arithmetic. So some of them are defined here. So when we consider addition, subtraction and multiplication, then how we calculate them in normal arithmetic also applies with modular arithmetic. So some of the rules that we'll see, for example, a mod n plus b mod n, all mod n, is the same as a plus b mod n, similar with subtraction and multiplication. Let's go through some examples and then come back to these rules. Just to make sure everyone's on the same page, everyone knows what's going on. And the example is I'm going to do here in, we can do them in any, with any value of n, but I'll do them with mod at nine, just to keep things interesting. For example, let's assume everything that I write here is in mod nine. Our modular, modulus is nine, mod nine. So say, sometimes to save space, they will not write mod at nine. I'll just write the normal operation. So let's start simple. What is six mod nine? Well, you can tell me the answer very easy, but we can write it in the full form. The way that we think of module, mod is we have some number multiplied by nine plus a remainder equals six. So some integer times nine plus a remainder equals six, the answer of six mod nine is that, that remainder. So in this case, what do we get? Zero. Zero times nine plus six. So the answer is six. Okay. Just a very, very basic way to look at the modular operator, modulus. 23 mod nine. Well, we can do it the same way. Some integer multiplied by nine plus a remainder equals 23. What's the answer? Or what's this integer? Two times nine is 18 plus five is 23. So the answer here is five. Although we don't, we will not use it in most of our cryptography, but just for interest. What about minus 24 mod nine? Same approach. Some value times nine plus our remainder equals minus 24. What's the answer? Try. Some number, some integer times nine plus something equals minus 24. What is the first, what is the multiplier and what is the remainder? What about, and note that this multiplier can be negative. Okay. Try negative three. Minus three times nine is minus 27. Plus three is minus 24. So the answer is three. Okay. So minus 24 mod nine is three. Okay. I don't think we'll see the negative mod. We saw it in Caesar cipher and the ciphers earlier. I think you've seen it there, but I don't think we'll see it much later than that. That's easy. That's very basics of modular arithmetic. Some properties that hold when we do modular arithmetic, when we add two numbers in mod n, when we multiply numbers in mod n, similar rules or laws that we've seen in our normal arithmetic. For example, this one is w plus x mod n is the same as x plus w mod n. So that law still holds. Similar, w times x times y, all times y is the same as w times in brackets x plus y all mod n. So the order in which we add them and multiply doesn't matter. And that's the same in our normal arithmetic. Two times three or three times two, we get the same answer. That's all it's saying there, these rules. And we can expand, for example, w times x plus y in brackets is the same, all mod n is the same as w times x plus w times y mod n. So that's a law that you know as well. And we also have identities. That is zero plus some number in mod n gives us that number mod n. And that's in normal arithmetic. Zero plus five is five. Zero plus five mod eight is five mod eight, which is five. And also with multiplication, our identity is one. One times some number gives us that number. So this is normal information. Something that you know about but you probably do not call it. We also will define what's called the additive inverse. For every integer in our set, z n, where n is our modulus, there's some other value z, lowercase z here, such that we add those two numbers together, we get zero. This other value z, we'd call the additive inverse of w. So every integer has an additive inverse. That is when we add one number to its additive inverse, we get zero in mod n. That's the definition there. Some quick examples for the additive inverse. And for me, all right, so for the additive inverse, and we're still doing it in mod n, mod nine. So just make note, everything on the example so far is in mod nine. Keep it simple. An additive inverse, let's call it AI. What's the additive inverse of three? What is, try, write it down, work it out. What is the additive inverse of three? And for a hint, when we use mod nine, remember our set, z nine. We have the values from zero, one, two, up to what? They are the numbers we're dealing with when we do mod nine. Everything, every answer is going to be a number between zero and eight. In fact, every input we can think of simply is a number between zero and eight. We operate our addition, subtraction, and so on. All operates on values within this set. So again, what is the additive inverse of three? Six. And let's go through the full way. The additive inverse is, we have three plus some number, mod nine, give zero. That's our definition of additive inverse. When you add the two numbers together, you get zero. And the number will be six here. Three plus six mod nine is zero. So we say the additive inverse of three is six. What's the additive inverse of six? Three. Three, okay? It goes the other way as well. So you can't say negative three? No, not negative three. Because with modular arithmetic, mod n, or in this case mod nine, everything is within the numbers zero to eight. We don't have negative numbers here. Whereas with your normal arithmetic, yes. You'd say the additive inverse of three in our normal arithmetic is minus three. Okay, that's correct. But we've got a different form here. In normal arithmetic, you operate on an infinite set of numbers. Here we have a finite set defined as zero to eight. What's the additive inverse of eight? Easy. The number when we add with eight, we get zero, one. One plus eight is zero in mod nine. Okay. So we have additive inverse. Every number in our set z nine has an additive inverse. So of those eight numbers, zero through to eight, you can find the additive inverse. Always every number, every integer in our set has an additive inverse. So from our operations, we can do addition. Addition in modular arithmetic is the same as in normal arithmetic. Just add the numbers and then finally mod by n. Subtraction. How do we subtract? Now let's switch back. In your normal arithmetic, how do you subtract numbers? Well, we said before, we can think of the operation as the inverse of addition. So subtraction is the inverse of addition. So we said, someone said the inverse of three, the additive in, the additive inverse of three in our normal arithmetic is minus three. Okay. So three, some number minus three is the same as that number plus its additive inverse. We use the same operation in modular arithmetic. Let's try it for subtraction with some examples. That is, subtraction in modular arithmetic is simply we add the additive inverse. So all still in mod nine. Let's give some examples for subtraction and start simple. What's seven minus three in mod nine? Well, subtraction is the same as seven plus the additive inverse of three. Mod nine. And we know the additive inverse of three is that additive inverse of three is six. So we get seven plus six, 13, mod nine because although I haven't written it, all of these operations in mod nine, which is four. Seven minus three is four when we use mod nine. Okay. That's easy. Let's try another one then. Two minus eight in mod nine. Mod nine. What is two minus eight? Try and calculate. Remember in mod nine, all the numbers are between zero and eight. So it's the same as two plus the additive inverse of eight. And the additive inverse of eight in mod nine is one. The additive inverse of eight in mod nine is one because eight plus one mod nine equals zero. So the answer is simply three. Two minus eight equals three. Okay. So that's something that's the first thing people get confused with. Don't apply your normal operations of your normal arithmetic. Now we're limited in a set when we do modulate arithmetic. In this case, mod nine arithmetic. Same you saw in the Caesar cipher is the shifting by eight positions but going backwards when we subtract. Remember because we wrap around effectively. We go zero up to eight, zero up to eight. If we start at two and go backwards, then we end up at three. If we go backwards eight positions. If we're at two and we move back eight positions in our Caesar cipher. One, two, three, four, five, six, seven, eight. We end up with three. So two minus eight is three. So we saw that in the Caesar cipher and the subsequent ciphers based on the Caesar cipher. It's just expressed mathematically here. So we can now do addition in modulo arithmetic. It's the same as our normal arithmetic. We've defined the additive inverse. When we add a number with its additive inverse, we get zero in mod n. And we know the operation for subtraction. It's simply a minus b is a plus the additive inverse of b all in mod n. Next operation. Multiplication. Same as in our normal arithmetic. So effectively the same. You can multiply and just mod the answer by n. So in mod nine, two times four is eight mod nine, which is eight. Two times five mod nine is 10 mod nine, which is one. So multiplication is easy. It's just our normal arithmetic mod nine. So addition, subtraction, multiplication. And the same as to do subtraction. We use the additive inverse because we think of subtraction as the inverse operation of addition. The inverse operation of multiplication is division. So to do division, we multiply by the multiplicative inverse. So we've got a new concept. Numbers can have an additive inverse in modulo arithmetic. Some numbers can also have a multiplicative inverse. And that's defined on our next slide. That was that was additive inverse. All integers have an additive inverse. We can also define a multiplicative inverse. A is a multiplicative inverse of B if A times B equals one in mod n. And that's the same as in the same concept as in our normal multiplication and division. In what would you say is the multiplicative inverse of three in our normal arithmetic? In our normal arithmetic? One third. In our normal arithmetic, three times one third equals one. Four times by one over four equals one. So in our normal arithmetic, we have a multiplicative inverse which is just one over that number. In modulo arithmetic, same concept. The multiplicative inverse, if we multiply the two numbers together, we get one mod n. Let's try some. Get that out of the way. Come back. Gonna crash. It's my computer crashed. Software is crashed. Let's try it on the board. Some multiplicative inverse examples in mod nine. So still everything in mod nine. What would the in some in abbreviate multiplicative inverse of let's say one? What is the multiplicative inverse of one? By definition, you multiply one number by its inverse and you get one. So that one's simple because one times by some number mod nine equals one. What is that number? One in this case. One times one mod nine is one. The multiplicative inverse of one is one. That's easy. What is the multiplicative inverse of two? So two times by some number mod nine equals one. That's the definition. What is that number? So two times something mod nine equals one. So five. Two times five is ten. Mod nine is one. So the multiplicative inverse of two is five. Multiplicative inverse of five? Two, we can see. If two times five equals one, then five times two equals one. It goes the same in the opposite book. As four, three times 12, four. Four times something equals one. What is that something when we mod by nine? I think, so again four times by something. All mod nine equals one. Four times seven equals 28. 28 mod nine is one because three times nine is 27. Easy. Three, multiplicative inverse of three. We won't go through all of them. Find the multiplicative inverse of three. Well, I try and fix my computer. Anyone have an answer? There is no answer. There is no multiplicative inverse of three because there's no integer in our set. That when we multiply by three and mod by nine, we'll get one. We all we need to consider really is the numbers zero through to eight because they are the numbers we deal with when we mod nine. Three times zero, three times one, two, three, four, five, six, seven, eight. When you mod by nine, none of those values will give you one. So there's no answer. Well, we say that three does not have a multiplicative inverse. Not all integers have a multiplicative inverse. All integers have an additive inverse, but not all of them have a multiplicative inverse. And more precisely, some integer a will have a multiplicative inverse in mod n if a is relatively prime with n. So five is relatively prime with nine. Therefore, it has a multiplicative inverse. Four is relatively prime with nine. Therefore, it has a multiplicative inverse. Three is not relatively prime with nine. And therefore, it does not have a multiplicative inverse. So not all numbers will have a multiplicative inverse. One more attempt. So let's list out numbers. What do we have? Just for reference, we have one, two. I think the ones we just calculated that have an inverse four, five, one map had an inverse of one, two had an inverse of five, four had an inverse of seven, five an inverse of two, seven, four, not five. Any others that have a multiplicative inverse in mod nine? Eight is relatively prime with nine. Therefore, it should have a multiplicative inverse. What is the multiplicative inverse of eight? It's, in fact, remember, it can only be these numbers from this set. It's itself. If this is a, and this is the multiplicative inverse of a. Eight times eight is 64, mod nine is one. So they are the multiplicative inverses in the set Z nine when we mod by nine. So not all integers have the inverse. Zero, three and six do not. So now we can do division because division is simply a divided by b is a multiplied by the multiplicative inverse of b. In the same way that a minus b was a plus the additive inverse of b, a divided by b is a multiplied by the multiplicative inverse of b. Some quick examples, what have we got? What's four divided by two in mod nine? So to go precise, we have four divided by two is four times by the multiplicative inverse of two, mod nine, which is four times five, which is 20 mod nine, which is two. 20 mod nine is two. Four divided by two is two. That was easy. Try this one. Six divided by seven. Find the answer. Six divided by seven in mod nine. Everything's in mod nine in these examples. Just four, six. Anyone else want to guess? So go through the, what's the multiplicative inverse of seven? I've listed them up the top in fact, four. So six times four. So is six times four, which is 24. And 24 mod nine is six because two times nine is 18. So six divided by seven equals six when we use modular arithmetic with n equal to nine. So we can now do the four main operations. Addition, subtraction, multiplication, division. Exponentiation and logarithm are more complex, but in fact based upon multiplication and division. Any questions? You need to get outside of your normal arithmetic and just follow the basic principles.  Remember all of our answers when we mod nine, the values between zero and eight, the integers between zero and eight. We don't have fractions. We don't have negative, we don't have negative numbers or fractions or numbers greater than eight when we do mod nine arithmetic. Of course, I'm just using nine for an example where it can be mod anything. Same principles. The two key things that will come up later, we've seen the additive inverse. Every integer has an additive inverse. Not every integer has a multiplicative inverse. Only if that integer is relatively prime with n does it have a multiplicative inverse. And that will become important when we look at the ciphers and the way, for example, RSA works. So we've done division. We're not going to at the moment go through the other operators. Let's quickly look at a couple of theorems and then one new concept, the Euler's totient function. In fact, let's not go through Fermat's theorem until after the break. Let's go direct to Euler's totient function and define what that is. And later we'll see it's used in Euler's theorem. And it's very important when we look at the asymmetric ciphers. Written as phi of n. In short, we may say the totient of n returns some value. And the value, this function, it returns the number of positive integers that are less than n and relatively prime with n. So what we do if n equals 10, we look at the integers from 1 up until 9, the integers that are less than n. So if n is 10, 1 to 9, and which of those are relatively prime with n. And that's the answer. So the totient of some number, we look at how many of numbers are less than that, which are also relatively prime with that number n. We'll see some special cases, but let's go through some simple ones first and then we'll have a break. Let's try. What is the totient of 10? What is Euler's totient of n equals 10? So by definition, it's the number of numbers less than 10, which are relatively prime with 10. So go through and look at all of them. So the long way is to look at all the numbers from 1, so effectively from 1 up to 9 in this case. Let's list all the numbers first, I will, so everyone's clear. So the question is, of those nine numbers, which ones are relatively prime with 10? And to help, what are the divisors of 10? Just to go simple, the divisors of 10 are 1, 2, 5 and 10. And remember, relatively prime is the greatest common divisor of the two numbers is 1. So 1, the greatest common divisor of 1 and 10 is 1. So this is a number. 2 is 2 relatively prime with 10. No, because 2, and there's a divisor 2, so the greatest common divisor of 2 and 10 is not 1. So it will not count, it is not relatively prime. Is 3 relatively prime with 10? Yes, 4? No, 4 has a divisor which is 2, it's greater than 1. 5? No, because 10 has a divisor of 5. 6? No, because 6 has a divisor of 2, as does 10. 7, yes, 8, 9, yes. That is 1, 3, 7 and 9 are all relatively prime with 10. Therefore Euler's totion of 10 is 4. The count of numbers, 1, 2, 3, 4. So the totion is how many numbers are less than n and relatively prime with n? So we went through the long way to do that. You'll try a quick, what's the totion of 24? Try and calculate the totion of 24. And then one more, once you've done that, the totion say of 11. So for the totion of 24, look at the numbers from 1 to 23, which ones are relatively prime with 24? We will do it after the break. Anyone have an answer? So simply look at the divisors of 24. That may help. So with the totion of 24, you need to go through and look at those numbers and you see is 1 is a relatively prime. 2 is not, because it has a common divisor of 2. 3 is in fact a divisor of 24, so therefore it's not relatively prime. 4 is a divisor of 24. So if you find all the divisors of 24, those numbers will not be relatively prime, except for 1, and any of the multiples of those numbers will not be relatively prime with 24. Anyone get an answer? Totion of 24, what is the totion of 24? The totion is the number of numbers which are relatively prime with it. The answer is 8, and the totion of 11 is 10. For 24, you have to confirm for yourself why it's 8. For the totion of 11, that's a little bit easier. Note that 11 is a prime number. So what are the divisors of 11? 1 and 11, it's a prime number. The divisors of 11 are 1 and 11. So look at the numbers from 1 to 10, and see which ones have a greatest common divisor with 11. And you'll find all of them. All of the numbers less than 11 are relatively prime with 11. That is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And that applies for all prime numbers. The totion of a prime equals that prime number minus 1, and that's on the previous slide. So that's a shortcut. But if n is a prime number, then immediately you can find the totion. It's just that prime number minus 1. Because the divisors of 11 are 1 and 11. So we compare them between the numbers from 1 up to 10. And of course none of them will have a common divisor of 11. They'll all have a greatest common divisor of 1. 1 and 1, 2 and 1, 3 and 1 and so on. The greatest common divisor will be 1. So if n is a prime number, we can determine the totion simply. The prime number minus 1. If n is not prime, if it's composite, then you need to calculate or count them. And that's what's here. All right, this is some special cases. The totion of 1 is always 1. The totion of a prime is p minus 1. Where p is the prime. And we'll give an example after break. Another useful property. If n is the multiplication of two prime numbers, then the totion of n is the totion of the multiplication of p multiplied by the totion of q. So there are some shortcuts. But if our n isn't a prime number, or is not made up as multiplying two prime numbers, then you need to manually calculate it. And again, this will be very important in our asymmetric ciphers because when we deal with big numbers, hundreds of digits, then manually determining the totion is practically impossible. Unless that n is a prime number. Let's have a break. And then when we come back after the break, we'll give a few more examples of the totion, and then we'll come back to Fermat's theorem and Euler's theorem. And then we'll, I think, we'll look at some hints for the exam.


From theCUBE Studios in Palo Alto in Boston, connecting with thought leaders all around the world, this is a CUBE Conversation. Hello everyone, this is Dave Vellante, welcome. We're going to do a little preview of ThoughtSpot Beyond and we're going to look at the intersection of cloud, data, search and analytics. For a decade we've been collecting all this information and tapping data sources from many, many different places. Now we're at the point where we can very cost effectively and quickly put data into the hands of many orders of magnitude or more users so that data can inform opinions and ultimately actions. With me is Sudeesh Nair, who's the CEO of ThoughtSpot. Sudeesh, it's always a pleasure to have you on theCUBE. Thanks for coming on. Absolutely my pleasure, Dave, thanks for having me. You know, it's ironic, I think that we start this decade with so much disruption to our lives. It's forced us to become digital businesses really overnight. I wonder if you could talk about the role of data as it relates to our digital lives. Yeah, I think the idea that data somehow directly impacts our lives sometimes can be far-fetched. That is because we don't really talk about it in the right way. Data can be this archaic mountain of things that people don't really connect with. What we should really be talking about is what data does, the byproduct, the end product of data, which is the signal that we get out of the mountain of data, the insight that we derive from it, and the action, the bespoke actions that makes our lives possible in this new world that we are living in. And if you really do a good job of talking about what data does for you or the byproduct of what the data does for you, I think people will understand that we are incredibly connected, incredibly dependent on the signals that we derive from the data that we are giving out to the world that we are operating in today. Yeah, we had to fire, ready, and aim because the speed at which we've had to adapt is we've never seen this before. And I'm wondering if you could share with us what you're seeing, I mean, what kind of challenges this creates for organizations, specifically in terms of being able to leverage their data assets. Yeah, see, I think if you think of the last eight, nine months, sometimes in our industry, it is easy to sort of look at this as an opportunity, more of an opportunistic way of looking at how can I sell more data-driven things when the world is sort of falling apart?  It is, you know, my sort of lesson in the last eight, nine months is to be more outside in as opposed to inside out. And that is why are we doing this is now more important than what we are doing. And in that context, my biggest lesson that I've learned is that the thing that stand in the way of delivering value for customers almost always is not technology, not product, and not even quality of data. A lot of data people will say it is the data quality that is holding me back from doing. It is lack of courage, lack of vision, lack of ability to sort of empathize with your customers and truly see what can we do to make their lives better where data-driven insights might be a part of it. So I really believe that organizations that are differentiating by, you know, providing better services where they use data to do that are clearly coming out their head as we are looking at the end of this global pandemic. You know, it's interesting what you're saying about data quality, because I agree with you. I actually think it's access to data because as a business user, I can look at data, ask a couple of questions and say, okay, this is, I can get pretty close to the truth. And if you think about organizations generally, but specifically business users, they've been clamoring for more facile access to data. And really the time is now for them to realize this vision. And I wonder if you could share with us like, what's happening in DotSpot's business in the past months? Because that's what you're all about, is that easy, fast access to data. Yeah, so I always talk about the decision-making pipeline. I know one end you have the data that customers are happy to give. However, it's a two-way street. They are saying, look, I'll give you my data. In return, I want you to do two things. Number one, make sure it is safe and protected. Number two, you are using that data to deliver bespoke experiences for me, bespoke services for me. That is, I'm giving you the data so you will get to know me and treat me as an individual, as a person with likes and dislikes that are different from someone else's. If you don't do that, you're breaking that contract. So when I think of this continuum of data, to insight, to knowledge, to action, action is where the users benefit. I sort of sometimes worry that the chasm that exists between the people who can speak the data, the SQL, the data warehouse people, who have usually the answers and not necessarily have the questions because questions are usually coming from the business users. So our sort of purpose in life as a company in the world has been simple. That is, let us break that barrier. Let's move that silos and then unify so that people with questions can get answers. People who know the business can get the answer from the data without any tax on the curiosity. Now it is easier said than done, but it is a journey. But I strongly believe that pushing the ability to inquire and get insights from the data all the way to the frontline where business users interact with their customers, the business's customers, the consumers, the clients. If you don't do that properly, there is no way to keep up with the velocity of change that the world is throwing at your business. So speaking of data sources, I mean, one of the data sources I sometimes look at, you look at the stock market as funny last month, Pfizer announces a very highly successful trial and the stock market goes up 800 points. So you sort of look at that and say, okay, it's a data point. I recently released a number of pieces on cloud and its impact. And you saw, after that, you saw a lot of cloud stocks, everybody panic, oh, sell tech. And even though, look, I've written, cloud's not immune to COVID, it's clear from our data that cloud migration has been very much accelerated since the pandemic hit and I don't really see that changing. I wonder if you could talk about the ways in which you see cloud changing, how organizations operate and really what's missing when it comes to getting the most out of their cloud investments, specifically around analytics. It is like any other function. Data analytics is not different in what the cloud does for the customers. I used to always talk about the world of computing, the world of technology as a race against commoditization. That is, imagine there is an ocean that is warming and there's an iceberg that is floating on it. As the ocean warms, the iceberg keep melting and if you wanna survive, you gotta keep going up the mountain, the iceberg mountain. In this example, the commoditization of technology is the ocean. Anything that you think is unique, anything that you think is proprietary is gonna get commoditized. And the reason why that's happening is because people wanna go up the value chain. That's the iceberg, that's the mountain. So if you use that metaphor, what you will see here is that people wanna go up the value that the data analytics deliver as opposed to how cool or how differentiated the process of delivering value is. And let me explain that in a, imagine that you are producing a lot of content. I'm pretty sure that you have ways to sort of collect the data on how it is making an impact. That is, how many people watched it? How many of them were young versus old versus sales versus engineering versus marketing versus execs. You can slice and dice the data. That is where today's data analytics stops. Now imagine, you can take it to the next level. That is, what impact is it having on my consumers? Are they able to get better jobs, for example, because of a technology that you talked about? Or the cubes ability to sort of democratize access, the way sometimes you take complex technology and simplify it. Is that making easier for some execs to catch up with the speed with which technology is changing? In turn, which makes their business more agile. So the point is our thesis is that when we stop data analytics at the noise level, the data level, the insight level, we are only doing half the job. We need to go all the way through that value chain, climb all the way up in that iceberg and think for the customer. What am I doing for the customer? I mean, there are recent examples of where banks have largest of large banks, where they had inherent bias when it comes to how they were giving loans to minorities and people of color, or the people who have an accent on the phone they're actually calling and customer support. These sort of things are not an AI problem or a BI problem. These are human problems. So by breaking the barrier between business users and their consumers, where data become an inherent part of decision-making, you can make tangible difference in the world. And I think that is what we are trying to do. I know it sounds somewhat naive and utopian, but I do think this is possible if you really approach it outside in. Well, and outside in thinking is critical. And I want to pick up on something you said about kind of moving up the value chain. And we've watched over the last decade sort of the sassification of many industries. You guys recently announced ThoughtSpot Cloud, which was your first sass offering.  What's the uptake like, the adoption? What are customers telling you about what it's doing for their business? Again, this is the same outside in story. It is relatively new. It's only been a month. The interest is pretty high and we have closed a handful of customers. So I don't want to claim victory yet, but the signs have been very positive. And it is not surprising because it aligns with that story that I talked about growing up the value chain. Traditionally, when we deploy ThoughtSpot, we deploy it in the customers VPC, their own cloud or in the data center. The problem is when you're doing that, they are responsible for integrating the data, connecting the data, prepping the data, managing there's a lot of work that goes through. With ThoughtSpot, is it possible for us to do as much for the customer with TS Cloud? ThoughtSpot Cloud. That is, you just go to ThoughtSpot Cloud and connect to your SaaS data warehouse services that you may have, whether it's Snowflake or Redshift or in a GBQ, Google BigQuery or Microsoft Synapse. And then get going immediately to give you an idea. A typical ThoughtSpot deployment used to take around four to five months. Now it is taking around 35 minutes. That's what ThoughtSpot Cloud does for our customers. And if it happens in 35 minutes, their business of delivering value to their clients is happening that much faster. Yeah, everything shifts to actually getting insights as opposed to setting stuff up. Setting stuff up. You know, one of the other things, Siddish, that I've been reporting on, I've said in the last decade, we kind of moved from really a product-centric world to one that's more platform-centric, particularly with cloud and SaaS. And the latest research that we've been doing shows that ecosystems, we think, are going to power the next wave of innovation. And I wonder what your view is of that premise and how you're thinking about ecosystems as a lever of growth. Yeah, this word platform is one of the most abused word in our industry because people like to say, oh, don't say product, say solution. And then if they don't say solution, use platform. Ideally, in reality, platform is useless if people are not standing on it, right? If you're standing on a railway platform, nobody's there, what's the point? The same thing applies to business, our business as to when it comes to platform. A platform is only a real platform. If there are other players making money of what you have built.  In that context, we have long ways to go. We have really long ways to go. I do think one of the sort of, I wouldn't say mistake, one of the oversights that ThoughtSpot had was not delivering on the vision of platform that is easy to make. It is easy to make for others to come together and do commerce on ThoughtSpot. And most importantly, make sure that it is not just easy, but when customers come to them, that one plus one is like 10 or 11, as opposed to one plus one equal two. That is something that we have to remedy and at the beyond conference next month, December 9th, you will see us make some interesting announcements around this thing. And it is one of my favorite sort of projects because once we do that very well, you will see that it becomes a platform. So think of strike, think of square. These are platforms because it may, their customer's lives easier, but at the same time, multiple companies could come together to deliver joint solutions where the sum is much bigger than the equals of the parts. And that is a vision that ThoughtSpot needs to really deliver on and beyond will be a stack. Yeah, I mean the power of many versus the resources of one. And this is well understood over time. And now we're seeing it really applied to our industry. You know, Siddish, a lot of the analytics that we produced today are the result of humans clicking and typing and interacting with systems. And that's obviously going to continue to grow. But you think about things like IoT, the build out of 5G. It brings this whole new dimension of machine to machine communications and tons of new data. Much of the data out there is analog today. It's increasingly become digital. How are you thinking about these trends at the edge in terms of the impact on your company and your customers? Look, I think if anyone asked me like, what does ThoughtSpot do for the data analytics world? My answer is very simple. We have introduced a new interface to access structure data that can be used by anybody. Search that is driven by AI, that's it AI driven search. That core idea is about scale, but more importantly rate of change. That's where the new inventions around 5G, where the bottlenecks are being removed at IoT and mobile. I mean, we want to put mobile as well. So you have mobile devices, IoT devices, very big pipe, and then cloud on the backend where processing and storing is cheap. So now if you think of that, it is a 12 length super high way all the way to the end user, all the way to the end device to the mothership. When you have that much speed and when you remove everything, you have to think about the asset, the artifacts that you build out of that kind of a data stream. That's where the old way of looking at dashboards will die. It's not a question of if or when it is dying. What we need is now to make sure that at that speed, when the data is changing much faster than ever before, you have new way to deliver insight to the people who can act on it, which is business users. And if you think of it, like there used to be cases where companies used to make supply chain decisions for the year. Now supply chain decisions are made monthly because you don't know what next month will look like with COVID. When you have annual decision become monthly decision, monthly decision become weekly decision, weekly decision become minute by minute decision, sometimes like pricing, social media sentiment changes, things like that. There is no way that you can depend on a Monday morning report or a Monday morning meeting. And then send out the, you know, here is what you need to do, action act items to the front end. Everyone should have their pulse on where the business is, which is where the data is going to help them. However, human experience is so critical. You don't want to remove human experience. That's why as we deliver more and more on 5G and IoT, making the data as it is changing and then delivering those signals, insights directly to business users in the frontline, he's going to be like the de facto way, businesses will operate. And I think we are just beginning that journey in terms of what is possible. Well, it reminds me of when we were kids, the coaches would tell us, go to where you think the ball is going to be, find opportunities for that open space, not to where it is today. And that's the notion of whether it's soccer or basketball or of course hockey, skate to the puck is obviously a famous term. So, how do you stay ahead of that disruption curve in a space like analytics? What are the innovation opportunities that organizations should be tapping today and beyond? I think I was thinking about this a lot myself, which is the important thing is to be ready to unlearn. And I know it is a simple thing, but it's one of the most difficult things because as you grow up in the organizations, as you become an exec, as you gain more experience, we actually calcify our knowledge. And that's a problem because things are changing. There are new way to do things, new opportunities. Being open to unlearning is going to be more critical than learning new things sometimes. And that will require humility. So I won't say it's a learn, go learn AI or go learn a new language or Python or coding. Those things might be necessary, but having that mentality of willing to unlearn and then having the courage to make some difficult decisions. If you do those two things, I think this is an exciting world. And if you're not, you're going to go the wayside of a lot of industries have been going. It's great advice. I mean, we saw that a lot coming into the pandemic. There was a lot of complacency around digital and there isn't anymore. Siddish, thanks so much for joining me in this CUBE conversation. It's always great to talk to you. Thank you for taking the time. I appreciate it. My pleasure. And thank you for watching everybody. This is Dave Vellante for theCUBE. We'll see you next time.


Hello, I'll slay the sync here. Microtonal music is so hot right now, or at least it was in 2019, perhaps it's passé now, but I'm going to talk about it in this video anyway. I'm going to very briefly describe what I mean by microtonal in a moment, but I'll say upfront that if you want to get a more in-depth discussion and more musical examples, then I recommend heading over to Adam Neely's channel where he's done a bunch of really fantastic videos on the subject. I'll link to some in the video's description. But as a primer, in Western music there's this fairly universal construct called an octave. If you take a note with a fundamental frequency and then double that frequency, you get an octave. So for example, if you take concert pitch A with its fundamental at 440 Hz and then you play a note at 880 Hz, that's an A octave above. In Western music, we take the space between a note and the octave above it and split it 12 times, giving us 12 notes in each octave, a 12 tone musical system. The way that we usually split up the octave is based on a set of ratios defined as equal temperament. Equal temperament is a kind of musical mathematical trick that results in a set of notes that sound pretty pleasant or consonant no matter what key or scale you play in, certainly good enough for jazz. There are many other tuning systems that, if you make the promise not to change the scale or key, will actually sound sweeter than equal temperament, but can sound dissonant if you modulate away from it. Equal temperament then is a compromise, but it's probably one worth making if you want lots of instruments to sound good together no matter what music they're playing. Microtonality asks and answers the question, what happens if I split up the notes differently? What if I stick with a 12 tone scale but change the way the notes are split up? What if I stick with the concept of an octave but split it 5 ways or 13 ways or 25 ways and so on? What if I ignore the idea of an octave and define a different fundamental interval? This can lead to a whole new world of musical colours, sometimes beautiful, sometimes challenging but charged with musical emotions previously unavailable to you and sometimes just plain ugly, but perhaps it's ugly that you're needing your music sometimes. There are a range of synths available today that allow you to switch between pre-defined or even import your own microtonal scales. Most notably at the more affordable end of the market, Korg caters to microtonal enthusiasts very nicely with the monologue mini-log and actually even the Vulcan modular which allows for microtunings which is very cool. At the time of recording the microfreak does not allow you to formally make use of microtunings but that doesn't mean that you can't explore microtonality and in this video I'm going to explore some of the options available to us as I go hunting for new musical flavours. Okay here is a basic non-microtonal patch, it's based on the harmonic oscillator. Those of you who are familiar with the microfreak may already be anticipating that we are going to be heading into the mod matrix in order to do something. So on the left hand side of the mod matrix we have the pitch destination and we have our various different sources down the side here. Now of course the thing that we'd usually do with the pitch would be to apply just a little bit of pitch modulation to get off vibrato which is lovely obviously but that's not why we're going today. So for my first suggestion what we're going to do is we're going to head down to the next row which is pressure. So if I apply some modulation and I'll put in a value of one at the moment with the patch based off and initialised patch what's going to happen now is as I apply pressure you can hear that I can get some pitch bend. Let me make it a little bit more obvious. So as I put more of my finger down I get a pitch bend. Now the neat thing of course on the microfreak is that this pressure is actually polyphonic so I can bend one note sharp while leaving the other one in place. So with pressure as our modulation source having a value of two from modulation amount will give us a semitones bend which is great if you want to do these sorts of bends like this but that's not actually the way I'm going to approach this. There's nothing wrong with approaching it this way. I'd probably move the value down to one so we have a quarter tone rather I should say and with careful playing you could slide into sort of half sharp tones but you will always get that gliding thing happening.  So pressure mode at the moment will be set to after touch which is what we're getting at the moment with our polyphonic after touch there. What I'm going to set it to instead is velocity. So that means now what I do afterwards is going to make no difference but how I play the note itself does. So we can do by playing carefully we can do these sort of half resolution things like you probably have to be a better keyboardist than me. Now that's going to get trickier as you use more than two fingers I suspect but it might get really interesting if we move to a way of sequencing the velocity. Okay so I've just gone and got my KeyStep Pro but everything I'm going to show you here you could happily do in the door really really easily. You could also do this on any other controller that's going to allow you note by note control of velocity. So basically got the patch from before just made it a little bit more mellow for reasons that will become clear I've also added reverb on. The other thing I've done with this patch is I've set the pressure or rather velocity to pitch to two in the mod matrix which means when I press it very lightly we get the real note and when I press it with as much of my finger on as possible we get a semi tone up. So what I've done the KeyStep here if we go into the step edit here when we look at this first chord here we can see that we've got these notes that are lit up on it and if I go into each of those notes we'll see that the velocity for each of those notes is set to zero that's actually zero doesn't look like it but it is and as I go into other steps and take a look at the velocity for the various notes in the step you'll see that actually I've got them set to different velocities so what that means I think this one's probably a good example here step six all of the steps in this one you probably can't see it because it's in the shadow of the knob but the velocity for each of these is set to 64 which is the center point which means in terms of our routing on the on the microfreak that means that we're going to be up a quarter tone so it allows us to get these really dreamy kind of feelings so this first step is in concert pitch this is about a quarter flat half flat that's half sharp I think that's back in concert pitch as is that and then that's just slightly sharp I think we're at half sharp and this is something that I had a nearly spoke about in one of his videos about microtonal stuff for kind of lo-fi feelings and that is that if you alternate between your micro tunings between say concert pitch and half sharp it doesn't feel anywhere near as jarring it still sounds dreamy and sort of uncertain but it's still kind of working and of course if you have a door or a control which allows you per note velocity you know you can tweak one note within a chord for example to be slightly sharp or slightly flat by using the velocity and any synth that allows a matrix mapping between the velocity and the pitch of a note you can do this on this is a trick that will work on a lot of different synths whether or not they support microtonality at all okay let's take a look at another approach this one I have to say is probably my favorite so I've got a little carpalus strung patch set up here which is nice but particularly especially going on there but you know the carpalus strung algorithm always sounds good now if we think about the way that the internal modulation matrix is wired on the microfig there's probably one source of modulation that we don't really think about because it seems so sort of intrinsic to the way that we play the keyboard and that is that the keyboard is a modulation source for the pitch so when I play one key up it's going to modulate our pitch by a semitone at a time right so there is actually a modulation source implicit in the keyboard and what's really interesting about the microfreak is that modulation source is actually represented on this final row here where it says key up now the place that you would usually take this I suspect is with your cutoff to make it brighter at the top and darker at the bottom and that's a perfectly adjustment way of using it the old filter tracking keyboard tracking is a classic and for good reason but as we've already seen one of our destinations is indeed the pitch so what happens when we apply a modulation amount to our keyboard against the pitch so if I just hold these two notes down here so that they drone essentially what's going to happen when we change the modulation amount away from zero if we go negative it's going to bring those notes closer together and if we go positive it's going to spread them apart without any modulation applied that's an octave so by spreading or compressing these these notes we're going to get microtonal intervals across our keyboard and it's basically going to throw our keyboard into a non-standard layout if you like I've found this to be quite an interesting way to approach the instrument what I usually do there's probably a scientific way of doing this to work out precise modulation amounts but the way I usually approach is I play an interval for example a minus seventh there and then as we change the modulation amount I go looking for points at which that works again and then I explore what I have so we've got those notes there kind of work with some interesting clashes you kind of got half half or other quarter note happening there and you get these interesting textures you might need to explore a little bit because something's going to sound just bad and of course if you find intervals that you'd like you want to make them a little bit more playable we can of course adjust the layout a little bit you find some of these things which are quite beautiful still line up quite nicely there starts to get that little bit of an ease properly discorded try in different registers because of the way that it's going to spread it things are going to be more extreme at either end of the octave range as well and you are going to essentially have to relearn the keyboard a little bit that's nice in a kind of ugly way and of course we could think about also applying pressure as a source to our to our pitch as well so that we have the opportunity to bend things into tune if we need of course you would never find some of these intervals across the keyboard normally because of course they don't exist and that's kind of exciting to me let's try a different interval that's a expand rather than compressed so maybe let's go for being able to bend that note sharp that's quite useful and you can find all of these textures that simply not be available otherwise of course you're probably not going to be sat quite nicely on the root of your of your other instruments so you're probably going to be out of tune even at the root so you might want to go into preset here and sorry not in preset does it you may want to go into master tuning and look at the sent offsets to push whatever you choose to be your roots towards what you're actually playing in or not you know because sometimes that might be fun as well the other thing that is really quite exciting sometimes is to make use of the chord function so if we hold on yes so i think the other place where this sort of expansion compression of the keyboard works really well is sort of in your sort of asset world where you have a baseline and you know baselines get stale when they're actually playing normal notes so let's see what happens if we make this a bit more nasty again you may want to go into your utilities into master tuning and find where your root note now lives i think this is quite a cool way of finding evil sounding baselines they don't live within normal scales that top note is kind of like a half sharp thing going on yeah three kind of inching now throwing some spice the glide random it's fun so anyway i hope you enjoyed that and had fun in our little excursion through micro tonality if you did then make sure you give the video a thumbs up and make sure that you're subscribed to the channel so you don't miss out on any upcoming synth fun and weirdness as always thank you so much for joining me until next time take care bye


Hey, Psych2Goers, welcome back to another video. Have you ever heard of the Myers-Briggs type indicator? Do you know what the INFJ personality type is? INFJ is the rarest of the Myers-Briggs personalities and stands for introverted, intuitive, feeling, and judging. Amongst their other features, INFJs are mostly known for their introverted behavior and their idealistic approach towards life. And while these rare behavioral traits can make them very valuable for society, like everyone else, it can also put them at a disadvantage, especially for their romantic life. So here are seven reasons why, as an INFJ, you may still be single. Number one, you won't settle for anyone other than your dream person. Would you end your relationship with your partner because they're not the person you've envisioned? As an INFJ, you're always striving to find someone who can connect with you mentally, emotionally, and even spiritually to a very intimate degree. You're always looking for someone who truly understands you and who can share your inner world with. But the problem comes when you won't settle for anyone less than what you have in mind. At the same time, the selectiveness that you have when forming relationships presents itself as a barrier for people who are interested and who genuinely want to know you better. Hey, Psych2Goers. Do you struggle to build deeper connections with others? Are you looking for ways to connect with people beyond the surface level? Today's video is sponsored by So Synced, a place where we can match partners by personality types based on the 16 personalities model. You can access it by clicking the link in the description below. Two, you stress over small things. Are you someone who always needs things to be perfect?  As an INFJ, you develop deeper ideas than the usual person. And although this is an incredible skill to have, it can also make you read too much into things. If you're constantly stressing over insignificant things that you fail to look at the bigger picture, then it could be a reason why you might find yourself still single. Number three, you wait for others to make the first move. Do you feel bad for initiating conversation because you think you'd become a burden for them? This is a common thought that INFJs have. Whether it's for them to text you first or to take you on a date. As an introverted person, you usually wait for them to make the first move. While it may be that you're afraid to be bothersome for them, this habit of waiting for others to approach you can also result in a lot of missed opportunities. We talked about the importance of your potential partner being attentive and remembering the little things, which is why SoSync could be the right app for you. They pair couples who have the right amount of similarities to get each other and just the right amount of differences to create that spark and go for deeper, meaningful dating. Upon taking the personality test, you discover your personality such as INFJ. So thoughtful or ENFP, so curious. Once you've mutually liked each other, you can start messaging. We wanted to say a massive congratulations to Hannah and Brendan who got married in December after meeting on SoSync, the dating app that matches compatible personality types. Hannah is a psyched goer who discovered SoSync through one of our videos. She downloaded the app, found Brendan and deleted the app within a matter of hours. Hannah is an ENFP and Brendan is an INTJ. They would be a perfect personality match on SoSync. Download the app for free today to meet that special someone on your wavelength. Make sure to check out the app in the description box below for more details. We encourage you to try it and give yourself a chance to find deeper love. Number four, you can be very stubborn. How strongly do you defend your values? One of your main personality traits as an INFJ is that you tend to stick very closely to your values, beliefs and ideas. Because of this, you might give off the impression that you're not willing to change your opinion even when proven wrong. This can be a very important factor for potential romantic partners as they may be put off by your stubbornness. Number five, you see past fake acts. Have you ever gotten into a fight with someone because you found them faking something? Although people may tell you that you're just assuming things, as an INFJ, you do have the ability to see past the surface and notice things that other people don't. Unlike others, you are very observant and will look out for things like people's body language, voice tone and facial expressions and being able to see past fake acts can disqualify more people than you might think when considering who you want to form a romantic relationship with. Number six, you don't do casual. Do you commit to relationships very fast because you don't want it to be a waste of time? If yes, then this may be why you're still single. One of your personality traits is that you don't like wasting time and effort on things that are not going to work out. This is also why you're so selective about who you form relationships with. However, when looking at romantic relationships, this trait may scare people off as most people usually prefer to start casually and not commit to too much too soon. And number seven, dating is a pain for you. Do you have a positive or negative impression of the dating experience? Although a lot of people find dating as bothersome, INFJs can feel overwhelmed by it. As an INFJ, one of your inferior functions is extroverted sensing. This means that you don't like it when a lot of sensory information is being thrown your way. So putting yourself out there and meeting new people can become overwhelming and exhaustive. As a result, you might find yourself avoiding dates altogether, which may be why you're still single. Do you recognize any of these signs in yourself? Let us know in the comments below. If you found this video helpful, be sure to like and share this video with those who might benefit from it. Subscribe and hit the notification bell icon to get notified whenever Psych2Go posts a new video. The references and studies used in this video are added in the description below. Thanks so much for watching and we'll see you in the next video.