Ladies and gentlemen, the President of the United States is seated. I have an opening statement. I want to say a few words tonight about three important issues that are now before the Congress. We've reined in government spending. With Graham Rudman, we can look forward to a disappearing deficit by 1991, but there are still a few obstacles in the way on our road to a balanced budget. And make the sensible adjustments we've suggested, some in Congress, apparently intend to take large and dangerous cuts out of our national defense. And again, we hear that constant refrain coming out of Washington, raise taxes. Well, it's time for Congress to take a responsible approach to spending decisions. And when it comes to taxes, let's get into the spirit of the times. I've said it before, and I'll say it as often as it takes. I'll veto any tax hike that comes across my desk. Not only will we not raise taxes before I leave office, I plan to make sure we have a balanced budget amendment that puts a permanent lid on taxes and doesn't let the government grow any faster than the economy. So we've made progress, but we have a ways to go on the budget. I'm glad to say, though, that we're moving on tax reform that will achieve fairness and promote growth. We're looking at a tax reform built in the Senate that's quite simply one of the best anti-poverty programs. One of the best job creation programs. And one of the best pro-family bills this country has ever seen all rolled into one. I hope the House and the Senate will move quickly to bring this bill into law so America can make a fresh start in 1987, and even lower tax rates, even more jobs, and even stronger growth. Finally, there is the upcoming vote on aid to the Nicaraguan Freedom Fighters. Workers must understand the urgency of the situation in Central America. Delay is deadly and plays right along with the Communist game plan, because while we may have tied our own hands, the Soviets, Cubans, and Libyans haven't tied theirs. With over a billion dollars of support and some of the most fearsome weapons in the Soviet arsenal, the Communist strategy is simple. Hold off American aid as long as possible in the hope they can destroy all opposition before help arrives. It's time for an up-and-down vote on freedom in Nicaragua, an up-and-down vote on whether the United States is going to stop Soviet expansionism on the American mainland while the price is still not too high and the risks are still not too great. We must act now on a bipartisan way to do the right thing, to rescue freedom in Nicaragua and protect the national security of the United States. Now, Helen, it's your turn. Your decision to tear up the Salk Treaty by the end of the year has caused great consternation among the allies, among members of Congress, on both sides of the aisle, among others, who fear that you are creating a more dangerous world. My question is, is this decision irrevocable? And I'd like to follow up. Well, Helen, I have to say that I can understand why they would be distressed with the way the news has been carried. But let me go back to what the situation really is. First of all, this treaty, which was signed seven years ago, was never ratified. Well, it was more than seven years ago, I guess. But for seven years, there is supposed to have been this restraint and this observation of the observance of the treaty's terms. And for seven years, this country has been doing that. The Soviet regime for seven years has been violating the restraints of the treaty. We found it necessary to, more advisable, to do away with two Poseidon submarines as we launched the last trident. But that, I had to make plain, was not, while it did keep us within the constraints of the salt agreement. That wasn't the reason, had there been no salt agreement, we would have done away with those two submarines because or dismantled them because of the cost and the military value of them or lack of it. But then what I said was that before we reached another point where this might be an issue at all several months away, which has to do with the arming of the 131st B-52 with a new air launch cruise missile. And in the interim period, I said that we could not go on unilaterally observing the constraints while the Soviet Union violated them and gained even greater superiority over us. And that we were going to be bound from now on by the necessity of maintaining a deterrent. We're not seeking to achieve superiority over them. But we're certainly not going to let them go on increasing their superiority over us. But I said, because we have these several months before that moment comes up, that we were going to do our utmost, since they themselves have talked of arms reductions, that we were going to do our utmost to see if we couldn't involve them in replacing this salt treaty, which first of all was never ratified, as I said, but second of all would no longer be in power if it had been ratified because it was stated for a limited period of time, that if we could replace that with a realistic program of arms reduction, which has been my goal ever since I've been here. Now we have the first Soviet leader to my knowledge that has ever voluntarily spoken of reducing nuclear weapons. And we want to follow up on that. It sounds like you are going to tear it up, Mr. President. Do you agree with Richard Pearl, who granted as Soviet supporters, members of Congress, who want to keep you within the limits of this treaty? I'm not going to make any comment on anyone who wants to keep us. But I did find it rather strange that some of the senators who spoke very critically of me, without really understanding what it is that I've tried to explain about this, some of them were members of the Senate when they refused to ratify the treaty to begin with. The treaty was really nothing but the legitimizing of an arms race. It didn't do anything to reduce nuclear weapons of the nuclear threat. All it did was regulate how fast and how much we could continue increasing the number of weapons. So I was always hostile to that particular treaty because it did not reduce weapons. And that's what we're going to do. But again, as I say, the Soviets have an opportunity to meet us now with regard to some of the very things they've been proposing, arms reduction. And we will observe the constraints, as to the same extent that the Soviet Union does. But we can't go on unilaterally observing this while they take off on their own with the violations that they've already made and probably more to come. Am I? Mr. President, NASA is awaiting your decision on how to replace the Challenger spacecraft. Could you tell us tonight how you would finance a fourth orbiter? And if you can't tell us that, could you explain what's holding up your decision? Well, for one thing, we're studying the report that we've received. And there are many things that have to be decided. There is a backlog now of space cargo that is supposed to be up there. And we have the problem of determining whether we shouldn't increase the number of unmanned launchers for many of those things that could put them in space, and then see where we can come with the eye. I believe me, I want to go forward, and I think we all do, with the shuttle program. But how soon we can get to that is a question. And in the meantime, should we emphasize more of the unlaunched to get, to move on that backlog that we have of cargo that needs to get into space? So I don't have an answer for you on this, except that, yes, I think we should go forward with another shuttle. Can I follow up, sir? Would that fourth shuttle, would you insist that that fourth orbiter incorporate all of the recommendations of the Rogers Commission when it is built? Well, again, we're still in the midst of studying that now that we've just received it, so I can't answer something as specific as that about that. Jerry? Two-part question, sir. You've left no doubt through your public statements of your determination not to permit Nicaragua to become another communist Cuba or a Libyan. What means are left to the United States if the Contras are defeated by any means, whatever, is a naval quarantine possible? I couldn't, and Jerry wouldn't comment on anything that might be further actions for us, because I don't think you could do that without informing them of anything we're thinking. And right now we have not. We have not planned for any contingency be gone to aiding the Contras, because we think that I've got to stop using that word. That was the Sandinistas title for them. And I don't like to do anything they're doing. So the Freedom Fighters, we believe with all the information that we have that they are capable of, at the very least, applying sufficient leverage that they could bring the Sandinista government to a negotiating table for a settlement. We would prefer that over a military settlement if that can be done. We know that there are thousands of recruits that are waiting to join the Freedom Fighters, and they need the weapons and ammunition and so forth for them. Another part of the question is, this week, in a speech you liken Mr. Gorbachev to Castro, Arafat, and Gaddafi, and I'd like to ask, what effect do you think this statement would have on future relations with the Soviet Union on a possible summit? I'm talking about the Georgetown speech. But I didn't think I'd lumped him in with them. Speech. I certainly, then, it was a bad choice of words because I didn't mean to do that. As I've said, he is the first Russian leader to my knowledge that has ever voiced the idea of reducing and even eliminating nuclear weapons. So I must have goofed someplace because, believe me, I don't put them in the same category. Gary? Mr. President, with the Supreme Court's decision today, allowing a woman to have an abortion, yet again another Supreme Court decision, will your administration let this be the law of the land, or are you going to look for another case to press your position on this matter? Wait a minute. Hit me again here. I think I was still answering Jerry's question. The Supreme Court decided today to not interfere with a woman's right to have an abortion. Is your administration going to pick another case to fight this position, or are you going to let it stand as a law of the land? We're going to see. If we interpret the decision right of the court, their objection was not to what we were trying to accomplish, but the fact that, evidently, the regulations, HHS that we asked for, were based on that previous bill that had to do with discrimination against the handicapped, and they, the court said they thought that this was putting the federal government there. They were getting into something that properly was the province of the state and all. So what we have to do is look for, what is the proper way we can do this? Because I feel very strongly that we're talking about a human life. And the case that prompted this entire act was one in which the determination is made that this life is to be taken away, and yet it isn't done as you would with an animal. It isn't done with a merciful putting to sleep, or they can't do that. So instead they just let it starve to death. And I just don't think that if our Constitution means anything, it means that we, the federal government, are entrusted with preserving life, liberty, and the pursuit of happiness. Well, where do we draw the line? Can we say to someone it's all right for you to, in whatever way you've chosen, dispose of this human life, for whatever reason? And I think, I just don't think we're finished with this problem at all. President DeFyker, pursue the questions on the, your decision on salt treating. In one, on one hand, you're saying that Soviets have continued to increase their superiority over us. On the other hand, you said that the treaty did not constrain either side in terms of the arms race, and it's one of the reasons you were not for it. It really can't be both ways.  Which way is it? Have the Soviets been able to increase superiority over this period of time, or has the treaty not been able to stop them? No, it hasn't been able to. The treaty actually set limits, as for example, that you could only have one new type of weapon now, that you could develop that didn't exist, and they have developed two instead of one. This was a violation. It also set numbers and figures so that it was a restraint to the extent of just not an all-out arms race with no limit on the way you could progress. But when you say about achieving, remember, we're still playing catch-up. They were building when we were dismantling, and we feel that, as I've said before, there's no way that we can allow them to reach for and get a superiority. And we don't want a superiority over them, but also we simply want to maintain enough of a deterrent that even with whatever superiority they have, it won't be enough for them to take the chance on the follow-up action that could happen. I can just follow that up, though. At the same time, your own arms control director, Mr. Edelman, has said that the Soviet violations have not had any great military significance. What is the possibility now, since the violations themselves, which have been disputed by some people, is to their significance, what is the possibility that by abandoning the treaty now, which as you just admitted has some limited significance in providing some degree of predictability, that we won't go into a complete arms race now? What's the replace saw at this point, and why make this decision now? I didn't make it now. I said, we've got several months here in which we're going to try to involve them in the things they themselves have been talking about, and that is a definite arms reduction program. This is the only thing that makes sense in the world, and I've been talking about this since 1980. And I said, I was sick and tired of agreements that just said, well, we'll only go at this pace in our increasing the number of weapons. Let's get around to getting rid of them as much as we can. Sir, that's true. Thank you, sir, for remembering a couple of weeks ago, you said that the problem of the hungry people in America is not due to the fact that they don't have food and the ability to get food, is that they don't know where to get it. And some four people we talked to at the time said, you're blaming the hungry people for being hungry. You're putting the blame on them. Well, I don't know who those people were. And I do have to say that I think there are people who lack the information, people out in the country that maybe don't know. And we've had plenty of evidence of that. But the simple truth of the matter is, we are spending on nutrition more than has ever been spent before, and more than $3 billion over and above what was spent in 1981, $18.6 billion, I think it is this year, that is being spent on this program. But in the interim, during the same time that we've been increasing, the private sector has gone all out in programs all over the country of meals for the hungry. Today, the federal government is providing, I think it's 93 million meals a day. And that does not count all those private agencies, too. So I think there is considerable merit for saying that it's difficult to believe that people are starving in this country because food isn't available. I just, as I say, I think that in many instances that people just don't know that where or how to go about it. And at the same time, I find it difficult also to find any cases of starvation and undernourishment. Mr. Chairman, if that is the problem of public education, why then did you cut out the one federal program that did just that, educate hungry people, educate the rural poor, educate elderly shut-ins about how to get food assistance? It was there and your administration cut it out. Because it was a case of, that was a case of simply the food stamps. And that's a program in which I think most people are aware of food stamps, and their neighbors are doing it in many cases if they haven't done it yet. And this was one in which they had as literally going door to door to knocking on the door to tell people how to become eligible or have you gotten your food stamps today? And we thought it was a waste that we'd rather buy more food stamps and pay for more food stamps than pay for the bureaucracy to do a thing of this kind. Leslie? President, you've just said that you really haven't made the salt decision yet. And I think there's a lot of confusion as to exactly where we stand on the salt decision. Are you going to go over the limits of the salt decision? Or are you going to dismantle another submarine and stay within the limits? Exactly. What are you going to do on salt? Well, Leslie, you're asking something. Yes, we will have a plane coming up to be armed with a cruise missile that would put us to that extent beyond the constraints of the limitation. Now, we've got several months before we reach that point. We've got several months in which to see if the Soviet Union, we have taxed them over and over again with regard to their violating the constraints. Now, on that basis, we're going to see if we cannot persuade them to join in the things they're talking about, arms reduction. And if nothing is done, then we'll make the decision with regard to that plane. There are reports that today in Geneva, the Soviets made a new proposal on reducing long-range strategic missiles. Is this the kind of proposal you've been looking for, and has it changed your opinion of what you're going to do on salt? I can't comment on it because of the confidentiality of the situation there in Geneva. But, yes, as of today, we have received this proposal. And now we're going to study that and see what they have in it. Sam? Mr. President, the Rogers Commission detailed a series of actions and inactions leading up to that shuttle disaster of individuals who knew that the O-rings had a problem but did nothing about it. And in the last 24 hours before the launch of engineers from Thayakal saying it's unsafe to launch, don't launch, but of pressure being put on Thayakal to reverse it. And yet William Rogers seems to think that the individuals involved should not be punished further. Their culpability should not be established. Do you agree? Yes, I do. We are still studying that report of theirs. But I don't believe that there was any deliberate or criminal intent in any way on the part of anyone. I think that with the great record of success that NASA has had, going all the way back to when men circled the earth in those capsules and then to men on the moon and now 24 successful shuttle flights, I think there was a complacency there. And yes, it's something that has to be corrected before every one of those takes off again. But I think it was just a carelessness that grew out of success. And I think that it's time for us also to remind ourselves of the tremendous record that NASA had and help now in the restoration of the program and they're going forward and to see that this cannot happen again. Maybe part of it was also due, I've often wondered this, if part of it wasn't due to the balmy climate of Florida and that it was difficult for anybody to believe that they'd had a cold snap that could render that o-ring dangerous. Sir, if I may, in our society if an engineer of a train falls asleep at the switch, we pursue him for negligence. Bus drivers, all through our society when people do things, even though they don't mean to kill anyone, as you've said in this case, they're brought into court if there's evidence that they've been negligent in some sort of criminal fashion. Why should these people be exempt from that kind of just review? Let me, Sam, let me plead waiting until we see the entire report until we've had a chance to read all of the testimony and everything else before making a decision. We put a man in there that we believe is going to do much. I've got to call on at least one red dress. Thank you, Mr. President, and I will have to follow. Immediately after the U.S. attack on Libya, you were particularly grateful to Prime Minister Thatcher for her help in allowing the United States to let airplanes take off from the U.K. Since then, American tourists have been staying away from England and Europe in droves, and Mrs. Thatcher has made a personal plea for Americans and their dollars to come back to the continent. Do you think that it's safe in Europe for Americans to return? And will you tell Americans whether they ought to go overseas this summer? You've asked me a very tough one in my position with what we know about the dangers throughout the world. I certainly don't want to be quoted as advocating a tourist rush in the face of the world the way it is. I'm going to be rather bold and just tell you that our ambassador recently had a little talk or something that was carried in Los Angeles Times, and it was to the effect that he believed that London was probably one of the safest cities in the world, and that he saw no reason for anyone to be fearful of that. Well, I have not argued with him on his making that point. My follow then is that we also read about the extraordinary security precautions that are going to be taken for the Statue of Liberty festivities July 4. Are you concerned that perhaps that's a pretty delectable domestic target? Yes, but I also have a great deal of confidence in our in our security people, and I can see where they would think that that would be a very inviting target for those who hate us and in the terrorist ranks and think that they might be able to embarrass us that way. Mr. President, the Agriculture Department has been severely criticized for its treatment of minorities in employment and service delivery. This despite your saying that you would not tolerate discrimination in the federal government, what are you going to do about the Agriculture Department? Bob, it's already being done with the Secretary of Agriculture. He's heard these allegations also, and as I understand it, they were allegations with regard to not being as fair as we as they should be with regard to women employment and to on the racial basis, to black employment. And the Secretary thought it all, the far flung and various agencies of the Agriculture Department investigation is underway right now to see if that's true because he absolutely is sworn. If it is, he's going to correct it because he doesn't want any discrimination either. What will you do to ensure that these things are carried out? That they are what? That they're carried out. Well, because I feel as strongly as he does about that, I'm going to be watching this very carefully. I don't want any hint or sign in our administration that there is any kind of discrimination of that kind. And I think I've got a record that should make you willing to believe that because as a governor in California, I eliminated a kind of quiet discrimination that had seen an unfair balance in employment and ended up appointing more members of the minority communities to executive and policy making positions than all the previous governors of California put together. So yes, I'm going to ride herd on this, but I have great confidence in the Secretary of Agriculture because he was doing this in California at the same time that I was governor. President, the Warsaw Pact said to be offering to withdraw a million of their troops that face us in the West. For those of us with families in Europe, that sounds like a lot. I know that you always like to deal with these offers in the confidentiality of Geneva, but isn't it perhaps time bearing in mind that nothing seems to have come out of Geneva for over a year to go with an offer like this, run with it and see what happens? You mean the offer that has just been given in Geneva? Well, as I say, there have been offers and we have made counter offers, much in the same thing and with pretty much the same end result as to numbers of weapons. And where the difficulty seemed to come in is the Soviet Union and the United States have somewhat different mixes of weapons that we believe are essential to, well, for theirs, we believe theirs is based more on an offensive nature. We believe ours is based more on a deterrent idea. And so sometimes we run into difficulties then in reconciling some of the means of getting to the same number of warheads being eliminated. This has kept us from having an agreement so far. Now this last agreement has come in and we don't know yet until we see it carefully. Is it a response to one of our counter offers? Does it in some way change some of their proposals and bring us closer to a negotiated position? And this is what we want more than anything so you can depend on it that we're going to make every effort. But it must be fair and balanced. It must not be an agreement in which one side is trying to maintain or increase in advantage over the other. So doesn't this make it all the more important to see Mr. Gorbachev as soon as possible this year? That's what I'd like. In fact, we're waiting to hear when this can take place. We suggested a date and evidently it was too early for them. They didn't suggest but they spoke publicly about a possible date and that was wrong for us because of the coming political campaign. But we still and I still believe that he wants a summit. I want a summit and I believe it's going to take place. I better spread around here someplace. With a red flower. Mr. President, the Pollard spy case has precipitated some confusion within your administration over the matter of how much Israeli spying there is in this country and if it goes beyond the Pollards, the Justice Department officials are telling us that it goes beyond the Pollards and they're continuing their investigation. The State Department officials have told us that there's no more Israeli spying here and they're satisfied and they seem to want to put an end to it. I wonder if you could clear up this confusion. The only thing I know is that the Israeli government has assured us a bunch of they can that they have never had any program of trying to get intelligence information from our country or in doing any spying on us. And so far, as I say, the Justice Department has said they will look to see if there is anything that they can find out. But so far there's been no evidence presented to us from anyone. What if they do come up with some evidence? What would you do? Then I think we'll have to deal with that then and find out whether it's a surprise to the Israeli government, whether someone was off playing their own game or not. Federal Reserve Chairman Volker made an unannounced trip to Mexico this week to discuss that country's financial problems. Are you worried that Mexico might unilaterally default or default on payments or totally default on its foreign debt? Well, I think this is a possibility with not only Mexico but a number of other countries that are having these debt problems that are much based on the high interest rates of the past before we reduced inflation. And obviously we'd like to be of help to them within the framework of the agreements that were reached in Korea by Secretary Baker. And we want to be of help as much as we can. Mexico is a next door neighbor. Many, our fortunes are linked on many fronts. And so we want to be of as much help as we can. And that was the reason for his trip. It's over already. Why don't you ask questions that can be answered yes or no?


What are loop devices? That's the topic for today, because this question comes up pretty frequently, especially from new to Linux users, novice Linux users, especially those of you that are running Ubuntu, because Ubuntu out of the box now, ships a lot of programs as snap packages already installed as snap packages. And when you run your standard list block command, LSBLK, you have all of these loop devices that are listed among your block devices. What are those loop devices? Well, let's start with what a standard block device is. That's typically a hard drive or a solid state drive or an optical drive, like a DVD drive, a Blu-ray drive, right? And then these loop devices, they're essentially pseudo devices. They're not really devices, they're virtual devices. You can think of it as a virtual device that allows you to mount a virtual file system. Essentially, a loop device is a file that can be mounted as a quasi block device. So a good example of this would be an ISO file, an ISO. You typically you'll mount an ISO and you can mount that thing as a device essentially, but really it's just a file. An ISO, all it is is an image file. And that's also what's going on with snap packages in Ubuntu, right? These snap packages, these are files, right? They get mounted as devices. They get mounted as a file system, essentially a virtual file system. So let me switch over to my desktop here and I'm gonna go ahead and launch your terminal and just to show you guys what most people complain about with this loopback device problem. It's not really a problem. When I run a LSB okay, I have a lot of snaps installed on my computer here. Well, not a lot, but I've got, I don't know, two dozen or so snap packages and they're all mounted as loop devices, right? And these are the loops and it actually specifies in the LSB okay command what is a loop device. And then down here, of course, these are the actual block devices. So these are legitimate drives. So I've got a bunch of SSD drives. I got a NVME drive. You can see I've got some partitions created on two of the drives. Those are partitions that are currently mounted. You can see on my computer, I've got of course the root partition. I also have a separate partition for my music directory because it's very large. I have that on its own disk mounted as its own separate partition. I actually did a video about that, how you can actually put a, like your home folder or music folder or video folder on its own separate drive and then mount that thing. I'll link to that video in the show description in case you guys wanna check that out. If I had any optical drives, they would also be listed here. I did fire up a virtual machine here. So this is a virtual machine of Ubuntu just running off an ISO. So if I do Control Alt T in this VM and zoom in here and I run LSBLK, I may have to zoom back out a little bit. You can see running the live ISO here. There's not much here. There's really no, you don't see any hard drives, right? Because all of this is running off the CD-ROM, right? That's the CD-ROM drive. It's mounted and then we have this read-only file system mounted as a loop and that read-only file system. Of course, it's gonna be the ISO and then we have all these snaps that are also part of the live environment that's already installed and they are all mounted as loop devices. Now, one of the complaints that people make with snaps being mounted as loop devices is if you have a lot of snaps installed, you've got a lot of output in this LSBLK command and a lot of people claim that, you know, snaps pollute the output in LSBLK because it's, you know, there's so much stuff in the output and they only wanna see their physical drives, right? Their physical block devices. They don't wanna see any of the loops. Well, this is rather easy to accomplish because honestly, there is a flag you can use. You can do LSBLK-E7 and it will remove all the loop devices and only return your legitimate block devices. And there's also a command you can run if you want to just list your loop devices. There's actually a command. Most desktop users are never gonna run but it's a LO setup, so that's a loop setup. And if you do loop setup space-L for list, I believe, yeah, that will list all the loop devices I'm zoomed way in so the output from that looks a little weird. Let me run that again and zoom out. There we go. So that is LO setup-L for list. You could also do LO setup-A for all. And it gives you a little bit different format but it gives you a similar list of information. They're not sorted in any kind of like numerical or alphabetic way, so I like to typically run that command with sort, pipe that into sort, that way you kind of get them at least numerically sorted. Now, I don't think I've ever created my own loop device but if you wanted to, it's rather easy to do. The first thing you need to do is find a loop device that's not in use and you could do LO setup-F for find and if you do it with no other arguments, what this will do, this will find the first unused loop. So in the output from the LO setup-A, you can see loop 17 is not here, right? We went 15, 16, 17 is not here, 18, 19. So the first unused loop that I could use for a new loop device would be loop 17. So let's go ahead and create a loop. So what I'm gonna do is first thing, we're gonna have to mount a file to the loop, right? Because again, these loop devices, they're essentially files that are mounted. So I'm gonna make a directory, I'll call this make a dear test loop will be the name of the directory and then I'm gonna touch a file, I'm gonna touch test loop and I'll call this my loop will be the name of the file. Now the byte size for this new file I just created, of course it's gonna be zero bytes because it's an empty file but you can't mount something, right? Unless you give it a specific size, it's gotta have a block size, right? So what I could do is I could use this F allocate command. What this does is allocates a specific amount of space to a file and I could do dash L, I could make the size anything, I could make it 10 gigs. I've got space on the drive for this so I'll make this a 10 gig file here and then what I'm gonna do is test loop slash my loop and then with sudo privileges because anytime you create a loop device or delete a loop device, you need sudo privileges. So I'm gonna do sudo lo setup and what was the first unused loop? It was a slash dev slash loop 17 and then we need the file that we're gonna use and of course that is test loop slash my loop. Then it's gonna ask for my sudo password and if I did that correctly, if I did it LSBLK, we should now see loop 17 listed, yes and there is loop 17 and you can see the mount point is empty because it is not mounted. You see all the snap packages, they are mounted. If they weren't mounted, you actually couldn't launch these snaps. So if I did a U mount for unmount and I unmounted one of these loops for the snaps, I actually could not use that program anymore. Now what I could have done for this new loop device, I mean, I could mount it.  Of course you've got the MKFS command, right? Make file system dot and then whatever file system you're creating so I could do extend for for the file system. I could do slash div slash loop 17. If I wanted to go ahead and create that file system, I'm not gonna do that though because this would, it's not something I plan on keeping but after making the file system, then of course, you know, I'd mount slash div slash loop 17. And of course I would have to mount that to a specific spot, you know, I'd have to create a directory or I could mount it to temp or whatever it is. Of course that's assuming I only am using this temporarily, if I wanted to make this a permanent like a mount point, obviously, then you would go into your file system table. I wasn't actually planning on going over most of this. I really was just gonna explain what these loop devices are for your snaps but you know, I could go into the file system table and I could, you know, add the mount point for this new loop device and then on a reboot, it should permanently always be mounted. Now I didn't actually add anything to any of that but had I gone through that just for sake of completeness, then you know, if I later wanted to delete this new loop device and mount point, what I would do is, I would do a sudo lo setup dash D for delete and delete slash dev slash loop 17 and it would destroy that loop. As a matter of fact, I do need to do that and now when I do LSB okay, I should no longer see loop 17 in the output. But I diverged quite a bit from what I originally wanted to talk about. So these loop devices that you're seeing for the snap packages, they're essentially, it's a file that is mounted. You can think of it as a virtual file system and these snaps have to be mounted. If they weren't mounted, you couldn't run the program. So if I did a U mount for example and I unmounted one of the loops, you know, pick one, I don't know. The leave very office one right here. You know, if I unmounted slash dev slash loop 11, right, I would no longer be able to run leave very office until of course I mount that back. And of course some people are gonna ask the question, you know, why would Ubuntu choose to mount these things as loop devices, these snaps? What's the benefit of that? And one of the benefits actually of using these loop devices is that you can use your loop device as a way to sandbox applications. So they contain all the necessary dependencies and they are sandboxed from the rest of the system. That's why they do these things as loop devices. It has like a real world benefit. Now before I go, I need to thank a few special people. I need to thank the producers of this episode. And of course I'm talking about Brian Gabe James, Matt Maxim, and Mitchell Paul West, why you bald homie, Alex Harmer, Dragon Chuck, Commander Rangri, Dioke George, Lee Marsstrom, Nate Erion, Alexander Paul, Pete Sortion, Vador Polytech, Realities for a Less Red Profit, Roland Steven, Tools Devler, and Willie, these guys. They're my highest tiered patrons over on Patreon without these guys. This quick little chat about loop devices would not have been possible. The show's also brought to you by each and every one of these fine ladies and gentlemen. All these names you're seeing on the screen right now. These are all my supporters over on Patreon because I don't have any corporate sponsors. I'm sponsored by you guys, the community. If you like my work, want to see more videos about Linux and free and open source software. Subscribe to DistroTube over on Patreon. Peace. And also Happy Hanukkah and Merry Christmas. Happy New Year.


Hello and welcome to NewsClick. Today we are going to be discussing the recent collapse of the power grid in North India and later in East and North East India. And to discuss this we have with us today Praveer Purkayastha, well-known commentator on NewsClick associated with the channel and who is also a power sector expert. Praveer, give me a little background as to why the grid collapsed. You see there are two sets of reasons which are being given. One is of course what the government is saying that there is a general crisis in the power sector that is overdrawed by various states and the other the real reason. Obviously overdrawals at a time which was the monsoons, the rains had already set in, it was raining that night, 2.30 at night on 30th July. It's completely unbelievable that they would have over withdrawals at that point of time. As I said by Punjab or Uttar Pradesh that's really not believable. What seemed to have happened was that there was a Beena Gwalya link and there are really two circuits on that and one of the circuits had been taken out because they are upgrading it to a higher voltage level, 765 kV. So therefore there was only one line operating on that corridor and the amount of power being transferred between the northern and the western grid seems to have been much higher than the capacity of the link. That link therefore collapsed that day and if that link collapsed it can have a cascading effect on the northern grid which it did. By the way this link has also collapsed earlier having caused cascading failures earlier that was in 2009 November and also according to the National Low Dispatch Centre itself on 29th of July there was what it calls a near miss. So there was a problem which seemed to have existed with a bottleneck of the transmission corridor that is one. The second part of it even when they knew that this problem existed it already surfaced on 29th of July. There is no reason why they did not take the step of reducing the intergrid transfers which they now have done after 30th and 31st grid collapses. So I think it is a set of technical failures which underlines this particular grid failures and also the fact that there are certain human failures of not taking steps in advance knowing that there is a particular situation developed. So let me ask you the average person would like to know the story about overdrawals seem to suggest that this is some unruly states being indisciplined and acting strangely whereas what you seem to be talking about is a problem in grid management. So who is responsible for the problem in grid management and how should that be tackled in future? You know there are two again two sets of issues of this one is that what is the nature of the grid and what is it supposed to do earlier the grid was supposed to transfer power from surplus areas to deficit areas. Now that did not demand a large amount of transfers of energy large amount of electricity transfers from one area to another. It was just the difference of what you had and what the other side needed that is all that needed to transfer that demands a lower order of capacity in some of the transmission corridors between grids. What has happened lately is that we have instituted this policy of what is called open access which is what the 2003 electricity act brought into being. With open access any utility any distribution company anywhere in the company can buy power from whichever generator sells it to him or her cheap. Now what it does is it changes the nature of the grid and then you are really trying to transfer large amounts of power across grids for what are called market reasons or open access for buying and selling. If you look at the US grid collapse which everybody is familiar with that also identify two reasons one is a weaker transmission network and half investments have not been made. And the second was that the market mechanism instituted in the United States less than even India had already seen large amounts of transfers of power which did not take place earlier. And therefore the grid really collapsed against the requirement which was not envisaged when it was originally built the same set of things here too. But coming to the issue that you had raised the second issue which is who is responsible for the grid. That responsibility of the grid originally existed with what is called the central electricity authority and the regional load dispatch centers for which there are four. Now unfortunately post 2003 electricity act the regional load dispatch centers have been brought in under the power grid and they have become a part of what the power grid cooperation or what is called the central transmission utility. And therefore they do not have regulatory teeth anymore and that is a problem because the cooperation cannot regulate independent bodies. And here again the philosophy is the markets will do what the regulator therefore says and markets automatically do not unfortunately act to set forth so to address a problem of this nature. So there are a set of technical problems associated with how with the ability to be able to transfer power in this way and perhaps more importantly there are these institutional problems. Given the new situation with the open access system what kind of measures do you think should be instituted in order to insulate the system from future such occurrences. You know Raghu I would really question whether we should have an open access policy at all because after all what we should really be looking as what are surpluses and deficits and try to really swap power across them. Why do I have to convert my grid to a marketplace which is not this purpose. So I think we need to really relook very seriously the open access issues because that means an investment in the grid of an order of magnitude higher than what we are envisaging which otherwise we would have to envisage. And do we really need to put in all that money for facilitating what is called a market. Do we really need a market for the power sector of open access policies because what it really means is transmitting large amounts of power for a few paisa benefit. And I think this itself is something we need to really question. Having said that irrespective of what mechanism is or is not in place we need to have institutions which can regulate the grid. And in that there is no question in my mind that the this whole regional load dispatch centers and the national load dispatch center should be separated completely from the power grid cooperation which is the mechanism which builds the grid. They are really responsible for putting in transmission lines running it and so on. But this regional load dispatch centers which decides really arbitrates between the utilities who distribute power and those who supply power. They have to be independent regulatory bodies and they should come back to what originally it was under the central electricity authority who should really be the grid administrator or what would be called the grid regulator. Now that is a physical task. It's a real time task.  You know that's really what you need to do. It's a real time operation of the grid we are talking about and that needs an agency. It cannot be a public sector cooperation that is not its task. And does this require fresh legislation or can this be done through executive action currently? You know currently it can be done through executive action to restore what it was. But if you really want to give it teeth then you need to modify the 2003 electricity act. Because I think the 2003 electricity act has this hole in it that it does not envisage who will regulate the utilities particularly for the purpose of grid stability. It assumes that somehow it will automatically happen if a certain set of steps are taken. If you go back to the earlier era you had the state electricity boards. You had the regional electricity boards though were not legal bodies but they were really bodies formed out of the state electricity boards who coordinated their withdrawals supply and demand. And how to swap power surplus and deficit power. I think that was a much better arrangement than what it is now. Now we have what is called unscheduled interchange which is a market mechanism by which if the frequency drops you are allowed to supply more power than what you have scheduled. And if you are drawing withdrawing power then you get a higher penalty if the frequency drops that helps to regulate the frequency it has. But that is not enough. You really need more regulatory teeth and I think that's the kind of institutional mechanism we have to build. And I think at the end of it we can start with the executive act but probably we will have to look at the modification to the 2003 electricity act. An inquiry of sorts has been instituted to go into the grid collapse. First do you think this inquiry will produce any knowledge which will lead to action in the right directions. And secondly do you think any institutional changes are likely to result from this inquiry. You know if you look at what the response of the minister has been and the response of the government has been is very unlikely to lead to a change. The first thing that happens here is the power minister who causes who is responsible finally for the power department. The grid collapses twice or two successive days. He blames the states. He says I have done a fantastic job and gets promoted to the whole minister of the country. So we are sending a signal that actually grid collapse is not something which is an important issue and the minister is completely not responsible for what's happening on the ground. So that is one set of message we have passed. The government has been shouting from the rooftops and this is something the power grid also has been saying. That's over withdrawal, over withdrawal, over withdrawal. When they know cholly well that this is not true. So I think the fact that the government already pre-judges events says a certain set of things also means that's the direction they would like the inquiry to take place. So I'm very skeptical that it will be the independent real inquiry of the grid failures. I think we are going to come to see some things which sort of covers up what has really happened.  But we'll certainly not examine the kind of issues we are discussing today. Finally, the issue of the regulatory structure or body that you've been speaking of. Over the last 10 years or more with liberalization of the Indian economy, there's more and more instances across the economy where so-called market forces are allowed to prevail and there is a very clear absence of regulatory authority felt. Do you think this is one more of these examples? I think it's absolutely true that this is certainly something that the markets cannot do. Markets cannot control the grid. The grid control is in milliseconds. So therefore the markets don't work and you need technical measures as well as human measures to see the grid is stable. But beyond that, I would like to really address the issue of what the power sector reforms have done and what market liberalization has done. We started reforming the power sector in the belief that the power sector is bleeding the statelics to boards of bleeding. In 1991, if my memory is correct, there was about 3,500 crores of accumulated losses in the statelics to boards. Five years into the reforms, those losses had gone to something like 12,000 crores. Now, after about 20 years of electricity reforms, apart from the Enron Fiasco and similar other Fiascos, now the accumulated losses of the power utilities is to the tune of 1,90,000 crores. 190,000 crores is the accumulated losses. So the power sector losses have increased ballooned through the power sector reforms. We have yet no analysis whether the reforms are in the right direction or we need a different set of reforms. I think the power grid collapses only one part of the crisis of the power sector. The power sector crisis is much bigger and if we don't address it properly, it's going to take the Indian economy down with it because A, it's a constraint, it's a huge infrastructural bottleneck. B, there is roughly about 400,000 crores of debt the power sector utilities have with the banks and the entire financial sector will collapse if we do not address the problem. Thank you very much.


Okay, welcome back everyone. We're here live at theCUBE. Exclusive coverage, SiliconANGLE's exclusive coverage of IBM Pulse Live in Las Vegas, and we are here, all the action, premiere cloud show for IBM. I'm John Furrier, the founder of SiliconANGLE. I'm Joe, my co-host, Dave Vellante. Our next guest is Ralph Rio, Research Director, Enterprise Software, ARC Advisory Group. Welcome to theCUBE. Thank you. So I got to ask you, what's your take on the show? You look at the, from a landscape perspective, how does IBM do it? Is it hanging together? Is the story hanging together? And what did they get good grades and where do they need to improve? Well, the show is fantastic. There are, as you probably know already, 11,000 people here, which is a huge increase from previous years. I think the story IBM has around cloud and the new cloud stuff is fantastic. I happen to focus on enterprise asset management and IBM has had a great story around that with the Maximo and TriRiger products. They had recently added a great story around mobility. So I think IBM has a fantastic product line off for around enterprise asset management.  That's some big messaging for them. So under the hood, what is the asset management, the facilities guys, supply chains, all these guys out there who are working with IBM, what does this show mean? Because you know, this was a Tivoli show, systems management, a lot of data center stuff. So how does that stuff fit into the packaging here? What new things are they announcing here that ties into the cloud, hybrid cloud expansion? Well, one thing they do is show their product roadmap. So people who attend the show get an inside track on what is going to happen in the future with the Maximo and Tivoli products and smart infrastructure in general. So one thing is the inside track. Another thing is that the products are very mature, but they still need new functions and new features. And IBM's adding those. So when you get to know the roadmap, you have a much better understanding of where it's going in the future. So Ralph, talk about, so Arcadvisory Group is a rather large research firm focused on the manufacturing sector, right? Your specialty is, as you said, asset management software, right? So talk a little bit about Arcadvisory research group and your customers. Oh, all right. ARC is what they call a boutique analyst firm. Actually we're a little on the small side. We only have about 80 employees altogether. We're focused on industrial and manufacturing. I would consider that Ralph, boutique plus. Many boutiques of four or five guys, right? Oh, all right, okay. That's pretty good, that's pretty good. It's a mid-market boutique. All right. Okay, it's not Gartner or IDC or Forester, but it's substantial, so. So with our focus on manufacturing, and we go from the plant floor, sensors, PLCs, DCS systems, clear up to ERP and enterprise asset management. So with that focus on the applications, we have deep domain knowledge that our clients like to learn about.  Yeah, so it goes from discreet industries, people like Boeing, all the way over to the continuous process industries, people like Dow and DuPont, and everything that you can imagine in between. So you serve primarily that buy-side constituency, and I'm sure the sell-side participates as well. But so I wanted to ask you, what's going on in that space? What are your clients, what are the changes that are going on? Every industry's getting disrupted. I mean, obviously your clients have had to deal with China now for a decade or more. Oh yeah, yeah. China and India, a whole outsourcing trend. What are the big trends you're seeing at the end customer level? Just a minor distraction. Most of the, there isn't as much outsourcing as the politicians would make you believe. If you look at the decline in manufacturer employment in the U.S. over the past 30, 40 years, 90% of it is due to automation. Only 10% of it is due to outsourcing. Now the politicians love to make that a big campaign stop, but the truth of the matter, that is not a significant factor. In terms of now trends for the second part of your question, sorry to go off on that tangent. That's good, that's good point. Good clarification. The second part of your question, what's new in enterprise asset management? One big aspect is mobility. Now what I'm talking about here is a mobile device in the hands of the technician where they can manage a work order while they're on the site doing the work. This does provide some improvement in efficiency, but the big benefit is the data integrity. So when you got good data going into your EAM system, it's real time and accurate, then people have more confidence in it and they use it. Now the second big thing going on is of course SAS. IBM at this conference just announced SAS for enterprise asset management for Maximo, and that is allowing smaller companies, and it's opening the market for smaller companies who may not be able to afford the IT infrastructure to be able to afford a robust EAM application like Maximo. And what about larger companies? Are you seeing a slow shift from the sort of CapEx intensive install the hardware and the software to that SAS model, or is that really largely going to be focused on the small enterprises? Well, nothing is black and white, but for the most part the big companies have the financial resources so they can afford to the CapEx and to buy the equipment. We're seeing for at least for now the larger companies and the major applications continuing to be, I'm talking Fortune 500 type companies, continuing to be on premise. Now there are other applications that they're bringing on new that will go SAS of course, but the mainstream applications in the Fortune 500 for the most part are still on premise. And is that because of the economic advantage of being on premise or is it concerns over security or is it also sort of competitive advantage and unique capabilities of the software customization that they're doing? Yeah, it's more around their cost of money is low enough so that they can afford to buy the equipment and the SAS business model isn't quite as attractive as a smaller company. Keep in mind the larger companies already have an infrastructure of technical people who can provide security. It's the smaller companies who don't have that infrastructure that having an on premise application that's connected to the internet creates a lot of risks that they really don't have the resources to manage. So they are much more likely to go to SAS. So does your research show or confirm that it is actually at some scale on whatever that crossover point is that it's actually more cost effective and more secure and probably more compliant to stay on premise? Does your research bear that out or is it still too early to tell? Again, there is no black and white here. For now, we see the larger companies staying with on premise Fortune 500. Go below the Fortune 500 and ask greater and greater adoption of SAS. For a lot of the reasons you mentioned, security, cost, and I can't get the skills to do security right. That's the smaller guys going, but so what I'm trying to get to, Ralph, and again, we may not have an answer here, is are the large companies holding on to their existing models because of economics slash security, is there a strong business case or is it more inertia? That's kind of the way things are done. It takes a long time to change. What's your gut feel there? Well, part of it is inertia, but right now the economics aren't as strong as it is for the smaller person. Let's talk about internet of things. That's something else that obviously is happening. AT&T and IBM have got together. You're seeing GE push the industrial internet. Big customer GE, big customer of IBMs, but in a way, the smarter planet and the industrial internet are sort of counter poised and competitive, right? So what do you make of the internet of things? What does it mean to your clients and your research? What does it show? Yeah, so when I talk about the internet of things, I'm going to focus around asset management. So here we're talking about assets in a plant or assets out in the field. So take power in a plant would be the generator, power distribution would be the transformers and the breakers and all that stuff out in the field. Those things need high uptime. One of the key metrics of why people get EIM systems is the uptime. When the equipment goes down, it has an impact on revenue. Also there's a lot of material can get lost so that impacts profitability. So just focusing for a moment on the uptime metric. What does the internet of things do? Well, it allows you to remotely monitor an asset and predict when it's going to fail so that you can take corrective action before it fails. Now that has a couple of huge ramifications. One is often a small component will fail and if you don't do anything about it, it will cascade into a much bigger problem. Much like if you run out of oil in your car, it's $20 worth of oil. If you don't take care of that, your engine's going to seize and that's going to turn into a $5,000 repair. So being able to anticipate failures has number one, use ramifications in terms of the cost of a repair. And number two, now you can plan the downtime rather than ugly unplanned downtime. And when you plan the downtime, then it's less likely to be a big repair and you can schedule it so it doesn't impact revenue. So this is anticipatory capability that you just described. There's I'm sure a number of dimensions to that. There's the interconnectivity, there's I'm sure some kind of mobile capability for points of control and access and visibility on the systems. There's also a big data analytics. So there's a lot of moving parts that I'm sure I'm missing five or 10. There's a lot of moving parts coming together. When you talk to your clients, which presumably a lot of engineers and the like, are there headwinds in terms of absorbing this stuff or are they ready to jump in, which is your sense? Yeah, the primary headwind we've seen for manufacturers is the security question. Often IT will become very concerned if an outside company has access to through the firewall to the equipment inside the facility. So that seems to be the major headwind. Okay, so it's a belief that a connected world is inherently less secure, which is probably true. Well, let me go in a little bit more detail because this varies by industry. If we were to talk about semiconductor, they've been doing this for five or 10 years where the supplier monitors the equipment because it's very complex equipment. They call it tools in that industry and they can go from the cheap one is 10 million to 500 million dollars and they're very complex. So the supplier monitors it and they send in technicians to repairs. So this has been going on in semiconductor for a long time. It's, depending on the industry, it migrates in. What I was talking about the resistance to because of security IT, I see that in food and beverage accounts, which are more constrained. They're fairly low margin constrained and may not have the IT resources to address it right now. Let's talk about the, John and I always like to talk about the horses on the track. Sort of the competitive outlook. So who are some of the supply side competitors that you watch? I mean, obviously IBM and the SAP is a big player and there are others. Layout, sort of who you see as the sort of gold standard of the, like to look at whales, barracudas and minnows. The whales out there and are there any sort of interesting mid-market companies that are emerging and any startups that you're tracking? Maybe share with us what you're finding there. Yeah, there's, ARC tracks 160 companies in their space as part of our market research. And there are a few leaders and we could characterize the leaders, the top six or so, in three camps. Either they're an independent best of breed like IBM Maximo. There are others that are part of a control system supplier, a DCS supplier. So they bring in a different attribute and then there are others that are part of the ERP application like SAP. And each account is different and how they go about choosing and selecting what's best for them varies quite a bit. So who are the guys we should be watching? Obviously IBM, SAP, Oracle's got to play here as well. Well, the, its IBM is the leader right now. Okay, so IBM's number one. It's number one. In terms of asset management. With Maximo and Troyerica, yes. And then we would follow by a company called ABB, the Ventextal Vision recently did, past few years, did some acquisitions. So that is the example of a control system supplier. They can supply DCS systems. And they now add EAM as part of the reliability story. And then you have your ERP people and that's both Oracle and SAP. They have their modules, add-on modules to their normal inventory management, et cetera. Do you track the size of the market, even in rough terms? Oh yeah. So that's a big part of what you guys do? In non-rough terms, very precisely. So you guys kind of like the IDC of your space? Yes.  Well, globally, it's roughly a $2 billion market. And surprisingly, it's growing about, I don't remember the exact number off my head, but it's larger than most software markets, it's in the order of eight to nine percent. Okay, so most software markets are probably growing what, four or five percent? Well, if you're an ERP, it's around five percent. Yeah, okay, yeah. All right, so it's growing at twice the rate of the market. So the maximum piece, which is an IBM acquisition, is part of the IBM strategy, IBM tries to find growth areas, bring them in, blue wash them, and then off and running. So that's a good move. $2 billion market growing at eight or nine percent a year. And what kind of potential does it have here? Do you see it continuing that kind of growth? Yes, because the, if you look at the CEOs or executive suites metrics, return on assets is a big metric for those people. And to manage that, you need an enterprise asset management system. And one that's global, let's just go get some more. You may ask the question, if I can, about dynamics, what I see. Do I see something a little interesting?  There is some dynamic behavior going on among some of the smaller suppliers. There's one that particularly attracts our attention. It's totally SaaS-based. It's called Dude Solutions. Dude? Dude. Like a dude? Yes, exactly like dude. So they have two applications, Facilities Dude and School Dude. And it's all SaaS, and they, with School Dude is the one that's really successful. And they focus in on schools, basically high schools for the most part. And so it's targeted at that particular segment of the market. It's a market that was unserved. So they've been able to grow the market by entering that area and would totally assess solutions. Really? So they're tracking school assets, like what, steam boilers? Well, yeah, you have that kind of stuff too, but you also have things like equipment. Equipment. Computers. Computers, it goes on and on and on. It's particularly nowadays. There's a surprising lot of assets in your average school. All right, Ralph, great stuff. Really good analysis. We'd love to go deep, John, with the... He loves to talk to the analysts. I'm just sitting here, just minding my own time. My final question for you is, as an analyst, you see things come and go. You've seen IBM make some moves. For the folks out there following IBM, they're seeing really some good vibe here. What is, why is the vibe so positive in your personal opinion? Well, particularly at this conference, a couple of dynamic segments of the market, software market, are being addressed by IBM. You know, one is SaaS and Cloud, very dynamic segment of the market. I mean, in the EAM space, among the smaller suppliers, we've seen over the past six years, remember I said I tracked 160, we've seen about 60 drop out of the market because there are on-premise smaller suppliers, and we've seen about 50 new ones come on board with the SaaS business model. Now, these are all smaller companies, but it's just a data point on how dynamic this market is in terms of adopting SaaS and Cloud, and IBM's right in the middle. It's table stakes now, and if you can't hang with the SaaS, you're out, right? Yeah, I agree. And speed is key. Another thing, speed is just, like the speed of value is another differentiator. Well, time to benefit is much quicker with a Cloud SaaS type approach. All right, Ralph, thanks for coming on theCUBE. We really appreciate it. This is SiliconANGLE's exclusive coverage of IBM Pulse, live in Las Vegas. I'm John Furrier, Dave Vellante. We'll be right back.


So, let's take a look at a more efficient way of performing a factorization. And so, we saw that you could factor n by using a difference of squares. And in general, one way we could find that was by finding two numbers, a and b, different numbers, whose squares were congruent mod n. Unfortunately, this in general takes too much time to be useful. It relies too much on happily picking the correct sets of numbers. And so, a more productive approach is to create such numbers whose squares are congruent mod n. And we'll approach that in the following way. We'll introduce the following term. A number is said to be b smooth. If all of its prime factors are less than or equal to whatever the number b is. And we can choose b to be arbitrary. And so, what this suggests is the following approach to factorization. What we might do is we might find some sequence of numbers and not necessarily consecutive numbers, but these are any set of numbers whose squares are all b smooth mod n. Now, when I take some of these numbers and multiply them together, because all of these numbers are formed by primes which are less than or equal to b, then when I multiply some of them together, I also end up with a number that's b smooth. And if I'm clever enough enough I have the right sequence of numbers, I have a chance of forming a product of some of these numbers, again not necessarily all of them, but some of these numbers whose square is a perfect square. So, for example, let's say I want to factor the numbers 63,787. And because I'm human, I'm going to choose to focus on values whose perfect squares are 19 smooth, which is to say all of the prime factors are 19 or less. And this does require the most amount of work here, so I have to kind of go through the numbers. And I find, for example, 439 squared congruent to 1360, which if I factor 2, 4, 5, and 17, likewise 441 squared, 3120 will factor as a product of primes that are less than 19. And I can find a few others that also satisfy this particular requirement. And the value 19 here I'll emphasize is really limited only by how much I want to work with. Again, because I'm human I'm going to limit myself to 19 smooth numbers, but if I were a computer and or if I were a computer program, this number could be as large as the largest prime that I want to work with. And so maybe I'll find another and at some point I'll decide I want to stop. And so I take a look at my list and I want to find a product of some of these numbers here that will give me a perfect square over here. And for right now I'll just make the observation that if I take the first number here, the fourth number, and the last number, let's get rid of all the rest of those. If I multiply these together, notice what's going to happen. Well there's my first number, 2 to the fourth 517, there's my second 2 to the third 7 squared 17, and there's my last 2 to the 11 times 5, and after all the dust settles, all of my prime factors have even powers, which means that the right hand side is a perfect square. The left hand side is a perfect square because it's a product of perfect squares. The right hand side is a perfect square because it is a product of primes raised even powers, and after all the dust settles, I find that I have produced the congruent 7270 squared congruent to 44942 squared. And then I can use my quadratic factorization method and my greatest common divisor of the difference between the two roots and the number I want to factor is going to be potentially one of the factors of the number, and that works out to be 227. And I can find the other factor 281. Well the difficulty with this approach is that I have to stare at this list of numbers and try to figure out how to put them together to form a perfect square. Fortunately, that's not actually that difficult if we do a little bit of algebra. So rather than rely on our keen powers of observation squirrel, we can do some algebra instead. Let's see, so what can we do here? All right, well so here's our idea here. Suppose I want to include some number of factors of this, some number of factors of this, some number of factors of this, some number of factors of this, some number of factors of this, and so on. So I want to include this number possibly more than once, so in practice it's not worth including it more than once, but if I were to do that, then what I can do is I can look at the number of primes in the factorization of the product. So for example, the number of twos in the product, well if I have x1 factors of this, I get four twos for each of those factors, so there's four x1 twos. I have x2 factors of this, and each of those contribute four twos, so again there's four x2 more twos. There's x3 factors of this, that doesn't give us any twos. There's x4 factors of this, that gives us three per factor, so there's three x4. There's eight per factor of this, and eleven per factor of this. So the number of twos in that product of x1 of these, x2 of these, x3 of these, and so on, the number of twos in that product is going to be given by that sum. Likewise, I can find the number of threes in that product. The ones that contribute to threes, the x2 contributes a three. The x3 contributes a three. And the x5 contributes a three. So there's my number of threes, and I can do the same thing for the other prime factors. Now here's why it's important that we work with b smooth numbers, because if I didn't have a b smooth numbers, I'd have two threes, five sevens, and potentially any prime up to whatever the largest prime I have. By focusing only on the b smooth numbers, I limit the number of, well these are equations, and I can do a little bit of algebra. Now, since our goal is to produce a perfect square, what I want to make sure of is that all of these numbers are even numbers. And I can work about two, because for two reasons. One, I only care whether these numbers are even, and so it doesn't make a difference to me whether this number is four, eight, 32, or 724. What matters is that it's not one, seven, 35, and so on. So I want to make sure that all of these are evens. Also, again, we're not going to ever take more than one factor of any of these numbers. So we might take zero factors, we might take one factor, but as far as this problem is concerned, no numbers besides zero or one exist, which says that it's just as easy to work on two. And so that system reduces considerably because things like eight x five, well that's a number congruent to zero mod two, and that's going to drop out entirely. And so I get a much nicer system of congruences. And I can apply some linear algebra to this system. I don't have to, it's just a lot easier if I do. Realistically, we are working with a system of eight unknown, so it's probably easy to apply linear algebra here. We have a system of congruences looking something like this. And we have a coefficient matrix looking something like this. And let's do a little bit of simplification. Now what's going to make our life much, much, much, much easier is that we're working mod two, which means that when I add one to one, I get zero. And everything else is just going to be what I would expect it to be. So I might reorder the rows a little bit. I'll move the seventh row up to the top. I'll swap those two rows around. And then I'll use this first row to clear everything below it. I'll add this to the third row. Remember, one plus one mod two is going to be zero. So I can add row one to row three, wipe those things out. And that column is all set. So now I'll move on to the second row. Now I'll take row two. I'll keep that in place. I'll add it to row three and row five. And I'll eliminate those. And again, my third row, I like that in place. I'm going to clear the third column. I'm going to take row three, add it to row four. Here's my row three, add it to row four. That's gone. Next row gone. Next row gone. And let's see. Now let's clear the fourth column. I'll clear those out, adding the numbers up. And last column wipes everything out. All right, now I'll convert this back into a system of equations. So what do I have? X one plus X four congruent to zero. That's our first row. X two, three, and five, congruent to zero. Three, four, five, and six. Four, five, six, and five, congruent to zero. And I can solve this using back substitution. So X five definitely has to be equal to zero. X four, if I make X four and X, if I make X four is zero, X five being zero, X six has to be zero. All of these being zero, X three has to be zero, both of these zero, X one has to be zero, X four zero, X one zero. If I make X four equal to zero, everything is zero, which doesn't give me any solution at all. It says take no factors of anything and that's not interesting. Here I'll take X four, kind of equal to one. That tells me that X six, if X four is one, X six also has to be one. And let's see, so I have X four, five, and six, and what do I have to X, X three? So four is one, five is zero, six is one. So that's one, one, X three has to be zero. X two, X three is zero, X five is zero, X two also has to be zero, if the congruence is going to be satisfied. And finally X one is going to be zero. And so remember what that tells me is that I should include the first factor, the fourth factor, and the sixth factor, which is what conclusion we came to earlier by just staring at the numbers. Here we did some linear algebra that made our lives a lot easier.