To episode 20, this episode is on applications of exponential and logarithmic equations. And this is, by the way, math 1050, excuse me, college algebra. I'm Dennis Allison, and I teach in the mathematics department at Utah Valley State College. Let's go to the list of objectives for this episode. First of all, we'd like to continue the discussion on logarithmic scales that we introduced at the end of episode 19. So we'd like to talk about the Richter scale and decibel level of sound. Then we'll move to exponential growth, radioactive decay, and Newton's law of cooling. Those are all equations that involve exponents and logarithms. OK, first of all, logarithmic scales. At the end of episode 19, we talked about the pH of a solution. And we were saying how numbers that are generally either very, very close together or numbers that are very, very spread out on the number line can be shown closer together if you take their logarithms. Now, let me give you an example. Take, for example, the Richter scale. Now, what would you be measuring if you measured it with a Richter scale? Earthquakes. Earthquakes, exactly. Now, earthquakes can vary in intensity, and sometimes they can be millions, even billions, of times more intense than other earthquakes, which are relatively minor tremors. So the question is, how do you describe the intensity of an earthquake when it can be billions of times more intense than some other earthquake? So here's what's generally done. If you go to the green board, suppose we say s is the minimum intensity of an earthquake that could be measured using technology. So this is the minimum intensity. And suppose there is an earthquake that occurs, and its intensity is measured to be i. So this is, let's say, the actual intensity of an earthquake that is measured on some occasion. So what we do is take the ratio i over s. Now, what we were just saying is sometimes the intensity of an earthquake can be millions or perhaps billions of times stronger than the minimum earthquake. So this ratio could be a million or even a billion. So what is generally done is you take the logarithm of that, which makes the number considerably smaller.  And this is the Richter scale measurement that you would normally hear in the press. So for example, what if we had an earthquake that was 1 million times greater than s? So i would be 1 million times s. If I substitute into that formula, look what the magnitude turns out to be. The logarithm would be the log of the ratio of 1 million s over s. Now just make sure I've explained that clearly. s represents the minimum intensity that could be detected by the equipment. And the earthquake is actually a million times greater than that. Well, this reduces to be the log of 1 million. And so a logarithm is an exponent. And so the question is, the value of this logarithm would be the exponent that you'd put on 10, base 10, to get a million. And I think that turns out to be 6. So if the Richter scale measurement is a 6, if you have, let's say, a 6.0 earthquake, then that means the earthquake was a million times greater than the minimum intensity that could be measured by the equipment. And in fact, earthquakes can be greater than that. Typical earthquakes that I've heard of recently have been in the scale of 3.4 to maybe 4.4, something like that. So they were less than a million times greater. But that does sound very intense, doesn't it? If the intensity were 3, if the Richter scale measurement were 3, it'd be 1,000 times greater than the minimum. And if the intensity or the Richter scale number were 4, it would be 10,000 times greater. And earthquakes have actually been detected up to about 8.9 for the Richter scale measurement. So that's up close to 1 billion times greater. OK, let me ask you a question about this then. Suppose we have, let's see, I better write my formula down up here at the top. m is equal to the log of i over s. So suppose we measure an earthquake and its intensity turns out to be 855,000 times s times that minimum intensity. So what would the Richter scale number for this be? Well, if I substitute that in for i, just like I did in the previous problem, I would get the logarithm of 855,000 times s all over s. But the only difficulty this time is we're going to have to use a calculator to determine this number because I don't think we're going to end up with something quite as easily evaluated as the log of 1 million was a moment ago. So this would be the log of 855,000 because the s's have canceled out back here. And I see everybody's got the calculators out there. Stephen, what did you get for that value? 5.93. A 5.93 is the magnitude. You notice this number is almost 6. And you see if it were 6, it would have been 1 million exactly. This is a little bit under that. So we're going to get a number a little under 6. But if the magnitude had been 5, that would have been the magnitude when the intensity was 100,000 since 10 to the fifth power is 100,000. So this would be somewhere between 5 and 6, closer to 6 because this number is closer to a million. OK, so that would be the Richter scale value. So the next time you hear of an earthquake and they give you the intensity as the Richter scale magnitude, this is how you determine how it compares with the minimum intensity that you could have detected at all. Now, there's a similar situation for measuring the decibel level of sound. And the formula for decibel level, if we go to the next graphic, I think we can see it on here. This is a summary of actually the three logarithmic scales that we've talked about in the previous episode in today. In fact, let's just go up to the top. There's our pH formula for a solution. The pH is equal to the negative log of the hydrogen ion concentration. And we said that if the pH were less than 7, it would be a CDK. And if the pH were greater than 7, it said to be basic. Then there's the Richter scale magnitude, M. M is the log of i over s. We just talked about that one. And now we come to the decibel level of sound. And the decibel level, we'll call it, actually, it should be db, not just b, but the decibel level db of sound is, and that should be 10 times the log of i over i0. So there are a couple typos there, but let me just correct that formula here on the green screen. So the decibel level, db, is equal to 10 times the log of i over i0. So there was a d omitted, I think, on that graphic. And there was a 10 omitted in the formula. But if you look on the website, I think you'll see this typed in in this form. Well, once again, if you're measuring sound, i sub 0 represents the minimum intensity of sound that can be detected. In fact, that would be so soft that you probably wouldn't be able to hear it. But it could be measured by an instrument. So i sub 0 represents the minimum intensity of a sound that could be detected. Now, you know, this value was actually determined some time ago, and modern electronic equipment can detect sounds even more faint than this, but they still use this basic number here. And i represents the actual intensity of the sound that you're measuring.  That would be the intensity of the sound that you hear. And that is measured numerically using electronic instruments. So then what you do is you take the ratio of i over i naught. So i would be some multiple of i naught. You cancel off the i naughts and take the logarithm. And then you multiply by 10. The reason you multiply by 10 now is because these numbers tend to be rather close together. So 10 helps to sort of magnify the numbers and stretch them out a little bit. So suppose we have a sound whose intensity turns out to be 100 times the minimum intensity that could be detected. OK, now that would still actually be a very soft sound. And so the decibel level of this sound would be 10 times the log of, let's see, i over i naught. That'll be 100 i naught over i naught, or i sub 0. And so this would be 10 times the log of 100 because the i naughts cancel off. Now what is the log of 100? It's 2, right. This is base 10. And 10 to the second power is 100. And the logarithm is an exponent. So this is actually 10 times 2. So the decibel level turns out to be 20. If I hadn't multiplied by 10, then obviously the answer would have just been 2. And if you don't multiply by 10, these numbers tend to be rather close together. So the purpose of the 10 in front is merely to kind of magnify them a bit and spread them out so they're a little bit further apart. So this turns out to be 20 decibel units for its intensity. OK, so those are the other two logarithmic scales I wanted to discuss that we had to move over from the previous episode, the Richter scale and the decibel level of sound. Let's now move to a totally different topic here and look at applications of exponential equations and logarithms to real life problems that we haven't really gotten to consider in much detail up until now. Let's go to the first graphic. This is the law of exponential growth. And it says the population n of t at time t is given by the formula n of t equals n sub 0 e to the rt power, where n sub 0 is the initial population and r is the rate of growth. Now this formula should sort of sound a bit familiar. We talked about something like this earlier when we were discussing compound interest. And who remembers what type of compounding used an exponential equation, something like this? Anybody recall? Continuous. It was continuous compounding. Very good. Yeah, so rather than having money compounded daily or money compounded in a bank account monthly or even annually, the money was being compounded continuously. That is, theoretically, every moment you wait to withdraw money from your account, you actually have a little bit more money in that account. So it's being compounded continuously. Well, populations grow in the same way. And I think we looked at an example or two of population growth as examples of continuous compounding. And what we mean by that is people are being added to the population. People are leaving the population. People die. People might move away from the city and change the population. And these sorts of things can happen during the day, at night, whatever. People are born. People die and so forth. So the population tends to be considered to change in a continuous manner. So it's not surprising that we would use an exponential function, just as we did for continuous compounding for money to represent continuous compounding for a population. Now, the difference is, if you go to the green screen, what I wrote the formula for continuously compounded money, we wrote a equals p, e to the rt power. p was the initial principal, the amount of money that you put into the account. And a was the amount in the account after t periods, or t intervals of time. And r was the rate of growth. This time, I'm writing the formula n of t equals n sub 0, e to the rt power. You notice how similar they look. p was the initial principal, n sub 0 is the initial population when you begin to take your measurements. r is the rate of growth, t is the number of years, and n of t will be the population after t years. For example, look what happens if I substitute in a 0 right here, n at 0. I would get n sub 0, e to the r times 0 power. Well, that's going to be e to the 0 power, which is 1. So this ends up being n sub 0. So the population at time 0 is n sub 0. Yeah, so that's exactly what we would have expected. Now, given more information, we can make predictions on the population at other times. Let's go to the first example. Let's go to the next graphic. In this example, it says the population of a nation is 4,200,000 and grows exponentially at an annual rate of 1.75%. What should the population be in eight years? Now, if I'm not mistaken back in an earlier episode for this section, we did a problem very much like this. So this is sort of a repeat of an earlier example. What should be the population after eight years? But then there's a second question that we've never done before, and that is, how long should it take to reach a population of 6 million people? Well, let's try solving both of those here on the green screen. See, what do we know? We know that the initial population, n sub 0, was 4.2 million. And so I think when I go to substitute this into my formula, I'll just put in 4.2 because that'll make it look a little shorter. And I'll remember that I'm computing these things in millions. Then we knew that the annual rate of growth was 1.75%, 1.75%. What would that be as a decimal? 0. what? 1.75%. 0.0175? 0.0175, thank you very much, exactly. So in other words, rather than putting in 1.75 for r, that's the percentage, we have to convert it to a decimal to substitute that in. So substituting those into my formula, we have the n of t equals 4.2 million times e to the 0.0175 times t power. Now you might say, Dennis, that's a very small exponent. Look at that small decimal you have there. This can't grow very rapidly. Well, let's see. The question in part a was to find out what's the population after eight years? So because this is the population in year t equals zero, I'll substitute in an eight, and n at eight is 4.2 e to the 0.0175 times eight power, times eight power. Now on my calculator, here's what I would do. If I were using my ti82, I would enter 4.2, and then I would press the button e to the x power, and then I would enter open parentheses, 0.0175 times eight closed parentheses, and then I would push an equal sign. By the way, when you close parentheses, what you'll see on the screen is a total of what's computed in the parentheses. So you have to hit the equal sign to go back and enter the, or to compute the entire amount. Has anybody computed that? I thought maybe some of you had computed that at your seat, so I didn't ask you to.  So if in the year t equals zero, the population is 4.2 million, let's say that if the population right now is 4.2 million, then in eight years, let's say eight years from now, it would be 4.83 million. So it's increased by about 600,000, a little over 600,000. That's because the rate of increase here is relatively low. Okay, now the second question, I'm gonna leave that formula up there and go to question b, was when will the population be 6 million? Well, we've never been able to solve a problem like this before. I think part a, we had actually worked a problem like that back in episode 18 or 19, something like that. But now what do we do if we wanna find out when is the population gonna be 6 million? Well, that means I want this to be 6 million right here, the n of t. Can we go to the green screen? Okay, so the question is, when will the population be 6 million? So I'm gonna put a six for the n of t, not 6 million, cause we didn't make it 4.2 million either. We're just going with the coefficients there. So six equals 4.2 times e to the 0.0175 t power. Now, you know, in order to solve for t, I need to get the t out of the exponent. That's probably gonna mean we'll use logarithms here, but we have this coefficient of 4.2, so I think I'll divide that out first. Six divided by 4.2 equals e to the 0.0175 t power. Okay, now, to remove an exponent, I'll need to take a log on both sides. Now, I could take log base 10, but what would be a more appropriate logarithm based to use in this situation? The natural log. Natural logarithm, because we have a base e here. You know, someone may say, Dennis, should you cancel off a six, because six will divide into 4.2 and six will divide into the six, obviously. Not really necessary, you can reduce it if you want, but I'm not sure what you're gonna do if you want, but I don't think that's really gonna save us much time, so I think I'll just leave it in that form. And I'll take the natural log of six over 4.2 and that's equal to the natural log of e to the 0.0175 t power. Now, this first expression I could write as the natural log of six minus the natural log of 4.2. That's using the second property of the four basic laws of logarithms. And on the other side, if I bring the exponent out in front, I have 0.0175 t out in front of the natural log of e. What is the natural log of e, by the way? One. It's one, yeah. So this is just a one right here. So what we're down to is the difference of these logarithms is equal to this decimal times t. So t is equal to the natural log of six minus the natural log of 4.2 all over 0.0175. And that is approximately, let's see, has anybody computed that? Okay, let me just compute it right here. What I get is, I'll work it over here on the side of the screen, the natural log of six minus the natural log of 4.2. I'll enter that and then I'll divide it by 0.0175. And I get about 20.4 rounding up 20.4. Now that would be in years. And so it's gonna take the population a little over 20 years to get up to six million people. You remember just a moment ago in part a, it took eight years to go from 4.2 to 4.83. Whoops, 4.83. And it takes about 20 years to go from 4.2 up to six million people. So that sounds about right under these conditions that it would take about 20 years. Okay, that's a population problem. Let's see how much time we have. I think I'll do one more example of a population problem. This time rather than the population of a city, let's say we make this a biology problem. And what if I have a sealed culture? So let me just draw something like this on the screen. Suppose we have like a Petri dish and there's a certain amount of bacteria that's growing inside the Petri dish. And let's say we, since we can't really count the bacteria one by one, I mean, they're just too small. What we do is we look at the population in terms of area, how much area is covered by the bacterium. So let's say that initially time t equals zero. Let's say the population was estimated to be 3,000 units of bacteria. Now they may not actually be 3,000 bacteria, but maybe 3,000 square units of bacteria in a small grid. And if that's the initial population, let's say that after two days, I'll call this T sub two, what if the population has grown to 10,000? Now, I mean, I'm not a biologist, so this may be too short of a time, too much of a time for a population to go from 3,000 to 10,000. But the question might be, what would be the population of bacteria after, let's say now that was two days going from 3,000 to 10,000. So let's say what would be the population after five days? What's the population after five days? Well, let's see, we're assuming the law of natural exponential growth. So that means I'm assuming that the number of bacteria is equal to m sub zero times e to the r t power. And we know what t sub zero is, it's 3,000. So n of t is equal to 3,000 times e to the r times t power. Okay, now we know that after two days, the population becomes 10,000. So if I put in a 10,000 on the left, what will I need to substitute in on the right? If the population's 10,000 after two days, how would I change what I've written on the right hand side? I think I'll just put in a two for the t, because this is after two days. So this would be 3,000 times e to the r times two power. So, let's see, in this equation, it looks like we could solve for r. And to solve for r, I'm gonna divide by 3,000. So 10,000 over 3,000 is equal to e to the two r power. I can cancel off the thousands and just say this is 10 thirds equals e to the two r power. And if I take a natural log on both sides, that says the natural log of 10 thirds is equal to the natural log of e to the two r. Can anyone tell me right off hand what is the natural log of e to the two r power? It's two r, exactly, that would be two r. And therefore r is equal to, can I squeeze, I think I can squeeze this in on the screen, r is equal to one half of the natural log of 10 thirds. Now the reason I'm writing it that way is because I wanna go back and substitute in for r up here in my original formula. And this says n of t equals, let's say n naught was zero, was 3,000 rather. So 3,000 times e to the one half ln of 10 thirds times t. Well if I take r times, here's r times t, that's gonna be t over two ln 10 thirds. Now the reason I haven't evaluated the natural log, like I haven't evaluated the natural log down here, is because I can actually reduce this expression. Look what happens now. I'll try to write this a little larger so you can see it better. n of t is 3,000 times e to the natural log of 10 thirds and then outside I'm gonna put t over two. Is it clear what I'm doing there? I'm taking a product in the exponent and I'm putting one factor inside on the e and I'm putting one factor outside on the t over two as t over two. And so e raised to this power, natural log power, to the t over two power is e to the product. Now I can reduce that to be 3,000 times, what is e to the natural log of 10 thirds? That's actually property four from our four laws of logarithms. If you take base e and raise it to a log base e of 10 thirds, you get 10 thirds. To the t over two power. So here's my formula for the population of bacteria at time t. It's the initial population times 10 thirds. It's no longer base e but 10 thirds to the t over two power. And I was able to bring in my natural logarithm on the base e to make that base change. Now the question we asked was what was the population after five days? So I'll substitute in a five here and I get 3,000 times 10 thirds to the five halves power. And let me just compute that and see what we get here. Let's see, if I put my calculator in the middle, will we be able to zoom in on that? Let's just try zooming in while I, yeah, here we go. Okay, so I'm gonna try computing 3,000 times the quantity 10 divided by three, close parentheses, because see, I want that entire fraction to be raised to the five halves power, raised to the five halves, I'll call it 2.5 to the 2.5 power, enter. And what we get here is 60,858. So we'll say it's roughly 61,000 approximately, 61,000. The reason I'm rounding off into such a small accuracy is because we can't really count the bacteria individually. So I'm just gonna say that the population's grown from 3,000 to roughly 61,000 as a rough estimate for that. Let's see if that makes sense. You notice in the first two days, the population more than tripled. So in the next two days, you'd assume that it would more than triple again. So when you get to, this was t equals zero, that was the initial time, this was after two days. So after four days, it should more than triple, it should be well over 30,000. And then in one more day, it should be up to maybe 61,000. So that sounds about right. Okay, let's go to a different application. And this one has to do with radioactive decay. Let's go to the next graphic. Okay, this is known as the law of exponential decay. It's almost identical to the law of exponential growth. It says the mass of a radioactive substance is given by the formula m of t, m for mass, m of t equals m naught e to the negative r t power. The difference is we have a negative in the exponent. And I've changed the name of the function from n to m, so that's a small change. And the reason there's a negative in the exponent is because if we go to the green screen here, you see when you have a radioactive substance, let's say that at time zero, you have this much of a radioactive substance. But over time, the radioactivity drops off. And the radioactivity gets smaller and smaller and smaller and it approaches, but theoretically, it never reaches zero. And let's say that the amount of radioactive material here was, I'll call it m sub zero for the amount of mass at time zero. And at some point, it will decay to exactly half of that right about here. This would be one half m sub zero. This is the time axis. And at some time, the amount of radioactive material will be only half of what it was initially. So this distance right here is referred to as the half-life. Now you might say, Dennis, what happens to the radioactive material? Why does it decay? Well, you see in a radioactive substance like uranium or plutonium or many other radioactive materials, what happens is these atoms that are radioactive, when they decay, what they give off are these subatomic particles, like alpha and beta particles and so forth. I'm not really a nuclear physicist to explain this probably very well. But what is left behind is a stable element. And so the radioactive material doesn't just disappear, it just becomes stable. But there's still some other radioactive atoms that are still decaying. And so over time, there become fewer and fewer and fewer of them. And the amount of time it takes for half of the material to become stable is called the half-life. Okay, so with that idea, let's go back to the Greenstein, let me just point out one more thing. With that idea, you see what happens is this curve is an exponential function, but it's decreasing rather than increasing. So this function is expressed as m of t equals m sub zero, that's a zero, e to the negative r t, and there's a negative because the function is decreasing. For population growth, the function is increasing and going up. But we have a function that's decreasing and approaching zero. Okay, if we go back to that graphic, we have a problem on that graphic that we'd like to solve. And the problem goes like this. It says a 300 milligram sample of polonium 224 has a half-life of 140 days. So the question is, how much remains after one year? Well, let me just ask the class a question about this. We have 300 milligrams to begin with and the half-life is 140 days. So after 140 days, how much radioactive polonium 240 should there be after 140 days? 150 milligrams. 150 milligrams, right, because half of it would have decayed and half of it is still radioactive. Now in another 140 days, half of that will decay and you'll drop from 150 to 75. And in another 140 days, half of the 75 will become stable and you'll be down to half of 75, which is 37.5. So you see how this keeps reducing by half every 140 days. Well, the question is, how much remains after one year? Okay, now a student might say, well Dennis couldn't you just keep reducing it every 140 days until you get to a year? But the problem is, you may not hit exactly on a year. You may go from just before one year to just after one year. So it's difficult to say how much there will be in the middle of an interval like that. So if we go to the green screen, I think we can solve this algebraically. Our formula says M of T equals M sub zero E to the negative RT. So when we talk about the law of radioactive decay, you have to remember to put a negative up there. And if you're talking about population growth, you put a positive in the exponent. Okay, now our initial amount was 300 milligrams. So I'll put a 300 right there, E to the negative RT. And we know that the half life is 140 days. Let me just make a note of that over here. Half life, 140 days. I didn't write half life very well. I hope you can read that, the half life. Well, that's gonna give me yet another value I can plug in here. Because what that means is, when T is equal to 140 days, then the mass is gonna be 150 milligrams. This was in days right here. So if I substitute 150 for the mass, I'll have to put in 140 for T. 300 E to the negative R times 140. I'll put parentheses around the negative R there. Well, you notice there's only one variable left here, and that's R. So by knowing the half life, and by knowing the initial mass, I'm able to calculate R. So that's what I wanna do next, is to solve for R. And to solve for R, the first thing I'll do is divide by 300, and that gives me a one-half, equals E to the negative 140 R. I wanna hit and multiply it out the exponent. But when the variable's in the exponent, how do I solve for it? Well, I've gotta get it on the ground, and that means use logarithms. So I think I'll take a natural log on both sides. The natural log of a half equals the natural log of E to the negative 140 R.  And as we said before, the natural log of E is one, so this is negative 140 R. So ln of one-half equals negative 140 R. Solving for R, I get negative one over 140 times ln of one-half. Okay, you might say, well, that's great Dennis. How are you gonna figure out how much of this radioactive material is left after a year? Well, what I have to do is get my formula precise. So I'm gonna take this R and substitute it right back up there. And this tells me that M of T is equal to 300 times E to the negative R power. Let's see, a negative R, R's already negative. Two negatives are gonna cancel. And that's gonna be one over 140 times the natural log of one-half times T. Now that looks really messy, doesn't it? But because I have a logarithm in the exponent, I can reduce this. I'm gonna write this as 300 times E to the ln of one-half. You notice I'm putting the log and the base E together. And what's left outside is gonna be the one over 140 and the T. So I'll just call it T over 140. What is E to the natural log of one-half power going to be? One-half. Is one-half, very good. So this tells me that M of T is equal to 300 times one-half to the T over 140. This is my formula for the mass after time T. Now you see it started off looking like this expression up here. And it ends up looking like a different exponential expression with a base one-half. You say how did base E become one-half? Well, what we did was we had a natural log in the exponent and I was able to change the base because of that, Susan changed that for us. Okay, so the question was, what is gonna be the mass that's radioactive, the radioactive material after one year? Well, let me just erase some of the things in the middle and I'll use the formula here at the bottom to calculate that. Are there any questions about this before I erase any of that? Anyone here in the classroom? Okay, if not, let me just take out this middle portion here. And I think I'll move my formula up here to the top to kind of get it out of the way. So M of T is 300 times one-half to the T over 140 power. That's the formula that we've created. And we wanna find out how much is left after one year? Can anyone tell me what I would do with this to figure that out? How much is left after one year? What would T be? One year? Well, except we were working this in days. So we can't plug in one, it'll think that means one day. 360. 365. 365. So I'm gonna calculate M at 365. Yeah, I think David had a good point. It seems like you'd plug in one for one year, but our units on time are days. So this would be 300 times one-half to the 365 over 140 power. And that is, let's see, you know, I could reduce that exponent a little bit. Well, on a calculator, I don't see that it has that much effect. But if I divide by five, it looks like we're gonna get 73 over 28, 73 over 28. I don't know that it was worth the time to take to divide that out, because on a calculator, this is gonna be computed rather quickly anyway. If you can zoom in on my calculator, I'll lay it right over the top of this. And we had 300 times the quantity one-half, so I'll say 0.5, raised to the power of, and the quantity is 73 divided by 28 closed parentheses. And I get a zero, let's see, maybe I left out a multiplication sign. Let me try that again. 300 times the quantity 0.5 closed parentheses, raised to the power of 73 divided by 20. Oh, gotta, let me go back here and enter parentheses. Open parentheses, 73 divided by 28 closed parentheses equals, there we go, 49 point, oh, let's say about 49.2. So I think the problem was I didn't put in a multiplication sign after the 300. So this will be about 49.2 milligrams. Let's just compare that with what we could calculate quickly. You know, originally, when time t equals zero, we had three, when time t equals zero, we had 300 milligrams. And then when time, when t was 140, we were down to 150 milligrams, because half of it decayed. And after another 140, that puts us up at 280, this'll be 75 milligrams, because half of the 150 decays. And after another 140, that's gonna put us more than a year, 420, it's gonna be 37.5 milligrams. So we figure the answer should be between 75 and 37 and a half, and we got 49.2. So I think that seems perfectly reasonable for this problem. Okay, let's see, let's go to the next graphic and look at Newton's law of cooling. Okay, here is the third application of exponential equations and logarithms. And Newton's law of cooling refers to Isaac Newton. And here's generally what Isaac Newton says. He says, if an object, let's see, if t sub zero is the initial temperature of an object, let's say you're taking a baked potato out of the oven. So t sub zero is the temperature of the baked potato. And t sub r is the constant room temperature. So let's say the oven is in a room that's 75 degrees. So when you take the baked potato out, the potato begins to cool, but the room stays at a constant temperature. So the room temperature is t sub r. Then the difference between the temperature, capital T at little t of the object and the room temperature, t sub r, the difference between the object temperature and the room temperature is equal to the initial difference of temperatures, which is t sub zero minus t sub r, times e to the negative rt power. Now, this is another instance very similar to radioactive decay. I have a negative in the exponent because the object is approaching room temperature. So the difference is approaching zero. Let me see if I can explain this with a graph and we'll come back to that graphing in just a moment. Okay, here's the time axis. Here's the temperature axis. And let's say here's the room temperature, t sub r. That's what I call t sub r. So I'm gonna draw a little dotted line across there. And when I take the object out of the oven, let's say its temperature is way up here because it's very hot, we'll call it t sub zero. This is the initial difference, t sub zero minus t r. So that difference is t zero minus t r. However, the object begins to cool and we're assuming the room temperature never changes. And therefore the difference begins to decay, the difference in temperatures. And so at any given time, capital T of little t is the temperature of the object and this is always up here at t r. So the difference in those temperatures begins to decay and that difference approaches zero. So the way this is expressed is to say capital T at little t minus t sub r, that would be the difference between the cooling object and the room temperature is equal to the initial difference. Okay, this was the initial difference over here times e to the negative r t power. So this time I have differences that are decaying, not the actual temperature, but the differences are decaying and this formula will tell me what is the difference in temperatures at any given time. Now if I solve for the temperature at time t, I just need to add t sub r on the other side. And so this formula looks like this, where I put t sub r added on the other side. And if we go back to the graphic, you'll see the second formula is also expressed on that graphic. Can we go back, there we are. So the first formula I wrote says that the instantaneous difference between the temperatures is equal to the initial difference times e to the negative r t power. R expressed in another form, capital T at t equals t zero minus t r e to the negative r t plus the room temperature. Now this is a bit of an idealized problem because if you take a hot object like a baked potato and set it in the room, it actually does change the room temperature ever so slightly. So the room temperature doesn't stay constant. But if we assume this is a big room, so there's a lot of air that would have to be warmed up. And let's say the air conditioning's running and so the heat is being blown away and the room temperature stays constant, then under those conditions, Newton's law of cooling applies. Okay, so we have an example of this. The example says a cup of coffee with temperature 200 degrees Fahrenheit is placed in a 70 degree room. After 10 minutes, the coffee temperature is 150 degrees. Find the temperature five minutes later. Okay, well let's take our formula. So first let me express my formula up here. The room or the object temperature is the initial difference in temperatures times e to the negative RT plus TR. That was because I moved it over from the other side. And the only reason I'm writing it this way is because it allows me to isolate the temperature of the object. Now, the initial object temperature was 200 degrees. And the room temperature, which we're assuming remains constant, is 70 degrees. And we know that the temperature of the object after 10 minutes was 150 degrees. Okay, what this is gonna allow me to do is to calculate R. And once I calculate R, and I know all the other numbers in here, then I can calculate the temperature at any given time. Okay, well let's just assemble this information into our formula. The temperature of the object at time t is the initial difference. Well, let's see, what's the initial difference in temperatures? 130. 130, so I'll put 130 there. e to the negative RT plus, then the room temperature is 70. Okay, now, that's my basic formula, but I don't know the value of R. So now I'm gonna substitute in the 10. And after 10 minutes, the temperature is 150 degrees, and I'll put in a 10 for t. So I get 130 e to the negative R times 10 plus 70. You notice this is an exponential equation, and there's only one variable, R, so I should be able to solve for it. Let's see, I'll subtract off that 70, and this gives me 80 equals 130 e to the negative 10 R power. Well, as before, I'll divide by 130, and I get eight over 13 equals e to the negative 10 R power. I'll take a natural logarithm of both sides, and the natural log of eight over 13 equals negative 10 R. I'm leaving out some steps here. You remember the natural log of e to this power is the exponent. And what this tells me is that R is equal to negative 1 tenth ln eight over 13. Hey, once I know R, I go back up here and I substitute it in. So let's write our formula over here. T of little t is 130 times e to the, let's see, now that says negative R. Well, the negative of R is a positive 1 tenth. I'll say t over 10, because there's a t out here I have to multiply by, times ln of eight over 13. Well, just as I've done in previous examples, what I need to do is get the natural logarithm with the base e. So this is 130 e to the natural log of eight over 13 raised to the power of t over 10. Let me write that a little bit better there. That's over a 13. Okay, here's the most important step. What is e to the natural log of eight, of eight thirteenths? Eight thirteenths. Eight thirteenths, okay, that allows me to make this formula look almost pretty. I know, I'm exaggerating. But it certainly looks a lot better than it did before. Okay, this is our formula for temperature. The question was, what's the temperature five minutes later? Well, five minutes after 10 minutes, that's gonna be after 15 minutes. So after 15 minutes, the temperature will be, oh, you know what, I forgot to add on my 75. There was, oh, no, 70. I forgot to add my room temperature on the end of that. I left off that guy. So after 15 minutes, we get 130 times eight over 13 to the 15 over 10 power plus 70. Well, of course, that's the three halves power. Let's go to the calculator and see how much this is. I'll put my calculator in the middle of this and we'll turn it on also. And so I need to take 130 times the quantity eight divided by 13. And I need to raise it to the 1.5 power. You know, we had 15 tenths, that's 1.5 power. And then I need to add on 70. And the temperature of the cup of coffee should be 132.7. So yeah, we'll say 132.8. So this is approximately 132.8 degrees Fahrenheit. Okay, so theoretically, that's what we would determine the temperature to be. Now you might say, well, Dennis, is that actually the temperature of the cup of coffee? Well, you know, in the real world, when you put a cup of coffee in a room, the coffee cools down, but also the room heats up ever so slightly. This doesn't take into account the heating of the room as well as the cooling of the coffee. So if the room stays at constant temperature, this should be a fairly accurate answer. But in real circumstances, this may be off by a degree or two, something like that. So, but this is all idealized. We have one more example I'd like to look at before we run out of time. This one's sort of exciting. Murder, they said. Okay, here's the situation. You've found a body. We assume the original temperature was 98.6. But when you find the body, when the police find the body, the temperature is 90 degrees Fahrenheit. And you've arrived at 9 o'clock. That's when you took this 90-degree temperature. So what you do is take another reading a little later. The temperature 15 minutes later is 88.8 degrees Fahrenheit. And the room has stayed 70 degrees Fahrenheit. When did the murder take place? Okay, so in this case, I'm going to let T sub zero not be the initial temperature of the body, but the temperature when the temperature was first taken, that was 90 degrees. So this would be at 9 o'clock. And at 9 o'clock, the temperature of the body was 90. The room temperature was 70. And I'll have to put a 70 over here. Now, we know that 15 minutes later, let's say 15 minutes later, well, we know that the temperature 15 minutes later was 88.8. So I'll put an 88.8 here. And I'll put in 15 minutes for T. That'll be 20E to the negative 15T plus 70. So 15, whoops, times R. So 15 minutes later, the temperature is 88.8. Now, what this does is allows me to solve for R. I'll subtract off a 70 and get 18.8 equals 20E to the negative 15R. And then as you've seen me do before, I'll divide by the 20. The 0.94 equals E to the negative 15R. Taking a natural logarithm on both sides, the natural log of 0.94 is negative 15T. I've left out the step where I bring the exponent out in front. It's just negative 15T. 15R. I'm sorry, there should be R's there on both of those. So solving for R, that's going to be negative 115th ln 0.94. Okay, now, with that, I go back to my original formula up here and I substitute for R. And now I have a clear definition of the temperature of the body. So this says the temperature at time T is 20 times E to the T over 15 ln 0.94 plus 70. I've done a little manipulation here. I've multiplied the T into the numerator. So this becomes the temperature at time T is 20 times E to the ln 0.94 power raised to the T over 15 plus 70. Now, what does this reduce to be here? E to the natural log of 0.94. It becomes 0.94. 0.94, exactly. So this is 20 times 0.94 to the T over 15 power plus 70. Okay, this is our definition for the temperature of the body at time T. We want to know when is the temperature 98.6. So I'll put 98.6 here and I'll solve for T. T is going to be a negative value because we're talking about times prior to time T equals 0. That was 9 o'clock. So I'm going to solve this for T. 0.94 to the T over 15 power plus 70. Well, to solve for T, I have to use logarithms again. I'll subtract off the 70 and I get 28.6 and the next step is divide by the 20. So I get 1.43 equals 0.94 to the T over 15 power. I'm going to take a logarithm on both sides. So I have ln of 1.43 equals T over 15 times ln of 0.94. I need a little room so let me move over to this other side here and we'll just chop that portion off there. So T is going to be 15 ln 1.43 divided by ln 0.94. Now how much is that approximately? Well, let's do this on the calculator. So if you can zoom in on this, we're going to get 15 times the natural log of 1.43 divided by the natural log of 0.94 and that's negative 86. We'll say negative 87. How about negative 90? That's an hour and a half, negative 90. So what we get here is approximately negative 90 minutes. So that says the murder was committed about an hour and a half before 9 o'clock so we figure the murder was at 7.30 p.m. More or less. Of course there's room for error but that gives us a rough estimate. Next time you're watching Law and Order you'll know how they figure these things out. Hey, I'll see you next time. We're going to be reviewing for exam number three. That's an episode 21. And you'll be able to use a calculator on some portions of this next exam for problems like this. We'll talk about this in the next episode and I will see you then.


Over nine months into the Trump administration, the president has made some notable foreign policy moves in his time in office. Those moves were examined on Monday night at Central Lakes College in Brainerd. Clayton Castle has that story. It's almost been a year since the election of Donald Trump as the 45th president of the United States. On Monday night, the Gordon Rosenmeier board for state and local government examined the foreign policy of President Trump so far with guest speaker and foreign policy expert Tom Hansen. Hansen is a former U.S. Foreign Service officer with the State Department and said that North Korea is the number one issue facing America from a foreign policy standpoint. Obviously, we have to find a peaceful resolution to the North Korea issue. There's a lot of saber-rattling going on right now that might be for effect. I mean, it might be a prelude to negotiating. We just don't know. The idea of stirring things up before negotiating, Hansen said, is detailed in President Trump's book, The Art of the Deal. President Trump's negotiating tactics are also being used in his bilateral foreign policy approach, as opposed to President Obama's multilateral approach. The world has networks that the U.S. had key positions within these networks, whereas the Trump people are saying no, no. Everything should be bilateral when we engage in multilateral negotiations we lose. And of course, we've pulled out of Trans-Pacific Partnership, Paris Climate Agreement, we're questioning NAFTA. As for the greatest threat facing the United States in terms of foreign policy, Hansen says it's the growing rhetoric surrounding nuclear war. If ever there should be a nuclear war, of course, ever since the nuclear genie came out of the bottle, that is ultimately the number one threat. Tom Hansen also presented in Brainerd this time last year, but he has seen fundamental differences in the political landscape since then. He says that being aware of the changing political, economic, and technological landscape is what he wants the attendees to take away from the lecture. We're living in a time of some fundamental shifts, both in world geopolitics, in other words the relations among large countries and in the world economy, and that these shifts also involve the new technologies that are emerging. Reporting in Brainerd, Clayton Castle, Lakeland News. Hansen currently serves as diplomat in residence at the Alworth Institute for International Affairs at the University of Minnesota, Duluth. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


There has never in history been a greater need for a large anti-war movement. Things are escalating more and more rapidly between the US centralized power structure and the few remaining nations with the will and the means to stand against its demands for total obedience, namely China, Russia, and Iran. The world is becoming increasingly split between two groups of governments who are becoming increasingly hostile toward each other, and you don't have to be a historian to know it's probably a bad sign when that happens, especially in the age of nuclear weapons. The US State Department's Victoria Newland is now saying that the US is supporting Ukrainian strikes on Crimea, drawing sharp rebukes from Moscow with a stern reminder of the peninsula being a red line for the Kremlin, which will result in escalations if in the conflict have crossed. On Friday, Ukraine's President Zelensky told the press that Kiev is preparing a large offensive for the deoccupation of Crimea, which Moscow has considered a part of the Russian Federation since its annexation in 2014. As Anatoly Levin explained for Jacobin earlier this month, this exact scenario is currently the one most likely to lead to a sequence of escalations ending in nuclear war. In light of the aforementioned recent revelations, the opening paragraph of Levin's article is even more chilling to read now than it was when it came out a couple of weeks ago. Quote, The greatest threat of nuclear catastrophe that humanity has ever faced is now centered on the Crimean Peninsula. In recent months, the Ukrainian government and army have repeatedly vowed to reconquer this territory, which Russia seized and annexed in 2014. The Russian establishment and most ordinary Russians, for their part, believe that holding Crimea is vital to Russian identity and Russia's position as a great power. As a Russian liberal acquaintance and no admirer of Putin told me, in the last resort, America would use nuclear weapons to save Hawaii and Pearl Harbor, and if we have to, we should use them to save Crimea. End quote. And that's just Russia. The war in Ukraine is being used to escalate against all powers, not aligned with the US centralized alliance, with recent developments including drone attacks on an Iranian weapons factory, which reportedly arms Russian soldiers in Ukraine, and Chinese companies being sanctioned for backfill activities in support of Russia's defense sector, following US accusations that the Chinese government is preparing to arm Russia in the war. Israel's Prime Minister Benjamin Netanyahu has reportedly been holding multiple meetings with top military officials regarding potential future attacks on Iran to neutralize the alleged threat of Iran developing a nuclear arsenal, a threat that Netanyahu has personally been lying about for years. If you've been reading antiwar.com, and if you care about this stuff you probably should be, you've been seeing new articles about the latest imperial escalations against China on a near daily basis now. Sometimes they come out multiple times per day. This past Thursday, Dave DeKamp put out two completely separate news stories titled US plans to expand military presence in Taiwan, a move that risks provoking China, and Philippines in talks with US Australia to join South China Sea patrols. Taiwan and the South China Sea are two powder keg flashpoints where war could quickly erupt at any time in a number of different ways. If you know where to look for good updates on the behavior of the US centralized empire and you follow them from day to day, it's clear that things are accelerating toward a global conflict of unimaginable horror. As bad as things look right now, the future our current trajectory has us pointed toward is much, much, much worse. Empire apologists will frame this trajectory toward global disaster as an entirely one-sided affair, with bloody fanged tyrants trying to take over the world because they are evil and hate freedom, and the US centralized alliance either cast in the role of the poor widow victim or heroic defender of the weak and helpless depending on which generates more sympathy on that day. These people are lying. Any intellectually honest research into the West's aggressions and provocations against both Russia and China will show you that Russia and China are reacting defensively to the empire's campaign to secure US unipolar planetary hegemony. You might not agree with those reactions, but you cannot deny that they are reactions to a clear and deliberate aggressor. This is important to be clear on, because whenever you say that something must be done to try and avert an atomic age world war, you'll get empire apologists saying, well, go protest in Moscow and Beijing then, as though the US power alliance is some kind of passive witness to all this.  If World War III does indeed befall us, it will be because of choices that were made by the drivers of the Western Empire while ignoring off-ramp after off-ramp. This tendency to flip reality and frame the Western imperial power structure as the reactive force for peace against malevolent warmongers serves to help quash the emergence of a robust anti-war movement in the West, because if your own government is virtuous and innocent in a conflict, then there's no good reason to go protesting it. But that's exactly what urgently needs to happen because these people are driving us to our doom. In fact, it is fair to say that there has never in history been a time when the need to forcefully oppose the warmongering of our own Western governments was more urgent. The attacks on Vietnam and Iraq were horrific atrocities which unleashed unfathomable suffering upon our world, but they did not pose any major existential threat to the world as a whole. Vietnam and Iraq killed millions. We're talking about a conflict that can kill billions. Each of the World Wars was in turn the single worst thing that happened to our species as a whole up until that point in history. World War I was the worst thing that ever happened until World War II happened, and if World War III happens it will almost certainly make World War II look like a schoolyard tussle. This is because all of the major players in that conflict would be armed with nuclear weapons, and at some point some of them are going to be faced with strong incentives to use them. Once that happens, mutually assured destruction ceases to protect us from Armageddon and the mutual and destruction components come into play. None of this needs to happen. There is nothing written in adamantine which says the US must rule the world with an iron fist, no matter the cost and no matter the risk. There is nothing inscribed upon the fabric of reality which says nations can't simply coexist peacefully and collaborate toward the common good of all beings, can't turn away from our primitive impulses of domination and control, can't do anything but drift passively toward nuclear annihilation, all because a few imperialists in Washington convinced everyone to buy into the doctrine of unipolarism. But we're not going to turn away from this trajectory until the masses start using the power of our numbers to force a change from more mongering militarism and continual escalation toward diplomacy, deescalation, and détente. We need to start organizing against those who would steer our species into extinction and working to pry their hands away from the steering wheel if they refuse to turn away. We need to resist all efforts to cast inertia on this most sacred of all priorities, and we need to start moving now. We're all on a southbound bus to oblivion, and it's showing no signs of stopping.


Continue from where we left off so doing this neural network trainer web application in Flask it's doing something training to hidden layer a neural network that predicts this trying to predict this sinusoid waveform you can change your training set size from 1 to 150 is default we try 100 just adding more data points in there so hopefully it helps the training maybe a bit we get about to actually get a good result of this just pop it in to HHPT quickly the problem that I'm trying to figure out well that's mean to some of you it will be obvious why does that happen but with the same parameters when we retrain a we don't get the same results every time just a bit odd that is happening if you know let me know if you know it's not even something LLM would have said it's very poorly phrased isn't it yeah but you can see here that we train the same thing using the same parameters the input is the same it has zero noise level and we get very different results and yes if you're unchecked by Nikas.com please go do so you'll be supporting the project that way so one suggestion as to what could be going on this random initialization we tried setting up a set number of seed function but that utility is not present so we're getting an error out of it it seems like TensorFlow.js doesn't have a built-in method to set global random seed and it's using building JavaScript math random function for generating random numbers which does not support setting a seed this means that the randomness in TensorFlow is not deterministic if we need deterministic behavior we need to mock the random number generation function used in the code to return predictable value but that won't affect the randomness in the TensorFlow.js library okay essentially two chatbots talking to one another what else was suggested use non-stochastic optimizer this isn't always feasible since stochastic optimizers are typically more effective but in some cases using non-stochastic optimizer might yield more consistent results and how do i do that let's ask co-pilot the model optimizer cgd aren't we selecting it from yes if you're using sgd like that aren't we meant to be the stochastic gradient descent let me just do it by selecting sgd as you can tell they are still different every time you train and so sgd stochastic gradient descent is non-stochastic optimizer this will override well no we don't want to do it we can just select sgd as default so we don't need that and select it as default in the html keep in mind that this might not always be the best choice stochastic optimizer is our friend better well first it doesn't even work it does not work so when using non-stochastic optimizer sgd does seem to make a difference the training is still different every time very different every iteration and what else increase model robustness okay that might require a separate prompt increasing model robustness making model architecture more robust can reduce the impact of robustness yeah we select it let's see if a core pilot can help with anything i think it's suggesting to add more layers two more layers for each hidden layer the number of units in these layers is the same as the original hidden layers the activation function is also the same adding more layers or neurons can make your model more complex and might lead to overfitting well thanks for that do we really need a more complex averaging results train model several times and average the prediction from each run start with that quickly by the way while it's generating yes someone was posting this what are they called what about this game right so i had the apparently this statistical inference so it should you need to find what's that are related to statistical analysis a very fun game of course and who wouldn't who would be better at playing this game that gpt4 but really it couldn't couldn't actually do it it couldn't generate code that actually possible directions what okay so it's searching so generated python code that is supposed to take that image it's turning it into a grid matrix it generated a list of a theme a wards related i'm sure it can generate like a zillion of them that's what it's good at right well i mean the actual llm and then python could just do the automated search and i know a cool thing about it yeah i'm thinking adding something like that to the to the website where you could play these games and select the topic so for example select whatever statistic so it gives you you know this one and you have to find this word but muscle might also give you eg and analysis and then you have to find what's related to eg analysis how cool would that be but of course we won't be doing those manually i think some people do we want to have something automating the generation of those letter grids pretty sure it can do it yeah i'm pretty sure it's having trouble to actually solve this one to play this game it's trying to run stuff on its own server which is never successful i don't even know why you know why bother so i need to run it locally might try it sometime maybe next week you have to remind me just read this quickly because i've been talking too much okay this is nice but we actually need to improve the code so assuming we do not need to make this model more complicated than it already is what can we improve on the visualization front the css code is not doing super well sorry for that had to sneeze like it there is a it was not snooze a mute button it can be very helpful yeah so that's what it looks like when when they use the css that we currently have but kind of it makes things a bit it how do i say it politely ugly and let's format the document quickly you only have about 86 lines of html the rest is the description we're not currently doing anything in the in python however it would probably could store you know each run on the server do i want your runs so if someone's using the website um it will actually send all the parameters and the result and the result should be just one value like the minimum a training loss function output and then we'll need like an iteration number this will be a table that we store i don't know is it useful though let me know what you think and yes go check out bioniccares.com all the tools i develop eventually available on this website they all being deployed eventually will be helping out the project by visiting the website and because you'll be watching some ads so don't forget to turn off your ad blocker when you do so let's do one more iteration css can we improve the css script currently when the window is wide the controls are not displayed on the side of the two charts can we fix this here is the code that we currently have so it becomes and not very usable okay so it's adjusted the controllers today still don't appear on yeah once something doesn't work in the first prompt it probably would not work at all so on the narrow screen it's working as expected however on the wider screen the controls don't seem to fit on the side of the two charts yep and regenerating the whole css obviously not gonna read it all there's no way i will however test that and it's 120 lines it's reduced the number of lines no it's not right it's still generating because i copied it halfway through generation that's not cool okay what a nerve okay so it's on small window it's fine on larger window it still doesn't fit the max width for the controls on larger screens doesn't work on the narrow screen they will just appear top to bottom this one does not okay still doesn't work on the larger screen the controls do not appear on the side of the two charts can we use a different approach on the larger screen just make sure that the controls fit make the on again on the larger screen make the charts with not not to be wider than two-thirds of the screen let's regenerate this thing okay seven eighty seven eighty a main content space flex dot center okay let's go see it works on smaller screen larger screen that stuff meant to be in there why is it not working need to make sure this one is not too wide train there what's this button called i've got train button why why is it too wide who knows train button they controls are still not on the side of the charts something is still wrong can you check the whole css code yep yeah when it's starting to generate slowly like this it's a very not good sign well this way have something working so i don't know if it's yeah you always want to fix everything before you know the big release but we won't be able to fix everything yes on the screen like this theory when you go mobile it's 412 a pixel width it also doesn't seem to be correct on a smaller screen uh painful why so painful came two columns sounds good and what are we doing to the canvas this should apply to aim all cases is it and we're moving padding on larger screen we want to make sure two columns are side by side that didn't work did funny business okay what's going on there's something not flexing something not flexing there's a problem um legs direction comment for the main content with padding as well then on a smaller screen it doesn't actually work this is a mobile it still doesn't work can we regenerate the whole css code start fresh yeah this is the problem with neural nets is like it's highly non-deterministic like as in when it shouldn't be that non-deterministic it's me let me turn off the css for a sec yeah i'll just keep it in this view yeah now it's kind of training okay now it's uh converging before it was doing funny stuff and yes there is a lot of things we could improve mainly we're just trying to improve the css then canvas box shadow okay don't need that okay larger screens so we get two thirds for the charts and one third for the controls coming up to two there is it yeah remove the smaller screen configuration stuff yeah whatever it's a bit odd but uh converge the training sets nice yeah sometimes just restarting the training helps which is a bit odd yeah there's too much random stuff uh unit shade don't like but uh yeah neural nets are not going anywhere yeah we're doing too much to fix the styling of it and let's go back to this yeah no let's wait it should be a simple training exercise the model should be as simple as possible we are just trying to predict the sinusoid so especially with no noise in it the prediction result should be perfect and then later we want to see how increasing noise in the sinusoid will reduce the performance of the prediction algorithm below is the code that we currently have any suggestions uh welcome while it's generating yeah we have this other thing that we would like to to do it's a bit of a game that's how we learn what are these things called a search puzzle and we just call it the puzzle we'll have a good puzzle don't we in for text that the image is broken should have it somewhere dead break can you see random in it i don't see anything i think like the way it's uh you know what the image is being displayed the letters are being displayed probably makes a lot of difference maybe if the inside boxes might help aren't they normally inside boxes puzzles like this where is data or did it just hallucinate well anyway it started generating um fighting code that we actually use uh want to use to solve these puzzles but if we can solve a puzzle then we should be also be able to generate more of these puzzles yeah that image that's not really an info file this is the prompt to like a prompt one prompt two files we can actually monitor how many sessions we had with a specific tool yeah the info text should have other things in it so we'd like a tool to be able to generate and solve a puzzles or like this and we want it as a flask application go yep stop programming it's more like the the other way around is it prompts the info will be yes stuff like that that would be a good uh info yeah we don't like multiple html's uh we'd like it to be visible in one window and yes we'd like it to be a flask application but most of the stuff if possible should be done in javascript so we don't spend too much electricity on the server okay well that one's generating we can go go back a couple things we'll turn this in can you turn this into html text and then obviously done is working much better as activation function we will read everything before publishing yeah so might want to change the optimizer to sgd by default select sgd as default instead of adam and the activation function and i want to be using can we use tanh as default instead of the relu no yeah so we have sgd as optimizer and tanh as the activation function because apparently it's better for sign or so at the prediction and yes it is doing much better i'm pretty happy with that it's not perfect so we want we don't want it to be perfect let's train again with more data points it's getting pretty close to zero the training was that's pretty good the question is what happens when we increase noise level let's just pop it through the roof and as before it's still pretty good probably could increase the noise level one more two steps off point one should be fine begin with can i have point five why do we need this number here and there so i have some minimal noise get down to point one a training loss if we increase the training does it getting yeah just below point one it's only marginal improvement increase the number of hidden layer size both the first and second to six and four see what happens it's pretty much the same learning rate yeah doesn't make much difference restart yeah let's do drinks that size the 100 noise level large the largest can take or yeah so well that's what we wanted that's what we wanted to happen to show how this increase noise the performance of this prediction reduces and when we move the noise to zero the performance should increase it's not white it's zero six as opposed to point four uh yeah so there you go pretty happy with it we'll try publishing it on the website still might do a few minor improvements have the text over there is pretty much the it's pretty much the prompts yes yes will be clashing because we have the style template for the whole project so we don't want the tool style sheets to interfere with one another and better finish up they yeah happy with that example of how to train a neural net can you give a summary we are currently live streaming on youtube so you could also do an out draw be nice yep what's the recent tool on binary chaos.com go check it out it was that plan out one but we also have the particle motion ccg label bot um really matter we need the template for what's this called particles to particles particles the hgm this is not a flask application this one yeah let's go for this is just JavaScript let's go for cardio bot cardio bot must be a flask up as it is a couple of things from it we need this my app a file for neural neural net and what else do we need in the html for this thing templates index html we need a bunch of stuff in the body in this header that's what yeah makes it look more familiar yes we can put ads already it's okay otherwise we'll forget later on to type uh is that thinking it's doing anything neural network trainer a web-based neural network training interface that allows train neural network on the fly even the browser using TensorFlow.js sounds amazing an image um we don't have an image to update this later right and we have the styles it says for for this tool and then for the whole project what and you know finish finish it up later on i'll see you in a bit let me know if there's any question put them in the comment don't forget to check out binary chaos.com you'll be helping the project this way


I'm shifting to you with the social what is you explain what going dark is like those platforms to email the text the direct mail which is just crazy the direct mail but what is your plan to implement it and I would love yet especially if you can walk through some of those examples of you showing it earlier so people can kind of all right of what that looks like practically all right I'll walk through it one more time okay so first of all like again you just want to use it's all leverage right so it's like you want to use the weight of these big giants their advantage so you can use public platforms to build your private your private platform so one of the things I've been testing so super phone if you guys don't know I'm not gonna pay for this but super phone.io is where you can go there's there's more than one text platform there's one called community now which I haven't tried but there are some things I'm unsure of about it that I don't necessarily like as much as super phone but can you touch on that really quickly yeah yeah one of my Ryan Leslie Stan but that's aside the point to community like one thing I've noticed is that they are focusing really heavily on big influencers grabbing big influencers to promote the brand and I think that it's watering down the message because everyone knows that did he's not really texting with you and super phone is designed its position as one is a one of like a one on one connection the way to position it is this is my actual phone so I think it's more helpful to people who aren't mega celebrities to there's a tech issue which I realized which super phone when you get into the systems you start sending out messages you realize that they make you put a personalized F name tag in all the messages meaning you have to have like hey Sean this is Daniel here's today's message or whatever you have to put a tag in there and I asked them why they did that because there are sometimes when I want to send messages why I don't want to have the first name in there and they said that one thing they found was that if you take out the first name and you only have the text and it's not personalized that means that when you send out a blast every text is the same and a lot of carriers block that it's spam because you know if you have 10,000 phone numbers and you send out 10,000 of the same hey what's up concert then I blah blah blah a lot of text carriers see that as 10,000 of the same message they're going to block back to that spam and I just that was just one example of I've seen a lot of the thought that's going to put into some of their features and like how they do things I'm like you guys aren't just making a product to make a product you actually put a lot of thought into the user experience around this and I appreciate that you know actually there's a solid team but in terms of like examples so the first thing is I'm testing all this stuff so I'm in the testing phases you know take what you want and see how it works for you the first thing I'm doing and I'll share my screen with you here is I'm running ads to my phone number which is like kind of again it's a little bit like antithetical because you're like wait a minute you're using the platform that you're bashing to get people to the private platform again I'm not bashing it I just want to know how I can utilize it to my best advantage here's an example of an ad I'm screen sharing on this this is an ad I'm running I'm tired of social let's have a real conversation texting me on myself as advice the advice is my little is my little slogan like it's like I'm daddy and then it's advice and advice and my number you know and it's subtle branding because it's like my little hashtag there and then I'm wearing my shirt and it's kind of distorted so it's a little bit of tension grabbing makes me look very light though I'm a little bit darker than that in real life and then there's my number and so I'm testing this now and I'm running this only to my warm audience and people who are on my email list and people who are on who are engaging with my social platform so it's just it's a kind of a closed circle because what I'm doing here is I'm not trying to bring awareness of me I'm just trying to convert existing fans who are already in my orbit because I figure like if you don't know me why would you text me so you don't need to know you this doesn't need to go any wider to my existing audience so this is one thing that I'm using which you know I'll see the results in this we'll see as it goes like what the results are on this another thing I'm doing is as I like it's in my bedroom now but I have hoodies in sweatshirts that printed out just for my own personal use well when I do talks now it's just a giant phone number you know and it's like text for his advice it's just my giant phone number so now when I get on video of me doing talks on in public for talks it's just very I know it's a little corny you know but like I don't care like it works does it work like even a few years ago the baby was going around in a diaper so true but I care you know you know so I'm going around with my phone number and obviously I'm putting my phone number on every single piece of content I actually might even change the main headline of my website to just be my phone number so I'm just like being as obvious and almost obnoxious as I can with that just because people who already like me will do it people who don't care don't care so the matter so that and then if you want I can walk you through how I use this in a real use case yeah do it okay it's gonna be super useful super useful so imagine you are you know I mean you can be an artist or you can be you can be a consultant or a coach or an entrepreneur who's doing service-based stuff I mean this is widely applicable like you can look you can think about this and don't think about my specific use case think about how you can use it but I have a I have an existing text message list so just a background on how I got that I've been I've been in this game for you know many years now and I was like smart and or fortunate enough to like have enough foresight to say maybe this data will be useful one day so I've been collecting phone numbers for years even though so like I already had the seeds of a Sith Lord I was going dark early I knew that I was gonna need this info but I'd never really used it you know so I've been collecting phone number since 2000 honestly 2014 so that'll give you some context how long this takes and I've been collecting them because I was doing what I was doing webinars every week I would use text message for reminders just like one off reminders I for a while I had there was another service called call loop which I don't use anymore and I wouldn't recommend but I was using them for text messaging this is like maybe five years ago so like I knew there was potential there but I didn't I wasn't fully on board but I do have the numbers deep in my database and like again it just shows you how useful data is like it's all about the data you know a quick little aside here when when Dollar Shave Club sold to Gillette for a billion dollars they weren't selling the razors they were selling the customer list okay because Gillette did the math and they said it will cost us more than a billion to get all these customers who are on subscription recurring revenue we might as well pay you guys a bill and we'll just take the customer list they're paying for data you know everything is data when you sell a company you're selling the data of that company especially if it's a recurring business anyway data is very useful so I have this data from years of like writing blog posts online and doing social media content and running ads so that's what I say I spent a lot of time and money to collect this stuff and you will too because this is a long-term play for you artists out there you entrepreneur whatever this is the long-term play so I have about 12,000 phone numbers 11 and a half thousand and I you know I brought him back from the dead recently in fact I only started texting these people the week of Christmas you know just to see if it would work of this like let me import this and see if it works and I sent out my first like happy holidays text and people a lot of people were like you know fuck you like unsubscribe you know get me off of this thing a lot well I mean you know from a list of 12,000 you know even if it's like 200 people that's a small percentage but it's a lot of fuck use but check this out on a list of 12,000 I only got one dick pic which I thought was amazing you know in terms of ratio ratio like you think it would be more right sick sick people so but but then what I learned was some of these people but here's my assumption my guess was that this data was okay people don't change their phone numbers nearly as often as they change their other things I still have my phone number from when I was in high school so I knew a lot of these numbers would still be good and and although I did get some people who like fuck you take me off this list I got a ton of people who are like oh my God Daniel I can't believe you're texting me this is amazing wow I've been following your work for how many years because my assumption was if you've been following my social on my email list and you still like my stuff if you got a text from me you wouldn't mind it like that would be okay you know if I got a text from my favorite author who's a New York Times best-selling author who you watch been following him all this bullshit you'd be like that's pretty cool and then if he actually text you back your mind will be blown you know so I did it and it worked and so like okay this is gonna work so the next like you know in a week and a half later like once the holidays hit no no this was like this was this was like this was like dissent like the last week in December I just said I'm gonna test this out and I said I'll text 11,000 people I'm like hey I'm thinking of doing a live meetup in LA on you know on January 4th which is this last weekend as of this recording so I gave them less than a week to decide usually people like when I've done a lot of live events usually people need like some some lead time just to like get the schedules I just want to do what happened so set out this this text and from the 11,000 people I got a hundred people to say yes I'm interested in learning more about that now the conversion around that isn't like super high but the same time it's the first time I've ever done this they're still learning that I'm texting them like there's some warming up to do I was a hundred people is still a lot and I know this because like I have a 44,000 person email list and it would be harder to get 11 or it would be harder to get a hundred responses of a yes from the email list probably that would be from the text just because I know open rates I know like just or even on social media like I have over 200,000 just on Instagram and I could do that shout on Instagram and I wouldn't get a hundred responses that say yes probably just because you just don't it just doesn't work as much as you think it does I can put it up on a story and I can have a thousand people see that I'm not gonna get a hundred responses so like to get that from my text message this other like it's pretty solid and and a lot of people probably didn't respond just if they weren't in LA so why would they respond to that I was gonna ask you did you target based on location well the thing is because this is old data like when you when you get people in Super Bowl for the first time it makes the put their location down but if you if I'm just importing data all I have is their name their phone number and their email address so I don't have all that data and I'm still enriching the data you know I'm still enriching it so I don't even have great targeting right now I'm still getting there but so this is the clear what is enriching the data me well you're a tech guy you know it's like enriching the data is like adding additional information adding additional fields of info to the data you already have and getting more complete data you know so if you only have an email a phone number and a name I want to get your location your birth date and your sex and all that stuff so I can geotag you and and so what's been happening is when people text me back and I realized I don't have all the information I'll say I have a little hot key on Super Bowl that says hey I got your info from my old email list thanks so much you know would you mind filling this out so I can keep in touch so I have your complete info and then they fill it out and I get their enriched data where I get like their location and then that way when I come to their city I can say I'm people are in New York and I can do my New York tag but I didn't have this when I was making that meeting and that's gonna take me all year to get that info like I'm not just gonna take me all year to get that info and I'm committed to that but so I got a hundred responses you know give or take and and then of that I said I email I texted them back and I said great here that here's the info and I sent them a little form and it was $50 and I got it was $50 the meetup it was less than a week and I got 30 people to sign up and I actually honestly miss some people who are interested so I probably had more if I would it was a lot to filter through but I got 30 people to sign up was 50 bucks so it's 1500 bucks on the front end not bad text message from text message you know not bad on the front end but keep in mind I have bigger channels than this on the top and I have social media which is like well over I don't know three or 400k combined and then I have an email list which is like tens of thousands of people this is my smallest channel with one text message so think about the levels of magnitude there so you know purchases on the front end 1500 bucks so there's a small amount of profit there because I pay for the space so anyway I get 30 people into the room this is last weekend you can go on my YouTube channel you can see the recap of this event and basically what I did was I did a three hour meet and greet seminar and a Q&A should have been five hours should have been longer honestly but it was three hours and then what I did was I sent out a feedback survey I'm gonna show you guys this feedback survey because it's so just slick daddy I mean if you're a marketer you know slick daddy and I was trying to tell my wife about this she's like I just don't care I mean she cares but you know it's like matter deciding for her it's a different kind of care you know here's the type form but I was thinking like whenever you have a funnel you want to be able to follow up with people or whatever you have whenever you're making a sale on the front end I've learned this from a lot of events you want to be able to have something to offer on the back end because I mean it's just how business is just how it should run like you have an offer otherwise you're just wasting all that attention in the room like you just you know it's like they're in there in person if they're there they're close fans who like you why wouldn't you have something for them you know so what I did was I sent in this feedback survey the feedback survey is very non-invasive because it does two things one it gets their feedback which they want to give their feedback and it gives them a chance to give me ideas for making the next events better and two it allows me to slip in a sale without sending them to a sales page because people are automatically like sales pages I mean they're fine they work but if they know they're going to a sales page they categorize as this is a sales page I'm looking at and there's a bit of a barrier there so what I did was as you're seeing on the screen I have a survey it says hey thanks so much for attending it was honor to meet you it takes a moment for the feedback so I go through the full name and their information by the way I already have all this info the reason I ask for it again it's just because you know from doing this for many years I know sometimes you don't have complete information and you want to be able to like let's say I need to export this list I just want to have all the info I don't want to have to go cross-reference my database or be like yeah I just I've just done it too many times I'm just like give me info again you know I just you know I'm tired man okay cuz now you can say I want to well whatever I would just want to do something specifically with the people who gave me feedback right right these are these people I have all the info but do I want to go through Superphone and convert again no I don't know so how would you rate the overall experience on a scale of one to ten by the way I'm starting off with low investment questions just to get them to start answering the survey that's some psychology there they're easy to answer you know what would you how much would you how likely would you be to come back to another event low investment now this is kind of like I mean it's a medium investment would your number one takeaway inside our breakthrough won't be an event how can we improve the event next time what questions you still have that you did not get to ask that at the event so these are allowing me to like tweak the events that I do in the future to just make them better tweak the messaging and then here's the cool thing so I'm considering doing some mini coaching packages to 10 people from the event so what does that first of all say considering meaning it's not really a sale I'm just thinking about doing this are you interested to 10 there's a little bit scarcity around that so it's like oh there's only 10 and then I thought about like having a whole sales phase and shit and I have all the coffee I can give but I don't I just didn't want to do a sales page I'm just like I want to do it you know so I just put this down for here you're gonna get an hour of my time to go deep on your challenges and will develop a strategic plan for your business I'll also give you access to my entire profit paradigm business curriculum which is just my the digital component of my coaching program and I'll check up on you to make sure you stay on track by the way that checkups gonna be an automated checkup from Superphone which they can hit me back on so investment is 350 would you like one of the 10 spots and so they can click no and they'll just be taken to a page that says you know they'll submit and they'll say thanks have a nice day thank you for your feedback but if they click yes it takes them right here to a payment page they put in their info then it's hip hooked up with Zapier, Zapier hooks up to Gmail, Gmail shoots them out a message that says thanks here's where you can book that's hooked up to my calendar and they schedule on the call so what happens is all I do is send them out a feedback survey they go through this thing I get feedback and sales with no additional effort and I opened up my phone the next day and I already saw bookings on my calendar and money on my stripe I was like excellent this is great you know and all this was and I didn't make any public office is all internal so the only people who bought other people who chose to go down that that lane with me you know and I wanna know how many text messages at this point I mean you know to my whole list it was I did one text message to my whole list one to your whole list once my whole list I did and then I did one follow-up to the hundred no I did two follow-ups to the hundred okay and then one follow-up with the survey so four text messages and this generated we got from the first send of this we got five bookings which five times 350 is you know like 1750 I think something like that so that's on top of the 1500 we already made so that's three plus grand and then I'll send this out again because it's all I'm doing the same can I get your feedback which is much less aggressive than saying can I get you to buy so I'll send this out again it's ahead and get your feedback guys but really what I'm doing is I make sure they see the author and so my goal with these is to low-key like I can get just 30 people to the event each time which I know we'll get better and better as I do more of these but if I can get just 30 people and make five grand off each event I'll do two of those a month I'll make an extra 10 grand that's extra 120k a year from just like from like no there's like no no imprint of that like no one sees it on social I'm not emailing it out it's just a couple text messages and it adds extra 120k to my bottom line all I'm doing is like simple automations and a little bit of texting love it no imprint on social you know it's hard to imagine but that's how things used to go down anyway right exactly that's that's how and that just goes to show you now and now I could go on social and I could try to you know build these spots with you know and I've done that for years I've done that and I could do I could do it that way but it just it doesn't work as well for me because I like to be targeted now what was the open rate when you sent it to that place and that's what this dark social out the open rate on what so you said that one text right what was the open rate on that one message that first message to the to everybody it's hard to say because they don't have statistics on open rates but I mean presumably you know text message open rates are very high you know if it's a good list it's gonna be as high as 98% who knows you know but I can tell you I can tell you on other things like I guess if it's a sign up I can tell you that I've had like I'll have as high as like on a whole list send a 5% quick through it which doesn't sound like a lot but like if I send a text message out to 11,000 people and I get 700 to 900 clicks that's a lot it might not sound like a lot but it's a lot because I know emails that and they're not like that you know I mean if you know the influencer game if you talk about Instagram stories oh people are so you know hyped up about swipe ups bro I've been on that game the swipe up click the rate is low dude it's so low you know because people are just it's being fed to them and they don't they don't they're not programs that but click the rates on texts are really really good on my targeted stuff rather only send it out to 100 people I would get like 90% quick through rate and again it's all about targeting so it's like can you get fine enough where only the right meet people get the right message and if you can figure that out that's for me that's gonna be extra I mean if I can tweak this this would be an extra 120 to quarter million dollars a year just for me like doing these little 30 person events around the country you know like love it why couldn't you do this with music why could you offer a VIP package why couldn't you offer them a meet and greet why couldn't you offer them you know shit I mean some people would do collabs like I mean there's so much of you could follow could be endless it's so many different direction


Democrats don't want Biden to be president again. A majority of Democrats now think one term is plenty for President Joe Biden despite his insistence that he plans to seek re-election in 2024. That's according to a new poll from the Associated Press NORC Centre for Public Affairs Research that shows 37% of Democrats say they want him to seek a second term, down from 52% in the weeks before last year's midterm elections. While Biden has trumpeted his legislative victories and ability to govern, the poll suggests relatively few US adults give him high marks on either. Follow-up interviews with poll respondents suggest that many believe the 80-year-old's age is a liability, with people focused on his coughing, his gait, his gaffes, and the possibility that the world's most stressful job would be better suited for someone Biden has previously leaned heavily on his track record to say that he's more than up to the task. When asked if he can handle the office's responsibilities at his age, the president has often responded as if he's accepting a dare, watch me. Democratic candidates performed better than expected in the 2022 midterm elections, a testament to Biden's message that he is defending democracy and elevating the middle class. Democrats expanded their control of the Senate by one seat and narrowly lost their House majority, even though history indicated there would be a Republican wave. Overall, 41% approve of how Biden is handling his job as president, the poll shows, similar to ratings at the end of last year. A majority of Democrats still approve of the job Biden is doing as president, yet their appetite for a reelection campaign has slipped despite his electoral track record. Only 22% of U.S. adults overall say he should run again, down from 29%, who said so before last year's midterm elections. The decline among Democrats saying Biden should run again for president appears concentrated among younger people. Among Democrats aged 45 and over, 49% say Biden should run for reelection, nearly as many as the 58% who said that in October. But among those under 45, 23% now say he should run for reelection. After 45% said that before the midterms. Already the oldest president in U.S. history, Biden has been dogged by questions about his age as he would be 86 if he serves a full eight years as president. He often works long days, standing for hours, remembering the names of strangers he meets while traveling, who want to share a story about their lives with him. Republican voters are unwilling to give Biden the benefit of the doubt, hurting his ratings.