![]() It depends upon your resting and maximum heart rates. The Karvonen Method is a way to calculate your target heart rate given the intensity of a work out. Yep! H is very small now because 9,999 out of 10,000 messages will be B - the world is certain! Health Target Heart Rate If we designate one of the messages as very likely to occur then the entropy should go down since there is very little uncertainty. If we make the number 11 most probable - 60% likelihood - then the entropy is only 0.95. ![]() When the messages are most uncertain - they each have the same probability - the entropy is maxed out at about 1.1. We can now calculate the entropy of the data given the various probabilities of messages: H(data, p = pmax) => 1.0986 # NOT a good value of p because it sums to 0.75 The p function must sum to 1 for all the possible messages. To do this, it needs to know the probability of a message being in X this information is provided by the p function. This function takes a set of values or messages X and produces the entropy of that set. Why not modify those stats to match your home town? Shannon's EntropyĮntropy of a variable is a measure of the uncertainty of its value. Hmm, there are only 3,000 18 year olds in Seattle - given my completely made up statistics above. Population given age = f(age) * population of seattle So what's the probability on an 18 year old living in Seattle? population of seattle = 620,778 #googled This means that 68% (one standard deviation) of people in Seattle are 33 years old, plus or minus about 7 years. ![]() Here is my population in Seattle of people's ages (not really): ages = The normal distribution gives the probability of a value x occurring based on an average of all possible values called the mean and a standard deviation stddev of those values around that mean. You can extract the real and imaginary parts of a complex number using these very clever functions: im(z) = 1/2i*(z - conj(z)) The complex conjugate negates the imaginary part of a complex number: conj(5i - 1) => -5i - 1 i^2 => -1Ī complex number is an imaginary number added to another number: b*i + a => b*i + a They are defined by the property that their squares are negative. Imaginary numbers are written as numbers multiplied by the imaginary unit i. We can even solve other linear equations: xy(a=,b=) => Now we can convert our two equations into one and solve for x and y: a * xy = b We can solve for x and y by taking the constants on the left hand side and putting them in a matrix: a = Īnd by putting the right hand side into a vector: b = Let's solve the following set of equations: 12x + 13y = 163 You can use matrices to solve a set of linear equations. Pretty impressive I think! Solving linear equations using matrices We were able to calculate 4/3*pi * r^3 using just three additions. Log volume = log c + log r + log r + log r => 21.0362 Instead we'll use logarithms and addition: log c = log10(4/3*pi) => 0.6221 I need to multiple a lot of numbers, 4.18888 and r three times to find the volume. The same trick worked for multiplication. Then they could simply add those numbers. ![]() ![]() When they needed to multiply large complicated numbers, they were smart and kept those numbers in the logarithm form. These engineers and scientists used a mathematical identity to make their jobs easier. This is easy enough, but gets quite tedious. How far is it as the crow flies? c(a=5miles, b=8miles) => 9.434milesīack before Calca, scientists and engineers had to do math using long hand. Let's imagine that to get to work I have to drive 5miles north then 8miles east to get to work. The square of the hypotenuse of a triangle is equal to the sum of the squares of its legs. So, if I just make $128,000 per month, I will be a millionaire in just over a year! Time to start looking! Mathematics Pythagorean Theorem What if I made more money? time til millionaire(job = $8,000) => 62.1253years Great! I wonder how long until I'm a millionaire? time til millionaire Let's see how profitable each day has been: daily profit I have a job and do a little gambling on the side: income = (job + gambling) * (100% - income tax rate) Here is my budget, how is yours different? Just change any of the numbers to match your life. Try editing the price and interest rate to see how much your dream home will cost. Looks like if I don't mind dropping $70,000, I can get a nice place for about $1,300 a month. Here in Seattle, you can buy a condo for about $250,000, or you can splurge to get a house on a bit of land for $350,000. ![]()
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