every negative number is less than every positive number, sometimes

Let's imagine that I am losing weight. And I weigh myself every day, and I record this weight, and I calculate the linear regression for the last ten days to find out how quickly my weight is going down. And from this linear regression, I find out how many grams on average I am losing per day recently, and I also calculate how many days at this rate it will take me to lose a kilogram. I'll call this number (how many days at this rate it will take me to lose a kilogram) D, to write it more briefly. I calculate it by dividing 1000 by the average number of grams lost per day. When the number D is smaller, it's better - I am losing weight faster. When the number D is larger, it's worse - I am losing weight slower. I draw a graph of the number D as a function of time. When this graph goes down, I am happy - I am losing weight faster. When the graph goes up, I worry - I am losing weight slower. Now let's consider the situation when I stopped dieting and my weight started to slowly go up. Then the number D will turn out negative. And where should I plot it on the graph? If I plot it below zero, which is even lower than I plotted very small (which means good) values of D, it will look silly - as if the situation has improved, as if I am losing weight even faster now than with very small values of D. But it's the opposite - now the value of D is bad, it's even worse than any positive value of D. So it makes sense to draw it on this graph somewhere up high, above all the positive numbers. And in this sense, in this case, I feel as if a negative value of D is greater than all positive values of D. I am still wondering what scale would be nice for the Y-axis of this graph. A regular linear scale is not very good because in it, negative numbers are below positive ones. I think it would be such a scale that in the middle would have infinity, going down from infinity would be smaller and smaller positive numbers, with the axis being very dense near infinity (because without this it wouldn't be possible to have both infinity and finite numbers on it), and then getting sparser and sparser until far down, in a place so distant that it's unreachable, there would be zero - which is such a D that means I am losing weight so fast that the loss of a kilogram happens instantly. And in the other direction, above infinity, there would be negative numbers, the higher the bigger (meaning the closer to zero, the smaller the absolute value - for example, going up the axis I would see -7, -6, -5...). And of course, symmetrically to what's below infinity, here too at first, near infinity, the numbers would be very dense, and then sparser and sparser until eventually somewhere high up, in a place so distant that it's unreachable, there would be zero - which is a D that means gaining weight so fast that gaining a kilogram happens instantly. And please, don't tell me to draw a graph showing how many kilograms I am losing per day instead.

comments:

2022.08.02 15:31 P.

Zaraz, ale pod pewnym względem to wcale nie jest dziwne. Ten wykres liczby D po prostu wygląda tak, jakbym narysował wykres pokazujący w funkcji czasu ile kilogramów dziennie tracę, a potem na osi pionowej każdą etykietę przemianował z "i" na "1/i".

Choć nadal oś, która wtedy powstaje, podoba mi się i ciekawi.

2022.08.03 06:18 P.

I poza tym ciekawe, że w żadnym znanym mi programie do robienia wykresów nie ma możliwości takiego definiowania nietypowej skali na osi Y. Nawet w gunplocie podobno: https://stackoverflow.com/questions/9617675/user-defined-scaling-in-gnuplot-for-y-axis-equivalent-to-set-logscale-y

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