The market is a controlled dynamic system. - page 268

 
yosuf:

Good idea, but in fact, these functions change, particularly at a=0.1, as follows and it would be great if you could animate them in a similar way:

a t Б Н П B+H+P
0,1 0 1 0 0 1
0,1 1 0,904837 0,090484 0,004679 1
0,1 2 0,818731 0,163746 0,017523 1
0,1 3 0,740818 0,222245 0,036936 1
0,1 4 0,67032 0,268128 0,061552 1
0,1 5 0,606531 0,303265 0,090204 1
0,1 6 0,548812 0,329287 0,121901 1
0,1 7 0,496585 0,34761 0,155805 1
0,1 8 0,449329 0,359463 0,191208 1
0,1 9 0,40657 0,365913 0,227518 1
0,1 10 0,367879 0,367879 0,264241 1
0,1 11 0,332871 0,366158 0,300971 1
0,1 12 0,301194 0,361433 0,337373 1
0,1 13 0,272532 0,354291 0,373177 1
0,1 14 0,246597 0,345236 0,408167 1
0,1 15 0,22313 0,334695 0,442175 1
0,1 16 0,201897 0,323034 0,475069 1
0,1 17 0,182684 0,310562 0,506754 1
0,1 18 0,165299 0,297538 0,537163 1
0,1 19 0,149569 0,28418 0,566251 1
0,1 20 0,135335 0,270671 0,593994 1
0,1 21 0,122456 0,257158 0,620385 1
0,1 22 0,110803 0,243767 0,64543 1
0,1 23 0,100259 0,230595 0,669146 1
0,1 24 0,090718 0,217723 0,691559 1
0,1 25 0,082085 0,205212 0,712703 1
0,1 26 0,074274 0,193111 0,732615 1
0,1 27 0,067206 0,181455 0,75134 1
0,1 28 0,06081 0,170268 0,768922 1
0,1 29 0,055023 0,159567 0,785409 1
0,1 30 0,049787 0,149361 0,800852 1
0,1 31 0,045049 0,139653 0,815298 1
0,1 32 0,040762 0,130439 0,828799 1
0,1 33 0,036883 0,121714 0,841402 1
0,1 34 0,033373 0,113469 0,853158 1
0,1 35 0,030197 0,105691 0,864112 1
0,1 36 0,027324 0,098365 0,874311 1
0,1 37 0,024724 0,091477 0,883799 1
0,1 38 0,022371 0,085009 0,89262 1
0,1 39 0,020242 0,078943 0,900815 1
0,1 40 0,018316 0,073263 0,908422 1
0,1 41 0,016573 0,067948 0,915479 1
0,1 42 0,014996 0,062981 0,922023 1
0,1 43 0,013569 0,058345 0,928087 1
0,1 44 0,012277 0,05402 0,933702 1
0,1 45 0,011109 0,04999 0,938901 1
0,1 46 0,010052 0,046238 0,94371 1
0,1 47 0,009095 0,042748 0,948157 1
0,1 48 0,00823 0,039503 0,952267 1
0,1 49 0,007447 0,036488 0,956065 1
0,1 50 0,006738 0,03369 0,959572 1
0,1 51 0,006097 0,031093 0,96281 1
0,1 52 0,005517 0,028686 0,965797 1
0,1 53 0,004992 0,026455 0,968553 1
0,1 54 0,004517 0,02439 0,971094 1
0,1 55 0,004087 0,022477 0,973436 1
0,1 56 0,003698 0,020708 0,975594 1
0,1 57 0,003346 0,019072 0,977582 1
0,1 58 0,003028 0,01756 0,979413 1
0,1 59 0,002739 0,016163 0,981098 1
0,1 60 0,002479 0,014873 0,982649 1
0,1 61 0,002243 0,013681 0,984076 1
0,1 62 0,002029 0,012582 0,985388 1
0,1 63 0,001836 0,011569 0,986595 1
0,1 64 0,001662 0,010634 0,987704 1
0,1 65 0,001503 0,009772 0,988724 1
0,1 66 0,00136 0,008978 0,989661 1
0,1 67 0,001231 0,008247 0,990522 1
0,1 68 0,001114 0,007574 0,991313 1
0,1 69 0,001008 0,006954 0,992038 1
0,1 70 0,000912 0,006383 0,992705 1
0,1 71 0,000825 0,005858 0,993317 1
0,1 72 0,000747 0,005375 0,993878 1
0,1 73 0,000676 0,004931 0,994393 1
0,1 74 0,000611 0,004523 0,994865 1
0,1 75 0,000553 0,004148 0,995299 1
0,1 76 0,0005 0,003803 0,995696 1
0,1 77 0,000453 0,003487 0,99606 1
0,1 78 0,00041 0,003196 0,996394 1
0,1 79 0,000371 0,002929 0,9967 1
0,1 80 0,000335 0,002684 0,996981 1
B = Exp(-at); H = atExp(-at); P = 1 - (1+at)Exp(-at)

Let's see what happens -- here, in this straightforward formulation, everything is clear and straightforward. BUT, if we talk about the significance of the Present as a function of the horizon, then we have to make up an inverse function.
 
avtomat:

Let's see what happens -- here, in this direct formulation, everything is clear and understandable. BUT, if we talk about the significance of the Present as a function of the horizon, we have to make up an inverse function.

In particular, on this stretch H is greater than P and B:

0,1 10 0,367879 0,367879 0,264241 1
0,1 11 0,332871 0,366158 0,300971 1
0,1 12 0,301194 0,361433 0,337373 1


Here is a "blink" for you, as it has shown itself! Consequently, sometimes more events can happen in the present than in the past and the future, e.g. at the time of the news.

 
yosuf:

Specifically. in this section here, H is greater than P and B:

0,1 10 0,367879 0,367879 0,264241 1
0,1 11 0,332871 0,366158 0,300971 1
0,1 12 0,301194 0,361433 0,337373 1


Here is a "blink" for you, as it has shown itself! Consequently, sometimes more events can happen in the present than in the past and future, e.g. at the time of the news.


As is often the case, inaccurate wording can lead to false conclusions. Here you have "the present" as a very limited interval, compressed into a momentary closure, while"the past" and"the future" are presented as open rays. So it would be more correct to say"Therefore, sometimes more events can happen in the present than at some moment of the past and atsome moment ofthe future, for example atthe time of news". This changes the meaning of the expression dramatically.
 
avtomat:

As is often the case, inaccurate wording can lead to false conclusions. Here you have "present" seen as some very limited interval, compressed into a momentary closed segment, while"past" and"future" are represented as open rays. So it would be more correct to say"Therefore, sometimes more events can happen in the present than at some moment of the past and atsome moment ofthe future, for example at the time of news". This changes the meaning of the expression dramatically.

This is what they actually look like and you have to imagine. how P, through, first widening and then, narrowing, hole H, eats B or B enters P through a variable hole H:


 

The "pie" of the dynamic process seems to be better represented as follows, where the white area is B, followed by the area H and below that by P, the notion of History (AND)=P+H had to be introduced:


 
yosuf:

This is what they actually look like and you have to imagine. how P, through, first expanding and then, tapering, hole H, devours B or B enters P through a variable hole H:



Yusuf, this is you presenting an isolated single act of the "present" beginning at time t=0, building up to its maximum value at time t=10, and then gently fading to zero. This entire act lasts for about T=80 moments of time (or epochs). This is, figuratively speaking, a stretched single shot, or in other words, a delta function smeared in time. For this single isolated act you construct its "past" and its "future", normalising everything by one. But these constructions are only valid fora single isolated act, i.e. it is a local "future" formed fora single isolated act.

But this single "present(0)" shot will be followed at the next moment (t=1) by the next "present(1)" shot, then at the next moment (t=2) by the next "present(2)" shot and so on - a long automatic burst. In this case all next again smeared shots are superimposed on the previous ones.

.

Each of these isolated single shots has its own local 'future'. And in doing so, each of these isolated single shots contributes to the formation of a global 'FUTURE', which can be thought of as a bundle of isolated single shots.

 

It might look something like this :

Here, for clarity, divide by p (see formula) so that the nature of the changes can be seen.

 
 
 

In this case, as would be expected, by the time t=80 saturation occurs.

The significance of the single shot contribution to the whole picture is approximately 1/27 = 0.036925

All this is for identical shots. But of course we remember that there is one shot versus another. And this can be taken into account by introducing weighting coefficients. But the task of determining the weighting coefficients is in itself complicated and ambiguous, although it is always possible to find some approximation.