“logic is reversible, but guesses are absolute” ~ TheVIP
Mathematics & Human Behavior
the purpose of this page is not to teach you mathematics .. there are so many books available in market for that, rather to show some of the beauties, just like humans & humans behavior, which led me to think that human behavior can be described using the language of mathematics, which is a sub-theme of this uber experiment
as you go though the stories below (not sure if will agree that they are stories, but that’s my intention), think how each describes certain behavior found in nature, & then correlate with something that humans do, or the phrases that we use to describes things in our life; e.g. a round peg in a square hole – an individual idiosyncrasy but a circle and square seem a perfect match with each other in mathematics (or geometry in this case) … so, what we call an irrational human behavior, would no longer feel irrational, if you visualize with help from mathematics .
of course, this is not a full recipe of my model .. rater, it’s just a tasting menu …!
the goal is to look at mathematics from a totally different perspective; so start enjoying the subject, if you haven’t done, until now ..!
a circle & a right angle triangle are the same thing … really ?
circles make the world go round & triangles give us a handle on them … the masculine & feminine divide of nature … like Shiva and Shakti … interesting … they are two manifestations of same energy
& the relationship between them is called trigonometry … a circle a simply a collection of all possible points at the edge of the hypotenuse of the right angle triangle as its angle (ø) varies between 0 & 360 across 4 quadrants … the hypotenuse of the triangle is same as the radius of the circle.
what if multiplication becomes as easy as addition ..?
ask a 3rd grader ?
unfortunately, he is not familiar with log function – that defines multiplication operations in terms of addition; as in above case, 10 * 10 * 10 can be calculated by simply addition 1+ 2 = 3; and then using log function
does calculus scare you ..?
there are two mathematical operators in calculus that can help understand the behavior of a curve that “seems” random .. derivation and integration .. using a derivative function one can project that in a time T + delta T, the curve will be at a new position, if we know where we are now (time = T) & the slope of the curve … similarly, the integration function of a market behavior function can be used to project the long-term behavior (0 < t < 00) … thanks to Mr. Newton again … & combine the results with human behavior function (described on Humans/Behavior page) … voila … the dinner is served ..!
in the picture on the right, f(x) is the function that defines market behavior … do you still remember calculus from high school or did you stay away from it because you thought would never need it in your life? don’t worry, all you need are the basics.
based on the above statements, i formulated that financial markets are project-able for short-term, totally un-predicatble for mid-term, but come to senses in long-term – VIP’s 2nd hypothesis
or in other words, first, markets can’t be predicted because the events that drive them can’t be predicted, but financial markets are project-able for really short-term OR long-term (Buffett style time-frame), but not in the middle.
Fourier transform
does the slide on left looks familiar .. think hard … isn’t the first slide on your left looks like a stock chart .. aha .. now, of course, the second question is how can you de-construct this randomly looking chart into a set of waves of various frequencies; well, that’s precisely what is called Fourier transform.
The Fourier transform can convert any complicated (funny looking, some call it random) function into an infinite collection of simple ones – as a variations of sines and cosines of different frequency … it allows us to switch between the “time domain” & the “frequency domain” although time is more intuitive, but frequency makes the math simpler because of trigonometry.
Descartes theorem
for every kissing (mutually tangent) circles, the radii of these circles satisfy certain quadratic equations; & by solving this equation, one can construct a fourth circle tangent to other three.
now think where do we have 4 things fitting into one to make use of this theorem in personal life & investments ..
okay, let me give one example:
even though you can’t predict the length of season in an year; right? & if you can, God bless you ..!
but for those who can’t know the following:
1) that the number of seasons in an year is 4; it doesn’t change year-by-year – everybody knows that ..!
2) even though you can’t predict the length of a season, their sum total of 4 has to be one year.. i.e. even though winter may be long, which may overlap spring, but it will likely cut down spring; so summer arrives.
3) & all four must finish in an year; or in other words, you can’t have each one of them lasting 6 months and extend into the year .. right ..?!
Chaos theory & butterfly effect
i started this project with a vision “to project market behavior over a short period of time” as it started with an assumption that NO ONE can predict market behavior <period>; especially, over a long-term that most experts do.
while studying butterfly effect within the context of Chaos theory, here are a couple of things that i learned:
1. financial markets “may be deterministic” although i really don’t follow that assumption in my models; markets behave as non-linear dynamic systems; i.e. a small change in input conditions can reflect a huge change in output
2. the projection, if at all possible, can only made for really short-term even with all sorts of caveats, & no long-term prediction or projection is absolutely NOT possible.
also, its proven that a dual rod pendulum generates vastly different outcome based on slightly different initial conditions; imagine, if i told you that market consists of 9 pendulums swinging simultaneously .. it would be like WoW .. 9 times ..!
funny thing is that i didn’t know about these characteristics of Chaos theory until recently (as in Sep 2020), while i developed my vision about a decade ago based on those assumptions, but now it makes sense to me, as to what it means.
Maths, Physics, e-motions & projections
can one project future ..? ……………………………… yes, you can, and in fact, anyone can ..!
but only for short-term, by connecting recent past with current and into little bit into future …
using physics, we can project the future of a moving object … describe the present in terms of kinematics (where an object is at present?) and future can be projected in terms of dynamics (where will it be in future?)
– think about a missile, whose path can be projected as a projectile .. you can project its future
– using the laws of motion, you can project where a car running at a speed in a direction will be at a point in time in future
but can you project the future of a human .. of course you can, all you need to know, where your mind is at present in terms of your emotions and the intensity of your emotions, which are caused based on stimuli
although you don’t have a damn clue, what am i talking about; i.e how do you measure current state of emotions; plus change in emotions based on external stimuli and then a change in behavior and then the actions taken on those behaviors … but, it is starting to makes sense … isn’t it ..?
statistics & projections
now let’s try statistics
i made this observation while on a beach in Santa Cruz, CA (Sep 2015) … imagine, you are standing on a beach, enjoying the sun & watching the waves … as you focus on waves, watch them closely coming towards you and then ending on the beach … continue to watch at least ten of them and picture them in your mind gathering their sizes (height) at a distance and where they are ending on the shore … now watch the 11th wave coming towards you … take a good look at its size at a distance & assuming there is no earthquake or tsunami happening in next few minutes (those will be black swan scenarios), can you project where the wave will end on the shore within a range of few feet … i am sure you can … and do you know what you just did … you used a probability based model coupled with standard deviation in your head to project where the wave will end.
you just projected the future ..!
enjoy nature’s show …
and, if you observe nature really closely and regularly … you can project the future on so many other things ..
take a case of a successful baseball player (or cricket if you are from England or India) … if you are a novice player like me, you are just looking for the ball as it coming towards you to hit it … you take a swing and the course of the ball decide whether you are going to hit or not … OTOH, the best players in the sport try to project the location of the ball in a much smaller grid … so, given a game between two teams, the match, the inning, assumed strategy of the other side, the thrower, last few balls thrown, the weather (wind, temp, etc.), the mood of the crowd & so forth, the hitter will do calculations in his head to project a location of the ball in a smaller grid …
a national level player will divide the space in front of him into smaller (let’s say 8×8 grid) or something close, rather than the whole space, to swing his bat … or let the ball go, if he is unable to make a good projection … the better player you are, smaller are your grids, and better are your choices to project the grid in which the ball will show up (statistically speaking) … and if you have this capability, acquired either by practice or given to you when you were born, then you will become a successful ball player.
here is how it works [of course only for a small number of people]: given there is a human on the other side across the field and given that there is enough historical data for the balls already thrown by this person in past, his behavior can be projected in a statistical context, and there are finite number of other important variables to consider, and the ball has limited options (within a grid) when it arrives at you … and if the hitter has all the historical data in his storage (mental memory), which are fed to the physical memory (hello, i am talking neuro-physics & computers here ..!) as the thrower starts running, and if the hitter’s CPU is fast enough to make the calculations & use the statistics & send the results to the hand for positioning and taking the swing … all in few seconds, as the ball is coming towards you at ~100 miles / hour — yes, the future can be projected in a statistical context & that will make you a successful ball player or cricket player, but it’s not everybody’s business, & so, leave the cricket to Sachin Tendulkar ..!
Sex and Mathematics
who wouldn’t be interested in this .. as Einstein is so 20th century ..!