Hi,
Working as a trader on nymex.
i had been trying to give the futures markets a game structure.
It was to be simple enough to be executed by anyone real time.
I wrote a paper in logic to explain how it works and how it is robust.
Could you please help me out with some feedback.
It's actually an interesting read, and no great knowledge is required of any mathematics or physics etc.
A few things turned up
so want to try posting it here to give it a try.
When i applied to examples in game theory, gives out more robust solutions. Also, better able to predict people.
Also surprisingly explains pi quite well and simple.
Well it's a paper of logic, not rather maths or physics, but essentially how that can be applied to both , to understand both better.
I had to define a few terms. I gave them the closest vocabulary i could find. Please ask any doubts/errors.
Would help a lot thanks.
Hi/Game structure for financial markets
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Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 6:14 am UTC
Last edited by nishank on Mon Jun 25, 2012 8:31 am UTC, edited 3 times in total.
- nishank
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 6:15 am UTC
http://www.4shared.com/office/owdlH3mI/ ... ecisi.html
Heres the link, bit easier to read.
Title- “ General Optimisation in decision making using logic”
I
Introduction
It gives out a simple theorem of logic, a statement, and a corollary.
The theorem gives out a simple max. way of solving for problems, either in finite boundary conditions or at infinite randomness.
The corollary examines how a sample point would deviate from the “max. true strategy” , as obtained for the group by using the theorem.
Applications:
Solved, within this paper,
1.)Firstly, for two problems of Game Theory – { Best matchup for 4 boys/4 girls , as well as Prisoner’s Dilemma (Iterative) }, it gives a scalable(in the sense best repeatable strategy) solution to both the problems in the real world. It also solves the same problems using more “precise” assumptions as well as lesser assumptions than game theory.
2.) Upon application to basic mathematics, points out to a question of mistake/misconception in Aryabhatta’s zero. Also tries to gives an explanation/definition for pi.
3.) Surprisingly,the same principles apply to physics.
Fresh and simpler approach to physics and mathematics consistent with the theorem.
Other possible applications
Can be applied, along with principles in maths, to problems where human element is involved.
Author - Nishank Gupta (NG) – IIT Roorkee(2009)
General optimization in decision making using logic
Statement 0: Any undefined quantity or let’s say infinity, I can assign a set of mean and deviation.Let me define this in two symbols "0" and "pi".
I might not know any specific “qualities” of this "0" and "pi", both might as well be irrational.
Let’s say I am studying a “property” of the undefined quantity. Hence, for multiple properties it can possibly have multiple mean, multiple deviation .{subsets}
Statement 1: Observations can only be made on the points of change.( Also till there is no change, no observation need/can be made).
Statement 2: With respect to change, there will be two qualities – one that of convergence, one that of divergence.
Statement 3:The more assumptions are made in a thoery, solution is only valid under the said assumptions, fails a lot more when the assumptions fail.
Defn:
Convergence- as changes occurs, collapses to a certain mean.(or restricts)
Divergence- as many changes, sometimes tries to converge to a mean, sometimes divergent, may as well be irrational.(eg pi in mathematics, human emotion(till date).)
Current No. of observations = N
Theorem : { C} R [V] , for this maxima weighted presence {C}, [V] on R give maxima truth.
{C} – Set of Constants.
[V] – Set of Optimized Variables.
R – Rules Applicable
Now,
we can say a Constant has a definite property of convergence, Variable has the definite property of Divergence.(essentialy C = will converge around some "0". V can diverge to some "pi". i.e irrationally never converges around at least one particular "0".("0" and "pi" as defined above)
{C} = w1*c1, w2*c2,w3*c3... etc. basically the weigthed average set of {C}.
similarly
[V] = w1*v1,w2*v2,w3*v3... etc, weighted average set of {V}.
R - Set of all the rules, under which {C} and {V} operate.
End of Defn.
Aim: To give a maxima/ minima output between, by the “presence” or “absence” of the weighted constants, variables that make up the undefined quantity.
Body: To arrive at any undefined quantity or infinity , the most logical way to do so is solve for the constants involved in the process by applying all the rules applicable in it, and then optimize all the random variables if needed using optimization techniques. The variables should be optimized last, first we should arrive at constants to simplify the problem.This is because if we assume the starting point of a theory from a variable. Theory will not be consistent when variable changes.
Note: we might not be able to say total "presence" or "absence"( in an maths allegory no exact 0 or 1 probability, still i can plot a spectrum.
Full: In any abstract or random infinity to arrive at ,lets say the constants involved are C1,C2,C3,C4….
The rules are R1,R2,R3,R4….
And the variables are V1,V2,V3,V4…..
Now, the most important thing would be to find the constants first.
Constant can come from a certain minimum assumption (wherein you made the mean of a min. variable as fixed, making it a constant).
Eg. Sun rises in the east ( only point of view of observer on earth)
Constant could be a statistical or mathematical fact, can come from general observation.
There are only 3 points of observations you can have for finding constants.
1.) In the en - masse (larger picture/integration) of things do we observe a constant behaviour?
2.)In the linear observation (single observation considered). do we observe something constant?
3.)In the way observations change , can we observe any constant property in the change?
Repeat: ( Detailed Explanation Appendix 1)
Variable – cannot be solved for exactly, unless we make it a constant, using one more assumption- in which case my error increases. I can only optimize a variable.Yet if i do the best optimisation the error would be very small. I would have best solved the problem to the desired accuracy if my optimisation was best(in the sense of robust).
This since it has divergence present too.
Examples of variables : emotions, people’s thoughts, speech , player’s form, weather,unknown quantity like the amount of charge left in the battery, would be a variable unless you can solve for it,pi in mathematics.
Repeat:The best(most robust) way to arrive at an abstract quantity or quality would be to first solve for the constant/constants in the equation, simplifying the problem, then optimize the variables in it.(basically first try and solve it with minimal assumptions, then assume more if you still cant solve it.) Let’s say the rules R1, R2, R3, R4 apply to the problem.
I am stressing robustness because sometimes problems are required to be solved for most accuracy, time is not a consideration.
Lets say that you have to take a decision between 0 and 1, fo x no. of observations.We can calculate the probability spectra around "0" and "pi", for the no of observations done till current "N".Essentially i can assign a probability min/max. solution on the presence or absence of constants and variables viz depending on how many weighted constants and weighted variables found in the current observations.This we can compare with all the previous outputs to give a current min/max probability( at what deviation it stands to the mean).We can now choose between the best and the worst probabilities, till current time of observation.
Since the process could be infinitely random, it could be that you may not arrive at absolute 1 or 0, implying that there is no absolute truth or false, unless you solve it using constants and rules alone. This would be the most robust way of decision making using observations.
End of Theorem.
Explanation:
Statement/ Mean and Deviation:
Any undefined object I can give some mean and deviation, a set of {0},s and {pi},s
First ,
We take a collection of the objects, see their mean and then try to identify if the collection has some definite property.
Basically, certainty increases in a larger set.
Eg. Human emotion.
If I give an individual’s emotions a mean and a deviation, then with no certainty can I say anything about the properties of that individual’s emotions.
If we take a collection of individuals, my certainty increases in a large enough set.
i.e in a large enough collection of soccer games, the average confidence of the average player from the home side is greater than that of the away side. ( This assumption would be way more fair than any assumption I make about the individual) So I fix the average confidence(home) as more than average confidence(away). I found a fix property in the mean.
The property being, C(H) > C(A). I found a constant.
Detailed Explanation –Appendix 1.
Corollary:
Now, for the undefined quantity, once we have obtained a maximum true strategy, or maximum true observation, identified by the “presence” of all/most constants and variables, on the rules-
For an individual observation, the “probabilistic” deviation from the max true strategy is proportional to the absence of the same constants and the variables. Deviation also identified using weights.
Basically, we can just see the deviation from max. true strategy instead of from minimum true strategy, to check how much an individual element might deviate from the maximum.
(Only used in Prisoner’s Dilemma).
Application in Game Theory.
Game Theory Problems.
Application in Game Theory.
Q1. John Nash went to a bar and saw 4 girls. He went there in a group of 4(including himself).
He wanted a strategy for best pairing up of 4 girls and 4 boys. The boys were to make a strategy in approach. Given is the order of looks/alpha to omega.
A B C D are the girls. {G} – set of girls
1 2 3 4 are the boys. {B} – set of boys
Sol: ( Method must be best scalable to apply the same strategy/ decision making in real world - So that problem is solved en-masse(bet on the highest probabilities).
or as demonstrated you try and bet on the emotional mean of society, to maximise your chances of winning, rather than optimising from self or for one general case)
Now applying logic.
Deriving the smallest assumption from the emotional mean of society.
Assumption : Emotional mean in girls of lets say ego is greater than boys.
In the sense girls are more likely to say no. E(G)>E(B)
Now, this is the fairest assumption ( also applies to most other animals around us, mate selection upto the female). This assumption comes from an observational mean of society. Might not apply to an individual girl/boy, but applies en masse.
So we have a constant with us ( which i obtained by applying min fair assumption)
E(g)>E(b)
The statement says, emotional mean of Ego in girls is greater than that of boys, en masse.(when concerning game)
Rule. : Game - All of them desire to match up. (desire means can still say no, but playing the game, else no game)
[ defining rules of game. again this is a min rule, just like min fair assumption and since E(g) > E(b), one of the girls can still say no, the desire for matchup would be more for boys from assumption]
Now for defining a strategy among boys, they have a variable to optimise - the girls ( their behavior en masse is a variable, for the boys they must use max strategy for max value desired)
Using an optimisation technique – Defining a line of sight for girls.
A - would be looking at 1, 2,3. Obviously highest chances for 1.
B- would be looking at 1,2,3.
C would be looking at 2,3,4.
D would be looking at 2,3,4.
I assigned them a mean and deviation in line of sight based on E(g). 1 is at more deviation than 2 to D.(giving a range of choice- no need to give it more range)
Looking at least E(g) girl , D, chances are less she'd go out with 4. if 3 goes and asks she might still refuse. For the most robust way, to get most number of girls the best risk reward would for 2 matching up to D.so i sacrifice 2 for D. (Note: it will eventually match up E(g) to E(b), less choice less E difference in sum, from rule)
hence.
2 = D
Now,
for A, she only has a choice between 1,3 . 2 is gone.Compare this with all {1,2,3}.
The chances are higher now that she pairs up with 1. ( if she still says no, well she'd have said mostly no anyways,she would have quite probably said no to 2 and 3)
If A says yes,
1=A.
now ,
B,C= 3,4
Now for B,C the only choices left are 3,4.
we can offer 3 to B first, if not then 3 to C.
If A says no you can get the best strategy anyways by now offering 1 to B.
This will maximise your chances of maximum boys pairing up.
The robustness of this method can be easily checked with the theorem.
In the sense that first i have bet on the constant, which was arrived at from a statistical mean, then optimised the variable later.Essentially i have bet on a fact first.
In this we are only betting on the emotional observable mean of society for max chances of winning.
Well so steps,
2 -- D
1 -- A
(3,4) -- (B,C) { Apply If’s else’s)
This solution is more scalable in the real world than the one obtained by
applying Game Theory.
Q 2. Prisoner’s Dilemma.
Similarly, we can apply the same method for Prisoner's Dilemma Problem .
Two prisoners A and B
Emotional mean Fear , F(A), F(B)
If A says guilty for B, B is imprisoned, for lets say 9 years.
If A says not guilty for B. B is imprisoned for 2 years.
similarly for B, and if both A and B say NG- Not Guilty, both get 3 years each.
Scalability.
Rule ( Both want to use highest probability strategy)
Now for real world, the problem is A isnt exactly sure what B is going to say.
If both A and B are to have a strategy, knowing the rules of the game, and the problem.
Both should just maximise their risk/reward for scalability. ( knowing if they use this strategy they win max en masse)
Both should just say NG. ( tradeoff for their F()). If a group of prisoners employ this strategy, they'd win maximum.Basically payoff for the group is much greater than individual's risk.
Solution:If iteration’s are allowed. Let me take a case. Prisoner’s A and B.
Case : One player is playing the game again and again. He remembers the previous inputs and outputs of the iteration and his real time decision is influenced by the risk/reward estimate he got from the previous iterations.Let’s say A is the subject. B is variable i.e B’s are changing for A.
Now, we have to optimise the individual A.( A and B being both the prisoner’s).
I can only optimise an irrationality, cannot exactly solve for A. Give him a probabalistic mean and a deviation from max . truth (his deviation from the mean of A's). Doing so would can help B in predicting A’s behaviour such that B can now Maximise his own Risk/Reward, based on A’s previous decisions.
Let us examine how A would deviate from the maximum true strategy of saying NG, every time.
Assumption 1: Deviations being controlled by an emotional quotient of fear E(F).(Only reason A would want to say Guilty would be out of fear of B pronouncing A Guilty, or also greed E(G), but more E(F), since strategy has been discussed).
Assumption 2:Memory function M for A. How many past games does he remember for decision making. M(A) = some n.
Note: All the assumptons are made for a mass of A’s . I say individually they might not hold in one A, but in let’s say 100 A’s the mean would act on these minimum assumptions.
Now,
Player A would deviate from rational decision making when E(F) goes beyond a certain point.
The feedback for A would be B’s decisions.
A would try to maximise his risk/reward, on the next iteration, based on previous iterations.
Now, lets say for A, B’s decisions would be infinitely random. Since B keeps on changing. (only A is fixed, many B’s - from case)
Giving out levels on E(F) where A’s decision making might deviate from mean.
0,1,2 --
Between 0 and 1 - most probability of rationality.ie. least deviation.
Between 1 and 2 - lesser probability of rationality and more deviation.
Beyond 2 - even lesser rationality and still more prob. of irrational decision. and so on.
Essentially, give {A} , set of A's a mean and deviation from max. strategy (NG), and then observe how individual A, diverges from that mean of {A} or give a probabalistic deviation of A from the prisoner’s mean to best predict his outcome.
Now, first solving for A ( to determine how A deviates from the mean).
A will try more to deviate to guilty if it has received as guilty more from the previous iterations, in the memory function.Basically E(F), fear or A has increases with G past inputs.
It will try and deviate to Guilty more if the other party says G.
i.e
A(mean) B
NG NG
NG G
NG G
--- ---
A might want to go for a deviation(Assum 1) on iteration 3, since the last time B had said Guilty, even though A said NG.
It would want more on 4th iteration and so on . (Assumption will hold unless E(F) decreases instead- much unlikelier case still)
The decision making would change only on the approach/breaking of some threshold value (The no. of hits A(mean) can take to definitely diverge to an irrational decision)
This threshold value can actually be arrived at after social experiments. But the value would only apply more precisely to a mass of A’s {A} and not to any individual A. It would be more accurate for the en-masse, rather than for individual A.
Lets say threshold would be, when E(F) crosses level 2.
we say threshold value = k times (punishment from B)/(payoff from max rational strategy)
Both punishment and payoff values are derived from Memory function of A.
So, once i know the threshold for {A}.
If now A is playing , for an iterative solution i can just see how A’s individual threshold differs from that of {A} i.e more threshold or less threshold, and then the likely or more probability decision that A is going to make on the next iteration if i know his memory function.
Each time A deviates faster from {A}(mean) i add a +1, and each time he deviates slower i subtract a 1, from 0 . Present value would be the current state of A, based on which i want to predict A’s next move.Values will give a probability spectrum on A.
In this way B can now actually decide to "punish" or "reward" A, depending on if A has a tendency to deviate "faster" from {A} mean or "slower" from {A} mean.
I can simply examine on the point of divergence to maximum predict A.
Game Theory only gives the chances of convergence given a long enough time
Examining now from Statement 3:
Assumptions of Game Theory.
"Game theory is a method of studying strategic decision making. More formally, it is the study ofmathematical models of conflict and cooperation between intelligent rational decision-makers.
The first known use is to describe and model how human populations behave. Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has come under recent criticism. First, it is criticized because the assumptions made by game theorists are often violated. Game theorists may assume players always act in a way to directly maximize their wins (the Homo economicus model), but in practice, human behavior often deviates from this model. Explanations of this phenomenon are many; irrationality, new models of deliberation, or even different motives (like that of altruism). Game theorists respond by comparing their assumptions to those used in physics. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific ideal akin to the models used by physicists. However, additional criticism of this use of game theory has been levied because some experiments have demonstrated that individuals do not play equilibrium strategies. For instance, in the centipede game, guess 2/3 of the average game, and the dictator game, people regularly do not play Nash equilibria. There is an ongoing debate regarding the importance of these experiments.[10]
Alternatively, some authors claim that Nash equilibria do not provide predictions for human populations, but rather provide an explanation for why populations that play Nash equilibria remain in that state. However, the question of how populations reach those points remains open."
"" Source : en.wikipedia.org/wiki/Game_theory
Game Theory applies to a rational set of thinkers. Eg. Computers are wholly rational. It does not exactly apply to people.It assumes that and tries to model human beings from scratch. Tries to give an optimisation for a variable first.
My point of argument is not that optimization, I know it is right, but it is still under those assumptions, which do not hold in the real world. In the real world, this can solve the same problems by using less assumptions, which will include the set that people are rational/irrational.
Well since i thought that the fault was in its assumptions, i might as well question the assumptions in other theories and try what happens, using this theorem.
Application to Mathematics
Basic assumption in mathematics is zero. Irrational numbers recur around rational numbers and rational numbers around irrational, on the number line.
Zero is a constant, wholly rational.
Now, assume if it has an irrational deviation from its mean, i.e you can never tell from 0’s Point of view, but still not hard to imagine very much.
It can pretty much have both irrational as well as rational components.
The rational component is fixed around a mean.
Well, no equation in mathematics can solve for this paradox, through mathematics. (you have to put it equal to zero). Also, Limit tending to 0+, and limit tending to 0-, point of convergence of both.
Well nonetheless it is assumed to be static. Which is not really a problem, since rationally we can only solve things by assuming a static starting point , zero. You have to define a zero to solve for everything else in mathematics. But the next assumption from there would make the problem even more complex, and specific.Also, more prone to error.
Coming on to pi.
Well, in terms of logic, attempt at defining pi is equal to.
Linearity of a circle / Linearity of a line
(line’s circumference/line’s length), for pi line’s length equal to diameter.
A circle might not have the property of linearity. Constant for a circle is, it has a property of bend or circularity.
Hence, pi is an error.
Let me explain more.
For circumference,
{Pi(r+theta)^2 – pi(r)^2}/theta , Limit. theta tending to 0.
We get, 2pi*r + pi*theta ,Limit. theta tending to 0.
Definition holds quite well except when r also closes to 0.
Also basically you are trying to cut a circle and straighten it into a line. The attempt will always have an error pi.
The number line might as well be discontinuous at pi.
The length, breadth , height we see around us are all closed spaces, why not the number line?
No, the number line is open.
At pi, imagine a slight bend, which you straightened into a line, to solve further using rational means, since you cannot anyways solve for that slightest of bends(can’t really cut it and make it into a line).
So, the attempt at finding value of pi is , the attempt to define an irrationality, in terms of rational numbers.
But, we have rational numbers between irrational too.
So a more correct form would be Max. rational distance between 0 and pi. Easier to define rational distances around irrational numbers. Both taken as symbols could denote min, as well as max. irrationality.(or recursive).(Number line being circular or…)
Hence, as you look rationally, more and more closer to 0, you will always find differentiable elements, or more irrational. Or, there would be no rational fractal/set.
The number line is infinite.i.e sample space is open
,in reality there is no open sample space.
at pi you make a mistake
if you start from 0.
if you fix 0 as a constant, you will never arrive at a rational value for pi.
pi is just a bend on the number line, the minimum of bends though.
No sample space is wholly open w.r.t to the quantity we are studying.
The divide by sign. Let’s say 4/5. 4 is defined from 0,5 is defined from 0.
now it is very true that probability is 0.8, but if 0 itself is irrational,then probability
is sometimes converging to 0.8 and sometimes diverging from 0.8, but it is very very close to it.
same logic.
0.000004/0.000005. would be more divergent from 0.8 than 4/5 was.
the more you differentiate things the more error you make.
Coming back to pi.
The basic statement in mathematics is distance between 0 and 1 is unity.( Would not really like to cite Brahmagupta’s Rules too)
Or is rational.
Well so coming from bend, d/dx of a circle is rational . i.e equal to 2pi*r if pi is also fixed.
Which is circle having the property of linearity – in its differentiation.
Again, a circle has no such property, it is just different.
For a circle.
d/dx^2 != rational. (!= not equal to or not similar to)
d/dx^3 != rational.
So on so on. , however a line can be defined as max you can enclose in that area, within a certain accuracy.
It should have been [pi]r from the start for a line.
(Pi*r)^2 for an area and so on.
Well, in the real world, no exact straight edges, all end up in circles, deeper you go, just find a circle, closed loop.
Even cosine, sine functions would fail, defined for sharp triangles, for small triangles, angle will become irrational too. Well so mathematics fails at a very microscopic view of thingsi.e comparing symmetry in the real world at microscopic scale. It would still hold pretty well for large values, since that error in symmetry is smaller now, compared to the value.
- Detailed Explanation Appendix 3.
Close.
Logic
Logic: Elements in logic.
Set
Symmetry/asymmetry in comparison
Change
Recursion
Error
Reset.
Set: Collection of symmetrical objects. Then subsets and supersets, based on what line of symmetry.
Comparison between two sets can be done on point of symmetry. ( =0).
Can also be done, if asymmetry, using “error” e and then symmetry.
There will be a change due to observation, and also, only change can be observed.
Once compared sets can be “clubbed”, around points of symmetry.
Starting from a basic fractal, a fractal set can be obtained.
The whole process can repeat on different “scales”.
The error is best observed as from the mean , rather than to a zero (just another mean).
Since we can observe basic “up” or “down” from mean. There would not be any problem even if mean is irrational, if the error is large enough – the difference can be quantized rational.
But if we observe the error as to a mean, then error itself will sometimes converge, sometimes diverge to the mean, if mean is also irrational.
These are the basic elements in logic.
Now,
The points in symmetry, can be either linear or circular
Also,
Simplest Equation in Nature.
( [ {A} = {B} ] )Probability of being equal.
{A} is set of symmetrical A’s.
{B} is set of symmetrical B’s.
[] – Repeat function, things might repeat asymmerically.
The aim is the comparison between, set of A’s and set of B’s, to get a line of symmetry.
The equality symbol will only hold a probability, since the act of observation will also bring about a change.we can assume rational symmetry.(we miss out on a few cases, but still again to solve it we are using minimum assumptions)
(or)
Observing along a set of A’s and comparing them to B’s. If all changes between both are symmetrical , then A would be symmetrical to B, with an error in observation e.
Statement: Change is a universal constant.
Ergo, even if you observe change, there will be a change in change.The “nature” of change is not linear. So for a long enough observation, eventually the feedback would be “bent”.
Thus, you would find a bend eventually, even if you go in a maximum straight line.
(Due to recursive nature of things, even if you run along symmetry, you will eventually find an asymmetry).
Now, along change there will be both attraction as well as repulsion. For balance, equal attraction and repulsion. Assuming balance.
Detailed explanation – Appendix 2.
Universe is more around logic than maths or physics.
Maths and physics are based on logic.
Appendix 1
In an infinite set of games, with fixed constant rules for all the said games, a general way of optimizing your bets.
First we identify useful constants. The constants could come from comparing a general mean of collection of things to another mean, simply as the mean being greater or smaller than the other i.e a useful property in the sum of things, which does not occur individually. Another way of finding a constant , would be to observe the change in the game. i.e if the change in a property of the game is constant or helps me arrive at a maximum probability of winning. Another constant, would be a simple rational constant. Eg. the number of players in the game is fixed.
The rules would be given, for the said game.( games could all have a variable output, but follow the said rules)
Lastly, we identify the variables like player’s form, weather, change in pitch conditions. These things cannot be exactly fixed around any mean.
Since, the number of games is infinite, I can assign a weighted average to each of the constants, then to each of the variables, depending on how much they impact the result of the game.
Lets say constants found are C1,C2,C3,C4.
Since, I have an infinite timeline, my best strategy of betting, so as to optimize my chances of winning –more rationally than by intuition, the best way to do so would be to identify the occurrence or recurrence of the constants on the timeline. I need not bet if there is no constant available at this time, since there would be no point in calculating the probability of winning if I start my bet on a variable. My maximum bets would be placed, when I see the concurrence of maximum constants. ( or you need not vary the bet size, simply place bets only when most constants are available, since anyways you have infinite set of games).
Let’s say at time t1, concurrence of constants, C1,C2,C3,C4.
At this time, I would want to optimize my variables now, so as to further identify my probability of winning.
The main point is that the process has to be scalable, so that you have you have a max rational strategy to apply.
Applying an analogy to soccer.
Eg.Suppose that you were given the problem of making money on a sample of infinite soccer games, there is no obvious or logical solution to the process, generally it would involve an emotive decision on part of the decision maker or the better.
First we’d try to solve for all the constants in the game,
ex: No. of players in each game in each side is 11 etc. But the individual players, their forms , the team’s performance etc are all variables. To set either as 1 or 0 would require an emotive judgement on part of one betting.
Now, the constants involved in the process could come from a statistical mean of lets say a large sample set of soccer games, using a fair set of assumptions.
Assumption: the player involved in the games are emotive and the average confidence of the average player in a team will influence the chances of winning.
The average confidence over a set of lets say a 100 games could be defined as a side being home/away.
The average confidence for average player of the home side over a set of 100 games would be larger and the chances of a home’s side winning would be larger.
Eg : in a set of 100 games lets say home side would win more than 50.(statistical mean)
Thus we have one constant E(C) home mean > E(C ) home away.
Similarly,
Stating that average fatigue of the average player will influence the side’s chances of winning.
The average fatigue over a set of lets say a 100 games could be defined as the average number of hours the average player has slept, the previous day before match.
More chances of less fatigue players winning the games.
Thus, one more constant.
E(F) More sleep < E(F) Less sleep ( Fatigue of those who sleep less is more on an average).
You cannot really make money by betting on just one constant.
Explanation: Even though for 100 games, the home side would win more games on an average (The quality of the teams will average out if I take a large enough sample space of games).
The money you make will depend on the rate being offered. Now, If a simple bid/offer rate is floated, since everyone knows about the home/away constant, this factor is automatically factored in into the rate through a feedback loop. Yet it is a statistical constant, better than any variable I have with me.
I look for other constants like fatigue.( the constants like no of players in a team, no of teams etc do not help at all, no difference between the two teams )
Now, to give a scalable strategy for betting on soccer, I simply optimize my variables such as a player’s form, team’s form, weather, as much as I can and choose only the games which have all the constants present, as well as all my optimized variables , to get the maximum probability of winning.
I have an infinite choice of soccer games, if let’s say in a game I have a few constants absent, or the variables are not optimized, I can simply choose not to bet. Since I have an infinite number of games anyways, I’ll find other games with constants being applicable as well as variables optimized.
End of Appendix 1
Appendix 2
Truth is defined as the value arrived at after thought for observation, in your sample space. The thinking process has both rational and irrational parts. Hence decision making is both rational and irrational, logic and emotion. Rationality and irrationality. Rationality is arrived at by first assuming the change in observation linear. D/dx = some constant.
Explanation:If I say the simple fractal for any object would be a line and circle. Even minutely , every line would have a circular end. No exact sharp corners observed in this world.( You can only call them sharp at an approximation, the more you observe , the more that approximation will tend to go wrong.) So rationality would be the maximum straight line you can draw or the maximum unbiased you can go, till a curve or circle is arrived at. Now, you optimize the smallest curve to be a straight line (d/dx= c, or if not d/dx2= c ,etc)(min assumption), and solve further(optimize), to arrive at the maximum rationality in your observations.
Basic logic by which you can arrive at the truth, is solve for the constants in the problem, apply the rules check if problem solved, then optimize another variable to become a constant. Every time you do this, check for the maximum truth obtained, i.e you get a truth maxima or minima along your observations.
Each time you go to measure the change, the measurement is through observation. For measurement you applied mathematics which had a basic assumption that 0 is fixed. One can only measure the change from yourself, or from the designed instrument. Since every instrument is rational, it would miss the irrational part.I can simply define the change as positive or negative from a mean, and then as more observations occur, more positive or less positive, from the previous observations. Same, with negative change . Only the change is fixed, your observation still has an inherent flaw for measuring it. If you take the first change to be linear. Eg. Assuming that 0 , which is an undefined quantity or infinity, has a mean and no deviation.
Lets define any unknown quantity, undefined thing as infinity[A]. Alone, [A] has no property. You can observe lets say a set of {A]’s and say the mean of this observation is ‘a’, a statistical constant from observations and give it an irrational deviation {[D]}. i.e set of [D], which when I add or subtract to mean, give me different [A]’s .
Now the maximum possible truth you can arrive at would be to solve for minimum ‘a’, minimum is being defined as least assumption constant. Constant has a basic property it has a mean and no deviation. Random variable has no mean, it sometimes converges or diverges to a mean.
Now, the equality symbol only has a probability , since you can only try and measure the change in A w.r.t B or vice – versa. If we assume both A and B to be rational, minimum first assumption, since without this we cannot compare. Or if we compare both their rational parts – then the equality symbol holds, since we can never say two irrational things are equal.
Hence change on a long enough scale can never be linear, somewhere along it will take a curve or bend – i.e things in nature have spiral behavior, or to state things simply, there is no such thing as an exact straight line. Mathematics maximizes rationality and assumes this change to be linear, by fixing 0 as a rational beginning of number line.
It does not hold true if the starting point 0, is not defined as a constant, but as a variable, which has both a mean and a deviation. Physics is the application of mathematics to real world observations.
Well so you were only trying to differentiate things from yourself.
First in length, breadth, height. Then mass , then time etc. Points of change.
Mathematics only applies in a model where the starting point of a thing is linear. Real world is more complicated, in the real world that assumption may not hold true.It only has a probability of holding true. You can only observe a change from a state.If I fix my starting point of things to a variable, may or may not be a constant i.e may or may not have affixed mean. But a collection of these things might have a few properties, might fix its mean around a few points eg{a,b,c,d } constant means, around which irrationality can be defined, as the deviation from the mean.since a change you cannot measure exactly, your observation will be inherently flawed. Basically there are only fixed points on irrationality, not irrationality between fixed points. To arrive at the max truth I would,
{[A]} how close to {[B]} how close only has a probability , which keeps on improving to arriving at the maximum rational thought in observation. If you say two things are exactly close. Eg 1 is a fixed distance away from 0. i.e 1 is 1 away in itself, your first assumption of 1 being mean is wrong in the real world, if you apply this mathematics in the real world.the problem is how many times a unity repeats in itself to give the maximum rational thought process. You cannot rationalize thinking beyond that. The other things are irrational in the decision making process. So if I base my number system around infinities or unknowns, rather than around constants i.e rational numbers. (there is no rational number) number in itself is a linear approximation of change. If I do that, there is no 0 or 1 , no exact 0 or 1 but we can arrive closer and closer by integrating the observation or by differentiating it. By seeing a collection of things or by seeing a difference in them. Since there is no exact 0 or 1. No exact truth or false. But for any decision making process we can give it a maximum optima based on past observations. The future has an irrational part too, is a result from this theory. And everything from Einstein’s relativity to number system. The problem of irrational numbers recurring in a rational number system, and applying that rationality to the real world. The most optimal way to arrive at the truth was simply based around the irrational things. The least effort method would be.
Desired change using minimum assumptions – Apply the rules of the game(question what is 0 or 1)(maxima or minima from observation) = Change seen? 0 or 1(1 if best till now , otherwise 0)
Recursively, increasing or decreasing the assumptions.
Prediction of GUT:
Quantity defined as mass, for the super set of universe , (i.e amount needed for the whole set to be in balance) compared to the quantity of mass found by rational means
is square root of (p)- 1. This can be checked easily on even wiki.
Solves for dark matter.
Uncertainty in symmetry solves for higgs boson.
Eg. First assumption linearity. That starting point of anything is constant. i.e 0 with just a mean and no deviation. i.e no irrational part in it. We get mathematics
A=B , the equality symbol has a 100% probability.
Second Assumption. Linearity in change in Linearity
If B=A, C=B, A=B, since ‘=’ symbol was probabilistic , you arrived at a lesser maxima of the truth.
Physics is derived from this, since first based on mathematics, then change in things if you apply maths to ordinary life and observation. You would assume you are the starting point. Which is a mean, but in reality your thought process has both a rational and irrational part. Logic and emotion, from which all thought is defined. Logic is linear to rationaltyi.e the process converges to a mean, and emotion has the property of deviation and irrationality, that it diverges in essence, has no true mean, and hence is irrational, has some deviation, what you try and measure can only be some change.
End of Appendix 2
Heres the link, bit easier to read.
Title- “ General Optimisation in decision making using logic”
I
Introduction
It gives out a simple theorem of logic, a statement, and a corollary.
The theorem gives out a simple max. way of solving for problems, either in finite boundary conditions or at infinite randomness.
The corollary examines how a sample point would deviate from the “max. true strategy” , as obtained for the group by using the theorem.
Applications:
Solved, within this paper,
1.)Firstly, for two problems of Game Theory – { Best matchup for 4 boys/4 girls , as well as Prisoner’s Dilemma (Iterative) }, it gives a scalable(in the sense best repeatable strategy) solution to both the problems in the real world. It also solves the same problems using more “precise” assumptions as well as lesser assumptions than game theory.
2.) Upon application to basic mathematics, points out to a question of mistake/misconception in Aryabhatta’s zero. Also tries to gives an explanation/definition for pi.
3.) Surprisingly,the same principles apply to physics.
Fresh and simpler approach to physics and mathematics consistent with the theorem.
Other possible applications
Can be applied, along with principles in maths, to problems where human element is involved.
Author - Nishank Gupta (NG) – IIT Roorkee(2009)
General optimization in decision making using logic
Statement 0: Any undefined quantity or let’s say infinity, I can assign a set of mean and deviation.Let me define this in two symbols "0" and "pi".
I might not know any specific “qualities” of this "0" and "pi", both might as well be irrational.
Let’s say I am studying a “property” of the undefined quantity. Hence, for multiple properties it can possibly have multiple mean, multiple deviation .{subsets}
Statement 1: Observations can only be made on the points of change.( Also till there is no change, no observation need/can be made).
Statement 2: With respect to change, there will be two qualities – one that of convergence, one that of divergence.
Statement 3:The more assumptions are made in a thoery, solution is only valid under the said assumptions, fails a lot more when the assumptions fail.
Defn:
Convergence- as changes occurs, collapses to a certain mean.(or restricts)
Divergence- as many changes, sometimes tries to converge to a mean, sometimes divergent, may as well be irrational.(eg pi in mathematics, human emotion(till date).)
Current No. of observations = N
Theorem : { C} R [V] , for this maxima weighted presence {C}, [V] on R give maxima truth.
{C} – Set of Constants.
[V] – Set of Optimized Variables.
R – Rules Applicable
Now,
we can say a Constant has a definite property of convergence, Variable has the definite property of Divergence.(essentialy C = will converge around some "0". V can diverge to some "pi". i.e irrationally never converges around at least one particular "0".("0" and "pi" as defined above)
{C} = w1*c1, w2*c2,w3*c3... etc. basically the weigthed average set of {C}.
similarly
[V] = w1*v1,w2*v2,w3*v3... etc, weighted average set of {V}.
R - Set of all the rules, under which {C} and {V} operate.
End of Defn.
Aim: To give a maxima/ minima output between, by the “presence” or “absence” of the weighted constants, variables that make up the undefined quantity.
Body: To arrive at any undefined quantity or infinity , the most logical way to do so is solve for the constants involved in the process by applying all the rules applicable in it, and then optimize all the random variables if needed using optimization techniques. The variables should be optimized last, first we should arrive at constants to simplify the problem.This is because if we assume the starting point of a theory from a variable. Theory will not be consistent when variable changes.
Note: we might not be able to say total "presence" or "absence"( in an maths allegory no exact 0 or 1 probability, still i can plot a spectrum.
Full: In any abstract or random infinity to arrive at ,lets say the constants involved are C1,C2,C3,C4….
The rules are R1,R2,R3,R4….
And the variables are V1,V2,V3,V4…..
Now, the most important thing would be to find the constants first.
Constant can come from a certain minimum assumption (wherein you made the mean of a min. variable as fixed, making it a constant).
Eg. Sun rises in the east ( only point of view of observer on earth)
Constant could be a statistical or mathematical fact, can come from general observation.
There are only 3 points of observations you can have for finding constants.
1.) In the en - masse (larger picture/integration) of things do we observe a constant behaviour?
2.)In the linear observation (single observation considered). do we observe something constant?
3.)In the way observations change , can we observe any constant property in the change?
Repeat: ( Detailed Explanation Appendix 1)
Variable – cannot be solved for exactly, unless we make it a constant, using one more assumption- in which case my error increases. I can only optimize a variable.Yet if i do the best optimisation the error would be very small. I would have best solved the problem to the desired accuracy if my optimisation was best(in the sense of robust).
This since it has divergence present too.
Examples of variables : emotions, people’s thoughts, speech , player’s form, weather,unknown quantity like the amount of charge left in the battery, would be a variable unless you can solve for it,pi in mathematics.
Repeat:The best(most robust) way to arrive at an abstract quantity or quality would be to first solve for the constant/constants in the equation, simplifying the problem, then optimize the variables in it.(basically first try and solve it with minimal assumptions, then assume more if you still cant solve it.) Let’s say the rules R1, R2, R3, R4 apply to the problem.
I am stressing robustness because sometimes problems are required to be solved for most accuracy, time is not a consideration.
Lets say that you have to take a decision between 0 and 1, fo x no. of observations.We can calculate the probability spectra around "0" and "pi", for the no of observations done till current "N".Essentially i can assign a probability min/max. solution on the presence or absence of constants and variables viz depending on how many weighted constants and weighted variables found in the current observations.This we can compare with all the previous outputs to give a current min/max probability( at what deviation it stands to the mean).We can now choose between the best and the worst probabilities, till current time of observation.
Since the process could be infinitely random, it could be that you may not arrive at absolute 1 or 0, implying that there is no absolute truth or false, unless you solve it using constants and rules alone. This would be the most robust way of decision making using observations.
End of Theorem.
Explanation:
Statement/ Mean and Deviation:
Any undefined object I can give some mean and deviation, a set of {0},s and {pi},s
First ,
We take a collection of the objects, see their mean and then try to identify if the collection has some definite property.
Basically, certainty increases in a larger set.
Eg. Human emotion.
If I give an individual’s emotions a mean and a deviation, then with no certainty can I say anything about the properties of that individual’s emotions.
If we take a collection of individuals, my certainty increases in a large enough set.
i.e in a large enough collection of soccer games, the average confidence of the average player from the home side is greater than that of the away side. ( This assumption would be way more fair than any assumption I make about the individual) So I fix the average confidence(home) as more than average confidence(away). I found a fix property in the mean.
The property being, C(H) > C(A). I found a constant.
Detailed Explanation –Appendix 1.
Corollary:
Now, for the undefined quantity, once we have obtained a maximum true strategy, or maximum true observation, identified by the “presence” of all/most constants and variables, on the rules-
For an individual observation, the “probabilistic” deviation from the max true strategy is proportional to the absence of the same constants and the variables. Deviation also identified using weights.
Basically, we can just see the deviation from max. true strategy instead of from minimum true strategy, to check how much an individual element might deviate from the maximum.
(Only used in Prisoner’s Dilemma).
Application in Game Theory.
Game Theory Problems.
Application in Game Theory.
Q1. John Nash went to a bar and saw 4 girls. He went there in a group of 4(including himself).
He wanted a strategy for best pairing up of 4 girls and 4 boys. The boys were to make a strategy in approach. Given is the order of looks/alpha to omega.
A B C D are the girls. {G} – set of girls
1 2 3 4 are the boys. {B} – set of boys
Sol: ( Method must be best scalable to apply the same strategy/ decision making in real world - So that problem is solved en-masse(bet on the highest probabilities).
or as demonstrated you try and bet on the emotional mean of society, to maximise your chances of winning, rather than optimising from self or for one general case)
Now applying logic.
Deriving the smallest assumption from the emotional mean of society.
Assumption : Emotional mean in girls of lets say ego is greater than boys.
In the sense girls are more likely to say no. E(G)>E(B)
Now, this is the fairest assumption ( also applies to most other animals around us, mate selection upto the female). This assumption comes from an observational mean of society. Might not apply to an individual girl/boy, but applies en masse.
So we have a constant with us ( which i obtained by applying min fair assumption)
E(g)>E(b)
The statement says, emotional mean of Ego in girls is greater than that of boys, en masse.(when concerning game)
Rule. : Game - All of them desire to match up. (desire means can still say no, but playing the game, else no game)
[ defining rules of game. again this is a min rule, just like min fair assumption and since E(g) > E(b), one of the girls can still say no, the desire for matchup would be more for boys from assumption]
Now for defining a strategy among boys, they have a variable to optimise - the girls ( their behavior en masse is a variable, for the boys they must use max strategy for max value desired)
Using an optimisation technique – Defining a line of sight for girls.
A - would be looking at 1, 2,3. Obviously highest chances for 1.
B- would be looking at 1,2,3.
C would be looking at 2,3,4.
D would be looking at 2,3,4.
I assigned them a mean and deviation in line of sight based on E(g). 1 is at more deviation than 2 to D.(giving a range of choice- no need to give it more range)
Looking at least E(g) girl , D, chances are less she'd go out with 4. if 3 goes and asks she might still refuse. For the most robust way, to get most number of girls the best risk reward would for 2 matching up to D.so i sacrifice 2 for D. (Note: it will eventually match up E(g) to E(b), less choice less E difference in sum, from rule)
hence.
2 = D
Now,
for A, she only has a choice between 1,3 . 2 is gone.Compare this with all {1,2,3}.
The chances are higher now that she pairs up with 1. ( if she still says no, well she'd have said mostly no anyways,she would have quite probably said no to 2 and 3)
If A says yes,
1=A.
now ,
B,C= 3,4
Now for B,C the only choices left are 3,4.
we can offer 3 to B first, if not then 3 to C.
If A says no you can get the best strategy anyways by now offering 1 to B.
This will maximise your chances of maximum boys pairing up.
The robustness of this method can be easily checked with the theorem.
In the sense that first i have bet on the constant, which was arrived at from a statistical mean, then optimised the variable later.Essentially i have bet on a fact first.
In this we are only betting on the emotional observable mean of society for max chances of winning.
Well so steps,
2 -- D
1 -- A
(3,4) -- (B,C) { Apply If’s else’s)
This solution is more scalable in the real world than the one obtained by
applying Game Theory.
Q 2. Prisoner’s Dilemma.
Similarly, we can apply the same method for Prisoner's Dilemma Problem .
Two prisoners A and B
Emotional mean Fear , F(A), F(B)
If A says guilty for B, B is imprisoned, for lets say 9 years.
If A says not guilty for B. B is imprisoned for 2 years.
similarly for B, and if both A and B say NG- Not Guilty, both get 3 years each.
Scalability.
Rule ( Both want to use highest probability strategy)
Now for real world, the problem is A isnt exactly sure what B is going to say.
If both A and B are to have a strategy, knowing the rules of the game, and the problem.
Both should just maximise their risk/reward for scalability. ( knowing if they use this strategy they win max en masse)
Both should just say NG. ( tradeoff for their F()). If a group of prisoners employ this strategy, they'd win maximum.Basically payoff for the group is much greater than individual's risk.
Solution:If iteration’s are allowed. Let me take a case. Prisoner’s A and B.
Case : One player is playing the game again and again. He remembers the previous inputs and outputs of the iteration and his real time decision is influenced by the risk/reward estimate he got from the previous iterations.Let’s say A is the subject. B is variable i.e B’s are changing for A.
Now, we have to optimise the individual A.( A and B being both the prisoner’s).
I can only optimise an irrationality, cannot exactly solve for A. Give him a probabalistic mean and a deviation from max . truth (his deviation from the mean of A's). Doing so would can help B in predicting A’s behaviour such that B can now Maximise his own Risk/Reward, based on A’s previous decisions.
Let us examine how A would deviate from the maximum true strategy of saying NG, every time.
Assumption 1: Deviations being controlled by an emotional quotient of fear E(F).(Only reason A would want to say Guilty would be out of fear of B pronouncing A Guilty, or also greed E(G), but more E(F), since strategy has been discussed).
Assumption 2:Memory function M for A. How many past games does he remember for decision making. M(A) = some n.
Note: All the assumptons are made for a mass of A’s . I say individually they might not hold in one A, but in let’s say 100 A’s the mean would act on these minimum assumptions.
Now,
Player A would deviate from rational decision making when E(F) goes beyond a certain point.
The feedback for A would be B’s decisions.
A would try to maximise his risk/reward, on the next iteration, based on previous iterations.
Now, lets say for A, B’s decisions would be infinitely random. Since B keeps on changing. (only A is fixed, many B’s - from case)
Giving out levels on E(F) where A’s decision making might deviate from mean.
0,1,2 --
Between 0 and 1 - most probability of rationality.ie. least deviation.
Between 1 and 2 - lesser probability of rationality and more deviation.
Beyond 2 - even lesser rationality and still more prob. of irrational decision. and so on.
Essentially, give {A} , set of A's a mean and deviation from max. strategy (NG), and then observe how individual A, diverges from that mean of {A} or give a probabalistic deviation of A from the prisoner’s mean to best predict his outcome.
Now, first solving for A ( to determine how A deviates from the mean).
A will try more to deviate to guilty if it has received as guilty more from the previous iterations, in the memory function.Basically E(F), fear or A has increases with G past inputs.
It will try and deviate to Guilty more if the other party says G.
i.e
A(mean) B
NG NG
NG G
NG G
--- ---
A might want to go for a deviation(Assum 1) on iteration 3, since the last time B had said Guilty, even though A said NG.
It would want more on 4th iteration and so on . (Assumption will hold unless E(F) decreases instead- much unlikelier case still)
The decision making would change only on the approach/breaking of some threshold value (The no. of hits A(mean) can take to definitely diverge to an irrational decision)
This threshold value can actually be arrived at after social experiments. But the value would only apply more precisely to a mass of A’s {A} and not to any individual A. It would be more accurate for the en-masse, rather than for individual A.
Lets say threshold would be, when E(F) crosses level 2.
we say threshold value = k times (punishment from B)/(payoff from max rational strategy)
Both punishment and payoff values are derived from Memory function of A.
So, once i know the threshold for {A}.
If now A is playing , for an iterative solution i can just see how A’s individual threshold differs from that of {A} i.e more threshold or less threshold, and then the likely or more probability decision that A is going to make on the next iteration if i know his memory function.
Each time A deviates faster from {A}(mean) i add a +1, and each time he deviates slower i subtract a 1, from 0 . Present value would be the current state of A, based on which i want to predict A’s next move.Values will give a probability spectrum on A.
In this way B can now actually decide to "punish" or "reward" A, depending on if A has a tendency to deviate "faster" from {A} mean or "slower" from {A} mean.
I can simply examine on the point of divergence to maximum predict A.
Game Theory only gives the chances of convergence given a long enough time
Examining now from Statement 3:
Assumptions of Game Theory.
"Game theory is a method of studying strategic decision making. More formally, it is the study ofmathematical models of conflict and cooperation between intelligent rational decision-makers.
The first known use is to describe and model how human populations behave. Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has come under recent criticism. First, it is criticized because the assumptions made by game theorists are often violated. Game theorists may assume players always act in a way to directly maximize their wins (the Homo economicus model), but in practice, human behavior often deviates from this model. Explanations of this phenomenon are many; irrationality, new models of deliberation, or even different motives (like that of altruism). Game theorists respond by comparing their assumptions to those used in physics. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific ideal akin to the models used by physicists. However, additional criticism of this use of game theory has been levied because some experiments have demonstrated that individuals do not play equilibrium strategies. For instance, in the centipede game, guess 2/3 of the average game, and the dictator game, people regularly do not play Nash equilibria. There is an ongoing debate regarding the importance of these experiments.[10]
Alternatively, some authors claim that Nash equilibria do not provide predictions for human populations, but rather provide an explanation for why populations that play Nash equilibria remain in that state. However, the question of how populations reach those points remains open."
"" Source : en.wikipedia.org/wiki/Game_theory
Game Theory applies to a rational set of thinkers. Eg. Computers are wholly rational. It does not exactly apply to people.It assumes that and tries to model human beings from scratch. Tries to give an optimisation for a variable first.
My point of argument is not that optimization, I know it is right, but it is still under those assumptions, which do not hold in the real world. In the real world, this can solve the same problems by using less assumptions, which will include the set that people are rational/irrational.
Well since i thought that the fault was in its assumptions, i might as well question the assumptions in other theories and try what happens, using this theorem.
Application to Mathematics
Basic assumption in mathematics is zero. Irrational numbers recur around rational numbers and rational numbers around irrational, on the number line.
Zero is a constant, wholly rational.
Now, assume if it has an irrational deviation from its mean, i.e you can never tell from 0’s Point of view, but still not hard to imagine very much.
It can pretty much have both irrational as well as rational components.
The rational component is fixed around a mean.
Well, no equation in mathematics can solve for this paradox, through mathematics. (you have to put it equal to zero). Also, Limit tending to 0+, and limit tending to 0-, point of convergence of both.
Well nonetheless it is assumed to be static. Which is not really a problem, since rationally we can only solve things by assuming a static starting point , zero. You have to define a zero to solve for everything else in mathematics. But the next assumption from there would make the problem even more complex, and specific.Also, more prone to error.
Coming on to pi.
Well, in terms of logic, attempt at defining pi is equal to.
Linearity of a circle / Linearity of a line
(line’s circumference/line’s length), for pi line’s length equal to diameter.
A circle might not have the property of linearity. Constant for a circle is, it has a property of bend or circularity.
Hence, pi is an error.
Let me explain more.
For circumference,
{Pi(r+theta)^2 – pi(r)^2}/theta , Limit. theta tending to 0.
We get, 2pi*r + pi*theta ,Limit. theta tending to 0.
Definition holds quite well except when r also closes to 0.
Also basically you are trying to cut a circle and straighten it into a line. The attempt will always have an error pi.
The number line might as well be discontinuous at pi.
The length, breadth , height we see around us are all closed spaces, why not the number line?
No, the number line is open.
At pi, imagine a slight bend, which you straightened into a line, to solve further using rational means, since you cannot anyways solve for that slightest of bends(can’t really cut it and make it into a line).
So, the attempt at finding value of pi is , the attempt to define an irrationality, in terms of rational numbers.
But, we have rational numbers between irrational too.
So a more correct form would be Max. rational distance between 0 and pi. Easier to define rational distances around irrational numbers. Both taken as symbols could denote min, as well as max. irrationality.(or recursive).(Number line being circular or…)
Hence, as you look rationally, more and more closer to 0, you will always find differentiable elements, or more irrational. Or, there would be no rational fractal/set.
The number line is infinite.i.e sample space is open
,in reality there is no open sample space.
at pi you make a mistake
if you start from 0.
if you fix 0 as a constant, you will never arrive at a rational value for pi.
pi is just a bend on the number line, the minimum of bends though.
No sample space is wholly open w.r.t to the quantity we are studying.
The divide by sign. Let’s say 4/5. 4 is defined from 0,5 is defined from 0.
now it is very true that probability is 0.8, but if 0 itself is irrational,then probability
is sometimes converging to 0.8 and sometimes diverging from 0.8, but it is very very close to it.
same logic.
0.000004/0.000005. would be more divergent from 0.8 than 4/5 was.
the more you differentiate things the more error you make.
Coming back to pi.
The basic statement in mathematics is distance between 0 and 1 is unity.( Would not really like to cite Brahmagupta’s Rules too)
Or is rational.
Well so coming from bend, d/dx of a circle is rational . i.e equal to 2pi*r if pi is also fixed.
Which is circle having the property of linearity – in its differentiation.
Again, a circle has no such property, it is just different.
For a circle.
d/dx^2 != rational. (!= not equal to or not similar to)
d/dx^3 != rational.
So on so on. , however a line can be defined as max you can enclose in that area, within a certain accuracy.
It should have been [pi]r from the start for a line.
(Pi*r)^2 for an area and so on.
Well, in the real world, no exact straight edges, all end up in circles, deeper you go, just find a circle, closed loop.
Even cosine, sine functions would fail, defined for sharp triangles, for small triangles, angle will become irrational too. Well so mathematics fails at a very microscopic view of thingsi.e comparing symmetry in the real world at microscopic scale. It would still hold pretty well for large values, since that error in symmetry is smaller now, compared to the value.
- Detailed Explanation Appendix 3.
Close.
Logic
Logic: Elements in logic.
Set
Symmetry/asymmetry in comparison
Change
Recursion
Error
Reset.
Set: Collection of symmetrical objects. Then subsets and supersets, based on what line of symmetry.
Comparison between two sets can be done on point of symmetry. ( =0).
Can also be done, if asymmetry, using “error” e and then symmetry.
There will be a change due to observation, and also, only change can be observed.
Once compared sets can be “clubbed”, around points of symmetry.
Starting from a basic fractal, a fractal set can be obtained.
The whole process can repeat on different “scales”.
The error is best observed as from the mean , rather than to a zero (just another mean).
Since we can observe basic “up” or “down” from mean. There would not be any problem even if mean is irrational, if the error is large enough – the difference can be quantized rational.
But if we observe the error as to a mean, then error itself will sometimes converge, sometimes diverge to the mean, if mean is also irrational.
These are the basic elements in logic.
Now,
The points in symmetry, can be either linear or circular
Also,
Simplest Equation in Nature.
( [ {A} = {B} ] )Probability of being equal.
{A} is set of symmetrical A’s.
{B} is set of symmetrical B’s.
[] – Repeat function, things might repeat asymmerically.
The aim is the comparison between, set of A’s and set of B’s, to get a line of symmetry.
The equality symbol will only hold a probability, since the act of observation will also bring about a change.we can assume rational symmetry.(we miss out on a few cases, but still again to solve it we are using minimum assumptions)
(or)
Observing along a set of A’s and comparing them to B’s. If all changes between both are symmetrical , then A would be symmetrical to B, with an error in observation e.
Statement: Change is a universal constant.
Ergo, even if you observe change, there will be a change in change.The “nature” of change is not linear. So for a long enough observation, eventually the feedback would be “bent”.
Thus, you would find a bend eventually, even if you go in a maximum straight line.
(Due to recursive nature of things, even if you run along symmetry, you will eventually find an asymmetry).
Now, along change there will be both attraction as well as repulsion. For balance, equal attraction and repulsion. Assuming balance.
Detailed explanation – Appendix 2.
Universe is more around logic than maths or physics.
Maths and physics are based on logic.
Appendix 1
In an infinite set of games, with fixed constant rules for all the said games, a general way of optimizing your bets.
First we identify useful constants. The constants could come from comparing a general mean of collection of things to another mean, simply as the mean being greater or smaller than the other i.e a useful property in the sum of things, which does not occur individually. Another way of finding a constant , would be to observe the change in the game. i.e if the change in a property of the game is constant or helps me arrive at a maximum probability of winning. Another constant, would be a simple rational constant. Eg. the number of players in the game is fixed.
The rules would be given, for the said game.( games could all have a variable output, but follow the said rules)
Lastly, we identify the variables like player’s form, weather, change in pitch conditions. These things cannot be exactly fixed around any mean.
Since, the number of games is infinite, I can assign a weighted average to each of the constants, then to each of the variables, depending on how much they impact the result of the game.
Lets say constants found are C1,C2,C3,C4.
Since, I have an infinite timeline, my best strategy of betting, so as to optimize my chances of winning –more rationally than by intuition, the best way to do so would be to identify the occurrence or recurrence of the constants on the timeline. I need not bet if there is no constant available at this time, since there would be no point in calculating the probability of winning if I start my bet on a variable. My maximum bets would be placed, when I see the concurrence of maximum constants. ( or you need not vary the bet size, simply place bets only when most constants are available, since anyways you have infinite set of games).
Let’s say at time t1, concurrence of constants, C1,C2,C3,C4.
At this time, I would want to optimize my variables now, so as to further identify my probability of winning.
The main point is that the process has to be scalable, so that you have you have a max rational strategy to apply.
Applying an analogy to soccer.
Eg.Suppose that you were given the problem of making money on a sample of infinite soccer games, there is no obvious or logical solution to the process, generally it would involve an emotive decision on part of the decision maker or the better.
First we’d try to solve for all the constants in the game,
ex: No. of players in each game in each side is 11 etc. But the individual players, their forms , the team’s performance etc are all variables. To set either as 1 or 0 would require an emotive judgement on part of one betting.
Now, the constants involved in the process could come from a statistical mean of lets say a large sample set of soccer games, using a fair set of assumptions.
Assumption: the player involved in the games are emotive and the average confidence of the average player in a team will influence the chances of winning.
The average confidence over a set of lets say a 100 games could be defined as a side being home/away.
The average confidence for average player of the home side over a set of 100 games would be larger and the chances of a home’s side winning would be larger.
Eg : in a set of 100 games lets say home side would win more than 50.(statistical mean)
Thus we have one constant E(C) home mean > E(C ) home away.
Similarly,
Stating that average fatigue of the average player will influence the side’s chances of winning.
The average fatigue over a set of lets say a 100 games could be defined as the average number of hours the average player has slept, the previous day before match.
More chances of less fatigue players winning the games.
Thus, one more constant.
E(F) More sleep < E(F) Less sleep ( Fatigue of those who sleep less is more on an average).
You cannot really make money by betting on just one constant.
Explanation: Even though for 100 games, the home side would win more games on an average (The quality of the teams will average out if I take a large enough sample space of games).
The money you make will depend on the rate being offered. Now, If a simple bid/offer rate is floated, since everyone knows about the home/away constant, this factor is automatically factored in into the rate through a feedback loop. Yet it is a statistical constant, better than any variable I have with me.
I look for other constants like fatigue.( the constants like no of players in a team, no of teams etc do not help at all, no difference between the two teams )
Now, to give a scalable strategy for betting on soccer, I simply optimize my variables such as a player’s form, team’s form, weather, as much as I can and choose only the games which have all the constants present, as well as all my optimized variables , to get the maximum probability of winning.
I have an infinite choice of soccer games, if let’s say in a game I have a few constants absent, or the variables are not optimized, I can simply choose not to bet. Since I have an infinite number of games anyways, I’ll find other games with constants being applicable as well as variables optimized.
End of Appendix 1
Appendix 2
Truth is defined as the value arrived at after thought for observation, in your sample space. The thinking process has both rational and irrational parts. Hence decision making is both rational and irrational, logic and emotion. Rationality and irrationality. Rationality is arrived at by first assuming the change in observation linear. D/dx = some constant.
Explanation:If I say the simple fractal for any object would be a line and circle. Even minutely , every line would have a circular end. No exact sharp corners observed in this world.( You can only call them sharp at an approximation, the more you observe , the more that approximation will tend to go wrong.) So rationality would be the maximum straight line you can draw or the maximum unbiased you can go, till a curve or circle is arrived at. Now, you optimize the smallest curve to be a straight line (d/dx= c, or if not d/dx2= c ,etc)(min assumption), and solve further(optimize), to arrive at the maximum rationality in your observations.
Basic logic by which you can arrive at the truth, is solve for the constants in the problem, apply the rules check if problem solved, then optimize another variable to become a constant. Every time you do this, check for the maximum truth obtained, i.e you get a truth maxima or minima along your observations.
Each time you go to measure the change, the measurement is through observation. For measurement you applied mathematics which had a basic assumption that 0 is fixed. One can only measure the change from yourself, or from the designed instrument. Since every instrument is rational, it would miss the irrational part.I can simply define the change as positive or negative from a mean, and then as more observations occur, more positive or less positive, from the previous observations. Same, with negative change . Only the change is fixed, your observation still has an inherent flaw for measuring it. If you take the first change to be linear. Eg. Assuming that 0 , which is an undefined quantity or infinity, has a mean and no deviation.
Lets define any unknown quantity, undefined thing as infinity[A]. Alone, [A] has no property. You can observe lets say a set of {A]’s and say the mean of this observation is ‘a’, a statistical constant from observations and give it an irrational deviation {[D]}. i.e set of [D], which when I add or subtract to mean, give me different [A]’s .
Now the maximum possible truth you can arrive at would be to solve for minimum ‘a’, minimum is being defined as least assumption constant. Constant has a basic property it has a mean and no deviation. Random variable has no mean, it sometimes converges or diverges to a mean.
Now, the equality symbol only has a probability , since you can only try and measure the change in A w.r.t B or vice – versa. If we assume both A and B to be rational, minimum first assumption, since without this we cannot compare. Or if we compare both their rational parts – then the equality symbol holds, since we can never say two irrational things are equal.
Hence change on a long enough scale can never be linear, somewhere along it will take a curve or bend – i.e things in nature have spiral behavior, or to state things simply, there is no such thing as an exact straight line. Mathematics maximizes rationality and assumes this change to be linear, by fixing 0 as a rational beginning of number line.
It does not hold true if the starting point 0, is not defined as a constant, but as a variable, which has both a mean and a deviation. Physics is the application of mathematics to real world observations.
Well so you were only trying to differentiate things from yourself.
First in length, breadth, height. Then mass , then time etc. Points of change.
Mathematics only applies in a model where the starting point of a thing is linear. Real world is more complicated, in the real world that assumption may not hold true.It only has a probability of holding true. You can only observe a change from a state.If I fix my starting point of things to a variable, may or may not be a constant i.e may or may not have affixed mean. But a collection of these things might have a few properties, might fix its mean around a few points eg{a,b,c,d } constant means, around which irrationality can be defined, as the deviation from the mean.since a change you cannot measure exactly, your observation will be inherently flawed. Basically there are only fixed points on irrationality, not irrationality between fixed points. To arrive at the max truth I would,
{[A]} how close to {[B]} how close only has a probability , which keeps on improving to arriving at the maximum rational thought in observation. If you say two things are exactly close. Eg 1 is a fixed distance away from 0. i.e 1 is 1 away in itself, your first assumption of 1 being mean is wrong in the real world, if you apply this mathematics in the real world.the problem is how many times a unity repeats in itself to give the maximum rational thought process. You cannot rationalize thinking beyond that. The other things are irrational in the decision making process. So if I base my number system around infinities or unknowns, rather than around constants i.e rational numbers. (there is no rational number) number in itself is a linear approximation of change. If I do that, there is no 0 or 1 , no exact 0 or 1 but we can arrive closer and closer by integrating the observation or by differentiating it. By seeing a collection of things or by seeing a difference in them. Since there is no exact 0 or 1. No exact truth or false. But for any decision making process we can give it a maximum optima based on past observations. The future has an irrational part too, is a result from this theory. And everything from Einstein’s relativity to number system. The problem of irrational numbers recurring in a rational number system, and applying that rationality to the real world. The most optimal way to arrive at the truth was simply based around the irrational things. The least effort method would be.
Desired change using minimum assumptions – Apply the rules of the game(question what is 0 or 1)(maxima or minima from observation) = Change seen? 0 or 1(1 if best till now , otherwise 0)
Recursively, increasing or decreasing the assumptions.
Prediction of GUT:
Quantity defined as mass, for the super set of universe , (i.e amount needed for the whole set to be in balance) compared to the quantity of mass found by rational means
is square root of (p)- 1. This can be checked easily on even wiki.
Solves for dark matter.
Uncertainty in symmetry solves for higgs boson.
Eg. First assumption linearity. That starting point of anything is constant. i.e 0 with just a mean and no deviation. i.e no irrational part in it. We get mathematics
A=B , the equality symbol has a 100% probability.
Second Assumption. Linearity in change in Linearity
If B=A, C=B, A=B, since ‘=’ symbol was probabilistic , you arrived at a lesser maxima of the truth.
Physics is derived from this, since first based on mathematics, then change in things if you apply maths to ordinary life and observation. You would assume you are the starting point. Which is a mean, but in reality your thought process has both a rational and irrational part. Logic and emotion, from which all thought is defined. Logic is linear to rationaltyi.e the process converges to a mean, and emotion has the property of deviation and irrationality, that it diverges in essence, has no true mean, and hence is irrational, has some deviation, what you try and measure can only be some change.
End of Appendix 2
Last edited by nishank on Wed Jun 13, 2012 7:19 am UTC, edited 1 time in total.
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 6:17 am UTC
I am stumped by its applications. Please help me out guys and give it a read.
I can give a much moro thorough write if it interests enough people.
I can give a much moro thorough write if it interests enough people.
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Re: Hi/Game structure for financial markets
by dshizzle » Tue Jun 12, 2012 2:54 pm UTC
Cant tell if troll or not.
Reality must take precedence over public relations, for nature cannot be fooled. - Feynman
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Re: Hi/Game structure for financial markets
by Cleverbeans » Tue Jun 12, 2012 3:26 pm UTC
The article fails to follow the outline you provided, and many statements are meaningless, others are simply gibberish. For example
This is nonsense, it doesn't even make sense in context nor does it make sense to me in any other way. I think it's also clear you lack the mathematical sophistication to describe your idea because of your challenge to Aryabhatta’s zero. In general, if a mathematical object with a well established definition and a clear, logical construction fails to model the problem you're trying to solve, it's better to make up a new mathematical object rather than try to redefine an existing one.
However, beyond that you may find that some of your ideas are contained in other optimization techniques, particularly linear programming and convex optimization. The language I'm familiar with is a little different than the language you've given, but you might find researching those subjects gives you the vocabulary you need to describe it. You can find a good course from Stanford by following the link to get you started.
nishank wrote:Assumption : Emotional mean in girls of lets say ego is greater than boys.
In the sense girls are more likely to say no. E(G)>E(B)
This is nonsense, it doesn't even make sense in context nor does it make sense to me in any other way. I think it's also clear you lack the mathematical sophistication to describe your idea because of your challenge to Aryabhatta’s zero. In general, if a mathematical object with a well established definition and a clear, logical construction fails to model the problem you're trying to solve, it's better to make up a new mathematical object rather than try to redefine an existing one.
However, beyond that you may find that some of your ideas are contained in other optimization techniques, particularly linear programming and convex optimization. The language I'm familiar with is a little different than the language you've given, but you might find researching those subjects gives you the vocabulary you need to describe it. You can find a good course from Stanford by following the link to get you started.
"Labor is prior to, and independent of, capital. Capital is only the fruit of labor, and could never have existed if labor had not first existed. Labor is the superior of capital, and deserves much the higher consideration." - Abraham Lincoln
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Re: Hi/Game structure for financial markets
by dshizzle » Tue Jun 12, 2012 4:38 pm UTC
It scares me that someone who deals with futures markets thinks about math this way.
Reality must take precedence over public relations, for nature cannot be fooled. - Feynman
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 6:00 pm UTC
Well, i wasn't really trying to construct a mathematical model in the first place.
It could simply have been a logical one.
Tell me exactly what doesnt make sense, ill try and explain it.
Assumption: E(G)> E(B).( Used term "ego" to quantify the statement "girls would be more choosy", since there is a difference in behaviour)
I am analysing the emotional differences that make up the problem.
This is the min. fairest assumption, derived from a statistical fact. A min. fair assumption from observation.
The thing is i found the theorem to be universally applicable.
Wouldn't have posted it here, if it didnt question 0.
I can with the theorem, Just saying let me give it an irrational deviation like pi has from mean, and then check what happens.
The case can be the case that deviation is nil,
But my first assumption is min. assumption. 0 fixed would be a subset .(Essentially i was trying to apply logic to real world problems, using this theorem)
In real world- No absolute 0, no absolute vacuum, no absolute 0k.etc
It could simply have been a logical one.
Tell me exactly what doesnt make sense, ill try and explain it.
Assumption: E(G)> E(B).( Used term "ego" to quantify the statement "girls would be more choosy", since there is a difference in behaviour)
I am analysing the emotional differences that make up the problem.
This is the min. fairest assumption, derived from a statistical fact. A min. fair assumption from observation.
The thing is i found the theorem to be universally applicable.
Wouldn't have posted it here, if it didnt question 0.
I can with the theorem, Just saying let me give it an irrational deviation like pi has from mean, and then check what happens.
The case can be the case that deviation is nil,
But my first assumption is min. assumption. 0 fixed would be a subset .(Essentially i was trying to apply logic to real world problems, using this theorem)
In real world- No absolute 0, no absolute vacuum, no absolute 0k.etc
Last edited by nishank on Tue Jun 12, 2012 6:36 pm UTC, edited 2 times in total.
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 6:03 pm UTC
did you get the theorem, ?
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Re: Hi/Game structure for financial markets
by dshizzle » Tue Jun 12, 2012 6:38 pm UTC
"math" and "logic" eh. You seem to have a rather cursory understanding of the meaning of those words. As to what doesn't make sense, basically the whole paper. It is not written in such a way that it puts forth any kind of coherent thesis, it could be that you do have some brilliant idea in there somewhere but the way it reads now is like the rambling of a pothead. If you want people to take your work seriously then try formulating your ideas in such a way that they are understandable. I'm sorry if that came off as rather rude, but what you have presented is not math, or logic so far as I can see. I am going to read it again, and see if there is something I am missing.
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Re: Hi/Game structure for financial markets
by dshizzle » Tue Jun 12, 2012 6:44 pm UTC
Could you perhaps give a concise statement of what you wish to prove?
Reality must take precedence over public relations, for nature cannot be fooled. - Feynman
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 6:54 pm UTC
Please do forgive me for the language, i should have posted in the logic section.
tell me what to give a better definition for, i'll try and get an edit done.
Please do not spam.
tell me what to give a better definition for, i'll try and get an edit done.
Please do not spam.
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Re: Hi/Game structure for financial markets
by dshizzle » Tue Jun 12, 2012 6:57 pm UTC
Not trying to spam, or be overly critical. What are you trying to prove? If your not trying to prove something then what are you suggesting?
Reality must take precedence over public relations, for nature cannot be fooled. - Feynman
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 6:58 pm UTC
Statement of Proof: More robust than game theory, explains maths and physics in nature, from a different perspective.
It's a super set.since it starts from min. assumptions.
It's a super set.since it starts from min. assumptions.
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Re: Hi/Game structure for financial markets
by dshizzle » Tue Jun 12, 2012 7:05 pm UTC
That is not a theorem, or a hypothesis.
I think your trying to describe what you hope your theorem would be, if it were true. I'm asking what is it?
nishank wrote:Statement of Proof: More robust than game theory, explains maths and physics in nature, from a different perspective.
I think your trying to describe what you hope your theorem would be, if it were true. I'm asking what is it?
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 12, 2012 7:21 pm UTC
I can plot a probability spectrum for truth, based on previous observations.Never saying exact 0 or 1.
Points to a general limit of observation, which could explain things in mathematics and physics better.
Do you also have any thoughts on the ideas mentioned.
Ill try and arrange it per the best language i can find. It'll take me some time.
I hope it was an interesting read anyways.
Seems it'll be way more difficult getting the point across than i imagined.
well if you have read the whole thing, it would have been a lot simpler.
The only point of this paper was to define what the game structure would look like.
It then became an interesting write. Per se i wasn't trying to prove something.
Points to a general limit of observation, which could explain things in mathematics and physics better.
Do you also have any thoughts on the ideas mentioned.
Ill try and arrange it per the best language i can find. It'll take me some time.
I hope it was an interesting read anyways.
Seems it'll be way more difficult getting the point across than i imagined.
well if you have read the whole thing, it would have been a lot simpler.
The only point of this paper was to define what the game structure would look like.
It then became an interesting write. Per se i wasn't trying to prove something.
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Re: Hi/Game structure for financial markets
by Talith » Tue Jun 12, 2012 9:20 pm UTC
I would suggest learning to write in a clear and coherent manner before trying to communicate what could be a bright idea. At the moment you are probably frustrated because no one can understand it, but others are equally frustrated because your writing is not clear in the slightest. Be very deliberate about your choice of words, stick to standards where they exist, and when they don't exist, make sure you clearly define new terms using other old and well established terms.
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Re: Hi/Game structure for financial markets
by Who, me? » Wed Jun 13, 2012 12:19 am UTC
nishank wrote:I can plot a probability spectrum for truth, based on previous observations.Never saying exact 0 or 1.
Points to a general limit of observation, which could explain things in mathematics and physics better.
Do you also have any thoughts on the ideas mentioned.
Ill try and arrange it per the best language i can find. It'll take me some time.
Still not sure what "it's" supposed to do. It's like if somebody handed you a turboencabulator and starting telling you how it works. You'd be a bit confused, because you have no clue what it actually does. Try to summarize/explain what it is you've found from the top down; from the most general idea to the most basic routine one. It can be difficult, especially if you're not completely sure yourself what you're explaining, but that's a good thing
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Re: Hi/Game structure for financial markets
by nishank » Wed Jun 13, 2012 6:56 am UTC
Oh, i get it now, let me engage in a discussion to explain it.
lets say you were given the task of betting on football games.
So that your strategy is scalable, howd you do it.
What'd be the best way of doing it.
Basically, what'll be the points in your decision making.
You have an infinite soccer games to choose from.
lets say you were given the task of betting on football games.
So that your strategy is scalable, howd you do it.
What'd be the best way of doing it.
Basically, what'll be the points in your decision making.
You have an infinite soccer games to choose from.
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Re: Hi/Game structure for financial markets
by nishank » Thu Jun 14, 2012 5:30 am UTC
Well it's written in logic, is consistent
the steps of logic are hard to follow maybe sometimes.
You'll get it i guess in a discussion better.
What factors would you think of if you have to bet on soccer games?
the steps of logic are hard to follow maybe sometimes.
You'll get it i guess in a discussion better.
What factors would you think of if you have to bet on soccer games?
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Re: Hi/Game structure for financial markets
by heyitsguay » Thu Jun 14, 2012 4:22 pm UTC
This might have some relevant information for you:
http://en.wikipedia.org/wiki/Dunning%E2 ... ger_effect
http://en.wikipedia.org/wiki/Dunning%E2 ... ger_effect
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Re: Hi/Game structure for financial markets
by nishank » Fri Jun 15, 2012 4:38 am UTC
Well its just an idea i got mate.
I don't really mind being wrong.
At the very least give me a chance to explain it.
ARgh. i didnt really expect many to understand it in the first place, i thought someone would, but rare chance of anyone reading it now ^^
Talking about a logic structure for a set of universal laws. That's my whole point. A little patience would certainly help the both of us here.
Sidenote: For a football games, what are the common elements ppl would bet on. I.e what would their points in decision making be.
For eg. You may bet based on your fav football player(messi , rooney etc. ) , fav team (etc)
If youre given the task what kind of strategy would you figure out to make money.
I don't really mind being wrong.
At the very least give me a chance to explain it.
ARgh. i didnt really expect many to understand it in the first place, i thought someone would, but rare chance of anyone reading it now ^^
Talking about a logic structure for a set of universal laws. That's my whole point. A little patience would certainly help the both of us here.
Sidenote: For a football games, what are the common elements ppl would bet on. I.e what would their points in decision making be.
For eg. You may bet based on your fav football player(messi , rooney etc. ) , fav team (etc)
If youre given the task what kind of strategy would you figure out to make money.
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Re: Hi/Game structure for financial markets
by t1mm01994 » Sun Jun 17, 2012 12:19 am UTC
Since you posted this in Logic Puzzles, I feel okay to bump this thread up a bit.
Are you a native English speaker?
You seem to misuse some words. Quite some words, in fact. Your entire style reminds me of some of our earlier friends who claimed to prove something that went wrong on several places, starting with a language barrier but what turned out to be complete gibberish even in the original language.
Are you a native English speaker?
You seem to misuse some words. Quite some words, in fact. Your entire style reminds me of some of our earlier friends who claimed to prove something that went wrong on several places, starting with a language barrier but what turned out to be complete gibberish even in the original language.
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Re: Hi/Game structure for financial markets
by nishank » Sun Jun 17, 2012 1:07 pm UTC
Point taken, judge it without understanding 
. Still hoping someone gets it.
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Re: Hi/Game structure for financial markets
by t1mm01994 » Sun Jun 17, 2012 3:11 pm UTC
Let me post that more carefully.
Are you a native English speaker?
Are you a native English speaker?
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Re: Hi/Game structure for financial markets
by nishank » Sun Jun 17, 2012 7:12 pm UTC
How does who i am matter.
Is the grammar incorrect?(i might have missed something in the editing of things, if you point out the mistakes i can correct them or give more explanations)
Terms have been defined.
No numbers needed since it's a paper of logic, not maths.
Well chill out, heres my point.
a) If you understand the theorem, let me demonstrate how it can work in football betting, and on game theory.
b). If you dont get the theorem. Well you know let me sort the whole mess in the discussion .
Is the grammar incorrect?(i might have missed something in the editing of things, if you point out the mistakes i can correct them or give more explanations)
Terms have been defined.
No numbers needed since it's a paper of logic, not maths.
Well chill out, heres my point.
a) If you understand the theorem, let me demonstrate how it can work in football betting, and on game theory.
b). If you dont get the theorem. Well you know let me sort the whole mess in the discussion .
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Re: Hi/Game structure for financial markets
by t1mm01994 » Sun Jun 17, 2012 10:41 pm UTC
Let's start at the beginning, at your definition of the word divergence. That seems quite dodgy to me (incorrect in grammar, too); defining divergence as "either trying to converge or diverging" seems circular.
Can you turn that into mathematical symbols? From what I see you're not quite comfortable in english, but symbols are a language we all speak.
EDIT: That said, a demonstration would never hurt, perhaps I can poke some sense into that...
Can you turn that into mathematical symbols? From what I see you're not quite comfortable in english, but symbols are a language we all speak.
EDIT: That said, a demonstration would never hurt, perhaps I can poke some sense into that...
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Re: Hi/Game structure for financial markets
by nishank » Mon Jun 18, 2012 3:46 pm UTC
Yes sir ,
well let me explain this term in detail.
Taking the example of football games, using the theorem,
constants available to me : No of players each side, no of balls, no .of referees, etc.
Like 11 players, 1 ball, 2 refs etc. these are linear constants: You can observe them through linear thinking. They are quite clear to everyone.
Notice: They dont change per game, no matter who perceives them, they will remain constant.
Now, lets say someone happens to bet, just cause they like messi.
They think messi is the best player in the world and hes going to score a lot of goals next game. ( might come true, might not too).
The individual player messi's performance in the future, is a variable, cant exactly pinpoint how he is going to play the next game (can say with high probability based on his past performance).
That variable has a quality of divergence. I cant exactly define how it is going to be, but can still optimise it to say for eg.- messi will do well. (i.e above the mean set of players).
Let me elaborate on this divergence now.
The theorem states a way of giving probability maximum or minima while studying an infinitely random input.
In other words an infinitely random object(every real sense analogy too).
We have some points in observations,
Now for the infinitely random object, i can put it as a sum of a few constants and few variables.
Constant: will definitely converge around some mean( eg. 11 players in football game, sunrises in east(w.r.t to earth) etc.)
Variable: Might or might not converge around any mean - eg. human emotion for one, changes everyday for everyone, never exactly remains the same, can never exactly say anything about one particular mean, or how well messi will do, or pi in maths - is never one specific number keeps changing, though can still give a desired significant value. etc.
The question that it can either be convergent or divergent comes from the limit in observation itself (you can never be sure sometimes, for eg . in 2 observations may not be able to derive any sure facts(if both are different or same), in three i can be more sure and then on.
Now, in a specific problem, there may not be any variables at all. maybe it can be solved using constants alone.(most linear problems)
The constants and variables have a weighted average attached, based on past observations( or states).
Well that about sums up the answer to your Question.
Now, coming back to the football theme.
I identified a few easy constants. But they are of no use to us in the process of money making( since the problem was that one had to bet.)
There are a few more constants i can arrive at.
Now, let me say, that Assumption: An individual player is an emotive being and his emotions impact the outcome of the game.
Also, statement; Any individual quality i can assign some mean and deviation.( i may or may not be sure of their values but i am sure that any quality will have a mean and a deviation)
Assigning an individual players emotion a mean and a deviation now.
i say,
The more confident team will win more on an average than the less confident team.
Confidence can be amply substituted by the home or away factor( it's meant to influence confidence),
i get, the average more confident player/team wins more than the average less confident player/team
So E(C home)> E(C away) , in other terms, i found another constant fact.
This constant applies to en masse of players( in the sense that i cant say the same thing for sure between any two home or away players, but applies to the whole group for sure)
please tell me if its lucid and clear till here so i can move on to the next part
well let me explain this term in detail.
Taking the example of football games, using the theorem,
constants available to me : No of players each side, no of balls, no .of referees, etc.
Like 11 players, 1 ball, 2 refs etc. these are linear constants: You can observe them through linear thinking. They are quite clear to everyone.
Notice: They dont change per game, no matter who perceives them, they will remain constant.
Now, lets say someone happens to bet, just cause they like messi.
They think messi is the best player in the world and hes going to score a lot of goals next game. ( might come true, might not too).
The individual player messi's performance in the future, is a variable, cant exactly pinpoint how he is going to play the next game (can say with high probability based on his past performance).
That variable has a quality of divergence. I cant exactly define how it is going to be, but can still optimise it to say for eg.- messi will do well. (i.e above the mean set of players).
Let me elaborate on this divergence now.
The theorem states a way of giving probability maximum or minima while studying an infinitely random input.
In other words an infinitely random object(every real sense analogy too).
We have some points in observations,
Now for the infinitely random object, i can put it as a sum of a few constants and few variables.
Constant: will definitely converge around some mean( eg. 11 players in football game, sunrises in east(w.r.t to earth) etc.)
Variable: Might or might not converge around any mean - eg. human emotion for one, changes everyday for everyone, never exactly remains the same, can never exactly say anything about one particular mean, or how well messi will do, or pi in maths - is never one specific number keeps changing, though can still give a desired significant value. etc.
The question that it can either be convergent or divergent comes from the limit in observation itself (you can never be sure sometimes, for eg . in 2 observations may not be able to derive any sure facts(if both are different or same), in three i can be more sure and then on.
Now, in a specific problem, there may not be any variables at all. maybe it can be solved using constants alone.(most linear problems)
The constants and variables have a weighted average attached, based on past observations( or states).
Well that about sums up the answer to your Question.
Now, coming back to the football theme.
I identified a few easy constants. But they are of no use to us in the process of money making( since the problem was that one had to bet.)
There are a few more constants i can arrive at.
Now, let me say, that Assumption: An individual player is an emotive being and his emotions impact the outcome of the game.
Also, statement; Any individual quality i can assign some mean and deviation.( i may or may not be sure of their values but i am sure that any quality will have a mean and a deviation)
Assigning an individual players emotion a mean and a deviation now.
i say,
The more confident team will win more on an average than the less confident team.
Confidence can be amply substituted by the home or away factor( it's meant to influence confidence),
i get, the average more confident player/team wins more than the average less confident player/team
So E(C home)> E(C away) , in other terms, i found another constant fact.
This constant applies to en masse of players( in the sense that i cant say the same thing for sure between any two home or away players, but applies to the whole group for sure)
please tell me if its lucid and clear till here so i can move on to the next part
- nishank
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Re: Hi/Game structure for financial markets
by t1mm01994 » Mon Jun 18, 2012 7:05 pm UTC
The sad thing is that your definitions are so far off normal things o.O
Convergence is the same as usual, but usually divergence is defined by the opposite of convergence, whereas here it is defined by... being variable, I believe.
But yeah. I'm going to paraphrase what you just said, in order to make sure I understand you:
There are constants in football, i.e. 2 goalies, a ball, other constant stuff.
There are variables too, i.e. each player's mood, form, or current level of stamina.
These variables can be assigned a mean and a deviation.
In other news, with equal skill, the more motivated team (in its entirity) will win a football match; this can be altered by playing home or away (I do not see how this follows from or connects to the past 4 sentences, or how this is related to math or logic yet)
Convergence is the same as usual, but usually divergence is defined by the opposite of convergence, whereas here it is defined by... being variable, I believe.
But yeah. I'm going to paraphrase what you just said, in order to make sure I understand you:
There are constants in football, i.e. 2 goalies, a ball, other constant stuff.
There are variables too, i.e. each player's mood, form, or current level of stamina.
These variables can be assigned a mean and a deviation.
In other news, with equal skill, the more motivated team (in its entirity) will win a football match; this can be altered by playing home or away (I do not see how this follows from or connects to the past 4 sentences, or how this is related to math or logic yet)
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Re: Hi/Game structure for financial markets
by Gwydion » Tue Jun 19, 2012 1:00 am UTC
So, the following may or may not be the intent of the original author - following in timm's footsteps, I've attempted to translate the original wall of text into actual English/mathspeak where I've been able. I've also chosen to freely interject my opinions, and hopefully those can be easily separated from the intended content. Unnecessarily all-caps words are places in which I'm trying to emphasize that a non-standard use of a traditional math term is being used, rather than changing the core language of the post. In places where the words are all lowercase, that's me using actual words as they apply in standard English/Mathematics and should not be seen as synonymous with the all-caps terms. Also, I've tried to inject a modicum of humor to keep the interest of anyone choosing to read this. In hindsight, I may have also gotten more and more frustrated with it as I went, so by the end it's a little more disjointed.
To the OP: is this what you had in mind?Dear sweet Jesus, that was a bad idea, but once I got started I just couldn't bring myself to stop halfway.
To the OP: is this what you had in mind?
Spoiler:
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Re: Hi/Game structure for financial markets
by Dopefish » Tue Jun 19, 2012 3:04 am UTC
Gwydion wrote:So, the following may or may not be the intent of the original author - following in timm's footsteps, I've attempted to translate the original wall of text into actual English/mathspeak where I've been able. I've also chosen to freely interject my opinions, and hopefully those can be easily separated from the intended content. Unnecessarily all-caps words are places in which I'm trying to emphasize that a non-standard use of a traditional math term is being used, rather than changing the core language of the post. In places where the words are all lowercase, that's me using actual words as they apply in standard English/Mathematics and should not be seen as synonymous with the all-caps terms. Also, I've tried to inject a modicum of humor to keep the interest of anyone choosing to read this. In hindsight, I may have also gotten more and more frustrated with it as I went, so by the end it's a little more disjointed.
To the OP: is this what you had in mind?Dear sweet Jesus, that was a bad idea, but once I got started I just couldn't bring myself to stop halfway.Spoiler:
Thank you sir, you deserve a medal. I just read all of that and enjoyed it thoroughly. I'm almost tempted to get a bottle of tequila and attempt to read through the OP's version to see how true to it you were. Almost.
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 19, 2012 12:08 pm UTC
No , not what i had in mind, I realise i should have explained things properly in the maths section, you got a bit lost. Give me some time to edit that.
The above thing was written to prove it to myself first.( so that everything was properly clear). I didn't obviously realise that it would be hard to understand. sorry for the error.The document is essentially right though.
Let me just explain the football case first.it'll be way easier to move on to the next things then.
I have an infinite sample of football games( in the sense of continuity, football games occur everyday).
If i have to choose a few x best set to bet on.
Looking for constants in the integration of observed objects.
one is E(C(home))>E(C(away))= C1.
Also, in a similar manner in which we obtained C1,
The less fatigue player(on an avg) will do better than more fatigue player.
E(F(less))>E(F(more))= C2.
I can associate fatigue to the avg no of sleeping hours on prev. night.
Looking at observations linearly, No. of football players, no. of teams, etc. dont really help much.
Also, i can find more constants, in the change of observations. ( These would be from second level assumptions though, unlike C1 or C2)
Like. how E of one player would vary after lets say scoring a goal.(statement of the kind this will happen if x has already happened)
So , lets say through the whole process we have now arrived at weighted set {C}.
For a given point in observation(or sample space). It will have any/all/none constants "present" from {C}.
Now, i have to choose the best points on the sample space to bet on.
I will arrange points, as per the weightage of constants present.
On these points, i can now observe all the variables ( eg rooney,messi doing well, particular team barca/manu, weather etc.) and give them a certain optimised value. as is always done.
I have an infinite choice of games, ill always find the games of my fav player, teams, but they would always be variables.
Instead better to first choose games with max. constants, then from this set choose other optimised variables to find the best games to bet on.
This is the best method of betting. ( another can only pick up better constants, get more variables right with better optimisation, but method would be same)
1 - this is still explaining the theorem, things will be way easier then, let me move on to corollary.
The above thing was written to prove it to myself first.( so that everything was properly clear). I didn't obviously realise that it would be hard to understand. sorry for the error.The document is essentially right though.
Let me just explain the football case first.it'll be way easier to move on to the next things then.
I have an infinite sample of football games( in the sense of continuity, football games occur everyday).
If i have to choose a few x best set to bet on.
Looking for constants in the integration of observed objects.
one is E(C(home))>E(C(away))= C1.
Also, in a similar manner in which we obtained C1,
The less fatigue player(on an avg) will do better than more fatigue player.
E(F(less))>E(F(more))= C2.
I can associate fatigue to the avg no of sleeping hours on prev. night.
Looking at observations linearly, No. of football players, no. of teams, etc. dont really help much.
Also, i can find more constants, in the change of observations. ( These would be from second level assumptions though, unlike C1 or C2)
Like. how E of one player would vary after lets say scoring a goal.(statement of the kind this will happen if x has already happened)
So , lets say through the whole process we have now arrived at weighted set {C}.
For a given point in observation(or sample space). It will have any/all/none constants "present" from {C}.
Now, i have to choose the best points on the sample space to bet on.
I will arrange points, as per the weightage of constants present.
On these points, i can now observe all the variables ( eg rooney,messi doing well, particular team barca/manu, weather etc.) and give them a certain optimised value. as is always done.
I have an infinite choice of games, ill always find the games of my fav player, teams, but they would always be variables.
Instead better to first choose games with max. constants, then from this set choose other optimised variables to find the best games to bet on.
This is the best method of betting. ( another can only pick up better constants, get more variables right with better optimisation, but method would be same)
1 - this is still explaining the theorem, things will be way easier then, let me move on to corollary.
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 19, 2012 12:21 pm UTC
@ prev guy. no i just said what i said, everything else is what you are saying. never said anything about how to make a team win.
You will not understand the whole thing if you just read a part. Only the whole thing has a meaning.if you read just one part it would prolly seem absurd.
let me explain it and then we can decide on the absurd part, better than deciding it right now.
You will not understand the whole thing if you just read a part. Only the whole thing has a meaning.if you read just one part it would prolly seem absurd.
let me explain it and then we can decide on the absurd part, better than deciding it right now.
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Re: Hi/Game structure for financial markets
by t1mm01994 » Tue Jun 19, 2012 1:06 pm UTC
Paraphrasing that, too:
There are more factors in concluding who'll win a game, mostly who's most energetic/feeling best. The winning team will likely get a morale boost.
If you factor all this correctly, you'll have the optimal way of betting.
I see how it's true, I don't see how it's at all helpful, ever. Yes, the best way of betting is correctly assessing all variables.
There are more factors in concluding who'll win a game, mostly who's most energetic/feeling best. The winning team will likely get a morale boost.
If you factor all this correctly, you'll have the optimal way of betting.
I see how it's true, I don't see how it's at all helpful, ever. Yes, the best way of betting is correctly assessing all variables.
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 19, 2012 1:27 pm UTC
t1mm01994 wrote:Paraphrasing that, too:
There are more factors in concluding who'll win a game, mostly who's most energetic/feeling best. The winning team will likely get a morale boost.
If you factor all this correctly, you'll have the optimal way of betting.
I see how it's true, I don't see how it's at all helpful, ever. Yes, the best way of betting is correctly assessing all variables.
Yes there are more factors. Those can only come from second level assumptions, (how do you qauntify whos feeling best?)the winning team will likely get a morale boost. morale boost given winning team. it's more uncertain. i wouldn't want to use this in my function, but even if you want to you'd surely still give it less weightage than C1,C2. It would be a sub set.the full superset being {C}.
Let me paraphrase that, the help you can get is you won't need to do the "factoring" all the time, you only factor in the variables when the constants are present in the observation point.Because you have infinite soccer games, it's best if you only factor in when {C} has higher weightage present, instead of doing it all the time , which would be lower than {C}.
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Re: Hi/Game structure for financial markets
by Gwydion » Tue Jun 19, 2012 4:16 pm UTC
So, if I'm understanding you right, you're suggesting that we try to identify those factors whose effect on the outcome are the strongest, which is to say not effected through an indirect mechanism, rather than try to recognize all of the possible factors involved? I'm still not sure why that isn't obvious on its face, and requires so much effort to demonstrate.
Some (more serious) suggestions to help clean up the original post, and for future reference:
1) When using established mathematical terms and symbols, make sure you're using them in the way that they are rigorously defined and applied.
2) If that definition is not suitable, create a new word or symbol and define that, but make sure it is not a word or symbol that is in common use elsewhere in the field. Nonsense words are acceptable as placeholders in this stage, and can be substituted for more common or appropriate words once you have a more clear grasp of the concept you're trying to express.
3) If people continue to have trouble understanding what you are trying to say, it may be a problem of language and communication rather than a flaw in the concept. It could always be the other, or both, but until the language discrepancy is resolved, it isn't possible to assess the rest.
4) If the original concept is a little fuzzy, examples can be very helpful in clearing up concepts. In contrast, if the original concept is unintelligible, it is difficult for readers to apply those examples in the way you intended. In that case, less is more (or more appropriately, more is less).
Rather than focusing on explaining your soccer analogy more clearly, can we return to the theory itself, which I think is even less clear? We seem to be "missing the point" that you're trying to make, which makes applying that point much more difficult.
Some (more serious) suggestions to help clean up the original post, and for future reference:
1) When using established mathematical terms and symbols, make sure you're using them in the way that they are rigorously defined and applied.
2) If that definition is not suitable, create a new word or symbol and define that, but make sure it is not a word or symbol that is in common use elsewhere in the field. Nonsense words are acceptable as placeholders in this stage, and can be substituted for more common or appropriate words once you have a more clear grasp of the concept you're trying to express.
3) If people continue to have trouble understanding what you are trying to say, it may be a problem of language and communication rather than a flaw in the concept. It could always be the other, or both, but until the language discrepancy is resolved, it isn't possible to assess the rest.
4) If the original concept is a little fuzzy, examples can be very helpful in clearing up concepts. In contrast, if the original concept is unintelligible, it is difficult for readers to apply those examples in the way you intended. In that case, less is more (or more appropriately, more is less).
Rather than focusing on explaining your soccer analogy more clearly, can we return to the theory itself, which I think is even less clear? We seem to be "missing the point" that you're trying to make, which makes applying that point much more difficult.
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Re: Hi/Game structure for financial markets
by nishank » Tue Jun 19, 2012 5:18 pm UTC
Gwydion wrote:So, if I'm understanding you right, you're suggesting that we try to identify those factors whose effect on the outcome are the strongest, which is to say not effected through an indirect mechanism, rather than try to recognize all of the possible factors involved? I'm still not sure why that isn't obvious on its face, and requires so much effort to demonstrate.
Some (more serious) suggestions to help clean up the original post, and for future reference:
1) When using established mathematical terms and symbols, make sure you're using them in the way that they are rigorously defined and applied.
2) If that definition is not suitable, create a new word or symbol and define that, but make sure it is not a word or symbol that is in common use elsewhere in the field. Nonsense words are acceptable as placeholders in this stage, and can be substituted for more common or appropriate words once you have a more clear grasp of the concept you're trying to express.
3) If people continue to have trouble understanding what you are trying to say, it may be a problem of language and communication rather than a flaw in the concept. It could always be the other, or both, but until the language discrepancy is resolved, it isn't possible to assess the rest.
4) If the original concept is a little fuzzy, examples can be very helpful in clearing up concepts. In contrast, if the original concept is unintelligible, it is difficult for readers to apply those examples in the way you intended. In that case, less is more (or more appropriately, more is less).
Rather than focusing on explaining your soccer analogy more clearly, can we return to the theory itself, which I think is even less clear? We seem to be "missing the point" that you're trying to make, which makes applying that point much more difficult.
1).Not the strongest, the surest, since i have to pick out my best bets. Which is the point on which i think you are confused.
Chuck all screw it, would have made godel proud though
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Re: Hi/Game structure for financial markets
by nishank » Mon Jun 25, 2012 8:22 am UTC
will explain this later . Thanks
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