Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Sunday, January 19, 2014

Something from Nothing

Finally I've decided to blog-out my - still not mature - thoughts on how Something can be created from Nothing.

It's all about philosophy and Math, but I'll try to keep it simple, as the most fundamental things in life are simple.

Also keep in mind that what follows is not necessarily 'true', but more a 'thought model' helping to explain and to grasp the phenomenon of creating 'something out of nothing'.


Basic Thoughts
Try to imagine Nothing....

After a few minutes of philosophizing you'll notice, it's not possible to imagine Nothing. All we can come up with, is the 'idea' of Nothing, as Nothing is in fact 'No Thing'.

Now, this idea is exactly what 'was', 'is', and for ever 'will be': an 'idea'. Not a specific idea, but the concept of an idea. That's enough. The concept of an idea  doesn't exist in space or time, it's simply there. It's the metaphor of the concept of Nothing. It's potential.

'Idea' is the only word that not only is defined as a noun (passive, object), but 'at the same time' also as a kind of verb (operator, action), as an idea is 'that what can be imagined'. You also 'have' an idea.

Hence, an idea is passive and active at the same time. In self-reference terms the idea is the imagination of an idea.

This idea is in fact what we call 'spirit' in the wider sense of the word. It's an intention, it has the 'potential' (power) of 'creativity', of creating a (positive) illusion. In other words: it's the basis of 'creation'.

Let's define this general concept of  'idea' by the symbol 'i'.


The idea Mathematically expressed
As an idea is 'not real' but imaginary, the most logical mathematical translation of an idea (i) is the mathematical unit imaginary number, denoted as well as: 'i'

'i' is a so called 'complex number' in mathematics with the core property that if you multiply it with itself, the product is "−1".

So i 2 = −1.

As we all now there's no real number that multiplied with itself is a negative number (−1). So (i) will do perfectly as mathematical translation, as we'll see further on.


Next Step: How to create 'Something'
Now we've accepted the general concept of an idea (i), the question is : how to get from an idea (of Nothing) to Something if we have Nothing else but an idea (i).

The problem, or better expressed 'our luck' is that we have nothing else but an idea (i). Fortunately the concept of the idea (i) is as well singular as (not literally) plural and also object as well as operator, as the concept of ideas is still an idea and the imagination of an idea is also an idea.

So all it takes for an idea to create a 'next stage idea' is to apply the idea-concept on itself as an object and operator. It doesn't matter which one is the object or the operator, as object and operator on the idea-level are the same.

Creating Antimatter
O.K. Let's demonstrate what happens if we imply (the concept of) an idea on itself while applying some basic simple 'complex mathematics' as defined above:

i i = i(i) = i 2 =  −1

As we can see, the result is a 'real number'. Not only is it real, but it's also negative.
We can and will interpret a positive real number as what we perceive in our world as 'space'. We can touch it and see it, it's real...
Therefore a negative real number can be interpreted as 'antimatter'.

So applying an idea on itself generates 'antimatter'

Creating Time
Now let's go on by applying an idea on antimatter
Here it is:

i i i(i(i)) = i(i 2) = i(−1) = −i 

This result ' −i' can be interpreted as 'time', as is also the case in the definition with regard to space-time by Minkowski.

As 'time'  = i , we can also express time as a kind of idea (thought) in the past (as the sign of time is negative). In other words (free interpreted): time is the perception of thoughts in the past. 

Creating Space
Now, in the last step we finally we can apply the concept of idea on 'time', resulting in:

i i i(i i i) = i(-i) = −i 2 = 1

This result can - as defined - be interpreted as 'space' or 'matter'.

So 'space' or 'matter' is more or less the result of thinking or thoughts about time.
In other words, 'space' or 'matter' is our perception (= projected idea) of time in the 'present'.

Applying the idea on space again [ i(1) = i ] would result in the concept of 'idea' again, which starts the cycle of creation from beginning again.


Conclusion
As I've demonstrated by applying a very simple model, we can construct a thought model that subsequently creates antimatter, time and space from the basic imaginary general concept of an 'idea'.


So all we need for creation is to apply and multiply our ideas.

Realize and appreciate that you as a human being are also a 'divine' product of idea-creation. By applying  your ideas in the real world, you contribute to this 'world'. Hopefully a 'better' world in line with the idea ..... Just Do It! 

Hope you liked this 'philosophy blog'. Please comment your thoughts and ideas on this!


Wednesday, December 24, 2008

Born Good or Bad? Polya helps

Were you born 'Good' or 'Bad'? The answer to this question can be given with help of mathematics!

Let's start with a simple model. When you were born, you had only a limited number of experiences. Let's assume you came to earth quite neutral, with one 'Good' (G) and one "Bad" (B) experience.
At this point in time, your (still unconscious) attitude and therefore expectation of a 'Good' (B) outcome of your next experience, will be 50%.

In line with the expression "You'll always reap what you sow" (Gal 6:7), or associative translated "You'll become what you X" (with X ='Think', 'Eat', 'Are', etc.)", your next experience will indeed turn out to be equally G or B.

Let's assume that providence decided, the outcome is G. Now you've become a more optimistic person. Your experience-bucket is filled with two G's and one B (experience), so your subjective 'colored' outlook on G's is 66,66% (2/3=[2 G's/(2 G's + 1 B)]) . You also look back on a relatively Positive Life Score of PLS=66,66% G's.
Would you have experienced a 'B score' instead, it would be the other way around and as a potential pessimist your outlook and PLS would have been lowered to 33,33% .

But happily you're a 66,66% (!) G-Score-optimist and life goes on. According to the same principles, the probability of scoring a new G-experience is now 66,66% instead of 50%.

As you may already notice, your PLS will more and more develop according your personal historical G- an B-experience track record.

A few questions that may rise, are:
  • Does your Positive Life Score (PLS) has a limit? And if so, what's that limit?
  • Once you're in a pessimistic phase, what are the changes of getting out?

Here's were the help of a great mathematician, George Pólya, comes in, by modeling the above situation in what is called:

Polya's Urn model
An urn contains G0 Green (Good) and B0 Black (Bad) balls. One ball is drawn randomly from the urn and is then placed back in the urn together with an (extra) ball of the same color.

Our Good&Bad exercise turns out to be a simplified two color Polya Urn Model (G0=1,B0=1) that is part of a large family of General Urn Models.

Properties
It turns out that this model has the following (translated)properties:
  • On any given moment in your life if you do not know what kind of balls have been drawing before, the expectation of drawing a Good or Bad ball (experience) is always G0 =G0/(G0 +B0) =50%.

  • On any given moment in your life, gaining a Good or a Bad experience depends on the track record of G&B experiences in your life. So if you've experienced G Good experiences and B Bad experiences, your changes of experiencing a next Good experience are equal to the track record of your Positive Life Score : PLS(G+B)=G/(G+B)

  • The relative influence of a G or B experience on the PLS decreases rapidly as the number of total experiences increases. Your PLS has a definitive limit in (life)time with equal changes of outcome on the interval [0,1].
  • As is clear from some simulations, the first 10 to 20 experiences in our life determine whether we'll become an optimist (PLS(∞)> 0.75) or an pessimist (PLS(∞)<0,25).







  • Moreover, the first 5 to 10 experiences in your life already determine the direction of our PLS in life. This means that our parents and teachers have an important role in guiding us in our baby and youngster phase to a positive balanced number of experiences (a more than average PLS).

    For example if on a given moment in life you have had 4 Bad experiences and 1 Good, the probability of having a next Good experience is 20%. What's more frustrating is that the probability in this case to get in three steps to a 50% level is only about 3% (=1/5*2/6*3/7) . This illustrates the heavy responsibility of our parents and teachers.

    That's why it's for example so difficult to change your religion. Once the first 50 religion experiences have been brought in by your parents, it's hard to change from Budha to Allah or Christ, or the other way around.

  • Once a more than average PLS is achieved, we're more likely to absorb a Bad experience without getting unbalanced. Parents and teachers can 'let go'.

Keep in mind, Polya's Urn is only a think-model to help you to become aware of the important mechanisms that play a role in becoming 'who you are' or 'what you'll be'.

Change?
Once you become experienced in life and your PLS direction has been set, you can only change this by either a Professional De or Re-programming (PDR) or a, what is called, Life Changing Experience (LCE). In PDR Bad experiences are taken away (i.e. out of the urn) and replaced by Good experiences, to regain trust and a higher confidence (PLS) level. In LCE's, your environmental or physical circumstances suddenly chance in such a way that you are forced to experience only just B (or just G) experiences. Another LCE is created by the change of context. What before were B experiences now turn out to be G experiences (or the other way around).

What if?
There are many other aspects that could be studied in relation to the Polya model. For example:
  • What would be the effect if an experience is not just only Good or Bad, but a mix.
  • What if a 'Good experience' doesn't trigger extra positive confidence (an extra G) but a negative experience (an extra B).

The answer in both cases is that almost always the PLS-limit=50% !, in other words: You'll become average.

But how does a little bit of extra Bad (or Good) influence the PLS limit? If you want to experiment and learn more about Good and Bad, go and visit Polya's Urn Experiment or look up the Math behind Polya's Urn

Math helps us to discover who we are or what we become...