Let's look at an argument that came up few months ago in a Cab discussion. The assumption here is that calculus and mathematics are correct, and that they do not break down in front of time itself.
We believe in present time, by which I mean that we have an ability to express the world around us at the current time. Now, this means that everything in this world can be expressed at the current time in a mathematical form. Moreover, any real phenomena has to take a non-zero time to change it's state. For, if it took exactly zero time, it would have two different values at a single point of time. This proves that the functional representation of any real world phenomenon is continuous and differentiable in time. While saying this, I would like to mention the following:-
1. I'm not assuming the knowledge of the function itself, only that it exists and it is differentiable in time.
2. The function need not be time-invariant. It only complicates the situation, but still, at any point of time, the function will have a value...
Let me elaborate the second point above. It's clear that whatever the function be, it'll have a value at every instant of time. Now, the question remains is that are these values predetermined in time? Knowing the values is not important here, though.
Let us try to disprove that the value is predetermined. Let us assume that there is at least one such function whose value at at least one instant in time is not predetermined. This can happen only when:-
1. No other function depends on this value, or the dependent function will also possess this property, and this extension can continue indefinitely. This would eventually mean that even the functions are not predetermined, which breaks the definition of a function. This is not allowed since we believe in mathematics.
If no other function depends on this value, the value and the associated phenomenon will be isolated from this world. This is the concept of "parallel untangled universes", and since they're untangled, there's no sense of knowing the time in other world, as it would not affect our world. In simple terms this value (and therefore the associated function) and the phenomenon gets excluded from our analysis
2. The value is a singularity, such as infinity. In that case, the value cannot be expressed, and therefore it is not predetermined. Moreover, this assumption does not break the association of this value with other functions, as there can be a function that transforms an infinity into a finite value.
So, from above, it seems clear that "except at singularities" every function and it's values are predetermined. This means that every finite thing in this world is predetermined, by some unknown mechanism. Interestingly, it means that if you know the current space-time position of an object, and you can avoid singularities, you can attempt to know the space-time at any other time, since it's predetermined.
This brings us to our first milestone: That efforts of astrology and science in trying to determine past / future values of a phenomenon are not futile. In the next article of this supposedly long (still unknown how long, but you see, it's predetermined) series, I'll talk about validity of our assumption and the corner case of singularity that has surfaced.
3 comments:
Interesting blog bro. Need to read it multiple times to make sense out of it :) Anywyz i will try my best to contribute something.
"Now, this means that everything in this world can be expressed at the current time in a mathematical form"
I feel this is a unsupported statement. Or maybe you need to expand your definition of mathematics.
"For, if it took exactly zero time, it would have two different values at a single point of time"
Physics talks about space-time and not just time. I dont know much of it but my understanding says that same time but separate in space should be possible (worm holes)
"This would eventually mean that even the functions are not predetermined"
I think a random function is the answer here. even then i dodnt understand what you mean when you say that the function is not predetermined. Its only the value of the function that is not predetermined and that depends on the input. At this point you will probably say that this input is itself a output of some other function. Agreed. And hence we reach the theory of free will. Let me come back to it later.
"the phenomenon gets excluded from our analysis"
The concept of parallel universes probably is the answer to your issue here. Speaking in your language, you can think of the primordial state as an initial function with a particular input and an un-predetermined output. And the separate outputs may lead to parallel universes.
So you reached a conclusion that everything is predetermined. I will move away from technical terms now.
You mean to say that each and everything is a part of pre-decided destiny. And the decision were taken by some higher power which we still dont understand. Possible. Also going by this thoery, one would also say that there was definitely some higher power who designed it otherwise it cant be predetermined. (We need somebody/something to determine it)
But in that case, if everything is known, why design such a complex model itself in the first place.
My personal understanding of this world is that the entire objective of the human mind is to discover that nothing is predetermined. Everything is possible. Remember the matrix?? The movie itself may be fiction but it is built upon the very powerful concept of self realization. The mind just needs to reach that state (You may call it nirvana)
Appologies for the long post. But it seemed an interesting topic.
Cheers
Extremely interesting discussion. Could you elaborate on why a not predetermined function is against the concept of Mathematics?
Other than that, I found the "singularity" aspect that you have discussed to be extremely interesting. What is singularity? It cant be expressed in time. Singularity cant be expressed by language as every word has a dual or opposite to it.
It is the unexpressible yet it is partially expressed in many forms just like u talk about the functions which convert infinity to a finite value.
It is my belief that the singularity lies everywhere, right within us, and we are just manifestations of the infinite singularity (infinite and single!) in the finite form.
Again, I dont speak of any God or creator or anything of the sort. I speak of nothingless, as that is the only thing that can ever be singular - a state of vaccuum, a zero. Thus, zero = one = infinity! Rest all is maya - the finite!
Wow!! Thanks guys...I never thought it'd turn into a discussion here :) Lemme try to clarify the points you've raised...
@KG: "Now, this means that everything in this world can be expressed at the current time in a mathematical form"
By mathematical, I speak of dependency, i.e. any phenomenon is expressible as a function of time (and other quantities of the world). I talk about functions right after this point.
@KG: "For, if it took exactly zero time, it would have two different values at a single point of time"
Yes, it talks of space-time. But the point here I wanna make is that any real world phenomenon will require energy to change it's space-time value. This means, you cannot change the space position of a "real world" entity in zero time. Of course, if you could do that, such particles need to move at infinite velocities.
As far as worm holes are concerned, it's a phenomenon due to difference in local velocities. The light has to take a longer path while a spacecraft can "slip" through a shorter path, thereby making it appear to have traveled faster than light, but only through the worm hole. Still, the phenomenon takes a non-zero time to occur.
@KG on random function: Do you think a random behavior is not predetermined. I'd say it is, only that for the observer, it's not possible to determine it. I'll write in much more details about the relationship of a phenomenon and it's observation in the next part of this series :)
Still to elaborate on this point, let me take an example. Suppose there's one phenomenon (and therefore a corresponding function describing it) that's not predetermined (by the super power, whatever it is). Now, due to entanglement theory, the neighbourhood phenomenon will be dependent on this "non predetermined" phenomenon, and therefore by extension, the whole neighbourhood will become no predetermined. And if you take it further, everything that's entangled will become non predetermined.
@KG on parallel universse. Yes, I agree. But my main objective here is to study the universe we live in, and to see how real world event affect each other. Of course, I think parallel universe and singularities are related, and I'll write about them in the next part.
@KG: Yes, all I concluded is that some super power has made everything in this world (and for that matters, as I'd explain in the next post, all parallel universes) pre determined. Of course, the ability to determine what will happen (or has happened) at a time other than the present is a different matter, and I'll talk about it when I discuss observation of phenomena.
@Shreyans: Thanks buddy for writing here. I mean to say that if a function becomes non predetermined, it no longer remains a function (after all, a function is about dependecies). A non predetermined function is an anomaly according to our definition of mathematics, right?
@Shreyans: About singularity, I feel these are the "inexpressible space-time points" which connect untagnled phenomenon / parallel universes. I'd deliberately not go into philosophical discussions about it as yet, for I'd leave it for the next posts :)
I've left quite a few things for the next posts, as I don't want to exhaust them before I write them...but you guys have given me reasons to write it quickly now...I'll try over this weekend...
Thanks once again
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