Jump to content

Recommended Posts

Posted

Eternal return theory is the idea that the universe has been and will continue to recur. 

 

Assuming time and space are infinite, imagine the probability of another world like ours existing, where everything plays out exactly like it has here on Earth, with me writing this post and you reading it. If "a mathematical certainty" wasn't your first thought then like myself you probably don't have as good of an understanding of infinity as you may have thought.

 

Another example is monkeys typing on a keyboard until a copy of Shakespear's Hamlet is produced. The likeliness is extremely low but through infinite time it's bound to happen. 

 

I'm sharing this idea just because I like it and want to know what other people think of it. 

 

 

 

Posted

The idea is true mathematically, there is no controversy there. With enough time, a random text generator will come up with Shakespeare. Where the question hits a bit of a wall is the uncertainty in the applicability of time. For instance, the concept of time breaks down at the big bang, and describing anything in terms of time may not even make sense. To put it this way, time may not have existed until after the big bang.

 

To go further with this, time may cease to be if the universe ends. Nobody really knows how it will end or what will happen exactly, but it is possible that the concept of time will break down. To go further, if the universe continues to expand, it may inhibit any possibilities of random text generators of working. If there are multi-universes, what if the universe with these particular laws is only created once, as is every other universe with its own laws? There still could be an infinity of universes, but only one universe with these particular laws.

 

The topic becomes a bit confusing when thinking about it practically because there is a lot we don't know. The idea works if we assume all remains constant, but that may not end up being true. Worse, there is no real understanding of time, which disallows any real prediction as to the real world viability of these ideas as predictions are based on time.

 

I find the idea to be rather cool and perhaps applicable, but I have no idea if it is. I listed some reasons why it may not be applicable, but it isn't really something we can say (as of now) is true or not practically. Assuming everything is the same, we can certainly say it is true.

  • Upvote 1
Posted

I find the idea to be rather cool and perhaps applicable, but I have no idea if it is. I listed some reasons why it may not be applicable, but it isn't really something we can say (as of now) is true or not practically. Assuming everything is the same, we can certainly say it is true.

 

I understand there is a lot of gray area when assuming that the universe is infinite, I don't expect anyone to prove this stuff. Maybe just dis/agree that it's a neat thought and e-fist bump me. 

Posted

Oh, I can certainly agree it is an amazing theory to think about. What I find fascinating is that not only will Hamlet be written is such a circumstance, but Hamot will be as well. If that isn't clear, the entire book of Hamlet will be written, but with the name and title all being replaced with Hamlot. The same is true for the name Bob, and Megan, and so on. Really, there will be any and every combination of spelling mistake possible with various instances of the book.

 

The question I have to consider is that if we actually ran this experiment, and ended up with the entire book of Hamlet, except the word "the" misspelled "thr" on page 45, would we consider that a success?

Posted

I've got a hypothesis that expands on that idea, it goes something like this -- the exit point of a black hole is a new universe being created, what we see as the coming into being of matter/energy in the early universe is much like the random movements at the bottom of a vortex (think water going down a drain, the end of the funnel moves wildly), this creates an infinite re/pro-gression loop -- I visualize this similar to the way a magnetic field reenters the magnetic object -- and much like a fractal/mandlebrot image it's identical at every level.quantum mechanics seem to cause some problems with the mandlebrot metaphor, this creates superficial differences in each level, the levels on the whole appear the same, but zooming into a particular point on one level will not be identical to the next.without quantum mechanics there's no room for "free will"...I've got a pet hypothesis that we (humans, maybe all animals) are a sort of "quantum event generator", in other words choice is a quantum event, tied into the fact that we are observers, in the quantum mech sense.regarding the typewriter monkeys, I wrote an algorithm for that, in perl -- 

# works on strings similar to how the "++" operator works on numbers# requires array references to the "current word" and the charset# current word is an array of positions within the charset which can# be translated back to a string using: join('',@charset[@current_word])sub inc_string {	my ($current_word_aref,$charset_aref)=@_;	my @current_word = @{ $current_word_aref };	my @charset = @{ $charset_aref };	my $cwlen = int(@current_word);	$current_word[$cwlen-1]++;	if($current_word[$cwlen-1] == int(@charset)) {		for(my $i=$cwlen-2; $i >= 0; $i--) {			if($current_word[$i] < int(@charset)-1) {				$current_word[$i]++;				for(my $ii=$i+1; $ii < $cwlen; $ii++) {					$current_word[$ii]=0;				}			return(@current_word);			}		}		for(my $ii=0; $ii <= $cwlen; $ii++) {			$current_word[$ii]=0;		}	}	return(@current_word);}-- to run that code in a basic way:@charset = (a..z,A..Z);@current_word[0]=0;while(1==1) {	print join('',@charset[@current_word])."n";	@current_word = @{ &inc_string(@current_word,@charset) };}
Posted

Samuel, there are contradictory physical theories as to space being infinite. I consume a lot of physics lectures and most of what I have heard is that it is unknown if space is infinite or not. There are some models that suggest it is, while others that do not. There are some on both sides who state each case as if it is fact. I know this is an appeal to authority and perhaps you have some expertise I do not have, but I feel uncomfortable with your claim.

 

I have heard that the universe is finite yet unbounded, does that fit into the theory in your post? I have heard that claim challenged as well, but I know it is pretty well accepted.

Posted

I have heard that the universe is finite yet unbounded, does that fit into the theory in your post? I have heard that claim challenged as well, but I know it is pretty well accepted.

What's the difference between "infinite" and "unbounded"? They sound like the same thing to me (a layman).

Posted

Samuel, there are contradictory physical theories as to space being infinite. I consume a lot of physics lectures and most of what I have heard is that it is unknown if space is infinite or not. There are some models that suggest it is, while others that do not. There are some on both sides who state each case as if it is fact. I know this is an appeal to authority and perhaps you have some expertise I do not have, but I feel uncomfortable with your claim.I have heard that the universe is finite yet unbounded, does that fit into the theory in your post? I have heard that claim challenged as well, but I know it is pretty well accepted.

you're likely more informed than I on this stuff, thanks for correcting that.I'm with Kevin on not really understanding the second part...but I think there's room in there for it to seem infinite, in the same way a möbius strip seems infinite, it could well be that the "origination events" are coming from a black hole in a universe being fed by a black hole from ours (the magnet thing)...does that make sense? of course, my hypothesis doesn't explain how it all got started in the first place.this is all wild speculation, mind you, and I pretty much lost interest in theoretical physics after gaining a very simplistic understanding of the quantum mech stuff. I figure it may not be possible to figure out the origins or size of the universe, and I don't see any practical implications if we did understand it all...philosophy, on the other hand, has the potential to be extremely practical and practicable.

Posted

 

the universe, or this universe, is not infinite, in regards to space, I believe this is fairly well established science...

If you can prove that I'd love to go halfsies with you on a nobel prize.

 

I'm with Kevin on not really understanding the second part...but I think there's room in there for it to seem infinite, in the same way a möbius strip seems infinite, it could well be that the "origination events" are coming from a black hole in a universe being fed by a black hole from ours (the magnet thing)...does that make sense? of course, my hypothesis doesn't explain how it all got started in the first place.

This is like if I ask for help with a math problem and you give me a riddle and an even more difficult math problem instead of helping me solve the original problem.

  • Downvote 1
Posted

so you're going to pretend I didn't acknowledge the correction? that's not very honest. nor is it very honest to say you want to know what others think then complain that they don't just agree. enjoy your mental masturbation, I'm out.

Posted

so you're going to pretend I didn't acknowledge the correction? that's not very honest. nor is it very honest to say you want to know what others think then complain that they don't just agree. enjoy your mental masturbation, I'm out.

Sorry I was still waiting for the "well established science". I didn't realize you were already defeated by the first person who mildly disagreed lol. Actually I never complained that you don't agree, I just find it annoying that I stated "Assuming time and space are infinite" and you're not assuming time and space are infinite. But that's nothing compared to a 34 year old man having a dramatic exit like some middle school drama queen... 

  • Downvote 1
Posted

What's the difference between "infinite" and "unbounded"? They sound like the same thing to me (a layman).

 

It isn't something I really understand as of yet, but it is a mathematical implication of the curvature of our universe. Unfortunately, it isn't one of those things that can be understood without being able to understand the math. To some this may sound like a cop out, but it is completely true, as there are few analogies that will get across the mathematical implications of 4 dimensional space. There is a similar issue with quantum mechanics, but it is worse. I found quantum mechanics far less confusing with the math as it explained a lot.

 

I am a bit weak in this area at the moment. I used to read a lot about this topic and understood it on a somewhat amateur level, but it has been a while. Below are some resources I found. At least according to wiki, an infinite flat unbounded universe seems to be best indicated by the data. This essentially means that there is no edge to the universe and that you can travel in one direction forever without reaching the same point again. It could be the case that one direction has a bound, while others do not.

 

This all likely sounds rather perplexing as how can something be infinite? I have lesser issue with that question and a more difficult time with the question of why anything exists at all. Not sure why, but it feels like non-existence would be more likely. To be clear, I have no qualm philosophically with existence existing, it is just the strange stupor the topic puts my mind in.

 

http://en.wikipedia.org/wiki/Shape_of_the_universe

 

http://www.fromquarkstoquasars.com/finite-yet-unbounded/

 

 

Posted

This all likely sounds rather perplexing as how can something be infinite?

Thank you for the resources, I will check them out! :)

 

But, I've never understood how this is confusing for people. It's probably because I'm ignorant, but it seems very simple to me. The "universe" is not an object. It's a concept, a category containing the entirety of currently existing objects. There is no requirement for it to behave in the same way as existing objects because, in short, it does not exist.

 

I'm curious what you think that of that. Am I saying that the sky is blue because blue is pretty? :)

Posted

But, I've never understood how this is confusing for people. It's probably because I'm ignorant, but it seems very simple to me. The "universe" is not an object. It's a concept, a category containing the entirety of currently existing objects. There is no requirement for it to behave in the same way as existing objects because, in short, it does not exist.

 

Not a problem.

 

There is an instinctual bias as to how we think things are, as opposed to how they are. It is difficult for people to disconnect from this, which leads them to dismissing ideas that seem to contradict how they believe things are. The best example of this is special relativity where time dilation and length contraction occurs. There have been many posts on this board that talk about how it is an idiotic theory and has no basis in reality, despite it being confirmed over and over and it being incorporated into modern electronics.

 

I believe it is best to assume that reality is beyond strange, and physics confirms this over and over again. 

 

You are correct that reality is a high level concept, at least how we view it now, though a distinction that becomes confusing is if the parts we see are actually not segmented and rather part of a large whole. This technical point really does not matter as far as organizing our knowledge of the universe, as that will most certainly be in parts, but reality might not have any parts and just be one thing.

 

To put it this way, is the universe the result of separate fundamental particles each interacting to create to larger whole; or does the larger whole appear to be broken up due to its concentrations of certain properties and certain areas, when rather it is all connected?

 

Below is some writing I did on the subject for a book I was writing. I included the first bit on reality just for some context. There may be some typos and such as it is a WIP.

 

Relation

 

 Reality,‭ ‬to be more specific,‭ ‬aspects of reality,‭ ‬exist in relation to other aspects in reality.‭ ‬To personify,‭ ‬parts of reality communicate with other parts through objective relationships.‭ ‬Knowledge of reality it gained through interpreting the precise relation between two parts,‭ ‬and using the data to gain information of each part.

 
‭ ‬As an example,‭ ‬think of light in its relation to objects.‭ ‬Light is composed of fundamental particles called photons.‭ ‬Objects such as chairs and computers are composed of atoms,‭ ‬which are arrangements of protons,‭ ‬neutrons,‭ ‬and electrons.‭ ‬When we see a computer,‭ ‬we are actually not seeing the object,‭ ‬yet we are seeing the photons emitted by the atoms that make up the computer.‭ ‬Though these photons are not the computer,‭ ‬through our perception of them,‭ ‬we are capable of knowing:‭ ‬that the computer exists,‭ ‬and where it is located spatially.‭ ‬This is only possible because the photons which are emitted by the molecules of the computer communicate information of the computer in some relationship.
 
‭ ‬For instance,‭ ‬the color of light emitted by an electron in an atom is determined by the nature of the atom.‭ ‬The light that an atom emits is completely dependent on‭  the composition of the atom.‭ ‬This means that the color of the light emitted has a consistent relation to the atom that emits it,‭ ‬and through an understanding of their relation,‭ ‬we are capable of knowing objective facts about objects through their relation to the light the emit.‭ ‬This is the technique that astronomers use to determine the chemical compositions of stars and clouds of gas. It is also a common high school chemistry experiment.
 
‭ ‬Precise knowledge of the relationship is not needed to perceive a relationship.‭ ‬The information color conveys to most organisms are related to their function and survival.‭ ‬A bird may not to choose to eat red colored berries because it relates the color of the berries to their poisonous nature.‭ ‬As humans,‭ ‬we observe that with most metals,‭ ‬temperature and color are related.‭ ‬If one sees a sword made of metal turn from its silver color to bright red under the hammer of a smith,‭ ‬we assume to know that the sword is very hot and that we ought not to touch it for quite some time.
 
‭ ‬There will be a more in depth coverage of relations in the following sections.‭ ‬Though the fallibility or non-objective nature of relations is brought up,‭ ‬I wish to stress that in this section I only intend to describe relations in reality.
 

...[some topics skipped]... 

Reality as Independent Parts

 

Reality is made up of a collection of parts which are independent enough to be considered independent.‭ ‬What I mean by independent enough is that though the phenomenon or matter may be apart of a greater whole,‭ ‬that at some level of scale and at this moment in time,‭ ‬they act independently enough from each other to be considered independent.
 
‭ ‬As an example,‭ ‬electricity and magnetism for much of history was thought to be independent of each other in reality.‭ ‬One could talk about electricity without referring to magnetism,‭ ‬and vice versa as it was presumed that they did not depend on each other.‭ ‬But with the work of physicists James Clerk Maxwell and Albert Einstein,‭ ‬they were discovered to actually be the same and were unified under a single concept called electromagnetism.‭ ‬To be more specific,‭ ‬it was discovered that what was known magnetism was congruent with the laws and understanding of the electric force,‭ ‬just in a different reference frame via Special Relativity.‭ 
 
In a similar way,‭ ‬temperature was thought to be a property of matter and independent to the concept of motion.‭ ‬It is as if you were to identify the color and shape of an object,‭ ‬in your description you treat the color and length as independent from each other in that the color of the object tells you nothing about the length.‭ ‬Upon rigorous scientific investigation,‭ ‬it was found that temperature is not independent from motion,‭ ‬rather that temperature is a measurement of the internal microscopic motions of the object.‭ ‬To go further with this,‭ ‬it was discovered that color and length are not independent attributes,‭ ‬rather that color is determined by the wavelength of a photon.
 
‭ ‬In the modern era,‭ ‬it is hypothesized by a number of physicists that the four known fundamental forces in the universe:‭ ‬the weak force,‭ ‬the strong force,‭ ‬electromagnetism,‭ ‬and gravity can be unified as all aspects of the same phenomenon.‭ ‬This has yet to be proven,‭ ‬but it certainly gives one something to think about.‭ ‬To quote physicists Richard Feynman.
 
‭ ‬At first the phenomena of nature were roughly divided into classes,‭ ‬like heat,‭ ‬electricity,‭ ‬mechanics,‭ ‬magnetism,‭ ‬properties of substances,‭ ‬chemical phenomena,‭ ‬light or optics,‭ ‬x-rays,‭ ‬nuclear physics,‭ ‬gravitation,‭ ‬meson phenomena,‭ ‬etc.‭ ‬However,‭ ‬the aim is to see complete nature as different aspects of one set of phenomena.‭ ‬That is the problem in basic theoretical physics,‭ ‬today—to find the laws behind experiment‭; ‬to amalgamate these classes.‭ ‬Historically,‭ ‬we have always been able to amalgamate them,‭ ‬but as time goes on new things are found.‭ ‬We were amalgamating very well,‭ ‬when all of a sudden x-rays were found.
 
‭ ‬Then we amalgamated some more,‭ ‬and mesons were found.‭ ‬Therefore,‭ ‬at any stage of the game,‭ ‬it always looks rather messy.‭ ‬A great deal is amalgamated,‭ ‬but there are always many wires or threads hanging out in all directions.‭ ‬That is the situation today,‭ ‬which we shall try to describe.
Some historic examples of amalgamation are the following.‭ ‬First,‭ ‬take heat and mechanics.‭ ‬When atoms are in motion,‭ ‬the more motion,‭ ‬the more heat the system contains,‭ ‬and so heat and all temperature effects can be represented by the laws of mechanics.‭ ‬Another tremendous amalgamation was the discovery of the relation between electricity,‭ ‬magnetism,‭ ‬and light,‭ ‬which were found to be different aspects of the same thing,‭ ‬which we call today the electromagnetic field.
 
‭ ‬ Another amalgamation is the unification of chemical phenomena,‭ ‬the various properties of various substances,‭ ‬and the behavior of atomic particles,‭ ‬which is in the quantum mechanics of chemistry.
 
‭ ‬The question is,‭ ‬of course,‭ ‬is it going to be possible to amalgamate everything,‭ ‬and merely discover that this world represents different aspects of one thing‭? ‬Nobody knows.‭ ‬All we know is that as we go along,‭ ‬we find that we can amalgamate pieces,‭ ‬and then we find some pieces that do not fit,‭ ‬and we keep trying to put the jigsaw puzzle together.‭ ‬Whether there are a finite number of pieces,‭ ‬and whether there is even a border to the puzzle,‭ ‬is of course unknown.‭ ‬It will never be known until we finish the picture,‭ ‬if ever.‭ ‬What we wish to do here is to see to what extent this amalgamation process has gone on,‭ ‬and what the situation is at present,‭ ‬in understanding basic phenomena in terms of the smallest set of principles.‭ ‬To express it in a simple manner,‭ ‬what are things made of and how few elements are there‭?
 
These unification might at first seem to pose a problem to the acquisition of knowledge of reality,‭ ‬yet does it really‭? ‬Though not yet confirmed,‭ ‬if all of the forces are unified into a single force,‭ ‬would this make us unable to differentiate between the force of electromagnetism and gravity‭? ‬Would it mean that their perceived independent properties of the forces were an unfounded unintelligible mirage‭? 
 
I would claim not.‭ ‬Though ultimately what was thought to be independence was not,‭ ‬these aspects of reality behaved in a manner which was independent enough to be not only perceived as independent,‭ ‬but to be modeled as independent.‭ ‬As demonstrated throughout the history of physics,‭ ‬accurately model reality as if it were a collection of parts has proven to be a valid method of coming to know the nature of reality.‭ ‬If a total unification is possible,‭ ‬like all other unification,‭ ‬it will come through an understanding of its parts.
 
‭ ‬To be more technical in my use of the term‭ “‬independent enough‭”‬,‭ ‬we can assume an entity is independent enough when its properties and behaviors come primarily from itself,‭ ‬as opposed to everything else.‭ ‬As an example,‭ ‬imagine a rock moving in the vacuum of space.‭ ‬It's movement and direction can be attributed almost entirely to itself,‭ ‬it movement is its own cause.‭ ‬There will be small effects of gravity from distant stars,‭ ‬but this effect is very small and insignificant.‭ 
 
  When an existent is in a state which is independent enough from existence,‭ ‬it is then possible to differentiate the existent from the rest of existence.
 
Posted

Ok, I know even less than I thought I did. Thank you for perspective.

 

To be more technical in my use of the term‭ “‬independent enough‭”‬,‭ ‬we can assume an entity is independent enough when its properties and behaviors come primarily from itself,‭ ‬as opposed to everything else.‭ ‬As an example,‭ ‬imagine a rock moving in the vacuum of space.‭ ‬It's movement and direction can be attributed almost entirely to itself,‭ ‬it movement is its own cause.‭ ‬There will be small effects of gravity from distant stars,‭ ‬but this effect is very small and insignificant.‭

So, this part seems confusing to me (as well as everything else, haha). Is the rock an extension of the vacuum, or of forces or some other connecting thingy that is the universe? I don't understand the implications as to why this is problematic to look at objects as independent. Just because a tree gets nutrients from the rotted leaves of the tree next to it, doesn't mean that they aren't two separate trees, right?

 

Is vacuum really a thing and not the emptiness that I believe it is? Are there no gaps? Because if there are gaps, then is that gap not part of the universe? Is the space beyond the bounds not the universe?

 

Is what I'm saying even making sense? 

Posted

So, this part seems confusing to me (as well as everything else, haha). Is the rock an extension of the vacuum, or of forces or some other connecting thingy that is the universe? I don't understand the implications as to why this is problematic to look at objects as independent. Just because a tree gets nutrients from the rotted leaves of the tree next to it, doesn't mean that they aren't two separate trees, right?

 

It has been a while since working on this paper, and something I'm struggling with is a balance between density and fluff. It is like if you over explain an idea: people get the impression you think they are an idiot, and if you under explain: people have a hard time understanding what you are saying. I hope that part of the confusion is in the loss of context, as I am quoting a passage from about 50 pages which I intended to build on itself.

 

Anyway, I am attempting to avoid another wall of text, so I apologize if this response isn't sufficient.

 

To address your question, I use this terminology to avoid complications with making claims about if reality is one thing or not, and to provide a precursor to the role of independence in relation to sensation, perception, and consciousness. A question in terms of perception is how it is capable of differentiating between existents, when a purely sensory based experience is incapable of any distinction. With perception: we can look at a painting and perceive all of the entities it contains, but with pure sensation: we receive all the same data but have no ability to see it as anything but one thing. Though I tried to avoid this, to quote myself

 

"Perception is the means by which an organism identifies aspects of reality through an analysis of sense data,‭ ‬and identifies existents which operate in a manner that is independent enough to be isolated from the rest of reality.‭ ‬The objects which perception identifies are entities.

 
‬A perceiving organism identifies part of reality as separate from all other entities,‭ ‬observes its nature as if it were a separate from all else,‭ ‬and ascribes the perceived nature to the entity.
 
‬Imagine a pixelated frame,‭ ‬in which all is green.‭ ‬A‭ ‬5x1‭ ‬block of the color red appears from the right,‭ ‬crosses the screen,‭ ‬and exits on the lower left.‭ ‬A purely sensational experience of this would only be capable of describing the colors or the entire whole, the notion of a red block and a green background would not exist.‭ ‬A perceptual experience would identify the red block as something that acts separately from the green background‭ ‬according to measured independence, that is that the green pixels do not move in relation to the block, and each bit of the 5x1 block moves in relation to every other bit of the block.
 
‭ Perception breaks up the sense data into segments,‭ ‬and does so according to causality and measured independence.‭ ‬Independence is measured in a manner that is similar to that of physics,‭ ‬which is to say that different segments of reality are compared to see if they are correlated or not.‭ ‬Segments whose correlation is minimal,‭ ‬which is to say not causal enough to be significant,‭ ‬can be seen as acting independent from the rest of all other segments.
 
‬Though this description sounds sufficiently complex,‭ ‬it is a basic task your brain performs every day.‭ ‬Imagine watching a somewhat minimalist animated movie.‭ ‬In identifying sense data that you can’t make sense of,‭ ‬you observe any relation the data has to everything else.‭ ‬If it has some relation,‭ ‬such as a fuzzy ball that stays in position above a person’s head,‭ ‬it is then possible to identify the data as hair.‭ ‬If it has no relation,‭ ‬further inspection is taken in seeing what affect the data has on other data.‭ ‬It may be seen that the character puts his hand on the object,‭ ‬and then runs his hand through his hair after,‭ ‬which might indicate that the object is a can of gel."

 

It is also a rebuttal/clarification to the idea that an existent's properties and behaviors are dependent on the rest of reality, with the existent having no role in its own behavior. This has large ties to free will which I discuss later in the book. A common argument against free will is to talk about your behavior in terms of everything else in reality, as if your own internal mechanisms are irrelevant, but this I won't get into as it is against board rules.

 

Is vacuum really a thing and not the emptiness that I believe it is? Are there no gaps? Because if there are gaps, then is that gap not part of the universe? Is the space beyond the bounds not the universe?

 

Is what I'm saying even making sense? 

 

Not quite in relation to my intention, and I take responsibility to this. Hopefully the above clarifies some stuff. I've found this subject material to be extremely difficult to think about and even worse to convey. If you'd be interested in a draft of this, I could tidy some stuff up and PM it to you. If not, that is fine.

 

The vacuum is a thing, strangely enough. Here is a podcast that goes into it, and it is an interesting listen even if you are an avid amatuer physics geek like me. Also there is nothing outside the bounds of the universe as current data suggests that there are no boundaries in our universe, that there is no edge. This sounds confusing, just as when we hear that the universe is expanding we first ask "what is it expanding into", to which the answer is that it isn't expanding into anything, rather parts are just getting further and further from each other.

 

I would say you are making sense, but that it is difficult to make sense of the answers as they are not intuitive. I am not at all an expert, just spent a lot of time listening to lectures and reading books, so what I am saying in this regard is somewhat regurgitation with a moderate amount of understanding.

×
×
  • Create New...

Important Information

By using this site, you agree to our Terms of Use.