Quora response: on the (in)finiteness of all mathematical knowledge

[I came across this vital question on quora short while back. The question is as follows: "Given an infinite amount of time and an infinite lifespan, will a person be able to discover all of mathematics? Why?" I found the question to be highly complex, and enjoyed very much the framing of the answer. The answer is almost essay-length, which is why I feel it is appropriate to commit it to this page. And yes, here's the link.]

I find this one of the most complex questions that I have seen so far on quora (and it hasn't been long). Before I begin framing an answer, let me make the following disclaimers:

A) Its going to be lengthy and read like a whole lot of gibberish,
B) I may not reach a conclusion,
C) I am not a mathematician - I did study mathematics in college as part of  computer science degree course, but that's about it.
D) And no, I am not stoned and haven't been smoking anything :D

I think the answer to your question may not even be mathematical - rather, it would probably be biological, or philosophical, or even metaphysical? The answer may not be about the infiniteness of the number theory or such like, either, because once you know how to generate the next and the previous number for any given number, you've probably figured it all out already. Also, if you have proved that something cannot be solved, then one way of looking at it would suggest that you have exhausted all information about it already. Rather, it is about the definition of knowledge and our perception.

At present, anyone digging popular science seriously might know that certain familiar Euclidian concepts of geometry are no longer valid ever since General Relativity came to be. Instead, Euclidian comes off as a special case of the more complicated Reimannian Geometry, which is supposed to paint a truer picture of our universe. Take, for example, the intuitive understanding of the straightness of a straight line. With General Relative declaring the fabric of space as being curved, you cannot picture your straight line to continue in its path all the way to infinity without bending. You might use your imagination to make a hole in the space fabric and push the line through the whole, but it will be meaningless and incorrect, because you cannot imagine the other side of the space fabric, because it has absolutely no meaning. It's calls for a major shift in the thought framework.

Similar with all knowledge, even. I am inclined to think all knowledge is not discovered, but rather invented. What defines a thing as a mathematical law is how interesting you perceive it to be. For example, a formula to find out the n-th even number is an interesting piece of knowledge, as is the proof that the system of even numbers is infinite. Discovering the individual even numbers, say, the 18,015th even number, or the 120,109,752th or each even number in between may not be mathematically interesting at all. There may be no inherent and absolute property attached to a question in each category; rather, it is our perception that introduces the necessary distinction.

To answer your question: whether a person with an infinite lifespan and infinite time may discover all of mathematics, the fast and loose answer would be yes, because it would seem that the mind is not infinitely powerful, and not with an infinite memory. There is only a finite amount of stuff that he would be able to classify as 'mathematically interesting'. It is like asking, can a computer with a finite amount of RAM but an infinite amount of secondary storage run an infinite number of programs concurrently without swapping any out (no it cannot!)? So, as our knowledge grows, the number of independent parameters needed to ask new questions that would grow so large that they would no longer fit the mind in one go. So, we would cease to ask new questions and when we have no more questions, that will be the end of all knowledge (I am assuming we can say we have 'discovered' all of mathematics when we have no further question about anything mathematical). 

But, it's not that simple. Some of the key things to consider are:
a) Does greater mathematical knowledge seem to imply knowing more unrelated things or less? For example, in physics, more knowledge could possibly mean less independent things to know. Like, at one time light, matter and electricity would have been perceived as three different things altogether, then someone comes across and discovers numerous subatomic particles and then we immediately eliminate them as mutually independent things. Then we stumble upon quarks, and they show us how subatomic particles are not 'fundamental', and then finally, we now discover strings, which is even more fundamental to a quark! It does seem like the growth of knowledge in physics is essentially a contraction, and might even have a visible end? It may not be the same for math, though, and more knowledge could well mean a genuine expansion of knowledge. Let us hope for some enlightenment here :)

b) Given a set of mathematically interesting (and possibly unrelated?) pieces of information, is it possible to always derive from them another mathematically interesting question? I have no idea how to go about proving this :D but I am going to give it a try someday. If the answer is no, then it might well mean that the end is once more in sight (limited by the finiteness of our own mind).

One other interesting question (or corollary) that crops up here is whether it is possible to measure the capacity of one's own mind. I feel it is somewhat akin to trying to paint the floor of a room without stepping outside of the room and yet not treading wet paint - it cannot be done! However, that doesn't mean that you cannot discover the boundaries of someone else's mind. Maybe then you could discover all of mathematical knowledge for that person (it should vary between people) ahead of said person in a finite time!

P.s. I realize my answer is a response to some inner narcissistic craving, and as such things go, full of holes. In which case, I would very much appreciate should someone set me on the right path :)

Yours sincerely,
Jude

Book Review - The Fountainhead by Ayn Rand

Ok, let us for a moment cast aside all debates about the pros and cons of capitalism over communism and whatnot. We know now that there are complete jerks in both schools of thought, and the whole debate is like trying to choose broccoli over aubergine (my kindest apologies to people who like both, or either. As far as I know, I never saw it that way). Rather, what I wish to talk about is the dangers of believing in a sudden inspiration, treating it as if it were a revelation from the realm beyond, just because it is somewhat beautiful, or incomprehensible, or both.

As always, I would like to illustrate this with a very personal experience. See, I am a depression amateur - seriously, I nominate upon me this new profession - I needn't explain or understand what it means, but I do believe it is a great idea (because I love it, and because if you criticize it, it hurts only up to a certain depth, and then it stops). So, one of these days I come up with this idea that depression is the result of a disruption in your humiliation balance. I think it is a good theory, it tells us why people who are at the pinnacle of success or at the very nadir of self-abasement are often most depressed: because, they have either too much or too little of it. Also, like Freud's theories (and most religions), it has the advantage of being formulated using vaguely defined terms, so it can never be disproved - merely adapted!

But then, one night as I was moderately drunk, I decided to top myself, and came up with a plan - that my current theory would be that depression is withdrawal symptom to the addiction to humiliation. If I understood only tiny bits of my former theory, I was entirely clueless about this one. More to the point, even in my alcohol-induced psychosis, I was sure that I was not quite there. But heck, it was beautiful, and I was high, so I posted a question about it on yahoo answers, and was immediately and methodically torn apart by a retired GP.

I think Ayn Rand underwent something of this sort while writing The Fountainhead. Her idea was beautiful, of course, that the people who need to depend on other people to provide meaning to their existence and endow them with 'prestige' are the inferior second-handers, and those that need only their ego to survive (and not the company of humans) are the really superior kind of people. She goes on to demonstrate how true selfishness is not a sin but rather a virtue and an ideal that can never really be achieved, which is rather sensible and picturesque, as such things go. Her theory lends support to the idea that the ego is not really a bad thing. But then, she makes a mess of it when she goes judgmental and preachy as hell. Now, take the case of Roark. Ok, Roark is completely oblivious to the opinions of the people surrounding him. So far, so good. But even Roark needs something. The difference is that while the grubby second-handers need people, Roark needs to feel his power over nature. So, he has to build things to assert that, or break mountains and stuff because, apparently, that is what presses his buttons. What's so good, or different about that? The true egotists would people who would not need to borrow anything from their surroundings for their survival! And yes, Roark also happens to need 'Murica, too.

But we forget that Howard Roark was beyond reproach, in that what he created was the next best thing to perfection. And, so were apparently Gail Wynand, Steven Mallory, Ellsworth Toohey, or Dominic Francon – they were the unparalleled champions at whatever they did, and so it was really easy for them to believe in themselves. What happens to those who are not good at anything, but refuse to be taken in by the second-handers? Ayn Rand conveniently keeps her writing off such topics. Also, is it just me, or is her hatred of women who are less fortunate in matters of physical beauty almost pathological?

Despite what I write, and despite its being bloated, predictable, and lacking a plot (a plot and plotting are not one and the same), I did enjoy her book in parts. I thought the manner in which Peter Keating gain ascendency over his colleagues was brilliant, as was the conversation between Peter Keating and Toohey towards the end of the Novel. The ‘Gallant Gallstone’ was a very clever invention (even though she knew that and made no pretense of hiding it). Also, I found her style to be very unlike anything I read, but that may be because I have not read that many books. I will now try to demonstrate her style more clearly with this tiny fragment of conversation (of my own invention):

The all-to-perfect objectivitist: But, what is it with you? I am sick of the same old stuff that man has been feasting upon for ages now. Wherever I go, it is just ice-cream, and coke, and the inevitable burger-patty. I mean, that was okay for people who would prefer to succumb to a heart attack rather than to boredom, but now we have facebook, goddammit!

Grubby second-hander: But what should we do about it?

TATPO: I think there’s a food for every individual, just as there is an individual to every food. Do you think you could understand that? I think the best thing that you could eat would be whole bananas fried in avocado oil. But, instead of allowing me to marvel at the sight of it, you would only stuff yourself with more chocolate, and pizza, and rocky-mountain oysters.

GSH: Oh, it’s perfectly all right. (Patting the protuberance in his midsection) In fact, I always crap everything out the very next morning.

TATPO: (Placing a sun-kissed hand upon his taut, masculine abdomen) with me, however, things go down only to a certain depth, and then they stop.

(A temporary lull in the conversation as each character tries to avoid the sideways glance of the other.)

GSH:  I get it, I suppose. But then, I suppose we all ought to like oranges.

TATPO: Once, when I was in Florida, I flew an F-16 over an orchard of orange trees and systematically destroyed each orange with a shot from a missile bearing a unique Paulo Coehlo quote, while simultaneously pleasuring myself with a fifteenth-century broomstick.

GSH: Good grief! Whatever would you do that for?

TATPO: To think I took you for someone who understood. But, let us not talk of this anymore, shall we,  and pass me that piece of toast and that jar of marmalade, would you?

(Greedy toast-munching follows.)

GSH: (with his mouth full) what do you think of my marmalade?

TATPO: (also with his mouth full) I do not think of your marmalade. 

All of this sounds horrendous, I know, but when you read the first few pages of the book that have been written in a similar vein, and realize that there are around 680 more to go, curiosity gets the better of you and you end up reading all of it. And, after you have done that and realized how you wasted away the greater part of a lifetime, there is nothing much left apart from rating it a nondescript 3 and quietly slipping away to your grave.

I think I like Catherine Hasley the best. I believe she realized very early on what a rotten propaganda-pushing gimmick it all was. Which is why, she quit the scene before the first quarter of the novel was up, and returned only for very brief episodes to express her contempt for the people she was burdened with.

Book review - Many lives, many masters by Dr. Brian L. Weiss

I cannot quite put into words my utter detestation for the book, it's author, and all or most of mankind! Given to skepticism all my life I was always weary of any mention of this book. I would always argue that since this book has been around for a good long time and since we are yet to discover all that much compelling evidence about reincarnation, there's probably a snag somewhere. Which is why until recently I never thought about actually reading it. 

Let me first tell you what caused me to overcome my inhibition. Someone very close to me is suffering from a bad bout of depression. One I was talking with her about the kind of psychiatrist she visits, she said that what she really needs is a session with Dr. Brian Weiss, that only he had the power to cure her. She has a masters in math, so I allow myself to be taken in. I immediately download the book on my kindle (it only costs about $2), get me a packet of chips, and set my teeth to it. 

Let me stress here - I approached the book with a totally open mind. In fact, since none of us could afford a session with Dr. Weiss even if we sold a kidney apiece, I was very keen to actually learn something from it, so that maybe I could actually use it on her to good effect. I was suitably impressed when Dr. Weiss opened the narrative with his brilliant curriculum vitae and what a strong scientific mind he has. And I have nothing against the whole idea of reincarnation either. In fact, whenever I happen to find a show on it on the discovery channel or some such place, I would make sure to watch it. 

When he began to describe in some detail he hypnotised Catherine for the first time, I was immediately fascinated and copied the entire thing in a note for reference. It was the 1853 BC thing that killed it for me. Why, Dr. Weiss? Had you merely said AD, maybe I would have been disenchanted a wee bit later. But you really couldn't wait, could you, glutton that you are? And then, as soon as the session ends, you immediately feel the need to inform the readers that you find that ape-shit baloney completely believable, even though you are the oh-so-scientific!

I am understandably shaken, but I decide to wait for the scientific explanation that would soon follow. So, I bite the bullet (or gulp down two beers) and resume with the book. But, after reading some twenty more pages of it, it seems that it goes only one way - downhill. Just when Catherine starts to choke as she recalls her throat being slit in a boat by none other than her current abusive boyfriend, I decide that enough is enough and that it will never get any more scientific than an episode of Monty Python. 

That night, I was so livid that I barely remember what I did. I faintly recollect having plonked my kindle down hard on the cheap coir mattress that is my bed and wishing Dr. Weiss' immediate demise and reincarnation with his face glued to his butt. But then, next morning when I regained my composure, I began to wonder - what wrong did Dr. Weiss really do? Or, if a fault had been committed, who exactly was the perpetrator of it? Is Dr. Weiss a scientific man? Yes, and I couldn't agree more. Is Dr. Weiss a good psychiatrist? He's an excellent one! He knows exactly what people want, and he gives it them by the truckloads. When he starts to talk about Catherine, he knows that his readers are immediately going to start judging her, so he wastes no time in telling us how beautiful Catherine is. And then, since he knows that not everyone is taken in by mere good looks alone, he at once jumps to how Catherine is abused in the hands of her own father, which is now getting a little old, really. But then, a better construct for garnering sympathy has seldom been engineered, and he is certain that he has the rapt attention of everyone present. 

From here follows a tale so bizarre as to put a pot-headed hippie to shame. Some stories are straight, some circular, and still others, elaborately ornate. This one is shaped somewhat like a Klein bottle. I did not stick around for the greater part of it, but I do believe that for once Twilight is a better love story! Even the end is pure genius - when it comes to squeezing out the tears from your hapless readers there is nothing more potent than the murdered child - the child of the tormented female protagonist of unearthly beauty. Dr. Weiss could count his dollars even before the whole of his plot hatched!

And yet, as I write this scathing review, I feel that something is not quite right. And that feeling of inadequacy comes from the mention of the 1853 BC. If he wished his readers to seriously believe what he wrote, why did he feel compelled to make such a blatant and obvious fib about something so unrelated to the rest of the story? If Catherine heard the dates in the wind, surely the wind would know better than to stick to the Georgian calendar? Or the utter nonsensical notion that someone in 1853 BC would know that the year as 1853 BC (for chirssake)! My best guess is that this is Dr. Weiss' plea for absolution. He is telling his readers - look, this here is absolute horsecrap, and if you choose to believe in it, so much the worse for you. For whatever that happens to you henceforth, the entire liability is yours, not mine! I actually respect Dr. Weiss for this honest admission of guilt, and this is why I struggle to find fault with him. 

Then who is to blame? Why, mankind, of course! Right now, it's more fashionable than ever before to turn atheist all of a sudden. When people look at the less developed nations and the religious extremism and mania that ties them, they are shocked and disgusted. This piece of fiction here just gives a perfect insight into how the whole thing works - why men and women ever since civilisation happened have found it easier to believe in bearded beings of the sky, ten armed goddesses, or men giving birth to women out their ribs than the most obvious piece of common sense. Or why somebody like Hitler can dupe an entire nation into killing 6 million for no good reason. People always find it so much easier when their is somebody to think their thoughts out for them, and nothing beats the sheer comfort of knowing that whatever mistakes you made, or howsoever bad your life turned out to be is the result of forces beyond your control. 

In a way, I owe a lot to this book. Having been an atheist most of my life, I have often been bothered by doubts such as what if it's all true what they say about god and religion, or can so many people all throughout history be wrong? This book reinstates my confidence in what I stand for, the right to thwart the attempts at deceit by other people an organisations, since this book is one of the best depiction of the way these powers work. And no, it does absolutely nothing to dissipate my interest in reincarnation, and once I finish posting this I will search for afterlife and rebirth on YouTube and binge-watch anything and everything remotely relevant. 

Yours sincerely,

Jude

Depression theory - first post

[At the start, this paced out like one of my writing without pausing games, but in the end I did stall momentarily here and there. Still, this piece is very much legit.]

Writing without pausing – that's the name of the game, isn't it? Well, for one, compared to then, I type much faster – what with the job that I do (I am a software engineer) – now I get so much lesser time to think. Te good part- well, since I did not write a single blog for so long, I make a lot of mistakes.

So, let me see, what was I thinking of a short while back? Inebriation, like, of course, that has to be it! And yes, depression. This one theory that I chanced upon while sober, and now I cannot seem to let it go. The theory, briefly, is this – that depression is the withdrawal symptom of the addiction to humiliation, and/or degradation. I think there is a difference, but when I write that I also think what I mean is that there is actually no difference – go figure!

We are addicted to humiliation, isn't it? It is that simple. Now, let me tell you, before you start doubting me and making snide remarks about all of this, I am really a connoisseur on depression, Fact is, my mother, my aunt, so many uncles that I cannot keep count, are a prey to this debilitating, and all consuming disease. As far as my own depression goes, it is really exceedingly simple – it is not depression at all, but a mild form of psychosis, with a dash of neurosis thrown in. And it is funny, that although I frequently talk aloud with myself, I am not schizophrenic. I am very much positive that it isn't so, because all the voices that go on inside my head (and yes, quite ceaseless) are very much my own.

But, onward with my theory – stand aside my own depression, may it never bar the way – the addiction to the degradation of self. It is really funny – and it is also one of the darkest aspects of our own selves, os I am pretty darn sure that should anybody chance to read this, they will not admit to any of these in their own miserable selves. Do you have that one constant, nagging dream - a wakeful dream, not one that disturbs the configurations of your sleep – that you are doing something that you really, really hate to do? Somebody told me that that is OCD, but I am pretty much sure that, just like homosexuality, we all have just a little bit of it in all of us. For me it is hair on the bathroom floor – that simple! Hair, for God's sake! I cannot quite tell you how much I abhor hair on the bathroom floor. I never, practically never, enter a bathroom barefooted. Rubber soles beneath my skin – that is my poison (after one has quit smoking – the one great habit (no matter what Freud claims to the otherwise) – what else is there, anyway?). And, funny thing is, so long as you have hair, on some or any part of your body, at some point, it is going to manifest itself atop the cover on your drain. So, I have these horrid, vivid daytime dreams that I have hair – and, that wet, horrid, bathroom floor hair – in no other place more sacred than my holy mouth!

Speak of torture! Now, I ask myself – why do I have these dreams so very recurrent (I think we better cease to call these dreams – maybe, thoughts? Certainly not fantasies!)? It feeds my degradation addiction. It is practically the only thing that keeps me from collapsing altogether. It is my little safety valve, and I am proud that it is no more sinister than this.

This is what I am speaking of. Depression sufferers, did you ever notice this? Your depression, almost always, and no matter what you might believe, has a very earthly trigger. Of course, you might argue that the trigger itself is of no consequence, and just about anything in its place ranging from the death of a cat to global warming could have pushed you on your way upon the highway to hell with equal or greater urgency, and yet it does seem that your depression also always needs to find a humble, worldly fire to feed it. And again, just about noone I met with depression has a depression in the middle of a crisis. It might be the adrenaline thing, or whatever chemical mash up that works (as I said, I am a software engineer), but severe depression (the ones that occur in fits and spasms and seem to make marvellous contortions at the expense of your sanity) always occurs 'after' the completion of a personal crisis or tragedy. It may be a very recently concluded episode, or one from your very remote past that has left an indelible imprint upon your subconscious (does that even exist?), but it is 'always' past tense.

So, my question is (and a horrible asker that I am) – is it possible to get addicted to degradation? And is depression merely a manifestation of the withdrawal symptoms of the addiction to degradation? Withdrawal symptoms can be awful – I would know since I evolved from three quarters of a pack a day smoker to a non-smoker in the course of a single day – and the only thing that keeps me from starting on it again is that I do not wish to drag me through that ordeal a second time – what if all our current treatment of depression has taken off on the wrong foot absolutely? I believe current treatment of depression attempts to raise the serotonin and endorphin levels of a person and is designed to make that person 'happier'. Instead, what if we actually did the reverse – make the person realize what a terrible crisis it is that they are going through and what horrid shadows their current persona is when compared to their cheerful, unadulterated past? I believe that wen a patient of acute depression is telling you how morbid his or her life has become, the person does not actually need your help in making it better. What that person needs, instead, is your concurrence – that you 'believe' that their humiliation is very real and their degradation absolute. That would, then, feed their inner Narcissus, and possibly and somewhat inadvertently steer them on the road to recovery.

Yours sincerely,

Jude