OTOH as a programming problem you can just cheat and store state somewhere to count the row width. This satisfies your interface requirements (python):

    lastJ = None
    def f(i, j):
        global lastJ
        if i != 0:
            return i * (lastJ + 1) + j
        else:
            lastJ = j
            return j


    N = 3
    M = 5
    seen = set()
    for i in range(N):
        for j in range(M):
            q = f(i, j)
            seen.add(q)
    assert sorted(seen) == list(range(N * M))

I think it isn't possible to find a function that works for arbitrary sequences. I know there is a function that works if the sets have the same size (n is size), it is trivial why those work. They have the form n^0 a + n^1 b, where a,b are in [1..n]:

      f :: Integer -> (Integer,Integer) -> Integer 
      f n (i,j) = i + (j - 1)*n
      -- For example: 
      f 3 <$> ((,) <$> [1..3] <*> [1..3])
      [1,4,7,2,5,8,3,6,9]

      f n m (i,j) = .. 

I know I can use a counter, but I don't like cheating :p

I need to draw your reasoning on a paper to see it or take some time for it. Little bit busy, working from home, having the kids and stuff :p

          f n (i,j) = (i - 1)*n + j 
 

I think you might be talking about CMU's Magnetic Levitation Haptic Interfaces: https://youtu.be/cMi75SrDbsk?t=12

I've used it before and it's pretty cool. It's strong enough such that when you hit a hard virtual surface it actually feels hard, and precise enough that when you drag across a brick-like surface it actually feels rough. Unfortunately I remember it having a tiny range of motion.

For your jointed arm "handle", I think they've managed to find a niche in surgical training simulations. I see a lot of similar products come up searching for 6DOF haptic devices (e.g. Phantom Premium 6DOF, Geomagic Touch, Force Dimension Omega 6)

First, I don't think alpha ever fully disappears.

Second, after speaking with twenty or so firms very few are using sentiment directly. Those that do, I suspect don't take the additional steps to build complex NLP based systems and weight insiders/experts. Even if you weight experts, the methods for doing so are also complicated (cross check against LinkedIn should be easy enough, but also limits information).

Anyway, I personally haven't seen much difference in the back testing.

I have always thought in mostly visual/symbolic terms. This made me really good with math early in my life, but it started failing when I began proof writing. Then I got the advice to "explain the problem to yourself and the solution will come naturally" from a friend who is really gifted at mathematical proofs. (And also later received similar advice in programming in the form of "rubber duck debugging").

Surprisingly, it works remarkably well and probably increased my problem solving skills tenfolds, or at least my ability to communicate the answer. I started using it for everything.

But it comes with the side effect of gaining a voice in your head. And that voice is a fucking vicious asshole to me. In the recent years the thoughts even started subvocalizing and I have to forcefully remember to make it stop. It's super embarrassing when there are other people around you.

I am sure this problem is unique to me because I have never heard someone describe it (other than partially matching symptoms of schizophrenia or tourette). But I am certain in my case when the voices started and I am not sure the superpower problem solving skills are worth the trade.

The voice of your own critical judgment can be vicious, but if you're on board with that you're not, nor are you somehow supposed to be, some kind of rational Messiah with all the perfections and answers, but rather regular person doing their best, subject to the usual problems and issues that beset humans all the time, it's much easier to remind the voice, almost as if going one voice deeper - giving the hyper critical voice it's OWN voice - that it's being harsh to a standard that virtually no one has ever or will ever meet, that there are reason you or other did things the way they did (even if those reasons include "we didn't have time to research any other way, and the resources that would've made it possible or trivial like it feels now came about after we finished this.").

Anyway - basic idea here is to give you voice a voice and whip back around and overflow into the regular critical space where criticism can be healthy instead of incessant and damaging. I hope it works for you! It works fairly well for me, but I'll admit freely that sometimes I do feel like such a massive twat that BOTH voice roll their eyes at me. XD

A negative voice is really just a bad habit that is hard to even see you have or that there's another way. It sort of just boils down to faking it for a while -- each time you criticize yourself, stop, think about why you are being way too critical and that it's not a really fair logical analysis, and speak to yourself kindly the same way you would to a friend. It feels super fake and pointless, but fake it for a while and all of a sudden you've developed a good habit instead that no longer feels so fake and actually works.

I am pathologically lazy. I, like a certain student wizard, will go to extreme lengths and effort to be able to be lazy.

I am a procrastinator. I am often afraid to act.

I have a tool, however, and it’s the drill sergeant in my head. He’s an absolute sonofabitch, and on so many occasions has been the voice that has told me to step forward, to pick up the phone, to pull myself together and go face the music. He’s an amped-up version of a drill sergeant I had, crossbred with the gunnery sergeant from FMJ.

He did, however, push me too damn far, and I found myself slowly falling apart from exhaustion and stress - so, like you suggest, I manifested another voice - this one more conciliatory, kinder, more understanding.

I made the second voice the drill sergeant’s wife - when he’s being a total dick, she intervenes, and importantly, he respects her opinion, even if I side with him - I have internalised a lot of his vim and vigour - but if he backs down, I’ll take it - if he doesn’t, then I’ll do as he damn well says.

So, now I’m the puppet of two self-invented alters, but I find they manage me pretty well. When I was building the business, just having sergeant dickhead was perfect - when I started running into the ground, I evolved my pantheon.

Anyway. I’m probably as mad as a bag of cats.

I wonder what proportion of people who do this had absent or disengaged parents.

https://news.ycombinator.com/item?id=20669830

+1 for "Feeling Good". It is the book that kicked off CBT (Cognitive Behavioral Therapy) and it gives you great perspective to seemingly simple questions like: what do most people feel, expect, and how to do they treat themselves? When I realized what a counterproductive jerk my inner voice was, I toned it down and it is far more productive now.

[1] https://youtu.be/Qv_etBsR_Ew

It sounds simple, but it's actually quite challenging to control inner discourse since you can't control your subconscious mind.

Some people puke in their mouth to embrace positive loops in their head. They think it is so fake. But it works. And of course I'm lucky and grateful.

A back and forth of willing and continual self criticism and self-love, based on a deep self optimism -- that's an example of wisdom I'd hope to pass on to my kids.

I've never thought of this as particularly abnormal, it's sort of just how my thought process materializes. I find it easier to vocalize, and since I don't normally want to annoy my friends, I just talk to the voice, and occasionally entertain what the voice might say back. Obviously there is no voice and it's a figment, but it helps, and that's all that really matters.

You can also have no ego/identity, which is the holy grail of many religions/philosophies.

Lately some communities have formed around creating additional identities personified as fantastic beings they call tulpas. Some of the people there can even see/perceive those identities.

Managing our egos/identities is a very powerful tool.

Perhaps practicing this habit (3rd-person self talk) so deliberately made this voice louder, but the way I dealt with this for myself was to journal. However, journaling is only possible if you use it as a CBT method. It can certainly make it worse if you use journaling to reinforce the negative internal vocalizations, a mistake I made for years when journaling.

It's normal I guess, or at least not pathological. I don't really care when it happens, its just my thoughts 'overflowing'.

The self loathing/vicious character might be some function of your self-image? Like others have said, cognitive behavioural therapy might be beneficial for you. it's very legit and mainstream, why not give it a try?

My current theory is that (contrary to what you might think) weed reduces dissociation, making reality more "real", so to speak. Dissociation can be an important defense mechanism; by interfering with this mechanism, cannabis can lead to discomfort and dysphoria. If weed makes you feel bad, it may be the case that there's something wrong in your life that you're trying to ignore.

(From a neurochemical standpoint, I wonder if it has something to do with dopamine dysfunction. I'm not certain, but it seems like co-administration of stimulants can reduce this dysphoric effect. But I don't want to have to snort Adderall every time I smoke weed.)

It's also possible that I'm wrong, and that certain people just lose the ability to enjoy weed at some point in their life. That would be unfortunate.

As a teenager I was high often, with the occasional fungal trip and it was never a thing.

And then somewhere in my mid-twenties, I noticed a point when I smoked too much, I started getting really down on myself, and then eventually realized it wasn't "me" but that voice.

I tried to ignore it. I tried different strains. No luck. I had one really bad episode after a delicious cherry pie made with weed butter by a chef friend while living in Seattle where I ended up on my couch for 8 hours catatonic in my self-hatred and despair.

Sometimes if I'm having a really good time with friends it won't bug me. Others, it's nearly debilitating. So I keep to 5mg or less in edibles, and only rarely. I miss it but it's not that big of a deal.

I worry more about my own mental health and if this is evidence of something more serious. I wish there were studies or something I could learn more from or partake in.

For long-term relief you're going to want to talk to a therapist, I recommend trying a bunch until you find someone that "clicks" for you and gets results. You have likely internalized some BS somewhere along the line, not too unusual on Earth really, nothing to worry about. But get it looked at sooner than later, eh? You should be able to localize the voice to particular place or places in your body that are tense and/or numb, where you have been "storing" tension or trauma in your musculo-skeletal system. Once you learned the internal auditory-linguistic feedback channel, your body started using it to get your attention. Sometimes a nice massage or hot bath is all that's needed.

Meditation is not actually about being free from thought. The goal of meditation is actually to notice when attention wanders, thoughts come walking in and pull back to the breath. That's the muscle you're strengthening. Each time you notice an intrusive thought, is actually a moment when you're actively meditating.

The goal of meditation is not to succeed at being free of intruding thoughts. It is to practice noticing intruding thoughts and bringing your mind back to focus.

Having an intruding thought while meditating is not a failure any more than lowering a weight while exercising is a failure. You can’t lift if you don’t lower.

You are describing a completely normal frustration with intrusive thoughts and are being entirely too self critical.

I suggest you reframe the act of "meditating" as being the moment when you become conscious of yourself being distracted, and bring your mind back to the object of meditation (the current moment/breath/mantra, etc). Think of it not like work, but more like a game you're playing. You can even tell yourself, "aha - noticed I'm thinking rather than following the breath," etc.

In other words, successful meditation is all about your mind wandering, you noticing it wandering, and you bringing it back. The more you notice the attention wandering and the faster you get at returning it to centre the more "meditating" you're doing.

Holding your mind rigid is just going to make you frustrated.

Incidentally, over time, learning to notice your attention wandering ever more quickly and bringing it back more reliably will produce new mental states. And over time your mind will wander much less often. But this is all something that's achieved indirectly. If you aim directly for the mental state you'll find it much harder if not impossible to achieve.

Personally, I found mindfulness (Headspace) helpful and accessible, and I've found that yoga gives me the same mental stability I got from the mindfulness

Having something else to focus on can help - chant a mantra (just "om" works okay if you don't wanna look for anything more Perfect For You), count your breathing and reset the count every time your inner voice interjects something or when you get to ten, stare at something (I like just staring at the grass sometimes and watching how my visual centers start acting when they get really bored with looking at it).

A big key is to stop being angry at yourself for failing to stop that internal monologue. It's a hard thing to do! Instead of beating yourself up, just shrug, forgive yourself for doing it (maybe even say "I forgive myself for failing to quiet my inner voice" out loud, this activates different parts of your brain), and go back to whatever you're doing to focus on next-to-nothing.

If you can block out the time, I found that my meditation skills got a lot better when I stopped trying to do it for a few minutes at a time and started setting a timer for thirty minutes. Some days I can stop thinking easily. Other times I keep on fighting it for like twenty minutes. But doing it for a long stretch like that gives you more chances for your twitchy brain to get bored and STFU.

It's much much less about just blanking out or how long you can maintain the focus and much much more about how you deal with all the craziness that your subconscious is doing to you. Minute by minute; each time it happens. Because it's not going to stop happening, during the exercise or not. Your mind is going to do what it wants; figuring out what you can do with that fact during the exercise then carries over to the rest of life.

I will add that it's taken me a long time to get to the point where I'm not frustrated with myself for getting distracted, so I'm not trying to say this is easy. On the contrary. But it's been worth it for me.

For meditation purposes, try not clearing your mind but just focusing on breathing. Endlessly counting your breath from 1 to 10 can be really useful, then forgive yourself every time you get lost and just start again.

In terms of judging try thinking about this: mistakes/errors don't exist, they are only a meaning we as humans have given to stuff that we dislike. In any situation, try figuring out how that situation is perfect for you at that moment, how could you have chosen that situation/moment ahead of time on purpose? It's not easy, but it's simple. How is everything in your life just perfect right now?

It's not about shutting those thoughts up at all. It's about recognizing those thoughts as they begin to enter your mind and using the meditation as a tool to either embrace those thoughts (sometimes we need to) but recognizing they likely aren't our reality and are likely just thoughts from past experiences or future expectations. It's your reaction to those thoughts that is really important and a lot of us who don't meditate tend to ruminate on things that we know aren't beneficial to us. It helps you learn to control that better.

I'd recommend following guided meditations, I specifically enjoy metta (kindness) meditation. Your instructor will occasionally tell you to allow those thoughts in so that you can get better at recognizing them as what they are, just thoughts, not something you have to act upon or believe. Then they'll typically have to go back to focusing on your breath which will make those thoughts disappear, even if only for a short time.

It takes practice. Don't fault yourself for not being a meditation guru. Nobody is. Just be kind and accepting to yourself as it happens. There's no rush. Some of my meditation sessions are much worse than others, just like my workouts.

After a month of daily meditation (which I'm unfortunately not doing lately) I become such a calm person. I still get that twinge of anger when someone cuts me off or traffics bad but I notice it as soon as it starts to enter my mind and I can control my output FAR better. Usually I just go "oh, that happened, it's out of my control, what I can control is my reaction to it."

That said, also be aware that meditation isn't the panacea that it's often made out to be. It certainly sounds like it's what you are looking for at this moment, particularly since you mention that you 'can't meditate'.

It's very hard at the beginning, but if you persevere, you'll eventually get there.

Just remember the first time you were doing push-ups. It's like that. Like doing push-ups with your mind. Very hard at the start, feels great after you get used to it.

Just sit.

"thoughts intrude"

Just sit.

"angry at myself"

Just sit.

"I give up"

Just sit.

Breath.

Just sit.

training the mind to go to that place of calm management, and eventually being able to not quite turn off the unwanted thoughts but to shift the inner monologue

I’m not saying it will help, but not all approaches to meditation get the same result and this one might really address what you are experiencing.

I recommend reading the book "Don't Shoot the Dog". It is about conditioning, but despite the book's name, most of the information applies to humans, too. It explains the details that matter, and how most people who try to use conditioning actually do it completely wrong.

One important insight is that using punishment to condition yourself almost always backfires. The reason is quite simple: every time you punish yourself for doing X, you are simultaneously conditioning yourself against two things: (1) doing X, and (2) noticing that you are doing X. If X is a bad habit, guess which one of these two things will be extinguished by conditioning first. And most people are already quite bad as self-understanding.

Therefore, perhaps the most important rule in meditation is to never punish yourself. (However, also don't punish yourself for breaking this rule. That would only mean breaking the rule twice.) Every time you punish yourself for "meditating incorrectly", you are going against what you are supposed to achieve by mediation. You are discouraging insight (to have made an error, that is a useful insight), and even discouraging meditation itself (the less you meditate, the fewer errors in meditation you can make).

In traditional Buddhist countries, beginners start with the loving-kindness meditation, and only later move to concentration exercises. Which is probably designed to avoid negative thoughts while practicing concentration. But many people in the West are likely to go straight to the concentration exercises, because they are looking forwards to increasing their productivity, and ignoring the loving-kindness meditation, because that's some stuff for hippies. And then they happily go and tell others to do the same. (Or course, a hippie who would only do the loving-kindness and never move on to concentration, would also be doing it wrong.)

The proper mindset for concentration meditation is unconditional self-love. You do it right, that's great! You do it wrong, hey, it's great that you noticed, and it's great that you keep trying regardless! Self-awareness and perseverance are wonderful traits, why would you ever punish yourself for having them?

Now the important thing is that you need to do this sincerely, not ironically (like, "I am such a loser, oh, good job noticing that, loser"). Self-deception would be the opposite of what you want to achieve. When I write that being self-aware (even of making mistakes) is preferable to not being self-aware (but making the same mistakes regardless), I totally mean it. But this attitude can be difficult to adopt, if you are not accustomed to having love expressed towards you (by others or by yourself). In that case, doing the loving-kindness meditation might help to overcome this obstacle.

I suppose that if you do meditation without punishing yourself, you will feel less exhausted. (Unless there are other reason, e.g. you were already exhausted, and mediation only helped you notice that better.)

tl;dr - to succeed at meditation, not being angry at yourself is more important than stopping your thoughts; you may want to train this skill separately

What I've noticed is that sometimes what I think "aloud" has little relation to what I actually do. I might acknowledge in my head that it would be logical or beneficial to take a certain action, but that very rarely translates into any increased motivation or desire to take that action.

Taking action involves your pre-motor cortex hence why being involved in sports, competitions on the think/do level is so beneficial, specially if it's done from younger ages.

The way that I view it, the brain is a cluster of neurons, but as you start to teach them to talk, sub-clusters start to talk. I view them as representatives in my mental congress (FWIW, I refer to myself as We when I discuss internally). Not all of these sub-clusters will agree, not all of them will be nice and most importantly none of them are you. You are the aggregate of them all.

The congress of your mind is not any of its representatives, and none of the representatives are the congress. Additionally, none of the representatives are smarter than the congress and the congress is not as smart as the smartest representative. The collective is more than the sum of its parts.

Every one has many parts of their mind that are toxic. Likewise there are many parts of your mind that are loving and generous. Those divergent sub-clusters of neurons don't get along and rarely agree. Like with good communication amongst people, the hard part is respecting those parts of your mind (even loving them as you might a toxic family member), allowing them to say their piece, acknowledging them without agreeing, and moving past their thought to more productive topics / view-points.

There are also parts of your mind that are not toxic, but they are negative. Its not always clear if negative leads to toxic or leads to benefit. For these, its helps a lot to reflect on their intention. For example, have you ever looked off a cliff or a tall building and "seen yourself falling"[1]? It can be easy to interpret that as being suicidal, however, digging deeper, while negative at first the intention is to save your life.

Allowing that thought to play out, you first feel the air, the cold rushing around you, eventually you get too close to the floor, or hit the floor, and the thought breaks. If you let it happen a few times, generally you'll find yourself still wanting the rush but find a better way to land. Can I hit the tree and live? Can I grab the power cables? What if I did a really cool roll? Eventually the pathways all converge and you always go splat. Then that part of your mind quiets, and it is clear to see the intention was to save you. And if you ever find yourself playing out a thought a few times and its generally toxic, flag it and apply the strategy for toxic instead.

I hope that was less of a ramble and ideally helpful.

[1] For the record this is very human, a lot of my very healthy friends and I all have this reaction, and it is not something to worry about at all.

Holy shit I have never heard anyone talk about this before on the internet or anywhere. I have this as well. It started for me in around 2013. Before then I had never thought in words, and I used to read solely visually. At that time for some reason I thought it would be a better idea to try to develop an internal monologue and try to talk my way through things.

I don't think it's really helped me in any way honestly. There are some problems at work that I find a bit easier to talk my way through in this sense but it's outweighed by how much more I ruminate now that I have this voice in my head. I also think I read more slowly now because I subvocalize. I think I have OCD because I cannot stop myself from subvocalizing, and if I try to stop I keep focusing on it in the back of my mind.

The only thing that's helped me were mild anti-psychotics that a therapist prescribed me a while ago that came with their own side effects. I have also seen a bit of change from trying very very hard to enact CBT-like practices on myself but it's slow going.

I'm not always good at self care, for example. This is a particular weakness that the Vicious Critic would exploit. One night, as I was laid up, incapable of doing pretty much anything, VC comes online and starts ripping me for failing to cook for myself and relying on delivery. A second voice came online... my angel (I don't mean this in a religious sense; this is a normal phenomenon among people who hear voices). "HEY! Be nice to klyrs!" And then their attention turned away from VC, and towards me. "I'm so sorry; you don't deserve that..." and proceeded to talk me through obtaining dinner in a kind and gentle manner. I thanked the voice for their care, and didn't hear from VC for quite a time.

After that incident, VC would still come back from time to time. The angel hasn't come back unbidden, but I can summon the voice to combat VC.

I understand that this process is taught through CBT or DBT. Long live DIY, I guess. But know that there's help available.

> But I am certain in my case when the voices started and I am not sure the superpower problem solving skills are worth the trade.

There appears to be a dichotomy among societies in the world. Ones where people who hear voices are considered gifted, and ones where they are considered ill. In the gifted societies, the voices are generally good and helpful like my angel. In the ill societies, the voices are generally malevolent like my VC.

You have a gift. But aspects of it have run amok. Ask your voice to be a part of the solution, and stop attacking you. Demand a respectful tone, and shut it out when it behaves poorly. Progress with your voice will neither be easy nor monotonic, but it is possible.

I don't know your exact situation, but perhaps you should just let the voice do its thing?

Just make sure it doesn't stop halfway through. I mean, if it wants to be a critical asshole that picks apart every little thing you think about, awesome! Because it, too, is something that you're thinking about, and presumably it ought to pick itself apart with the same ferocity.

I mean, if your inner critic isn't critiquing its own criticisms, then that sounds like it's not being critical enough.

---

To add, this problem is intrinsic to governments, where checks-and-balances are needed. For example, we can't have a government or police force that's beyond scrutiny; if anything, a government/police-force must be harsher and more unforgiving of itself than of the population it governs/polices.

Likewise, your inner critic has to be harsh with itself. It has to critique itself for what it does, including the costs it imposes on you in terms of taking your time-and-energy, much as a government must regulate its own budget to remain sustainable.

And if it's starting to screw up your life, and its existence is making stuff worse for you, then that's empirical proof that it's messing up. That it needs to get more aggressive at critiquing whatever it's doing wrong that makes your life worse.

I have it. I call him: the observer. You are right, the observer is a giant asshole, almost by definition, in that's his precise purpose. (though there have been a few rare moments of compassion from him)

You are right that it is entirely a mental model, and not an involuntary part of me. But, I voluntarily rely on the model enough, that without it I don't function as effectively.

In my case, there are 3 people in my mental model of self. The doer, the thinker and the observer. The doer is simply my place-holder for impulse control and ability to convert ideas to practice, with the thinker being what I most closely associate with myself.

The observer is really helpful. It helps me see some blind spots in my own judgement and has made me pretty good at figuring out how others will respond to situations. But, I really do need to make him shut up, in situations where I need to be taking initiative or be bold.

It is not problematic for me, as I don't think it manifests physically in front of others (it's different when I am alone), but it has played a huge role in making me capable of gaining holistic views of things. I'd rather have it than not.

The observer could be a bit kinder though.

Oh my god yes. Because it knows all of your weaknesses and where it hurts and goddamn bastard always is ready to point out the flaws you make, rather than the good stuff.

I often think myself is my biggest enemy.

What does that mean? Is it too annoying as a phenomenon, or does it confront/criticize you?

I don’t think I have an audial voice in my head, but when I think, something like silent voice tries to build itself there. It actually doesn’t help, only slows me down x10. Best productivity comes with the flow state for me (it also destroys my social abilities, but f* them anyway).

Speaking with people who write, I found that roughly half of them can have a litteral chat with their caracters in their head, me included, I would not be surprised if it were correlated (people who cannot where chocked that it could be possible).

I talk to myself a lot. And swear at myself a lot. But it's all in good fun, and occasionally some insight pops up.

Also, given my privacy hobby, I end up talking about myself in the third person. But only in the vaguest terms.

I remember first reading about this in "the power of now", which describes this alter ego as a protection mechanism as well, like that little voice will always come up with reasons why not to do something.

Experiencing life that way will make it easier to write a book, so it would be a mistake to rely on book authors as the sample set. Also, "quiet" minds might have adopted the vocabulary and phrasing "noisy" minds never suspecting that the language they have adopted was meant literally, not metaphorically.

I have a quiet mind. It is rare that any part of mind is forming sentences or phrases unless I am trying to communicate in writing or in speech. This is true even when I am coding or debugging with the exception that I will slowly repeat the name of a variable or function to myself as an aid to short-term memory.

I write more than most people do; most of what I write is not intended to be read by anybody but me.

About 25 years ago, in my 30s, I stopped being able reliably to remember what item I came for when I leave one room of my apartment to get something in a different room. After a few years of putting up with the unreliability, I started a habit of choosing one or two words to describe the item I am after, then repeating the word or words slowly till the item is in my hand.

In my 20s, I would spend a lot of my alone time going over recent conversations. In particular, if someone said something aggressive or unfair to me, I would spend a lot of brain time coming up with comebacks or words I wish I had said in reply. Then I noticed that I have no need or desire to keep on talking to people who are so quick to jump to conclusions about me that it is important for me to get quicker with my comebacks and replys, so I stopped putting brain time into that skill.

Some describe that there are two voices, first is the thinker, second the proofer. The thinker thinks, the proofer proofs. But that's a very specific description.

What might be the difference is that some physically articulate and form words, whereas others keep it to their minds and thoughts, and many try to silence it entirely.

The book Siddhartha also gives this an interesting spin, although that's a novel.

The problem of talking to myself outloud ... not a problem! Turn on the camera and call it livecoding.

At work I use a notebook to write down my voice so it has an outlet. We apparently talk to each other in first person plural.

Have a look at the book: Zen mind, beginners mind. It was one of the best things I discovered for myself. Hope you'll find it useful.

I've intentionally practiced reading aloud lately to counter it. (only sometimes, generally with someone else to read to; it helps)

I guess one can train yourself to "switch", e.g. by focusing on the next word faster than the voice can follow.

I used to think this way, it was very hard to study or go deep into abstract concepts for long periods, but it is useful to some extend, I was able to get a "decent life as an responsable adult" with this system in my head. you ended learning anything you studied, but I felt uncomfortable, uneasy,tired all the time, full of anxiety in social events of any kind, to the point I got into a deep frustration and depression that leaded to unemployment twice in my life. all because of my internal voice, it can get very uncontrollable, it fools you in to thinking that this voice is the only resource you have in your mind. that the voice is you.

unemployed, with a lot of time in my hand, I started to learn math, specifically,I got into category theory thanks functional programming. the subject just fascinated me. I started a really hard journey ,I got really deep into that rabbit hole, all of this ,with my anxiety at full and my brain in complete chaos. but I continued, even when I couldn't grasp any of the concept explained in the articles and books I read. I just continued mindlessly like a zombie, and at some point I really thought that I was losing my mind. suddenly, one day, watching a video on YouTube about philosophy, I heard the expansion of the famous phrase, cogito, ergo zoom. and everything , from one moment to the next, started to make sense, things like monads, functors, implications of Cartesian products, etc.. were concepts that I could handle naturally, I was being overloaded with new knowledge that seemed to came from nowhere. it was the most exciting feeling I had in my life. I started to see everything different. the reflection of the tangible world in my mind was changed forever.

now, I just try to transform everything, every interaction, memory or concept to a category theory diagram in my head. my mental model was altered when I discovered that everything can abstracted to dots and arrows moving around and "zoomed" in and out if you filter the unnecessary noise that comes from your senses and your own brain, which is a lot. once you find a simple system to do that mechanically , it starts to be something like blinking or breathe. you are focused with clear mind, all the time, from the first thoughts in morning to the last one before sleep, is such a fantastic feeling. I started to be very aware of this just few days ago and it feels like magic, I can't control it in full but I truly think I'm someone new.

I'd give anything to turn mine off.

https://www.quora.com/Why-dont-more-women-participate-in-pro...

Since this is meant to be a graduate level research course, I wonder if any cutting edge topics have been added since? Were there any major advances or new ideas in fundamental data structures in the past few years?

For example back when recaptcha was introduced, trolls tried to transcribe everything as the n-word (since you only had to get one of the two words correct).

These cases can obviously be noticed and fixed but it's harder now that the training data is opaque right?

Here's an example snippet by Peter Norvig that is beautifully formatted:

  def neighbors4(point): 
    "The four neighboring squares."
    x, y = point
    return (          (x, y-1),
            (x-1, y),           (x+1, y), 
                      (x, y+1))

  def neighbors8(point): 
    "The eight neighboring squares."
    x, y = point 
    return ((x-1, y-1), (x, y-1), (x+1, y-1),
            (x-1, y),             (x+1, y),
            (x-1, y+1), (x, y+1), (x+1, y+1))

The main takeaway is that a linear expected utility doesn't make sense.

It would've told you to bet all your wealth every game, which does result in a higher linear expected value, where you win (1+1.1)^N with probability 1/2^N at time N, but 0 otherwise. But no real human would take the bet of extreme high payoff at extremely rare chances with ruin otherwise.

Also see St. Petersburg paradox for a similar "paradox" resolved with expected utility theory.

To start, EVERY utility function that is both increasing and sublinear will agree that Kelly is the best strategy. Whether square root, log, or bounded - it doesn't matter. The details of your utility function are unimportant.

What matters is that each iteration of an investment strategy multiplies your net worth by a random factor. But log turns multiplication into addition. And statistics has very strong results about sums of independent variables.

The result is that with 100% odds, a player following Kelly will eventually wind up ahead of any other static strategy that you could choose. Both wind up ahead and eventually remain ahead. Which is why a wide variety of utility functions will conclude that Kelly is the optimal strategy.

This is simply false. This is easy to check for the sqrt utility case. You can calculate the optimal proportion for a single bet and note that it's different than for Kelly, and then you can calculate the utility-function-given-that-you're-about-to-make-a-bet and check that it's still proportional to sqrt. So by induction you are always going to bet the same proportion no matter how many bets you have to make, and this proportion is different from Kelly.

> The result is that with 100% odds, a player following Kelly will eventually wind up ahead of any other static strategy that you could choose.

This is true in the sense that the probability tends to 100% as the number of bets tends to infinity. But this doesn't make Kelly optimal, because in the event that the Kelly isn't ahead the expected utility of the other strategy could be much higher than Kelly.

As for the 100% odds answer, what I said was true is true in the sense that it is actually true. No ands, ifs, or buts. With 100% odds, Kelly eventually wins over any other strategy. Period.

The question of whether this makes Kelly optimal is not the question that the theorem was trying to answer. And therefore is irrelevant. Now in fact this does make Kelly optimal for a wide range of utility functions. But far from all possible ones.

The point being that it is important to separate a mathematical point from our interpretation of what that point implies. When you confuse the two then you get yourself into an unnecessary muddle. Kelly is a statement about the probability of one strategy beating another. It isn't a statement about how you should bet.

  E[ln(X_1*...*X_N)] = sum E[ln(X)]

But if we use square root as our utility instead:

  E[sqrt(X_1*...*X_N)] = prod E[sqrt(X)]

Where did I go wrong?