Posts

OECD agenda [Link] 2019-05-30T09:51:58.849Z
Open thread, September 25 - October 1, 2017 2017-09-25T07:36:19.474Z
Open thread, September 18 - September 24, 2017 2017-09-18T08:30:37.911Z
Open thread, September 11 - September 17, 2017 2017-09-11T07:46:02.103Z
Open thread, September 4 - September 10, 2017 2017-09-04T07:41:03.866Z
Open thread, August 28 - September 3, 2017 2017-08-28T06:11:19.159Z
Open thread, August 21 - August 27, 2017 2017-08-21T06:13:35.045Z
Open thread, August 14 - August 20, 2017 2017-08-14T07:48:13.195Z
Open thread, August 7 - August 13, 2017 2017-08-07T08:07:01.288Z
Open thread, July 31 - August 6, 2017 2017-07-31T14:41:09.485Z
Open thread, July 24 - July 30, 2017 2017-07-24T07:28:26.052Z
Open thread, July 10 - July 16, 2017 2017-07-10T06:31:11.395Z
Open thread, June 26 - July 2, 2017 2017-06-26T06:12:35.196Z
Open thread, June. 12 - June. 18, 2017 2017-06-12T05:36:02.328Z
Open thread, May 29 - June 4, 2017 2017-05-29T06:13:51.683Z
Open thread, May 22 - May 28, 2017 2017-05-22T05:44:05.910Z
Open thread, May 8 - May 14, 2017 2017-05-08T08:10:15.778Z
Open thread, May. 1 - May. 7, 2017 2017-05-01T15:55:32.361Z
New Year's Prediction Thread (2014) 2014-01-01T09:38:03.372Z
Open Thread, October 7 - October 12, 2013 2013-10-07T14:52:51.109Z
Meetup: Ljubljana 2013-10-04T10:32:04.028Z
[Link] Intelligence, a thermodynamic POV 2013-07-21T12:44:09.102Z
Rationality Quotes June 2013 2013-06-03T03:08:50.803Z
New Year's Prediction Thread (2013) 2013-01-01T14:03:54.596Z
Rationality Quotes December 2012 2012-12-03T02:33:14.356Z
[LINK] How rational is the US federal state 2012-10-30T08:56:59.232Z
Questions for shminux 2012-06-22T19:35:38.437Z
[META] Karma counting problem 2012-04-18T07:51:36.365Z
Rationality Quotes March 2012 2012-03-03T08:04:55.112Z
Packing savant program 2012-02-20T08:27:17.181Z
Automatic programming, an example 2012-02-01T20:55:18.448Z
[META] Karma, its positive and negative component 2012-01-25T21:31:05.607Z
[LINK]The Edge's yearly question 2012-01-16T06:51:05.412Z
Who's in the AI business? 2012-01-15T16:53:58.165Z
NonGoogleables 2012-01-12T13:23:37.330Z
[Link] There is nothing like "intelligence", only an evolution is going on 2012-01-10T17:54:47.481Z
Rationality quotes January 2012 2012-01-01T10:28:45.564Z
Best wishes for 2012 2011-12-31T18:09:46.578Z
The Kolmogorov complexity of a superintelligence 2011-06-26T12:11:38.392Z
Open Thread, March 2011 2011-03-08T08:38:02.858Z
South/Eastern Europe Meeting in Ljubljana/Slovenia 2010-11-02T18:26:17.877Z
A puzzle 2009-04-25T02:33:00.000Z

Comments

Comment by Thomas on What would it look like if it looked like AGI was very near? · 2021-07-12T17:28:30.268Z · LW · GW

It was a slippery slope, with those Neural Networks. They were able to do more and more things, previously unimagined to be possible for them. It was a big surprise for everyone, how good they were at chess, 3600 or so Elo points. Leela Chess Zero invented some theoretical breakthroughs, soon to be exploited by more algorithmic, non-NN chess engines like Stockfish, for its position evaluation function. Even back then, I was baffled by people expecting that this propagation will soon stop, due to some unexpected effect, which never came. Not in chess, nor anywhere else.

It was indeed a matter of "when", not of "maybe not" anymore. Yes, those first mighty AI's were quite fake, they have no real clue. Except that this mattered less and less and it was less and less true. In an increasing number of fields. 

It was only a matter of time when the first translators from the gibberish weight tables learned by NN's, to exact algorithms will emerge. Something which people have previously done, stealing ideas from Leela, implementing them with rigor into algorithmic schemes of Stockfish -- AI learned as well. Only better, of course.

By then, the slope was very slippery, indeed. I still can't comprehend, how this wasn't clear to everyone, even back then, less than 10 years ago.

Comment by Thomas on Open and Welcome Thread - April 2021 · 2021-04-18T23:30:14.122Z · LW · GW

It's nothing wrong with the Googling method. Besides, one could search for <<pizzeria at the end of the world papa mamma>>. Should work now, too.

Maybe, next year's solution to this problem will be "at least 13".

Comment by Thomas on Open and Welcome Thread - April 2021 · 2021-04-18T07:20:14.720Z · LW · GW

You are right. It's 12 or more different kinds of pizza. If it was 1 kind of pizza served, he could be certain, that one kind of pizza was at the majority (in that case at all minus one) orders. Since somebody could order a salad. But only one without pizza, to avoid equal orders by pizza kind.

Even if there were 11 different pizza kinds on the menu, Marco could be sure, there is the majority kind of pizza there. Since this Fraenkel conjecture has been proved up to 11 by now.

But for 12 or more, no one really knows yet. Probably it's true, but who knows. Congratulation, you were rather quick. Despite the fact, the problem formulation looks vague to you.

Comment by Thomas on Open and Welcome Thread - April 2021 · 2021-04-17T21:39:06.618Z · LW · GW

After some time, a new math puzzle. 

https://protokol2020.wordpress.com/2021/04/17/pizzeria-at-the-end-of-the-world/

Comment by Thomas on Technological stagnation: Why I came around · 2021-01-27T14:42:08.526Z · LW · GW

I don't see how "2.5 batteries" could mean "independence from fossil fuels". 

Comment by Thomas on Stupid Questions October 2020 · 2020-10-22T08:17:49.361Z · LW · GW

Perhaps, it's not you who is missing something.

Comment by Thomas on On exact mathematical formulae · 2020-10-01T18:16:23.032Z · LW · GW

I recently discovered there's no closed-form formula for the circumference of an ellipse

Yes. I've asked the computer, to give me some simple approximation formula then. This came out:

 

 

 

It's quite good when b >> a.

Comment by Thomas on Results of $1,000 Oracle contest! · 2020-06-18T19:27:56.231Z · LW · GW

Well, Oracle, which under 1000 words question, would be answered by the most influential answer for our future? What answer to which question would be the most earthshattering?  

Comment by Thomas on March Coronavirus Open Thread · 2020-03-27T15:33:46.488Z · LW · GW

CROSSPOST from my blog:

https://protokol2020.wordpress.com/2020/03/27/covid-19-a-view-to-a-kill

The R0 factor for this illness, which denotes the average number of people infected by a carrier, isn't a constant, it's a function of time. R0 = R0 (time). In fact, it's a function of more parameters and not just time. For example, if quarantined, R0 should be close to 0. There are many unknown factors here, of course, some even known. Some push this now well known R0 term bellow 1, others above 1. It's all about reducing R0 below 1, and the illness will die out. Otherwise, the number of sick people will go through the roof, by the exponential growth function manner.

All of the above is very well known and understood and repeated over and over again now.

Then you get infected, you caught the virus somehow, what now? Your cells will spread the virus among each other by the factor R0IC !

R0IC is the average number of cells, one infected cell will further infect on average. "IC" in standing for "Inter-Cellular". This is again not a constant but is a function of time and many other known and unknown factors. For example time, temperature, the immune system activity and so on. R0IC = R0IC (t, T, ISactivity, ..., ). At least as complex as the transmission factor R0 between humans, is the transmission factor R0IC between cells. When R0 falls bellow 1 for a considerable time period, the epidemics burn out. When R0IC  falls bellow 1 for a considerable time period, the particular human's illness burns out.

The last paragraph above is a less well-known fact, but it's a fact none the less. Spreading of this virus among cells, in a way closely imitates the spreading among humans. Medical doctors and medical nurses work hard to minimize R0IC in already infected people. They might call it differently, but it is what it is. Stoping the intercellular infection, "flattening the curve" inside the patient's body, "delaying the disease" inside the patient's lungs -- you name it!  Medical professionals thus "delay the disease" inside you, hoping that the immune system will kick in and do the same until done.

Now, when you are infected and breath, you inhale more or less clean air and exhale quite a lot of viruses. Soon, you are inhaling some previously exhaled viruses back and some of those might infect an additional lung cell.  By breathing through SCUBA, there are no previously exhaled viruses and therefore this R0IC should go down slightly, shouldn't it? By breathing some higher oxygen concentrations than normal, this R0IC should go down even more. Since oxygen is a bit toxic for COVID-19.

By breathing some WARMER air than normal, this R0IC should go down even more, since the COVID-19 virus doesn't like hot air, does it? Especially if the air is salty or smells of some detergent, pure alcohol and so on, it's killing the viruses. Some even inside your nose and downward, perhaps.

Then, you may, sometimes after infection, during the asymptomatic phase, run up the hill in sunny weather. Puffing like an old locomotive, you will exhale a lot of viruses. Fortunately, nobody is with you and those exhaled viruses will die under the Sun. Again, you even so slightly decreased the R0IC factor and "flattened the curve" of the internal infection between your cells. You may as well try to inhale some eucalyptus hot vapors under the towel, as they suggest already. Perhaps you should insulate yourself in a sauna. Not too hot, not too humid, but just enough for you to survive and not the virus. Under medical control, of course!

And then perhaps, medical doctors should think about their doctrinal procedures for COVID-19 in this light and to refine these suggestions above considerably. I am no medical doctor! But then again, Marylin Vos Savant was no mathematician either but gave a valuable lesson to Paul Erdos himself. There are times when IQ matters the most.

Anyway. When and if you are infected with COVID-19, in the presymptomatic phase, keep the R0IC down as much as you possibly can. The second symptomatic phase may never come. Doing so, you will (ever so slightly) lower the R0 too!

DISCLAIMER: This is not official medical advice, not even unofficial medical advice. Contact your MD if or when feel ill!
Comment by Thomas on Open Thread May 2019 · 2019-05-30T09:54:36.583Z · LW · GW

https://www.oecd.org/going-digital/ai/principles/

Either I have no clue, either ...


Comment by Thomas on 2018 Year In Review · 2019-01-03T23:45:11.175Z · LW · GW

I've done some benchmarking in 2018. I benchmarked an "AI software" we devised, by some benchmarks mostly I invented, too. Which doesn't look very good, I know, but bear with me!

For one, I have given an unsolved Sudoku puzzle to this software with two working names, "Spector" and/or "Profounder". It concluded, that for every X and every Y: X==Y implies that column(X) != column(Y) and row(X)!=row(Y). (Zero Sudoku topic knowledge by Spector is, of course, a necessary condition.)
With several unsolved Sudoku puzzles, Spector concluded that subsquare(X) != subsquare(Y). Just for one puzzle, the concept of "3 by 3 subsquare" isn't economical. It's economical for several of them, though.
The second benchmark I invented, was giving the string "ABCDEFGHIJKLMNOPQRSTUWXYZ" to Spector. The string generating algorithm would be simpler if the letter "V" wasn't missing. This is the way Spector notices something might be wrong with the given string. (Zero alphabet topic knowledge by Spector is, of course, a necessary condition.)

Yet another benchmark was numbers from 3 to 122. Each labeled by 0 or 1, depends if it's nonprime or prime. The simplest generating algorithm is a sort of Eratosthenes sieve. Not for numbers, but for their labels. Spector finds and generates it, with zero knowledge about primes.

Another benchmark was inspired by a mistake someone made. There is a nursing school here somewhere, which sends their students to practice in a nearby hospital for a day or two every week. Except for freshmen in the first year. They teach them everything else in this school, of course, including the gym (boys and girls separated there) and they feed them all once a day, too. It's standard in this part of the world. But the school does not feed them when they are at the hospital.

So they forget to feed girls from 2B department on Thursdays when they are in school. They forget to include that into their schedule. Boys from 2B have eaten while girls were exercising, but poor girls were forgotten and nobody noticed.

I asked Spector, giving him the school schedule in CSV format if anything is wrong with it. Spector did conclude, that every student has a lunch break once a day when not practicing, except for those girls on Thursday. Which was (probability-wise) odd enough to be significant.

Spector/Profounder is all about one mayor and three to five lesser tricks. To find a generating algorithm for every part of any data it gets. This is the mayor. Then to see if some small data alteration would mean a significantly simpler generation. Then to evaluate the probabilities and needed complexities. And then Spector also asks itself, what data changes are possible but which conserve already observed rules. Which is particularly handy in the unsolved Sudoku case for example.

We will do some more benchmarking this year.

Comment by Thomas on An Extensive Categorisation of Infinite Paradoxes · 2018-12-15T07:26:34.434Z · LW · GW

For Eve and her apple pieces. She may eat one piece per second and stay in Paradise forever because at any given moment only a finite number of pieces has been eaten by her.

If her eating pace doubles every minute, she is still okay forever.

Only if she, for example, doubles her eating pace after every say 100 pieces eaten, then she is in trouble. If she supertasks.

Comment by Thomas on Open thread, January 29 - ∞ · 2018-01-29T09:08:39.391Z · LW · GW

I tend to agree. I don't know is it just a habit or something else, like a conservative profile of myself and many others, but that doesn't really matter.

The new site isn't that much better. Should be substantially better than this one for a smooth transition.

Comment by Thomas on AGI · 2017-11-08T07:50:40.307Z · LW · GW

Please, focus only on what has been said and not on how it has been said.

Now, there is a possibility that all is wrong from my side. Of course I think how right I am, but everybody thinks that anyway. Including this Temple guy with his "don't code yet"! I wonder what people here think about that.

One more disagreement perhaps. I do think that this AlphaGo Zero piece of code is an astonishing example of AI programming, but I have some deep doubts about Watson. It was great back then in 2011, but now they seem stuck to me.

Comment by Thomas on AGI · 2017-11-07T10:41:22.170Z · LW · GW

Knowledge is information error-corrected (adapted) to a purpose (problem).

No. Knowledge is just information. If you have some information how to solve a particular problem, it's still "just information".

There are no hard and fast rules about how error-corrected or to what

Those rules are just some information, some data. How "fast and hard" are they? When there is a perfect data about the fastest checking algorithm, then it's still "just data".

The field started coding too early and is largely wasting its time.

Perhaps. How do you know what people know and who is coding already, prematurely or not?

If you joined the field, I would recommend you do not code stuff.

I wouldn't give such an advice to everybody. I don't know what some people might know. Let them code, if they wish to.

Certain philosophy progress is needed before coding.

I agree, that you need some philosophy progress, you don't know if all others need that too. At least some may be completely unknown to you or to me.

good non-AGI work (e.g. alpha go zero, watson)

Isn't their coding premature as well?

which they hope will somehow generalize to AGI (it won't, though some techniques may turn out to be useful due to being good work and having reach)

I am not as sure as you are. They hope they will do something, you hope they will not. That's all.

wasting their time

Maybe you are a time waster Mr. Temple, yourself. Your claim that "coding AGI" is premature is just a guess. It's always possible that one is wrong, but saying "you people don't have the right theory, stop coding" ... is super-wrong. You don't know that. Nobody knows, what somebody else might know already.

people are super focused on predictions but not explanations.

A good prediction can only be done if you have a good theory/model about the mechanisms involved. So every decent predictor models anyway. The best predictor possible has a correct model. Which doesn't always imply that its predictions are right. Sometimes there isn't enough data for that. Even in principle. But to predict is to model!

some even deny there are non-empirical fields like philosophy

Some are dirty bastards also, and some have friends in low places and aunts in Australia. But you seem to imply, that all should share your view about "non-empirical fields like philosophy". Yeah, right.


It has been enough. At least my last remark I gave, was already unnecessary.

Comment by Thomas on Kialo -- an online discussion platform that attempts to support reasonable debates · 2017-11-05T14:04:50.361Z · LW · GW

I don't like it, at all.

As you see, my argumentation for that is just like yours. Nonexistent.

Comment by Thomas on Open thread, September 25 - October 1, 2017 · 2017-09-25T07:41:18.398Z · LW · GW

A problem.

Comment by Thomas on Open thread, September 18 - September 24, 2017 · 2017-09-22T19:01:34.233Z · LW · GW

There are 143 primes between 100 and 999. We can, therefore, make 2,924,207 3x3 different squares with 3 horizontal primes. 50,621 of them have all three vertical numbers prime. About 1.7%.

There are 1061 primes between 1000 and 9999. We can, therefore, make 1,267,247,769,841 4x4 different squares with 4 horizontal primes. 406,721,511 of them have all four vertical numbers prime. About 0.032%.

I strongly suspect that this goes to 0, quite rapidly.

How many Sudokus can you get with 9 digit primes horizontally and vertically?

Not a single one. Which is quite obvious when you consider that you can't have a 2, 4, 6, or 8 in the bottom row. But you have to, to have a Sudoku, by the definition.

It's a bit analogous situation here.

Comment by Thomas on Open thread, September 18 - September 24, 2017 · 2017-09-22T10:44:28.205Z · LW · GW

Say, that we have N-1 lines, with N-1 primes. Each N digits. What we now need is an N digit prime number to put it below.

Its most significant digit may be 1, 3, 7 or 9. Otherwise, the leftmost vertical number wouldn't be prime. If the sum of all N-1 other rightmost digits is X, then:

If X mod 3 = 0, then just 1 and 7 are possible, otherwise the leftmost vertical would be divisible by 3. If X mod 3 = 1, then 1, 3, 7 and 9 are possible. If X mod 3 = 2, then just 3 and 9 are possible, otherwise the leftmost vertical would be divisible by 3.

The probability is (1/3)*(((1+2+1)/5))=4/15 that the first digit fits. (4/15)^N, that all N digit fit.

Actually, we must consider the probability of divisibility by 11, which is roughly 1/11, which further reduces 4/15 per number to 40/165. And with 7 ... and so on.

For the divisibility with 3, we render out not only one permutation of N-1 primes but all of them. For the divisibilty with 11, some of them.

It's quite complicated.

Comment by Thomas on Open thread, September 18 - September 24, 2017 · 2017-09-20T19:52:41.291Z · LW · GW

Interesting line of inferring... I am quite aware how dense primes are, but that might not be enough.

I have counted all these 4x4 (decimal) crossprimes. There are 913,425,530 of them if leading zeros are allowed. But only 406,721,511 without leading zeros.

if leading zeros ARE allowed, then there are certainly arbitrary large crossprimes out there. But if leading zeros aren't allowed, I am not that sure. I have no proof, of course.

Comment by Thomas on The Copenhagen Letter · 2017-09-19T22:15:35.493Z · LW · GW

Well, I said something in line with "people may need some stuff to live and declaring that we should "put people before that stuff" is a silly way to present the situation". Maybe not as silly as it's a demagoguery.

But then I changed my mind and decided to not participate in a discussion at all. But somehow couldn't erase this now empty box.

Comment by Thomas on The Copenhagen Letter · 2017-09-19T18:25:20.933Z · LW · GW
Comment by Thomas on The Copenhagen Letter · 2017-09-18T18:58:17.507Z · LW · GW

tl;dr

But I saw this:

Time to put humans before business.

Time to put humans before oxygen, too? Silly stuff.

Comment by Thomas on Open thread, September 18 - September 24, 2017 · 2017-09-18T15:02:08.206Z · LW · GW

The bottom and the rightmost prime can both have only odd digits without 5. The probability for each prime to fit there is then only (2/5)^N times that. We can't see them as independent random numbers.

Comment by Thomas on Open thread, September 18 - September 24, 2017 · 2017-09-18T12:21:10.245Z · LW · GW

Very well. What do you think, are there arbitrary large squares possible or not?

I think not. Even in binary notations NxN and above, probably don't exist for an N, large enough.

Comment by Thomas on Open thread, September 18 - September 24, 2017 · 2017-09-18T11:33:07.431Z · LW · GW

Congratulation! It's essential that you don't tell the algorithm, at least for now. You have an extra solution, where every horizontal has its equal vertical. Which is perfectly okay, but I wonder if that is the property of your algorithm?

Comment by Thomas on Open thread, September 18 - September 24, 2017 · 2017-09-18T08:33:13.358Z · LW · GW

A problem to ponder this week.

Comment by Thomas on 2017 LessWrong Survey · 2017-09-13T19:53:51.816Z · LW · GW

My country isn't from the list of the default choices. So I type it and pressed Enter. It's all I remember.

Comment by Thomas on 2017 LessWrong Survey · 2017-09-13T10:18:02.812Z · LW · GW

Previous session is set to be finished.

Your browser reports that it was used previously to answer this survey. We are resetting the session so that you can start from the beginning.

Click here to start the survey.

I have just pressed Enter after my country's name. Fix this!

Comment by Thomas on Open thread, September 11 - September 17, 2017 · 2017-09-12T19:14:18.744Z · LW · GW

There is a mountain on the Moon's south pole, where the Sun is always shining. Except when it's covered by Earth, which is rare and not for a long time. A great place for a palace of the Solar System's Emperor.

Comment by Thomas on Open thread, September 11 - September 17, 2017 · 2017-09-12T17:20:55.130Z · LW · GW

Can't use the Moon. It's already booked and reserved for a computronium.

Comment by Thomas on Open thread, September 11 - September 17, 2017 · 2017-09-11T07:48:19.883Z · LW · GW

We have a problem.

Comment by Thomas on Automatic programming, an example · 2017-09-11T07:10:29.983Z · LW · GW

Kepler's law isn't O=constant*A. This is very wrong, silly even.

Comment by Thomas on Open thread, September 4 - September 10, 2017 · 2017-09-04T07:42:30.279Z · LW · GW

No problem this week, just an appreciation for people of LessWrong who can be right, when I am wrong.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-09-01T12:46:41.994Z · LW · GW

Say, that SB has only 10 tries to escape.

The DM (Dungeon Master) tosses his 10 coins and SB tosses her 20 coins, even before the game begins.

There are 2^30, which is about a billion possible outputs. More than half of them grants her freedom.

We compute her exit by - At the earliest x>y condition in each output bit string, the DM has also the freeing coin toss.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-09-01T07:57:32.107Z · LW · GW

1._round_________________1____________________8______0.125

2._round________________15___________________64______0.234

3._round_______________164__________________512______0.32

4._round_____________1,585________________4,096______0.387

5._round____________14,392_______________32,768______0.439

6._round___________126,070______________262,144______0.481

7._round_________1,079,808____________2,097,152______0.515

8._round_________9,111,813___________16,777,216______0.543

9._round________76,095,176__________134,217,728______0.567

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-31T19:21:20.542Z · LW · GW

Your basic idea is right here. But ... this product isn't that straightforward.

Say it's the 100th session. It is a lot of ways, that x becomes greater than y exactly this time. Especially if the formula is x>y+sqr(y) or something alike from the Chebyshev's arsenal.

If the session is then 101st, this new small probability isn't much smaller than it was in the 100th session.

Still, you may be right that the product (1-p_n)*(1-p_n+1) ... converges to 1/2 at the most.

Well, I doubt it.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-31T19:02:05.273Z · LW · GW

Interesting. Do you agree that every number is reached by the z function defined above, infinite number of times?

And yet, every single time z != sleeping_round? In the 60 percent of this Sleeping Beauty imprisonments?

Even if the condition x>y is replaced by something like x>y+sqrt(y) or whatever formula, you can't go above 50%?

Extraordinary. Might be possible, though.

You clearly have a function N->N where eventually every natural number is a value of this function f, but f(n)!=n for all n.

That would be easier if it would be f(n)>>n almost always. But sometimes is bigger, sometimes is smaller.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-31T16:47:30.898Z · LW · GW

So, you say, the Sleeping Beauty is there forever with the probability of at least 1/2.

Then she has all the time in the world, to exercise this function which outputs z. Do you agree, that every natural number will be eventually reached by this algorithm, counting the double tossings, adding 0 or 1 to x and 0 or 1 to y and increasing z, until x>y?

Agree?

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-31T13:31:47.036Z · LW · GW

Right. There around 1 you often can actually multiply an infinite number of factors and get some finite result.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-31T12:53:38.341Z · LW · GW

Define flip values as H=0 and T=1. You have to flip this fair coin twice. You increase x=x+value(1) and y=y+value(2) and z=z+1. If x>y you stop flipping and declare - It's the z-th round of the game.

For example, after TH, x=1 and y=0 and z=1. You stop tossing and declare 1st round. If it is HH, you continue tossing it twice again.

No matter how late in the game you are, you have a nonzero probability to win. Chebyshev (and Chernoff) can help you improve the x>y condition a bit. I don't know how much yet. Neither I have a proof that then the probability of exiting is > 1/2. But at least that much it is. Some Monte-Carloing seems to agree.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-31T09:42:32.370Z · LW · GW

I think that was not his question. Hi didn't ask about product integral of f(x), but "product integral of x".

EDIT: And that for "small x". At least I understood his question so.

Comment by Thomas on Is life worth living? · 2017-08-30T12:46:24.162Z · LW · GW

Me too. And death not worth dying!

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-29T21:39:32.375Z · LW · GW

I am afraid, that multiplication of even countably many small numbers yields 0. Let alone the product of more than that, what your integration analogous operation would be,

You can get a nonzero product if the sum of differences between 1 and your factors converge. Then and only then. But if all the factors are smaller than say 0.9 ... you get 0.

Except if you can find some creative way to that anyway. Might be possible, I don't know.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-29T06:56:59.608Z · LW · GW

Sure. But not only to 7/16 but to the infinite number of other values, too. You just have to play with it longer.

The question now is, can the coin make it better, too? If not, why it can only make it worse?

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-28T20:58:57.450Z · LW · GW

The coin can at least lower your chances. Say, that you will say 3 if it is head and 4 if it is the tail.

You can win at round 3 with the probability 1/4 and you can win at round 4 with the probability 1/4.

Is that right?

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-28T15:33:50.612Z · LW · GW

You will always say the same number each time, since you are identical each time.

That's why you get a fair coin. Like a program, which gets seed for its random number generator from the clock.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-28T14:57:36.808Z · LW · GW

True. You can do it worse than 1/2. Just toss a coin and if it lands head up choose 1, otherwise choose 2.

You can link more numbers this way and it can be even worse.

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-28T14:24:48.584Z · LW · GW

Say, you must always give a positive number. Can you do worse than 1/2 then?

Comment by Thomas on Open thread, August 28 - September 3, 2017 · 2017-08-28T14:02:59.405Z · LW · GW

Can you do worse than that?