My take on that is that whatever were the *intentions* of whoever was Satoshi, doesn't really matter.  My personal opinion is that it was a quite bright guy in his basement, but it can be just anything, from the Chinese government to a terrorist organisation.  It doesn't matter.
Satoshi did some brilliant things, and set up a system which has its own dynamics.  That dynamics does not correspond to what Satoshi claimed he made it for, but are the natural consequences of how it was designed.

When we see that, there are some logical possibilities about intention:

a) Satoshi knew perfectly well how this system would evolve, but needed to tell something else to trick people into using it (conspiracy view)

b) Satoshi, bright as he was, made some fundamental mistakes and had some fundamental misunderstandings (my personal opinion)

c) Satoshi came as close as one can get to what was doable at that point, and anything seriously different would not have worked ; in other words, at that point, it was simply impossible to have a system as he pretended, and he came as close as was possible, but no cigar.

I say this, because bitcoin is based upon a totally flawed economic understanding of ideal money, inspired by the "gold bugs" doctrine of sound money ; and has as its core, a deflationary spiral like rarely one has seen any.   As such, bitcoin can never be a mainstream currency, because there is no system included that will provide sufficient elasticity in its offer for its value to remain constant, which is a requirement of ideal money (which will be also a unit of account) ; on the contrary, it is heavily publicized as something that will strongly grow over time, and will make you rich if you adopt soon enough.  Bitcoin is hence designed as a very strongly speculative asset, to be hoarded and to be traded, with high volatility, and high deflation (=gain in value).

Many choices in the design of bitcoin make that it is not going to be a widespread, largely decentralized, generally used payment system ; however, it has everything to be a speculative asset that would make the toxic derivatives that caused the 2007 crash to look like stable money compared to it.


I think bitcoin was a kind of next logical step, and it had the right timing, after the financial crisis of 2007-2008.  Note that this financial crisis had nothing to do with the fiat payment system ; but rather with the reckless speculation of financial institutions on "virtual" complex derivatives.  The ironic thing is that bitcoin took as economic model, exactly something that leads to a highly speculative asset, while pretending to replace the "broken" fiat payment system.  It is this irony - the fact of being able to speculate heavily (which was the main cause of the 2007 financial crisis) while pretending to cure a non-broken system (the fiat payment system) - that was the success story of bitcoin.

On the other hand, without the lure of high speculative prospects, to turn $27 investors in future billionaires, something like bitcoin would never have taken off (hinting at my (c) option above).  So maybe it was necessary to have this irony, of pretending to make an "honest robust payment system" based upon the most heavily charged greater fool speculative asset one has seen in ages ; as no truly honest payment system would ever have taken off.

Be careful with "backed by math".  It is backed by the math that a miner consortium decides to put into the software they are running to make the block chain.  You may think that the 21 million coins are "fixed by math", but that's not true.  They are only fixed by the lines of software that are running now on the nodes of the miner pools.  The only thing that withholds them from changing that, is the *psychological* barrier ; the fact that this was so hammered into the minds of the users that if ever they dare to change that, the whole belief system crumbles.  But it is not "backed by math", at all.

Where does this 21 million come from ?  It comes from the fact that there's a piece of software that has a counter, and every 210 000 blocks, it halves the block reward.

Here's that piece of code:


It means that during 210 000 blocks, there were 50 coins ; then there were 25 coins in the next 210 000 blocks, etc....

As 50 + 25 + 12.5 + 6.25 + .... = 100

we have that in total, *if this piece of software continues to run unchanged for the next 100 years or so*, there will be 210 000 * 100 = 21 000 000 coins in total.

If tomorrow, all the miner pools together (there are about 20 of them) decide to change those few lines of code, you can print just as many bitcoin as you want.  No math, apart from the trivial math that calculates the sum when you have the lines of code, in the same way that "the math determines the emission of fiat currency", when a central bank prints, say, a million dollars a day, you can say that "the math" fixes the amount of dollars printed per year to 365 million.

This is also more or less my sentiment, when I evolved from "enthusiastic freedom money" to "why are some idiots speculating" to "ah, actually, that's what it was made for!".  That said, speculative stuff to pump money out of the weak, in the hand of the rich, may have a long life !

Be careful.  They are working on SIMILAR blocks, but each pool has made his own block, with its own picking of transactions from the mem pool, and with its own specific order of course.  They are working on top of the same consensus block, 469997, of course, because this one has been published.

This is what tricked me in trying many times too. And yes, they warned me and I didn't want to believe I couldn't get him to see this simple fact.  franky1 is not a total ignoramus concerning crypto, so it is beyond comprehension that he has a misunderstanding on which he is locked in so hard that nobody can get him out of there.... but there's no hope I'm afraid.  

But I'm starting to see part of franky1's confusion.  Yes, of course, all miners work on average about 10 minutes on EACH BLOCK.  When they win a block, they were only working on it for about 10 minutes.   It seems that "all the rest was wasted".  Probably franky1's confusion comes from the fact that "if there hadn't been that bastard of a competitor, I could have continued working on the block instead of having to give up on it and start all over again with a fresh one". So if, each time I WIN, I only needed about 10 minutes on average, I would only need 10 minutes on those that I had to give up because a bastard of a competitor forced me.

I think that is the core of his reasoning.

But this is wrong, because, exactly, it is not a race, but a lottery, like jonald tried to explain.

There is statistically not a single difference between mining on the same block, or changing blocks.  Your probability of success doesn't change.  It is as if you  had to throw different dice.  You chances of throwing a number don't change because you use different dice.  In other words, the fact that a "bastard of a competitor" forced you to change the block doesn't alter anything to your chances of winning one.  But I can somehow understand how this can be counter-intuitive, because by far most tasks we know, are a cumulative effort towards a result.

Let us try once more (you see, I'm tricked again in trying !).

Let us say that the "block on which you are working" is the specific dice you throw.   If I give you 3 red dice, and you need to throw 3 times a 6, you will have to try several times.  I have 3 blue dice and I try too.  You have one chance out of 216 to get 3 times a six.  Now after you've thrown 50 times without success, I have also thrown 50 times, and hey, I have 3 six !  At this point, you have to leave your red dice, and you have to use my blue dice now, while I take grey dice.  And we continue playing.
Do you think that you were "close to having 3 six" with your 3 red dice, and because I was a bastard of a competitor, forcing you to abandon the red dice, you can start over again ?

At each "round" (each second, say), both of us throw our dice.  As each of us has 1 chance in 216 to have a triple six, there will be a triple six found every 108 seconds on average, do you agree ?  But you will only find a triple six, on average, every 216 seconds, and me too.  The fact that I am present, doesn't change your chances of winning the next time.
It is only in very rare circumstances, that both of us win at the same throw.  In that case, one of us gets orphaned.  But that only happens very rarely.  Most of the time, each time you win, I don't win, and vice versa.  And whether I win or not, doesn't change the rate at which you win.

No, the system is designed to make mining almost NOT profitable.  Of course, there will always be a margin, because one still needs to be motivated to do something.  If mining were absolutely not profitable, nobody would do it apart from some idealists.  If mining needs to be an industry, then of course *some* profit margin needs to exist. 

But the whole idea is that, if mining is profitable beyond the small margin without which you quit, it will be attractive for others to start mining too (if they can get the same conditions).  Then more blocks will be solved because these newcomers will also solve blocks, and hence the difficulty will go up.  Now, with given technology, "difficulty going up" means the economic cost of making a block goes up.  You will consume more electricity and it will take a longer time to make a block.  Your hardware investment will return less per year, and your running costs will be higher.  It is up to you to see if the fiat value of what you gain with a block is worth it.  At a certain point, this dips below what you consider interesting, and you quit.  It is when just as many miners quit as new miners come in, that an equilibrium is found.

What is nice about this, is that the level of technology doesn't matter, and the block reward doesn't matter, in principle: difficulty will adjust so that the *economic cost* of mining will always be about equal to what is generated in fiat value by the mining, minus the margin below which you don't consider continuing in this business.

That doesn't mean that mining will give the same margin for all players !  After all, the conversion of "difficulty" in "economic cost" depends very much on the conditions in which you obtain your hardware, you can put them at work, and at what cost you can obtain your electricity.  Mining will concentrate in those places where this is cheapest (like any mass production industry).

In fact, this is the side effect of this highly competitive market: only the most competitive *environments* can do mining, and with economies of scale, this automatically leads to a lot of concentrated mining in the hands of a few Chinese, simply because electronic production is cheap there, environmental laxness allows for cheap electricity and so on ; conditions which are difficult to achieve elsewhere.  You can't have a system of fierce competition of "dumb stuff" (calculating trillions of hashes is "dumb stuff" in a way), and think it will be equally distributed over the world.  It will concentrate in those places where there is a competitive edge, and economies of scale will make that "the big supermarket will compete out the small neighbourhood store".

My take on this is that bitcoin, and crypto in general, doesn't suit their way of doing business.  After all, what extra business would they acquire, and what hassle would it bring them ?  Amazon has its own "money": amazon gift cards.  *these* you can buy with bitcoin if you want to. 
The whole model of Amazon's business is to have a very secure financial treatment, with the full legal machinery behind it.  You are almost never scammed by amazon.  This is why the credit card model with the possibility of reversible payments and legal framing is extremely important for them.  Anarchist obscure irreversible payment methods have not really a place in their business plan.  They are the opposite of dark markets, for which crypto is the ideal payment method.

Indeed, this was the a priori nice idea, that miners would enter in profitable competition, making mining as such more and more difficult and less and less profitable, so that, no matter what is the price of bitcoin, most of its newly created coins would need a wasted economic value close to their actual value, apart from the small margin that miners keep interested.   As such, it seemed that bitcoin would burn all "seigniorage", getting rid of that problematic aspect of "printing money".

The real use of crypto currencies, apart its main application, which is speculation and greater-fool game, is for those payments where fiat cannot go, is dangerous, expensive or difficult.  Main application: dark markets.
But there can be other kinds of payments where you don't want law and rule to go, or where law and rule are in such disordered state that there's no clear way to pay with fiat.  I could think of financing forbidden projects or activities, extortion, bribing, ordered killings, hostage taking.... on one hand ; and of sleazy business like porn, hookers, unregulated night life, unregulated gambling and so on on the other hand.

And yes, there are some geeks who like to pay regular stuff with crypto too !
 
The biggest draw backs of most crypto is that they are hugely deflationary, and hence the speculative part will always by far prevail over any actual currency usage, it will never become a stable unit of account (impossible with speculative non-stabilized assets) and so each time you deal in it, you take a risk of volatility.

Another issue is of course, that if using fiat for the purpose would be dangerous, don't use a transparent block chain.

That's the essence of a greater-fool game, and all of crypto, bitcoin included, is a greater-fool game.
(apart from those few who use it simply as a means of payment, by quickly obtaining coins, transacting, and selling them).

That said, in a greater fool game, there ARE winners ; they need "adoption" however, to have armies of losers financing their gains ; and they draw in the losers by showing how they can (dream to) be "winners".

It is the core of crypto.  And that's because most if not all crypto is based upon deflationary stuff.
Deflationary stuff is always greater-fool.

Why not simply use the chain that is exactly like bitcoin, but does that, and is called LTC ?  Litecoin runs 4 times faster than BTC, has (hence) 4 times more room on the chain, is (hence) 4 times quicker in confirmation ; and hey, it even got Segwit even though that doesn't serve any purpose for the moment on an essentially empty chain.

It sounds like people are complaining that each time they buy, say, a Ford-T it doesn't have this and it doesn't have that.  I'd say, go to the dealer next door, who sells Toyota.  Maybe it is a product that has the things you want ?

Ok, that's more or less how I understood it.  But the tricky part is that, with relatively small amounts in channels, you have to be at "average wind still places" for them to be able to function a certain time before being "pushed against a wall".
None of your channels can be on a "systematic flow" from one place to another.  If you are, your channels will quickly be "exhausted" in the meaningful direction, at which point you have to settle and reload them (ok, you can wait for the occasional transaction in the other direction, true).

Suppose, in our example, that Joe regularly receives payments in bitcoin, and has his favorite bitcoin store at Bob's, who is a bitcoin-accepting merchant.  This means that Alice will regularly see payments that go from Joe to Bob.  Very rarely, Bob pays Joe in bitcoin, which would be the way to relieve Alice's exhausted channels (in one direction).

In fact, in the given situation, when Joe has done 2 payments, Alice's channels are exhausted: Joe/Alice is at 0 / 2 and Alice/Bob is at 0 / 2.

Now, Alice can wait for the occasional transaction that Bob does to Joe.  But most of the time, where she is, these payments go in the other direction.   So the best Alice can do, is to settle, and start again a channel with 1 / 1 with Joe, and 1 / 1 with Bob.  To be exhausted again after 2 payments.

In this particular case, it makes absolutely no sense for Alice to use the LN: she does more on-chain settlements than transmitting LN transactions !

Suppose now, that Joe is rich.  He has 100 BTC which he might spend at Bob's.  But Alice isn't rich.  She's just operating her LN node.
Joe could open an asymmetric channel to Alice: 100/1.  But Alice cannot open an asymmetric channel to Bob.  She has only one BTC left.
So she opens a 1 / 1 channel with Bob.

Joe pays two times 0.5 BTC to Bob through Alice.  Joe/Alice is now at 99 / 2 ; but Alice/Bob is at 0/2.  And Joe cannot send another transaction to Bob through Alice without Alice settling first with both guys, take the 2 BTC from the Joe/Alice channel, and start over:

99/1 and 1/1 respectively.

Suppose on the other hand that Alice is also rich.  No problem this time:

Joe opens an 100/5 channel with Alice, and Alice opens an 100/1 channel with Bob (she knows that Bob only receives coins, and rarely spends them, but she wants some engagement from him).

This time, Joe can do 200 LN transactions through Alice towards Bob, before they are in 0/105 and 0 / 101, and need to settle.

200 transactions for 2 settlements, that's fine.

This example is, I admit, extreme.  But it shows how "being a rich node" increases dramatically the efficiency of using an LN node.

Thanks for that update from someone in the business !

My point is simply that "Joe's full node in his basement" is not going to stop miner pools communicate blocs if ever the protocol that Joe's full node is running doesn't comply with the protocol all miners are running, and that the speed of connection between mining pools confirms this.

As such, Joe's "full node in his basement" is not "keeping the mining pools in check" and cannot stop them from getting one another's blocs to continue building the bloc chain according to the protocol that miner pools agreed upon (whatever that is).

Ah, that's NOT how I thought it was working.

I thought that you had essentially "independent" channels in 2-2 links, but that the lightning network allowed "combined" instructions, namely if you *accept* a payment on one channel, you are *obliged* to send a payment on your other channel along the path, or the payment on the first channel was not valid.

However, bitcoins locked in one channel remained in that channel, and bitcoins locked in another channel remained locked in that channel.

At least, that's how I understood it.

In other words:

If Joe has a 1/1 channel with Alice (each one BTC) and Alice has another 1/1 channel with Bob, then:

Joe can send 0.5 BTC to Bob through Alice, in such a way, that the channel between Joe and Alice now shifts to 0.5/1.5 and the channel between Alice and Bob now shifts to 0.5/1.5.

So net, Joe lost 0.5 BTC and Bob won 0.5 BTC.

Alice won 0.5 BTC in her channel with Joe, and lost 0.5 BTC in her channel with Bob.

I thought that was the basic idea of LN.

But there's no way for Alice to take out 0.5 BTC from her channel with Joe, and put it in the channel with Bob, without settling on chain.

Anyone any comments if I'm wrong ?

Concerning the "miner pool network back bone", I think one can see proof of that in the following plot:

https://blockchain.info/charts/n-orphaned-blocks?timespan=2years

or even more telling when taking 7 day averages of the DAILY number of orphaned blocks:

https://blockchain.info/charts/n-orphaned-blocks?timespan=2years&daysAverageString=7


Clearly, we see that the probability to get an orphaned block has dropped significantly these last two years, which means that the synchronisation between miners has smaller and smaller time jitter.  Miner pools are faster and faster aware of each-other's blocks and right now, the time window in which the important pools are aware of one-another's blocks is less than 2 seconds (estimated 1.2 seconds) from the orphaning rate.

In 2015, we have grossly 1.5 orphaned blocks per day, which puts us at a "synchronisation time between pools" of (144 blocks per day):

(1.5 / 144) * 600 seconds = 6.25 seconds.

Recently, we see rather 0.29 blocks per day, so (0.29 / 144) * 600 = 1.2 seconds.

This means that in 2015, it took the major pools about 6.25 seconds to receive a block from another miner, and to check it ; today, this time is only 1.2 seconds.

This, while the block size

https://blockchain.info/charts/avg-block-size?daysAverageString=7&timespan=2years

increased by a factor of roughly 2 (from about 450 KB in 2015 to 0.9 MB now).

This essentially means that the connection speed between the major pools increased by a factor of 10.4 over 2 years time.

Can you reload it with new bitcoins without on-chain locking in of those bitcoins in the channel ??
I understand you can move them back and forth as many times as you want, but the contents of the channel is fixed once and for all (until settlement), no ?

I bought a small reserve of bitcoin when it was in the few hundred $ range, mainly to have a reserve to buy services on the internet (VPN / VPS stuff).  The funny thing is that I now have way, way too much for this usage.  So I don't need to buy bitcoin any more, I have more than enough for what I want to buy with it in the near future.  And I put a few coins aside, which I will cash out when bitcoin rises to the promised $500 000.- a coin and buy a few houses for each of my kids with it.  If they drop to zero, which I also expect, well, I will still have bought all the stuff on the internet I ever planned to buy with bitcoin, so I don't care.  What I will never do, is cash out before 500 000.-.
(well, I agree that I may be tempted around $450 000.-).  Below that, I couldn't care less.

And I won't buy any more.  I have more than enough "bitcoin money" for all I will most probably ever buy with it.

The "time to next event" in a Poisson stream of rate lambda (= on average lambda events per unit of time) has an exponential distribution, given by:

P(Delta_T) = lambda * exp(- Delta_T * lambda)

This means that the probability for the time to the next event to be between Delta_T and Delta_T + dt equals

P(Delta_T) * dt

(it is a probability DENSITY)

https://www.probabilitycourse.com/chapter11/11_1_2_basic_concepts_of_the_poisson_process.php

As such, the total probability for Delta_T to be smaller than 1/lambda (which is your question) amounts to:

integral P(Delta_T) dDelta_T taken from Delta_T = 0 to 1/lambda

which gives us: 1 - 1/e = 0.632...

So there's 63% chance to find it in less than the average time (10 minutes).

The reason why it amounts to nevertheless the average time, is that even though there's only 37% chance to be longer, it can be REALLY longer sometimes.

EDIT:
If you want a more intuitive picture, your question is probably "how can the average be at value X, and not have half of the probability on the left, and half on the right" ?

The point is that the average value is not the MEDIAN value (which has, exactly, as a definition: half the probability left, and half, right).

Think of it this way: think of a metal object, a kind of bar, but such that its thickness is exponential.  It is thick on one side, and its thickness diminishes exponentially to a very, very thin needle on the other side.  Now, the "average" is the centre of mass, the spot where you have to hold this bar so that it remains in equilibrium.   Well, that centre of mass is not in the spot where there's an equal mass on the left and the right, but rather, the "short" part will have a bigger mass than the "long" part, simply because the long part has a bigger lever arm.

You can feel that by thinking about this still the following way: suppose you put on the two extremities of a ruler, a weight of 1 kg and a weight of 200 g.  In order to keep the ruler in equilibrium on your finger, you'd need to hold it much closer to the 1 kg weight than to the 200 g weight.  So at that "centre of gravity", you still have more weight on the side of the 1 kg, but its lever arm is shorter ; and you have less weight on the 200 g side, but its lever arm is longer.

This is a property of Poisson processes.  In fact, exactly the same things happen with elementary particle detection.
The union of two Poisson processes is again a Poisson process that has a "count rate" that is the sum of the individual processes.

https://www.probabilitycourse.com/chapter11/11_1_3_merging_and_splitting_poisson_processes.php

So, if you have 10 miner pools which each, win a block, on average, every 100 minutes, their combined Poisson streams are a Poisson stream with an average of 10 minutes.

The picture there is a very good illustration of the mining process:



Orphaning happens when two "merger points" happen so close in time, that the "late" one was still working on the wrong block.  This happens when they are "closer in time than the time needed to learn the existence of the new block.

The particle detection analogy is the following:
Each miner pool corresponds to a certain intensity of particles (say, photons).  All the mining pools together make up the intensity of the total beam.  A particle detector (photomultiplier) sees them arrive at a rate of one every 10 minutes ; but each beam individually is of lesser intensity.
The "orphaning" corresponds to the dead time of the detector in this case.
If you switch off the beams of the other miners, and only keep one, you have lower intensity, and hence a lower count rate in the detector.

Pool mining is just distributing the hash tasks over different miner "customers" but it acts as one single miner.  

Apart some small overhead, there's normally no difference between, say, 10 independent miners, and these 10 miners pooling together, as seen from the outside.

The reason for pooling is that these independent miners would simply only win, say, 1 block every year ON AVERAGE, but the POOL will win 10 blocks a year on average.  This makes the miners have more UNIFORM income.

Like the buying of bitcoin.  No difference.