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Author Topic: LN+segwit vs big blocks, levels of centralization.  (Read 8855 times)
mackenzied
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May 03, 2017, 02:49:20 PM
 #161

I think the "crypto as currency" part will shine once physical cash is removed, never before. Theres millions of people out there surviving by working under the radar. The typical guy doing small scale construction work like remodeling or fixing kitchens, or plumber type of jobs, tons of freelancers doing website stuff, coding etc.. I don't know, there's an endless stream of cash being used to work to avoid taxes because it's the only way those people can pay the bills.

This is also my view on crypto, as an underground economy money, like cigarettes in prison, to avoid state, law and taxes.  However, for these people, it shouldn't be a speculative tool, it shouldn't be used by big finance and it shouldn't be large enough to get on the radar.

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Once cash is removed, those people will be *forced* to learn about bitcoin and use it to get paid in exchange of their services. Then word of mouth will spread and everyone will be using it as a substitute for cash that never enters the banking system.

I'd rather have them learn about monero or zcash, honestly.  Bitcoin is too traceable, has too high visibility now.  But even these coins are too speculative.  Zcash did an effort to have a sensible emission curve in the beginning.  Monero, at least, has tail emission.



An underground economy, it really took place in this world, however, though, it still revolves around bitcoin, a currency that has gained a lot of attention. That is why, that economy is not really secret, it is still seen by governments. Monero and Zcash are a good idea to use as coin to develop the underworld, but it needs a safer development.

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May 03, 2017, 05:17:00 PM
Last edit: May 03, 2017, 07:37:31 PM by deisik
 #162

Andy buys bag of apples for £10 from Bob, who then buys bag of onions for £10 from Clare. Velocity is 2.
Clare buys a chair for £10 from Dave = velocity is 3 and so on.
The higher the velocity = higher transactions made.

You should consider the situation with reference to time

The inflationary effect follows from the changing relationship between the time it takes to produce some good (which remains constant) and the velocity of money (which increases). For an outside observer it looks as if more money is chasing the same amount of goods per unit of time, which causes inflation (producers raise the prices). Henry Hazlitt explains it pretty well in his book (in the part on the dangers of excessive saving, i.e. hoarding), though he considers the opposite situation, i.e. when people stop spending and prefer saving, thereby decreasing the velocity of money (which leads to deflation)

I think you have H H on hoarding, velocity, inflation misunderstood.

Inflation/deflation - increase/decrease in money stock/supply = Inflation/deflation - increase/decrease in bitcoin stock/supply. Bitcoin stock is 21m and the supply is getting lower as bitcoin approach 21m. No inflation but can have deflation via permanent lost bitcoin

I've read him literally decades ago

But he certainly didn't talk about inflation and deflation of monetary base (as you mean it), but rather about prices of goods and services. It is really hard to misunderstand Hazlitt, he is one of the most coherent and easy to understand authors. But if you continue to insist, I will find his book and quote him to you, though, I think you can easily find him yourself. In any case, this understanding of inflation and deflation is inconsequential since I made it perfectly clear that by inflation I mean depreciation of currency while by deflation, consequently, its appreciation. I guess you will have to stick to my use of terminology since this discussion (about the velocity of money affecting inflation rates) was my invention, after all

Please do so. I will await for the quote.

Yes i have read the book, plus many many other economic books. I think, over the decades your memory is playing tricks on you.

No. If everyone were to create and stick to their terminology, then the human race will not communicate clearly with each other. We should do our best to follow the dictionary and the original meaning of the word, using the correct semantics.

This is not my terminology, after all

I'm not going to brag about how many economic books I've read since this is bullshit. Books don't make you any smarter (though they can give you some knowledge), and this is not a pissing contest at that (read I don't care). Nevertheless, if you are not quite happy with me using inflation and deflation in the sense I use them, you can substitute inflation with depreciation and deflation with appreciation. I will look into Hazlitt later (the matter is not about Hazlitt, anyway)

Related definitions
The term "inflation" originally referred to increases in the amount of money in circulation.
So yes i will stick with the original

As I said, I don't really care

Apart from that, you may not pretend that you don't understand what I'm talking about (in respect to inflation), especially if you read so many economic books as you claim. Anyway, I looked into Hazlitt, and he does actually mean inflation as an increase in monetary base. But he specifically elaborated on the matter by mentioning "monetary inflation" a few times, to avoid possible confusion. Obviously, this presupposes that inflation can also be understood as price inflation (and this usage is most widespread today). Conversely, he mentioned deflation only three times, and it was not very clear what he actually meant to say, i.e. deflation of prices or contraction of monetary base. In short, this is a childish attitude (kinda "think different")

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May 03, 2017, 07:42:59 PM
Last edit: May 04, 2017, 09:13:47 AM by deisik
 #163

You certainly underestimate miners' roguishness (or whoever acts through them). While I agree that miners might be discouraged from clearing the mempool but this just proves how rogue they are. And here's the crux of the matter. What prevents them, first, from flooding the network with spammy transactions, and, then, filling the blocks with this trash? And right then we are back to square one, or even worse, since we would have larger blocks then (read it will be more difficult for Bitcoin nodes to support the network)

Well, this is built into bitcoin from the first day.  After all, the diminishing bloc rewards, and the necessary transition to fees paying for mining need a fee market that can be pressurized to the level the market can bear ; that is, the highest possible fees that can be extracted from the system without making it crumble under its own costs.  Bitcoin was simply designed that way, by combining reward halvings, inflationary spiral, and PoW.  Whether that was intentional or not is a question of course, but the reality is that this is an unavoidable consequence of the design

Why do you tell me all that?

I've heard it many times from you already. Wtf, I myself told you basically the same a few times by now, though in a more concise manner and to the point. Nevertheless, if you are so good an economist (as you seem to think), could you explain in a few words how increases in money velocity affect prices, i.e. raise price inflation (not to be confused with monetary inflation) at a microlevel. You can take an example of the One dude as a starting point, and I will see how really good you are in practice. Let's get ready to rumble!

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May 04, 2017, 07:45:37 AM
 #164

could you explain in a few words how increases in money velocity affect prices, i.e. raise price inflation (not to be confused with monetary inflation) at a microlevel.

I did already.  Of course, increasing velocity increases inflation.   But monetary velocity is something that is hard to influence with technical means, it has a life of its own.  Greater adoption doesn't necessarily mean proportionally greater velocity, which would be needed to oppose the deflationary effect of "sound money" (no or very small debasement).  In fact, the more economic circles would get closed, the less conversion to and from fiat would be necessary, and the lower the velocity would be (if bitcoin were a currency, not used for speculation and hodling).

Your theory needs velocity to increase proportionally with adoption to keep a more or less constant price.  This has never been seen.
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May 04, 2017, 08:27:15 AM
Last edit: May 04, 2017, 09:07:10 AM by deisik
 #165

could you explain in a few words how increases in money velocity affect prices, i.e. raise price inflation (not to be confused with monetary inflation) at a microlevel.

I did already.  Of course, increasing velocity increases inflation.   But monetary velocity is something that is hard to influence with technical means, it has a life of its own.  Greater adoption doesn't necessarily mean proportionally greater velocity, which would be needed to oppose the deflationary effect of "sound money" (no or very small debasement).  In fact, the more economic circles would get closed, the less conversion to and from fiat would be necessary, and the lower the velocity would be (if bitcoin were a currency, not used for speculation and hodling).

Your theory needs velocity to increase proportionally with adoption to keep a more or less constant price.  This has never been seen

If you think that you did, please post a link to your reply

I don't deny that increasing velocity increases inflation, price inflation, obviously (I'm not going to catch at irrelevant details here or otherwise indulge in nitpicking). It would be rather strange if I now started to decry what I had been basically preaching myself. I just wanna hear your explanation of the way velocity actually affects prices at the level of separate economic entities (i.e. individuals and businesses), i.e. how how it works in practice at the lowest level. Show us your real understanding of the matter!

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May 04, 2017, 08:45:44 AM
 #166

If you think that you did, please post a link to your reply

I don't deny that increasing velocity increases inflation, price inflation, obviously (I'm not going to catch at irrelevant details here or otherwise indulge in nitpicking). It would be rather strange if I now started to decry what I had been basically preaching myself. I just wanna hear your explanation as velocity actually affects prices at the level of separate economic entities (i.e. individuals and businesses), i.e. how how it works in practice at the lowest level. Show us your real understanding of the matter!

Funny game.  *you* are the one making a bold statement, namely that an asset which has a decreasing debasement curve and an increasing economic adoption, will nevertheless be able to keep a more or less constant value and hence be a reasonable "unit of account" which is necessary for that asset to be a credible currency, because of the increased currency velocity (mainly because of the adoption of segwit and LN).

Remember that that was your "rebuttal" to my claim that bitcoin, being an asset with strongly limiting and "inverse" debasement, is designed to fall into a severe deflationary spiral and hence cannot be a serious currency.  You claimed that this lack of sufficient debasement was going to be compensated by the increase in velocity that "automatically goes" with increased economic adoption.  I'm still waiting for your argumentation demonstrating such.

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May 04, 2017, 09:00:28 AM
 #167

If you think that you did, please post a link to your reply

I don't deny that increasing velocity increases inflation, price inflation, obviously (I'm not going to catch at irrelevant details here or otherwise indulge in nitpicking). It would be rather strange if I now started to decry what I had been basically preaching myself. I just wanna hear your explanation as velocity actually affects prices at the level of separate economic entities (i.e. individuals and businesses), i.e. how how it works in practice at the lowest level. Show us your real understanding of the matter!

Funny game.  *you* are the one making a bold statement, namely that an asset which has a decreasing debasement curve and an increasing economic adoption, will nevertheless be able to keep a more or less constant value and hence be a reasonable "unit of account" which is necessary for that asset to be a credible currency, because of the increased currency velocity (mainly because of the adoption of segwit and LN).

Remember that that was your "rebuttal" to my claim that bitcoin, being an asset with strongly limiting and "inverse" debasement, is designed to fall into a severe deflationary spiral and hence cannot be a serious currency.  You claimed that this lack of sufficient debasement was going to be compensated by the increase in velocity that "automatically goes" with increased economic adoption.  I'm still waiting for your argumentation demonstrating such

I don't understand what you are talking about

The really funny thing is that I can explain very easily in layman terms how change in money velocity affects inflation rates. And note that I never pretended to be a good economist or just an economist at all in the first place while whenever I questioned your economic understanding, you were very aggressive in respect to my remarks. Now you have a perfect chance to actually put your words where your mouth is, so to speak. So come and prove it that you are not a loudmouth, after all. On the other hand, using a lot of buzz words (like "inverse debasement" and "decreasing debasement curve") won't change a thing. I hope you understand that

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May 04, 2017, 09:18:26 AM
 #168

I don't understand what you are talking about

That's often our problem.

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The really funny thing is that I can explain very easily in layman terms how change in money velocity affects inflation rates.

Congrats.  So ?  We all know how money velocity affects inflation rates.  I can explain very well Pythagoras' theorem.  So ?

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And note that I never pretended to be a good economist or just an economist at all in the first place while whenever I questioned your economic understanding, you were very aggressive in respect to my remarks.

Questioning someone's understanding is not a form of argumentation, it is rhetoric.  I don't have to pass a degree here.  You were essentially claiming that I didn't know anything about economics (which doesn't really matter does it), because I was claiming that something with an emission curve that goes in the opposite direction as its adoption, is never going to get a stable value, but is perfect for a speculative asset.

You claimed that I didn't understand anything about economy, because I wasn't taking velocity into account.  My reply was that even though you are perfectly right that velocity enters the equation too, it cannot sensibly compensate the huge deflationary effect that you get from the lack of adaptation of the emission curve and the adoption.

In other words, yes, "theoretically, the velocity enters the equation, but doesn't matter much concerning the statement made."

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Now you have a perfect chance to actually put your words where your mouth is, so to speak. So come and prove it that you are not a loudmouth, after all.

I don't have to.  Me being a loudmouth or not alters in no way the validity of an argument.

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On the other hand, using a lot of buzz words (like "inverse debasement" and "decreasing debasement curve") won't change a thing. I hope you understand that

Well, you could easily understand what I mean by those terms.

NORMALLY, a currency has a debasement which is a feedback from its inflation/deflation rate, to try to reach a set target (for instance, 2% inflation rate).  This means, apart from some velocity effects, that the debasement curve goes with the economic growth of the economy bought with the currency.

With bitcoin, however, this curve has an inverse behaviour: it was debasing A LOT when there was essentially no adoption and very, very small economic growth (the early years), and it is debasing less and less (percent wise) when economic adoption grows. 

This is what I summarize under the term "inverse debasement".

The "debasement curve" is the percentage growth of the monetary mass.  A decreasing debasement curve indicates that percent-wise, the monetary mass grows less, and less (and might even effectively go negative, if more coins get destroyed than there are made).  Bitcoin has a severely decreasing debasement curve: bitcoin's monetary mass grows less and less, percent-wise. 

A normal currency has essentially a debasement curve that follows its economic growth.  Apart from velocity effects, which are rarely "always in the same direction", such a debasement curve makes that there is not much inflation or deflation.

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May 04, 2017, 02:01:04 PM
 #169

I don't understand what you are talking about

That's often our problem

I would rather argue that it is mainly your problem

Indeed, I could understand what you meant to say, and that might make some sense, after all (I mean what you said). But your problem (as I said) is you don't say it in the simplest possible way. Personally, I'd rather think that you are deliberately trying to use convoluted terms and ideas when you in fact could make do with simple words and provide genuine explanation at that (if that was your intention, of course). I for one try to explain everything as simple as possible. If you can't explain something in simple terms, that basically means that you don't understand the matter yourself. And the fact that you can't properly explain how changes in money velocity are working at the level of households proves exactly that

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May 04, 2017, 02:22:44 PM
 #170

Indeed, I could understand what you meant to say, and that might make some sense, after all (I mean what you said). But your problem (as I said) is you don't say it in the simplest possible way.

Because that takes a lot of effort and re-working.  When I read myself what I write, it is most of the time extremely clear to myself Smiley
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May 04, 2017, 02:42:15 PM
 #171

Indeed, I could understand what you meant to say, and that might make some sense, after all (I mean what you said). But your problem (as I said) is you don't say it in the simplest possible way.

Because that takes a lot of effort and re-working.  When I read myself what I write, it is most of the time extremely clear to myself Smiley

So can you explain in simple terms the mechanism through which money velocity affects prices?

Indeed, the example of the One dude doesn't make a lot of sense since he obviously meant to say that the amount of money remains the same since by inflation he meant expansion of monetary base (I hope I don't sound like you now). But there's still more to that if you start thinking of it. So how the change in velocity of circulation would be working at that level, at the level of Alice, Bob, and Carol, i.e. why should prices inflate if the money turnover rate rises?

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May 04, 2017, 03:36:11 PM
 #172

So can you explain in simple terms the mechanism through which money velocity affects prices?

You mean, explain Fisher's formula ?
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May 04, 2017, 04:25:21 PM
 #173

So can you explain in simple terms the mechanism through which money velocity affects prices?

You mean, explain Fisher's formula ?

Fisher's formula is of no importance here

I've seen that post of yours. This is a macrolevel "explanation", and it is not interesting. You should understand that all economic effects start small. What is GDP at the household level? It is many small businesses offering their goods and services in the neighborhood, and large corporations, of course. But they all contribute to GDP, big or small. In the same manner, I want you to explain how money velocity (changes thereof) is working at that level, i.e. how it actually makes the prices grow. Obviously, inflation as well as GDP starts there. Basically, I ask you to explain the mechanism which transfers changes in the velocity of money into inflation

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May 04, 2017, 06:35:45 PM
 #174

So can you explain in simple terms the mechanism through which money velocity affects prices?

You mean, explain Fisher's formula ?

Fisher's formula is of no importance here


I can hardly think in other than mathematical terms.

Of course, there's always a fancy handwaving "explanation", but the real knowledge is in the formula, not in the "explanation", although human brains like often explanations more than logical links.

I will give it a try, but first I will explain the formula, and you will see that the velocity is in fact a kind of "fudge factor" to make it work, but has also a possible, but somewhat flawed, "explanation".


Here it goes:

Suppose that, in a given period (say, a year), an economy of Q "value units" has been bought with a given currency, and that the price of a "value unit" is P coins of that currency.

Then it is quite straightforward that the total amount of coins that "went over the counter" is:

Q x P

But is this the same coin that went back and forth ?  Or are all of the coins used for that ?

Here, we have to, artificially, divide all the available coins (total sum M) into packs of coins that have been spent a certain number of times.  This fundamentally hurts the fungibility of the coins, and is what makes our argument somewhat artificial.  But let us say that, of the M coins:

m0 have not moved ;
m1 have been spent once ;
m2 have been spent twice ;
m3 have been spent three times
....
mn have been spent n times.

You can think of that of individually recognizable coins, that went never over the counter, went once over the counter, twice, ...

As such, the total amount of coins that went over the counter is:

m1 + 2 m2 + 3 m3 + .... + n mn

This must of course be equal to Q . P.

Now, let us divide and multiply by M:

Q . P =  M . ( m1/M + 2 m2/M + ... + n mn/M)

If you look at it, the last factor, V = ( m1/M + 2 m2/M + ... + n mn/M)

is the weighted average of the number of times a coin was spent during the given period.

Indeed, 1 is taken with a weight m1/M ; 2 is taken with a weight m2/M, .... and n is taken with a weight mn/M.

These weights add up to 1 (if we include "0" with a weight m0/M).

That's what we call the "velocity of money".

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I've seen that post of yours. This is a macrolevel "explanation", and it is not interesting.

Well, nevertheless, there's no other way to define "velocity of money" which is why von Mises rejected the concept.

But there IS a handwaving explanation to this "velocity":

it is the weighted average of the number of times the same coin is spent.  Now, that's annoying, because "the same coin" goes from hand to hand, and so is not the individual action of an individual.  But there is a handwaving relationship:
you can think as the "velocity" as related to the "weighted holding times" of a coin.  Now, as much as "the number of times a same coin is spent" is not individually determined, the "holding times" are.

However, V is NOT the inverse of the weighted holding times.  It is the "inverse of the harmonic weighted holding times".  But, because we are handwaving, we can pretend that we didn't see the word "harmonic" and, kinda, consider that the velocity is more or less inversely related to the average holding time of a coin by an individual.


This is why "hodling" makes the velocity fall to the floor, but "hodling" is not a currency usage, so this reasoning breaks somewhat down.  We're talking about currency usage, where "acquiring" the coins and "spending the coins" is done in the economy, against "products of value" that contribute to Q.  So you win coins by working for instance, and you spend them on groceries.

As such, you can see that the "average holding time" is about half a month, if you are paid every month ; but that's not entirely true, because the merchant you pay, will maybe pay more quickly a provider.  Or somewhat slower.  

In any case, the "velocity" of a currency has more to do with the habits of paying and getting paid, than anything else.  

It can have something to do with the mood of the economy.  If you are confident in the future, you spend quickly your money.  If you are less confident, maybe you keep some money for next month.  This is why the velocity is influenced by the "economic mood".

But it doesn't undergo orders-of-magnitude swings if it is a currency.
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May 04, 2017, 07:02:33 PM
 #175

~snipped~

I'm sorry but you didn't reveal the transfer mechanism between money velocity and inflation

And I didn't ask to explain what the velocity of money is. This concept is pretty straightforward and intuitive ("user-friendly"). I have given a few references to the explanation of this notion to the One dude (if I'm not confusing him with someone else). If you didn't get it, I want you to explain in detail how increasing money velocity actually affects prices. Your references to mathematics are largely irrelevant since they don't explain anything, they are just equations (they may mean anything), and I want to see if you really understand what's going on behind these equations (which is what genuine knowledge is about since it is about what happens in reality). Apart from that, I could explain what I ask in a few short sentences, and you will understand my explanation perfectly. So your excuses for not being able to explain it in a simple and concise way are actually fake and simulated since you obviously don't understand how money velocity translates into inflation in practice (i.e in real life, which has nothing to do with formulas). Basically, I just ask you to describe the process how it actually happens in life

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May 04, 2017, 07:21:06 PM
 #176

~snipped~

I'm sorry but you didn't reveal the transfer mechanism between money velocity and inflation


Ah, the price of a unit of value being P coins, of course, the value of a coin is C = 1/P.

As such, given that we have Q.P = M.V

it follows trivially that C = Q / (M.V)

what more is there to say ?

The fact that there is a formal link, doesn't imply any kind of causal relationship of course, but there doesn't need to be one: the formula fixes the relationship.  The surface of a rectangular room is S = W . L, but you can just as well say that the length is a consequence of the surface and the width, as saying that the surface is a consequence of the length and the width. 

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And I didn't ask to explain what the velocity of money is. This concept is pretty straightforward and intuitive ("user-friendly").

Not at all straightforward, because it is essentially a macro-economic fudge factor, because you have to "follow individual coins".

The inflation/deflation is the variation of P = 1/C.

P = M.V / Q

So, if Q rises, we get deflation a.e.e..
If M rises, we get inflation a.e.e.
If V rises, we get inflation a.e.e.

But this is just a formal relationship from a trivial accountancy consideration.  It doesn't imply any causality or dynamical relationship. 

Adoption = Q rises, slowly first, then very much, and then slowing down again (S-style curve)

V, for a currency, is a matter of people's paying habits and mood.

M, for bitcoin, is a saturating kind of curve, with a steep rise in the beginning, and levelling off quite quickly.

==> P falls like a stone (and yes, is somewhat modulated by variable V) EVEN IF IT WERE A CURRENCY which it isn't.

==> P is not a "fairly constant unit of account". 
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May 04, 2017, 07:41:29 PM
 #177

~snipped~

I'm sorry but you didn't reveal the transfer mechanism between money velocity and inflation


Ah, the price of a unit of value being P coins, of course, the value of a coin is C = 1/P.

As such, given that we have Q.P = M.V

it follows trivially that C = Q / (M.V)

what more is there to say ?

Are kidding or what?

I want you to describe real life events which translate into these formulas. Just learning a few formulas is not a big deal, you should understand what processes they generalize or conceptualize. If you don't understand these processes, you are just mindlessly parroting. When you increase the amount of money in circulation, more dollars (or whatever) start chasing the same amount of goods and that leads to inflation. You can describe this process by a formula, but if you don't understand what is actually hidden behind it, your true knowledge is essentially equal to zero. Formulas are secondary, you should fist understand what actually makes them such and such

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May 04, 2017, 07:47:27 PM
 #178


Are kidding or what?

I want you to describe real life events which translate into these formulas.

All the knowledge is concentrated in the math.  If you understand the mathematical relationship, you know everything there is to know.  All the rest is just fluffy talk for human brains and their animalistic representations, if they are not trained in formal thinking.  "dollars chasing goods" is something that recalls primitive humanoids with spears running after mammoths, or their pictures on cave walls.
Sometimes, one needs to go through these fuzzy images if the mathematical inspiration doesn't come right away.  But once the mathematical relationship is there, all is said and done.
So my idea of "understanding" is rather the opposite: as long as you just have pictures in your human brain, you're not really understanding it.  Once you get formal relationships, true understanding is established.

You can't really understand atoms, as long as you have no clear view on the solution structure of its wave equation.  You can't understand a chemical link without a clear understanding of the different stationary solutions.  Once you have that, you can again start handwaving to make a short cut because it is simply too hard to see the entire solution set in your mind's eye.  But that's because it's a short cut, and you're giving up understanding to satisfy your limited brain capacity, and still get an illusion of understanding (which can be good enough for the problem at hand, but don't be surprised to be surprised at certain effects).

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May 04, 2017, 08:16:27 PM
 #179

I run a non-mining full node; it entertains me to do so.  I configure it to allow 60 links (8 outbound (default) and 52 inbound).  Although it does vary, I do find my node runs along with near the maximum number of links all the time.  Well, after a restart, sometimes it can take many hours to build back up.

Although the miners could (and probably do otherwise how do they get transactions?) run a full node (or more than one for redundancy?), there's nothing obliging them to accept many incoming links.  Wouldn't that leave users fighting for limited connections without folks like me?  Should I increase my link count even more?  I configure my mobile phone based wallet to only connect to my full node exclusively.  Sometimes I can't get a link so I go to my full node a disconnect a peer (sorry).

So far I have plenty of bandwidth, CPU, and storage.  I guess I would be ok with a bigger block but would be very happy with a cap on transaction size.  Am I helping at all to keep things decentralized?

If I drop off then it might not be such a big deal but if other folks like me do then what?
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May 04, 2017, 08:19:14 PM
 #180


Are kidding or what?

I want you to describe real life events which translate into these formulas.

All the knowledge is concentrated in the math.  If you understand the mathematical relationship, you know everything there is to know.  All the rest is just fluffy talk for human brains and their animalistic representations, if they are not trained in formal thinking.  "dollars chasing goods" is something that recalls primitive humanoids with spears running after mammoths, or their pictures on cave walls.
Sometimes, one needs to go through these fuzzy images if the mathematical inspiration doesn't come right away.  But once the mathematical relationship is there, all is said and done.
So my idea of "understanding" is rather the opposite: as long as you just have pictures in your human brain, you're not really understanding it.  Once you get formal relationships, true understanding is established.

You can't really understand atoms, as long as you have no clear view on the solution structure of its wave equation.  You can't understand a chemical link without a clear understanding of the different stationary solutions.  Once you have that, you can again start handwaving to make a short cut because it is simply too hard to see the entire solution set in your mind's eye.  But that's because it's a short cut, and you're giving up understanding to satisfy your limited brain capacity, and still get an illusion of understanding (which can be good enough for the problem at hand, but don't be surprised to be surprised at certain effects)

Atoms are irrelevant

You can't understand them (provided you really can't since I don't know), but that has more to do with the limitations of our understanding as such (because we basically live in another world). Nevertheless, you can't possibly deny that in the total majority of cases mathematics is a tool which is used to describe real processes (to conceptualize and generalize them in abstract language). But with just this abstract language you can't walk very far. Sometimes it works in reverse but even in those rare cases people still try to grasp what all these formulas actually mean, what is behind them (even if their understanding is still limited by their skulls). There is an idea of abstract mathematics but this is certainly not the case here. Without understanding the underlying events and processes you would be at a loss when confronted with harsh reality or just the questions like I'm asking you. That basically proves that you are thoughtlessly juggling formulas without actually understanding their true meaning. In other words, if a = b x c, then b = a / c. That's what all your "genuine" knowledge can be reduced to

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