rpietila Wall Observer - the Quality TA Thread ;)

[rpietila]

Which graph can you point me to for the 5.25-year exponential trend line?

Code:

https://i.imgur.com/ycT9ulP.png

[BitchicksHusband]

The reason is that people who buy on overstock or tigerdirect are just buying more bitcoin to replace what they spent.  They originally bought the bitcoin as an investment, they are excited to be able to use it for something, but they don't want to exit their position.

I always buy back the same or exceeding the amount I just spent. It's a rule I've always stuck to over the years.

Yes.  We gave some away at Christmas and just bought back what we gave.  It is nice to end up with the same amount or more Bitcoin at this stage of it's growth for sure!

Actually, I got those for free on a trade selling high on the impending China news and buying low afterward (in December).

[AnonyMint]

The beauty of the 5.25-year trendline with exponential fit (R^2=0.93 which is pretty darn good) is that it takes into account every worry of every person who has ever owned or not owned bitcoins. I put more weight on that than the individual worries of a single person.

You put a lot of weight in your humongous pride, as if someone presenting analytical discussion is worried. I am not worried about the BTC price. I could careless because I don't own any BTC nor am I itching to buy any. And you put a lot of weight in arbitrary curve fits.

And people who think they know every thing for sure (and you don't even enumerate the arbitrary assumptions in your model), eventually get a lesson in respecting chaos. Maybe not this time. No one knows. But eventually yes.

I hope you realize the following chart is arbitrary BS.

Which graph can you point me to for the 5.25-year exponential trend line?

Code:

https://i.imgur.com/ycT9ulP.png

And why not drawn like this? A least squares fit is an arbitrary choice of slope, because the curve you are fitting is not very linear. The 2011 outlier is your big problem with choosing this arbitrary fit. And we can't really trust that early data back in 2010.

The green line looks much more accurate to me. It removes that bubble from 2013 and follows a trendline from before the bubble started. Or we stay with the purple trendline, in which case the price is almost down to the purple line.

You need to update your chart. The price is now lower than shown.





Also refer to my upthread post quoted below pointing out that adoption (and thus BTC ≅ adoption^2) is likely log-logistic, not logistic. Thus we see the first slope to 2011 was higher, then the slope from 2012 to 2014 was the purple line, and now we may be ready to transition into an even lower slope, such as the green line.

We should now shift into yet again a lower adoption slope than from July 2011 to December 2013.

What a heck makes you think so at a face of universal awareness that is just achieved?

Math Risto. You can't deny math. Here is the shocking revelation...

Because if you put a ruler on the chart along the bottoms of unique addresses on the log 10 chart, you see the slope was higher before the July 2011 crash, than it has been since 2012.

Also it is very likely that Bitcoin adoption is not logistic where the maximum rate of adoption is at 50% of the adoption as follows:

http://en.wikipedia.org/wiki/Diffusion_of_innovations


Because Bitcoin is not adopted for utility, rather the probability distribution of the adopters is power-law because that is the distribution of money[1] as follows.

http://en.wikipedia.org/wiki/Power_law


Thus Bitcoin adoption is log-logistic as follows. Note that for B=1/2 which is the power-law distribution, that the slope of the log-logistic function gradually declines for the life of the curve. And that is exactly what we are seeing happen thus far as I stated above.

http://en.wikipedia.org/wiki/Log-logistic_distribution




[1] A. Dragulescu and V. Yakovenko. Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States

[smoothie]

Which graph can you point me to for the 5.25-year exponential trend line?

Code:

https://i.imgur.com/ycT9ulP.png

Thanks.

[Peter R]

Blockchain.info has now removed the "holes" from their charts, allowing me to update my Metcalfe Value plot.  Although we don't have price data prior to the opening of MtGox mid 2010, I was able to use the Metcalfe model to extrapolate backwards to the genesis block.  The extrapolated value of all bitcoins in circulation was approximately $10,000 in 2009, before beginning the now famous trajectory to the moon in 2010.  

The constant of proportionality in Metcalfe's law (V ~ N²) was also quantified for each of the two proxies for N.  For example, using the number of transactions per day excluding popular addresses for N, the model best fit the market cap data with a constant of proportionality equal to $1.50.  In other words, the model predicts that the bitcoin market capitalization is approximately equal to $1.50 multiplied by the square of the number of TXs per day (excluding popular addresses).

I am still stunned that the Metcalfe model so accurately corresponds to the actual market cap over 4 years and over 1,000,000% growth in market cap.  The plot confirms for me that the value of bitcoin comes from the network of people who use it.  If we keep finding new ways to use bitcoin, the rest will take care of itself.  

[ArticMine]

...

What fool would lose 3-5% spread (at least) on two times exchanges instead of paying 0% to spend the fiat with a credit card?

The costs of a credit card transaction can vary widely, from under 1% to even over 50%.

You failed to grasp my point that the credit card holder pays 0% (or even gets cash back). What the merchant pays is irrelevant, unless the merchant is giving that 3-5% discount to the Bitcoin purchaser. Even with a discount, it is bad tradeoff because we are pushing our ecosystem to hell.

...

My point is that in some cases the cost the the "credit card holder" can be upwards of 50% or even not be able to make the transaction in the first place. The case of an individual having to purchase a prepaid "credit card" in order to make an online purchase and spending more on "fees" then the amount of the purchase is a real case situation. I have said this over two years ago and will say it again. The low hanging fruit for Bitcoin has a FICO score of 350 or thereabouts or lives in a country that is blocked, or is under age 18,  or wishes to purchase goods or services from an "high risk" merchant across an international boundary etc etc.

The cost to the merchant can be very relevant particularly if the transaction fall into the "high risk category". Ever wonder why so many retailers refuse international credit card transactions for example? Not every transaction involves a consumer with an 800+ FICO score purchasing goods or services in person from a large retailer.

[BitChick]

Blockchain.info has now removed the "holes" from their charts, allowing me to update my Metcalfe Value plot.  Although we don't have price data prior to the opening of MtGox mid 2010, I was able to use the Metcalfe model to extrapolate backwards to the genesis block.  The extrapolated value of all bitcoins in circulation was approximately $10,000 in 2009, before beginning the now famous trajectory to the moon in 2010.  

The constant of proportionality in Metcalfe's law (V ~ N²) was also quantified for each of the two proxies for N.  For example, using the number of transactions per day excluding popular addresses for N, the model best fit the market cap data with a constant of proportionality equal to $1.50.  In other words, the model predicts that the bitcoin market capitalization is approximately equal to $1.50 multiplied by the square of the number of TXs per day (excluding popular addresses).

I am still stunned that the Metcalfe model so accurately corresponds to the actual market cap over 4 years and over 1,000,000% growth in market cap.  The plot confirms for me that the value of bitcoin comes from the network of people who use it.  If we keep finding new ways to use bitcoin, the rest will take care of itself.  

Very interesting.  We are experiencing a huge surge in growth so hopefully the price follows soon.  Thanks for your work on this.

[AnonyMint]

Blockchain.info has now removed the "holes" from their charts, allowing me to update my Metcalfe Value plot.  Although we don't have price data prior to the opening of MtGox mid 2010, I was able to use the Metcalfe model to extrapolate backwards to the genesis block.  The extrapolated value of all bitcoins in circulation was approximately $10,000 in 2009, before beginning the now famous trajectory to the moon in 2010.  

The constant of proportionality in Metcalfe's law (V ~ N²) was also quantified for each of the two proxies for N.  For example, using the number of transactions per day excluding popular addresses for N, the model best fit the market cap data with a constant of proportionality equal to $1.50.  In other words, the model predicts that the bitcoin market capitalization is approximately equal to $1.50 multiplied by the square of the number of TXs per day (excluding popular addresses).

I am still stunned that the Metcalfe model so accurately corresponds to the actual market cap over 4 years and over 1,000,000% growth in market cap.  The plot confirms for me that the value of bitcoin comes from the network of people who use it.  If we keep finding new ways to use bitcoin, the rest will take care of itself.  

Thanks. Very important work, as it enabled me to make the log-logistic theory, since money is apparently ALWAYS adopted by power law distribution not Gaussian (bell curve).

Noted it is mcap and not price, yet the are close proxy to each other now, since coin debasement is only 11% per annum now.

My TA. I put a ruler along the bottom of the green line since 2012 and looks it needs to come down to 3/5 current value to meet the trendline again. Which corresponds very roughly to $300.

P.S. Indeed any activity even promoting Bitpay transactions and driving our idealism into the toilet will satisfy our greed (for a while and that is a poetic note).

...

What fool would lose 3-5% spread (at least) on two times exchanges instead of paying 0% to spend the fiat with a credit card?

The costs of a credit card transaction can vary widely, from under 1% to even over 50%.

You failed to grasp my point that the credit card holder pays 0% (or even gets cash back). What the merchant pays is irrelevant, unless the merchant is giving that 3-5% discount to the Bitcoin purchaser. Even with a discount, it is bad tradeoff because we are pushing our ecosystem to hell.

...

My point is that in some cases the cost the the "credit card holder" can be upwards of 50% or even not be able to make the transaction in the first place. The case of an individual having to purchase a prepaid "credit card" in order to make an online purchase and spending more on "fees" then the amount of the purchase is a real case situation. I have said this over two years ago and will say it again. The low hanging fruit for Bitcoin has a FICO score of 350 or thereabouts or lives in a country that is blocked, or is under age 18,  or wishes to purchase goods or services from an "high risk" merchant across an international boundary etc etc.

The cost to the merchant can be very relevant particularly if the transaction fall into the "high risk category". Ever wonder why so many retailers refuse international credit card transactions for example? Not every transaction involves a consumer with an 800+ FICO score purchasing goods or services in person from a large retailer.

So you are arguing that most can't get a credit card or can't use, so they are selling Bitcoin to purchase and then replacing their Bitcoin. I find this so far off the relevance scale. Majority of Bitcoin holders weren't unable to purchase anything online before Bitcoin came along. That is an extreme assumption. We know Bitcoin appeals to tech people who surely had mapped out how to buy online many years ago.

I am arguing that a huge market for using Bitcoin in retail transactions is those who cannot get or use a credit card. This is in many cases an entirely different group of people from those who choose to invest or speculate in Bitcoin.

And that is off topic to the point I was making. But I don't disagree with you on your point, it just doesn't refute the point I was making.

I am arguing that a huge market for using Bitcoin in retail transactions is those who cannot get or use a credit card. This is in many cases an entirely different group of people from those who choose to invest or speculate in Bitcoin.

yes, I agree, this is one of the key purposes for this technology, but sadly such a small portion of what it is used for today.

Peter Thiel's Paypal doesn't allow filipinos to receive payments (or at least didn't until a year or two ago), because the USA wanted the Philippines to first enact laws to end bank secrecy, support anti-terrorism, have an AML and KYC law, give the IRS access to any private data requested, etc.. Philippines has complied, so now they got upgraded by Moody's, Standard & Poors, etc.. So now they get fattened with debt. Lovely world and now we bow like good slaves to Peter and give him control of our Bitcoin.

P.S. the law of unintended consequences a.k.a. chaos when politicians make laws is why you are reading this thread in reverse.  

Also I want to add that I understand it is very difficult to get merchants to hold BTC. But I am not in a rush to have merchants and fiat slavery. I am willing to invest in my future freedom for the long-term and be patient. I am not a greedy bastard.  I live simply.

[ArticMine]

I am arguing that a huge market for using Bitcoin in retail transactions is those who cannot get or use a credit card. This is in many cases an entirely different group of people from those who choose to invest or speculate in Bitcoin.

[chessnut]

I am arguing that a huge market for using Bitcoin in retail transactions is those who cannot get or use a credit card. This is in many cases an entirely different group of people from those who choose to invest or speculate in Bitcoin.

yes, I agree, this is one of the key purposes for this technology, but sadly such a small portion of what it is used for today.

[jmw74]

Bitpay and coinbase are on the edges of the bitcoin economy.  What's important to note is that they continually push the edges outward.

Just as merchants were motivated to accept bitcoin through bitpay (because it's virtually no risk), the same will happen with those merchants' suppliers.  And once that happens, the merchants don't need to completely convert to fiat anymore.  Eventually the merchant can keep their income in bitcoin, and it's the suppliers who use bitpay.  

What's going to stop the edges from moving outward?

Talk about fantastical dreaming. I thought I was really far out there with wanting an anonymous coin.

So in order to stop rape, first we need to rape until everyone is raped, then we can suddenly stop raping because everyone has a rape kit.

You won't get to even 1% coverage before the entire ecosystem has been co-opted by centralization and fiat regulation. Dance with the vampires only if you want to be bitten and converted.

I guess the love of greed can make one think up any kind of irrational excuse to continue in that greed.

I have absolutely no idea what you're talking about here.  How does stopping rape relate to the adoption of bitcoin?

The only possible government attack I see on bitcoin that can succeed is the 51% mining attack.  All your other concerns I think are overblown, you give governments too much credit.
 

What fool would lose 3-5% spread (at least) on two times exchanges instead of paying 0% to spend the fiat with a credit card?

And cause a premature capital gains event.

If you lose money on the two exchanges, how do you have capital gains?

Do most people in Bitcoin have only 3 - 5% gains.

Nope, they gain much more.  So your criticism about losing a few percent on fees is ridiculous.

[creekbore]

The beauty of the 5.25-year trendline with exponential fit (R^2=0.93 which is pretty darn good) is that it takes into account every worry of every person who has ever owned or not owned bitcoins. I put more weight on that than the individual worries of a single person.

You put a lot of weight in your humongous pride, as if someone presenting analytical discussion is worried. I am not worried about the BTC price. I could careless because I don't own any BTC nor am I itching to buy any. And you put a lot of weight in arbitrary curve fits.

And people who think they know every thing for sure (and you don't even enumerate the arbitrary assumptions in your model), eventually get a lesson in respecting chaos. Maybe not this time. No one knows. But eventually yes.

I hope you realize the following chart is arbitrary BS.

[/quote]

I have to say I find this interchange to be most revealing and astute.
Those of us with no or little BTC investment seem to be ridiculed for being 'scared' when asking questions of the sermon.

And, as I posted up thread, my main problem with all of this is the certainty that is expressed, much of which is based on a line drawn through a graph.  But spending a lot of time reading through the forum (and the other place) I am getting the feeling that expectations are shifting...a few weeks back revisiting the four hundreds was "highly unlikely".  Now I see a lot more talk of the three hundreds.

With regard to BitPay....I too have struggled with AnonyMint's problem with it (beyond the political) but am I right in saying Bitpay will constantly be selling coins for fiat, which will impact price? But the whole idea of BTC changing the world politically has always been a non-starter.

@AM -- Also, the concept of confiscations?  Won't the nouveau riche be the first to be targeted?  Is it not a good idea that Risto, Goat et al share some of their wealth around rather than spending it on vanity projects?  As nouveau poor I see little wrong with this.

But loved the comment about markets....have adopted for my sig.

[AnonyMint]

Bitpay and coinbase are on the edges of the bitcoin economy.  What's important to note is that they continually push the edges outward.

Just as merchants were motivated to accept bitcoin through bitpay (because it's virtually no risk), the same will happen with those merchants' suppliers.  And once that happens, the merchants don't need to completely convert to fiat anymore.  Eventually the merchant can keep their income in bitcoin, and it's the suppliers who use bitpay.  

What's going to stop the edges from moving outward?

Talk about fantastical dreaming. I thought I was really far out there with wanting an anonymous coin.

So in order to stop rape, first we need to rape until everyone is raped, then we can suddenly stop raping because everyone has a rape kit.

You won't get to even 1% coverage before the entire ecosystem has been co-opted by centralization and fiat regulation. Dance with the vampires only if you want to be bitten and converted.

I guess the love of greed can make one think up any kind of irrational excuse to continue in that greed.

I have absolutely no idea what you're talking about here.  How does stopping rape relate to the adoption of bitcoin?

You really can't wrap your mind around the analogy?

"So in order to stop rapefiat-takeover-of-Bitcoin, first we need to rapefiat-takeover-of-Bitcoin until everyone is rapedhas-fiat-takeover-of-Bitcoin, then we can suddenly stop rapingfiat-takeover-of-Bitcoin because everyone has a rape kitpretends-to-accept-BTC-but-really-accepts-fiat."

The only possible government attack I see on bitcoin that can succeed is the 51% mining attack.  All your other concerns I think are overblown, you give governments too much credit.

How can I say in a nice way that I think you are incredibly naive.

What fool would lose 3-5% spread (at least) on two times exchanges instead of paying 0% to spend the fiat with a credit card?

And cause a premature capital gains event.

If you lose money on the two exchanges, how do you have capital gains?

Do most people in Bitcoin have only 3 - 5% gains.

Nope, they gain much more.  So your criticism about losing a few percent on fees is ridiculous.

How did wasting money become ridiculous?

And for what benefit did it serve? To promote the fiat use of Bitcoin which will enslave all of us.

[creekbore]

creekbore, I am trying to do some work now on log-logistic curve fitting.

This post will be deleted soon.

OK, thanks, just explain it in terms for us thickies dwelling in the IQ130s

[SlipperySlope]

Blockchain.info has now removed the "holes" from their charts, allowing me to update my Metcalfe Value plot.  Although we don't have price data prior to the opening of MtGox mid 2010, I was able to use the Metcalfe model to extrapolate backwards to the genesis block.  The extrapolated value of all bitcoins in circulation was approximately $10,000 in 2009, before beginning the now famous trajectory to the moon in 2010.  

The constant of proportionality in Metcalfe's law (V ~ N²) was also quantified for each of the two proxies for N.  For example, using the number of transactions per day excluding popular addresses for N, the model best fit the market cap data with a constant of proportionality equal to $1.50.  In other words, the model predicts that the bitcoin market capitalization is approximately equal to $1.50 multiplied by the square of the number of TXs per day (excluding popular addresses).

I am still stunned that the Metcalfe model so accurately corresponds to the actual market cap over 4 years and over 1,000,000% growth in market cap.  The plot confirms for me that the value of bitcoin comes from the network of people who use it.  If we keep finding new ways to use bitcoin, the rest will take care of itself.  

Your model continues to boggle my mind.

I try to perform at least one Bitcoin transaction daily. Either by spending some, buying some, transferring some, or most often by receipt of mining earnings.

Suppose that I am responsible for permanently increasing the daily quantity of transactions by one. Today's adjusted number of transactions reported by Blockchain.info is 58,006, and your model projects a market cap of $1.50 * 58,006 * 58,006 = $5,047,044,054.00. My contribution makes the adjusted number of transactions 58,007, and the corresponding market cap is 5,047,218,073.50. The difference between the two market caps is $174,019.50. As the total number of Bitcoins at the time of writing is 12,591,775, my one incremental daily transaction lifts the corresponding price per bitcoin by 0.013 USD.

Right?

[AnonyMint]

Your model continues to boggle my mind.

I try to perform at least one Bitcoin transaction daily. Either by spending some, buying some, transferring some, or most often by receipt of mining earnings.

Suppose that I am responsible for permanently increasing the daily quantity of transactions by one. Today's adjusted number of transactions reported by Blockchain.info is 58,006, and your model projects a market cap of $1.50 * 58,006 * 58,006 = $5,047,044,054.00. My contribution makes the adjusted number of transactions 58,007, and the corresponding market cap is 5,047,218,073.50. The difference between the two market caps is $174,019.50. As the total number of Bitcoins at the time of writing is 12,591,775, my one incremental daily transaction lifts the corresponding price per bitcoin by 0.013 USD.

And this is why Quantity Theory of Money says M x V = value, not M alone. This is why selling out to fiat via Bitpay robs us of the square of the count of transactions and puts that value in fiat instead. The value of a network is the velocity times the position, not just the position, i.e. if all the actors (hodlers of money or nodes) don't interact then the network is a beautiful pile of do-nothing.

[Peter R]

Your model continues to boggle my mind.

I try to perform at least one Bitcoin transaction daily. Either by spending some, buying some, transferring some, or most often by receipt of mining earnings.

Suppose that I am responsible for permanently increasing the daily quantity of transactions by one. Today's adjusted number of transactions reported by Blockchain.info is 58,006, and your model projects a market cap of $1.50 * 58,006 * 58,006 = $5,047,044,054.00. My contribution makes the adjusted number of transactions 58,007, and the corresponding market cap is 5,047,218,073.50. The difference between the two market caps is $174,019.50. As the total number of Bitcoins at the time of writing is 12,591,775, my one incremental daily transaction lifts the corresponding price per bitcoin by 0.013 USD.

Right?

Yes.  This is what the model implies, and it has reliably held since the opening of MtGox.  Your additional daily transaction adds $174,019.50 of value to the market cap, or $0.013 to each bitcoin.  It seems too simple, but on the other hand I cannot believe that the goodness of fit is just coincidence; is there something truly at play here that we haven't fully come to understand?

I do agree with your assessment that one should try to find ways to use the system in useful ways (like you are doing).  For my part, I will now be looking to hire people in bitcoin space for contract work that I would have normally hired locally--this will increase usage of the network.  
  

[AnonyMint]

Most of you can't picture in your head as I (and some others here probably) can, so I need to show you chart for you to get that "Ah ha" epiphany.

I lack the math software to do a proper log-logistic curve fit. Here follows my eyeballing and rough fit to the change in slope.

The run from Oct to Jul 2011 had a slope of 2/7mos and from Jan 2012 to Jan 2014 had a slope of 2/24 mos. The cumulative distribution function shown superimposed in blue below is 1/1+(1/x)^0.5. Thus from x=0 to x=0.25 for the Oct to Jul 2011 run has a slope of 1/1+sqrt(1/0.25) = 1/3 = 0.33 and from Jan 2012 to Jan 2014 is from x=0.25 to x=0.50, thus 1/1+sqrt(1/0.5) = 0.41. So 0.33-0 = 0.33 and 0.41 - 0.33 = 0.08. And 0.33/0.08 = 4 and 24/7 = 3.5. So we can see ratios of the slopes match closely. So this is a reasonable curve fit as the proportional vertical heights also match. A quantitative fit would be more accurate. The accurate fit is probably a bit less steep in the early portion and less flat in the latter. So this would be more favorable than the one I overlaid.

Any way, if this theory is correct, then you can clearly see that Bitcoin will stop rising as fast and that it is due to fall down in price significantly before it rises again and more slowly than the past. From here on the slope from x = 1 to x = 1.5 is only 0.05, thus 5/8 of the rate of increase we've on the log 10 chart since Jan 2012. Note that is 5/8 of a rate of increase that is exponential in the power of 10.

It is roughly saying we won't significantly surpass $1000 in 2014. I don't know where the correctly fitted curve would be right now, so I can't project where the price should be now and where it will be nominally. I think the slope projection is more close to accurate, so we can say that if the theory is correct (that distribution of money holders is a power law distribution as the cited research and common knowledge says it always is), then price appreciation will slow down specifically to 0.05 units on the log 10 chart per month where 1 unit is 10X appreciation. So if we bottom at $400, then price after 20 months should be $4000. Again this is a very rough eyeballed fit and would expect the refined fit to have a slightly higher slope maybe 0.06, so make that 16 months instead.

It seems too simple, but on the other hand I cannot believe that the goodness of fit is just coincidence; is there something truly at play here that we haven't fully come to understand?

What is hard to understand? Reed's Law is another way of stating Metcalf's Law. It is quite clear that in a network with N nodes, there arre N^2 possible interconnections. Thus the value of the network interaction is N^2. How hard is it to understand that without communication and interaction, there is no leverage of each other. How can I use your knowledge if I can't interact with you? Why do we become smarter by posting in this forum. Etc..

[aminorex]

I want a Klein bottle.  There is a stock of 1000 waiwai on the wampum market.  It is not moving.  It is bidless.  But they travel well by air, so I take one waiwai from the stock, by buying it on the market.  The market moves against me.  I.e. the value of one waiwai increases.  I sent one waiwai to Alice by European swallow to pay for a Klein bottle.  Alice wants wampum, so she sells the waiwai on the wampum/waiwai market.  The market moves against her.  I.e. the value of one waiwai decreases.  Net impact on waiwai/wampum: Zen.

Youtube videos of my Klein bottle go viral.  1100 teenage girls in Uruguay want Klein bottles, at various times, 100 each day.  As more and more school girls trade wampum for waiwai, the stock of waiwai declines, the cost in wampum increases.  100 waiwai are held by pidgeons.  Alice takes the waiwai from the pidgeons and sells them for wampum the next day, but by that time 100 more Uruguayan school girls have pidgeons in the air.  For 11 days, the stock of waiwai on the wampum market is reduced by 10%.  Uruguayans 101 to 1100 pay 20% more for the waiwai, and Alice gets 118% as much wampum for her Klein bottles as she would have were the waiwai rates constant.  If Alice's ten cousins start marketing their Klein bottles to Moldovan gigolos, whose pidgeons are twice as slow, those transactions will remove twenty times as much waiwai from the supply/demand balance on the wampum markets, and the price will rise confoundedly.   The result will be a waiwai bubble.

PQ=MV, the value of the money stock is M, denominated in PQ/V.  Increasing V decreases M.  Increasing the number of times a waiwai can flip during a fortnight, say by using African swallows instead of pidgeons, will increase laden air speed, thus decreasing the wampum per waiwai.

Using bitpay keeps BTC in the air.  That creates a churning marginal demand which decreases the supply on the fiat market.  If you buy immediately before spending, and the merchant takes fiat, then the time in the air is small.  If you buy in anticipation, V decreases, and the effective air time, from the point of view of the exchange market, is quite long.  Using bitpay also adds to the bid and to the ask on the market, thus increasing liquidity, which in turn makes bitcoin marginally more efficient (less slippage) and less risky (as liquidity is available when it is needed).

If everyone makes a different color of Klein bottle, and everyone wants to collect the whole set, then there are N^2 pidgeon flights which need to occur.  The first pidgeon reduced the stock of waiwai by a factor of 0.999.  The second person, by a factor of 0.998,  the n^2 person by a factor of 1-0.001*n^2.  As a result the cost of a waiwai rises by a factor of k*e^(n^2).

[SlipperySlope]

Your model continues to boggle my mind.

I try to perform at least one Bitcoin transaction daily. Either by spending some, buying some, transferring some, or most often by receipt of mining earnings.

Suppose that I am responsible for permanently increasing the daily quantity of transactions by one. Today's adjusted number of transactions reported by Blockchain.info is 58,006, and your model projects a market cap of $1.50 * 58,006 * 58,006 = $5,047,044,054.00. My contribution makes the adjusted number of transactions 58,007, and the corresponding market cap is 5,047,218,073.50. The difference between the two market caps is $174,019.50. As the total number of Bitcoins at the time of writing is 12,591,775, my one incremental daily transaction lifts the corresponding price per bitcoin by 0.013 USD.

And this is why Quantity Theory of Money says M x V = value, not M alone. This is why selling out to fiat via Bitpay robs us of the square of the count of transactions and puts that value in fiat instead. The value of a network is the velocity times the position, not just the position, i.e. if all the actors (hodlers of money or nodes) don't interact then the network is a beautiful pile of do-nothing.

Using bitpay keeps BTC in the air.  That creates a churning marginal demand which decreases the supply on the fiat market.  If you buy immediately before spending, and the merchant takes fiat, then the time in the air is small.  If you buy in anticipation, V decreases, and the effective air time, from the point of view of the exchange market, is quite long.  Using bitpay also adds to the bid and to the ask on the market, thus increasing liquidity, which in turn makes bitcoin marginally more efficient (less slippage) and less risky (as liquidity is available when it is needed).

One of the ways I spend bitcoin is to buy gift cards from Gyft or Giftcard Zen. Unfortunately the coins get converted into fiat right away and my subsequent use of the gift card at, for example, Amazon does not add to the Bitcoin economy. I expect that as the Bitcoin economy grows, business to business bitcoin transactions will also grow enough to keep the flow going once a merchant receives my coin.