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Author Topic: A difference of opinions at the Bitcoin Foundation regarding the XBT proposal?  (Read 5035 times)
opossum
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October 24, 2014, 02:28:42 AM
 #41

Why can't we recalculate bitcoin as=100 satoshis, then we end up with just bitcoin [XBI or XBT=100satoshi] and satoshi itself.
Why some people so hung up on bitcoin being 100mil satoshis? This change would be very easy to implement.

Do you serioulsy think redefining a word is an easy task? Considering how many people already talk about Bitcoin (maybe it's less than 1% of the world, it's still a big amount)
I agree. I think that redefining how we measure Bitcoin (in terms of terminology) would wreck havoc on bitcoin related commerce, as people would be confused as to exactly how much value is being asked for when someone is selling a certain product or when negotiating a price, this would result in people not wanting to deal in bitcoin 


 
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October 24, 2014, 03:26:18 AM
 #42

I'm on the working group. There are lots of options for units to go with an ISO 4217 currency code. Would XBT = 100M satoshis (1 bitcoin) be better than XBI = 100 satoshis (1 bit)?

I have over 20 years experience working on FX systems, and I strongly advise that the primary objective here, with the standards authorities, is:

[An official ISO code] = 100 satoshis.

If Bitcoin is to remake the mainstream financial world, this will give it a massive advantage, but obtaining any other official standard will be of little benefit in comparison.

Can we get two currency codes? Doubtful, but is worth discussing.

If we can get two currency codes, that would be excellent. However, the standards people would want to see them alphabetically contiguous, so XBT:XBU could fly, but XBI:XBT is improbable.




Thx for the input. Is the two decimal bits a better choice than the 8 decimal bitcoin? The advantages of two decimal places is obvious...the advantage to using bitcoins is you could prepend a micro symbol that doesn't case fold to a letter that could be interpreted as M for mega...Unicode has a separate SI prefix micro.

Hardforks aren't that hard. It’s getting others to use them that's hard.
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October 24, 2014, 03:30:34 AM
 #43

I'm on the working group. There are lots of options for units to go with an ISO 4217 currency code. Would XBT = 100M satoshis (1 bitcoin) be better than XBI = 100 satoshis (1 bit)?

If XBT = 1 bitcoin, I don't foresee people writing 0.00098 XBT to describe the cost of bubblegum. People _might_ write 980 XBI though.

I certainly feel that XBT for 1 bitcoin is a better choice than XBI for 1 bit, mainly because the term "bitcoin" is far better established (one can even look it up in the dictionary).  Currency codes are very much a realm for formality, accuracy, unambiguity, and stability; XBI for one "bit" is simply not appropriate today given the youth and contention surrounding the term.  If the 100-satoshi unit is desired (e.g. for decimal point-related issues) and the working group wants to push this now then I think the only appropriate term to build around is "microbitcoin".  This is not the end of the world (The formal UK currency name is the cumbersome "Pound sterling" yet, GBP works and people get by with slang such as "pounds" or "quid" in everyday situations).

People are unlikely to write "0.000 98 XBT" or "980 XBI" in my opinion but they may well write "980 bits".

I think we need more community input on this choice. Can we get two currency codes? Doubtful, but is worth discussing.

Just in case the working group hasn't seen it, here's an Old, short, Bitcoin Foundation discussion on the topic.

Another related idea that I think needs community input is getting a Unicode currency symbol(s). We are all used to using BTC for bitcoin and some are starting to use ƀ for bits...unfortunately, a capital ƀ is Ƀ, which is also used for 1 bitcoin. Nothing like a capitalization error to cost you 1 million times more than you wanted to spend!

Should we try to get Unicode characters for 1 bitcoin and 1 bit? Just bits? Just bitcoin?

A benefit of using 1 bitcoin as a standard is that the symbol µ is separately encoded in Unicode from the Greek letter μ (which case folds to the Greek letter M).

Therefore, 1 µXBT and 1 µBTC shouldn't accidentally change value at the whim of a shift key.

I quite like the µBTC idea.

Another thought: Perhaps a "µ" with a bar through it, "µ" say, would be easier to get given that "₥" for a mill already exists and is currency agnostic.  I could certainly see prices like "1500µ" (or "µ1500") being commonly read as "fifteen hundred bits" but also sometimes "fifteen hundred mikes" or "one point five mills".

I feel worth stressing a second time is that, given the current upset surrounding the 100-satoshi term, it might be wise to simply work on a currency code for the "bitcoin" unit for now, leaving the issue of the smaller unit to settle for a few years.

Disclaimer: While I've honestly tried to be unbiased and logical, it's no secret that I openly oppose the term "bit" for 100 satoshis.

I like the m-mill / μ-micro idea. Very clever.

Hardforks aren't that hard. It’s getting others to use them that's hard.
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October 24, 2014, 03:59:59 AM
 #44

don't need to redefine any word
AAPL was $700/share and after a stock split (1:7) it became $100/share with increase in unit numbers, but not value
Nobody is talking about changing the number of fundamental units (which are 2.1 quadrillion satoshis)
Just split bitcoin 1:1000000 and say that it (defined as XBT or XBI) is now only 100 satoshis, but you have 21 trillion of such "bitcoins" or "bits" or "whatever" (XBT or XBI)
The concept of a stock split is familiar to EVERYBODY

I'm not part of EVERYBODY, it seems. It's not the first time I've been excluded, though.

And yes, if 1 Bitcoin = 100000000 units, but then 1 Bitcoin = 100 units, that's exactly what “redefining” means.

An economy based on endless growth is unsustainable.
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October 24, 2014, 04:07:18 AM
 #45

what difference bteween BTC and XBT?
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October 24, 2014, 04:34:56 AM
 #46

don't need to redefine any word
AAPL was $700/share and after a stock split (1:7) it became $100/share with increase in unit numbers, but not value
Nobody is talking about changing the number of fundamental units (which are 2.1 quadrillion satoshis)
Just split bitcoin 1:1000000 and say that it (defined as XBT or XBI) is now only 100 satoshis, but you have 21 trillion of such "bitcoins" or "bits" or "whatever" (XBT or XBI)
The concept of a stock split is familiar to EVERYBODY

I'm not part of EVERYBODY, it seems. It's not the first time I've been excluded, though.

And yes, if 1 Bitcoin = 100000000 units, but then 1 Bitcoin = 100 units, that's exactly what “redefining” means.

I guess I'm not part of EVERYBODY either. LOL

Saying that you don't trust someone because of their behavior is completely valid.
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October 24, 2014, 04:39:21 AM
Last edit: October 24, 2014, 04:58:11 AM by Biodom
 #47

don't need to redefine any word
AAPL was $700/share and after a stock split (1:7) it became $100/share with increase in unit numbers, but not value
Nobody is talking about changing the number of fundamental units (which are 2.1 quadrillion satoshis)
Just split bitcoin 1:1000000 and say that it (defined as XBT or XBI) is now only 100 satoshis, but you have 21 trillion of such "bitcoins" or "bits" or "whatever" (XBT or XBI)
The concept of a stock split is familiar to EVERYBODY

I'm not part of EVERYBODY, it seems. It's not the first time I've been excluded, though.

And yes, if 1 Bitcoin = 100000000 units, but then 1 Bitcoin = 100 units, that's exactly what “redefining” means.

sorry about "everybody", it was presumptious of me. I guess, I meant everybody who ever traded actual stocks on the stock market.

What I propose is simple: do a virtual 1:1,000,000 stock split of bitcoin (mathematically) to 21 trillion units, then call these units (each=100 satoshis) as you please (either "bitcoin" still-which I would prefer- or "bits" or even something else). What symbol to give them is largely irrelevant because they will be the winner due to greatly improved ease of use and adherence to two decimals after period standard for most currencies, which is much more familiar to people outside of the current bitcoin community.
However, after any stock split, you still call the stock by the same three-four digit symbol (hence AAPL for Apple) and full name, but the the number of shares/units changes, obviously. Nobody calls it redefining, but it is admittedly so in the narrowest sense (you redefine the number of outstanding shares that company has in a stock split).

From a practical point it is also simple: define a major unit as 100 satoshi (not 100,000,000) and make satoshi a minor unit at 1:100 of the major unit.
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October 24, 2014, 11:26:27 AM
 #48

Another thought: Perhaps a "µ" with a bar through it, "µ" say, would be easier to get given that "₥" for a mill already exists and is currency agnostic.  I could certainly see prices like "1500µ" (or "µ1500") being commonly read as "fifteen hundred bits" but also sometimes "fifteen hundred mikes" or "one point five mills".

I like the m-mill / μ-micro idea. Very clever.

Thanks.  Glad I could help.

If we can get two currency codes, that would be excellent. However, the standards people would want to see them alphabetically contiguous, so XBT:XBU could fly, but XBI:XBT is improbable.

Interesting.  Do you have a source for this?
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October 24, 2014, 11:39:24 AM
 #49

How do you think this would sound to the CNBC TV quacks?

"There will only ever be 2.1 quadrillion satoshis in the world."
http://en.wikipedia.org/wiki/Names_of_large_numbers#Usage_of_names_of_large_numbers

Also, I can imagine the CNBC money-honeys not understanding "bits" and going on air to say:
"BREAKING NEWS: XBT has now been approved for bitcoin and 21 trillion is the new limit!"

Founding Director, Bitcoin Foundation
I also cover the bitcoin economy for Forbes, American Banker, PaymentsSource, and CoinDesk.
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October 24, 2014, 01:01:32 PM
 #50

How do you think this would sound to the CNBC TV quacks?

"There will only ever be 2.1 quadrillion satoshis in the world."
http://en.wikipedia.org/wiki/Names_of_large_numbers#Usage_of_names_of_large_numbers

Also, I can imagine the CNBC money-honeys not understanding "bits" and going on air to say:
"BREAKING NEWS: XBT has now been approved for bitcoin and 21 trillion is the new limit!"
Uhhh....yikes. That sounds like collapse...the exact opposite of what's happened the last 5 years.

Hardforks aren't that hard. It’s getting others to use them that's hard.
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October 24, 2014, 01:08:24 PM
Last edit: October 24, 2014, 03:52:30 PM by Biodom
 #51

How do you think this would sound to the CNBC TV quacks?

"There will only ever be 2.1 quadrillion satoshis in the world."
http://en.wikipedia.org/wiki/Names_of_large_numbers#Usage_of_names_of_large_numbers

Also, I can imagine the CNBC money-honeys not understanding "bits" and going on air to say:
"BREAKING NEWS: XBT has now been approved for bitcoin and 21 trillion is the new limit!"
Uhhh....yikes. That sounds like collapse...the exact opposite of what's happened the last 5 years.

Actually, J. Allaire of Circle did refer to 2.1 quadrillion satoshi or [units] in several public speeches.
Besides, with 21 trillion units you can start working toward unity(equality) with $$ since high tens/~hundred of trillions is where world GDP is.
Why would this be a collapse-no, instead of artificial scarcity it would be seen as an adequate number of units and we will work from low value per 100 satoshi to higher.
I can predict that this alone will cause a dramatic increase in activity because people will perceive having much more [units].
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October 24, 2014, 03:29:11 PM
Last edit: October 24, 2014, 04:40:08 PM by Goldmundo
 #52

One important thing to note with regards to the OP, Mr. Jon Matonis seems to like to express his personal opinions without being careful to not sound like he is speaking in the name of the Foundation. So, whatever opinions he expressed in the said CoinBase article are his personal opinions and not necessarily that of the Financial Standards Working Group. While the group itself does not yet have an official recommendation, it seems to me (and this is my personal subjective perception) that XBT = 100 satoshis = 1 bit is the prevalent option both within the group and wider community.

I believe if we are going to have this worldwide currency and have people really start using it in every day life, it definitely cannot be expressed with 8 decimals. Reasons are technical, psychological, accounting related, all mentioned already.

It seems that there are some real obstacles within the Bitcoin system as it is at the moment. But I am honestly hoping that we will reach consensus on changing the system to be future-proof rather than sticking with the status quo thus crippling the growth of Bitcoin, potentially fatally.

As for the idea of having two units, one for ISO and another for display, I think this is a confusing half way solution that will make bitcoin different from other currencies and thus more difficult to understand and embrace. I can't stress enough: the number of people currently using bitcoin is a tiny tiny group which could very well be considered a beta testing group. There should be no worries of causing confusion by switching to bits (or bitcoins worth 100 satoshis each) as the main unit on all levels. Why? Because all the people who know what is going on will make the switch very easily, while all the people who don't know what's going on couldn't care less and it will make no difference to them.

My mother started using bitcoin recently. If her balance on Circle changes from 0.5 bitcoins to 500000.00 bitcoins while the displayed US dollar amount stays more or less the same, I guarantee you she will not even notice. And even if she does, she might ask me "How come I now have 500K bitcoins? Does it mean I'm now insanely rich?" And I'll say "no mom, they just changed the denomination unit" to which she will reply "ah, ok." End of story.

I don't even want to start thinking about explanations to new comers when they would start asking how come there is this big unit called XBT which I see on trading sites, but when I log into my account on Coinbase I see these bits.. What are the two? Why do we have both? And on this third site they are using some uXBT, and then I also saw somewhere amounts in milibitcoins, is that also bitcoin just with a different name? etc etc..... It's such a mess! It's already difficult as it is to explain to people some things about bitcoin, let's make it easier, please, not more difficult.

https://dl.dropboxusercontent.com/u/54619107/Goldmund/hotlink/2-options.jpg
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October 24, 2014, 05:42:29 PM
 #53

It may be useful to quote Jon Matonis' comment from that article. He has some solid points:

Quote
Thank you all for engaging on this important topic. When it comes to XBT and where to set the decimal, I don't think there is a right or wrong answer --- it's a matter of perception and
managing trade-offs and people will sit at different places along that spectrum.

So, here are my detailed reasons for maintaining XBT as a one full bitcoin (1.00000000):

a) We get one shot at setting XBT and minor units within the ISO standards body, so we should not base a plan around what makes "visual" sense at the time (Zimbabwe did not keep going to the ISO for re-pegging as they massively added zeroes. If gold goes to $10,000 per ounce would you recommend adjusting base unit to grams?);

b) The white paper from Satoshi references 21 million as a finite limit for bitcoin issuance. Although he entertains adjusting commas and decimal displays in his post, the public perception and the 21 million limit has taken on a greater importance with the financial world than initially realized. Changing it now would undermine those perception gains. Moving the decimal point to bits would change the finite limit to 21 trillion "bits" or 2.1 quadrillion "satoshis" definitely not inspiring to the economic notion of scarcity (CNBC TV quacks will say the new limit for bitcoin is now 21 trillion!);

c) For better or worse, pricing in currency units implies relative scarcity of that unit. Italy was constantly ridiculed when it required 2,000,000 lira to purchase an everyday household item. They are not the only example. Sure, a newbie can acquire more bits, but it trivializes
the pricing mechanism;

d) XBT is already quoted as 1.00000000 on respected forex sites, such as XE.com, Bloomberg, Reuters Eikon, and CNN. Even Oanda.com quotes it this way although they still use BTC. Moving to a "bits" expression would start to make bitcoin (XBT) a joke currency like Dogecoin;

e) Some will say it's just as a display. But the ISO decimal setting will be more than a display --- it will be the default in the legacy financial world. Instead of changing that default in the reference implementation and instead of changing 1XBT = 1.00000000, I recommend
all other wallets/apps select their preferred display, of which there will be many.

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October 24, 2014, 06:40:16 PM
 #54

It may be useful to quote Jon Matonis' comment from that article. He has some solid points:

Quote
Thank you all for engaging on this important topic. When it comes to XBT and where to set the decimal, I don't think there is a right or wrong answer --- it's a matter of perception and
managing trade-offs and people will sit at different places along that spectrum.

So, here are my detailed reasons for maintaining XBT as a one full bitcoin (1.00000000):

a) We get one shot at setting XBT and minor units within the ISO standards body, so we should not base a plan around what makes "visual" sense at the time (Zimbabwe did not keep going to the ISO for re-pegging as they massively added zeroes. If gold goes to $10,000 per ounce would you recommend adjusting base unit to grams?);
how is this related to gold?

b) The white paper from Satoshi references 21 million as a finite limit for bitcoin issuance. Although he entertains adjusting commas and decimal displays in his post, the public perception and the 21 million limit has taken on a greater importance with the financial world than initially realized. Changing it now would undermine those perception gains. Moving the decimal point to bits would change the finite limit to 21 trillion "bits" or 2.1 quadrillion "satoshis" definitely not inspiring to the economic notion of scarcity (CNBC TV quacks will say the new limit for bitcoin is now 21 trillion!);
There is NO reference to 21 mil units in the white paper entitled "Bitcoin: a peer-to-peer electronic cash system".

c) For better or worse, pricing in currency units implies relative scarcity of that unit. Italy was constantly ridiculed when it required 2,000,000 lira to purchase an everyday household item. They are not the only example. Sure, a newbie can acquire more bits, but it trivializes
the pricing mechanism;
Since when currency units imply scarcity? Currency units imply utility in everyday life. World GDP is ~90 trillion $$.
Historical references (to Italy) are largely irrelevant.


d) XBT is already quoted as 1.00000000 on respected forex sites, such as XE.com, Bloomberg, Reuters Eikon, and CNN. Even Oanda.com quotes it this way although they still use BTC. Moving to a "bits" expression would start to make bitcoin (XBT) a joke currency like Dogecoin;
Well, respected forex sites can reprogram their computers

e) Some will say it's just as a display. But the ISO decimal setting will be more than a display --- it will be the default in the legacy financial world. Instead of changing that default in the reference implementation and instead of changing 1XBT = 1.00000000, I recommend
all other wallets/apps select their preferred display, of which there will be many.

Additional comments:
1. having 21 trillion XBT[XBU]/[new]bitcoin/bits=100 satoshi will bring total number of bitcoin major units closer to major nation GDP values and would facilitate:
a. more commerce simply because everyone will have more units. This is is trivial mathematically, but beneficial psychologically.
b. easier understanding from people who are known to be unable to properly process multiple digits after the period in value evaluation.

2. Bitcoin can work toward eventual unity (equality) with the dollar, yan or other major currency (yen to yuan to $ to euro)

3. If bitcoin is a currency, can Mr Matonis provide an example of a currency that is valued at ~$300-400? There is none, of course, so this historical precedent works against bitcoin having 8 digits after the period.

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October 24, 2014, 07:14:48 PM
 #55

3. If bitcoin is a currency, can Mr Matonis provide an example of a currency that is valued at ~$300-400? There is none, of course, so this historical precedent works against bitcoin having 8 digits after the period.

How is this relevant for the definition of “currency”?

An economy based on endless growth is unsustainable.
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October 24, 2014, 07:49:30 PM
 #56

Does anyone has actual knowledge regarding ISO application?
Do we know for sure that it is possible?
Who will prepare/submit the application? Bitcoin Foundation?

Also, how does the approval process work? Is it:

1) There are very specific criteria, if those are met - application is automatically approved' or
2) Approval/decline is solely an ISO's decission (even if criteria are met, they can reject the application)?


In either case, if the criteria are currently met (such as Bloomberg/Reuters reporting, exchanges, international payments and recognition) - these are met by the bitcoin in it's present shape (8 decimals), not by 'bits' or bitcoin=100 satoshis.

I can't imagine ISO approving application for XBT=bitcoin=100 sat based on multiple factors, including Bloomberg reporting on bitcoin, while Bloomberg reports on bitcoin being 100,000,000 sat.

Seems to me that forcing the denomination idea can jeopardise the application.

If you want XBT= bit or bitcoin=100 sat, isn't the correct way of action first to make everyone switch to 'bits' and then apply for the ISO code?

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[/tabl
Biodom (OP)
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October 24, 2014, 08:14:09 PM
 #57

3. If bitcoin is a currency, can Mr Matonis provide an example of a currency that is valued at ~$300-400? There is none, of course, so this historical precedent works against bitcoin having 8 digits after the period.

How is this relevant for the definition of “currency”?

Because if it is a commodity, then there are commodities priced as high or higher per unit (gold, platinum, etc.)
However, there are no currency units priced in hundreds of US dollars.
My argument was to refute opinions based on prior anecdotes (how everyone laughed at Italy, whether we will measure bitcoins in grams or Zimbabwe-all provided by Mr. Matonis in one go)
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October 24, 2014, 08:15:49 PM
 #58

If you want XBT= bit or bitcoin=100 sat, isn't the correct way of action first to make everyone switch to 'bits' and then apply for the ISO code?

Essentially, yes, but you don't have to call these units bits "officially".
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100 satoshis -> ISO code


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October 24, 2014, 09:10:20 PM
Last edit: October 24, 2014, 09:22:09 PM by solex
 #59

If you want XBT= bit or bitcoin=100 sat, isn't the correct way of action first to make everyone switch to 'bits' and then apply for the ISO code?

Essentially, yes, but you don't have to call these units bits "officially".

the term "bits" is not important in the ISO code discussion. The benefit of ISO currency codes that they provide a standard for inter-system communication, financial data storage and transmission from computer to computer around the world. ISOs do not need to be seen by the public. People use US$ informally instead of USD, and A$ instead of AUD.

People who want to see BTC and the existing Bitcoin amounts 1.23456789 on their screens, can still do so, even if this amount is stored as XBT 1234567.89 in an accounting system.

Reading what Jon Matonis has written, makes me think that he needs to talk more with IT people who work on accounting and payment systems.


Interesting.  Do you have a source for this?
Sorry, no, just personal experience from interacting with standards people during securities issuance.

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October 25, 2014, 11:18:26 AM
 #60

I tried to compile an overview of possible choices for an ISO 4217 application, and assigned codes for easy reference.
Here's the list, ordered alphabetically:


[BI2] — Apply for 1 XBI = 100 satoshis, with one subunit and two decimal places.

[BT2] — Apply for 1 XBT = 100 satoshis, with one subunit and two decimal places.

[BT8] — Apply for 1 XBT = 100000000 satoshis, with various subunits and eight decimal places.

[BU2] — Apply for 1 XBU = 100 satoshis, with one subunit and two decimal places.

[ST0] — Apply for 1 XST = 1 satoshi, with no subunits and zero decimal places.

[UB2] — Apply for 1 XUB = 100 satoshis, with one subunit and two decimal places.



I think it would be beneficial if we work through the list of choices and discuss the pros and cons of each item individually.

Here are my thoughts:

There is a serious problem with variant [BT2] because the currency code XBT is already used on a lot of sites with the definition 1 XBT = 100 million sats. When the ISO committee sees that the proposed unit is grossly incompatible with current practice, they will certainly reject the application.
This means that all those sites would have to switch to the new definition 1 XBT = 100 sats before we can submit the application. This switch would require a huge organisational effort. There would need to be consensus for a specific "switch date", when the old definition (1 XBT = 100 million sats) gets replaced with the new definition (1 XBT = 100 sats). Given Bitcoin's decentralised nature, it would be hard (if not impossible) to find consensus for any particular date.
And even if the switch is successful, people would wonder how to pronounce the unit XBT: Those people who traded on sites that just switched would certainly perceive this as a stock split, and thus call it "new bitcoin" (versus "old bitcoin" with previous definition). The "bits" proponents, on the other hand, would call it "bit", while still refering to 1 million bits as a "bitcoin".
Some people would accept this re-definition, others won't. I think it is likely that this will create a schism in the Bitcoin community. It is also likely that certain players will use this situation to spread fear, uncertainity, and doubts about Bitcoin.
Even if all of the above difficulties are successfully handled, this would slow down the standardisation process for additional — I guess — six to twelve months.

A much more frictionless approach would be [BT8]. In this case the standardisation process would be quickest, because the code XBT is already widely employed and it would be (comparably) easy to convince the ISO people to officialise this de-facto standard.
The big disadvantage here are the eight decimal places. Most financial software allows a maximum of four decimal places. Eight is too many. It is also very inconvenient for human users, thus requiring any front-ends to support a customised (non-ISO) display.

The options [BI2], [BT2], [BU2], and [UB2] have in common that they would give preference to one of the many names for 100 satoshis, which means that the other groups would be dissatisfied and flamewar against it. Finding a consensus here seems to be very difficult, maybe impossible. This would also slow down the standardisation process for some time, because one needs to wait for consensus to emerge.
The advantage here is that quite a lot of currencies (especially in western cultures) use two decimal places, too, which means that this would make Bitcoin more familiar to users of these currencies.

Lastly, the option [ST0] doesn't have a "B" in it, which requires people to understand the distinction between a currency (like "Sterling", "Renminbi") and its unit (like "pound", "yuan"). This proposal has the advantage that there are no naming issues, and no conflicting meanings, i.e. the standardisation process would be frictionless. It wouldn't create any kind of schism in the community. It also has a kind of intellectual purity because values are expressed in exactly the same format as they are transmitted by the protocol and stored in the blockchain, i.e. plain integers.
The disadvantage here is that prices will often be expressed in thousands of satoshis, probably written as "k sat" (with the "k" being postfixed to the number) or "ksat" (with the "k" being prefixed to the unit).
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