A new notation for Bitcoin?

[thoughtfan]

Something along these lines may well have already been proposed and if it has, please direct me to the thread.  However, there's always a chance this is actually a new and revolutionary idea .

Introducing 'powerbitcoin' (^BTC) ...

1 BTC = 21.1 ^BTC
half a Bitcoin = 20.5 ^BTC
quarter of a Bitcoin = 20.25 ^BTC (pronounced 'twenty dot two five powerbitcoin')
21 million BTC = 28.21  ^BTC
1 satoshi = 13.1 ^BTC

... another way to think about, to write, communicate and calculate Bitcoin quantities based on, but with a less cumbersome ‘feel’ than scientific notation (or decimal floating point notation).

This is something I’ve been thinking about I’d like to run by you folk see what you think.

The question is would enough people be able to understand and accept that the first number you encounter, the number to the left of the dot (not a decimal point) gives us the scale (denomination or ‘exponent’ ) of the value of Bitcoin whilst that on the right gives us the amount or ‘detail’?  I suggest all that is required is an acceptance for instance that a 22.x value is ten times as big as a 21.x number to make practical use of it.  The rest is just familiarity.

I’m a big fan of the concept of scientific notation as a means of easily being able to think about numbers of any magnitude from very large to very small.  But perhaps one of the reasons for its lack of widespread adoption is that the accepted way of writing, and especially of pronouncing, standard notation are very unfamiliar and too ‘nerdy’ sounding for most people (e.g. ‘Five point two three seven times ten to the power of eight’).  This is necessary in the scientific world because there is a need to be able to ‘translate’ from scientific notation to decimal and back.  There is an inherent need in most situations for the number represented to refer to an entity that is counted or measured.  Anybody using it therefore needs to have enough of an understanding of mathematics to be able to do the 'translation'.

But this is not the case when it comes to Bitcoin because underlying the ‘quantities’ of Bitcoin is ‘merely’ a lump of distributed encrypted code.  The unit chosen to launch Bitcoin into the world was one Bitcoin but it is in the long term just a reference point to be divided or multiplied to the extent required.  As far as I can see it what counts for Bitcoin is relative value so as long as the relationship between two numbers is understood the need to write or even to think of a number as x followed by y zeroes or zero point y zeroes followed by z becomes unnecessary.

If Bitcoin use is to become widespread and its value to increase such that ‘quantities’ exchanged for most goods and services are in micro or milibitcoin there’s no way of getting away from a need for users to think about numbers of different magnitudes than what they’re used to.  So why not abandon the need for all the different denominations and instead use something entirely new.  

I have provisionally chosen an arbitrary tiny divisor that should (for the foreseeable future) negate the need for negative exponents so the idea of positive for large and negative for small numbers is something else people don’t need to get their heads around.

I’m already using it to think of and write the amount of Bitcoin I am spending, the amount I have in my wallet or in the exchange.  I’m using formulae to change it back and forth in my spreasheets and will want software (e.g. a mtgox api) to handle it.

So let me summarise my case for 'powerbitcoin':

•   No need to count digits (or use commas) to see how big or small a number is;
•   The first number you see tells you immediately the scale of the value of Bitcoin.
•   No need to agree and learn potentially confusing names and symbols (such as microbitcoin and satoshi) for denominations.
•   Expressing numbers from the immensely large to the immensely small, irrespective of the value of Bitcoin in terms of other currencies or commodities becomes really easy.
•   The length of the latter number is decided purely only on the accuracy requiring to be expressed.
•   There is no need ever to translate the numbers into decimal notation (with masses of zeroes) because with there being no entities to count, what counts is only value relative to other values.
•   Logarithm rules of adding or subtracting exponents for multiplication and division make calculations easier.
•   If the ability to use powerbitcoin notation becomes widespread maybe people will be less inclined to say stupid thing like ‘billion or trillion or whatever’ when it comes to amounts governments are borrowing/printing etc.  In these matters size matters (/rant)

OK, so maybe I’m not the one to present the case against but disadvantages as far as I can see them are:

It’s brand new and totally unfamiliar;
It may require more of an understanding of mathematics by users than I am currently thinking;
Its use in spreadsheets and other software requires a formula or function for conversion in order to do calculations;
It may be a while before we can buy a calculator for use of Power Bitcoin (but there’s no reason not to have a ^BTC calculator app for smartphone);
If this became a 'meme' and powercoin was common parlance on the forums it would make Bitcoin look even more nerdy to your average folk than it already does!

Initial thoughts?
 
Edit:   Doh!  I just realised I got 'exponent' and 'significand' the wrong way round!  Corrected 

[knight22]

Way to much complicated for a majority of people.

Here a related topic: https://bitcointalk.org/index.php?topic=109851.0

[deepceleron]

People don't think in logarithms. They won't know how much to send to buy 5 items at 20 whatever-the-fuck-BTC. Bitcoin is already established, 1 BTC was 1 BTC at 1/10000 the current value and still will be 1 BTC in the future.

[Stephen Gornick]

Just as people know the difference between a dollar and a cent, they'll be able to figure out the difference between a bitcoin and a millibit.

BTC   - bitcoin,
mBTC - millibitcoin (0.001 BTC) nickname "Millie"/"millibits"
μBTC - microbitcoin (0.000001 BTC) nickname "Mike"/"mikeys"

 - http://en.bitcoin.it/wiki/Units

[ninjanips]

Just as people know the difference between a dollar and a cent, they'll be able to figure out the difference between a bitcoin and a millibit.

BTC   - bitcoin,
mBTC - millibitcoin (0.001 BTC) nickname "Millie"/"millibits"
μBTC - microbitcoin (0.000001 BTC) nickname "Mike"/"mikeys"

 - http://en.bitcoin.it/wiki/Units

This seems to be the standard already in place, atleast by wallet software.

[thoughtfan]

Appreciate your feedback folks.

Not quite ready to let go of the idea yet but plenty food for thought.  At least I aired it and it was read by thinking people.  Thank you.

[pgibson]

I'm a little upset myself at the dogma of the current units in place.
I made a primitive spreadsheet to look at the binary "bits" so to say, but I admit I don't have a practical solution to the problem I see of the units mis-representing the actual value these coins hold.
I suppose one can patch their favorite client to allow different units in the GUI, but it's all the same in the blockchain. Representation is a social issue. It's too bad there's no "metric vs Imperial" battle here, choices make it alot easier for people to accept the existing institution

http://pgibson.sdf.org/binarylook.xlsx

[thoughtfan]

@pgibson

I'm a little upset myself at the dogma of the current units in place...

I can not comment on your experience but based on what I've read so far 'dogma' seems a bit strong.  However, I have to admit to being slightly bemused as I read related material that some people come across a little protective of the status quo when it comes to Bitcoin units and their naming.

The reason for my bemusement is the idea of anything (other than the code itself) being 'established' - especially in an 'always has and always will' kind of way - considering how potentially early we are in the history of Bitcoin.  If demand and frequency of transactions is to reach a stage such that trade in the smaller 'denominations' are commonplace the number of Bitcoin users today will be dwarfed as a proportion of the whole.  So whilst I wasn't in the Bitcoin community early enough to be in on the discussion when 'it was decided' what the nomenculture of subdivisions should be, regardless of what the consensus among the current active members may be, could it be somewhat premature to be closing doors to other options?

Having said all this my guess is that for most it's nothing like dogma at all, rather having thought it through many have concluded and will remain convinced unless persuaded otherwise, that the way it is is also the way forward.  That is to be expected.

To me though, and given your response and the link knight22 kindly posted, I'm not alone in thinking the fact that the current 'language of representation' of Bitcoin is not 'hardwired' into Bitcoin in its native format opens the field wide open in terms of how we represent it, talk about it and most importantly, think about it.  It's a big neon sign that says: 'New Paradigms This Way'!  It's too big an opportunity in my eyes to be satisfied with a slight variation on the theme of the way people have always thought about money and numbers.

But whilst part of my argument against the whole, 'mikes/millies/satoshies' thing is that it is a wasted opportunity it is not either similar enough to what people are used to to take on board without having to think differently.  And if users are going to have to think differently anyway, why not do so in a way that is going to serve them better in terms of more of a grasp of quantities of money, from the vast to the tiny?  The thing is my guess is most people might be able to imagine a tenth of a penny/cent or whatever from the currency with which they're familiar but beyond that?  Whatever currency we look at (since decimalisation in the 70s in the UK) there's a primary unit and a secondary unit one hundredth of the size.  That's it.  If ever there was a need to go smaller it's long past now to the vast majority of users of most currencies with the inflation that's inherent to fiat currencies.  The only numbers outside of common usage  are large ones (typically those beyond the value of their home) and as I alluded to earlier, politicians can get away with all kinds of outrageous financial behaviour simply because most people don't get and don't care about the difference for instance between a billion and ten billion.  As for numbers less than one I hope I am not underestimating the intelligence of the general populace when I guess that the vast majority, at the rare times they actually think of numbers smaller than one, just think of them simply them as 'small'.  Smaller numbers, even the denominations nowhere near as small as the satoshi, are totally unfamiliar territory to the majority.  I don't see that giving the denominations friendly names  (whilst having to know the relationships between them) overcomes this problem.

As an aside I have a theory people are a lot less frugal with their money when it's so easy to be dismissive of smaller amounts of money as 'not much money'.  If the money one possesses or handles was seen as a sliding logarithmic scale there may be a higher tendency for people not to think 'wastefully' about it according to denomination.

So that's why I'd like to see something along the lines of my 'power bitcoin' suggestion become popular.

What I have said above however says nothing about the challenges that have been raised about my proposal.

First I'd like to address 'people don't think in logarithms'.  This I can not deny.  It is (or rather the associated inability to deal with all but a small range of numbers) is one of the symptoms of an innumerate society as put forward by John Allen Paulos in his book 'Innumeracy'.  There is no denying, as deepceleron says above, that calculating the price of '5 items at 20 whatever-the-fuck-BTC' is easier than the same with logarithm.  But this is only true for as long as people are only having to consider one or two denominations.  If houses, cars and cans of beans are each in their own denomination; if all (or most) of these denominations are less than one Bitcoin and if the relationship between these denominations have to be learned, remembered and be borne in mind to get an idea of the scale of money being talked about, again, I can't see this as being a simpler solution.

How do most people calculate the price of buying 5 items @ £/$ 80, 800 or 8,000 each?  Don't they lose the zeroes, do the sum then add the zeroes back in?  Likewise (for those who can do it) for 5 items @ 0.00008 BTC each to get to 0.0004?  Is it really more difficult, in the case of the latter, to multiply 5 items by 16.8 ^BTC to get 17.4?

If these kinds of mental calculations required an understanding of the mathematics that underlies it (going by how few know how to square or cube a number) I think I'd be onto a non-starter.  But you don't need to be able to add ten to the power of whatever to the number in order use this notation (at least you don't need to know that that's what you're doing).  What I'm saying is I'm not buying the 'too complicated' argument.

But maybe theorising about perceived difficulty among the general population is a bit of a waste of time.  Maybe I could do some initial research with my friends and family see how they get on.

As for favourite clients and GUIs this is one of the beauties of an idea such as this in that it's not a big deal if a few like the idea to have someone write some code and to be able to put it to work.  It doesn't matter in a couple of years whether it's 99% or 1% of users still thinking of all quantities in relation to One Bitcoin.  'Power Bitcoin' might become and remain a niche ultra-geek hobby or could ride a meme-wave and if found to be of general value, even break onto the shores of other currencies and larger (and smaller) numbers in the wider world.

Anyone game on having a go?

[thenixedreport]

I have no problem with the current way btc is handled (millibitcoin, etc....).

[bitcoinbear]

Something along these lines may well have already been proposed and if it has, please direct me to the thread.  However, there's always a chance this is actually a new and revolutionary idea .

Introducing 'powerbitcoin' (^BTC) ...

1 BTC = 21.1 ^BTC
half a Bitcoin = 20.5 ^BTC
quarter of a Bitcoin = 20.25 ^BTC (pronounced 'twenty dot two five powerbitcoin')
21 million BTC = 28.21  ^BTC
1 satoshi = 13.1 ^BTC

Ok, this sorta makes sense to me, but I am not seeing where the first part of the number comes from? Why is the range from 13.1 ^BTC to 28.2099999999999999 ^BTC?

Why not use the satoshi as the base, then the range would be from 1.1 ^BTC to 15.21 ^BTC, with 1.00 BTC = 8.100 ^BTC?

If I understand correctly, 1 USD is about 19.94 ^BTC right now?

When comparing prices, can you do things like: 1 USD was selling for 20.100 ^btc the other day, but now it is down to 20.094 ^btc?

[casascius]

I have an idea, why don't we just count bitcoins using the tonal number system.  It's way easier and more pure.

Read more http://en.wikipedia.org/wiki/Tonal_System

After reading it, read it again http://en.wikipedia.org/wiki/Tonal_System

And again http://en.wikipedia.org/wiki/Tonal_System

[thoughtfan]

I have no problem with the current way btc is handled (millibitcoin, etc....).

... as I guess it would not be a problem for a good majority of those already using Bitcoin.  Good job really!  It would be a shame if waiting on consensus for an alternative would hold up the project

As things are though, I see no reason to stop looking at other options.

[thoughtfan]

@ bitcoinbear

Ok, this sorta makes sense to me, but I am not seeing where the first part of the number comes from? Why is the range from 13.1 ^BTC to 28.2099999999999999 ^BTC?

It's arbitrary!  Considerations include:

I have read somewhere that the Bitcoin code has already built in the means of subdividing the 'satoshi' by another 10^8 and in order to accommodate that I considered 16.1 ^btc as the smallest representation of 1 btc.  But then adding 'just' another potential 5 orders of magnitude gives it even more potential (calculations might be done on  for example prices per unit using numbers smaller than the minimum transaction unit as they are with fractions of cents/pennies these days).  It means for the foreseeable future even the tiniest bitcoin decimal still do not require the basic ^btc unit to be anything other than an integer thereby avoiding the potentially confusing need to use negative exponents (the bit preceding the dot)*.

Why 21.1 ^btc for one?  I sort-of like it.  Thinking about it there may be a personal history thing there because I used to be useless at my times tables and 3x7 happened to be one of the few I could remember and I think as a consequence I have an emotional attachment to the number 21   Of course I have no authority here in saying 'THIS IS WHAT IS' and would be quite happy see that change if justification (or preference by a number of others) were to come forward.

Why not use the satoshi as the base, then the range would be from 1.1 ^BTC to 15.21 ^BTC, with 1.00 BTC = 8.100 ^BTC?

I will admit to this looking tidier!  But first I wanted the system to accommodate the 'next subdivision' (should that happen).  I think having a two digit exponent for the denominations currently in use starting around the 20 mark (if only slightly) would help with visual differentiation from numbers expressed in decimal.  Again, I have nothing substantive to support this.  The third reason (though 'reason' is a grand word for my train of thought on this aspect of it!) is almost to make the point that it doesn't matter because it is not the intention that people using 'power bitcoin' notation need ever to translate it in terms of the ultimate number of minsicule units being referred to.  As long as the 'conversion' back and forth from normal bitcoin notation is easy then that's enough as far as I can see.

If I understand correctly, 1 USD is about 19.94 ^BTC right now?

Yup, you got it

When comparing prices, can you do things like: 1 USD was selling for 20.100 ^btc the other day, but now it is down to 20.094 ^btc?

I can't see why not.  And now that you've brought it up I why not leave flexibility in software so people can set their preference either to 'normalise' after every calculation (losing preceding zeroes) or to keep a bunch of calculations using a single exponent until reset manually.  Likewise with a preference to put in trailing zeroes (as you did with 20.100) if it helps.

Thanks all for your feedback by the way.  Whether this idea fizzles out when people stop posting to this thread or if it actually gains momentum is less important to me than the fun I'm having thinking it through and having others think it through and letting me know what you think.  As they say in London, Nice one

Tf

* I don't know whether it would be best to stick with the formal descriptors of 'exponent' for the number before the dot and 'significand' for the number after or to think up something more snappy - I have no preference.  Again I don't really have a preference between putting it at the beginning - e.g. -21.1 though I guess it would be more correct to use 21.-1  (both meaning minus 1 btc).  The latter looks a bit strange but I don't know.  Thoughts?

[thoughtfan]

I have an idea, why don't we just count bitcoins using the tonal number system.  It's way easier and more pure.

Read more http://en.wikipedia.org/wiki/Tonal_System

After reading it, read it again http://en.wikipedia.org/wiki/Tonal_System

And again http://en.wikipedia.org/wiki/Tonal_System

Thanks for the link casascius.  I've always had respect for those who think: "Why not put to one side everything that's been and see if something better can be had by starting anew?" (Why do you think I'm attracted to the concept Bitcoin )

Also, I enjoyed binary in school and still think hex is really neat.  In a way it's a shame we weren't evolved with eight fingers on each hand!

I guess by 'more pure' you mean it is a closer representation of the underlying bits?  I can see that it would be easier in terms of relating to the bits.  But that is taken care of by the software so I'm afraid I can't see how it helps in that respect.

I see the advantage of having the additional 6 units before needing to add a column meaning we can get to much larger numbers without anywhere near as many zeroes.  But I don't see how it's easier in terms of either usage - mental arithmetic in hex not being something most of us are used to - nor in terms of adoption (hex being rarely used nor understood outside of programming).  And it still doesn't get us away from the issue, on the assumption that Bitcoin gets reasonably widely adopted, that the vast majority of transactions will be in numbers smaller than one.

It may be that I just can't see the advantage because I'm too invested in my idea so if you would indulge me by elaborating on the pros of adopting a base-16 system I'm more than willing to listen

[bitcoinbear]

When comparing prices, can you do things like: 1 USD was selling for 20.100 ^btc the other day, but now it is down to 20.094 ^btc?

I can't see why not.  And now that you've brought it up I why not leave flexibility in software so people can set their preference either to 'normalise' after every calculation (losing preceding zeroes) or to keep a bunch of calculations using a single exponent until reset manually.  Likewise with a preference to put in trailing zeroes (as you did with 20.100) if it helps.

So it makes sense that if you go down from 19.100 you go to 19.099, but what if you go up? 18.99 + 18.01 --> 19.100, you can't keep 18 as the exponent.

Hrmm, I think having the dot makes it look too much like a regular decimal. Maybe you could use a different separator in your notation, like 'x' or '#', or ';' or something:

1.00 btc = 21x100 ^btc  -  18x9 ^btc + 18x1 ^btc = 19x10 ^btc
1.00 btc = 21#100 ^btc  -  18#99 ^btc + 17#1 ^btc = 19#10 ^btc
1.00 btc = 21;100 ^btc  -  18;09 ^btc + 18;1 ^btc = 18;19 ^btc

For subtracting (or using a negative number) you should put the - before the exponent, to be more clear you could add parenthesis:
21.10 ^btc - (21.10 ^btc) = 21.0 ^btc

Wait, have we determined how to represent 0 in this system? would it be 0.0 ^btc? or just 0 ^btc?

[Ryland R. Taylor-Almanza]

People don't think in logarithms.

Are you sure about that? http://www.huffingtonpost.com/ben-thomas/whats-halfway-between-1-and-9-kids-and-scientists-say-3_b_1982920.html

[thoughtfan]

So it makes sense that if you go down from 19.100 you go to 19.099, but what if you go up? 18.99 + 18.01 --> 19.100, you can't keep 18 as the exponent.

Well spotted sire

I think the simplest solution would be for people to be get used to handling more than one exponent at a time.  I'm not sure if it's too much of an ask though (again getting me back to taking this idea out there for real-world responses).  It's true if not set for auto-normalisation the exponent would have to be bumped up by one - and if the preference was set to only work with one exponent at a time the others in the equation/formula could be converted too.

Hrmm, I think having the dot makes it look too much like a regular decimal. Maybe you could use a different separator in your notation, like 'x' or '#', or ';' or something:

1.00 btc = 21x100 ^btc  -  18x9 ^btc + 18x1 ^btc = 19x10 ^btc
1.00 btc = 21#100 ^btc  -  18#99 ^btc + 17#1 ^btc = 19#10 ^btc
1.00 btc = 21;100 ^btc  -  18;09 ^btc + 18;1 ^btc = 18;19 ^btc

One of the things I like about the way I've proposed it is that it does indeed look like a decimal, the ^ being the sole marker.  I'm not saying I'd defend that position till the death if differentiation at the risk of feeling 'weird' was deemed to be a higher value than familiarity at the risk of confusion.  I'm not at first glance however enamoured by any of the three you've proposed:  The 'x' looks like a multiplication; the '#' is widely used in the US to denote a number in a list and the ';' is too easily confused with a ':' which means (especially with the numbers we're talking about) looks like the time in 24 hr clock.

Not that I'm intending to be dismissive but I'm not persuaded yet.

Wait, have we determined how to represent 0 in this system? would it be 0.0 ^btc? or just 0 ^btc?

I certainly hadn't.  Do you have a preference?  Couldn't people use either interchangeably?

[Stephen Gornick]

I have an idea, why don't we just count bitcoins using the tonal number system.  It's way easier and more pure.

[...]
Thanks for the link casascius.  I've always had respect for those who think:

I think he was baiting you.  This isn't the first time Bitcoiners have heard of Tonal Bitcoin.  It, um ...,  it ...   well ..., um., , I guess we're just not ready for such advanced thinking.

 - http://en.bitcoin.it/wiki/Tonal_Bitcoin

[bitcoinbear]

One of the things I like about the way I've proposed it is that it does indeed look like a decimal, the ^ being the sole marker.  I'm not saying I'd defend that position till the death if differentiation at the risk of feeling 'weird' was deemed to be a higher value than familiarity at the risk of confusion.  I'm not at first glance however enamoured by any of the three you've proposed:  The 'x' looks like a multiplication; the '#' is widely used in the US to denote a number in a list and the ';' is too easily confused with a ':' which means (especially with the numbers we're talking about) looks like the time in 24 hr clock.

I think it is important to make it just different enough that people do not confuse it. 19.10 btc is very different from 19.01 ^btc.

How about something like ²¹100 ^btc = 1.00 btc, so ²⁰5 is a cheap pizza, ¹⁹94 is a USD, etc?

[thoughtfan]

I think he was baiting you.  This isn't the first time Bitcoiners have heard of Tonal Bitcoin.  It, um ...,  it ...   um., .. well, I guess we're just not ready for such advanced thinking.

 - http://en.bitcoin.it/wiki/Tonal_Bitcoin

Fair cop guv   Consider me baited!  Thanks for pointing it out Stephen.  I had kinda guessed that was the case but as a general principle tend to prefer (especially as a newby) to tread as on eggshells and respond accordingly rather than to presume.  Also I was too excited about my take on this to research further into the Tonal angle right now so I appreciate the link.  As I said at the top of the OP I'm quite happy to be pointed to stuff showing how far behind the curve I am.  I'd rather that than feel obliged to digest the whole of the bitcointalk archive before feeling qualified to stick my neck out.

As for the 'advanced thinking' thing, I had not intended to imply I consider myself more 'advanced' than you folks here and I apologise if I came over that way.  One of the attractions for me is in 'being around' people from whom I can learn.  The 'need' I see for something along the lines of the 'power bitcoin' arises out of my personal preference for making life easier than having to count the number of zeroes (whether before or after the decimal point) to find out how big or small a number is.  And if I with my barely passable understanding of logarithmic and exponential principles could do with something simpler, couldn't the general public too?  Hence my 'offering'.

I won't stifle my creativity on the assumption that nothing I come up with is likely to be groundbreaking.  If only one in a thousand of my ideas actually ends up contributing something of substantial value won't it have been worth you putting up with my ramblings in the meantime?

Edit:  Since writing this I have seen from here that casascius is* one who sees bringing Tonal to Bitcoin as 'polluting' and as detrimental to the overall Bitcoin project.  My guess therefore is that he also might not be the most welcoming of the 'power bitcoin' idea.  Can't win 'em all!

* ...or was in early 2011.  I'd rather people didn't assume my point of view on anything is immovable and therefore won't assume the same of others.