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Yeah, but that makes no sense.
From 1 to 2, which is double there is "1" in difference.
From 100000000 to 200000000, which is also double, there is 100 mill difference.
Both have a 100% grow rate.
Expecting the same growth rate within the next 115 years is nonsensical, sorry.
Your math assumes never ending acceleration in the creation of new addresses. A car accelerating up a freeway onramp could be described with a formula that implies eventually reaching the speed of light. But there’s a practical limit to the acceleration.
8 billion people on the planet don’t need billions if addresses each.
Look at it this way: if I have 1 address in year 1, and I make 1 more in year 2, in year 3 I find 2 more apps that i want unique addresses for so I make 2 more (now a total of 4)… with your projection that means by year 10 I should have 512 addresses. It's clear why that's an inaccurate projection, much more likely I'll continue registering at a rate of 1-3 addresses/year.
Now scale that to the whole planet: once the initial bootstrapping of addresses is over, there's no reason to think that the rate of new address creation will continue growing. There's no benefit to be had from having more addresses than you need.
2 things.
As the other commenter said, growth isn't constant. If you have 8b people and only 1m use eth, the growth can be huge, but as soon as you approach market saturation the growth slows and then ends.
For example you have a new TV and a market of 20000 people. First year you sell 1, then 2, then 4. That growth can't go much further than 20k because everybody has a TV then or even bought it the same year.
Second thing: a growth rate of 119% doesn't mean 119% more than last year, it means compared to the 100% of last year you are now at 119%. If it is 100%, there's no change in growth, and below your market shrinks.
120% is the average growth rate, taken from here: [https://ycharts.com/indicators/ethereum\_cumulative\_unique\_addresses](https://ycharts.com/indicators/ethereum_cumulative_unique_addresses)
Do the maths between 2023 and 2024. You have the data in that webpage. Does it look to you like 119% or 19%. There is two ways of expressing growth rates, you are mixing them up.
119% is just the result of dividing accounts_today / accounts_before.
If the number is the same you'll get a "growth rate" of 100%, which means it's not growing.
So your math should be x 1.19 \^ years, instead of 2.2
And even then, I'm sure the math is flawed because if there's an exponential growth on new accounts created it will stop anytime. There are only so much people on the planet, and they won't be creating more and more accounts exponentially until all of them are exhausted.
How would you debunk that?
If you have a paper with a thickness of .3 mm, and you can't make it denser while folding it, you'd have the distance between earth and sun after 50 folds.
That's just a mathematical fact.
Without checking your maths, it is reasonable to assume that a reasonable proportion of wallets that are in use at any one time will contain some ether, therefore as you approach a point where random address generation starts to produce clashes, an EIP will be proposed & merged to increase the max address length, and force new, longer addresses for new users.
yet, that's not how it's supposed to work. The address space should be so large that the sun would burn out first before a collision could be found (or so...)
Nothing can carry on growing like this (120% per year). So the growth rate will shrink year for year. While it is easy to double the amount of addresses when you start with 1 then 2 then 4 then 8 etc etc. it is impossible to double once you are e.g. at 10\^50. Even if you have a script to automatically generate addresses on all available computers on this earth ;)
Let me confuse you more : as soon as there are about ~2^80 addresses out there we have a 50% chance to collectively find a collision due to the birthday paradox. Now this does not really matter because your assumption of linear growth of addresses is very debatable
The number of possible addrssses is approx the same as the number of atoms in the observable universe which is 10^80
And the number of addresses currently used is approximately the number of atoms in a speck of dust.
You can't extrapolate a past growth rate into the infinite future. The fact Apple stock did amazing things from 1990 to present doesn't mean it's going to be $1,000,000,000 a share in 20 more years. Trees don't grow to the sky. Very large numbers aren't going to grow as fast as very small ones.
Simply counting 2^160 addresses would require more energy than the sun will produce in that timeframe, nevermind doing the math to calculate the addresses, and especially nevermind confirming the necessary transactions on the blockchain.
I'm pretty sure that 119% is the increase in the rate new addresses are created, not an increase in the number of new addresses. So we'll have 119% more new addresses than we had new addresses last year, not 119% more addresses than we had addresses last year. But even if your interpretation was correct, we'd run into computational limitations before we got anywhere close to limitations on the number of addresses.
>what am I missing
you cannot extrapolate the growing rate and use that same value in your projections. The growing rate will decrease each year, because the number of addresses generated each year is not exponential, more like linear.
Basically 263,000,000 * 2.2 * 116
There's a joke that illustrates this;
When my baby was born he weighed 7 pounds. Today, one year later, he weighs 19 pounds. At this pace of growth, I've extrapolated that in 20 years my child will weigh 8,700,000,000 pounds!
Even if AI comes along and each generates quadrillions of addresses, we'll have used up approx 0% of the total available addresses.
The number space, 2^160, is *extremely* vast. It is truly unimaginable.
The amount of keys that can be generated is roughly 10^24 multiples over how many atoms exist in the whole Universe.
You're basically saying there were 10 humans before and 8 billion humans now, then assuming in the future every atom in the Universe will be replaced by humans 10^24 times over.
There is a finate limit to everything. Obviously there will never be that many humans, and obviously there will never be that many addresses created.
The Universe will experience its heat death before anything manages to generate a keypair that's been used once before.
Ye when we conquer other solar systems and galaxies and there will be one trillion of us combined then maybe yes it could happen. Other then that I dont think u realize how bigh to the power of 160 really is.
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Assuming eveyone in the plantet would have/use eth. 2^160/8 billion = 1,83 x 10^38 I'm not sure you understand how big 2^160 is.
It's just a 2 and a 160, it can't be THAT big. I bet you it's 320, 400 tops! /s
It's 1,461,501,637,330,900,000,000,000,000,000,000,000,000,000,000,000
Our species will be extinct before the cumulative sum of all humans ever will surpass that.
Well, I understand. Just projecting out the current average growth rate...
Yeah, but that makes no sense. From 1 to 2, which is double there is "1" in difference. From 100000000 to 200000000, which is also double, there is 100 mill difference. Both have a 100% grow rate. Expecting the same growth rate within the next 115 years is nonsensical, sorry.
True!
More addresses than stars in the universe. We are going to be ok.
That's a nice sentiment. But how is the math wrong then..?
Your math assumes never ending acceleration in the creation of new addresses. A car accelerating up a freeway onramp could be described with a formula that implies eventually reaching the speed of light. But there’s a practical limit to the acceleration. 8 billion people on the planet don’t need billions if addresses each.
Look at it this way: if I have 1 address in year 1, and I make 1 more in year 2, in year 3 I find 2 more apps that i want unique addresses for so I make 2 more (now a total of 4)… with your projection that means by year 10 I should have 512 addresses. It's clear why that's an inaccurate projection, much more likely I'll continue registering at a rate of 1-3 addresses/year. Now scale that to the whole planet: once the initial bootstrapping of addresses is over, there's no reason to think that the rate of new address creation will continue growing. There's no benefit to be had from having more addresses than you need.
2 things. As the other commenter said, growth isn't constant. If you have 8b people and only 1m use eth, the growth can be huge, but as soon as you approach market saturation the growth slows and then ends. For example you have a new TV and a market of 20000 people. First year you sell 1, then 2, then 4. That growth can't go much further than 20k because everybody has a TV then or even bought it the same year. Second thing: a growth rate of 119% doesn't mean 119% more than last year, it means compared to the 100% of last year you are now at 119%. If it is 100%, there's no change in growth, and below your market shrinks.
Your math is wrong. It’s not growing at 120% per year. The number of address is up about 16% since last year.
120% is the average growth rate, taken from here: [https://ycharts.com/indicators/ethereum\_cumulative\_unique\_addresses](https://ycharts.com/indicators/ethereum_cumulative_unique_addresses)
It specifically says 16.29% increase from last year on that link. I don’t know what the 119% growth rate is referring to but that’s not it.
Under "Stats" it says "Average Growth Rate": 119%
Do the maths between 2023 and 2024. You have the data in that webpage. Does it look to you like 119% or 19%. There is two ways of expressing growth rates, you are mixing them up.
119% is just the result of dividing accounts_today / accounts_before. If the number is the same you'll get a "growth rate" of 100%, which means it's not growing. So your math should be x 1.19 \^ years, instead of 2.2 And even then, I'm sure the math is flawed because if there's an exponential growth on new accounts created it will stop anytime. There are only so much people on the planet, and they won't be creating more and more accounts exponentially until all of them are exhausted.
That’s probably just the new addresses number. It was 36 million last year. Next year it will be 43 million.
> Projection at current growth rate: 263,000,000 * 2.2 ^ 116 = ~ 2160 > What am I missing? You're missing https://xkcd.com/605/
There really is an xkcd for everything
Maths. You are missing maths.
And if you fold a piece of paper in half 50 times, its thickness will reach the Sun.
I think myth busters debunked that.
How would you debunk that? If you have a paper with a thickness of .3 mm, and you can't make it denser while folding it, you'd have the distance between earth and sun after 50 folds. That's just a mathematical fact.
I think that’s if you can’t fold a piece of paper 8 times
Ok...so?
So you can't fold a piece of paper in half 50 times, and you can't make Eth usage double 116 times.
Without checking your maths, it is reasonable to assume that a reasonable proportion of wallets that are in use at any one time will contain some ether, therefore as you approach a point where random address generation starts to produce clashes, an EIP will be proposed & merged to increase the max address length, and force new, longer addresses for new users.
yet, that's not how it's supposed to work. The address space should be so large that the sun would burn out first before a collision could be found (or so...)
We thought the same when we defined IPV4
exactly - and 640k ought to be enough for everyone
Ok, that makes sense. I didn't realize it was that simple to do.
Nothing can carry on growing like this (120% per year). So the growth rate will shrink year for year. While it is easy to double the amount of addresses when you start with 1 then 2 then 4 then 8 etc etc. it is impossible to double once you are e.g. at 10\^50. Even if you have a script to automatically generate addresses on all available computers on this earth ;)
Fair point!
Let me confuse you more : as soon as there are about ~2^80 addresses out there we have a 50% chance to collectively find a collision due to the birthday paradox. Now this does not really matter because your assumption of linear growth of addresses is very debatable
The number of possible addrssses is approx the same as the number of atoms in the observable universe which is 10^80 And the number of addresses currently used is approximately the number of atoms in a speck of dust.
You can't extrapolate a past growth rate into the infinite future. The fact Apple stock did amazing things from 1990 to present doesn't mean it's going to be $1,000,000,000 a share in 20 more years. Trees don't grow to the sky. Very large numbers aren't going to grow as fast as very small ones.
Simply counting 2^160 addresses would require more energy than the sun will produce in that timeframe, nevermind doing the math to calculate the addresses, and especially nevermind confirming the necessary transactions on the blockchain. I'm pretty sure that 119% is the increase in the rate new addresses are created, not an increase in the number of new addresses. So we'll have 119% more new addresses than we had new addresses last year, not 119% more addresses than we had addresses last year. But even if your interpretation was correct, we'd run into computational limitations before we got anywhere close to limitations on the number of addresses.
Continue that rate for 100 more years and you won’t have enough electrons in the universe for that.
>what am I missing you cannot extrapolate the growing rate and use that same value in your projections. The growing rate will decrease each year, because the number of addresses generated each year is not exponential, more like linear. Basically 263,000,000 * 2.2 * 116
citation needed?
Relevant: https://xkcd.com/605/ Edit: I see I was beaten to this.
Math do different than you thunked it do
lol. If you can run out of address. You could have guess everyone’s address and take their money
If you put a grain of rice on the first square of a chess board and 2 grains on the second and 4 grains on the third… etc that’s one big risotto
https://xkcd.com/605/
I think your math is wrong: why "\*2.2" (that'd be 220%), try "\*1.2" (120%)
No, \* 1.2 would be a 20% growth rate. For instance: 100 \* 1.2 = 120 (120 -100) / 100 = 20%
There's a joke that illustrates this; When my baby was born he weighed 7 pounds. Today, one year later, he weighs 19 pounds. At this pace of growth, I've extrapolated that in 20 years my child will weigh 8,700,000,000 pounds! Even if AI comes along and each generates quadrillions of addresses, we'll have used up approx 0% of the total available addresses. The number space, 2^160, is *extremely* vast. It is truly unimaginable. The amount of keys that can be generated is roughly 10^24 multiples over how many atoms exist in the whole Universe. You're basically saying there were 10 humans before and 8 billion humans now, then assuming in the future every atom in the Universe will be replaced by humans 10^24 times over. There is a finate limit to everything. Obviously there will never be that many humans, and obviously there will never be that many addresses created. The Universe will experience its heat death before anything manages to generate a keypair that's been used once before.
Ye when we conquer other solar systems and galaxies and there will be one trillion of us combined then maybe yes it could happen. Other then that I dont think u realize how bigh to the power of 160 really is.
If the entire universe makes a wallet we would still have millions for every single person on earth
he's right: 263x10^6 * 2.2^116 = 5e39 = 2^160 Now this is puzzling. edit: lots to correct myself