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You do realize your mathematical problem here, yes?

Start with one universe and 1 portal. It gets turned on, two universes, both with portals.

You turn on your portal again. Four universes, all with portals. One of them activates. Eight universes. Two of them are turned on one right after the other. Thirty-two universes. Three of them turn on portals. Now 256 universes, all with portals. Ten portals get turned on the next day: 662,144 universes. The next day is a quiet one; only 50 of those universes turn on their portals.

You're now at 2.9514 x 10²⁰ universes. How many of them decide to turn on their portals?

It doesn't matter what kind of numbering or naming system you chose; you'll very quickly realize you've run out of any kind of practical method.

ADDENDUM

Additional problem: how can you know what name your universe is? If opening a portal causes all the universes as they currently exist to duplicate exactly, then how do the "new" universes know they're new, especially if they're created as a result of someone else triggering a portal in a universe no longer connected to yours?

ADDENDUM ADDENDUM

In response to the suggestions about naming schemes:

Just for giggles, let's suppose of those 2.9514e²⁰ universes I mentioned previously, 100 activate portals. Now we're at 3.74e⁵⁰ universes. Another 100 activate: 4.74e⁸⁰ universes that require unique names. Now, bit of a problem: there's only an estimated 10⁸⁰ atoms in the universe.

How much of your universe are you dedicating to just keeping the name written down somewhere?

Let's suppose it takes a nanosecond to update record name in a universe and transmit that information on to the connected universe(s) so it knows to update its name as well and pass it on. And, to play fair, we'll only consider the 2.9514e²⁰ universes, so all of them have free atoms to actually build a computer and have memory and such. It will take about 9,359 years for information to propagate through the existing network. Which, of course, will soon reach the heat death of the universe to let everyone one that another portal opened somewhere and the name changed. Again. And doesn't take into account any time needed for coin flips.

And that's passing information from one universe to another in a nanosecond. A time span in which light will move in a vacuum about 30 centimeters.

You do realize your mathematical problem here, yes?

Start with one universe and 1 portal. It gets turned on, two universes, both with portals.

You turn on your portal again. Four universes, all with portals. One of them activates. Eight universes. Two of them are turned on one right after the other. Thirty-two universes. Three of them turn on portals. Now 256 universes, all with portals. Ten portals get turned on the next day: 662,144 universes. The next day is a quiet one; only 50 of those universes turn on their portals.

You're now at 2.9514 x 10²⁰ universes. How many of them decide to turn on their portals?

It doesn't matter what kind of numbering or naming system you chose; you'll very quickly realize you've run out of any kind of practical method.

ADDENDUM

Additional problem: how can you know what name your universe is? If opening a portal causes all the universes as they currently exist to duplicate exactly, then how do the "new" universes know they're new, especially if they're created as a result of someone else triggering a portal in a universe no longer connected to yours?

ADDENDUM ADDENDUM

In response to the suggestions about naming schemes:

Just for giggles, let's suppose of those 2.9514e²⁰ universes I mentioned previously, 100 activate portals. Now we're at 3.74e⁵⁰ universes. Another 100 activate: 4.74e⁸⁰ universes that require unique names. Now, bit of a problem: there's only an estimated 10⁸⁰ atoms in the universe. Now keep going on this process. There will come a point where the information required to store the universe's name will exceed the information available in the universe. Probably a lot sooner than you think.

How much of your universe are you dedicating to just keeping the name written down somewhere?

Let's suppose it takes a nanosecond to update record name in a universe and transmit that information on to the connected universe(s) so it knows to update its name as well and pass it on. And, to play fair, we'll only consider the 2.9514e²⁰ universes, so all of them have free atoms to actually build a computer and have memory and such. It will take about 9,359 years for information to propagate through the existing network. Which, of course, will soon reach the heat death of the universe to let everyone one that another portal opened somewhere and the name changed. Again. And doesn't take into account any time needed for coin flips.

And that's passing information from one universe to another in a nanosecond. A time span in which light will move in a vacuum about 30 centimeters.

ADDEN...whatever

The name change thing is going to create a problem on its own. Once any universe opens a portal, information has to be sent to other universes to update designations. Now imagine a situation where in any given second, there's a 1 in a trillion chance any given universe will open a portal. Which is, obviously, a very small chance.

With 3e²⁰ universes, that means that in any given second there will be on average 300 million portals opened. And you're going to get the announcement your name has changed. Three hundred million times. Per second. Now imagine what's happening the next second.

You do realize your mathematical problem here, yes?

Start with one universe and 1 portal. It gets turned on, two universes, both with portals.

You turn on your portal again. Four universes, all with portals. One of them activates. Eight universes. Two of them are turned on one right after the other. Thirty-two universes. Three of them turn on portals. Now 256 universes, all with portals. Ten portals get turned on the next day: 662,144 universes. The next day is a quiet one; only 50 of those universes turn on their portals.

You're now at 2.9514 x 10²⁰ universes. How many of them decide to turn on their portals?

It doesn't matter what kind of numbering or naming system you chose; you'll very quickly realize you've run out of any kind of practical method.

ADDENDUM

Additional problem: how can you know what name your universe is? If opening a portal causes all the universes as they currently exist to duplicate exactly, then how do the "new" universes know they're new, especially if they're created as a result of someone else triggering a portal in a universe no longer connected to yours?

You do realize your mathematical problem here, yes?

Start with one universe and 1 portal. It gets turned on, two universes, both with portals.

You turn on your portal again. Four universes, all with portals. One of them activates. Eight universes. Two of them are turned on one right after the other. Thirty-two universes. Three of them turn on portals. Now 256 universes, all with portals. Ten portals get turned on the next day: 662,144 universes. The next day is a quiet one; only 50 of those universes turn on their portals.

You're now at 2.9514 x 10²⁰ universes. How many of them decide to turn on their portals?

It doesn't matter what kind of numbering or naming system you chose; you'll very quickly realize you've run out of any kind of practical method.

ADDENDUM

Additional problem: how can you know what name your universe is? If opening a portal causes all the universes as they currently exist to duplicate exactly, then how do the "new" universes know they're new, especially if they're created as a result of someone else triggering a portal in a universe no longer connected to yours?

ADDENDUM ADDENDUM

In response to the suggestions about naming schemes:

Just for giggles, let's suppose of those 2.9514e²⁰ universes I mentioned previously, 100 activate portals. Now we're at 3.74e⁵⁰ universes. Another 100 activate: 4.74e⁸⁰ universes that require unique names. Now, bit of a problem: there's only an estimated 10⁸⁰ atoms in the universe.

How much of your universe are you dedicating to just keeping the name written down somewhere?

Let's suppose it takes a nanosecond to update record name in a universe and transmit that information on to the connected universe(s) so it knows to update its name as well and pass it on. And, to play fair, we'll only consider the 2.9514e²⁰ universes, so all of them have free atoms to actually build a computer and have memory and such. It will take about 9,359 years for information to propagate through the existing network. Which, of course, will soon reach the heat death of the universe to let everyone one that another portal opened somewhere and the name changed. Again. And doesn't take into account any time needed for coin flips.

And that's passing information from one universe to another in a nanosecond. A time span in which light will move in a vacuum about 30 centimeters.

You do realize your mathematical problem here, yes?

Start with one universe and 1 portal. It gets turned on, two universes, both with portals.

You turn on your portal again. Four universes, all with portals. One of them activates. Eight universes. Two of them are turned on one right after the other. Thirty-two universes. Three of them turn on portals. Now 256 universes, all with portals. Ten portals get turned on the next day: 662,144 universes. The next day is a quiet one; only 50 of those universes turn on their portals.

You're now at 2.9514 x 10²⁰ universes. How many of them decide to turn on their portals?

It doesn't matter what kind of numbering or naming system you chose; you'll very quickly realize you've run out of any kind of practical method.

You do realize your mathematical problem here, yes?

Start with one universe and 1 portal. It gets turned on, two universes, both with portals.

You turn on your portal again. Four universes, all with portals. One of them activates. Eight universes. Two of them are turned on one right after the other. Thirty-two universes. Three of them turn on portals. Now 256 universes, all with portals. Ten portals get turned on the next day: 662,144 universes. The next day is a quiet one; only 50 of those universes turn on their portals.

You're now at 2.9514 x 10²⁰ universes. How many of them decide to turn on their portals?

It doesn't matter what kind of numbering or naming system you chose; you'll very quickly realize you've run out of any kind of practical method.

ADDENDUM

Additional problem: how can you know what name your universe is? If opening a portal causes all the universes as they currently exist to duplicate exactly, then how do the "new" universes know they're new, especially if they're created as a result of someone else triggering a portal in a universe no longer connected to yours?