24 replies to this topic

[JonesGuy]

I remember there was a thread regarding percentages.

These percentages were commenting that if one can reduce the risk of dying by a certain rate, then it would be theoretically possible to live forever.

Could someone please describe the math involved? I find that I don't intuitively understand it, so I'm not able to explain it well.

[jaydfox]

I'm busy at the moment, but if no one has answered this in the next couple hours, I'll post links to past discussions of the math involved (posts by myself, Aubrey de Grey, and others).

[jaydfox]

Here is one from Aubrey with some beautiful math:
http://www.imminst.o...t=20#entry38728

Here's an objection raised later in that thread that I think is a correct objection, at least on principle:
http://www.imminst.o...t=80#entry39422

But I find a very strong answer to that objection in the following post (this post is in different thread, but if you read it, you'll find it answers tiresias's objection):
http://www.imminst.o...952

And probably read this whole next thread here, at least the first few posts and then my first few posts: there's a lot of good math, especially from me, spiced up with my being quite arrogant with someone who tried to make a blanket statement that immortality is impossible (when what he may have meant to say is that it is very improbable. Besides, it was in the Free Speech Forum. It's a shame so much good stuff is trapped in there...):
http://www.imminst.o...T&f=137&t=4697

It seems to me that there should be other good gems out there in the forum, from at least a year and a half ago, i.e. from before I joined ImmInst. I vaguely remember reading some posts that explained the asymptotic probability of living forever, but it's hard to search for them with Google. A more intelligent data miner would be necessary, one that can be even rudimentarily intelligent.

[JonesGuy]

Thanks! I'll read it soon.

[olaf.larsson]

If you live "for ever", I would say you will not have to die at a specific age, becouse you dont loose fitness with age. Even if you live "for ever" there could a big chance that you will die somehow anyway, by an accident for example.

[jaydfox]

If you live "for ever", I would say you will not have to die at a specific age, becouse you dont loose fitness with age. Even if you live "for ever" there could  a big chance that you will die somehow anyway, by an accident for example.

Well, in the short term that seems to be the case. In the long term, accident rates can be reduced so low, and we can have such a sustainable progress in lowering accidental death rates, murder rates, suicide rates, and even politically-induced homicides (wars, terrorism, etc.), that we could make the claim that we'll probably never die. By "probably never", I mean that there will come a time, somewhere between 75 and 500 years from now, when most people alive will have better odds of living forever than of picking the winning number in a game of roullette (1 in 38). The 75 year figure assumes the Singularity is driven by a "Friendly" AI, and that the AI becomes powerful enough to prevent wars, terrorism, etc., and start massive emigration from earth. If the route of the Singularity is through computer-enhanced humans, then the war and terroism variables remain, so I've hedged my bet with the 500-year figure. I seriously doubt it'll take that long before we've reached immortality escape velocity. (I say "immortality" escape velocity, as opposed to "longevity" escape velocity, for good reason. I'll be discussing the math and the distinctions in my blog in the coming week or two, depending on how long it takes to draft the articles.)

In fact, probably less than a thousand years from now, if you're still alive, your odds of living forever are probably going to be better than 1 in 4. That includes all risks of death: disease, war, terrorism, murder, accidents, suicide, heat death, etc. (Note, we just don't know whether heat death will be a problem, so the best we can do is assign a probability to it, and this point, given how little we know, we must assume a rather high probability that we'll overcome heat death. But yes, if you're concerned, we can factor the probability of heat death into this 1 in 4 figure.)

The trick is living until then. And the first step to that is either a Friendly AI-driven Singularity, or accomplishment of some version of SENS/neoSENS in humans.

[JonesGuy]

Jay, thanks for digging these up for me. I was trying to explain it to someone, but hadn't thought it through enough to be able to defend the position well. Thanks to your efforts, after 15 minutes of reading, I'm well prepared again.

[Clifford Greenblatt]

For a personal life span to be infinite within nature, the size of the person would have to grow without bound. If a person's size has a finite limit, then there is some absolute minimum, nonzero rate of annihilation. That absolute minimum rate would determine an absolute maximum half life for the person. With unbounded growth, the person could have sufficient redundancy to recover from any partial loss. However, unbounded growth presents very tricky challenges. How can remote parts of a person communicate with each other if communication is limited by the speed of light? If the unbounded person is too dense, then the person collapses into a black hole and cannot survive. Possibilities of expanding into new universes through wormholes are highly speculative. These involve speculations about the possibility of negative energy to stabilise wormholes. I do not know whether anyone has done a rigourous mathematical treatment on the thermodynamic limitations of a person expanding into new universes, if granted an assumption of the stable wormhole could be produced.

[jaydfox]

Possibilities of expanding into new universes through wormholes are highly speculative.

Again, this is a probability issue which we can factor into one's probability of living forever.

Also, regarding infinite growth. The person's growth rate would have a minimum bound of a linear increase in the number of possible states, which translates into a (roughly) logarithmic growth in size. So long as the universe doesn't stop expanding, it's easily within reason that its growth rate will exceed a logarithmic growth rate, and hence there will be plenty of room. Remote commucation between parts of a self presents practical limits on quality of life, but otherwise doesn't affect the original argument. The main limitation I still see is heat death.

[JonesGuy]

And heat death is certainly not proven.

Jay, thanks again, and for that article you wrote about this topic. I've used the same maths with regarding to immortal tyranny, to show that it's possible to remain a tyrant forever, as long as the risk of being overthrown was reduced over time.

[Clifford Greenblatt]

Can you imagine your head someday becoming bigger than the Earth?
Can you imagine your head someday becoming bigger than the solar system?
Can you imagine your head someday becoming bigger than the galaxy?
Can you imagine your head someday becoming bigger than the present known universe?
Can you imagine your head someday becoming 10^(10^(10^(10^(10^(10^10))))) times bigger than the present known universe?
Can you imagine your head someday becoming 10^(10^(10^(10^(10^(10^10))))) bigger than that?

[Clifford Greenblatt]

I find it difficult to fully imagine, but the limits of my imagination don't necessarily represent the limits of physical possibility in this universe and beyond. If the questions are rhetorical, intended to illustrate the apparent absurdity of the speculation, then I probably shouldn't be surprised by the reaction.

The question is not necessarily rhetorical. It is an essential question to sort through when considering an infinite life span. Most life extension discussions, understandably, do not go this far, because life extension technology for the near future is a prerequisite to life extension technology for the far future. However, unbounded personal growth issues become essential for life extension in the far distant future, in which most immortalists desire to participate. It would take an advanced physicist, such as Brian W., to even begin to sort through such a big question.

[jaydfox]

Can you imagine your head someday becoming bigger than the Earth?
Can you imagine your head someday becoming bigger than the solar system?
Can you imagine your head someday becoming bigger than the galaxy?
Can you imagine your head someday becoming bigger than the present known universe?
Can you imagine your head someday becoming 10^(10^(10^(10^(10^(10^10))))) times bigger than the present known universe?
Can you imagine your head someday becoming 10^(10^(10^(10^(10^(10^10))))) bigger than that?

Yes, the numbers are large. And yes, they're just a drop in the bucket compared to how big they'll really get.

However, my point about a logarithmic lower limit on expansion rate should help illustrate that growth can be curbed to such an extent that one can prevent one's self from growing more than an arbitrary amount, e.g. 1 meter, in the time it takes to communicate between opposite extents of one's self. In fact, such would simply be a growth rate inversely proportional to time, which if integrated for radius would give such a logarithmic growth rate.

The fact that growth rate can be limited to a fixed increase in radius per whatever amount of time it takes for communication to cross one's self should give us hope that the system can grow in a controlled manner (i.e. that opposite sides do not grow terribly unruly). Of course, with a linear increase in state-space, the "lifestyle" of such a being isn't going to be terribly impressive. One can overcome this limitation by exceeding the logarithmic growth rate, which as I said was really just a lower bound. A plausible upper bound limitation would be constant linear growth, or cubic growth in mass or volume. However, this latter approach clearly depends on being able to maintain a minimum growth rate of the universe (which seems possible, perhaps even likely with currently known physics, i.e. accelerating expasion).

[jaydfox]

However, my point about a logarithmic lower limit on expansion rate should help illustrate that growth can be curbed to such an extent that one can prevent one's self from growing more than an arbitrary amount, e.g. 1 meter, in the time it takes to communicate between opposite extents of one's self. In fact, such would simply be a growth rate inversely proportional to time, which if integrated for radius would give such a logarithmic growth rate.

During my morning commute, I realized I had the math wrong here. What I described is a growth rate inversely proportional to diameter, not time.

Consider:
dy/dt = a
-- linear growth

dy/dt = at
-- quadratic growth

dy/dt = ay
-- exponential growth

Now, on the flipside:
dy/dt = 1/a
-- linear growth

dy/dt = 1/at
-- logarithmic growth

dy/dt = 1/ay
-- pseudo-logarithmic growth.

By pseudologarithmic, consider a simple case: discrete math, initial conditions t=1, y=1

Using the logarithmic approach (dy/dt = 1/at), we get:
At t=1, y=1, dy/dt=1
At t=2, y=2, dy/dt=1/2
At t=3, y=2.5, dy/dt=1/3
At t=4, y=2.833, dy/dt=1/4
At t=5, y=3.083, dy/dt=1/5
At t=n, y~=ln(n)+1.5, dy/dt=1/n

Using the pseudo-logarithmic approach (dy/dt = 1/ay), we get:
At t=1, y=1, dy/dt=1
At t=2, y=2, dy/dt=1/2
At t=4, y=3, dy/dt=1/3
At t=7, y=4, dy/dt=1/4
At t=11, y=5, dy/dt=1/n
At t=n(n-1)/2 + 1, y=n, dy/dt=1/n

As you can see, this is actually greater than logarithmic, because the growth rate is maintained for a longer period of time before decreasing by a given percentage/fraction. Anyway, it's still sub-linear. Just an interesting mathematical side note.

Edit: italicized "time" in leading blockquote, addressed the time versus diameter issue in the first unquoted paragraph, and added "pseudo-" to the line "Using the pseudo-logarithmic approach (dy/dt = 1/ay), we get:".

Edited by jaydfox, 20 February 2006 - 05:52 PM.

[Clifford Greenblatt]

Does anyone know about any estimates on the rate at which total mass in the universe is increasing? Increase in volume alone cannot satisfy the need for unbounded personal growth. The total mass of the universe must grow without bound and it must grow at a sufficient rate to permit the possibility of preventing the personal survival probability from vanishing with time.

OTOH, the possibility of negative mass could solve the total mass problem and also permit extremely high concentration of particles without collapse into a black hole. However, the possibility of negative mass or negative energy is extremely speculative and the manufacture of it within the universe may present some thermodynamic impossibilities.

[JonesGuy]

Is there an official essay on this topic? The essay at longevitymeme doesn't not seem to go into the math in detail (unless I can't find the link).

I'm finding the argument to be very useful.

[jaydfox]

I don't think there's an essay on it. I want to write one, but I haven't had the time lately, being busy with ImmInst-related business (and not just the LM situation).

If I get time in the months ahead, I plan to write something up that addresses the math as well as the implications. It'd probably be something worth being co-authored, as I'm mostly interested in the math and probably not eloquent enough to do justice to the philosophical side of things. It would be quite geeky if I wrote it alone. [glasses]

[JonesGuy]

Okay, I'll link to the other threads mentioned then. Thanks.

[lunarsolarpower]

Several ideas I came up with thinking about this. Really you don't need to increase in connected volume to continually decrease your odds of total destruction. Once you've managed to turn yourself into an internet-like entity, you simply have to make the many nodes continue to occupy more diverse regions of the space/quantum vacuum available to them. Now the difficulty comes in dealing with the limitations of transmitting data between nodes at speeds <= c. It seems that consciousness could be split into two elements. One, that would operate at the individual node would be extremely fast. Given sufficient resources, it could be a dozen or more orders of magnitude faster than current mental processing. The second would be the eternal part of the consciousness. This would be the connection between the nodes that were ever growing farther away from each other. It would have a sense of time that would compare to our current concept in the same way that a meter stick compares to Planck's length. What sort of experiences an entity such as this would have is something I don't think we can even pretend to fathom. At each node it would seem to be living a complete existance as an entity. However on a higher meta level, a whole other level of understanding and experience would be taking place.

[Live Forever]

lunar, I think that faster than light communication might indeed be possible. It has to do with the Heisenberg uncertainty principle, and how partcles that interact with each other can communicate "instantaneously" with each other.

Of course, I could be totally off base, but I seem to remember reading something about it awhile back.




Edit: Ok, I did a google search, and came up with this (3 page) article that lays it out:
http://www.physicspo...leId=213&page=1

Here is some more on the Heisenberg uncertainty priciple and how it could be used for FTL communication:
http://www.seti.org/...94993&ct=295500


Edit #2: Also, here are a list of several (21) possible ways to have faster than light travel/communication:
http://math.ucr.edu/...fLight/FTL.html

Edited by liveforever22, 31 March 2006 - 01:57 AM.

[jaydfox]

In theory, such FTL interactions do occur, and IIRC, they have been verified. However, no one has devised a means of detecting the interactions as anything other than random noise, since part of the information required to confirm the effect cannot propogate faster than the speed of light. [sad]