we see that it takes about 10^6 years to evolve a new species,

10^7 years to evolve a genus,

10^8 years to evolve a class,

10^9 years to evolve a phylum,

and less than 10^10 years to evolve all the way from the primeval slime to Homo Sapiens.

If life continues in this fashion in the future, it is impossible to set any limit to the variety of physical forms that life may assume.

What changes could occur in the next 10^10 years to rival the changes of the past?

It is conceivable that in another 10^10 years life could evolve away from flesh and blood and become embodied in an intrstellar black cloud (Hoyle, 1957) or in a sentient computer (Capek, 1923).

Here is a list of deep questions concerning the nature of life and consciousness.

(i) Is the basis of consciousness matter or structure?

These are questions that we do not know how to answer. But they are not in principle unanswerable. It is possible that they will be answered fairly soon as a result of progress in experimental biology.

Let me spell out more explicitly the meaning of question (i). My consciousness is somehow associated with a collection of organic molecules inside my head. The question is, whether the existence of my consciousness depends on the actual substance of a particular set of molecules or whether it only depends on the structure of the molecules. In other words, if I could make a copy of my brain with the same structure but using different materials, would the copy think it was me?

If the answer to question (i) is "matter", then life and consciousness can never evolve away from flesh and blood. In this case the answers to questions (ii) and (iii) are negative. Life can then continue to exist only so long as warm environments exist, with liquid water and a continuing supply of free energy to support a constant rate of metabolism. In this case, since a galaxy has only a finite supply of free energy, the duration of life is finite. As the universe expands and cools, the sources of free energy that life requires for its metabolism will ultimately be exhausted.

Since I am a philosophical optimist, I assume as a working hypothesis that the answer to question (i) is "structure". Then life is free to evolve into whatever material embodiment best suits its purposes.

The answers to questions (ii) and (iii) are affirmative, and a quantitative discussion of the future of life in the universe becomes possible. If it should happen, for example, that matter is ultimately stable against collapse into black holes only when it is subdivided into dust grains a few microns in diameter, then the preferred embodiment for life in the remote future must be something like Hoyle's black cloud, a large assemblage of dust grains carrying positive and negative charges, organizing itself and communicating with itself by means of electromagnetic forces. We cannot imagine in detail how such a cloud could maintain the state of dynamic equilibrium that we call life. But we also could not have imagined the architecture of a living cell of protoplasm if we had never seen one.

_Biological Scaling Hypothesis. If we copy a living creature, quantum state by quantum state, so that the Hamiltonian of the copy is

H_c = lambda U H U^(-1), (55)

where H is the Hamiltonian of the creature, U is a unitary oprator, and lambda is a positive scaling factor, and if the environment is similarly copied so that the temperatures of the environments of the creature and the copy are respectively T and lambda T, then the copy is alive, subjectively identical to the original creature, with all its vital functions reduced in speed by the same factor lambda._

From this point on, I assume the scaling hypothesis to be valid and examine its consequences for the potentialities of life. The first consequence is that the appropriate measure of time as experienced subjectively by a living creature is not physical time t but the quantity

u(t) = f INT(0,t) theta(t') dt', (56)

where theta(t) is the temperature of the creature and f = (300 deg sec)^(-1) is a scale factor which it is convenient to introduce so as to make u dimensionless. I call u "subjective time".

The second consequence of the scaling law is that any creature is characterized by a quantity Q which measures its rate of entropy production per unit of subjective time.

If entropy is measured in information units or bits, and if u is measured in "moments of consciousness", then Q is a pure number expressing the amount of information that must be processed in order to keep the creature alive long enough to say "Cogito, ergo sum".

I call Q the "complexity" of the creature.

For example, a human being dissipates about 200 W of power at a temperature of 300 K, with each moment of consciousness lasting about a second. A human being therefore has

Q = 10^23 bits. (57)

This Q is a measure of the complexity of the molecular structures involved in a single act of human awareness. For the human species as a whole,

Q = 10^33 bits. (58)

a number which tells us the order of magnitude of the material resources required for maintenance of an intelligent society.

A creature or a society with given Q and given temperature theta will dissipate energy at a rate

m = kfQ theta^2. (59)

Here m is the metabolic rate measured in ergs per second, k is Boltzmann's constant, and f is the coefficient appearing in (56). It is important that m varies with the square of theta, one factor theta coming from the relationship between energy and entropy, the other factor theta coming from the assumed temperature dependence of the rate of vital processes.

I am assuming that life is free to choose its temperature theta(t) so as to maximize its chances of survival. There are two physical constraints on theta(t). The first constraint is that theta(t) must always be greater than the temperature of the universal background radiation, which is the lowest temperature available for a heat sink. That is to say

theta(t) > aR^(-1), a = 3.10^28 deg cm, (60)

where R is the radius of the universe, varying with t according to (7) and (8). At the present time the condition (60) is satisfied with a factor of 100 to spare.

The second constraint on theta(t) is that a physical mechanism must exist for radiating away into space the waste heat generated by metabolism. To formulate the second constraint quantitatively, I assume that the ultimate disposal of waste heat is by radiation and that the only relevant form of radiation is electromagnetic.

There is an absolute upper limit

I(theta) < 2 gamma (Ne^2/m hbar^2 c^3) (k theta)^3 (61)

on the power that can be radiated by a material radiator containing N electrons at temperature theta. Here

gamma = max[x^3(e^x-1)^(-1)] = 1.42 (62)

is the height of the maximum of the Planck radiation spectrum. Since I could not find (61) in the textbooks, I give a quick proof, following the Handbuch article of Bethe and Saltpeter (1957). The formula for the power emitted by electric dipole radiation is

I(theta) = SUM(p) INT dOmega SUM(i,j) rho_i (omega_ij^4/2.pi.c^3) |D_ij|^2. (63)

Here p is the polarization vector of a photon emitted into the solid angle dOmega, i is the initial and j the final state of the radiator,

rho_i = Z^(-1) exp(-E_i/k theta) (64)

is the probability that the radiator is initially in state i,

omega_ij = hbar^(-1) (E_i - E_j) (65)

is the frequency of the photon, and D_ij is the matrix element of the radiator dipole moment between states i and j. The sum (63) is taken only over pairs of states (i,j) with

E_i > E_j. (66)

Now there is an exact sum rule for dipole moments,

SUM(i) omega_ij |D_ij|^2 = (1/2i) _jj = (N e^2 hbar / 2m). (67)

But we have to be careful in using (67) to find a bound for (63), since some of the terms in (67) are negative. The following trick works. In every term of (63), omega_ij is positive by (66), and so (62) gives

rho_i omega_ij^3 < gamma rho_i (k theta/hbar)^3 (exp(hbar omega_ij/k theta)-1) = gamma (rho_j - rho_i) (k theta / hbar)^3. (68)

Therefore (63) implies

I(theta) < gamma(k theta/hbar)^3 . SUM(p) INT dOmega [ SUM(i,j) (rho_j - rho_i) (omega_ij 2pi c^3)|D_ij|^2 ] . (69)

Now the summation indices (i,j) can be exchanged in the part of (69) involving rho_i. The result is

I(theta) < gamma(k theta/hbar)^3 . SUM(p) INT dOmega [ SUM(i,j) rho_j (omega_ij 2pi c^3)|D_ij|^2 ] , (70)

with the summation now extending over all (i,j) whether (66) holds or not. The sum rule (67) can then be used in (70) and gives the result (61).

This proof of (61) assumes that all particles other than electrons have so large a mass that they are negligible in generating radiation. It also assumes that magnetic dipole and higher multipole radiation is negligible. It is an interesting question whether (61) could be proved without using the dipole approximation (63).

It may at first sight appear strange that the right side of (61) is proportional to theta^3 rather than theta^4, since the standard Stefan-Boltzmann formula for the power radiated by a black body is proportional to theta^4. The Stefan-Boltzmann formula does not apply in this case because it requires the radiator to be optically thick. The maximum radiated power given by (61) can be attained only when the radiator is optically thin.

Afer this little digression into physics, I return to biology. The second constraint on the temperature theta of an enduring form of life is that the rate of energy dissipation (59) must not exceed the power (61) that can be radiated away into space. This constraint implies a fixed lower bound for the temperature,

k theta > (Q/N) epsilon = (Q/N) 10^(-28) erg, (71)

epsilon = (137 / 2 gamma) (hbar f/k) mc^2, (72)

theta > (Q/N) (epsilon / k) = (Q/N) 10^(-12) deg. (73)

The ratio (Q/N) between the complexity of a society and the number of electrons at its disposal cannot be made arbitrarily small. For the present human species, with Q given by (58) and

N = 10^42 (74)

being the number of electrons in the earth's biosphere, the ratio is 10^(-9).

As a society improves in mental capacity and sophistication, the ratio is likely to increase rather than decrease.

Therefore (73) and (59) imply a lower bound to the rate of energy dissipation of a society of a given complexity.

Since the total store of energy available to a society is finite, its lifetime is also finite. We have reached the sad conclusion that the slowing down of metabolism described by my biological scaling hypothesis is insufficient to allow a society to survive indefinitely.

Fortunately, life has another strategy with which to escape from this impasse, namely hibernation. Life may metabolize intermittently, but may continue to radiate waste heat into space during its periods of hibernation. When life is in its active phase, it will be in thermal contact with its radiator at temperature theta. When life is hibernating, the radiator will still be at temperature theta bu the life will be at a much lower temperature so that metabolism is effectively stopped.

Suppose then that a society spends a fraction g(t) of its time in the active phase and a fraction [1-g(t)] hibernating. The cycles of activity and hibernation should be short enough so that g(t) and theta(t) do not vary appreciably during any one cycle. Then (56) and (59) no longer hold. Instead, subjective time is given by

u(t) = f INT(0,t) g(t') theta(t') dt', (74)

and the average rate of dissipation of energy is

m = kfQg theta^2. (75)

The constraint (71) is replaced by

theta(t) > (Q/N)(epsilon/k)g(t). (76)

Life keeps in step with the limit (61) on radiated power by lowering its duty cycle in proportion to its temperature.

As an example of a possible strategy for a long-lived society, we can satisfy the constraints (60) and (76) by a wide margin if we take

g(t) = (theta(t)/theta_0) = (t/t_0)^(-alpha), (77)

where theta_0 and t_0 are the present temperature of life the present age of the universe. The exponent alpha has to lie in the range

1/3 < alpha <1/2, (78)

and for definiteness we take

alpha = 3/8. (79)

Subjective time then becomes by (74)

u(t) = A(t/t_0)^(1/4), (80)

where

A = 4f theta_0 t_0 = 10^18 (81)

is the present age of the universe measured in moments of consciousness.

The average rate of energy dissipation is by (75)

m(t) = kfQ theta_0^2 (t/t_0)^(-9/8). (82)

The total energy metabolized over all time from t_0 to infinity is

INT(t_0,infinity) m(t)dt = BQ, (83)

B = 2AK theta_0 = 6.10^4 erg. (84)

This example shows that it is possible for life with the strategy of hibernation to achieve simultaneously its two main objectives.

First, according to (80), _subjective time is infinite_; although the biological clocks are slowing down and running intermittently as the universe expands, subjective time goes on forever.

Second, according to (83), _the total energy required for indefinite survival is finite_.

The conditions (78) are sufficient to make the integral (83) convergent and the integral (74) divergent as t -> infinity.

According to (83) and (84), the supply of free energy required for the indefinite survival of a society with the complexity (58) of the present human species, starting from the present time and continuing forever, is of the order

BQ = 6.10^37 erg, (85)

about as much energy as the sun radiates in eight hours.

The energy resources of a galaxy would be sufficient to support indefinitely a society with a complexity about 10^24 times greater than our own.

These conclusions are valid in an open cosmology.

It is interesting to examine the very different situation that exists in a closed cosmology.

If life tries to survive for an infinite subjective time in a closed cosmology, speeding up its metabolism as the universe contracts and the background radiation temperature rises, the relations (56) and (59) still hold, but physical time t has only a finite duration (5). If

tau = 2 pi T_0 - t, (86)

the background radiation temperature

theta_R(t) = a(R(t))^(-1) (87)

is proportional to tau^(-2/3) as tau -> 0, by virtue of (2) and (3). If the temperature theta(t) of life remains close to theta_R as as tau -> 0, then the integral (56) is finite while the integral of (59) is infinite. We have an infinite energy requirement to achieve a finite subjective lifetime.

If theta(t) tends to infinity more slowly than theta_R, the total duration of subjective time remains finite. If theta(t) tends to infinity more rapidly than theta_R, the energy requirement for metabolism remains infinite.

The biological clocks can never speed up fast enough to squeeze an infinite subjective time into a finite universe.

I do not need to emphasize the partial and preliminary character of the conclusions that I have presented in this lecture.

I have only delineated in the crudest fashion a few of the physical problems that life must encounter in its effort to survive in a cold universe. I have not addressed at all the multitude of questions that arise as soon as one tries to imagine in detail the architecture of a form of life adapted to extremely low temperatures.

Do there exist functional equivalents in low-temperature systems for muscle, nerve, hand, voice, eye, ear, brain, and memory? I have no answers to these questions.

It is possible to say a little about memory without getting into detailed architectural problems, since memory is an abstract concept. The capacity of a memory can be described quantitatively as a certain number of bits of information. I would like our descendants to be endowed not only with an infinitely long subjective lifetime but also with a memory of endlessly growing capacity. To be immortal with a finite memory is highly unsatisfactory; it seems hardly worthwhile to be immortal if one must ultimately erase all trace of one's origins in order to make room for new experience.

There are two forms of memory known to physicists, analog and digital.

All our computer technology nowadays is based on digital memory. But digital memory is in principle limited in capacity by the number of atoms available for its construction.

A society with finite material resources can never build a digital memory beyond a certain finite capacity. Therefore digital memory cannot be adequate to the needs of a life form planning to survive indefinitely.

For example, a physical quantity such as the angle between two stars in the sky can be used as an analog memory unit. The capacity of this memory unit is equal to the number of significant binary digits to which the angle can be measured.

As the universe expands and the stars recede, the number of significant digits in the angle will increase logarithmically with time.

Measurements of atomic frequencies and energy levels can also in principle be measured with a number of significant figures proportional to (log t).

Therefore an immortal civilization should ultimately find ways to code its archives in an analog memory with capacity growing like (log t).

Such a memory will put severe constraints on the rate of acquisition of permanent new knowledge, but at least it does not forbid it altogether.