Sunday, April 23, 2023

The Disintegration of Science

In the 1990s, the science wars were fought between advocates of science and folks who saw flaws in science. Nowadays, the science wars underway are between folks claiming scientific support for wildly differing claims. Does our global use of fossil fuels for energy have significant impact on the climate? Are covid vaccines safe and effective? Of course scientific progress is driven by debate, so perhaps these disagreements are healthy.

A healthy organism is constantly fighting off infections and other disturbances. The integrity of an organism is constantly under threat. For a while, various homeostatic processes manage to preserve that integrity, but eventually those processes are overwhelmed, and the organism loses its integrity. Sometimes this lack of integrity means the death of the organism, but it can also mean division into multiple separate organisms. Presevation of integrity and subsequent loss of integrity can happen at many scales, from single cells to cell colonies to insect colonies to human societies.

Science nowadays, for the most part, maintains a very healthy level of integrity. A key component of this integrity is the vision of scientific knowledge as a coherent whole. All the bits and pieces of our scientific knowledge fit together somehow, or eventually will. We're always discovering inconsistencies, but our processes of research and mutual critique keep these inconsistencies under sufficient control that the overall integrity of the system is not under threat. The loud arguments over e.g. climate change are a sore point, but they are certainly at a small enough scale not to threaten the entire system.

And yet... these superficial rashes could be symptoms of a larger systemic problem. Is the rough coherence of scientific knowledge something inevitable? What processes maintain this coherence? What could threaten this coherence?

The coherence of science is maintained by a kind of circulatory system. Information circulates: researchers publish papers but also exchange preliminary results, critiques of draft versions of papers, and also text books and other coordinated summaries of scientific knowledge. People circulate: researchers meet to discuss their work, but also visit each other's laboratories to collaborate on research. Students are trained in one research organization and then get hired to work in other research organizations. Equipment and materials circulate: measuring devices can be calibrated to common standards. Experimental samples are exchanged between laboratories.

What would precipitate the disintegration of science would be the breakdown of this circulatory system. Circulation is supported by the larger social context. Freedom of the press allows research results to be published. Freedom of travel allows people to collaborate. Free trade enables the exchange of equipment and materials.

These freedoms are the hallmarks of liberal society. Science and liberal society have emerged together since early modern times. A free market of ideas allows the best ideas to emerge. Basing policy on effective ideas leads to success and growth, to progress. This progress provides a platform for further exploration, leading to better ideas, more effective policies, and further growth. We have been riding this feedback loop for four hundred years. It's not just science that is coherent, but our global society.

The general pattern in biological systems is that growth is followed by decline. Perhaps this time it will be different, but that is a position that requires a lot of faith! Just as science, liberalism, and progress supported each other in a feedback loop of expansion, there are signs that the same feedback loop may be picking up momentum in the direction of decline.

Of course one can pick a measure of prosperity to support whatever argument one wishes to advance. But it really seems like the financial crash of 2008 is one we have not really recovered from. The rise of vehement anti-liberalism is largely driven by the failure of liberalism. We were promised progress but that is not what we are experiencing. The underlying cause for the lack of progress is probably our reaching various ecological limits, but that's not a message that sells. Science and liberalism have built their castles on progress. As progress falters, so will liberalism, and so will science. Liberalism maintained the circulatory system on which scientific coherence depended.

Of course change is the nature of things. How science might best maintain itself in a new dark age, that is one worthy puzzle. It is valuable to step back a bit, to try to think strategically. How things will unfold in the coming decades and centuries, it is impossible to foresee with any accuracy. What is more feasible is to consider a range of possible trajectories, and to prepare responses across some plausible range. Insurance policies, diversified portfolios, hedged bets: these are effective approaches to dealing with uncertainty. We need to bring these approaches into our investments in scientific research programs.

Thursday, March 30, 2023

Heat Pump Efficiency

Thermodynamics is a fundamental branch of physics. It gets a bit subtle: I find myself getting tripped up often enough!

The cornerstone of thermodynamics is the Carnot cycle, an ideal process for converting heat to work. It's a model for what steam engines do, for example. The Carnot cycle sets a limit on how efficient an engine can be: it is not possible to convert all the energy from heat to mechanical work.

A heat pump is simply an engine running backwards. An engine has heat flowing from a hot reservoir to a cold reservoir, converting some of that heat to mechanical work. A heat pump uses mechanical work to push heat from a cold reservoir to a hot reservoir. The amount of heat added to the hot reservoir will be the sum of the energy from the work and the heat energy removed from the cold reservoir.

To heat a home, one can use a natural gas furnace, or one can use a heat pump. The heat pump runs off electricity, much of which is generated from an engine running off natural gas. Energy is lost when the natural gas heat energy is converted to electricity, but then energy is gained when the electricity is used to heat the home. Since the heat pump is just an engine running backwards, these losses and gains are in some sense reflections of each other, and might seem to cancel out. But they don't!

The missing detail is that there are three heat reservoirs involved. The engine at the utility power generation plant has energy flowing from a furnace to the environment, converting some of that to electrical energy. The heat pump has energy flowing from the environment to the interior living space, driving that with electrical energy:

The two efficiency factors have inverse forms, but the numbers involved are different, so they don't cancel each other.

Plugging in some roughly plausible numbers, a graph can be generated for maximum effiency of the overall system as a function of the outside temperature. As the outside temperature warms to near the interior living space temperature, the round trip efficiency increases without bound. At cold temperatures, the utility's power generation engine can run more efficiently, but the reduction in effectiveness of the heat pump is more dramatic, so the overall effiency is reduced.

Friday, March 24, 2023

Aperiodic Tiling

I've been seeing reports of an aperiodic tiling. At first, I couldn't imagine how a tiling could be aperiodic. Now the pendulum has swung to the other extreme, where it seems trivial:

The tile is just a 1x2 rectangle. Mostly they are all placed vertically, but there is a line along which horizontal tiles are placed. One could interpret the pattern of absence or presence of a horizontal tile in the sequence of columns as expressing a fraction in base 2. If the fraction is irrational, the pattern will be aperiodic. Hmmm, even if there was just one horizontal tile in the middle, the pattern would be aperiodic!

There must be some trickier definition in play, of what aperiodic means. But anyway, now it doesn't seem so impossible!

Friday, March 17, 2023

Scientific Equipment

Galileo did not invent the telescope. Galileo looked at the night sky with a telescope that someone else built. Scientists do sometimes invent and build the equipment they need, but in general scientists take advantage of existing equipment to enable them to do science. Science is not a free-standing activity; it is an integral part of a much larger world. Science uses its connections with the world, just as the world uses science.

This relationship of mutual use creates a self-reinforcing feedback loop. Scientific discoveries enable new equipment to be constructed, and new equipment enables yet further scientific discoveries. The astounding technological capabilities of our time are the fruit of this system. However, the system is more complex. Our global-scale industry has global-scale impact on the environment. Climate change may be the most immediate concern, but we are seeing many other effects too. It is of course difficult to predict exactly how environmental limits will impace the availability of scientific equipment. But a starting point would be a reflection on the variety of ways that science uses what the world makes available.

Instruments with which to observe and measure natural phenomena are surely at the head of the list. Nowadays we have telescopes in orbit, detecting a wide range of electromagnetic frequencies: not just in orbit around earth, but around other planets too. And we have robots on the surface of Mars, observing at close range. At the tiniest scale we have particle accelerators and electron microscopes. Chromotography, spectroscopy, magnetic resonance imagery... a catalog of today's observation and measurement equipment would fill an encyclopedia.

Another way that science uses what industry provides is the acquisition of raw materials. All kinds of very pure simple and complex substances are available. There is also a rich variety of materials processing equipment by which raw materials can be processed to form both experimental samples and also custom observational devices. Vacuum pumps are a curious sort of equipment, since their function is to remove material rather than to supply it. But vacuum pumps are fundamental to preparing a suitable environment for observations, back to the time of Boyle at the birth of modern science.

Recording experimental observations can rely on little more than paper and pencil, though nowadays all sorts of automated recording devices make continuous accurate measurement and recording possible. A variety of automated analysis can be performed by computers, so the scientist need only attend to a summary report.

Science is a communal enterprise. Scientists compare results, critique each other's methods, exchange tools and materials, hire each other's students, etc. The worldwide transportation and communication networks make these exchanges possible. Scientists travel, too, to observe phenomena that occur at special locations, such as biological species in their native habitat, or geological phenomena in place.

Another sort of equipment that science needs is social. At the most basic level, there need to be scientists, people with the capability and freedom to pursue scientific research. The various physical equipment necessary must not only exist but be made available for use by scientists. For the self-amplifying feedback loop of scientific advancement to work, industry must be confident in the validity of scientific results so that the know-how produced by science will be applied to produce the next generation of more capable scientific equipment.

The reader is invited to augment this list. But a further exercise is to consider what impact environmental limits might have on any of these sorts of equipment. There could be other potential feedback loops that get excited as we enter some new regime of system behavior. It is not impossible that environmental limits push industry into less efficient processes, which accelerate the impact of those limits.

It seems clear enough that science has a large share of responsibility for creating our modern world, with all its miraculous technological capabilities. That is another facet of the self-amplifying feedback loop: powerful people understand how science has enhanced their power, and so they promote scientific research. We certainly seems to be at very real risk of entering a new regime, where our miraculous technological capabilities are seen instead as driving us ever more violently against environmental limits. Just has science earned support by taking credit, science may well lose support by taking blame.

Science is not a free-standing activity, but is embedded in a multi-faceted world. This relationship has been at the heart of modern industrial civilization, which is about 200 years old. We seem to be headed for a major shift. If science is to survive the shift in good health, the scientific community will need to find ways to adapt to the new patterns.

Friday, March 10, 2023


Our actions have consequences. When we're being careful, we choose our actions so they'll have the best possible consquences. Most commonly what this means is that we try to change the world so it satisfies our desires more. But our actions don't just change the world, they change our selves. We often divide our activities into two phases, e.g. rehearsal and performance. The purpose of rehearsal is to refine our capabilities. Performance is when apply those capabilities to create an aesthetic experience for an audience, for example. But this division is just a rough cut. All of our actions change who we are at the same time that they change the world.

This division of experience into self and world is problematic. An athlete might consider their own body to be a component of the world. One's actual self might be perhaps the rational component of mind, something constant underlying even one's shifting mental capabilities. One of the essential insights of the Buddhist tradition is that the search for this constant underlying component of the self is futile. And yet this framework of thinking, e.g. "I will do this," seems practically unavoidable. If we want to use a conceptual framework of self and world, how can we think about this without getting distracted by illusions?

Organizational behavior is a doorway to a different perspective. It is not just individual human beings who act. All kinds of organizations act: political, military, industrial, academic, religious, etc. At a planetary scale, all of humanity acts. A basic principle of systems theory is that analysis starts with a clear definition of the system to be analyzed: what is part of the system, and what is not. A complementary axiom is in easy reach: the self is what is not in the system. The key point here is that the division of experience into self and world is like establishing a coordinate system or a frame of reference. It has no ontological foundation but is a practical step to allow conceptual elaboration for solving specific problems.

In organizational situations, it is commonly understood that actions both change the world and also change the self, i.e. change the organization engaged in the action. Teams develop cohesion by working together.

That what we are is a dynamic pattern that is constantly being shaped by our actions and experiences, that an important factor in choosing our actions is how those choices will reshape who we are... this perspective seems easier to achieve when we feel safe and secure. When things are good, we are happy to train ourselves to make them even better. When things are difficult, our entire focuse is on fixing problems with the world so we have no desire or opportunity to train ourselves. People do train themselves to be able to respond to difficult situations, though mostly that is to make themselves more capable of making whatever necessary changes to the world. But sometimes people do understand that shaping the world to meet their desires is not going to go very far, and they need to shape their own expectations. Aging gracefully can include such adjustments. What an older person can do is not the same as what a younger person can do. There is a lot less frustration in playing the hand you've been dealt.

At the planetary scale, the growing human population and the growing levels of consumption are driving us up against ecological limits, mostly prominently due to climate change but many other problems are accelerating too, such as aquifer depletion and ocean desertification. The reflex response is to demand that the world change in order to let us preserve our way of life. But of course our way of life is always changing and will continue to change as a consequence of our actions. However one chooses to partition the situation, it is always a dance between self and world. Our habits change, our understandings change, our values change. This dynamism is both a challenge and an opportunity. If our response to our discomfort is to become ever more stubborn and insensitive, we can certainly ramp up the level of mutual frustration to a catastrophic breaking point. But if we can respond to discomfort with care and flexibility, then we can discover tender joys in the most suprising places.

Friday, February 10, 2023

What Is To Be Done?

We are constantly faced with decisions about what to do, at every scale. Oranges are on sale: how many should I buy? Fossil fuels are creating climate havoc: should we switch to nuclear fission power?

In the simplest situation, one can foresee with sufficient accuracy the results of each alternative action, and choose the one with the most positive result. This formula outlines some major dimensions of a decision-making situation. One needs a set of alternative actions from which to choose; one needs to understand the results of each possible action; one needs to evaluate each of these possible results.

Commonly enough it is not possible to predict accurately the results of actions. We must decide in the face of uncertainty. We might have a pretty good idea about the probilities of the possible results of each possible action. For example, in a card game, we can calculate quite accurately the probabilities for each combination of cards we might draw from a well-shuffled deck. When developing a financial plan for living in retirement, actuarial tables can give reasonable estimates for survival to whatever age. Comparing the uncertain results of various possible actions is quite difficult. Given a choice between one action whose result is a certain $1, against another action whose result is $0 with probability 99% and $100 with probability 1%.... the expected value for each action is the same, $1. Whether to buy a raffle ticket for $1, that is a choice where expected return is not going to sufficient information to make a decision.

Many real world situations do not permit probability calculations with any realistic promise of accuracy. Probabilities are applicable in situations that repeat. Of course situations never repeat exactly, but a large number of situations can be similar enough so that the outcomes of each possible action can be tabulated to provide guidance for what to do when the situation occurs yet again. But sometimes situations don't repeat with any reasonable similarity. What's the probability that Donald Trump will be elected President in 2024? Of course one can assign this whatever probability seems appropriate, but there is no way to check this number against the facts. In situations like this, one can look at the set of plausible outcomes of each possible action. An action might turn out well, or might turn out badly. How well? How badly? Comparing these sets of plausible outcomes is not simple or mechanical, but that's what's required for deciding on what action to take.

Sometimes a decision involves a significant action that takes place essentially at a single point of time. For example, if I am considering a major purchase, at some point I have to signal my decision to complete the transaction. But oftentimes what is called for is an ongoing series of actions. There is deciding what to cook for dinner tonight, and then there is deciding on my diet, on my pattern of meal selection. I don't have to plan out my meals for the rest of my life; I can decide on meals more or less on the spot, depending on my schedule, my activities, the availability and prices of various food items, etc. In a game like chess, there is no way to plan out the full sequence of moves one should make in order to win. Each move must take into account the preceding moves of one's opponent, which cannot be predicted with anything like sufficient accuracy. One can, however, potentially decide on a strategy. A plan is a sequence of actions. A strategy is like a table of possible situations that might arise in the future and what action to take in each situation. Market orders versus limit orders in the stock market would be an example. A market order is the decision to buy or sell some number of shares. A limit order is conditional: whether any shares are bought or sold depends on the market price. A market order is a plan, a limit order is a strategy.

Deciding on a strategy can be very difficult. It can be impractical or impossible to tabulate all the possible situations that can arise in the future. And when one encounters a situation in the future, one might choose a quite different action than whatever had seemed the wisest back when one was contemplating future possibilities. Our understanding of actions and outcomes evolves: we are always learning, or at least we can be learning. So an effective strategy for action is one that enhances the quality of one's future decisions, by providing opportunites for learning along the way, and leaving open as wide a range of possible actions in the future as possible.

We should not be planning to imprison ourselves; we should be planning to liberate ourselves.

Tuesday, January 31, 2023

Fission Power

Evidence continues to mount that fossil fuel combustion is causing climate havoc. Floods and droughts, damage to cities and farms: it is becoming clear to more and more people that we need to wean ourselves off fossil fuels somehow. This is, however, an enormous challenge. We humans live very large on the earth nowadays, in our combinations of large populations and comfortable lifestyles. We consume energy globally at a rate of about 20 TeraWatts. We cook, heat our homes, drive our cars, run our factories... energy is fundamental to our modern way of life. Most of this energy comes from fossil fuels: coal, petroleum, and methane. To avoid enormous difficulties from any total change to our way of life, we need to substitute non-fossil sources to continue to provide energy at the required scale. Maybe in the future we will develop new sources, but in the next few decades at least we will need to rely on existing technology. Renewable sources such as solar, wind, and hydro are already in widespread use. Energy storage systems can help bridge the gap between fluctuating supply and fluctuating demand. But how to scale up renewable sources to meet the requirements of our modern society remains a daunting challenge. Nuclear fission is another existing technology that already provides steady reliable power at large scale. It is an very real option on the table for addressing climate change.

When your credit card bill is due and your checking account is empty, it is tempting to pay one credit card bill by borrowing from a different credit card. The general temptation is to solve short term problems by creating even larger long term problems. It's not an entirely invalid approach, but it's definitely smart to go down that road with eyes wide open. If we do choose to ramp nuclear power up by the factor of about 25x that would be needed to meet our energy needs, how might that move fit into a longer term strategy?

The long term strategy for modern society is rather cloudy but still worth considering. There is not going to be any kind of consensus possible, but that shouldn't stop a person from thinking about it. Some of the main options:

  • The world is due to end quite soon, so a long term strategy has no application.
  • We cannot have any idea about the future. Long term planning is an absurd pretense.
  • Technology will continue to advance at an ever more astounding pace. Any problems we create now will easily be fixed by the people of the future with their capabilities that will be almost miraculous by our present standards.
  • Maybe after a few thousand more years of expanding population and increasing comfort, humanity will start to bump up against actual planetary limits, but there is no point in worrying about that now.
  • We are clearly hitting real planetary limits already. But it takes time for us to shift our various systems, such as agriculture, to more sustainable patterns. We cannot continue to consume energy at today's rate, but we need a few decades to shift. The immediate dangers of climate change mean that we need to shift to non-fossil sources sooner than we can reduce our energy consumption. Nuclear power can provide a bridge from today's unsustainable way of living to a future sustainability.
It's worth thinking through what nuclear power would look like under these various scenarios. To ramp up nuclear power by 25x over the next decade or two is already a daunting prospect. If energy consumption continues to double every 50 years or so... what this would mean exactly in terms of uranium mining, waste management, fuel transport, etc. - I don't have answers, but it would be worth exploring such possibilities.

To flesh out such visions of how nuclear power could be scaled up in the future, perhaps the baseline assumption might be that everything goes according to plan. But effective engineering requires us to think about what might go wrong. If we are considering the option of walking down a tightrope to get to our destination, we'd be wise to understand how high off the ground that rope is!

Some of the unpleasant surprises worth considering:

  • Natural disasters such as earthquakes can cause radioactive material to escape containment.
  • Safe management of nuclear material can require a somewhat advanced level of industrial capabilities to make available the necessary equipment and materials. Even with scaled up nuclear power, other factors could cause our industrial capabilities to be significantly reduced.
  • All kinds of human bungling are not just possible but unavoidable. People are not perfect - not even close to perfect.
  • It's not just that people make mistakes. People will quite deliberately act to benefit themselves at whatever cost to others. It may be possible to build a very safe reactor, but it will cheaper to build one that is less safe.
  • People are always involved in conflicts at every scale. Nuclear technology can be weaponized in any number of ways. Of course we have very many nuclear explosive devices already built and ready for action. But the more we have fissile material circulating and the machinery for refining it etc., the easier it will be to build more explosive devices.

    Weaponization is not limited to nuclear explosives. Depleted uranium is already in widespread use in various types of bullets and other projectiles, just because of its metallurgical properties. Easy availability of radioactive materials will make them attractive for all sorts of uses. Various sorts of dirty bombs, conventional explosives coupled with radiactive shrapnel, are also straightforward possibilities. We have seen in the Ukraine where Russian troops occupied nuclear power facilities, because Ukrainian forces would not likely attack them there because of the risk of releasing radiative materials into the environment.

  • Nuclear technology can be a source of conflict. A nation might be developing nuclear technology for entirely peaceful purposes, but this unavoidably also increases their ability to build nuclear weapons. Their enemies will be motivated to attack and destroy their nuclear facilities, to cut off that nuclear capability.
It's also important to think about how we should evaluate consequences. We could just decide that it is too difficult to wean ourselves off fossil fuels, and just accept the ensuing climate change. We could cut our energy consumption dramatically to avoid climate change, and just accept the ensuing disruptions to our way of life. Or, if we decide to scale up nuclear power and some of the possible negative consequences arise, how bad could they be? Nowadays I see folks arguing that nuclear war wouldn't be so bad. Perhaps any cost short of human extinction should be considered acceptable. Even if ramping up nuclear power leads to human extinction... well, humans will surely go extinct sooner or later anyway, and if nuclear power improves our lives before that point, maybe it is a worthwhile bargain.

Understanding the various risks is very difficult. Many of the numbers involved are simply unknown, especially when the time scales involve many thousands of years. But there are also more complicated sources of uncertainty. Government inspectors will help prevent dangerous cost-cutting in nuclear facilities, but then government inspectors are themselves corruptible too. Nuclear advocates will point out that there have been no documented fatalities due to plutonium toxicity. But of course the people that handle plutonium employ many safety measures. Is plutonium safe because we know how dangerous it is? It's a bit like how the Mutually Assured Destruction provided by nuclear weapons has made the world a safer place, in some sense or other.

How can we decide what to do, in a game with such high stakes, with such high uncertainty, faced with such paradoxical logic? At least if we can get some common understanding of the predicament, that might be a start!

Tuesday, January 24, 2023

Steady Growth

There is a notion around that humanity requires steady growth to be healthy and happy. Steady growth clearly cannot continue for long on a finite planet. So there is another related notion around, that interplanetary colonization is required for humanity to be healthy and happy. Even the solar system is finite of course, so interstellar colonization is a natural next step. Why not intergalactic?!

But there are other physical limits that will constrain growth. Of course it could be that we will discover that our notions about physical limits are not accurate. But then our notions about the need for growth could be wrong, too. Any and all of our ideas could be wrong, but still, we're thinking beings; if we expect to succeed with interstellar colonization, we'd better hone the precision of our thinking!

One of the most fundamental physical limits in our theories today is the speed of light. Perhaps we'll find a way to colonize other galaxies, but it will take us a very long time to get to any of them!

Steady growth generally means exponential growth. Over a generation, the growth in whatever segment of the population will grow in proportion to the size of that segment. If health and happiness is to be equitably distributed, and if health and happiness requires growth, then growth will be exponential.

Physics comes in because humans, whatever else they might be, are also physical objects. The disciples of Ray Kurzweil might quibble: perhaps humans, in essence, are actually information. But even information requires some minimal physical substrate to be stored and processed! In any case, I am certainly not proposing that the specific numbers of my back-of-envelope calculations here should be taken with any seriousness. My point here is that steady growth will eventually bump up against the physical limit of the speed of light. I invite everyone to run the numbers as they see fit.

Suppose humanity's domain is some large sphere, centered on the earth presumably, and stretching out through interstellar space toward the distant galaxies. Since humanity is steadily growing, its domain is also growing. If humanity is growing exponentially, the volume of its domain will also be growing exponentially. Of course humanity can grow, to some extent, while in some fixed domain. That's what we've been doing on earth so far.

What exactly the carrying capacity of earth is, that's difficult to say. But, again, there are physical limits. The earth's mass is about 10^13 times the total mass of humanity. If the population grows at a steady 1% per year, then in about 3000 years, the total mass of humanity will exceed the total mass of the planet earth. Obviously we will run into serious trouble long before that; it is difficult to predict the exact course of our battle against limits to growth. The point of my quick calculations here is that they set some quite hard bounds. If humanity is to continue to grow at a steady 1%, certainly before 3000 years have gone by, we will need to be well down the road of interplanetary colonization.

It's easy to run similar numbers for the solar system. In less than 5000 years, the steadily growing mass of humanity will exceed the total mass of the solar system. Probably we will not find a way to digest the sun, so we will need to be colonizing distant stars well before then.

So let's say that we have spread out in the galaxy out to some radius R. If humanity is growing at 1% per year, the volume of its domain must also be growing at 1% per year, and then the radius will need to grow at 0.3% per year. Once that radius hits 300 light years, that steady growth will require the radius to grow more than one light year per year, i.e. faster than the speed of light!

So a reasonable bound on steady growth of 1% per year is that the domain of humanity will hit a hard physical limit at radius 300 light years. That's a volume of about 3 x 10^61 cm. Given the rough density of galactic matter, the total mass in that volume would be about 3 x 10^40 grams. A human weighs about 10^5 grams, so that would be a maximum population of about 3 x 10^35... assuming humans have incorporated all material into their bodies! Today's population is about 10^10, so that's a population growth of a factor of 3 x 10^25. At a steady 1% growth rate, we'll hit the speed of light in about 6000 years.

Of course these rough calculations involve many very unrealistic assumptions. There is no way that humanity will absorb into their bodies the entire mass of galactic matter inside a sphere of radius 300 light years. But even if they could, we'd hit the speed of light in 6000 years, given a steady 1% growth rate. 6000 years is already not an absurdly long time - it's roughly our historical horizon. Absurdly generous assumptions about the success of humanity's battle against the limits to growth already run into limits that are not absurdly far away.