## Saturday, September 12, 2020

### Path Dependence and Tipping Points

[This is a transcript for the video embedded below. Part of the text may not make sense without the graphics in the video.]

Most of the physics we learn about in school is, let’s be honest, a little dull. It’s balls rolling down slopes, resistance proportional to voltage, pendula going back and forth and back and forth... wait don’t fall asleep, that’s what I will not talk about today. Today I will talk about weird things that can happen in physics: path dependence and tipping points.

I want to start with chocolate. What’s chocolate got to do with physics? Chocolate is a crystal. No, really. A complicated crystal, alright, but a crystal, and a truly fascinating one. If you buy chocolate in a store you get it in this neat smooth and shiny form. It melts at a temperature between thirty-three and thirty-four degrees Celsius, or about ninety-two degrees Fahrenheit. That’s just below body temperature, so the chocolate will melt if you stuff it into your mouth but not too much earlier. Exactly what you want.

But suppose your chocolate melts for some other reason, maybe you left it sitting in the sun, or you totally accidentally held a hair drier above it. Now you have a mush. The physicist would say the crystal has undergone a phase transition from solid to liquid. But no problem, you think, you will just put it into the fridge. And sure enough, as you lower the temperature, the chocolate undergoes another phase transition and turns back into a solid.

Here’s the interesting thing. The chocolate now looks different. It’s not only that it has lost some of its original shape, it actually has a different structure now. It’s not as smooth and shiny as it previously wass. Even weirder, it now melts more easily! The melting point has dropped from about thirty-four to something like twenty-eight degrees Celsius. What the heck is going on?

What happens is that if the chocolate melts and becomes solid again, it does not form the same crystal structure that it had before. Instead, it ends up in a mixture of other crystal structures. If you want to get the crystal structure that chocolate is normally sold in, you have to cool it down very carefully and add seeds for the structure you want to get. This process is called “tempering”. The crystal structure which you get with tempering, the one that you normally buy, is actually unstable. Even if you do not let it melt, it will decay after some time. This is why chocolate gets “old” and then has this white stuff on the surface. Depending on what chocolate you have, the white stuff is sugar or fat or both, and it tells you that the crystal structure is decaying.

For our purposes the relevant point is that the chocolate can be in different states at the same temperature, depending on how you got there. In physics, we call this a “path dependence” of the state of the system. It normally means that the system has several different states of equilibrium. An equilibrium state is simply one that does not change in time. Though, as in the case of chocolate these states may merely be long-lived and not actually be eternally stable.

Chocolate is not exactly the example physicists normally use for path dependence. The go-to example for physicists is the magnetization of a ferromagnet. A ferromagnet is a metal that can be permanently magnetized. It’s what normal people call a “magnet”, period. The reason ferromagnets can be magnetized is that the electron shell structure means the atoms in the metal are tiny little magnets themselves. And these tiny magnets like to align their orientation with that of their neighbors.

Now, if you find a ferromagnetic metal somewhere out in the field, then its atomic magnets are almost certainly disordered and look somewhat like this. To make the illustration simpler, I will pretend that the atomic magnets can point in only one of two directions. If the little magnets are randomly pointing into one of these directions, then the metal has no overall magnetization.

If you apply a magnetic field to this metal, then the atoms will begin to align with the field because that’s energetically the most favorable state. At some point they’re just all aligned in the same direction, and the magnetization of the metal saturates. If you now turn off the magnetic field, some of those atoms will switch back again just because there’s some thermal motion and so on. However, at room temperature, the metal will keep most of the magnetization. That’s what makes ferromagnets special.

If you turn on the external magnetic field again but increase its strength into the other direction, then the atomic magnets will begin to line up pointing into that other direction until saturated. If you turn down the field back to zero, again most of them will continue to point there. Turn the external field back to the other side and you go back to saturating the magnetization in the first direction.

We can plot this behavior of the magnet in a graph that shows the external magnetic field and the resulting magnetization of the magnet. We started from zero, zero, saturated the magnetization pointing right, turned the external field to zero, but kept most of the magnetization. Saturated the magnetization pointing left, turned the field back to zero but kept most of the magnetization. And saturated the magnetization again to the right.

This is what is called the “hysteresis loop”. Hysteresis means the same as “path dependence”. Whether the magnetization of the metal points into one direction or the other does not merely depend on the external field. It also depends on how you got to that value of the field. In particular, if the external field is zero, the magnet has two different, stable, equilibrium states.

This path-dependence is also why magnets can be used to store information. Path-dependence basically means that the system has a memory.

Path-dependence sounds like a really peculiar physics-y thing but really it’s everywhere. Just to illustrate this I have squeezed myself into this T-shirt from my daughter. See, it has two stable equilibrium states. And they keep a memory of how you got there. That’s a path-dependence too.

Another common example of a path dependence are air conditioning units. To avoid a lot of switching on and off, they’re usually configured so that if you input a certain target temperature, they will begin to cool if the temperature rises more than a degree above the target temperature, but will stop cooling if the temperature has dropped to a degree below the target temperature. So whether or not the air condition is running at the target temperature depends on how you got to that temperature. That’s a path-dependence.

A common property of path-dependent systems is that they have multiple stable equilibrium states. As a reminder, equilibrium merely means it does not change in time. In some cases, a system can very suddenly switch between different equilibrium states. Like this parasol. It has a heavy weight at the bottom, so if the wind sways it a little, it will stay upright. That’s an equilibrium state. But if the wind blows too hard, it will suddenly top over. Also an equilibrium state. But a much more stable one. Even if the wind now blows into the other direction, the system is not going back to the first state.

Such a sudden transition between two equilibrium states is called a “tipping point”. You have probably heard the word “tipping point” in the context of climate models, where they are a particular pain. I say “pain” because by their very nature they are really hard to predict with mathematical modeling, exactly because there are so many path-dependencies in the system. A glacier that melts off at a certain level of carbondioxide will not climb back onto the mountain if carbondioxide levels fall. And that’s one of the better understood path-dependencies.

A much discussed tipping point in climate models is the Atlantic meridional overturning circulation. That’s a water cycle in the atlantic ocean. Warm surface water from the equator flows north. Along the way it cools and partly evaporates, which increases the density of salt in the water and makes the water heavy. The cool, salty water sinks down to the bottom of the ocean, comes back up where it came from, warms, and the cycle repeats. Why does it come back up in the same place? Well, if some water sinks down somewhere, then some water has to come up elsewhere. And a cycle is a stable configuration, so once the system settles in the cycle, it just continues cycling.

But. This particular cycle is not the only equilibrium configuration and the system does not have to stay there. In fact, there’s a high risk this water cycle is going to be interrupted if global temperatures continue to rise.

That’s because ice in the arctic is mostly fresh water. If it melts in large amounts, as it presently does, this reduces the salt content of the water. This can prevent the water in the atlantic overtuning circulation from sinking down and thereby shut off the cycle.

Now, this circulation is responsible for much of the warm wind that Europe gets. Did you ever look at a world map and noticed that the UK and much of middle Europe is North of Montreal? Why is the climate in these two places so dramatically different? Well, that atlantic overturning circulation is one of the major reasons. If it shuts off, we’re going to see a lot of climate changes very suddenly. Aaaand it’s a path-dependent system. Reducing carbondioxide after we’ve crossed that tipping point will not just turn the circulation back on. And some evidence suggests that this cycle is weakening already.

There are many other tipping points in climate models, that, once crossed can bring sudden changes that will stay with us for thousands of years, even if we bring carbondioxide levels back down. Like the collapse of the Greenland and West Antarctic Ice Sheet. If warming continues, the question is not whether it will happen but just when. I don’t want to go through this whole list, I just want to make clear that tipping points are not fear mongering. They are a very real risk that should not be dismissed easily.

I felt it was necessary to spell this out because I recently read an article by Michael Shellenberger who wrote: “Speculations about tipping points are unscientific because levels of uncertainty and complexity are too high, which is exactly why IPCC does not take such scenarios seriously.”

This is complete rubbish. First, tipping points are covered in the IPCC report, it’s just that they are not collected in a chapter called “tipping points,” they are called large scale singular events. I found this out by googling “tipping points IPCC”, so not like it would have taken Shellenberger much of an effort to get this right. Here is a figure from the summary for policy makers about the weakening of the atlantic overturning circulation, that’s the tipping point that we just talked about. And here they are going on about the collapse of ice sheets, another tipping point.

Having said that, tipping points are not emphasized much by the IPCC, but that’s not because they do not take them seriously, but because the existing climate models simply are not good enough to make reliable predictions for exactly when and how tipping points will be crossed. That does not mean tipping points are unscientific. Just because no one can presently put a number to the risk posed by tipping points does not mean the risk does not exist. It does mean, however, that we need better climate models.

Path-dependence and tipping points are cases where naïve extrapolations can badly fail and they are common occurrences in non-linear systems, like the global climate. Just because we’ve been coping okay with climate change so far does not mean it will remain that way.

I want to thank Michael Mann for checking parts of this transcript.

1. ""resistance proportional to voltage,""

1. Surprisingly that applies to a certain group of resistors - called Voltage Dependence Resistors (VDR's) - but I'm sure it was a blooper. Ah well, it was brief and didn't distract from an excellent discourse on tipping points.

2. I'm referring to Ohm's law, resistance proportional to voltage given constant current. Could you please clue me in what's wrong or funny about this?

3. Sabine, normally one expects a constant resistor and the current is proportional to the voltage.
Have fun, Stefan

4. I see no difficulty in taking out one resistor and putting in another. And in any case, I was merely referring to one of the best known consequences of one of the best known equations from school-physics, not to a particular way of making a measurement. So, keep on laughing if you wish, but I think what I said is correct.

5. Sabine is correct. The resistance of a system is defined as the ratio of the voltage and the current, typically written as:

R = V/I

Since this is a definition, it always holds true. So strictly speaking, R is always directly proportional to the voltage. It is also always inversely proportional to the current. It's just that sometimes, the current depends linearly on the voltage :
I(V) = C V
so, when you calculate the resistance, you get a constant that does not seem to depend on I or V anymore.
R = V / C V = 1 / C

This is Ohm's law. The first equation is quite general and only becomes Ohm's law with this particular relationship between current and voltage. Hope this helps and is not to pedantic...

6. A variable resistor is a rheostat. In Ohm's law one quantity is held constant, one is varied and the other measured.

7. With all due respect, but this is complete, utter nonsense. Resistance is a material property and (as far as linear response goes) independent of voltage. Stating that resistance is proportional to voltage is equivalent to saying that the diameter of a tube connecting two glasses is proportional to the difference in water levels. Physically just nonsense.

8. Resistance is arguably not independent of voltage, that's what Ohm's law says. The two are proportional to each other, and resistance is also inversely proportional to the current. This is merely a verbal reformulation of the equation. If you want to claim that Ohm's law is physical nonsense, please take your anger elsewhere; I don't have time for this.

9. You are mistaken Fred. Resistance is not only defined in linear response. It's definition is always R = V/I. This is always true. Even for non-ohmic materials or outside of the ohmic voltage range, i.e. when the current as a more complex relationship to the voltage than just the linear dependence of Ohm's law.

For example, if you look at the I-V (current vs voltage) characteristics of a p-n junction diode (just go on wikipedia to see it: https://en.wikipedia.org/wiki/Diode#/media/File:Diode_current_wiki.png) you can calculate the resistance at every point of the graph by dividing the value of current by the value of the voltage. Note that I have seen students being misled by Ohm's law into thinking that the resistance is the slope (derivative) of the curve. These students incorrectly think the resistance is zero in the flat portion of the curve, while the correct statement would be that it is very large (finite voltage divided by a small [leakage] current).

You are right to think of resistance as a material property, but you must also remember that those properties depend on external factors, such as temperature, voltage, current, magnetic field, etc. In your classical analogy, imagine the water pressure is large enough to stretch or burst the straw (giving it a larger diameter).

10. Ohm’s law describes the relationship between voltage, current, and resistance in an electric circuit— but Ohm’s Law does not define the “causal relationship” between those three quantities. The causal relationship is determined by the specific construction of the circuit. (In some texts the varying quantity of a circuit is written in lower case in Ohm's Law to indicate the causal relationship.)

In most circuits that are shown in introductory physics courses there is a voltage source which remains roughly constant so that if resistance is increased the current drops. In a circuit with a constant current source, then if the resistance is increased the voltage across the resistance increases. There are constant-current sources in advanced electronics, but in both cases the causal relationship is not resistance a function of voltage; in the former it is current a function of voltage and resistance, and in the latter, voltage a function of current and resistance.

According to Harvard and other sources,

"A non-Ohmic device is one that does not have a constant resistance. A light bulb is a simple example; the filament undergoes huge changes in temperature when current passes through it. Therefore, the resistance of the filament is not constant, rather, it increases with increased current."

That is, when resistance does vary as a function of the other quantities, Ohm's Law does not apply.

Conclusion 1: "resistance is proportional to voltage according to Ohm's Law" is misleading.

Conclusion 2: nobody is perfect.

(If these conclusions have already been reached by the time this comment is received, please do not publish it.)

11. I think I should correct my comment above, I was referring to the equation "R = V/I", which (as I only realized now) is not always referred to as Ohm's law.

12. Resistance is a property of an object or device. The corresponding material property is resistivity.

Best,
--Ajit

2. I guess the uptake is that with global warming our chocolate is going to change its crystal structure��. That chocolate is a crystal is something I did not know. When winter comes, I tend to eat a lot of chocolate. It has a mood uplifting effect in the fast of the endarkening.

I worked on orbital dynamics and early on this was with respect to black-birds spy-sats. This was work with the INTEL community, and one job I did for a year is to use intelligence data to determine the probability various nations were developing nuclear weapons. I took a course that might be called “atomic bombs 101.” A critical component of nuclear weapons are plutonium pits, which are mini-atomic bombs. The plutonium is configured metallurgically in a certain allotrope. The crystal structure is such that when the metal is compressed under the shock wave of explosives Pu nuclei are in a denser configuration so they absorb neutrons more efficiently. This allotrope is not stable and plutonium pits have to be cycled out to be reconfigured in the right allotrope. BTW, as this was done in the early 90s a couple of nations have come on as nuclear states, and we had them fingered back then.

The tipping point with global warming is like crossing the event horizon of a supermassive black hole. There is nothing particularly noticeable about that event. Such an infalling observer might have various laser ranging measurements with spacecraft outside and know based on those data approximately when they have crossed the horizon. With global warming we have had similar warnings. 20 to 25 years ago it was stated this tipping point would come when there is permafrost melting. Early last decade (2000-2010) alarm bells were sounded when methane releases were measured out of fissures measuring meters in diameter. Then at the start of this decade alarming measurement found these fissures had grown to kilometers. Now permafrost melt is catastrophic and huge craters and sink holes are pockmarking the landscape in N. Canada and Siberia. Methane is being released enormously and it is some 30 times the IR photon absorbing and scattering molecule than CO_2. Have we crossed the climate horizon or tipping point?

There is also the politics of the day that is solidly in the denial camp. I will make a prognostication that if Don-the-Con t’Rump is reelected president of the United States we will cross this tipping point irreversibly. I have seen several bumper stickers and banners with “Trump 2024.” He will become a dictator and dealing with global warming will be off the table. The national front parties in Europe will probably follow the lead and scramble for power, where upon off we go into the brave new world of a global heated planet.

I am not terribly optimistic these days. Even if Biden wins the contest we may only have a brief repose from this insane march into neofascism. I have grim suspicions we will not use that time to reverse the climate problem.

There are three possible answers to Fermi’s question, “Where are they?” This so-called Fermi paradox on the absence of space aliens may have 3 answers. The first is they are very rare and consequently too distant to communicate and certainly travel to each other. Evolution of life on Earth suggests the evolution of extremely brainy animals is not that frequent, and the same might hold for intelligent life on other planets. The second answer might be as Stanislaw Lem proposed; we may simply not be able to recognize it if we do detect it. The final answer is that technically capable intelligent life may most often reconfigure their environment in a way, so they snuff themselves out. We may be playing the suit of cards masterfully.

1. "The tipping point with global warming is like crossing the event horizon of a supermassive black hole."

Well, tipping points are reversible, in principle. So, it's not like we'll necessarily all die (as presumably we would if we fell into that black hole), it's "just" that there'll be much unnecessary suffering.

2. It might also depend on what we mean by tipping point. A classical black hole is in some ways the simplest object in the universe. Quantum mechanically the opposite is the case. The atmospheric and climatic system of a planet, and in particular Earth, is hideously complex.

The primary tipping point I am thinking of is where with permafrost melt that even if we reduced or even ended CO_2 production climate heating will still race away on us. We might well be there. This may not necessarily mean our doom, though it will probably mean difficulty with agriculture and with a human population expected to top 10 billion sometimes this century that will be problematic. The only way I think at some point to avoid disaster will be geoengineering. This can involve a range of things from putting aerosols in the atmosphere, iron in oceans to stimulate phytoplankton and even spacebased ideas. What I call the big “OH SHITS REPORT” is likely to come in the forthcoming years or 1 to 2 decades, where the far right and libertarianism ideologies in the US, the stupidest collection of ideas, and other right winged and denialist nonsense will be swept away. If heeded, then we will have to engage in a program combined with urgency of the Manhattan project combined with the Apollo moon program to geoengineer our way out of this predicament.

Of course, maybe the emergent neofascist rulers of the world will not relinquish power and we will then face this “singularity.” Think of the bizarre rightwing nonsense over Covid-19, where even wearing a mask is being called some conspiracy by a cabal of people with Fauci to take socialistic control of the economy. Any bet the same crappola will occur with an urgent called to rework the energy balance in Earth’s atmosphere? You betcha!

3. I think the majority of people (with average IQ 100) are capable of thought if they have to, but would rather rely on tribal intuition and instincts, which are what "leaders" like President Trump appeal to. Maybe someday there will be a tipping point where education and training and access to information will enable that majority to make democracies functional. People like Dr. Hossenfelder and Dr. Crowell are helping to push us towards that tipping point.

The late Iain Banks wrote novels about a future in which that tipping point had been reached (although there were still problems). One feature which made sense to me was that there was no more money. Civilized society supplied the needs for survival and the opportunity to pursue and become expert in one's interests. Favors could be traded, but nothing needed to be bought or sold. In such a civilization Trump would have no leverage.

I share Dr. Crowell's suspicion that we will never reach that point, however.

4. There is a fourth possible answer to Fermi's question - where are they?

This is nicely covered in the science fiction trilogy by Cixin Liu - The Three Body Problem, The Dark Forest, Death's End.

5. I replied in part to your post here below. My point is that we may not know we pass the tipping point when we do. We will cross it most likely, if in fact maybe we have not already.

6. Lawrence: I think people, politically speaking, will only respond to pain: Literally, psychologically, financially. The question is if the pain can come quick enough and hard enough that ignoring and ridiculing the science is no longer an option.

I think we are starting to see this in part in the USA, in California and the Hurricane vulnerable Gulf and East Coast. The platitudes of the Right don't offer any effective solutions, and "God's Will" is BS when your home (and whole town) is incinerated or washed out to sea. That's the kind of pain it takes to say "Let's give those eggheads a crack at it."

And there will just be revolution and mass death, famine and disease if the pain is widespread enough; that will end the carbon emissions. I think it is a race, no question, and I think civilization lies in the balance.

I did not think this 40 years ago, but now? It is entirely possible that collectively speaking we humans are just too stupid to survive.

3. Lawrence that is, interesting: We seem to share a bit more background than I realized, at least in terms of working with intel communities. My interactions were more on the emerging-tech and AI research side, though, so I was mostly able to stay clear of long spells in dark closets. I assume we never bumped into each other? Your side is the one into I watched friends sometimes move into... and then I'd literally never see them again for years, even though they worked just two interconnected buildings away!

I am a bit more optimistic about long-term outcomes. Clear and impactful recognition of dangers not previously understood, when implanted firmly in large segments of a population, can itself have a powerful and positive resetting and hysteresis effect.

Sabine, alas, I am clearly badly out of touch with many areas of modern social discourse. I had never even heard of this Michael Shellenberger fellow before, even though I am deeply familiar with the pros and cons of some of the nuclear arguments he makes.

So, coming in cold when looking him up, I can say in full honesty that some of this fellow's statements about environmental impacts of global warming being "overblown" struck me as, so say the least, bizarre and surreal. It was particularly jolting to read such idiotic blather during the same week in which the entire west coast descended into a pretty good approximation of the Dante's Inferno, from the red darkness at noon that affected millions, to a horrifying decline in air quality that affected hundreds of thousands, and finally, alas, to the apparent live incineration of at least dozens and likely hundreds (no one know yet) of people who in many case lived in areas where wildfires had never before even been a factor worth considering.

That last group in particular may have been disinclined during their final agonizing moments of life to view climate change as some overblown and abstract argument about which they never should have even spent a moment of concern.

Here's a related philosophical question, one that is well understood by the psyops side of the intel community: On a per-falsehood basis, which of the following is more effective? The falsehood uttered by a person who enjoys lying so much that the non-thinking parts of his body turn orange in embarrassment? Or the falsehood uttered by someone with a long history of persuasive, fact-based, well-reasoned, and popular positions on issues related but distinct from the falsehood?

Operationally, it really doesn't matter whether the falsehood was maliciously intended or sincerely believed by the specific person who uttered it. In fact, having the falsehood spoken by a true believer is by far the more effective and desirable of the two possibilities.

1. An important erratum: I somehow managed to edit or leave out the critical ending clause of my final sentence in the above comment:

"... In fact, having the falsehood spoken by a true believer is by far the more effective and desirable of the two possibilities [if your intent is malicious, since sincere belief makes a malicious falsehood far more persuasive.]"

Both at the personal and political levels, it is a good idea both to be aware of and to know how to defend against a broad range deception-based malicious strategies. But for that smaller group of people who are tempted not just to defend against malicious strategies, but to apply them to enemies real and perceived, it is worth pointing out that aside from the ethical concerns, there are quite pragmatic reasons why this is a very bad idea, especially in the long term.

The long-term success of a society is determined to a remarkable degree not only by the resources available to it, but also by how effectively it integrates and leverages the insights and intelligence of its citizens in using those resources. It is this integration of contributions into a coherent and society-spanning fabric that makes a society more effective than the simple sum of its parts.

Such fabrics cannot exist without phenomenal levels of trust. Without such trust the sharing of both insight and resource degenerates into increasingly fine-grained forms of feudalism. Eventually, so many resource are spent on local defense, and so few on integrating insights and resources, that the society degenerates to local survival strategies that cannot sustain large populations.

In the creation and continuation of exchange fabrics that allow societies to innovate and "behave smartly", there is no greater corrupting effect, no acid that eats more deeply into the sustaining threads of trust that form the fabric, than for members or subgroups of that society to engage freely in malicious deception without fear of reprisal.

Societies also have tipping points. The descent from a society with a well-formed and self-sustaining fabric of trust into the anarchy of deep-set mutual distrust is not a pretty thing to behold, and in the end it benefits no one.

In short, there are some extremely pragmatic reason why both individuals and societies should shy away from extensive use of malicious deceit in both politics and even warfare. We seem instinctively to have an intuition for the importance of this fabric, an instinct that leads the vast majority of normal-range personalities to react positively to actions that contribute to this fabric. There are at least two words that describe these responses, which incidentally can never be meaningfully claimed by a person, only demonstrated by that person through their actions. The words? Honesty and integrity.

2. I am not saying we will not reach the tipping point. It is more that we will probably not know it right away when we do. I used the comparison of a black hole, where one has no local signal of crossing the event horizon. Of course at some point tidal forces start to take effect and then you know you are in trouble. Maybe an historical analogue is more apt, where during the 5th century probably few people had any sense that the Roman Empire was falling.

The climate tipping point, the one where runaway greenhouse warming is determined to happen, is either pretty close or we may indeed have crossed it. Our only prospect for the future is geoengineering. This will be fraught with difficulties and unexpected consequences. Even if we do that it requires people shake off the delusional nonsense that currently clouds our thinking, roll up sleeves and get to real work.

4. I live in the state of Oregon in the US. The climate induced fires this week got within five or six miles of my house. I take climate change a lot more personally than I did a week ago. I don't know if we are at a climate tipping point, but we will eventually get to an action tipping point where enough people have good reason to take climate change personally and then effective action will happen.

If you follow politics and polling closely you will find good reason to understand that we are at a political tipping point.
The current adminstration is going to be wiped out and the new adminstration will have policies much more reflective of science on both the virus and climate change.

Lastly, I just add that when the President spouts nonsense so will a lot of the people. When the President talks facts and science so will a lot of the people. I tell my son to always remember that the reason stuff gets in the news is because its the exception rather than the rule. The rule is that most people are getting up in the morning, getting their kids off to school, going to work and doing all the routine things that good people do to make a better world for themselves, their families, and their fellow citizens. In two months those people will speak up, loudly.

5. Nick Bostrom on the AI "tipping point":

"Maybe an earth covered by nanobot infrastructure that is used only to produce space-colonising self-replicating probes that can transform the universe into whatever structure the AI places the highest value on, with humans being swept away as a side effect of that effort. We should aim to engineer the AI so that it's an extension of us, and of our will. So that it's on our side rather than trying to achieve something at odds with our aims. We ideally would want to keep it boxed up, but if it's superintelligent it will likely sooner or later escape that box. We want to be sure that even once out of its box, it's trying to help us."

1. If you want to invoke AI as a way to solve or mitigate these problems, I think it is not going to involve the universe. Even if we put von Neumann probes in space there will always be a lot more universe than these could ever reach.

What might be done is to put AI nanobots at the L1 point 1.5 million km towards the sun. These are “fed” raw materials to replicate themselves and they manage to station-keep an orbit at this L1 point. They can be solar powered and use various tiny propulsion systems or electric fields and so forth to remain there. The point of building this up is a cloud of them would Mei scatter light and reduce the solar irradiance on the Earth. The very presence of these would serve as optical scatterers that would send a small percentage of light on an EM scatter lobe that misses the Earth. If the solar irradiance were reduce by .05% that might about do the trick.

This geoengineering method would not solve ocean acidification. Another problem with geoengineering in general is the fossil fuel industry will promote the idea that since this is “solved” we can burn fuel with abandon. Oh and yeah, it will take a lot of AI nanobots out there to do the trick.

6. Dr. H,, and all who express political opinions:
Coping with tipping points affected by humanity involves coping with humanity. That arguably can involve "levels of uncertainty and complexity" too high to make scientific decisions based on speculation. Limited data and assumption sets make decisions based on statistics and probability risky enough.
This may be worth remembering before expressing contempt or anger at those who may simply disagree with you, assuming you aren't infallible.

1. "Limited data and assumption sets make decisions based on statistics and probability risky enough. This may be worth remembering before expressing contempt or anger at those who may simply disagree with you, assuming you aren't infallible."--Korean WPD

Here are USA news items I read just today:

The USPS had a plan to send 5 reusable facemarks to every household in early April. Even had a press release ready. The White House blocked the plan.--Washington Post

Breaking News: C.D.C. scientists didn’t write the virus testing guidance on its website last month, and it was published against their objections, officials said.--NY Times

HHS & the Office of Budget & Management siphoned \$700M from CDC's budget for Operation Warp Speed, Bloomberg News reports. \$300M of that was for HHS's Don't Worry, Be Happy ad campaign about the coronavirus pandemic.

Idaho pastor who repudiated using a mask ends up in ICU with COVID-19.--CNN

Poll workers signed up to work the November election in a county near St. Louis were urged in an email to “act surprised” if voters ask why they aren’t wearing masks given the coronavirus threat.--AP

Scans for strokes can inadvertently reveal COVID19 infection. The viral disease causes clots that can cause strokes. New research.--medicalxpress.com/news

I feel I have long passed the point where contempt and anger are justifiable. There's plenty of data available, some just haven't accepted or won't process it.

2. JimV,
There are indeed plenty of available data.
Enough to support each of several pov's on just about any political issue.
The choice of sources for these data, of whether or not to search for opposing data, of searching for possibly unsuspected collateral effects, of doing personal research on relative significances to competing goals ... these are made by individuals.
Contempt and anger can go in any direction. So can efforts at understanding and friendship.
To paraphrase Khruschev's explanation on why most deaths in Korea occurred during the years of "Peace Talks," war is easy to start, but not always easy to stop.
That is the point of the part of my comment to which you refer.
With kind intentions, Bert

7. For years I always thought of hurricanes/typhoons as giant, convective, air conditioning systems that transfer warmth from the ocean surface to the thin upper atmosphere where it radiates away to space in the infrared band. This, along with smaller scale convective systems like thunderstorms, will at least help delay the onset of our planet's climatic tipping point, buying us time to reduce our carbon footprint.

8. “Now, this circulation is responsible for much of the warm wind that Europe gets. Did you ever look at a world map and noticed that the UK and much of middle Europe is North of Montreal? Why is the climate in these two places so dramatically different?”

Surely, many emigrants from northern Europe, like my paternal gr-grandfather Johann from the village of Ostereistedt (lat. 53.3 degrees) east of Bremen, must have experienced some level of shock at the temperature extremes in the US northeast. New York City (lat. 40.7 degrees), where Johann settled, has experienced temperatures from -26.11 C. (-15 F.) to +40.56 C. (105 F.) over the years. These temperature variations undoubtedly are much more extreme than the temperature range he experienced in his ancestral village of Ostereistedt,

1. David Schroeder, The Gulf Stream carries a lot of warm water from the Gulf of Mexico to the far north of Europe. That is why it is so much warmer here in comparable latitudes than in North America. A striking example is Murmansk, in the north of Russia. Murmansk is the northernmost ice-free port. And because it is ice-free, "Red October" could start from here :-)
Have fun
Stefan

2. Stefan Freundt. Thank you. I’ve long been aware that the Gulf Stream warms Western Europe, but I didn’t realize that its influence extended all the way to Murmansk. I remember reading that palm trees, and other sub-tropical plants, grew at the southwest tip of England due to the Gulf Stream. Working for 21 years at an Oceanographic institute I had firsthand experience of the power of the Gulf Stream. Our research group used to tow an instrumented catamaran back and forth across the boundary of the stream just off Cape Hatteras. The change in atmospheric temperature and humidity was quite dramatic as we crossed from the cold North Atlantic waters into the Gulf Stream.

Studying weather and climate has become an informal hobby of mine in recent years. This summer I decided to track the expansion of the snow cover in North America by monitoring satellite coverage at the Climatereanalyzer site maintained by the University of Maine. So far very little change from midsummer has occurred with only a small increase on Baffin Island, and a few other scattered locations. I assume a sort of tipping point will occur when the snow cover reaches a certain extent, with a commensurate rise in albedo, allowing a massive dome of extremely cold air to build over the Canadian Artic and sub-Artic. At that stage we will start getting our Polar Vortex outbreaks typically between the tail end of November and the end of February.

9. Hallo Sabine, einzig: Sie sagen damit ganz deutlich, dass Sie theoretische Physikerin sind und noch nie einen Lötkolben in der Hand gehalten haben. Aus praktischer Sicht ist es wesentlich einfacher Strom proportional der Spannung zu haben und den Widerstand konstant, als ständig Widerstände aus der Platine aus und einzulöten...
Im Übrigen habe ich großen Respekt vor Ihrer Arbeitsleistung und von den Liedern gefällt mir "catching light" und "Theory of everything" (**) am besten und höre sie immer wieder gern.
(**) ist der letzte Punkt auf meiner bucket Liste - aber das wissen Sie ja...
Viel Spaß Stefan

1. Ich hab schon mal gelötet, danke, und ich verstehe durchaus, wovon ihr redet. Ich keine Aussage über eine Messung gemacht hab sondern schlicht über eine Eigenschaft einer Gleichung, was einige Leute hier wohl schwer zu verstehen finden.

2. Hello Sabine,
a resistor is a macroscopic object.
If you apply different voltages to it,
the flowing current is proportional to the voltage.
The Ohm' law was developed from such an experiment.

Surely physics is not the arbitrary rearrangement of an equation - or is that how you see it?

In quantum mechanics this is unfortunately common practice to find and solve an equation
without asking how the objects should fulfil it...
Have fun Stefan

3. To say the obvious, a rearranged equation is still the same equation. I was not talking about resistors, I was talking about resistance. Even I know that the resistance of a material can change, despite the fact that I am merely a dumb theoretical physicists.

10. Sabine,

My own best reading of Stefan’s intent is this: For most circuits and power supplies, all three V=IR variables are in play. Thus if you remove one resistor and solder in a new one, it is usually the current that will vary inversely to the resistance. The voltage may go up a little, but never beyond the rating of the battery.

On the other hand, one can most definitely buy “Constant Current Power Supplies" (Google for a PDF spec) that dynamically adjust voltage to maintain constant current. Within their ratings, such adaptive power supplies can for example double the voltage if resistance is doubled.

-----

Enough of that. What I find far more interesting is how you managed to sneak in a subtle but pointed example of how even a simple equation of three variables cannot be separated from the human cognition and interpretation, which makes more complex abstractions exponentially riskier to explore as they inherent and multiply such issues during their construction from simpler assertions. The result is a powerful argument for your own book, “Lost in the Math.”

The problem of how to capture the informal constraints that reality inevitably places on otherwise mathematically precise systems is a huge problem in AI and robotics. A humorous but all-too-plausible example is this: If you ask a robot to trim a tree, what is to keep it from sitting down on same limb that is about to saw off? This is the robot equivalent of a human painting himself into the corner of a room.

The AI rules that prevent dangerous interpretations of pristinely mathematical goals and equations are (not very originally) called “common sense” rules. Common sense rules are critical to human problem solving, and in AI systems a good set of such rules can make every aspect of AI more effective, from how it interprets raw sensory data to how it navigates vast systems of equations without wasting 99.999% of its time on futile exploration branches.

In the late 1900s huge amounts of time and money were spent trying to give computers common sense. Almost all such efforts failed, usually miserably. It took widespread use of neural nets to begin making some real headway in putting “common sense” into AI and robotic systems, but most would agree that even this is an incomplete and in many ways brute-force approach to the problem.

So, Sabine, that is why your sneaky example is so delightful.

If a simple and well-verified algebraic physics equation, one with only three variables V=IR, nonetheless requires an decidedly non-trivial suite of “common sense” cognitive rules to make its interpretation physically meaningful and specific, what then are the odds that the loftiest and most context-free equation edifices of theoretical physics have any real physical meaning at all? These castles must after all be constructed bottom-up from just such equations, often multiplied in ways tht increase their collective risk.

Here’s a specific example from string theory. For a Euclidean n>2 embedding space, an object can have n-2 unique types of holes — not different hole counts (genus), but non-comparable holes with different dimensionalities. Since we live in the only space where there is just one type of hole, we tend to think of holes as “simple”, but this just us being parochial. Now here is the odd thing: String theory includes extensive references to holes in higher dimensional objects, yet it neither acknowledges nor enumerates the specific types of holes intended. String explorers instead seem to think that the “common sense” they have from everyday use of 3D holes is sufficient guidance to navigate these massive stacks of formalisms safely.

Given that Sabine has snuck in such a nice example of how even an equation a simple as V=IR is far more subject to diverse physical interpretations than we might think after all of its “common sense” interpretation rules are taken into account, what are the odds that navigations of string formalisms that include holes in n-dimensional objects are in any way connected to physical reality?

Lost in Math, indeed.

1. Terry Bollinger: I tend to think this V=IR kerfuffle is just an example of EE dogma. They learn the equation, then learn the only way it is ever used (resistance is a constant!) and replace their knowledge with a less-informative shortcut, "the way it is always done."

I think that is human nature; a kind of thought optimization at the expense of completeness. We build up the dogma and culture of the field, and eventually forget the alternative modes available to us.

I think this is an argument of Engineering Religion vs a mathematician parsing a 4th grader's equation. I'm rather astonished the engineers are arguing at all.

As opposed to saying, "What?! Oh. Yeah, I guess that's true."

2. Dr. A.M. Castaldo,

That’s an excellent and far much more succinct kerfuffle analysis than mine, and I concur fully! (I suspect you had a course in kerfuffle analysis that was not available to me during my matriculation.)

My alma mater (Missouri University of Science and Technology) has some of the largest EE graduation classes in the country. No one else notices us because all these EEs end up in either St. Louis or Kansas City. Apart from the occasional riverboat pilot and city-annihilating President, we Missourians do tend to keep to ourselves a bit, myself being perhaps a bit of an exception.

So, when I saw the remarkably visceral reactions to Sabine's simple and absolutely correct physics statement, my first amused thought was similarly "EE worldview versus physics worldview!"

Issues like this are astonishingly important for understanding how to build a machine intelligence. Just like humans, though in strikingly different ways, computers are bound in attempting to understand an effectively infinite universe by their finite modeling resources, which by comparison are infinitesimally small. This is always the challenge, and it always requires dramatic compromises. The real trick is to compromise without curdling, to make the compromises but keep open the options to change, and always to look for ways to improve.

You said it far better and far more succinctly than I did: “I think that this human nature, a kind of thought optimization at the expense of completeness.”

Exactly! There is this constant balancing act in all intelligent systems, from microbes up to global societies, between over-optimization and adaptability. Thus one reason why the COVID pandemic early on resulted in some serious supply shortages in certain economic sectors (“certain economic sectors”, hah! read: toilet paper) was over-optimization of international supply chains in ways that devastated their ability to reconfigure quickly. This tension is fundamental to life itself, and is vital component of the long-term dynamics of both species and entire ecosystems.

Thus both robots and humans optimize at the expense of completeness, a theme also seen in Sabine’s flat-earth essay. An old and very sharp AI friend of mine at Penn State, John Sustersic, did a marvelous and I think highly relevant quick analysis of Sabine’s flat-earth topic from an AI perspective the Facebook comment thread starting at the address below. (Sorry Sabine, there’s no Google search for it.) Similarly to Sabine, but from an AI perspective, Dr Sustersic’s point is that such belief sets can work very well within a certain context, and can even be considered “optimal” within that context, even when they are flatly wrong in some broader context. As humans, we all do this all the time, leading to viewpoints that become deeply an emotionally entrenched in how we analyze even an assertion as simple as V=IR.

Finally, apart from emotional entanglements, heuristics or “common sense” rules also often provide hints of some greater complexity lies hidden beneath a simple equation. Prince de Broglie did after all figure out that particles are also waves literally by doing not much more than thinking really hard and creatively about another algebraic equation with only three variables. Though it seems complicated due to the matrices he used, Dirac’s prediction of the positron similarly arose mainly from contemplating the equivalent of one of those special relativity triangles I talked about a couple of Sabine posts ago.

So here’s an example of how this kerfuffle also contains an interesting question: Why is it so much easier to build a constant-voltage power supply than it is to build a constant-current power supply? Is there a deeper reason for this?

I’ll that one as a challenge. What do you think?

3. Terry Bollinger: What do you think?

I must defer. I am a math guy with a CS PhD. I did work for about a decade in embedded systems, back in the 80's, writing boot level code in assembly (without an OS) for dozens of kinds of electronic devices; both military and commercial. So I spent a LOT of time working with Electrical and Mechanical engineers, but no formal training. My speculations would be worthless.

4. I think an apology may be due to the EE majors (of which I am not one), at least on these grounds:

"Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other."--the Internet

Ohm's Law does not say resistance is proportional to voltage; it says resistance is proportional to V/I, voltage divided by current. In about 99% of all circuits, doubling the voltage will not double the resistance.

Would you say that according to Einstein's Law, the speed of light squared (in a vacuum) is proportional to the energy?

Secondly, the reason a constant current device is more complicated than a constant voltage source is the same reason that cruise-control is more complicated than a gas pedal. Voltage is the motive force for current. To maintain a constant current vs. changing resistance requires a feedback system to measure current and adjust voltage accordingly, as cruise-control adjusts for going up and down hills.

(Sorry, but the something-is-wrong-on-the-Internet syndrome forced me to get out of bed at 1 AM to type this.)

5. Hi JimV,

Interesting response!

If I understand you rightly, your point is that for both V=IR and E=mc^2 the first two variables (V, I and E, m) are the easy-to-change ones that form ratios, while the third variables (R and c^2) are the constants of those two ratios. Thus if you rearrange them to R=V/I and c^2=E/m, you end up in the odd situation of attempting to calculate a constant in terms of two variables. This obviously misses the point of defining such a ratio constant in the first place.

I agree that this is a good way to phrase the issue. Ignoring for the moment that the analogy is not quite true, since c is a fundamental and universal constant of physics while resistance is both device and situation (e.g. temperature) dependent and has a huge range of possible values, let’s look at your question:

“Would you say that according to Einstein's Law, the speed of light squared (in a vacuum) is proportional to the energy?”

In other words, would it ever make sense to treat c like a variable?

Below is a quote from Minkowski’s famous 1908 lecture Space and Time, in which he (not Einstein!) introduced the concept of integrated spacetime:

“If we now increase c to infinity, so 1/c converges to zero, it is clear from the figure that the branch of the hyperbola leans more and more towards the x-axis…”

Think about that. As a theoretical physicist, Minkowski was willing not only to make c a variable, but to use such a variable as the central part of his argument for how to construct classical space and time.[1]

This is just part of what a theorist does: Explore and upset “givens” that everyone else assumes are fixed. A good physics theorist will by intent take the most abstract view of an equation, and then ponder that abstraction to see if there is some new way of thinking of it. This is how they expand their understanding of how the world is built and what its deeper structure might be.

Thus I don’t think your example is necessarily incompatible with what has already been said: Applied and theoretical physics can often use the same equations in very different ways. Thus an electrical engineer focuses and relies on the mostly invariant nature of “resistance” — and incidentally, it’s worth pointing out that the seemingly simple consistency of a resistor is actually an incredibly complex and non-intuitive emergent effect of solid-state physics, one that is valid only a narrow range of conditions and could not easily have been predicted ab initio from quantum mechanics. A theorist might in contrast focus on such an equation in the most abstract fashion possible to look for new insights.

So: Are there any insights that might be gained from R=V/I?

Well, sure. For one thing, both the quantities on the right are deeply fundamental because they deal with local counts (voltage) and flows (current) of charged particles (electrons and sometimes protons). Resistance is in sharp contrast one of those complex emergent effects that is very difficult to predict without more details and more data. For this reason, the ability to define resistance in terms of more fundamental quantities is a very handy simplification, just as temperature is a simplification of the incredibly complex thermal motions of vast numbers of particles.

So again, it’s good to be willing to explore, if only to look for new perspectives that may not have been as well explored as they should have been.

-----

6. [1] Having mentioned Minkowski’s 1908 thought experiment about altering the speed of light, I should also point this out: His conclusion from that argument is simply wrong.

What Minkowski claimed was that if you increase the speed of light to infinity, the result is a symmetry group that is equivalent to classical, non-relativistic space. Alas, what you actually get is a mathematical singularity in which motion of any type is impossible — a boring, point-like space in which nothing can happen.

The easiest way to show why this is true is to use the Euclidean special relativity right triangle (t: (r/c), t’) that I described in an earlier Backreaction comment. The vertical hypotenuse t is rest-frame (observer) elapsed clock time, the lower (r/c) leg is distance traveled by the moving (observed) object, and the upper t’ leg is clock time elapsed by a clock on the moving (observed) object.

The problem is not complicated: If you set c=∞, then (r/c)=0 and all motion — all concept of spatial distance — disappears, leaving a point-like space moving only through time.

What Minkowski was attempting to get at was that the larger the ratio of c is to the typical velocity of physical objects, the more “Euclidean-like” the spatial subset of spacetime will appear. This case is best represented not by a V-shaped hyperbola (Minkowski’s infinite c), but by setting c to a finite velocity and instead insisting that the speed of material objects always remain very small in comparison to c. This situation is always just a convenient subset and never a true mathematical limit, since attempt to create some kind of absolute “slow limit” to the speed of material objects simply creates a second level of special relativity, and far more complex set of symmetries that have nothing to do with what is observed in our universe.

The figure that best represents the almost-classical case is the group of right triangles for which the distance-traveled sides (r/c) are all “very short”, causing the other t’ to be very close to t — that is, the right triangles for which there is no appreciable time dilation. This is of course the situation we humans live in most of the time, and it enables us to approximate xyz as simple Euclidean with fully orthogonal time. We perceive space as the set of very short (r/c) legs at the bottom of a set of very skinny right triangles. Because this set of very short triangle legs is almost perpendicular to time, staying within it allows us to get away with using this sloppy approximation of the space and time relationship.

The bottom line is that rather than being an extreme limit to the Poincaré symmetries, as Minkowski speculated, classical space can never be more than an illusion enabled by c being much larger than human velocities. That is all classical space really is and ever can be: An approximation.

11. https://www.pnas.org/content/115/33/8252

"Our analysis suggests that the Earth System may be approaching a planetary threshold that could lock in a continuing rapid pathway toward much hotter conditions—Hothouse Earth. This pathway would be propelled by strong, intrinsic, biogeophysical feedbacks difficult to influence by human actions, a pathway that could not be reversed, steered, or substantially slowed.

Where such a threshold might be is uncertain, but it could be only decades ahead at a temperature rise of ∼2.0 °C above preindustrial, and thus, it could be within the range of the Paris Accord temperature targets.

The impacts of a Hothouse Earth pathway on human societies would likely be massive, sometimes abrupt, and undoubtedly disruptive."

12. https://www.nytimes.com/2020/09/15/opinion/letters/trump-coronavirus-climate.html

To the Editor:

Re “Spurred by Fires, Trump and Biden Clash on Climate” (front page, Sept. 15):

You refer to President Trump as a president “who has long scorned climate change as a hoax.” But the reality is more sinister: Much as we’ve recently learned about Mr. Trump’s views on the coronavirus, he has been well aware of the reality of climate change.

How do we know? Because in your own newspaper, on Dec. 6, 2009, Mr. Trump was part of a group that purchased a full-page adurging action on climate change, in which he (and the group) stated, “If we fail to act now, it is scientifically irrefutable that there will be catastrophic and irreversible consequences for humanity and our planet.”

So Mr. Trump knows the scientific truth, but for political purposes he chooses to lie about it to the American public. Apparently, he has so little respect for his own supporters that he just assumes they are too unintelligent to recognize what he himself knows to be “scientifically irrefutable.”

Jeffrey Bennett
Boulder, Colo.
The writer is the author of “A Global Warming Primer.”

1. If the information is correct in an article written on 16 September, 2020, by David Stockman at Lew Rockwell's website, titled: "The Planet's Not Angry...", then the California government is negligent in its forest management policies. Stockman states that: "Academics believe that between 4.4 million and 11.8 million acres burned each year in prehistoric California." If this is true, and I haven't yet searched for the study or studies, that he is referring to, then blame for these fires is being mis-assigned to global warming. Further down in the article is an image of tree rings from an ancient California redwood, showing burn scars for La Nina years starting at the year 1696 well before the Industrial Revolution.

Based on the ideas presented in the article, by suppressing forest fires during non La Nina years; that normally would burn the underbrush that serves as kindling for future blazes, California is creating the conditions for perfect (fire) storms of monumental proportions. The accumulation of combustible fuel within the Golden State’s forests becomes a loaded mouse trap, needing just a slight nudge to tip it over the edge, unleashing enormous conflagrations.

Please note that I’m not questioning evidence for global warming by mentioning this article, just that the cause of California’s wildfires may be mis-attributed.

13. Hello Sabine,

happy birthday.

If I insulted you at Ohm Law, I'm sorry.
It was not my intention.

You are the best.
You're better than Sean Carroll with his theory of many worlds.
You are better than Ian Stewart (*), who as a mathematician does not consequently stick to logic.
You are better than Harald Lesch (**) who said in every third broadcast,
one can only falsify a theory, but unfortunately is not able
to consequently keep this up.
But most of all you have this blog and face the problems in physics in public.
The only physicist better than you is Robert Betts Laughlin (***),
but he has no blog.

I will never argue with you about many-worlds or string theory.
Both are useless in my eyes.

I wish you a nice day
Stefan

(*) Ian Stewart is wonderful at explaining things that can be explained.
And from him I got the joke:
It is proven that log(log(n)) for n against infinity also tends to infinity.
But nobody has ever observed this.

(**) I always liked the Alpha-Centauri broadcasts very much
and also he is very good at explaining things that can be explained.

(***) Laughlin says more clearly than anybody else what does not fit together in physics.

14. I'm interested in how we might progress a more scientific society. It would be comforting to discuss something like tipping points in Sabine's drift here. In the meantime, our social world ticks over electing the likes of Trump, Johnson, Bolsinaro and others in systems with dubious 'alternatives'. Even the Economist holds there are only 20 full democracies in 167 nations they look at. The transfer of scientific knowledge into our global-social systems can often appear negligible other than as pollution. Physics may often be in groupthink as Sabine points out, but society is in the grip of agnotology and precarity. Over simplifying to the extreme, science needs to be in our politics in some reversal of our attempts to keep the Baconian Idols of 'common society' out of our thinking and deliberations. The list of stuff we need to protect ourselves against in the cosmos, global pollution and our biology soon gets huge. The neglected tipping point may be how we scientists tip ourselves back into the precarity of arguing without our current protections.

15. An old fashioned regenerative radio receiver is sort of an analogue to the mechanisms that regulate our planet’s climate. This method of amplifying weak radio signals was invented by Edwin Armstrong in 1912. It operates on the principle of feedback to reach what might be termed the ‘goldilocks’ zone of desirable signal strength. The incoming radio frequency (RF) signal would be fed multiple times through a vacuum tube, or a transistor in later years, gaining strength on each pass, until the desired amplification was achieved. If the feedback was too great signal saturation would occur, possibly blowing out the eardrums of the listener if he/she were wearing headphones. The fine boundary between just the right amount of signal gain and too much gain in a regenerative receiver is like the tipping point that would lead to a runaway greenhouse effect on planet Earth.

16. One could be forgiven, here in New England, for believing that our global climate has reached a tipping point. October here in the northeast USA has been remarkably mild, today reaching 67 degrees, and still holding at 63 degrees at 5:45 PM. The next 3 or 4 days are the same. But a quick look at the weather map shows a vast Canadian cold front pressing on the New England’s door, with a vast area of the Midwest and all the way down to Texas under its grip. Not one to waste a good opportunity I was out biking with cycling shorts and short sleeve shirt, clocking in 17 miles this afternoon. This great weather has enabled me to reach within 8 miles of 2400 miles this season, which I’ll polish off easily tomorrow on the way to a season objective of 2650 miles (about 4265 km). While northeasterners might lament the return of cold weather, there’s a certain reassurance that the much feared global climate tipping point is not yet at hand. Hopefully, it can be staved off until proper measures are in place to prevent it from happening at all.

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