Does Consciousness Cause Collapse of the Quantum Mechanical Wave Function?

No.

First, at this point I am reasonably confident that collapse actually happens.  Either it does or it doesn’t, and non-collapse interpretations of QM are those that have unfounded faith that quantum wave states always evolve unitarily.  As I argued in this paper, that assumption is a logically invalid inference.  So given that we don’t observe quantum superpositions in the macroscopic world, I’d wager very heavily on the conclusion that collapse actually happens.

But what causes it?  Since we can’t consciously observe a (collapsed) quantum mechanical outcome without being conscious – duh! – many have argued that conscious observation actually causes collapse.  (Others have argued that consciousness and collapse are related in different ways, such as collapse causing consciousness.)  In this blog post, I discussed the consciousness-causes-collapse hypothesis (“CCCH”) in quantum mechanics.  I pointed out that even though I didn’t think CCCH was correct, it had not yet been falsified, despite an awful paper that claimed to have falsified it (which I refuted in this paper).

Two things have happened since then.  First, I showed in this paper that the relativity of quantum superpositions is inconsistent with the preparation of macroscopic quantum superpositions, which itself implies that CCCH is false. 

Second, this paper was published a few days ago.  Essentially, it’s a Wigner’s-Friend-esque thought experiment in which a poison-containing breaks or does not break at 12pm, per a QM outcome, but the person in the room will be unconscious until 1pm.  That’s it.  If CCCH is correct, then collapse of the wave function will not occur until the person is conscious at 1pm... but if he is conscious at 1pm, how could the wave state possibly collapse to an outcome in which the person dies at noon?  It’s a very simple logical argument (even though it is not explained well in the paper) that is probably valid, given some basic assumptions about CCCH.

So when does collapse actually occur?  I’ve been arguing that it happens as soon as an event or new fact (i.e., new information) eliminates possibilities, and the essentially universal entanglement of stuff in the universe (due to transitivity of correlation) makes it so that macroscopically distinct possibilities are eliminated very, very quickly.  For example, you might have a large molecule in a superposition of two macroscopically distinct position eigenstates, but almost immediately one of those possible states gets eliminated by some decoherence event, in which new information is produced in the universe that actualizes the molecule’s location in one of those position eigenstates.  That is the actual collapse, and it happens long before any quantum superposition could get amplified to a macroscopic superposition.

Bitcoin, Speculation, and Legal Tender Laws

Note: I took Banking Law, and received one of only two As, at Georgetown University Law Center under Prof. Daniel Tarullo who, from 2009 to 2017, was a Governor of the Federal Reserve Board.

Bitcoin is currently at $43,389.

And everything you need to know about Bitcoin is contained in that one sentence.  In other words, beyond its cost, there is nothing interesting about Bitcoin (or any other electronic “currency”).

Oh, there are interesting facts about where it comes from (and the monumental waste in “producing” it), as well as the utility of block chain technology (which is actually independent of electronic currencies).  But there is nothing interesting about a Bitcoin itself, which is just a seemingly random string of bits.  This isn’t true of gold or silver or wine or emeralds or cars or real estate.  Sure, one of my rental houses might have a market value of $150,000, but there are lots of interesting facts about it other than its “exchange rate” in dollars.  For example, it provides my tenant shelter, modern plumbing, electric conveniences, a big back yard, etc.  And we can debate all day about the intrinsic value of gold, but it is a good electrical conductor and people like wearing it as jewelry.  At least it does something. 

In sharp contrast, Bitcoin doesn’t do anything.  And it’s not because it’s a string of bits.  Hell, software is just a string of bits and so is the information in your favorite movie or Netflix show.  Unlike these, 1BTC is literally a useless string of bits that is simply recognized as “one Bitcoin” by the open-source Bitcoin algorithm.  Its only value is that ascribed by those who own it and/or want it.

“OK, so what?” asks the enthusiast.  “That’s also true of fiat money like the U.S. dollar.”

My three-word answer: LEGAL TENDER LAWS.

Look, there are a thousand reasons to hate Bitcoin, so I’m not going to mention any of them except the one that no one else seems to be talking about – namely, the fact that governments extract wealth from their citizens in the form of taxation, and taxes will always be payable in the governments’ chosen currency.

There is a common fear among Bitcoin enthusiasts that the government will eventually act to shut down electronic currencies.  Sure, that’s a possibility, but that’s not the main problem with Bitcoin.  The real problem – which almost no one seems to realize – is that the government is never going to accept Bitcoin in payment for taxes.  There is no government on Earth that accepts Bitcoin as payment or as legal tender.  Why?  Because accepting payment in an alternative currency devalues their own state-sanctioned currency.  Historically, there are a few shitty rogue governments that have been so incompetent with their own monopoly over currency issuance that their economies are either effectively or legally dollarized.  Zimbabwe springs to mind with its moronic (and fascinating!) $100 trillion bills.  Within the states and territories of the United States, the U.S. dollar is legal tender, which means that all debts, particularly debts to local, state, and federal governments, are payable in this currency and nothing else. 

You cannot pay your New York property taxes in British Pounds.  You must pay it in U.S. dollars or else the state will foreclose on your property.  If you happen to have a bunch of British Pounds, luckily there are 67 million people on an island across the Atlantic who need British Pounds to pay their property taxes to their government.  The meeting of supply with demand creates an exchange rate.  You cannot pay your U.S. income taxes in Indian Rupees.  If you happen to find yourself awash in Rupees, there are 1.4 billion people who need Rupees to pay taxes to their government, and the resulting currency market will allow you to exchange your Rupees for Dollars so you can pay your income tax bill.  The government has a monopoly on the use of force, and it will ultimately use that force to collect taxes on income, sales, property, value-added, etc.

So let’s say you use 2BTC, which you bought ten years ago for a nickel (or whatever) to buy a Tesla automobile, as Tesla apparently plans to start accepting it in payment.  Under the Internal Revenue Code, that is a realization event that makes you liable for taxes on $86,778 in gains.  But you cannot pay this tax in Bitcoin, nor will you ever be able to.  (The Federal Reserve owns the planet.  OK, it sort of shares it with a few other central banks, like the Bank of England, the European Central Bank, etc.)  And since no other government forces its citizens to pay taxes in Bitcoin, there is no “exchange rate” for Bitcoin.  To pay your taxes, you have to get U.S. dollars either by earning them or selling more Bitcoin, which means that the value of Bitcoin must always be denominated in some other country’s currency.

In other words, because Bitcoin is not and never will be legal tender in any country, it will never stand on its own.  The question will always – always, always, always, always, always – be “How much is Bitcoin today?” 

And that’s a problem... an insurmountable problem for Bitcoin enthusiasts.  When you are about to make a purchase in a store in Paris, the clerk doesn’t have to ask, “How much is the Euro today?”  In fact, to most Europeans, that question wouldn’t even make sense.  After all, 1 Euro is 1 Euro!  The store clerk does not need to look up the “value” of the Euro in terms of other currencies or commodities.  She doesn’t care.  She knows she needs Euros to pay her rent, her bills, and – most importantly – her taxes.  But Bitcoin is different.  A price will NEVER be fixed in Bitcoin... every transaction involving Bitcoin will ultimately involve some person or computer asking the question, “How much is Bitcoin today?”

I don’t want Bitcoin because it has no intrinsic value or use.  Governments don’t want Bitcoin because it devalues their monopoly on currency issuance.  And here’s the thing.  Even Bitcoin owners and enthusiasts don’t want Bitcoin. 

“Andrew, shut up.  Of course they do – that’s why they bought it!” 

Wrong.  They bought it because they think others want it.  (Conversely: if they did not think others wanted it, then no one would buy it.)

I used to collect old U.S. coins because I thought they were fascinating and I loved the history.  When I would share my collection with other numismatists, occasionally one of us would say something like, “Can you believe how much this coin is worth?!”  But that wasn’t the focus of our conversation.  We talked about minting, and history, and coin material and condition, and fascinating mint errors like double-struck coins, etc.  The point is that there was substance to the conversation because we actually enjoyed and valued and appreciated the asset, with “dollar exchange rate” a secondary consideration.

Not so with Bitcoin.  After countless conversations with Bitcoin enthusiasts (who tend to show up in droves at Libertarian conventions), I have learned that conversations revolve almost entirely around these two general topics:

* “The price of Bitcoin is $_____... can you believe it?!”  (Sometimes it’s way up, sometimes it’s way down – the only apparent consistency in the Bitcoin price is its volatility.)

* “Death to the Dollar (or Pound or Yen or Transnistrian Ruble)!”

In other words, even Bitcoin owners and enthusiasts don’t value Bitcoin per se – of course they don’t!  It’s just a useless string of bits!  Rather, they value it in terms of its selling price in dollars.

Let that sink in.  Bitcoin enthusiasts hate the U.S. dollar so much that they purchase a useless string of bits whose value – as judged by their own conversations – is determined by the number of those hated U.S. dollars they can sell it for.  That is madness.

The last thing I want to mention is speculation.  If I can pick a booger and manage, through suave argumentation, to convince a handful of people that it is worth a million dollars – is it actually worth a million dollars?  Value is a very subjective thing and the phrase “market value” only has meaning in an efficient and rational market.  The fact that Bitcoin is at $43,389 is exciting to a lot of people.  There are people who will pay this amount and more for 1BTC.  There may very well be people who, under the right conditions, would pay $1 million for 1BTC.  Just keep in mind that it is pure speculation.  Unlike a tulip, which at least offers the tiny subjective value of being easy on the eyes, Bitcoin’s only “value” is its price as denominated in fiat currencies.

And as much as one might despise the U.S. dollar for its lack of intrinsic value, it at least has the ability to prevent IRS agents from confiscating one's property.  Bitcoin cannot do that.  It cannot do anything.

Bitcoin is currently at $43,389.

And that’s all there is to say. 

Fucking COVID

First, let me say that there are many, many, many, many people in the world who are suffering far worse than I am.  But invalidating my own feelings just makes my suffering worse.  Here are some ways I am suffering and feeling frustrated, irritated, and disconnected as a direct result of this virus.

I am sick of decisionmakers only considering the fatality rate of the actual virus when making strong pronouncements, rules, and/or edicts.  I made this point back in April in my only Facebook post on this topic.  There are lots of other factors that should be considered in the analysis, such as:

·         People who are dying of starvation because the slowdown in the world economy, thanks in part to shutdown orders, is literally depriving the millions of people in the world who already can barely feed themselves.  Even among those who aren’t literally dying of starvation, there are untold millions who are dying from otherwise preventable or treatable diseases and problems because of their falling real incomes.

·         People who are dying of suicide, alcoholism, drug overdoses, and complications of depression and poor physical and mental health brought on or exacerbated by this crisis.

·         The overall decrease in happiness (“utility”) in the world, linked to economic slowdowns, physical and emotional isolation, etc., etc.

I hate that it has only recently become somewhat socially acceptable to mention these other factors.  Yes, public policy must consider lives potentially lost to COVID, but it should not ignore lives and livelihoods that may be lost as a direct result of these policies. 

I am sick of being told what to do by authoritarians acting unilaterally.  Yes, governors and mayors (as heads of their respective executive departments) have short-term emergency powers, but this situation is no longer short-term.  Long-term legal solutions should be effected by legislatures and tempered by courts.  There is absolutely no good reason or explanation for why, a year after the virus first hit U.S. soil, decisions about which New York City restaurants can open and at what capacity are still being decided at the arbitrary whim of a single person.

I am sick of the fatigue and the ever-changing goal post.  In March of last year, we were told that shutdowns and closures were temporary so that we can “flatten the curve” so as to not overwhelm the healthcare industry.  We did that.  And then the curve started dropping.  But then the goal changed to something like, “We need to stay locked down until we reduce the positivity rate below X%.”  Where did that come from?  More importantly, such a number is absolutely meaningless unless there is consistency in the rate at which people are tested.  If New York’s positivity rate is 3%, for example, and South Dakota’s is 30%, does that imply that South Dakota is far worse off than New York?  Of course not.  If New York freely tests anyone and everyone (and if people’s jobs there depend, as they often do, on regular testing), then a 3% positivity rate might actually mean that, say, 1% of the population has the virus... while if South Dakota only tests people who are hospitalized and who have COVID symptoms, then their 30% positivity rate might actually correspond to, say, 0.1% of the population having the virus.  (On a recent trip to Florida, I discovered just how complicated, expensive, and inconvenient it was to get a COVID test, while in NYC I can easily get a free test any day of the week just a couple blocks from my apartment.)  The fact that I have to explain this very simple example to show how statistics can deceive – and which no one seems to be talking about, including the condescending intellectual elite who have weaponized the word “science” – is irritating and mind-boggling.  (As a side note, the weaponization of the word “science” is especially infuriating when scientists whom we should trust, like Dr. Fauci, simply make up numbers to manipulate public perception.  I think his intention was good, but that’s irrelevant – it makes him lose credibility as a scientist.)

I am sick of masks.  I hate wearing them.  They are not just uncomfortable, but I hate that they impede communication.  They muffle voices and hide facial expressions and moving lips, all of which are used in human communication.  I hate having to speak more loudly to people because of the muffling of my mask, and I hate that my facial expressions are similarly muffled.  It just makes me less likely to interact and communicate with people at all.  It makes me not want to go anywhere or do anything, which is fine because there is nowhere to go and nothing to do anyway.

I am sick of never knowing what is required, legally or socially, and I am sick of feeling pressured to act in ways that I know are baseless or even irrational.  Are we supposed to wear a mask AND “socially distance”?  What is the protocol for inside versus outside?  No one suggests (I don’t think!) that spouses should wear masks around each other, but what if my wife works closely with a small group of people who eat together out of necessity?  Does that mean she can invite them and their spouses over to our house for a mask-free game night... or must we play an awkward game of cards in which we’re all separated by six feet and breathing through N95 masks?  Literally the social fear of not knowing all the rules (because there is no consistent set of rules) is enough to want to avoid gatherings at all, no matter how desperately we might need them for our emotional survival.  I can’t even imagine being a single college student today and being told to wear a mask and not kiss while having sex.  No normal human would do this, right?  It sometimes makes me wonder if those in charge are playing a massive prank to see just how far they can push the rules.  (“Do you think we could get restaurants to agree to a 6% maximum occupancy and serve only pureed entrées that are sucked through a straw attached to their mask?”  “Yeah!  And all male patrons should be required to wear N95 condoms!”)

Moreover... Do these rules arise from a responsibility to others or to myself?  For example, the virus is spread by saliva and mucus, so if I don’t talk or even open my mouth... if I cover my face when I sneeze... then how can I spread it to anyone, particularly if I’m already standing six feet away?  This issue has come up a few times when I was wearing a mask over my mouth but not my nose.  (Apparently I have a big nose, which makes a mask even more uncomfortable.)  If I have to sneeze, I pull my mask up – which is disgusting, of course, but I guess that’s what others have to deal with.  Beyond sneezing, there is essentially no risk of me spreading a virus to others from my nose, yet I’ve been ordered by various people out in public to cover my nose.  I usually do, to avoid a confrontation, but why should I?  One might reply, “Because you can get the virus with your nose exposed, and you have a responsibility not to get the virus that you can then spread to others.”  But that doesn’t make sense.  If I’m already careful about not spreading germs to others, then what right does anyone have to tell me that I can’t assume a risk to myself?  Do I have the right to acquire the virus if I want?  If I decided that I just wanted to get the virus for, say, the antibodies it would provide, and I knew someone infected who was happy to provide the requisite saliva, is it my right to choose?  I think the answer in a genuinely free country is obviously yes, but I can hear the protests already!  Anyway, my point is that there is room for actual debate about the pros and cons of each rule and how they depend on situation, but what actually happens – at least in my case – is that the social complications and awkwardness of trying to balance my own comfort with my aversion to offending people with my attempt to read social cues with my unwillingness to let bullies dictate rules for everyone else with my efforts to prevent spreading COVID to my older relatives and friends with my desire to actually have fun while other people have fun... ugh... all this just makes me say “Fuck it” and stay at home.

I am sick of the phrase “socially distance.”  Whoever coined it was either a complete idiot who doesn’t know what the word “social” means, because the requirement is actually to physically distance, or was brilliant, because they knew that the constant physical distancing would, over time, emotionally wear people down and cause them to socially isolate from others.

I am sick of the polarized extremes that force people to pick a “team” and prevent them from thinking for themselves.  Do I really have to choose being either a condescending elitist mask nazi or a confederate-flag-toting anarchist?  Can’t I just say that this forced economic shutdown and physical isolation must end soon without being accused of wanting people to die of the virus?

Personally, here is how I am suffering from COVID... and I am suffering:

My primary hobby is travel.  I’ve been to 96 countries.  I canceled three trips last year, including a six-week round-the-world trip with my wife who had just finished a grueling four-year physician residency during which I barely spent any time with her.  Not only have I not traveled anywhere in the past year, but there appears to be no end in sight to this “pandemic” (another word I am sick of), with prospects of returning to any semblance of normalcy diminishing by the day.  I can’t plan anything.  The rules keep changing.  Do I need to wait until after I’m vaccinated?  At this rate, it might not be until summer, and by then, will there be a hundred new vaccine-resistant variants/mutations?  Will I be traveling in some country that was “open” when their government suddenly closes their borders?  Will I be walking around some foreign city but all its museums and restaurants are closed and I’m staying in an otherwise deserted hotel?  This all just makes me feel very hopeless and depressed.

This “virtual” learning is a disaster.  I don’t learn well this way and I suspect that few others do.  I have absolutely no idea how kids are dealing with this.  Oh, that’s right – they’re not.  I started a graduate physics program at NYU specifically for the opportunity to make friends, collaborate with colleagues, have interesting discussions, and learn with others.  The in-person time with professors and fellow students has always helped me to learn and to feel connected, but there is NONE of that now.  Death to Zoom.  Yes, some classes are offered “in-person” (or “hybrid,” which is almost worse than just plain “virtual”) and I took General Relativity last semester in part because it was in-person.  To do so, I satisfied all the requirements but what was the reward?  On average, there was only one other student in class, and even if there were more, there were no rooms or areas in which we could actually collaborate, so what was the point?  I am taking one class this semester, in part to keep my affiliation with NYU, but if normal in-person learning does not resume by Fall (and by “normal” I mean being able to go through one fucking day without thinking about masks, socially distancing, vaccines, nasal swabs, reduced capacity, etc., etc.), then I don’t see the point of continuing in the program. 

I am not connecting with people.  As an INTJ, I can certainly enjoy plenty of alone time, but I need connection, as do all humans.  It is depressingly ironic that I am calling and emailing people less now that I am connecting with them less in person.  That’s due to several factors:

·         We need in-person connection, in part because of body language and other nonverbal communication; spontaneous ideas and adventures happen when people are physically together that can’t happen when we’re staring at each other over Zoom; and we experience new things together that are actually worth talking about later!

·         In-person connection inspires deeper connection and a desire for follow-up phone calls and emails.

·         Right now, we aren’t, as a society, doing much, so there’s not much to talk about.  I have little interest in talking to a friend over the phone about COVID, my lack of connection in physics, my lack of traveling... my lack of anything!

Setting aside my dearth of social connection, I am experiencing the additional detriment of lack of connection in physics.  A little over two years ago, I started working essentially full-time in the field of the foundations of physics and the physics of consciousness, etc.  I have made significant and rewarding progress, both in learning as well as innovating and contributing.  Not only do I now have a relatively deep understanding of the foundations of quantum mechanics that has allowed me to make several contributions, I’ve also come to a deeper understanding of the relationship between physics and consciousness, free will, and other deep philosophical issues.  So that’s good.  However, it’s hard to do anything alone for a long time.  Even Henry David Thoreau eventually had to leave Walden Pond and rejoin society.

And in large part I’ve been working on physics entirely alone.  I’ve tried really, really, really hard to connect with people.  I started two different physics masters programs (ECU and NYU); I prepared to attend two conferences (one canceled and the other almost uselessly virtual); I’ve reached out directly to hundreds of professors, paper authors, graduate students, etc.; I’ve written and posted my own papers and YouTube videos; yada yada yada.  Despite these efforts, I feel almost completely disconnected and alone in this field.  Almost no one understands me, what I’m working on, or what I’ve figured out.  Among my friends and family, this work is far beyond the understanding and interest of anyone I know, although my wife and a couple other people certainly try!  Among people in the actual field – people with whom I’ve been trying to connect for several years now – maybe 1% of these contacts have actually resulted in any meaningful connection.  I am profoundly thankful for and humbled by these few contacts, and several of them have been both intellectually and emotionally supportive.  Ironically, among the tiny handful who have both understood and validated my work, a few of them happen to be the top of the top.  For instance, as I mention in this post, this paper was rejected by referees until the journal’s chief editor, Carlo Rovelli himself, took the extremely unusual step of publishing it despite the reviews because it raises “an interesting and well-argued point.”  I won’t give further details in this post, but as it turns out the reviewer I described in this post – who was one of the only people to actually understand and validate the argument I made in this paper – is one of the most intelligent, original, and influential thinkers in the field.  So I certainly am thankful for the few genuinely positive connections I’ve made, although it’s just not enough (at least right now) to emotionally and intellectually sustain me.  I need to go to conferences and attend classes and have in-person connections to keep me feeling stimulated, inspired, and connected.  Right now – and in the foreseeable future – that is simply impossible. 

So my suffering comes down to this: I am just not looking forward to anything.  I feel like my life is perpetually on hold with every day undetectably bleeding into the next.  I am sick of constantly waiting for normalcy.  I am sick of not knowing when, or even if, I will be able to travel, to efficiently learn about the physics of consciousness, to emotionally connect with friends, to intellectually connect with colleagues.  I am sick of not knowing when I will again feel engaged, inspired, in flow.

Pain is usually a sign that something’s wrong.  If I feel my hand burning, it might be because of some miswired neurons or something wrong with my skin, in which case medication might be appropriate.  But it might also be because my hand is in a fire, in which case the best solution is to pull it out!  Poor mental health – depression, anxiety, etc. – presumably evolved in humans to help us identify and fix problems and to ultimately thrive.  Sometimes, poor mental health is due to chemical imbalances that can be addressed with medication.  Sometimes it’s due to emotional trauma that can be addressed with counseling.  Sometimes it’s due to poor physical health that can be addressed with diet and exercise.  To the extent that poor mental health is the body reacting inappropriately to the world, then by all means let’s address the symptoms.  No sense in feeling the pain of anxiety when there’s nothing to feel anxious about... take a pill for crying out loud!

But sometimes, poor mental health is a direct result of circumstance and it’s the body’s appropriate response to dangerous or unhealthy surroundings.  Dulling that pain with a pill might only serve to increase one’s tolerance to what is, or should be, an intolerable situation.  I can’t speak for anyone else, but it is clear to me that the world I live in is currently intolerable.  Not that I can’t tolerate it, but that I shouldn’t. 

I don’t know what the solution is.  Like many others, fatigue is setting in.  If I knew for certain that normalcy would return by, say, July, then I could wait it out.  But if I am honest with myself, I am having growing doubts that normalcy will return at all, much less by summer.  Maybe it’s time to accept that the world I grew up in is gone forever: one in which everyone had more-or-less the same source of news and people didn’t choose their news media based on the “facts” they want to believe; one in which people could go to parties, dance clubs, restaurants, and theaters without constantly worrying about viruses; one in which human connection was almost exclusively in-person; one in which I might have 20 close friends who know my good and bad sides and with whom I can be vulnerable, instead of 2000 Facebook “friends” or 200,000 Instagram “followers” who envy my beautiful and successful life but know nothing about my doubts or sadness or despair because I only post the enviable stuff.

Maybe it’s time to mourn the loss of that world and move on.  (I suppose with such low expectations, I can only be pleasantly surprised if normalcy actually does return later this year...)  I don’t know what to do, but I know I have to do something differently.  Maybe it’s time to abandon physics for awhile and take a road trip with my dog to some national parks.  Maybe I need to build something – maybe not quite the scale of the Agora Grand, but nevertheless interesting and useful and creative.  Who knows?  Suggestions welcome! 

Thank God for my wonderful wife and my friends and family, even if I don’t connect with them as often as I should.  Thank God that I am well fed and live in a nice apartment with amenities that Cleopatra could only dream about.   Thank God I can still think with clarity.

 

God – please give me the grace and peace to accept the things I cannot change, the courage and strength to change the things I should, and the clarity and wisdom to know the difference.

Is Scalable Quantum Computing Possible? And Why Does It Matter?

Tomorrow I begin a class on quantum computing at NYU, taught by Javad Shabani.  In preparation, I am reading Scott Aaronson’s fascinating Quantum Computing Since Democritus.

The notion of quantum computing is simple.  Computers rely on bits – transistors that serve as little on-off switches.  By starting with an initial string of bits and then manipulating them in a particular way according to software (e.g., turning “on” or 1 switches to “off” or 0, etc.), a computer can essentially perform any calculation.  Computers don’t need to be made of transistors, of course, but that tends to be much more efficient than using, say, Tinker Toys.  A quantum computer is simply a computer whose bits are replaced with “qubits” (quantum bits).  Unlike a classical bit that can only take the state 0 or 1, a qubit can be in a superposition of 0 and 1 (or, more precisely, state α|0> + β|1>, where α and β are complex amplitudes and |α|² is the likelihood of finding the qubit in state |0> and |β|² is the likelihood of finding the qubit in state |1> if measured in the {|0>,|1>} basis). 

The reason this matters is that because there are “infinitely many” (well, not really, but certainly lots of) possible states for a single qubit, because α and β can vary widely, while there are only two states (0 or 1) for a classical bit.  In some sense, then, the “information content” of a qubit (and ultimately a quantum computer) is vastly greater than the information content of a classical bit (and corresponding classical computer).  If you think your iPhone is fast now, imagine one with a quantum computer processor!

At least... that’s the advertisement for quantum computing.  In reality, there are several problems with actual quantum computing.  I won’t dig too deeply into them, as they’re well described by articles such as this, but here are a few:

·         Nobody knows what to do with them.  There are a couple of particular kinds of software, such as Shor’s algorithm for factoring large composite numbers, that would have useful implications for cryptography and information security.  Beyond that, there don't seem to be many real-world applications of quantum computers that would be significantly faster than classical computers.

·         Qubits must remain isolated from the rest of the world (except for their entanglements with other qubits) during the computation, but this is a massively difficult problem because of decoherence.  You can have a microSD card with literally billions of classical bits... you can stick it in your pocket, use it to pick a piece of chicken out of your teeth, drop it in the toilet, probably zap it in the microwave for a few seconds... and it will probably still work fine.  (Full disclosure: I’ve never actually tried.)  But qubits are so ridiculously sensitive to influences from the world that it takes a huge multi-million-dollar system just to adequately cool and isolate even a dozen qubits.

·         Even if there were a way to adequately isolate lots of qubits, as well as entangle and manipulate them in a way necessary to execute a useful algorithm, and even if you could do this for a reasonable price on a reasonably sized device, error correction seems to be a major problem.  Errors are caused (at least in part) by decoherence, and quantum error-correction means are supposedly possible in principle, but these means (e.g., requiring 1000 additional error-correcting qubits for each existing qubit) may prove seriously problematic for the future of quantum computing.

At the end of the day, the real question is not whether a “quantum computer” consisting of a handful of entangled qubits is possible – of course it is, and such computers have already been built.  Rather, it is whether the problems of isolation, decoherence, and error-correction will prevent the possibility of "scaling up" a quantum computer to some useful size.  Aaronson famously offered $100,000 for “a demonstration, convincing to me, that scalable quantum computing is impossible in the physical world.”  I want to know the answer to this question not just because it’s such a massively important question pervading modern science and technology, but also because of its relationship to my own work on consciousness, with implications going both ways.  Specifically, what might the physical nature of consciousness tell us about the possibility of scalable quantum computing, and what might the possibility of scalable quantum computing tell us about the physical nature of consciousness?

Here’s an example.  I have been arguing for some time (e.g., in this paper and this post) that macroscopic quantum superpositions, like Schrodinger’s Cat (“SC”) and Wigner’s Friend (“WF”), can never be demonstrated, even in principle, because any “macroscopic” object (e.g., a dust particle, a cat, a planet, etc.) is already so well correlated to other objects through a history of interactions (including “indirect” interactions because of transitivity of correlation) that it can never exist in a superposition of macroscopically distinct position eigenstates relative to those other objects.  Of course, the majority opinion – practically the default position – among physicists and philosophers of physics is that WF is possible.  Nevertheless, even those who claim that WF is possible will admit that it’s really difficult (and perhaps impossible) in practice and will often resort to the plausibility of conscious AI (i.e., “Strong AI”) to save their arguments.  David Deutsch in this article, for example, spends dozens of pages with lots of quantum mechanics equations “proving” that WF is possible, but then spends a half page saying, essentially, that OK, this probably isn’t possible for an actual flesh-and-blood human but we might be able to do it on a computer and since it’s obvious that consciousness can be created on a computer... blah blah...

The problem, of course, is that not only is it not obvious, but I showed in these papers (here and here) that consciousness actually cannot be created on a computer because it is not algorithmic.  So if the possibility of WF depends on AI being conscious, and if computer consciousness is in fact physically impossible, then there must be some explanation for why WF is also physically impossible – and that explanation may equally apply to the impossibility of large quantum computers.  Further, many proponents of the possibility of computer consciousness, such as Aaronson, suspect that we’ll need a quantum computer to do the job, in which case the possibility of WF and conscious AI may hinge on the possibility of scalable quantum computing.   

Anyway, this is all to say that much of what I have discovered, innovated, and now believe about consciousness, quantum mechanics, information, Wigner’s Friend, etc., is closely related to the question of whether scalable quantum computing is possible.  Before actually beginning the class on quantum computing, here is my prediction: I think that scalable quantum computing is, in fact, impossible in the physical world.  Here’s why.

First, the possibility of scalable quantum computing, like the possibility of macroscopic quantum superpositions, follows from the assumption of “U” (i.e., the “universality” or “unitary-only” assumption that a quantum wave state always evolves linearly).  But U is an invalid logical inference as I argue in this paper; I actually think it is irrational to believe U.  In other words, it seems that the primary argument in support of scalable quantum computing is actually a logically invalid inference.  Further, I think that most of those who believe U (which is probably the vast majority of physicists) don’t even know why they believe U.  As a bettor, I would say that the smart money goes on those who actually understand (and, better yet, can justify) the assumptions they make.  The fact that so many of those who believe in scalable quantum computing also assume U leads me to doubt their claims.

Second, the possibility of scalable quantum computing depends on foundational questions about quantum mechanics, and very few scientists (including those who assert that scalable quantum computing is possible) actually understand quantum mechanics.  I know this may sound arrogant... how can I possibly claim to understand QM well enough to conclude that so few people do?  Well, that isn’t what I said – although, incidentally, I do believe I now understand QM at a level far more deeply than most.  You don’t have to understand a topic to be able to identify logical contradictions.  Unlike my brilliant physician wife, I know next to nothing about medicine or the human body, but if I heard a doctor say, “The brain does X” and then later say “The brain does not do X,” then I will know that the doctor does not understand the brain.  So it is with QM.  Here are a couple of papers in which I’ve addressed contradictions by physicists discussing QM (here, here, and here), and it drives me absolutely bonkers at the cognitive dissonance required for a physicist to say something like “Schrodinger’s Cat is both dead and alive.”

Third, and most importantly, I think that scalable quantum computing will run into the same problem as macroscopic quantum superpositions, which (as discussed above and in the cited papers) I think are impossible to create and empirically demonstrate.  I’m not sure it’s exactly the same problem, but it’s really similar.  For example, I argued here that when a tiny object measures the position of a measuring device, it inherently measures the position of other objects in the rest of the universe, whose positions are already well correlated to that of the measuring device.  Will that argument apply to, say, a million qubits that are entangled with each other but isolated and uncorrelated to other objects in the universe?  I don’t know, but it certainly suggests a similar problem. 

On a related note, I have argued that a superposition state of a single particle can grow via quantum dispersion, but as the object grows in size, a potential superposition suffers two problems: reduction in the rate of dispersion (thanks to the Uncertainty Principle) and increase in the rate of decoherence.  We can do double-slit interference experiments on objects as large as maybe a thousand atoms, although anything much beyond that seems to be impossible for all practical purposes.  I suspect the same problem, or something comparable, will arise with groups of entangled qubits.  In other words, I am reasonably confident that there is a set of quantum superpositions that are physically impossible to empirically demonstrate, even in principle – and I would bet that whatever physical mechanism prevents such superpositions would also prevent scalable quantum computing.   

But I don’t know for certain.  For example, I don’t know how an individual qubit is placed in an initial (superposition) state, nor do I know how groups of qubits are entangled and manipulated in the way necessary to perform the desired algorithm.  It may turn out that the only real limitation is decoherence, and perhaps error correction may indeed be adequate to overcome decoherence limitations.  I sincerely doubt it, but these are the sorts of questions I am looking forward to answering this semester!

Do Conscious States Depend on History?

I’ve had a few additional thoughts further to my recent post on counting conscious states, particularly on the extent to which a given conscious state is history-dependent (i.e., depends on its history of prior conscious states) and whether a particular conscious state can be created de novo (i.e., from scratch, without the person experiencing that state having actually experienced previous conscious states).

Imagine that a person has actually experienced a particular series of conscious states (which of course depend, at least in part, on the stimuli sensed).  For the sake of simplicity, I’ll just assume that there’s a conscious state for each stimulus “frame,” and for ≈10 distinct frames/second, there are about 300 million stimulus frames per year.  I’m 43 now, and not sure whether we should start counting conscious frames from birth or sometime later, but let’s say that I’m just about to experience my ten billionth conscious state.  In my last post, I gave a (very, very) rough estimate for the minimum number of information bits necessary to specify such a state.  That number may be large – say, on the order of a trillion bits – but it’s not ridiculous and is less information capacity than many people have on their mobile phones.  Whatever that number happens to be – that is, the minimum number (B) of bits necessary to specify a particular conscious state – the point is this: By assumption, the instantiation of those B bits in the configuration necessary to create conscious state C₁ will indeed create that state C₁.  (For the following argument, it doesn’t matter whether the mere existence/instantiation of that particular configuration of bits is adequate, or whether that configuration must be executed on some general-purpose computer/machine.)

In other words, by assumption, some conscious state C₁ is sufficiently encoded by some series of B bits that may look like: 0011010100110111110... (trillions of bits later)... 10001001111100011010.  There may be a lot of bits, but the idea is that if physicalism is true and the information content of any given volume is finite, then any particular conscious state must be encoded by some string of bits.  If this seems odd to you, it’s definitely the majority opinion among physicists and computer scientists who actually think about this kind of stuff.  For example, Scott Aaronson characterizes the situation this way:

“Look—I don’t know if any of you are like me, and have ever gotten depressed by reflecting that all of your life experiences, all your joys and sorrows and loves and losses, every itch and flick of your finger, could in principle be encoded by a huge but finite string of bits, and therefore by a single positive integer. (Really? No one else gets depressed about that?)”

For the record, I don’t get depressed about that because I don’t believe it’s true, although I’m still trying to formulate my reasoning for why.  OK, so let’s assume that I have in fact experienced ten billion conscious states.  The state I am currently experiencing is C_{10,000,000,000} (let’s call it C_T), and a tenth of a second ago I experienced conscious state C_{9,999,999,999} (let’s call it C_T-1), and a tenth of a second before that I experienced C_{9,999,999,998} (let’s call it C_T-2), and so on back.  Again, by assumption, each of these states is encoded by a particular string of bits.  So here’s my question: is it possible to just recreate state C_T  de novo without, in the process, also producing state C_T-1?

Here’s another way of phrasing the question.  Is the person who is experiencing conscious state C_T someone who actually experienced C_T-1 (and C_T-2 and so on back), or someone who just thinks/believes that he experienced C_T-1?  Is there a way to produce someone in state C_T without first producing someone in state C_T-1?  I don’t think so; I think that state C_T is history dependent and literally cannot be experienced unless and until preceding state C_T-1 is experienced.  After all, if conscious states are indeed history independent, then the experience of C_T is precisely the same no matter what precedes it, and that could lead to some odd situations.  Imagine this series of conscious experiences:

Series #1

C₁₀₀₀: sees alligator in the distance

C₁₀₀₈: gets chomped by alligator

C₁₀₄₅: puts tourniquet on chomped arm

C₂₀₀₀: eats own birthday cake

C₃₀₀₀: rides on small plane to experience skydiving

C₃₀₉₀: jumps out of airplane to experience thrilling freefall

C₃₁₁₄: pulls rip cord of parachute

C₃₂₀₅: lands safely on ground

 

If conscious states are history independent, then the person’s experience at C₃₂₀₅ is precisely the same even if the physical evolution of the world actually caused the following ordering of conscious states:

Series #2

C₁₀₄₅: puts tourniquet on chomped arm

C₃₀₀₀: rides on small plane to experience skydiving

C₁₀₀₈: gets chomped by alligator

C₃₀₉₀: jumps out of airplane to experience thrilling freefall

C₂₀₀₀: eats own birthday cake

C₃₁₁₄: pulls rip cord of parachute

C₁₀₀₀: sees alligator in the distance

C₃₂₀₅: lands safely on ground

 

I can’t see how the above series would make any sense, but more importantly I can’t see how, even if it did make sense, the experience of conscious state C₃₂₀₅ could possibly be the same in both cases.  If I’m right, it’s because conscious states are history dependent and state C₃₂₀₅ actually cannot be experienced immediately after C₁₀₀₀.

I’m not sure where I’m going with this.  If conscious states are history dependent (which is what I’ve suspected all along, as in this paper) then lots of interesting implications follow, such as that conscious states cannot be copied, consciousness is not algorithmic, etc.  (I believe I've already independently shown these implications in this paper.)  The above analysis certainly suggests history dependence but is not a proof.  Maybe the way to prove it is by first assuming that conscious states are independent of history – in which case conscious state C₃₂₀₅, for example, can be created de novo without first creating conscious state C₃₂₀₄ (which can be created de novo without first creating conscious state C₃₂₀₃, etc.) – and then see whether that assumption conflicts with observations and facts about the world.

Remember that, by assumption, state C₃₂₀₅ is just instantiated by a (very long but finite) string of bits, say 0011010100110111110...  So imagine if we start with a long series of on-off switches all initially switched off.  We turn some of them on until eventually we have instantiated the correct series (0011010100110111110...), which encodes state C₃₂₀₅.  But it does not (and cannot) matter the order in which we flip those switches.  I have to think more about the mathematics, but I suspect that in guaranteeing that C₃₂₀₅ is independent of history, so that it and every preceding conscious state can be instantiated independently of its own history, we will end up needing far, far more bits than my original estimate of N^T.  I suspect that even the most conservative estimate will show that if conscious states are history independent, then consciousness will require far more information storage than is currently believed to reside in the brain. 

Then again, I really don’t know.  This is still just the initial seed of a thought. 

Counting Conscious States

Information is physical, which means there is a limit to the amount of information that can fit in a given volume.  If you try to cram more information into that volume, the physical mass of that information will literally collapse into a black hole.  That limit is called the Bekenstein bound and is truly a massive limit.  For instance, the total informational bound that could be contained in a volume the size of the human brain is around 10^42 bits, which means that the total number of possible brain states is around 2^(10^42).  The total informational capacity of the entire visible universe is on the order of 2^(10^120) states.

Why does this matter?  Physicalism (as contrasted with dualism) says that conscious states are produced by physical states; if a first conscious state is distinct from a second conscious state, then they must be produced by different physical states.  All of my papers (and most or all of my blog posts) so far have assumed physicalism is true, in part because anyone who doubts physicalism is usually condescendingly dismissed, ignored, or scoffed at by the scientific community, and in part because I don’t see why the Creator of the already ridiculously complicated universe would have omitted a physical explanation/mechanism for consciousness.  In other words, unless there is a reason to believe that consciousness does not entirely depend on underlying physical state, I see no need, for now, to reject physicalism.  Nevertheless, physicalism would be falsified if one could show that the number of distinct conscious states exceeded the number of physical states, because that would require that a single physical state could produce more than one distinct conscious state.

One avenue for evaluating physicalism, then, is to literally count distinct conscious states.  For example, if one could show that the total number of possible distinct conscious states by a particular person exceeded 2^(10^42), then that would prove that consciousness cannot depend (entirely) on the brain; if one could show that the number of possible distinct conscious states exceeded 2^(10^120), then that would literally falsify physicalism. 

A few years ago, Doug Porpora wrote a fascinating paper that attempted to prove that the total number of distinct conscious states is actually infinite.  One of his arguments, for instance, is that if we assume that there are some natural numbers that we cannot think about, then there must be a maximum number (call it Max) that we can think about and a minimum number (call it Min) that we cannot think about.  But if we can think about Max, certainly we can think about Max+1 or Max^2, which means that Max is not the maximum number we can think about and the original assumption (that there are some natural numbers that we cannot think about) is false.  A related argument is that by identifying the minimum number that we cannot think about (and even naming it Min), we are thinking about Min, which means that Min is not in the set of numbers that we cannot think about!  Again, the original assumption is false.  There is more to the argument than this but it gives you the general flavor of its proof-by-contradiction strategy.  One commenter has attempted to refute Porpora’s argument in this paper, and Porpora may be working on a reply. 

This got me thinking again about the importance of counting distinct conscious states, which very few people seem to have attempted.  Of course, if Porpora’s logical argument is correct, then physicalism is false because even though 2^(10^120) is a ridiculously and incomprehensively large number, it is still trumped by ∞.  But we should also realize that both of the quantities we are considering are extremes.  Infinity is extreme, of course, but so is the Bekenstein bound.

Let’s take a more realistic approach.  There are something like 100 billion neurons in the human brain.  If each neuron acts like a digital bit, then the total number of distinct brain states is 2^(100 billion).  Neurons are actually complex cells with very complicated connections to each other.  I don’t think any neuroscientist seriously regards neurons as acting in any way like digital bits.  However, I do think it is interesting to ask the question of whether or not the number of distinct conscious states exceeds 2^(100 billion).  If there were a way to answer that question – by somehow counting conscious states – then it would do a couple things:

·         Assuming physicalism is true, discovering that the number of distinct conscious states exceeds 2^(100 billion) would confirm that the brain is not a digital computer with neurons acting as digital bits.

·         It would provide a methodology for counting conscious states that may provide further insights about the physical nature of consciousness.

On that note, let me suggest such a method.  First, let me start with the notion of one stimulus “frame,” which is the particular collection of physical stimuli that one might detect through the five senses at any given moment.  Let’s assume that there are N consciously distinct (frames of) stimuli.  What I mean by that is that there are N different combinations of stimuli from the person’s senses that the person would be able to distinguish.  Consider these different sets of stimuli:

·         Watching a sunset while hearing crashing waves while tasting white wine while smelling the salty ocean while feeling sand under one’s feet;

·         Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet;

·         Watching a sunset while hearing seagulls while tasting white wine while smelling the salty ocean while feeling sand under one’s feet.

If we actually took the time to list them, we could certainly produce a very, very long list of consciously distinct stimuli.  Some of them might differ very subtly, such as two stimuli that are identical except for the temperature of the sand differing by one degree, or a slight difference in sound frequency distribution from the seagulls, or a slight but perceptible difference in the cloud distribution above the sunset.

What matters, in enumerating consciously distinct stimuli, is whether a person could distinguish them, not whether he actually does.  If he could distinguish two stimuli, either by consciously noticing the difference or simply having a (slightly) different conscious experience based on the difference, then that difference must be reflected in the underlying physical state.

So how many such distinct stimuli are there?  Lots.  One could certainly distinguish millions of different visual stimuli, many thousands of different sounds and tactile sensations, and at least hundreds of different tastes and smells.  This is a ridiculously conservative claim, of course; there are professional chefs, for example, who can probably differentiate millions of different tastes and smells.  On this very conservative basis, there are probably far, far more than 10^18 (around 2^60) distinct stimuli for any given person.  If there were only 10^18 distinct conscious states or experiences, then in principle it would only require about 60 bits to specify them. 

However, history matters.  Conscious experience does not depend just on one’s stimuli in the moment, but also on prior stimuli (as well as prior conscious experience).  To specify a person’s conscious experience, it is not enough to specify his current stimuli, as his experience will also depend on past stimuli.  For example, imagine the different conscious experiences at time t1:

Case A – No significant change from t0 to t1:

t0: Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet.

t1: Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet.

Case B – Significant change from t0 to t1:

t0: Watching a sunset while hearing crashing waves while tasting white wine while smelling the salty ocean while feeling sand under one’s feet.

t1: Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet.

The stimulus at t1 is the same in both cases, but the conscious experience would clearly be different.  In Case A, the person may simply be enjoying the surroundings, while in Case B, he may be confused/surprised that his wine has suddenly changed flavor and color.

What that means is even if the information necessary to specify the particular stimulus at time t1 is 60 bits, that information is not sufficient to specify the person’s conscious experience at that time.  In other words, history matters, and instead of just counting the number of possible distinct stimuli, we need to consider their order in time. 

So, for N consciously distinct stimuli, let’s assume that one’s conscious experience/state at a given time is sensitive to (i.e., depends on) the time-ordering of M of these stimuli.  The total number of possible states, then, is just the permutation N!/(N-M)!, but assuming that N>>M, this total number of states ≈ N^M.  

So in the above example, the number of possible physical states necessary to allow the person to consciously distinguish Case A from Case B is not N, but N^2.  If N requires, say, 60 bits of information, then at least 120 bits are required to specify his conscious state at time t1.  But of course the situation is far worse.  We can imagine a series of ten consecutive stimuli, ending at time t9, which the person would consciously experience in a manner that depended on all ten stimuli and their order.  It makes no difference whether the person actually remembers the particular stimuli or their order of progression.  As long as he has a conscious experience at t9 that is in some (even miniscule) manner dependent on the particular stimuli and their order, then that conscious state is one of at least N^10 states, requiring at least 600 bits to specify.

Now note that his experience at t9 is a unique one of at least N^10 states, just as his experience at later time t19 is a unique one of at least N^10 states, and so forth until time t99.  But if his conscious experience at time t99 is sensitive to the ordering of his conscious experiences at t9, t19, t29, etc., then the conscious state at t99 is one of at least N^100 states, requiring at least 6000 bits to specify.  Once again, this analysis has nothing to do with whether the person remembers any specifics about his prior stimuli or experiences; all that matters is that his conscious experience at t99 depends to some degree on the ordering of experiences at t9, t19, etc., and that his experience at t9 depends to some degree on the ordering of stimuli at t0, t1, etc.

It’s easy to show, then, that the total number of possible conscious states is N^T, where T is the total number of individual “frames” of stimulus that one experiences over his life.  How many is that?  Well, 100 years is about 3 billion seconds, and we certainly experience more than one “frame” of stimulus per second.  (Otherwise, TVs would not need a refresh rate of around 30 frames/second.)  So, for 10 frames/second, we might estimate the total number of possible conscious states at about N^(30 billion).  If N is 2^60, then the total number of conscious states is 2^(1.8 trillion), requiring at least 1.8 trillion bits to specify.

I find it fascinating how close this is to the number of neurons (100 billion) in the human brain.  For extremely rough back-of-the-envelope calculations like this, an order or two of magnitude is certainly “close.”  The storage capacity of the human brain has been estimated somewhere in the tens to thousands of terabytes, and once again the above rough estimate is within a couple of orders of magnitude of this amount.

What this tells me is that this method of counting distinct conscious states is viable and potentially useful and valuable.  By getting better estimates for the number of stimuli that a person can distinguish, for example, we might find that the rough estimate above (≈ trillion bits) is far too high or far too low, which could then provide insights on our understanding of the brain as: a computer; a digital computer; a digital computer with neurons acting as bits; and the independent source of consciousness.  Of course, such an analysis will never get us anywhere near the Bekenstein bound or infinity, as addressed by Porpora’s paper, but I still think we can learn interesting and important things about the physical nature of consciousness by counting distinct conscious states.

Finally, I think the above analysis hints at something fundamental: that consciousness is history-dependent.  This is something I discuss at length in my paper on the Unique History Theorem, but the above arguments suggest a similar conclusion by a very different analysis.  If one’s conscious experience at time t99 depends to some degree on his experience at t98, which in turn depends on his experience at t97, and so on back, then it may not be possible to produce a person de novo in a particular conscious state C1 who has not already experienced the particular sequence of conscious states on which state C1 depends.

In any event, I think it makes sense to seriously consider and estimate the number of potentially distinct conscious states, taking into account a human’s sensitivity to different stimuli and the extent to which ordering of stimuli affect conscious states.  I think this approach could yield potentially fascinating knowledge and implications about the brain and the physical nature of consciousness.