Typical Atmospheric Mind

FBI assessment of Paul Erdos:

[Erdos] is in the abstract field of mathematics and is purely a mathematician with typical atmospheric mind as related to factual things, that is, he is of the genius type who lives within his mental scope, and that it is difficult to know him personally.”

More in this recent video. Apparently they wondered why he avoided national loyalties, and how he has good ties in Communist countries.

The Existential Crisis Iceberg

Youtuber Alex O'Connor summarizes The Existential Crisis Iceberg.

There is an assortment of philosophical theories that deny our existence, and make everything not what they appear to be. I have discussed examples here, such as the simulation hypothesis, many-worlds theory, and superdeterminism. There are more.

Most of these cannot really be proved true or false, but believing them requires abandoning science as we know it.

Yes, I think it is beneficial to be aware of these theories, even it is kooky to believe in them.

Many worlds offers quantum immortality. Hugh Everett believed in this, reportedly. He would die in various branches of the universal wave function, but there would always be a branch in which he lives, and his consciousness would persist in that branch, so he would be immortal.

If you really believed this nonsense, you could buy a lottery ticket, and rig a machine to kill you if you do not win the jackpot. Your consciousness will then go with the branch that wins the lottery, and you will be rich.

Many physicists say that they believe in many-worlds theory, but they sure do not act like it.

Here is David Deutsch, trying to explain away the quantum suicide paradox. He describes a scenario, where you can stay at home and risk getting killed by a meteor from outer space, or drive to the grocery store and get killed in a car crash. A normal person would say that the meteor is so unlikely as to not worry about it.

But if you believe in many-worlds, it does not make sense to compare the probabilities of the parallel worlds. Both are just as real as each other. So why not play Russian roulette, or buy that deadly lottery ticket?

He says that he solved this problem. He says you have to make decision somehow, and a rational person will make decisions as if the probabilities are meaningful, so we get the same human behavior whether we believe in many-worlds or not.

I am not persuaded. Maybe I did not understand his argument. Listen for yourself.

Statistician Denies Probability Exists

Some say that quantum probabiliities are real and physical, while other say that all probabilities are just subjective estimates of human belief. I think neither is quite right.

David Spiegelhalter writes in SciAm:

Probability Probably Doesn’t Exist

All of statistics and much of science depends on probability—an astonishing achievement, considering no one’s really sure what it is ...

My argument is that any practical use of probability involves subjective judgements. ...

At the sub-atomic level, the mathematics indicates that causeless events can happen with fixed probabilities (although at least one interpretation states that even those probabilities express a relationship with other objects or observers, rather than being intrinsic properties of quantum objects). ...

There is a limited range of well-controlled, repeatable situations of such immense complexity that, even if they are essentially deterministic, fit the frequentist paradigm by having a probability distribution with predictable properties in the long run. These include standard randomizing devices, such as roulette wheels, shuffled cards, spun coins, thrown dice and lottery balls, as well as pseudo-random number generators, which rely on non-linear, chaotic algorithms to give numbers that pass tests of randomness.

In the natural world, we can throw in the workings of large collections of gas molecules which, even if following Newtonian physics, obey the laws of statistical mechanics; and genetics, in which the huge complexity of chromosomal selection and recombination gives rise to stable rates of inheritance. It might be reasonable in these limited circumstances to assume a pseudo-objective probability — ‘the’ probability, rather than ‘a’ (subjective) probability. ...

In several of those situations, a math calculation gives a probability that is accurate to several digits. This clearly reflects an objective physical reality, and not just a human belief. On the other hand, I don't think that probability is as real as energy or momentum. Probability cannot be directly measured, but only indirectly estimated by running repeated samples.

The proponents of many-worlds theory also deny that probably exists, for other reasons. They believe that all possibilities happen in their own universes, and that it makes no sense to say any are more likely than others.

Mathematical Truths can be Proved

SciAm gives this explanation of Goedel's theorem:

You will never be able to prove every mathematical truth. For me, this incompleteness theorem, discovered by Kurt Gödel, is one of the most incredible results in mathematics. It may not surprise everyone — there are all sorts of unprovable things in everyday life — but for mathematicians, this idea was a shock. After all, they can construct their own world from a few basic building blocks, the so-called axioms. Only the rules they have created apply there, and all truths are made up of these basic building blocks and the corresponding rules. If you find the right framework, experts long believed, you should therefore be able to prove every truth in some way.

But in 1931 Gödel demonstrated otherwise. There will always be truths that elude the basic mathematical framework and are impossible to prove. And this is not a purely abstract finding, without implications for practical situations. Shortly after Gödel’s groundbreaking work, the first provably unprovable problems emerged. For example, it will never be possible to clarify how many real numbers exist within the mathematical framework currently in use.

This is a typical explanation, and I know what they are trying to say, but it is misleading.

In spite of this, it may well be possible to prove every mathematical truth from the axioms, in some way. How would we ever know that it is the truth, unless it is proved in some way? It just might not be provable within a particular system.

People read this and conclude that the method of mathematical axioms and proofs does not work. But it does. Every provable statement is true in every model, and every statement true in every model can be proved from the axioms. Goedel proved that. That is what justifies using first order logic as the basis for mathematics.

ZFC serves as a suitable axiom system for all of mathematics.

Even before Goedel, it was known that set theory had countable models, so a model of the real numbers might have only countably many reals in use. Yes, it seems strange, but it does not undermine the use of axioms and proofs to find truths about reals. The set that enumerates those reals is not in the model.

People say it is shocking that a mathematical system cannot prove, from within the system, its self-consistency. But not really. Such a proof would not make much sense anyway. Inconsistent theories can prove their own consistency, as they can prove anything.

Goedel's incompleteness theorem was indeed a profound and important theorem, but popularizations of it are so misleading as to be not helpful.

Quantum Computer Stocks Rise and Fall

Quantum computer startup stocks have been skyrocketing, as Dr. Bee notes, but Nvidia just threw cold water:

The shares of IonQ Inc. and other companies linked to quantum computing tumbled on Wednesday, after Nvidia Corp. Chief Executive Officer Jensen Huang said that “very useful” quantum computers are likely decades away.

“If you kind of said 15 years for very useful quantum computers, that would probably be on the early side. If you said 30, it’s probably on the late side,” Huang said in a question-and-answer session during Nvidia’s analyst day. “If you picked 20, I think a whole bunch of us would believe it.”

Shares in Quantum Computing Inc., D-Wave Quantum Inc. and Rigetti Computing Inc. dropped more than 30%, while IonQ fell about 29%. These stocks have soared in recent months amid excitement about the technology’s potential, which was heightened last month following a quantum computing breakthrough by Alphabet Inc.

Nvidia has been profiting, a little, from the quantum computer hype and people simulate the QC on its processors.

I think that having a useful quantum computer in 20 years is optimistic. People do not usually invest, based on waiting 20 years to get a return.

Update: Dr. Quantum Supremacy weighs in:

yes, there’s a lot still to be done, and twenty years might well be correct. ...

On the other hand, I can’t say with certainty that high valuations are wrong! ...

For whatever it’s worth, my own family’s money is just sitting in index funds and CDs. I have no quantum computing investments of any kind.

Update: One of those QC companies responds:

Today’s classical computing hardware is limited by computational capacity and power requirements in ways that will likely prohibit society from ever being able to solve some of its most pressing problems.

IonQ’s current #AQ 36 Forte Enterprise systems are already providing insight to solutions for customers today, and our upcoming #AQ 64 Tempo systems in 2025 and next-generation #AQ 256 systems will enable us to tackle increasingly complex problems to deliver near-term business value. One of the areas facing the most significant potential disruption is strong AI, where we believe natively quantum AI will outperform classical AI.

No, quantum AI will not outperform classical AI in the next 50 years.

More Useless Quantum Teleportation

Quantum teleportation is a technology in search of an application.

News story:

An engineering team at Northwestern University has achieved a breakthrough in quantum teleportation, demonstrating the feasibility of transmitting quantum information alongside classic internet traffic. As research advances, we could enter a new era in communication technology, where quantum and traditional networks can coexist to offer unprecedented levels of security and speed.

Engineers at Northwestern University have demonstrated quantum teleportation over a fiber optic cable already carrying Internet traffic. This feat, published in the journal Optica, opens up new possibilities for combining quantum communication with existing Internet infrastructure. It also has major implications for the field of advanced sensing technologies and quantum computing applications.

Quantum teleportation, a process that harnesses the power of quantum entanglement, enables an ultra-fast and secure method of information sharing between distant network users. Unlike traditional communication methods, quantum teleportation does not require the physical transmission of particles. Instead, it relies on entangled particles exchanging information over great distances.

How can anyone make sense of this?

We already have cables efficiently and securely sending internet traffic. Now Northwestern engineers have figured how to use those cables to send messages over those cables without sending any particles! And they do it without interfering with the internet traffic on those cables! If they are not sending anything over the cables, whe do they need them?

I think I see what they are trying to say, but I do not see how it is of any value. It does not "offer unprecedented levels of security and speed." It is just a curiosity.