Invention of Projective Geometry

SciAm reports:

This demonstration of his recently discovered laws of perspective is said to have occurred sometime between 1415 and 1420, if his biographers are correct. The use of the laws of perspective amazed bystanders, altered the course of Western art for more than 450 years and, more recently, led to mathematical discoveries that enable elliptic curve cryptography. This is the security scheme that underpins Bitcoin and other cryptocurrencies and has become a fast-growing encryption method on other Internet platforms as well.

The article explains how the above art inspired projective geometry, over the next few centuries.

You would think that Microsoft and Google would be able to quickly adapt to a superior software technology, but that has not happened.

Elliptic curve cryptography is a relative latecomer to the encryption game. The first suite of tools did not appear until 2004, far too late to become a standard for the Web but early enough to adopted by the inventors of Bitcoin, which launched in 2009.

Its status as the de facto standard for cryptocurrencies made people more familiar with it and more comfortable implementing it, although it still lags behind RSA encryption, the standard method in use today, by a wide margin.

Yet elliptic curve cryptography has distinct advantages over RSA cryptography: it provides stronger security per bit and is faster than RSA. An elliptic curve cryptographic key of just 256 bits is roughly as secure as a 3,072-bit RSA key and considerably more secure than the 2,048-bit keys that are commonly used.

Current thinking is to abandon elliptic curve cryptography, and switch to new quantum-resistant protocols.

The trouble is, if the industry could not switch from RSA to ECC, how will it switch to quantum-resistant?

ECC is superior to RSA in every respect, except compatibility with ancient systems. ECC is is faster, more secure, less error-prone, and smaller. The new quantum-resistant methods will be worse in all those things, except that it will supposedly resist some quantum computer that might be built in 50 years.

Most people think that non-euclidean geometry means curved manifolds, such as a sphere or hyperbolic space. But the original non-euclidean geometry was projective geometry. Projective geometry also indirectly led to the discovery of relativity.

Think of it this way. A geometry could be defined by the formula for the distance between two points. On a more elementary level, a geometry can be defined by what the lines are. In special relativity, the light rays are the lines of particular interest, and they are different from Euclidean geometry.

Carroll addresses Weaknesses of Many-worlds

I have criticized many-worlds theory as unscientific nonsense, as it requires rejecting probabilities, does not make predictions, and cannot reconcile theory with observations.

In case you doubt this, listen to Sean M. Carroll, a leading advocate of many-worlds. Here is his latest podcast:

19:02 Victor Tiffany says "After you answered my question about energy conservation in the many worlds interpretation of 19:08 quantum mechanics you added there are real worries that you can have about many worlds but energy conservation is 19:14 not a true scientific worry." So what are those real worries

i think I've said what the real worries are at different 19:20 times but you know not everyone listens to every word so I'll I'll it's worth mentioning again. It's been a while Um I 19:25 think there are two sets of worries that are that are valid um one is the 19:30 question of deriving the born rule the probabilities in many worlds and it's 19:36 not that I don't think we can I think we can I think I know how to do it but the 19:41 origin of probability in many worlds is very very different than what it would 19:46 be in a truly stochastic theory or in a truly stochastic theory. um single world 19:52 theory you can just say well there's something that we don't know and can never know about what will happen next 19:58 in quantum mechanics. And the best we can do is assign a probability to it And we can figure out what that probability is by looking at 20:05 the frequencies of previous events and we get that the born rule fits the data and it all sort of makes sense It's at 20:10 least it not only does it make sense but it's comfortable and familiar to us Okay

20:16 Whereas in many worlds as has been pointed out many many times uh every allowed outcome happens The word allowed 20:23 is super important there Some outcomes are not allowed all outcomes that are supported by the Schroinger equation and 20:30 the current state of the quantum state of the universe are allowed which is very very different than saying everything happens but anyway many 20:37 different uh outcomes actually do happen and with 100% probability they will 20:42 happen in one of the branches of the wave function. right if I have a spin that is a superposition of spin up and 20:48 spin down I measure its spin in one branch it's definitely going to be spin up in the other branch. it's definitely 20:53 going to be spin down nothing probabilistic about it So where do the probabilities come from and again.

I 20:59 think there's an answer to this question and it has to do with self-locating uncertainty and things like that But the 21:05 kind of answer it is is deeply different than the kind of answer it is in the case of a truly stochastic theory. And 21:11 therefore I think it is okay to worry that we are cheating Uh you know we know what the answer is that we want to get. 21:18 We want to get the borne rule We want to get that the probability is proportional to the wave function squared I think we do get that in a very natural way but a 21:25 very different way than what we're used to. So we should be thinking very very deeply about whether we're just cheating 21:31 ourselves.

The other thing to worry about in Everett is that it's a very austere 21:37 theory. So the origin of structure broadly construed in the quantum state 21:42 of the universe is a big question Why do we see a world with three-dimensional space and you know matter and energy 21:49 rather than just seeing a wave function. okay again I think it's perfectly possible to answer this question but I 21:56 think it is much less answered than the probability question because you know the answer that we want is a lot more 22:02 detailed and structured as it were than just the probability question.

So there's a lot of work to be done and this is one 22:09 of the biggest things that I'm working on myself right now um how do you take that abstract quantum wave function and 22:16 divide it up using words like emergence and coarse graining and and effective theories and things like that and say 22:22 that oh look there's a classical limit with matter and particles and things like that. The reason why this is a 22:29 uniquely Everettian problem is because Everett's theory is the simplest theory 22:34 of quantum mechanics. Um it is the one that doesn't have any extra stuff It just has the quantum state and the 22:41 Schrodinger equation.

Other approaches to quantum mechanics don't need to address 22:46 the structure problem because they just put the structure in as part of the 22:51 posits of the theory. You have particles moving in space if you're bohmian. You 22:56 have certain ways that the wave function collapses if you're an objective collapse person And all of these rely on 23:02 this extra structure. So they quote unquote answer the question by just in 23:08 you know making an assumption that it's there right and maybe it is there that's perfectly valid I think that it is 23:14 better if we can derive it from something more fundamental but that doesn't mean that it's not uh uh work to 23:21 actually do that derivation

If you listen carefully, he is acknowledging that these are problems with many-worlds. Probabilities do not make sense. Maybe it will all be explained by "self-locating uncertainty" or some other concept yet to be developed.

And it predicts wave functions as the "simplest theory", but no one has figured out how to relate the theory to what anyone observes.

The phrase "not even wrong" applies here. There is no theory that is scientific in any way. It is all a delusional fantasy. He complains that Pres. Trump is probably not going to renew his federal grant to philosophize about this stuff, but this is crazier than transgender mice. There is no possibility of any good coming out of many-worlds theory.

Any scientific theory has to face the fact that if you look at the range of possible events, some things happen and some do not. Many-worlds theory says you get a simpler theory by dropping that fact, and assuming that anything can happen. It refuses to even say that some outcomes are more likely than others. It assures us that future work will make it all make sense somehow.

Listen to Carroll if you think I am misrepresenting many-worlds.

Columbia and Harvard are Anti-American

Peter Woit continues to rant:

Obviously I’m not a lawyer, but it’s impossible for me to believe that under the US constitutional system the president can legally issue an order to remove funding from an institution either because he thinks (see point 67 in the complaint) “Wouldn’t that be cool?” or because he wishes to take control of an institution he doesn’t like and remake it to his liking. ...

Since the beginning of this I’ve been highly frustrated by the difficulty of getting people (from the Columbia trustees on down…) to focus on what seems to me the simple and obvious issue: it’s a complete collapse of the US constitutional system to allow the executive to just defund an institution that displeases him, with the excuse for this defunding not relevant. If you accept that this is OK, you are accepting that dictatorship is OK.

No, it is not a dictatorship. Pres. Trump was popularly elected, and he is doing what he promised the voters.

Columbia and Harvard are anti-American. They break laws against racial discrimination. They are controlled by extreme leftists. They deny free speech to conservatives, while they coddle Gaza advocates who celebrate killing Jews. They get billions in government contracts, and overcharge for administrative overhead.

The colleges have an obligation to obey the law with the federal tax money they get. Every previous President threatened to withhold money if colleges do not comply. The only thing different today is that the colleges are dominated by Trump-haters.

Columbia and Harvard do a lot of good research, but most of it has no public value. The government is running big deficits, and a lot of things need to be cut.

Physicists have talked for decades on the benefits of string theory, anti-deSitter space, black hole interiors, supersymmetry, multiverse, and many other ideas of no practical value. It is all dishonest.

Scott Aaronson posted similar rants, but now announces

It’s crucial for people to understand that, in its total war against universities, MAGA has now lost, not merely the anti-Israel leftists, but also most conservatives, classical liberals, Zionists, etc. with any intellectual scruples whatsoever.

No. Harvard is suing Trump, but will likely lose on the main issues. Harvard will surely compromise, make some changes, and continue to be left-wing propaganda.

From a comment on Aaronson's blog:

I think it would be very beneficial to analyze the demands that Harvard fights so fiercely; perhaps some of them actually make sense. Would you mind if we take a look?

1. A non-specific preamble about leadership.

2. Merit-based hiring; no more racist preferences; screen for plagiarism. What’s wrong with any of that? Do you want less qualified professors with the politically preferential background? Do you want plagiarism?

3. Merit-based admission. What’s wrong with that? Do you want legacy and politically motivated student accepted and the most qualified rejected?

4. Pretty much “don’t admit Hamas operatives who misinform and inflame students.” What’s wrong with that? Do you want the horrible antisemitism of Harvard, Yale, Columbia to persist?

5. Viewpoint diversity. Indeed, social sciences and humanities department turned into echo chambers where academic discourse is effectively suppress. Would it be wrong to stop screening against conservatives and to allow faculty and students express a variety of opinions?

6. Stop antisemitism; report incidents of antisemitism. What’s wrong with that? Do you want the hatred to continue?

7. Get rid of DEI. DEI is one of major reasons for much of the above trouble. DEI is openly racist and contrary to merit-based hiring and admissions.

8. Accountability for misdeeds. Is anybody offended by the proposition that Harvard “forbids the recognition and funding of, or provision of accommodations to, any student group or club that endorses or promotes criminal activity, illegal violence, or illegal harassment”?

9. Whistleblower protection.

10. Transparency.

What’s so awful in any of these demands that Harvard should “fight fiercely”?

A lot of this has to do with Jewish issues, but my guess is that most Americans do not care about those issues, one way or the other.

Jews are going nuts with Hitler comparisons. Others wonder: was Hitler really trying to do the above ten items?

Woit refuses to admit that the colleges have a problem. Aaronson admits that the colleges have a problem, and agrees with Trump telling them to improve, but does not agree with Trump threatening to cut off money:

To win scientists’ everlasting love and support, all a more conservative political movement would need to offer is:

(2) We’ll fund and appreciate you, minus that other stuff.

All Trump can do is to threaten to cut off money, if he wants them to change. Columbia and Harvard have still refused to obey Trump's interpretation of the law.

Update: Aaronson and Woit still disagree.

My Definition of Science

I posted:

Broadly speaking, science consists of making observations, formulating theories, making prediction probabilities, and then making measurements to reconcile theory with experiment.

All science obeys all four steps, as far as I know.

I criticized many-worlds theory as only obeying the first two. It uses observations and the Schroedinger equation, but does not make predictions or reconcile experiments.

People find that surprising, but it is true. Making a prediction inherently implies that other things do not happen. But many-worlds theory says that all the other possibilities also happen. Probabilities are meaningless in the theory.

Astrology is better at being a science. It uses astronomy observations, has a theory, and makes predictions. It just doesn't reconcile experiments.

Ancient astronomy easily qualifies as science, even though they had flawed ideas about the underlying motions and causes.

Superdeterminism fails all four steps. It does none of them. It is not based on any theory or observations. Its advocates argue that our observations do not even reflect the natural laws, because unseen forces prevent us from testing those laws. If a drug seems to do better than a placebo in a controlled strudy, then it was only because the sicker patients were accidentally put into the placebo group.

String theory does not make predictions or reconcile experiments. Whether it does the first two steps is debatable.

A lot of theoretical physics today has no connection to experiment. An example is theorizing about the interior of a black hole. Or inflation-created universes beyond our horizon.

Watch Google Dodge Quantum Questions

This CNBC interiew is filled with quantum computer hype, and includes a Google quantum AI spokesman answering questions.

Not really. He dodges all the questions, and just babbles with things like "there's a lot of nuance in quantum computing".

Google Lost The AI Lead. Can Quantum Put It Back on Top?

I do not agree that Google lost the AI lead, or that quantum will help it in the AI race. Google has been a leader in AI for about 15 years. It is still at or near the top with protein folding, chess and go, and Gemini 2.5. And of course its big money-maker, which is using AI to target ads for everyone.

The supposed Google AI lead is based on a popular 2017 paper, but a new Nature journal survey rates a Microsoft AI paper as the most cited in the 21st century.

Scott Aaronson makes an appearance expressing skepticism about Microsoft's quantum computer.

In another video, physicist Angela Collier celebrates Bezos Blue Origin sending six women into space. Just kidding. She does a 40-minute rant against it.

And Peter Woit and Scott Aaronson are still arguing over the proper response to Trump being Hitler reincarnated. The basic facts are that Columbia and Harvard are extremely rich, they are not complying with federal law, they are receiving billions of dollars contingent on obeying federal law, they are refusing to comply, and they are squealing about Trump threatening to withhold those funds. Their faculties are dominated by leftist Trump-haters who do not want to compromise.

Woit and Aaronson think this could have been settled in quiet negotiations. Or maybe they think colleges should not have to obey the law, I am not sure. But it is extremely clear that Columbia and Harvard will not comply unless funds are withheld. Harvard already lost a racial discrimination case in the US Supreme Court, and it continues to discriminate as before.

The arrogance of these colleges was on full display when their presidents testified before Congress in Dec. 2023. The public backlash was so fierce that those presidents ended up resigning. You would think that these colleges would be eager to obey the law, but they stubbornly refuse.

Woit and Aaronson pointedly disagree on some Jewish issues, but that seems minor compared to their hysterical Trump hatred, and their overdramatizing of these colleges being held accountable. I doubt that they realize how much they seem like spoiled children.

Can Gravity be Renormalized?

A big achievement of XX century Physics was renormalizing quantum electrodynamics (QED), by Feynman and others. That showed how infinities could be canceled out, so the theory can make predictions in all energy ranges.

QED is a gauge theory on the circle group. Then 'tHooft showed renormalization applied to gauge theories over other groups. Since the known particles were classified by group representations of other groups, that opened the way to the Standard Model. They just had to use the groups already linked to the the particles, and apply gauge theory renormalization.

Gauge theory was the only known renormalizable theory, so there was no choice.

Not everyone agrees that renormalizability is so important. The later invention of effective field theory seemed to bypass renormalization. String theory also provides another approach.

Attempts to quantize gravity have failed because general relativity is not renormalizable. This led people to say string theory is the only game in town, except for maybe loop quantum gravity. Neither approach has produced a quantum gravity theory.

I did not know that general relativity could be easily modified to a theory that is renormalizable.

Luca Buoninfante posts a new paper:

An important theoretical achievement of the last century was the realization that strict renormalizability can be a powerful criterion to select Lagrangians in the framework of perturbative quantum field theory. The Standard Model Lagrangian (without gravity) is strictly renormalizable from a perturbative point of view. On the other hand, the inclusion of gravity seems not to respect this criterion, since general relativity is perturbatively non-renormalizable. The aim of this work is to provide concrete evidence that strict renormalizability is still a valid criterion even when applied to gravity. First, we show that adding quadratic curvature terms to the Einstein-Hilbert action gives rise to a strictly renormalizable theory known as quadratic gravity. Second, we argue that this unique theory represents the most conservative approach to quantum gravity and, at the same time, is highly predictive, as it can explain new physics beyond general relativity already in the sub-Planckian regime.

The simplest way to define a physics theory is to specify the Lagrangian. If you do that for the Standard Model, you can fit it on a t-shirt.

General relativity is the theory derived from the scalar curvature R being the Lagrangian. Or subtract a constant, for general relativity with a cosmological constant. This paper says that you just have to add a quadratic term in the curvature, such as R² or other contractions of the squared Riemann tensor, and you get a renormalizable theory. News to me. This model is sometimes called Starobinsky inflation, and used to explain the early universe.

We do not have any way to test quantum gravity, so the best argument for this approach is that renormalizability has been such a crucially important criterion in the past. It is how we got the Standard Model.

Adding a quadratic term is a bit like Einstein adding the cosmological constant to general relativity. It could not be measured at the time, and was intended to improve the global properties of the theory. It was only measured 80 years later.

Maybe someday this quadratic gravity will be seen as the natural way to modify general relativity to handle extreme conditions.

Everybody always says that quantum mechanics and gravity are incompatible. There is no experiment that shows a problem, so there is only a theoretical incompatibility that might only apply at the center of a black hole or in the first nanosecond of the big bang.

Now I question this. As this paper explains, just add a couple of quadratic terms to the gravity Lagrangian, and there is no problem renormalizing quantum field theory predictions. The only problem is that we do not have experimental data to determine the coefficients of those extra terms. Presumably they are small enough not to affect the known celestial mechanics and cosmology.

So we have a perfectly good quantum gravity theory, with a couple of undetermined coefficients. Those coefficients are too small to affect any of our observations. Viewed that way, it is incorrect to say that there is any incompatibility between gravity and quantum theories.

A few years ago, you could have said that general relativity was incompatible with the concept of a quantum zero point energy. Now the cosmological constant is accepted, and that is believed to be the energy. Maybe we just need to add one or two more cosmological constants, and quantum gravity will cease to be a theoretical issue.

About World Quantum Day

Monday was World Quantum Day:

This Doodle celebrates World Quantum Day, an annual celebration that improves understanding of quantum physics and technology. The date, April 14th, represents the first three digits of Planck’s constant, which describes the relationship between the energy and frequency of a quantum of energy (such as a photon): 4.14×10−15 eV·s