Laurent Nottale, a french astrophysicist, may not be widely recognized, and may even cause knee-jerk reactions from some. I personally believe that he qualifies as a genius in physics, and in the light of some recent reactions, I believe that it is necessary to explain why.

#### It’s not because he’s been nice with me…

First, I must explain that my admiration for Nottale is not due to some personal relationship with him. As a matter of fact, all my interactions with him were rather unhappy.

Years ago, in 1994, Science & Vie published an article entitled “*Le big bang en question*” (questioning the Big Bang theory). This was about a guy named Laurent Nottale, totally unknown to the general public at the time, and to me in particular. I found his phone number and called him to mention that I had found the article extraordinary and that I had ideas I’d like to share (it took years for these ideas to materialize in a usable form). He was extremely cold, only asking how on earth I had gotten his phone number, and basically hung up on me.

Things did not improve much after that initial contact. In the years since then, I believe that I sent about 3 or 4 e-mails, mostly questions about his work, and I do not recall ever receiving an answer. So my personal relationship with Laurent Nottale is certainly not the reason I find him to be a genius.

#### Criteria for scientific genius

To me, there are 3 factors that are key to “genius class” scientific advances, which I will illustrate with Einstein:

- Intuition about the foundations and principles. Einstein’s intuition was that it was possible for the speed of light to actually be invariant while preserving the fundamental Galilean property that all speeds as defined relative to an observer.
- Technical prowess. Einstein’s use of tensors and non-Euclidean geometry in general relativity were masterful for the time. While he disagreed with quantum mechanics in general, it was certainly not by lack of understanding or inability to grasp their mathematics.
- Experimental validation, i.e. retrodictions and predictions. Retrodictions “predict” already known phenomena, whether explained correctly by present theories (“classical retrodictions”) or at odds with them (“distinguishing retrodictions”). True predictions are even more impressive, since they announce before the experiment is carried out what the result should be. Einstein’s retrodiction included the standard law of gravitation (a classical retrodiction) with a slightly different formulation for the perihelion of Mercury (a distinguishing retrodiction). His predictions included the bending of light under gravity

#### The null test: Example of non-genius

Let us validate that these criteria are discriminant with a null test. Let’s take a non-genius, for example myself, and try them.

- Intuition about the foundations and principles: I hope that there is some good intuition in my theory of incomplete measurements, but this may be over-evaluating myself.
- Technical prowess: As the same article should prove, my technical abilities are relatively low. I’m certainly not advancing the world of mathematics with the few demonstrations I made in that article.
- Experimental validation: There are some retrodictions in my article, including distinguishing retrodictions with quantum mechanics (e.g. that you cannot find a particle on the moon without putting a detector there, unlike what the most commonly held interpretation of quantum mechanics tells you). There are practically no predictions. Now, when I wrote the article, I thought that non-instantaneous or non-simultaneous collapse of the wave functions would lead me to genuine predictions, but I since then found experiments had already been done that turned these into boring retrodictions [Note to self: add links]…

OK, so depending how you evaluate my intuition and retrodictions/predictions, I get at most 2 out of 3, so I’m not a genius. Well, we knew that already, not a big deal…

#### Are my genius criteria selective enough?

But I’m just chaff. If the criteria are to be selective enough, they have to be really difficult to meet. So we can try them with someone like Brian Greene, according to Wikipedia one of the best known string theorists. Is he a genius according to my genius test?

- Intuition: he has plenty of it, and as a matter of fact, I recommend the first half of a book like The Fabric of the Cosmos to give you a pretty exhaustive laundry list of all possible intuitions about physics today.
- Technical prowess: Brian Greene has published many articles which are in general pretty impressive (at least to me). He knows how to write equations I would be totally unable to write.
- Experimental validation: That’s where most string physicists fall short today. At this point, string theory is lacking in the predictions department, largely because it is a little bit under-constrained. There are too many free parameters to tweak, so much so that you need an “Anthropic Landscape” to explain why our own universe would even be the one that exists among the infinite set of possibilities in the multiverse.

So Brian Greene gets 2 out of 3. That is not bad, but he still fails (for the moment at least) the genius test. He still stands a chance, though, as soon as string theory starts making verifiable predictions.

#### Does Laurent Nottale pass the genius test?

So now we have a genius test that identifies Einstein as a genius, clearly identifies me as a non-genius, and for the moment puts Brian Greene only in the potential genius category. Based on these basic sanity checks, the test looks good to me.

Now back to our primary topic, Laurent Nottale. Does he pass my test?

- Intuition: The original intuition of his scale relativity is beautifully simple, and closely mimics Einstein’s for special relativity: it is possible to write a theory where there is an invariant length while preserving the daily experience that we can only measure lengths in relationship to one another.
- Technical prowess (This is where I may diverge from some of his critics): The use of fractal mathematics to model what happens beyond the horizon of predictability for a system is, I believe, masterful today, just like Einstein’s use of non-Euclidean geometry at the beginning of the twentieth century. Granted, this makes his work rather difficult to follow (though he writes in a way that I personally find rather easy to read compared to many scientists). I usually need 5 or 6 steps to really understand what he does in a single step. But with very few exceptions, every time I really dug into it, I ultimately figured out that his reasoning appeared well founded (if not necessarily well elaborated). Now, it’s possible that it’s simply my own limits that prevent me from seeing what is obviously wrong, but I don’t think so because of the third criterion.
- Experimental validation: Laurent Nottale did not make one, two or three small predictions or retrodictions. With him, they come by the truckload. Actually, there are so many that it’s really easy to believe “it’s just not possible, it must be fake”. I think on the contrary that this indicates that a grand new principle has been found that lets us explore a variety of domains that were closed to us before.

#### Conclusion

So here you have it. I do believe that Laurent Nottale is a scientific genius. I may be wrong. Just give me your opinion in the comments area, it is open…

Bravo pour cette confiance dans le travail de Laurent Nottale que je partage. Son attitude froide à votre égard est probablement dû à sa méfiance suite à la manière dont il est traité par la communauté des scientifiques français. Je pense qu’il faut donc l’excuser.Pour l’aspect “génie”, je crois que, oui, sa théorie est géniale !Quant à Sylvain Poirier, je crois que vous avez sacrément bien jugé le personnage, et avec humour.Continuez !cordialementPhilippe

I agree with Philippe about Laurent Nottale. When a long time ago, I read his book about scale relativity. I found it marvelous. all became clear. His last discovery about the reason of electronic spin due to space time fractality is fantastic. LE BLOG DES CICADELFS

Nottale is a crackpot. The only work of genius was convincing you that he is anything but. It’s not science or mathematics, it is simply nonsense.

I can tell you that Proteus (here above) is Sylvain Poirier himself.

I can tell you that Proteus (here above) is Sylvain Poirier himself.

you did a good job explaining the basics of nottale, congratulation. of course he is a genius but physicists are an arrogant, ignorant lot who love to trash geniuses and bio-ethics… specially because they dont understand new maths,. einstein suffered both. mathematicians adopted him first, physicists didnt understand non-euclidean maths. Nottale works with fractals and they dont know fractal geometry. my work http://www.unificationtheory.com is basically a fractal generalization to all systems of the universe. the complex model dumbfolds people, the simple one marvels them. what nottale should do is write a very simple book in english for the masses and then physicists will read him. this happened to me. only when i wrote a simple one i got big time attention from the 'community' (then i entered the field of bioethics and got 'knee-jerk reaction' but that is another story… take care. and if you want to learn more about an even wider generalization of fractals and non-euclidean geometries enjoy this one:http://journals.isss.org/index.php/proceedings50th/article/viewFile/29/200

Proteus, could you provide just one proof of Notalle's mistake?