A New Way of Seeing Nature

Question: What is fractal geometry? 

Benoit Mandelbrot: Well, regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don’t become any less complicated.  Closer and closer, or you go farther or farther, they remain equally complicated.  There is never a plane, never a straight line, never anything smooth and ordinary.  The idea is very, very vague, is expressed – it’s an expression of reality. 

Fractal geometry is a new subject and each definition I try to give for it has turned out to be inappropriate.  So I’m now being cagey and saying there are very complex shapes which would be the same from close by and far away.

Question: What does it mean to say that fractal shapes are self-similar?

Benoit Mandelbrot: Well, if you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.  That is, the straight line has a property of self-similarity.  Each piece of the straight line is the same as the whole line when used to a big or small extent.  The plane again has the same property.  For a long time, it was widely believed that the only shapes having these extraordinary properties are the straight line, the whole plane, the whole space.  Now in a certain sense, self-similarity is a dull subject because you are used to very familiar shapes.  But that is not the case.  Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.  And those shapes, which I studied and collected and put together and applied in many, many domains, I called fractals.

Question: How can complex natural shapes be represented mathematically?

Benoit Mandelbrot: Well, historically, a mountain could not be represented, except for a few mountains which are almost like cones. Mountains are very complicated.  If you look closer and closer, you find greater and greater details.  If you look away until you find that bigger details become visible, and in a certain sense this same structure appears at those scales.  If you look at coastlines, if you look at that them from far away, from an airplane, well, you don’t see details, you see a certain complication.  When you come closer, the complication becomes more local, but again continues.  And come closer and closer and closer, the coastline becomes longer and longer and longer because it has more detail entering in.  However, these details amazingly enough enters this certain this certain regular fashion.  Therefore, one can study a coastline **** object because the geometry for that existed for a long time, and then I put it together and applied it to many domains.

Recorded on February 17, 2010
Interviewed by Austin \r\nAllen

\r\n

What are fractals? The man who invented the term—and the geometry to go along with it—explains how complex natural shapes such as mountains and coastlines can be represented mathematically.

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CRISPR therapy cures first genetic disorder inside the body

It marks a breakthrough in using gene editing to treat diseases.

Credit: National Cancer Institute via Unsplash
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This article was originally published by our sister site, Freethink.

For the first time, researchers appear to have effectively treated a genetic disorder by directly injecting a CRISPR therapy into patients' bloodstreams — overcoming one of the biggest hurdles to curing diseases with the gene editing technology.

The therapy appears to be astonishingly effective, editing nearly every cell in the liver to stop a disease-causing mutation.

The challenge: CRISPR gives us the ability to correct genetic mutations, and given that such mutations are responsible for more than 6,000 human diseases, the tech has the potential to dramatically improve human health.

One way to use CRISPR to treat diseases is to remove affected cells from a patient, edit out the mutation in the lab, and place the cells back in the body to replicate — that's how one team functionally cured people with the blood disorder sickle cell anemia, editing and then infusing bone marrow cells.

Bone marrow is a special case, though, and many mutations cause disease in organs that are harder to fix.

Another option is to insert the CRISPR system itself into the body so that it can make edits directly in the affected organs (that's only been attempted once, in an ongoing study in which people had a CRISPR therapy injected into their eyes to treat a rare vision disorder).

Injecting a CRISPR therapy right into the bloodstream has been a problem, though, because the therapy has to find the right cells to edit. An inherited mutation will be in the DNA of every cell of your body, but if it only causes disease in the liver, you don't want your therapy being used up in the pancreas or kidneys.

A new CRISPR therapy: Now, researchers from Intellia Therapeutics and Regeneron Pharmaceuticals have demonstrated for the first time that a CRISPR therapy delivered into the bloodstream can travel to desired tissues to make edits.

We can overcome one of the biggest challenges with applying CRISPR clinically.

—JENNIFER DOUDNA

"This is a major milestone for patients," Jennifer Doudna, co-developer of CRISPR, who wasn't involved in the trial, told NPR.

"While these are early data, they show us that we can overcome one of the biggest challenges with applying CRISPR clinically so far, which is being able to deliver it systemically and get it to the right place," she continued.

What they did: During a phase 1 clinical trial, Intellia researchers injected a CRISPR therapy dubbed NTLA-2001 into the bloodstreams of six people with a rare, potentially fatal genetic disorder called transthyretin amyloidosis.

The livers of people with transthyretin amyloidosis produce a destructive protein, and the CRISPR therapy was designed to target the gene that makes the protein and halt its production. After just one injection of NTLA-2001, the three patients given a higher dose saw their levels of the protein drop by 80% to 96%.

A better option: The CRISPR therapy produced only mild adverse effects and did lower the protein levels, but we don't know yet if the effect will be permanent. It'll also be a few months before we know if the therapy can alleviate the symptoms of transthyretin amyloidosis.

This is a wonderful day for the future of gene-editing as a medicine.

—FYODOR URNOV

If everything goes as hoped, though, NTLA-2001 could one day offer a better treatment option for transthyretin amyloidosis than a currently approved medication, patisiran, which only reduces toxic protein levels by 81% and must be injected regularly.

Looking ahead: Even more exciting than NTLA-2001's potential impact on transthyretin amyloidosis, though, is the knowledge that we may be able to use CRISPR injections to treat other genetic disorders that are difficult to target directly, such as heart or brain diseases.

"This is a wonderful day for the future of gene-editing as a medicine," Fyodor Urnov, a UC Berkeley professor of genetics, who wasn't involved in the trial, told NPR. "We as a species are watching this remarkable new show called: our gene-edited future."

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