Ciro Santilli @cirosantilli 40

A group of Chinese researchers have just published a paper claiming that they can—although they have not yet done so—break 2048-bit RSA. This is something to take seriously. It might not be correct, but it’s not obviously wrong.

We have long known from Shor’s algorithm that factoring with a quantum computer is easy. But it takes a big quantum computer, on the orders of millions of qbits, to factor anything resembling the key sizes we use today. What the researchers have done is combine classical lattice reduction factoring techniques with a quantum approximate optimization algorithm. This means that they only need a quantum computer with 372 qbits, which is well within what’s possible today. (The IBM Osprey is a 433-qbit quantum computer, for example. Others are on their way as well.)

Bacteria replicate at colossal speed. [...] In two days, the mass of exponentially doubling E. coli would be 2664 times larger than the mass of the Earth.

Luckily this does not happen, and the reason is that bacteria are normally half starved. They swiftly consume all available food, whereupon their growth is limited once again by the lack of nutrients. Most bacteria spend most of their lives in stasis, waiting for a meal. Nonetheless, the speed at which bacteria do mobilize themselves to replicate upon feeding illustrates the overwhelming strength of the selection pressures at work.

The lists of steps in my mind are organized in hierarchies. I follow a routine procedure before going to sleep. The first step is to brush my teeth. But this action is in turn broken into a smaller series of steps, the first of which is to put toothpaste on the toothbrush. That step in turn is made up of yet smaller steps, such as finding the toothpaste, removing the cap, and so on. The step of finding the toothpaste also has steps, the first of which is to open the bathroom cabinet. That step in turn requires steps, the first of which is to grab the outside of the cabinet door. This nesting actually continues down to a very fine grain of movements, so that there are literally thousands of little actions constituting my nighttime routine. Although I may have difficulty remembering details of a walk I took just a few hours ago, I have no difficulty recalling all of these many steps in preparing for bed - so much so that I am able to think about other things while I go through these procedures. It is important to point out that this list is not stored as one long list of thousands of steps - rather, each of our routine procedures is remembered as an elaborate hierarchy of nested activities.