I just tested this out and it doesn't seem true.

The two storing methods seem similarly precise over most of the range of fractions [0,1], sometimes one gives lower spacing, sometimes the other. For instance, for fractions from 0.5 to 0.638 we get smaller spacing if using [0,100], but for 0.638 to 1 the spacing is smaller if storing in [0,1].

For very small fractions (< 1e-38), it also seems more accurate to store in the range [0,100] since you are representing smaller numbers with the same bit pattern. That is, because the smallest nonzero positive float32 is 1.40129846e-45, so if you store as a float32 range [0,1] that's the smallest possible representable fraction, but if you're storing as a float in range[0,100], that actually represents a fraction 1.40129846e-47, which is smaller.

For the general result, see for yourself in python/numpy:

    x = np.linspace(0,1,10000)
    plt.plot(x, np.float64(np.spacing(np.float32(x*100)))/100)  # plot spacing stored as [0,100]
    plt.plot(x, np.float64(np.spacing(np.float32(x))))  # plot spacing stored as [0,1]

For War and Peace, I didn't know russian, so I tested different translations before going ahead. The translator makes a big difference, I found some translations hard to read.

I had your feeling with Ulysses, though. No translation issue there. Couldn't make it very far.

That would make me curious how the timestamp error occurred: software, hardware? Camera or Navigation code? I assume they have very high standards, what was the process failure point?

Presumably they use some kind of Kalman Filter, but those are easy to program to account for missing frames, or frames at non-discrete timepoints, perhaps even for screwy camera images if the programmer had a reasonable prior for the likelihood of it happening. Kalman Filters by design account for measurement error.

In humans, the haploid phase of the lifecycle is single-celled, while the diploid phase is multicellular. In contrast, in mosses and fungi the haploid phase is multicellular while the diploid phase (sporophytes/zygote) is single-celled.

Red blood cells are discussed in the article.

IBM's new and rising supercomputer architecture, POWER9, supports hardware IEEE binary128 floats (quad precision). Their press claims the current fastest supercomputer in the world uses POWER9.

The ppc64 architecture (still produced by IBM) supports "double-double" precision for the long-double type, which is a bit hacky and software-defined, but has 106 bit mantissa.

And ARM's aarch64 architecture supports IEEE binary128 long-doubles as well, though it is implemented in software now (by compiler). Maybe they plan a hardware implementation in the future?

Disturbances in a field propagate through space similarly. A disturbance of the field at a point only affects the value of the field in the immediate spacetime surroundings, just like a water wave. I would call that "local" and non-spooky. Whether or not there is "mechanical contact", whatever that means, is irrelevant.

This is in contrast to Newton's theory of gravity, where the force of gravity was spookily felt instantaneously across space.

See for example this 2014 PNAS article "Quantum nonlocality does not exist": http://www.pnas.org/content/111/31/11281

You can find plenty more if you google. I personally agree with the ideas of that paper in a broad sense if not in detail, as do many people.

Second, if you are trying to argue that locality is no longer a guiding principle, note how the standard model is quantum-mechanical so obeys bell's inequality, yet we still call it "local". Locality was a key guiding principle of the standard model.

He seems to think Newton accidentally disproved the concept of locality through his theory of gravity. It's true that philosophers largely gave up on locality in the 18th century because of Newton, but that was only temporary: In the 19th century the principle of locality came back with a vengance after Maxwell.

Today the principle of locality is a key component of the Standard model: The Hamiltonian of the standard model is local, meaning you can compute what happens at a point in spacetime knowing only what is going on in an infinitesimal region around it. Even outside the standard model, LIGO proved that graviational waves exist, and therefore gravity is a local phenomenon.

Einstein was famously prepared to give up on quantum mechanics because it seemed to violate the principle of locality, which he thought was more important. That is still debated sometimes, though whether quantum nonlocality exists seems to be a matter of interpretation and is also different from the kind of locality chomsky is talking about. Locality is still a key principle in physics.

Some is, eg some linux/gnome devs are paid to contribute. But many smaller projects/components are volunteer-only.

https://bitinfocharts.com/comparison/bitcoin-transactionfees...

https://blockchain.info/charts/avg-confirmation-time

Who knows what they would be if bitcoin was actually used to buy things.

Aren't you supposed to be taxed on the value of a good/service/gift received even if it was given to you for free? What is the "true value" of tuition?

I don't think waiving tuition will work, assuming tuition is taxed like most other things.

His point in this new article is that instead of one big "oxygenation event" there may have been multiple. But he sticks to his story that the creation of an ozone layer by photosynthesis was the key step in saving the oceans. He argues both Mars and Earth had oceans originally (confirmed by Mars Satellite observations), which were gradually diminished by a process in which ultraviolet light splits atmospheric water, minerals on the surface absorbed the oxygen (rusting, making Mars red) leaving the hygrogen to blow away. But life on earth pumped extra oxygen into the atmosphere, faster than minerals could aborb it, creating the reactive ozone layer which prevented hydrogen from blowing away, thus saving the oceans from their fate on Mars.

[1] nick-lane.net/wp-content/uploads/2016/12/Oxygen-and-life.pdf

The discovery of photosynthesis caused the "great oxygenation event" which pumped oxygen into the atmosphere. Oxygen reacts with atmospheric hydrogen to form water. Without the oxygen, the very light hydrogen molecules would float to the top of the atmosphere and are easily blown away by solar winds, which is what happened on Mars. But with high oxygen concentrations on Eath, hydrogen molecules react to form heavier water molecules before they have a chance to be blown away, and thus hydrogen and water are retained.

I read about this in the book "Oxygen" by Nick Lane.

In the 2d example in the post, you would rescale the coordinates so the unit cell is from (-pi,pi) in both dimensions, and then the distance formula would be

    sqrt(((cos(x1) - cos(x2))**2 + ((sin(x1) - sin(x1))**2 + ((cos(y1) - cos(y2))**2 + ((sin(y1) - sin(y1))**2)

(I forget the name of this system, but it is commonly used for calculations involving dihedral angles in MD simulations)

SPR is an algorithm already used to reconstruct 3d objects from a set of 2d images produced by an electron microscope, typically of a protein on a flat surface.

I haven't read the paper here, but I suspect a key part of the algorithm is that it can only reconstruct objects with symmetry planes: The airplane, chair, car are all symmetric across an axis. This greatly constrains the possibilities the algorithm has to search through. In em-reconstruction the user often specifies what they think the symmetries are beforehand.

-- Their trades are profitable f = 51% of the time, and they do N = 3 million trades per day.

-- Their net profitability per day is thus (well approximated by) a normal random variable with a mean of f and a standard deviation of sqrt(f(1-f)/N), or 3e-4

-- The probability of this value being less than 50% is well approximated by norm.cdf(0.5, 0.51, sqrt(f(1-f)/3e6)) which gives 2.4e-263

In other words they only expect one loss per 10^263 days, which is much larger than the age of the universe. They are actually doing much worse than expected because they lost on one day.

Philadelphia has a number of red light cameras which each generate about 10,000 tickets a year. That's about 30 tickets a day for each camera, $100 per ticket. 12 cameras generate $9 million a year [1].

If 30 people are "running" the red light each day, does that say more about the drivers or about the setup of the red light?

[1] http://www.nbcphiladelphia.com/traffic/transit/Red-Light-Cam...

What about the beautiful and often very precise linear relationship between radioactive dating of the fossil record, and genetic dating using the molecular clock?

What about the beatiful correspondence often found between the principle components of genetic variation and geographical position (isolation by distance)?

What about all the biochemical discoveries related to DNA function (including the existence of DNA itself), how mutations occur, about heritability?

What about everything we've discovered about genome composition and how it changes over time? (duplicate genes, pseudogenes, transposons, hotspots of various kinds).

Is a DNA sequence less precise than a spectral line?