Viewing profile — cfgauss2718

Even if you could get around the payload and energy density (power autonomy) constraints, which are very stringent, this seems like a dead product. Sure, it’s a cool project for so…

We know from the No Communication theorem that quantum entanglement does not transmit information between classical observers who have no role in preparing the initial state of the…

This series by lecturer Frederic P. Schuller is astounding work of thorough mathematical exposition delivered with clarity and charisma. This body serves as an exemplary introducti…

In quantum field theory (standard model of particle physics), photons are the quanta of a field (naturally identified with the quantized electromagnetic field, or U(1) gauge field)…

I think are overstating the strength of the No Communication Theorem. It does not state that communication via quantum entanglement is impossible in all cases; the theorem is weake…

I love when grammatical mistakes become unintentional puns

Here’s maybe a useful example. Consider a scalar potential function F on R^3 that describes some nonlinear spring law. At a point p=(x,y,z), the differential dF can be thought of a…

Can you provide some examples of important tensors in physics for which the underlying vector space is infinite dimensional? I’m most familiar with the setting of tensor fields on …

Yes, the “multi linear map” definition is accessible to an undergraduate who has taken linear algebra. However, the more common meaning of tensor in physics, like the metric tensor…

Here here! Functions do not depend on your choice of coordinates, only the components of tensors do! I think this is why it’s important to keep covariance and contravariance in min…

I think the point above is that in physics tensor is usually overloaded, and those practicing physicists when they speak of tensors are more often referring to tensor fields, and m…

Very well, let’s just agree that in physics (r,s) tensors usually refer to sections of the tensor product of some fixed number of copies of the tangent bundle (r copies) and cotang…

Agreed, I can’t help but feel there is some overcompensation driving the style of writing. It was difficult to finish.

There are some interesting parallels to ideas in this article and IIT. The focus on parsimony in networks, and pruning connections that are redundant to reveal the minimum topology…

Nothing about this research violates conservation of energy. The article as written is advocating using excess solar or wind energy as input to this CO2->CH4 conversion process (wh…

On a glance, the Chichilinsky theorem assumption of smoothness for the mapping between voter preferences And the vote result (the relation phi) seems burdensome. For example, many …

The multiverse may be a consequence of Everett’s theory, but the reality shattering nature of that consequence warrants scrutiny of the theory. Consider one of Xeno’s paradoxes. On…

How is the answer “everything that can happen does happen, just in an alternate universe that is identical except for the outcome of one single measurement” a parsimonious answer t…

Sympy is a poor tool to learn because it simply doesn’t scale to problems one most often encounters, even in schooling. Frankly, CAS are so general and unintelligent that problems …

If one thinks of a metric as a “distance measure”, which is to say, how similar is some input x to the “feature” encoded by a layer f(x), and if this feature corresponds to some su…

Yes of course any positive definite matrix can be used as a metric on the corresponding Euclidean space - but that doesn’t mean it’s necessarily useful as a metric. Hence I think i…

This NFM is a curious quantity . It has the flavor of a metric on the space of inputs to that layer. However, the fact that W’W remains proportional to DfDf’ seems to be an obvious…

You raise a fair point, I do think that it’s important to understand how the properties of the data manifest in the least-squares solution to Ax=b. Without that, the only insights …