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wbhart

2,458 karma · joined December 22, 2010

I am a computer algebra/computational number theory researcher. I spend most of my time maintaining the Flint C library, and the Nemo.jl and Singular.jl libraries. I also work on algorithms for fast arithmetic.

My favourite languages are C and Julia.

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wbhart··on Does memory leak? (1995)
Missiles don't always hit their intended target. They can go off course, potentially be hacked, fall into the wrong hands, be sold to mass murderers, fail to explode, accidentally fall out of planes (even nuclear bombs have historically done this), miss their targets, encounter countermeasures, etc.

Nobody is claiming that this was done for reasons of good software design. It's perfectly reasonable to suspect it was done for reasons of cost or plain negligence.

There's a reason tech workers protest involvement of their firms with the military. It's because all too often arms are not used as a deterrent or as a means of absolute last resort, but because they are used due to faulty intelligence, public or political pressure, as a means of aggression, without regard to collateral damage or otherwise in a careless way.

The whole point here is the blase way the technician responded, "of course it leaks". The justification given is not that it was necessary for the design, but that it doesn't matter because it's going to explode at the end of its journey!

wbhart··on A Map of Mathematics
For those unaware of it, here is a "map" of mathematics that mathematicians use, called the Mathematics Subject Classification:

https://cran.r-project.org/web/classifications/MSC-2010.html

It is arguably less useful for someone who is not a mathematician, but does illustrate how difficult the problem of classifying all of mathematics is.

Both "maps" have their uses.

wbhart··on EGA Chapter 1: The Language of Schemes
The main problem has not been the language it was written in. It's hard going mathematically as well (for average graduate students at least). A few people have started translation projects, but gave up after realising that by the time they had translated more than a few pages, the French was actually pretty easy to follow. The maths, however, was not so easy.

It is really nice to see someone finally translated more than a whole chapter though.

wbhart··on The Rotating Lepton Model
How common is it for a physics theory to be able to compute so many quantities without fudge factors to make it all work out? I'm not a physicist, so I'm currently imagining this could be quite significant. Is that how physicists are reading it? Also, can any physicists comment on whether this is a top journal.
wbhart··on Let's remove quaternions from every 3D engine (2018)
y^2 = 1 because it is the sum of the dot product (1) and the outer product (0). The latter is because the parallelogram between y and y has zero area. The former is just the length of the vector y.

Some memorisation is required, but it is in terms of things that are easily visualised.

wbhart··on Let's remove quaternions from every 3D engine (2018)
It means the things in the basis, x^y, y^z and x^z have an easy to understand interpretation in ordinary 3D space, namely the parallelogram between x and y (in the case of x^y), for example.

It's also easy (after reading the article) to understand the operations that can be performed on these things.

It's not as obvious what i, j and k in the quaternions correspond to, or why they have the multiplication table that they do. It's an algebraic construction, not a geometric one and hence more difficult to visualise.

wbhart··on Not everyone has an internal monologue
I have an inner monologue, but I wouldn't say I was like "hearing" anything. For me it feels a bit more like the muscle movements in my larynx are played out as though I was going to speak the words. I can imagine a voice speaking at the same time if I want, but that's not how it is normally.

I tried reading at the same time as thinking of different words. I can certainly read the words whilst thinking of different ones, but I can't understand what I read very well. Probably it could be done with practice.

However, if I have planned a sentence that I want to type, I can type it whilst listening to someone else or thinking about something else. It's slightly more error prone though.

I can certainly imagine pictures in my mind without any monologue running at all. But this also isn't my normal mode of thinking. It's not helpful because I don't normally associate abstract concepts with pictures, but with words and symbols and abstract memories of things that worked in similar situations before.

I believe I can recall all my senses or imagine them in my head. I don't seem to dream in words though, but in pictures, mostly. I'm also a much more visually stimulated person than an auditorially stimulated one.

wbhart··on Tech’s Next Revolution Might Be Open Source Semiconductors
Is the real barrier to CPU production open source of the logic design or is it in research into chip production, node design, including hundreds or potentially thousands of process steps, maximising yields, segmentation of the market and other marketing issues, defining standards, chipset design and integration, validation, the generally prohibitive cost of building fabs and actually producing the chips and getting sufficient capital to make inroads into the marketplace, e.g. with OEMs.

The idea that open sourcing the logic is going to make other companies competitive with a financial behemoth like Intel is really a stretch.

wbhart··on Postdoc Myths
They can do that with people who will be teaching, since that is bringing funding in for the university. But they don't do it for Research Assistants, because once the funding for the project the Research Assistant is paid from (usually a fixed term grant of a 2-3 years) runs out, then the university would have no income to match the cost of the salary. As there may be hundreds or thousands of such salaries, this would result in a funding shortfall of something of the order of $100m a year (including overheads). And that is to say nothing of the expensive equipment such employees might need to continue their work.

Project centred research does not bring in income for universities on an ongoing basis, which is what the argument about core funding is all about. If more funding were core funding, not tied to a specific project, then it would be possible for universities to do the right thing and provide career paths for Research Assistants.

Please note: I'm not arguing that universities in the UK are doing the right thing. I used to work as a postdoc there and understand very well what the author of the Postdoc Myths list is talking about. I'm simply answering the question as to why universities can't just do the right thing.

wbhart··on Cerebras’s giant chip will smash deep learning’s speed barrier
From the perspective of an outsider, I can't see how a company like this could survive. They claim on the one hand to have done something really amazing and are at the stage where they are looking for customers. Normally, you'd expect them to be touting performance figures to secure such investment. Instead, they've decided to keep the performance secret. And they've managed to find some "expert" who says this is normal.

Does anyone here have expertise in this area? Is this the model for a successful company in this area?

wbhart··on Jimmy Wales has quietly launched a Facebook rival
I don't think a social network based on subscription will work. Although I could afford it, only a tiny proportion of my Facebook friends could afford an expense like that.

The endless unresearched opinion on Facebook drives me mad. But unless you only want to have friends who are rich enough to agree with you, this is dead in the water.

wbhart··on 1984, the Year of the 32-bit Microprocessor (1984)
The Zilog z80000 wasn't introduced until 1986, but was pipelined and was in some respects about 6 years ahead of Intel. Apparently they are still used today in embedded application, though there was one moderately successful machine based on them back in the day.
wbhart··on Clang Solves the Collatz Conjecture?
There's only of the order of a billion values to check. It's known to be true for all those values.
wbhart··on Ask HN: Are there books for mathematics like Feynman's lectures on physics?
When I did analysis at university, I read Rudin instead of the recommended text. When the exam came around, I tried to generalise all the problems on the exam and gave answers which did not impress the person marking it, as they looked nothing like the standard solutions. As a result, I very nearly failed analysis. I wasn't particularly upset, as I used to consider my exam grade as a reflection of how well the course was taught, rather than a grading of my own comprehension. This is not a level of arrogance I would recommend to students looking to pass their exams.
wbhart··on Ask HN: Are there books for mathematics like Feynman's lectures on physics?
It's extremely difficult to write a mathematics textbook in the intuitive style. There are some reasons for this.

Firstly, much of mathematics is symbolic and any description of equations in an intuitive style is unnecessarily verbose if it abandons the symbolic approach, essentially taking one back to descriptions like those used in ancient Greece before the invention of algebra, e.g. "and the third part of the first is to the second part of the first as the fourth part of the area is to the square on the gnomon".

The second reason is that an intuitive style supposes that one can answer natural questions that might arise, in an order that they are likely to arise in the mind of the student. Often the natural questions are much more difficult to answer mathematically, or the answers are not known.

The third reason is that concepts have arisen historically for non-obvious reasons, or reasons only known to experts with far more knowledge than the reader is expected to have, or the originator of the ideas did their best to obscure their motivation. This makes it extremely hard to motivate certain concepts naturally (intuitively) since such motivations are simply not known. For example, it is not hard to motivate solvable groups through a study of solubility of polynomial equations. But it is much harder to motivate the related concept of nilpotent groups, where the true motivations lie far deeper in the theory than the concepts themselves.

The fourth reason is that it is a massive effort to come up with good examples. Even the best textbook authors often struggle to come up with accessible examples for the concept they are trying to explain. Often, good examples require a really broad knowledge of mathematics that goes way beyond the narrow field being taught. Examples end up being very artificial, and neither intuitive nor typical, as a result.

Don't get me wrong. If someone told me something like the Feynman lectures existed for mathematics, I would salivate and spend a lot of money to acquire them. But having experimented with many styles of writing notes for myself on mathematics over the years, I well appreciate how hard, or perhaps impossible the task would really be. Of course there are some oases in mathematics where such an intuitive approach is possible.

wbhart··on Intel slashes prices in face of AMD competition
I'm no Intel fanboy, but I think it is too early to speak of Intel's demise. They are still making a lot of money. I mean, AMD only has single digit penetration into the datacentre market, for example, and Intel is still compelling on mobile.

And I suspect the real answer is they set their targets too ambitiously with their new node. Their 10nm was simply too big a jump with too many unproven technologies, with too many unexpected obstacles.

But I wouldn't count them out of the game just yet. They are an aggressively competitive company. They'll be back.

wbhart··on The 64 Milliseconds Manifesto
They missed the remaining portion of the manifesto:

* Websites making controversial claims should state clearly the claim in the first paragraph

* Controversial claims should be backed up by at least a summary of a well reasoned argument within the first 5 paragraphs.

* Controversial claims should be backed up by citing sources.

wbhart··on A Lunar Space Elevator Is Feasible and Inexpensive, Scientists Find
Thanks but that's not what I asked.

I asked what is the difference in delta-v between getting from the surface of the earth to GEO vs getting from the surface of the earth to Lunar orbit.

The answer is, there is almost no difference.

wbhart··on A Lunar Space Elevator Is Feasible and Inexpensive, Scientists Find
Does someone know what the difference in deltav would be to get to geostationary orbit from earth vs getting to lunar orbit from earth? A citation would be helpful.

I've tried looking this up, but from previous comments on this paper, I infer that I am misunderstanding something.

wbhart··on India to Attempt Moon Landing at the Lunar South Pole Today
Unfortunately it could not have been hovering though. The velocity was almost certainly too high for the spacecraft to handle.
wbhart··on The Spaceline: a space elevator alternative achievable with current technology
Can you point to the specific section of the paper where this is calculated. I admittedly only skim read, but I did go through the whole thing, and I'm convinced I missed this kind of analysis somewhere.
wbhart··on The Spaceline: a space elevator alternative achievable with current technology
A pointer to where they compute this in the paper would be helpful. There are a lot of comments to just read the paper because they calculate this or that, but I quickly read the thing through and either missed all these points being covered, or it's not actually considered.
wbhart··on The Spaceline: a space elevator alternative achievable with current technology
I meant to compare getting to GEO (as proposed in the paper) as opposed to Lunar orbit.

Of course the way I worded this is a bit lose, and it's not completely free, but according to the figure in that Wikipedia article, the difference between getting into geosynchronous orbit and getting to lunar orbit from earth seems to be only about 0.1km/s, which is negligible compared to the total cost. So my basic point still stands.

It's actually really expensive to get to GEO.

wbhart··on The Spaceline: a space elevator alternative achievable with current technology
So they found a material which won't degrade in 24 hours due to radiation from the sun, or a way to shield it? And what about the mismatch between the rotation of the moon around the earth and geostationary orbit? And they figured out how to go around the van Allen belts to prevent frying sensitive electronics in the payload? And when the payload gets close to the moon, they have a way to stop it plunging to the surface of the moon for unscheduled disassembly?

Of course the cheapest part of getting to the moon is the bit between the edge of space and moon orbit. Approximate current cost: $0. Approximate cost after placing 40,000kg fishing line in the way....

I'm also pretty sure crawling along a fishing line will be prohibitively slow compared to letting a rocket coast with its engines off.

wbhart··on The Human Brain Can Create Structures in Up to 11 Dimensions
I don't agree. The brain does not create structures in up to 11 dimensions, full stop. This is a popular science article. To use that word from standard vocabulary to describe something that just happens to use the same word as some utterly esoteric mathematical definition is misleading at best. And then to imply that the brain creates such structures is just compounding the problem.

What about, "The amazing connectivity of the human brain", or "Researchers unravel the mathematics of connections in the human brain"?

There's absolutely no need to confuse readers by conflating unrelated concepts.

I could make up my own definition of dimension, e.g. the dimension of a manifold needed to embed some bizarre variety with some cleverly defined homological correspondence to slices of brain material I looked at under the microscope, thought of as simplices. I might then get 276 dimensions. Do I then get a press release for this? It's utterly meaningless. "Mathematician discovers that our brains live in a 276 dimensional universe".

wbhart··on The Human Brain Can Create Structures in Up to 11 Dimensions
Right. In other words, it has nothing to do with the human brain creating structures in 11 dimensions. It's a total misreading of the science.

This particular claim has been making the rounds for quite some time. It's total rubbish.

wbhart··on Major book publishers sue Amazon’s Audible over new speech-to-text feature
I am not convinced by this. Amazon does not at any point convey a copy of the written work to the customer. At no point does such a copy exist, nor can it conceivably be constructed from the technology Amazon are supplying to their customers.

This is not (if I understand correctly) a PDF document they can download and read, it's a technology that allows the words that are currently being spoken to be seen in written text.

At no time does a legally significant quantity of the written work get conveyed to the customer. Amazon will just ask the publishers to show where this alleged copy of the textual work resides in their system. They won't be able to do so, as it doesn't exist there.

This does seem to be what they are in fact arguing. And I think they will prevail. I would not expect them to prevail if they offered a pdf of the book or if their software actually contained a copy of the original text that was being conveyed to the customer.

wbhart··on YouTube blocks recording of public domain Schubert/Liszt composition
Rousseau found a way around the block. He uploaded the video again in a way that caused it to be claimed, rather than blocked, by a different company. He'll still have to dispute it, but YouTube is not obliged by law to take down content that only received a claim. The video is no longer blocked.
wbhart··on YouTube blocks recording of public domain Schubert/Liszt composition
This is everything to do with the DMCA. YouTube claims it is required by law to take down content that receives a takedown notice. That law is the DMCA. Edit: I'm probably wrong. It seems a claimant can also issue a block. They do not have to issue a takedown notice. That seems to be the problem right there!!

(However) I find it really difficult to believe the claimant in this case has no control over what YouTube does, as they have previously claimed. It may have been Content ID that got the identification wrong, but the claimant should not issue a block if it is a false claim.

Anyhow, Rousseau found a way around it by uploading a new version that received a copyright claim from a different company, instead of a block. He'll still have to go through the dispute process, at least we can watch the video because YouTube is not obliged to (and does not) take down the video.

wbhart··on YouTube blocks recording of public domain Schubert/Liszt composition
I assume you are being facetious. Rousseau doesn't owe anything to any publisher. Just checking you understood this.
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