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A LUT is pretty wasteful. You only have a one bit significand, so the mantissa and sign bits are boolean binops, and the exponent is a 2 bit adder.

I don't believe any AV software out there attempts to solve the trolley problem. It's just not relevant and moreover, actually illegal to have that code in some situations.

You can't get into a trolley situation without driving unsafely for the conditions first, so companies focus on preventing that earlier issue.


If you have a couple hundred dollars, you can get a chip made through tiny tapeout [0].

[0] https://tinytapeout.com/


Very cool! I meant more hands on diy fab, like how I make my own pcbs. It seems farming out my designs to be produced (hdl->chip) at reasonable one-off costs is a plausible avenue now, which is exciting as well. I've probably been exposed to too many toxic chemicals already anyways and should readjust my bucketlist plans...

Fixed point and Floating point are extremely similar, so most of the time you should just go with floats. If you start with a fixed type, reserve some bits for storing an explicit exponent and define a normalization scheme, you've recreated the core of IEEE floats. That also means we can go the other way and emulate (lower precision) fixed point by masking an appropriate number of LSBs in the significand to regain the constant density of fixed. You can treat floating point like fixed point in a log space for most purposes, ignoring some fiddly details about exponent boundaries.

And since they're essentially the same, there just aren't many situations where implementing your own fixed point is worth it. MCUs without FPUs are increasingly uncommon. Financial calculations seem to have converged on Decimal floating point. Floating point determinism is largely solved these days. Fixed point has better precision at a given width, but 53 vs 64 bits isn't much different for most applications. If you happen to regularly encounter situations where you need translation invariants across a huge range at a fixed (high) precision though, fixed point is probably more useful to you.


There are applications where the difference between fixed-point and floating-point numbers matters, i.e. the difference between having a limit for the absolute error or for the relative error.

The applications where the difference does not matter are those whose accuracy requirements are much less than provided by the numeric format that is used.

When using double-precision FP64 numbers, the rounding errors are frequently small enough to satisfy the requirements of an application, regardless if those requirements are specified as a relative error or as an absolute error.

In such cases, floating-point numbers must be used, because they are supported by the existing hardware.

But when an application has more strict requirements for the maximum absolute error, there are cases when it is preferable to use smaller fixed-point formats instead of bigger floating-point formats, especially when FP64 is not sufficient, so quadruple-precision floating-point numbers would be needed, for which there is only seldom hardware support, so they must be implemented in software anyway, preferably as double-double-precision numbers.


The core of my multiplayer arena game is in fixed point

I wanted absolute certainty that the rollback netcode would result in identical simulations on any platform, and integer math provides that. With set of wrapper functions and look up tables for trig it’s not that much worse than using regular floats

I am still uncertain if I actually would have been fine with floats, being diligent to round frequently and staying within true integer representable range… but now at least I’m far less afraid of game desyncs and it wasn’t that much work

Cross platform, cross USA games have been stable and fun to play, no fixed point complaints here


Floating point determinism has been a personal bugbear of mine for a number of years. You still have to be careful, but it's at the point where it's less work than switching to fixed point (cheap as that may be). There are even libraries [0] [1] that implement full reproducibility with negligible overhead. Compilers shipping incorrectly rounded stdlib functions remains an issue, but they're slowly improving. Language level support for float reproducibility is in the C++ pipeline, and already a design consideration on the Rust side. In a decade or so determinism issues might be a distant memory once you've ensured same inputs to the same instructions in the same order.

[0] https://github.com/J-Montgomery/rfloat

[1] https://github.com/sixitbb/sixit-dmath


    i.e. the difference between having a limit for the absolute error or for the relative error.
The masking procedure I mentioned gives uniform absolute error in floats, at the cost of lost precision in the significand. The trade-off between the two is really space and hence precision.

I'm not saying fixed point is never useful, just that it's a very situational technique these days to address specific issues rather than an alternative default. So if you aren't even doing numerical analysis (as most people don't), you should stick with floats.


The reason no one wants to talk is that these discussions are always co-opted by racists wanting to affirm their beliefs, regardless of the underlying science. Reich in particular is borderline deliberate about attracting those sorts with his lab's research, because of how badly he chooses to handle the topic and terminology of race.

>Reich in particular is borderline deliberate about attracting those sorts with his lab's research, because of how badly he chooses to handle the topic and terminology of race.

Sorry, do you have any examples? His views that I've read [0, 1] are scientifically rigorous and terminologically precise, deftly navigating the politics that some consider extremely controversial. To wit, one of my favorite passages from [1], which deals specifically with terminology:

   But “ancestry” is not a euphemism, nor is it synonymous with “race.” Instead, the term is born of an urgent need to come up with a precise language to discuss genetic differences among people at a time when scientific developments have finally provided the tools to detect them. It is now undeniable that there are nontrivial average genetic differences across populations in multiple traits, and the race vocabulary is too ill-defined and too loaded with historical baggage to be helpful. If we continue to use it we will not be able to escape the current debate, which is mired in an argument between two indefensible positions. On the one side there are beliefs about the nature of the differences that are grounded in bigotry and have little basis in reality. On the other side there is the idea that any biological differences among populations are so modest that as a matter of social policy they can be ignored and papered over. It is time to move on from this paralyzing false dichotomy and to figure out what the genome is actually telling us.
This particular passage is on p. 253 of [1], but everything in Chapter 11 ("The Genomics of Race and Identity," pp. 247-273) is well worth the read.

[0] https://www.nytimes.com/2018/03/23/opinion/sunday/genetics-r...

[1] https://sackett.net/reich_who_we_are_and_how_we_got_here.pdf


It's unfortunate that the URL happens to be buzzfeed, but there was an open letter to Reich by other academics about his terminology in the book you're quoting [0]. The short of it is that social categorizations we believe in like race intersect with genetics in a very complicated way. Reich is a world-class expert in genetics. He simply commits the same error as many other other experts in discounting the complexity of subjects he's adjacent to, but not directly an expert in.

I get that this is a high standard to hold him to (and I sure as heck don't meet it myself), but he should do better given his visibility in public discourse.

[0] https://www.buzzfeednews.com/article/bfopinion/race-genetics...


The crux of that letter is the "need to recognize that meaningful patterns of genetic and biological variation exist in our species that are not racial." This is true. However, this does not mean that there aren't also meaningful patterns of genetic and biological variation that do stratify according to ancestry (not race!). The letter tries to handwave this away, claiming that "[f]or several decades billions of dollars have been spent trying to find such differences. The result has been a preponderance of negative findings despite intrepid efforts to collect DNA data on millions of individuals in the hope of finding even the tiniest signals of difference." This is simply not true, as studies like the subject of this discussion demonstrate.

The letter also states that "[t]he public should not cede the power to define race to scientists who themselves are not trained to understand the social contexts that shape the formation of this fraught category." Also true! This is exactly why Reich explicitly avoids discussing "races" but rather populations and ancestries, which are rigorously defined strictly in terms of genetics. With respect to population structures and ancestry, Reich is indeed an expert.

I'll add that very few of the signatories of that letter have any experience, let alone expertise in genetics. Here are the first few:

  Jonathan Kahn, James E. Kelley Professor of Law, Mitchell Hamline School of Law

  Alondra Nelson, Professor of Sociology and Gender Studies, Columbia University; President, Social Science Research Council

  Joseph L. Graves Jr., Associate Dean for Research & Professor of Biological Sciences, Fellow of the American Association for the Advancement of Science, Section G: Biological Sciences, Joint School of Nanoscience & Nanoengineering, North Carolina A&T State University, UNC Greensboro

  Sarah Abel, Postdoc, Department of Anthropology, University of Iceland

  Ruha Benjamin, Associate Professor, Department of African American Studies, Princeton University

  Sarah Blacker, Postdoctoral Research Fellow, Max Planck Institute for the History of Science, Berlin

  Catherine Bliss, Associate Professor, Social and Behavioral Sciences, UC San Francisco
Out of the 67 signatories, I counted approximately 5 who might have sufficient genetics expertise to offer a meaningful scientific counterpoint to Reich's work (this is being charitable, as I included titles like "Professor of Biological Sciences," which is no guarantee.) The rest were in fields like anthropology, sociology, law, and history.

     This is simply not true.
Yes, because it's not an argument the letter is making. Everyone can name a meaningful genetic patterns of genetic variation that follow ancestry like lactase persistence. The argument is in the second paragraph:

    But his skillfulness with ancient and contemporary DNA should not be confused with a mastery of the cultural, political, and biological meanings of human groups.
It's not an argument that Reich gets the science wrong, so other geneticists being on the list is neither here nor there. When he says things like:

    But as a geneticist I also know that it is simply no longer possible to ignore average genetic differences among “races.”
in NYT opinion pieces, it's that he's not understanding how terminology interacts with public discourse. The next paragraph goes on to use the unclear term "west african", not exactly a great example of careful language either.

The list is mainly people in fields that deal with these things, as you'd expect.


>Yes, because it's not an argument the letter is making.

It literally is though. The full quote from the Buzzfeed piece is:

  Reich’s claim that we need to prepare for genetic evidence of racial differences in behavior or health ignores the trajectory of modern genetics. For several decades billions of dollars have been spent trying to find such differences. The result has been a preponderance of negative findings despite intrepid efforts to collect DNA data on millions of individuals in the hope of finding even the tiniest signals of difference.
>The argument is in the second paragraph:

  But his skillfulness with ancient and contemporary DNA should not be confused with a mastery of the cultural, political, and biological meanings of human groups.
Reich never purports to make cultural or political arguments, just biological ones.

>When he says things like: But as a geneticist I also know that it is simply no longer possible to ignore average genetic differences among “races.”

Note that he put "races" in quotes. The point he was making here is that sometimes genetic ancestries can intersect quite well with traditional notions of "race" [0]. But often times they do not, especially in the case of admixed populations [1].

[0] https://www.nature.com/articles/s41598-023-32325-w/figures/1

[1] https://link.springer.com/article/10.1186/s12859-019-2680-1/...


    Note that he put "races" in quotes.
I know, but we both see how a random member of the public could easily read it. My argument, after all, is that the way he communicates is sloppier than it should be for the subject matter and prone to public misunderstandings.

> "need to recognize that meaningful patterns of genetic and biological variation exist in our species that are not racial." This is true.

There's an implicit assertion in that statement, that we're currently not recognizing that meaningful patterns and variation exists. But that's nonsense. We are all perfectly aware that some groups digest lactose better, some are less vulnerable to skin cancer, some drop like flies to common tropical diseases, some completely dominate long distance running competition etc.

So there's got to be some particular differences he's referring to that he thinks are papered over. He should spell out which.


Fortunately, there are many wise laymen such as yourself in the internet to correct him.

Not the person you were replying to, but: did you read that letter?

It is horribly argued. It's mostly poor analogies and non-sequiturs. It's no wonder Buzzfeed was the only place they could get to publish it.


> race intersect with genetics in a very complicated way

Please explain the complications. Use scientific terms only.


The biggest complication is that the current notion of human race is largely based on skin color (with a few adjacent physical traits), which has very little to do with population genetics. In particular, black skin color is a dominant genetic trait, meaning that you can easily have individuals and even entire subpopulations that are black skinned, but have much more genetic similarity to traditionally white skinned populations (being descendents of a few black skinned individuals who married into a larger white skinned population) - while they would still be categorized as "black" in terms of race. Conversely, genetically isolated black skinned populations are also often lumped together as "the black race".

Another major complexity is that some races are defined more by genealogic ancestry than by genetic ancestry or easily identifiable physical characteristics. For example, people are normally considered Jewish if they have a Jewish mother. This leads to many genetically disparate subpopulations being lumped together as a Jewish race.


> but he should do better given his visibility in public discourse.

Why? He presented real verified science. Anyone who is offended or does not like it ... well, too bad... the world does not care. Facts are facts. He does not owe you or anyone else comfort. He presents cold hard truth, and sometimes truth hurts. Tough.


I haven't read much from Reich, so I don't know his position. But I've understood that the current best practice in human genetics is to explicitly justify the population descriptors chosen for each study, rather than using any fixed set of descriptors given from the outside.

There are two main types of genetic descriptors: those based on genetic similarity and those based on ancestry groups. Genetic similarity is quantitative, and individual samples often have multiple labels attached to them. Ancestry groups are discrete categories based on quantitative measures. If it's appropriate to use descriptors based on genetic ancestry groups in a study, it's usually also appropriate to drop samples that don't fit neatly in any single group.

Sometimes it's more appropriate to use descriptors based on environmental factors, such as ethnicity or geography. Environmental descriptors tend to be correlated with genetic descriptors, but they are not the same.


Science is about truth not social outcomes.

People keep wondering why trust in scientific findings is in free fall. A big part of it is because many scientists have become comfortable lying when they feel it’s for a noble cause.


I really don't care if the people around me have physiological differences from me. It would be wonderful to explore that and such differences. But as OP pointed out the discussion gets co-opted by people who would kill others over physiological differences. How is such a viewpoint conducive to a peaceful society where millions of people with physiological differences exist?

For good reason, the wider community isn't able to have a productive conversation about it. I wouldn't even call that a noble reason, but a necessary one, unless you would be okay with inviting people that want you dead into discussion on scientific consensus.


> people who would kill others over physiological differences

Most of them just want to enforce borders. And then the dogma that we are all the same is co-opted by people who would see their ethnic group wiped out, as they are told that they don't even exist except as a meaningless social construct, and their desire for ethnic self-preservation is therefore illegitimate - there is nothing to preserve!

The same rhetoric targeting Palestinians: https://blogs.timesofisrael.com/perpetuating-the-myth-of-a-p...


>And then the dogma that we are all the same is co-opted by people who would see their ethnic group wiped out

Are you referring to certain people? People sympathetic to Palestinians? I mean yeah obviously it's wrong to preach equity for me but not for thee, but I'm not really going to get into a pissing match about Israel/Palestine, sorry, because that's deflection from my point.

So there are two choices here:

1) Allow scientific discussion on physiological differences or avoid it. Particulary, physiological differences that don't necessarily effect health outcomes but also performance metrics.

2) Do not allow such discussion, and declare an axiom: normalize physiological differences across homo sapiens.

You're right to call the latter dogma, although not in the pejorative sense.

You brought this infamous conflict up to propose that because option two can be used by bad actors, then we should not normalize option two, and freely discuss physiological differences between people.

If you are of a group that has physiological differences scientifically proven to be inferior, you are immediately in an outgroup. You will experience discrimination. Because few (and I'm being generous, perhaps no one truly) can talk about physiological differences without building and holding prejudice. Pragmatically that is just not the case. It's why endless ethnic conflicts exist.

I simply cannot formulate an argument for why this should ever be allowed. It sounds like a horror show if you're on the receiving end. A horror show minorities of many types live through every day.

To lay "ground rules" so that we do not scrutinize our fellow brothers and sisters on unalienable traits is an ethical imperative to prevent us tearing each other apart. This then leaves only one line, the line where people are more than happy to discriminate based on these unalienable traits, and I think it's perfectly acceptable to ostracize them since they encourage ripping each other's throats out, willingly or as a useful peon.


Nobody talks about "performance metrics" when distinguishing between Sumatran and Siberian tigers. What happens instead is humans try to preserve their populations and distinctions. "It's all the same" is corrosive to preservation.

Superiority is absolutely a distinguishing feature when preserving their populations and distinctions. It's why racial genocides even occur.

The problem is that if you don't stick to truth and make an attempt at objectivity, others will step in to fill the void. This is how you sow division and undermine trust in science.

I'm having a very hard time understanding a society where research is openly conducted on innate physiological differences between people, and bad actors don't use this official research to practice open discrimination. The lesser of the two evils is to draw a line and tell people to just accept these differences.

Scientists are not lying. Reich is notable in his field and no-one is disputing his genetic research.

What scientists are wary of is how any discussion in the field gets jumped on and twisted into ammunition to reinforce racist beliefs, whether the science actually supports this or not.


“What scientists are wary of is how any discussion in the field gets jumped on and twisted into ammunition to reinforce racist beliefs”

Yet nothing ruined the reputation of the scientific establishment more in recent time than their tendency to change their behaviours and adapt their beliefs for political motives


There are always those trying to discredit scientists who do not reinforce their personal beliefs.

> The reason no one wants to talk is that these discussions are always co-opted by racists wanting to affirm their beliefs

So? People need to stop undermining science and openly sharing information because some people have bad ideas.


Berlin specifically has a few meters of soil separating it from that period, but that's not always true. I've excavated millennia-old sites barely centimeters under the surface. Others are buried under meters of soil overnight. There's also natural processes moving things around in the soil (e.g. rabbits, freeze-thaw cycles), and human processes (e.g. tilling).

I wouldn't jump immediately to modern collector, nor does the article.


The southwest has plenty of layers on layers. Tucson is built on a Spanish fort, which is built on native villages on top of yet older native villages going back almost 4,000 years, as one example.

For another example, most neighborhoods in eastern phoenix are built on top of old Hohokam villages, adjoining older basketmaker sites. The canals throughout the city often follow the old Hohokam canals. Fun fact, the Intel Chandler campus is on top of old hohokam suburbs of Pueblo de los muertos, which is buried under the modern suburbs.


There's plenty of middle ground between an unchanging SQL schema and the implicit schemas of "schemaless" databases. You can have completely fluid schemas with the full power of relational algebra (e.g. untyped datalog). You shouldn't be using NoSQL just because you want to easily change schemas.

Echoing the efficiency. I just returned from a 1mo trip living out of the 45L, including a supply of dead-tree books.

That said, I've only had it a year and it's clearly not new anymore. Paint wear on the rivets, for example. I expect it'll be in rough shape when it's accumulated as many miles as the travel bag it's partially replacing.


The argument is that a universal basis would be capable of solving arbitrary polynomial roots. The rest is an argument that the group constructed by eml is solveable, and hence not all the standard elementary functions.

It wouldn't be a math discussion without people using at least two wildly different definitions.


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