It's like Newton not only discovering calculus but also inventing its modern syntax and writing the best textbook on the subject.
Newton was basically just trying to communicate with a handful of experts, many of whom didn't even speak English, so he just didn't see what he did as something that demanded a lot of attention paid to prose style. I actually find the writing style of some of Newton's contemporaries to be really beautiful and readable (Margaret Cavendish's Observations upon Experimental Philosophy is a surprisingly fun read). As is some of Descartes (like his Meditations). But those are definitely outliers.
(I think it was either Gleick's book on Information Theory, or the Drunkard's Walk, but it could have been any of the half dozen books I've been absorbed into lately)
Modern science and mathematics would be just as unapproachable if everything were required to be expressed in some standard-but-largely-inelegant framework in order to be taken seriously.
And thus he created a writing style that is predominant to this day! :(
I wish math used a pythonesque and popular alternative language, so that very low- or high-level 'assumptions' weren't blocking a greater audience from participating in the field. Although I'm familiar with it, I find it sometimes a little too elitist, because almost every symbol requires an explanation, before it can be used. Javascript and Python have this great balance, I feel is urgently needed in Maths.
Unfortunately, it doesn't generalize across specialties.
By comparison, the programmer chooses names explicitly based her own understanding and modeling of the problem, which may confuse others.
both approaches have their strengths and weaknesses.
I think you mean sub-sub-sub-subspecialty. I don't often read mathematics papers but when I do, it's infuriating how people think that [squiggle] has a universally understood meaning when in actual fact there are only a handful of people in the world (most of whom probably work in the same building as the author) who use [squiggle] to mean that.
Bear in mind, though, the papers are written for that same group. For good or for ill.
You mean, like p in statistics?
"In addition to being the 18th letter of the Greek alphabet, sigma also means 'sum' and 'deviation' in the mathematics world. Learn what each symbol looks like and how each formula works."
It first hit is titled,"Sigma Notation - Math is Fun", with the text 'Sigma Notation. Σ This symbol (called Sigma) means "sum up"'
I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math. Fun too. You really need to know the names of things to start to understand them and ask people about them.
I think the reason people like compact formulas is that it is much easier to understand and check a formula if one can have the whole thing in eyes view.
At the very least it means it takes 2 searches, one to find the name of a symbol, and a second to search using that, sometimes I can't do that if the notation is an image of TeX output. Then it becomes "what does box symbol with line through it mean" or something.
Thankfully StackExchange now renders math notation in a way that can be copy pasted, but still, here's an example I was reading recently that started as an ascii email chain and moved to stackexchange, I feel like it was more easily readable before.
It's still tough to Google that Π(u) is the same as the rect() function
https://dsp.stackexchange.com/questions/42495/implication-of...
> I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math.
But the original point was that for someone who doesn't know math, writing it in a more english-like notation wouldn't be helpful. But because of search engines it is.
In this case google is probably simply case insensitive.
I still can't get over the fact that google removed advanced search syntax.
Though AFAIK Google ignores those common words anyway.
Google used to conduct a relatively straightforward string matching search. That means if you used words like "what" you could end up with unrelated matches, or lower quality matches, because they would match with the word "what".
Now, bear with me, these days google seems to use some kind if machine learning to suggest results to you based on what others have searched and chosen.
What does this mean, practically? At least two things: 1.Laymen have to think less critically, less technically when searching. Considering google is, for the average person, basically the window to knowledge, I think this is ultimately a disservice to society.
2. Search quality for technical information seems to be declining, now that laymen and non-laymen alike are searching using the same " extra" words and, I may just be projecting a poor understanding of neural nets here, but our technical results end up getting sort of clustered with everything else.
Am I the only one who has this problem with the decline of google search's technical relevance? Maybe I'm doing something wrong...I still think what google has done to make the internet more accessible may be a net harm to society.
But nowadays, it's not as simple as just machine learning to understand your query, but the way the information is stored is less and less like a text storage. If I search for something involving "car' it's very likely I'm okay with results containing "sedan", "vehicle", or various brand/model names of cars. I'm also probably fine with "vehcile" or "vehiclle" or "carr" but not "cat". And Google is well aware of this and considers this when building their model.
Furthermore, the way you ask SHOULD change answers, especially because it attempts to automatically answer you at the top of the page. A search for Sigma and What generally means I want to know what it means, how to use it. But a search for "why" should bring up the historical reasoning Sigma was chosen over another letter, or another culture's alphabet entirely. That's too much information to fit into any result for simply "Sigma", and the query is too vague to help pare it down.
I do agree with you though that it is declining for technical information. But I think overall it has gotten much better at becoming a general "window to knowledge" and I think it's worth the tradeoffs.
Also, a notation that is suited to one field (programming), may not be necessarily best suited to another (mathematics). Personally I feel much the opposite of you: mathematical notation is often clean and expressive, while programming language and its string-of-chars constraint makes for much more difficult to understand notation.
Yes, it's clean, if you know all symbols. But it's an unnatural mental burden. We think in patterns and structures. Our language should be similar, because what we express with language is unavoidably self-similar.
I'm gratefull for all the replies, as it seems to underline that this thought resonates strongly. Notation hinders understanding and the farther away symbols deviate from structures we use everyday, the stronger. Even though I personally prefer Unicode/Pictograms, it can't be that we have to reinvent Notation evertime that subsums recurring structures in programming, mathematics, physics, chemistry and every other conciously disconnet field in the same way. Because of universal properties I don't know about.
Yes, field specific notation has it's local and inherent beauty, but the price is too high! We can't fix education globally, at least not at this stage of our development. Thus we should drop efforts put into keeping Notations diconnect. It will widen the knowledge gap between the systemically uneducated majority stronger and stronger.
A solution? Biomimicry has always been our strongest weapon! I think nature is also far ahead in adopting a universal and often times visual language, we only acknowledge when we become isolated experts in a narrow sub-field, such that the language reveals itself.
It's acceptable to have rich symbols, if we can't get an universal notation based on a better generalizing (structural?) representation instead. I guess some of you may think about a more readable form of set-theory, others of geometric computing or mathematical manifold theory. Whatever it is that makes nature so efficient in reusing sub- and system-languages via controlling structures is what we should also define, understand, formalize and adopt throughout all fields via government backed efforts. I believe this is more important than I can currently imagine for our long-term future. An universal language, able to describe not only other languages, but also defining properties of complex systems, that's so alien it might work.
I think I've unknowingly stated a probably open mathematical problem. But can't put my finger on it. Can someone help?
PS: Sorry for coming late, deadlines coupled with a awfully slow laptop...
I've been meaning to go at it but I'd like to know in advance how outmoded its theories and concepts are.
Leibniz called, he wants his calculus back.
Fundamentally correct? Evolution is neither demonstrable nor falsifiable, so it's not scientific.
Disclaimer: I'm an atheist.
[0]http://www.cell.com/trends/ecology-evolution/abstract/S0169-...
There are still many areas where we don't know the exact machanics, but evolution in itself is a fact.
Both can alter function. One is observed the other not (according to those who argue micro/macro).
Yes.
> By evolve I mean macro evolution.
There is no such thing as "micro" vs. "macro" evolution in evolutionary theory. There's just evolution. Species are not absolute boundaries; they are just convenient labels we use to group organisms for purposes of taxonomy.
Lots of hand waving and no substance.
They are used as concepts to organize things to make them easier to understand. They are not used to make actual predictions.
In addition, what testable predictions has evolutionary theory made about existing organisms on this planet? Not interested in any prediction about things long past as you can modify any theory in any field to match up to such findings. What can evolutionary theory predict today that we can test as an outcome by going out and finding those predictions in living organisms today? That should be an easy question to answer if there is any veracity in the evolutionary model/theory.
I mentioned antibiotic resistant bacteria elsewhere in this thread. You can find plenty of other examples if you look at the scientific literature in this field.
> Not interested in any prediction about things long past as you can modify any theory in any field to match up to such findings.
No, you can't. Evolution makes quite specific predictions about what we will not find in the fossil record--for example, J. B. S. Haldane's famous response when asked what could falsify evolution: "fossil rabbits in the Precambrian". Alternative theories for how the life we see on Earth today came to be make no such predictions--they could "explain" fossil rabbits in the Precambrian as well as anything else.
More generally, evolution predicts that we should find a "tree of life" like the one we find--where we can compare relationships between organisms that we derive using DNA, fossils, anatomy, and other evidence and find that, to within a good approximation, they all agree. Alternative theories for how the life we see on Earth today came to be make no such predictions--they offer no reason why all those different "trees of life" should be the same or even close to each other.
So predicting that you won't find something in the fossil record is it, is it? These kinds of predictions are hollow in the extreme. If the evolutionary model/theory cannot make predictions about what should be seen today then it is of little worth, in the same way that the current crop of climate models cannot make predictions of any worth.
The "tree of life" that evolutionary theory "predicts" has so many problems that it also is not worth much, if anything. So, back to the question at large, what valid definitive predictions is the evolutionary model/theory making today that we can go test in the living organisms of today?
I will say it again, I was and had no problems with the evolutionary model/theory until I started seeing the major dissonance between the experimental results being obtained and the interpretations that the evolutionary biologists were making on those results.
Evolutionary theory and practice today has all the trappings of religious dogma and one becomes anathema to the community if one doesn't subscribe to it tenets. This is not science. It is much like how the Catholic Church operated during the Spanish Inquisition.
There are no silly questions. I have come across many who promote scepticism except in areas in which they are "true believers". Some of these areas include evolutionary theory, climate change, big bang, dark matter, dark energy, etc.
There is nothing wrong with not subscribing to specific points of view, if you find that those models/theories have problems. You are allowed to ask questions and even be sceptical.
In some ways the dissonance between macro (astrophysics) and micro (quantum mechanics) is another good example where being a sceptic and asking the question "What have they missed in the promoted theories/models?", is a good thing. It is like the battles that go on between string theorists and non-string theorists. There is so much emotional involvement when it's only about some possible theories that may have some possible applicability.
Science is not about "truth" and when it becomes about "truth" it has changed from science to religion/philosophy. The way many of the participants and proponents of various fields and associated theories/models act, they are making it a religious discussion about "truth".
Science is about discovering information about the physical world around us and developing applicable models/theories that we can dispense with if they prove inadequate. It is not about dogmatic adherence to specific theories/models.
I put evolutionary theory on the same par as intelligent design. Neither of these views are science, they are philosophical/religious in nature.
I believe in Jesus Christ as creator of the universe and all that exists. It behooves me to gain an understanding of that universe and how it runs. To understand the rules by which it works, to understand the processes that occur. This means creating models and theories on how it works and when more information to come to light, being able to dispense with flawed ideas and theories. Theories give insight so that we can gain a better understanding of how things work. For me that gives a greater appreciation of how great is my God.
Will I understand the universe in any great detail during my life here. No. But is sure is fun to gain what understanding I can. We know so little and yet we have a propensity towards being dogmatic about what we do know. This is strange attitude, considering that we are continually finding out things that challenge our existing theories and models all the time.
Let's be enthusiastic about learning more about the universe and less about being dogmatic in holding to the very flawed theories and models that are the current "flavour of the day."
The more dogmatic people are towards the "correctness" of their theories and models the longer it will take for advancement in our understanding to occur.
Just an example for you. There is a potential model (actually the merging of two models) that could merge the strong force, electromagnetic and gravity into a single consistent electromagnetic model. Whether or not it has any viability, I cannot at this time see. But it is does have potential. I am having to relearn a lot of the mathematics I did 40 years ago as well as learn how to use Maxima to test if there is any potential viability. For me this is fun and I am enjoying looking at this. It may lead nowhere. So be it. I am not going to get emotionally entwined with the idea. It is just an interesting potential.
Really? What other models make this prediction?
> Nor is this feature of the bacteria a definitive example of evolution as such.
Why not? It's change in the genes of a population in response to selection pressure, that increases its fitness under that selection pressure.
> I was and had no problems with the evolutionary model/theory until I started seeing the major dissonance between the experimental results being obtained and the interpretations that the evolutionary biologists were making on those results.
Can you give some specific examples? From actual peer-reviewed literature, not pop science presentations? I agree that in their pop science books, articles, etc., evolutionists say all kinds of things that they would never get away with in an actual peer-reviewed paper (Dawkins is a particularly egregious offender in this regard). But pop science is not actual science, and you can't judge the actual science by its pop science presentations. The same thing happens in every field. I see pop science presentations of physics all the time, even by Nobel Prize winning physicists, that are full of misstatements and misrepresentations that would never pass in a peer-reviewed paper. But that doesn't make the physics itself wrong.
> There is a potential model (actually the merging of two models) that could merge the strong force, electromagnetic and gravity into a single consistent electromagnetic model.
Do you have a reference?
You're splitting hairs on semantics to hold onto your untenable position that evolution is not scientific.
Of course, even if we found a perfectly preserved fossil of a T-Rex from two million years ago, it likely won't falsify the whole theory of evolution, because there are simply too many evidences for that. It would be like saying "We found evidences that George Washington did not in fact die in 1799! The whole theory of the American Revolution is now in question, and the Aliens-did-it theory should be considered as good as the mainstream version!"
Do you believe in mutation?
One thing that is a certifiable fact is that species are not fixed. As shown by the fossil record, new species can show up and old species go extinct. And in a smaller time scale, the artificial selection that happens with domesticated plants and animals shows that there can be significant changes in species.
Once we realize that some sort of evolution must be happening the question becomes to explain what mechanism is behind it. One of the initial hypothesis was the Lamarckian theory that animals can pass on to their offspring traits that they acquired via their lifestyle. This was eventually proven false when we found no evidence that this is not how genetics actually works. Darwin's theory of natural selection is still with us because it withstood the test of time, not because it is unfalsifiable.
This is very clear if you read Darwin's books. He was aware that there are many things that would contradict his theory if they were true and he spends lots of chapters refuting them.
A more modern source I like to point to is Talkorigin's list of 29 evidences for macroevolution. It covers many of the things known to Darwin and more recent developments such as genetics, molecular biology and new fossil finds. http://www.talkorigins.org/faqs/comdesc/
Lamarckian theory might not be _completely_ false. There is definitely epigenetic inheritance, in which traits (reflecting the state of a parent) can be passed on without being explicitly encoded by nucleic acid. Whether epigenetic inheritance is a stable-multi-generational way of transferring traits is a little up in the air. But I wonder if Lamarck will get a modicum of vindication from the biology textbooks in the long run.
That being said, epigenetic inheritance does not falsify evolution by mutation.
Being 'scientific' is not required for an idea to be correct (nor does it imply the idea is correct).
Though frankly, when they said "fundamentally correct" they meant "doesn't have any significant conflicts with our current knowledge of the subject".
But what I'm saying it that evolution is neither scientific nor correct.
"Macro-evolution" (to use your term) is the best most likely correct explanation for life according to the available evidence. Much like Newton and Einstein it is likely that any theory that "replaces" evolution will be a superset of Darwinian evolution rather than a replacement.
And for the record there are examples of evolution occurring at the macro scale right now in the form of ring species where neighboring pairs produce viable offspring but more distant species don't. eg: A -> B -> C -> D where A & B occasionally mate and produce offspring that results in gene mixing between the subgroups, but A & D cannot produce viable offspring. If B or C goes extinct this will trigger speciation by breaking the chain, permanently stopping the mixing of genes between the now separate chains. Look at the greenish warbler or euphorbia tithymaloides.
The Russian Domesticated Red Fox[1] is a great example of selective pressure at work and how it can produce dramatic changes in a species (though this is necessarily artificial in order to obtain results on human time scales).
[1]: https://en.wikipedia.org/wiki/Russian_Domesticated_Red_Fox
You bring up ring "species" without defining what "species" means in this regard . I recently did a small survey trying to find out what the specific definition of "species" was. To my disappointment, I find that there is no specific definition within the literature that applies across the board. This particular word can mean anything from some sub-grouping that has distinct characteristics to another sub-grouping, in which members of both sub-groups are able to produce viable reproducing offspring that have merged characteristics, all the way up to having two groups that cannot produce any kind of offspring under any circumstances.
The literature is very adept at doing a lot of hand-waving about how the model works and what predictions are made.
Though the model may be the current generally accepted model, it does so on very weak foundations. People are allowed to question the veracity of the model and hold it to criticism without having to provide an alternative. It is allowable to question any model/theory in any way without the proponents getting on their high-horses and taking their marbles home. There are no silly questions.
But the way it is presented today, it can be and should be treated with scepticism as, in many ways, it is dogma not science.
There is much the evolutionary model doesn't answer and should be under continual experimental testing to test the veracity of any of its claims.
Having the existence of mutation and genetic variation (including antibiotic resistance or chemical resistance) does not in any way signify that the evolutionary model (Darwinian) is correct or even viable.
Going back to your ring species example, wolves, coyotes and domestic dogs were/are considered to separate species, yet we are no finding that all three are producing reproductively viable offspring. So, a valuable question to ask is "Are they the same species but different sub-groups or are they separate species that have undergone some biological change that now allows them to cross breed?" A second question to ask is "Is this an example of the existing evolutionary model (as per its predictive capabilities) or is this an example which will work against that model?"
Lastly, the term macro-evolution has a history going back to 1927, with its use falling in and out of favour with evolutionists and palaeontologists since then. Even within the evolutionary community, there is a wide distribution of opinions as to how different "species" arise and the relationships between them.
On the whole, the model fails to explain the wide variety of different organisms and their associated grouping and relationships. Unless many more experiments can be done showing the actual applicability of the model across a vast range of different organisms and it being able to predict expected change in groupings that can be tested, it will continue to remain a hand-waving model and nothing more.
Anyone can challenge the evolutionary model (or any other model/theory) without having to provide an alternative. If people cannot accept that, then they are in no position themselves to ever challenge any proposal put forward that they disagree with without first presenting a fully viable alternative. As they say, "ya canna ha ya cak en et it tu".
The one thing that I do find amusing is that theologically, the Darwinian evolutionary model fits in very well with Hindu theology. This was brought to my attention in reading various papers presented by Hindu theologians/guru's.
"Evolution occurs" is science - it is reproducible and falsifiable.
"We are the result of evolution and descended from single cell organisms" is not reproducible nor falsifiable. I would agree with your claim that this is not science.
Sure it is. It makes all kinds of testable predictions, which have been confirmed. One good example is the evolution of antibiotic-resistant bacteria, which IIRC was predicted by (among others) Alexander Fleming, who discovered penicillin. If more people had listened to that prediction of evolutionary theory (which was obvious even when it was made and is even more obvious today, when we can sequence bacterial DNA and see it changing in response to selection pressures imposed by the use of different antibiotics), we would not have the major problem with resistant bacteria that we have today.
I think you need to look into something known as a "fluctuation assay". Basically a microbiologist grows a batch of bacteria from a single cell, for some number of generations, then puts them on a petri dish under a low dosage of antibiotics, in order to kill those which have not evolved some immunity during previous generations.
The survival percentage has been shown to correlate with genetic mutation rate of the bacteria strain in question, which was tested by directly sequencing the genomes.
If they didn't correlate that would be a falsification of evolution.