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A new kind of thinking needed?

  1. Jan 25, 2010 #1
    Up front: I'm a total layperson with no formal scientific training. I'm also a rational human being who doesn't believe in mumbo-jumbo but can allow for there to be plenty of counterintuitive reality that we haven't yet discovered. No Bigfoot or Nessie talk, but, you know, open-minded.

    So I recently viewed a moving speech by Carolyn Porco (on youtube at watch?v=qGSv-uZCOyY). She is very fond of Galileo, and credits him, more or less, with the invention of the scientific method. I'm not sure I can believe this to be true, as it seems obvious to me that the scientific method (at least the basic idea of testing one's opinions against reality) is hard-wired into our behavior (just watch your kids), and it seems staggering to me that it took us so long to formally articulate the concept. But ignoring that point for the moment, it occurred to me that until Galileo, human reason had really gone as far as it could go, and a new way of thinking was required.

    It has always bothered me that the extremes of our knowledge (e.g., quantum and relativistic phenomena) are so out of whack with our intuitions. It's a good point that we evolved in this middle order of magnitude so we lack good intuitions at the extremes. But science has been challenging our intuitions for centuries--quantum mechanics and relativity weren't the first surprises, after all. Yet every time our intuitions have been challenged, we've quite readily assimilated our new discoveries into our thinking, and without even realizing it we absorbed the surprises into our intuitions. But extreme phenomena still challenge our intuitions--we can't seem to assimilate them. Hence the craziness of string theory, for example.

    It seems to me that perhaps we need a new cognitive tool in order to take the next big step in human understanding. The scientific method is an indispensable tool--we'll always need it--but we need a new, additional tool. A new way of thinking, some mode of thought that we can train ourselves to use that will allow us to have a better, and intuitive understanding of the extremes.

    Having such thoughts rolling around in my mind, I discovered Daniel Tammet, who has a rare and extreme form of high-functioning autistic savant syndrome. He can do amazing math and language stuff, without trickery. It's just that his mind works differently. And I guess he has written a book suggesting that we can train ourselves to think like he does.

    So the big question behind this long speech is this: has anyone thought to discuss the extremes of our physics with any of the Daniel Tammets of the world, to see if they have anything interesting to tell us? Perhaps some patterns that the rest of us aren't seeing?
     
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  3. Jan 26, 2010 #2

    Chronos

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    Intuitive constructs are insufficient to supplant mathematical formalisms. In other words, you belong in the IR submission forum. You might be right but you are appealing to the wrong audience.
     
    Last edited: Jan 26, 2010
  4. Jan 26, 2010 #3

    Chalnoth

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    Except an intuitive understanding of the world around us really isn't necessary to science. It can be kind of appealing, I suppose, but it isn't necessary. And our brains are probably physically incapable of it, just as we are physically incapable of visualizing four dimensions.
     
  5. Jan 26, 2010 #4
    I'm not saying that an intuitive understanding is necessary, and I am in no way suggesting that we do away with the tools that have brought us this far, such as mathematics. I'm using our lack of an intuitive model (your example is perfect: our inability to intuitively grasp a fourth dimension) as a suggestion that we're coming close to the limits of our existing mental tools. I'm saying that perhaps in the same way that Galileo's philosophical approach (test your opinions) was an extremely useful (and at the time novel) tool in advancing our understanding, we might be at a point where we need some new models, some new ways of thinking about things, some new math.

    I'm not appealing to an audience. I'm not promoting an agenda. I am simply asking, after having given some background on where the question is coming from, whether anyone on this forum knows whether any physicists have talked with any of the savants of the world to see whether their unique ways of visualizing mathematics and other symbolic systems could be helpful in advancing our understanding.
     
  6. Jan 26, 2010 #5
    I've read people that are quite critical of Galileo, and suffice to say that things are a lot more complex than they first seem, and as with most things historical, it's better if you read some competing narratives to see what really happened.

    It's pretty obvious to me that the scientific method is *not* hard-wired into our behavior, since most people get it wrong. It's also worth noting that most of our current ideas on what science *is* date from the 1950's. Thomas Kuhn wrote his book in the 1950's, and Popper's ideas came from the 1920's. If you asked a scientist in the mid-19th century and one today on what they are doing, you probably will end up with very different answers.

    1) String theory might be wrong. From a physics point of view, I'd consider it a massive colossal wild goose chase.

    2) There are people that *do* have deep intuition about string theory. It's all a matter of staring at something every day for several years, and after a while you develop a "gut feeling" for how things work or don't work.

    Science usually doesn't work with big steps. It works with lots of little steps. The problem is that the reality is messy, and if you take huge big leaps without data, you are likely to end up not only being wrong, but unable to figure out that you are wrong.

    Personally, I've found that things like google, wiki and mathematica are extremely research tools because they make it easier to teach mathematical concepts. A lot of the problem with physics is that you don't have the ability to "play" with objects, and if you have a computer program that lets you play with 4 dimensional hyperbolic spaces the same way that 3-year olds play with blocks, it's much easier to develop an intuition about how things work.

    One curious thing though is that some impressive mental feats turn out to be pretty useless in physics and mathematics. The ability to memorize Pi to 22514 digits turns out to be an interesting trick, but it's something that is completely useless in the sciences, because you can log into google and end up with pi calculated to 100000 digits.

    Already done. If you talk to a mathematician or a mathematical physicist, then you'll find that there is no huge shortage of people that have very deep intuition about mathematical structures. One problem is that to even *communicate* what is going on requires about a decade of effort. A lot of higher mathematics involves getting to the point where you can write down what you are seeing in your mind.

    The other thing is that the skills that creates a great mathematician often makes for a lousy physicist and vice versa.
     
  7. Jan 26, 2010 #6
    Who is "we"? Most physicists don't have any problem intuitively grasping fourth dimensional spaces. In order to do any special relativity, you have to have intuitive understanding of Minkowski spaces, and it's not hard to develop this sort of intuition when dealing with flat Minkowski spaces.

    Giving people an intuition about Minkowski and infinite dimensional Hilbert spaces is something that's pretty essential for any undergraduate physics curriculum, and people have worked out the techniques for doing that. Dealing with that is kindergarten stuff.

    Do you have something specific in mind? One problem with talking about "new stuff" is that you need to be pretty familiar with the "old stuff" to know what's missing.

    I think that a pretty large fraction of theoretical physicists and mathematicians *are* high functioning savants with pretty unique ways of visualizing mathematics. One thing about a lot of mental abilities is that they fall on a spectrum with people at one end able to "fake normal" and people at the other end completely unable to function socially.

    Personally, I think that there are some interesting cognitive science things to be explored, but it's really tough to do this.
     
  8. Jan 26, 2010 #7
    Your response is making me see my own subtext. What I really want is to be involved, at least as an informed spectator, in the scientific conversation, but the conversation is getting away from me as a layperson. I jumped at Tammet's mesmerizing description of the way he traverses symbolic landscapes as a possible way to make the conversation more accessible to me and my ilk.
    Hilariously true; also applies to us engineers, although I'm not sure how many of us are high-functioning.
     
  9. Jan 26, 2010 #8

    Chalnoth

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    Well, unfortunately, that really isn't easy. In much of modern science, we have now moved so far away from the realm of the ordinary, away from the world which our brain evolved to understand, that we just aren't equipped to understand these new facts.

    This means that we have to supplant our ability to intuitively understand with mathematics, and that, sadly, requires a lot of study to get right.

    Now, granted, once scientists have discovered some interesting new fact, it is a very good idea to try to explain that fact in plain language that everybody can at least begin to grasp, instead of just leaving it in mathematics. But the plain language translation of the real scientific finding (which is always mathematical in nature) should not be confused as being a terribly good description of reality: plain language just isn't suited to the task.
     
  10. Jan 26, 2010 #9

    DevilsAvocado

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    (Pure speculations from another layman)

    Computers gonna (must) change everything
    I make a prediction that computers are going to play a much much greater role in tomorrow’s science. Google, Wiki and math software is cool, but is going to look like 'kindergarten' to the next generation.

    (Of course I do not know for sure, but) Logically the 'volume' of scientific knowledge is growing for every year, and soon or later we will end up in a situation where the new students have to start reading 24h a day at age of 5, to be able to graduate at 35, and by then most of them will have lost their juvenile creativity, significant for many important discoveries in science. The alternative is to become a narrow specialist, with a very limited perspective, or to work in large teams, which can produce more meetings than science.

    Naturally, the scientists of tomorrow need good and basic knowledge, to be able to be creative and to ask the right questions. But why spend 10 years on studying complicated math – if the computer can give you the right answer in 10 seconds...?? My favorite, Albert Einstein, was not a mathematical genius. Many of his ideas started as picturing thought experiments, and later he got help with the complicated math (I know 'reality' isn’t that easy these days...). I think you hit the nail:
    So how about a brand new CSS? A Computer Science System with advanced AI that understands your questions, which have a database network with the entire collective scientific knowledge of the latest 2000 years? That collects and explains the information you need for the moment, but not only that; it checks in a few seconds if the math behind your idea is valid! Cool, right!? :smile:

    And the new CSS will of course provide a graphical environment with 4 dimensional building blocks, to play with. In fact you will be able to personally enter the 4D world! Real cool, right!? (Please, don’t ask about the costs... :biggrin:)

    To communicate the new science to the public, computer graphics must play a much bigger role than today. Joe the Plumber will not spend 10 years on math, to understand the first 10% of string theory, just to be informed: "Sorry Joe, it was a wild goose... :redface:"

    To me, the mathematical representation of 4-dimensional Euclidean space means (almost) nothing:

    [tex]\| \mathbf{x} \| = \sqrt{p^{2} + q^{2} + r^{2} + s^{2}}[/tex]

    But this catches my interest, and urges me to check out more at Wikipedia etc:

    8-cell-simple.gif

    If the gap between the scientists and the public (and scientist in other fields) grows further, I think it will be very negative for the future of science...

    My (highly speculative) hope is that mathematics and computer language is 'morphed' into a 'human scientific language', that don’t requires the knowledge and explanations of 'Egyptian hieroglyphs', before one can start calculate. After all, there is only one basic arithmetic binary operation – Addition of natural numbers. Everything else is derived from that operation...

    And most important of all – the kids of today use computers as one of their favorite toys, this will change the world, if nothing else!

    (And now I will duck and put my boxing gloves on... :wink:)
     
    Last edited by a moderator: Apr 24, 2017
  11. Jan 26, 2010 #10

    Chalnoth

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    Computers already play a huge part in today's science. A large fraction of science today revolves around using computers to analyze data, using them to produce simulations, as well as just communicating the results to one another.

    Instead of the amount of education required getting extended, scientists become more specialized. First you need a good basis in the scientific field. This basis really doesn't change much through the years. Then you're trained in your specific area, sometimes with field-specific classes, often by apprenticing to a professor. Often professional scientists like to branch out in a couple of different subfields, but it's not reasonable for any professional scientist today to be an expert in all subfields of a single discipline.

    Basically, if the mathematics can't be learned easily by a human, a computer isn't going to fare any better. Complex mathematics may take a few years of training, but most of that isn't so much in grasping the complexity as in just developing a mental toolkit used to solve problems. It's these problem-solving skills that are really needed to be a good scientist, and computers are just a tool that can be used by scientists to do this. Unless we develop real AI, computers aren't ever going to be a replacement for human problem-solving skills.

    We already have such online databases. The arXiv stores the vast majority of information about physics, for instance. The problem is that it isn't so easy to just trivially query a store to determine whether a certain idea or other is valid. Granted, mathematicians do make use of certain computer programs to determine whether or not a mathematical proof is valid, but this not only requires some training as to how to translate the language of the proof into language the computer can understand; it is also not something that will actually help with a lot of the mathematics used in science. The reason for this is simple: often the problem with bad math in science isn't that the math isn't internally consistent (which is often a problem), but instead is a problem with the mathematics being incorrectly applied to the physical system in question. And that's not something a computer can test easily.

    Certainly public communication of science is extremely important, as well as communication between fields, but really, these lines of communication are quite open, as near as I can tell, if only you are willing to look for them.

    That's not reasonable because plain language isn't specific enough. Granted, some programming languages are more readable than others, but human language will never work.
     
  12. Jan 26, 2010 #11

    DevilsAvocado

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    That’s very true. I was thinking more of the next generation of IT, which will probably make today’s technology look like an 'abacus'...

    But isn’t that a 'problem' that will grow for every generation...? As the volume of scientific knowledge is growing – your 'personal field' is shrinking... or?

    I agree. We need real AI systems before any real change can take place. Still, it will always be the scientist who provides the creativity in the interaction with computers (I think... at least for 1000 years or so...). But it might not be that far away, Chess computers beat the best players in the world now and then, and Chess is all about math. The real 'messy' thing, I think, is to answer 'simple' questions (in the interaction) like; "Good morning! How are you today?", and the 'bright' box answers; "Please define to-day." :smile:

    arXiv is absolutely great by today standards. Just imagine if you showed this for a scientist in 1950? All papers searchable and available in seconds! Anywhere in the world!! What I’m thinking of is the next step in this technology. Today, if you search for "Quantum fluctuation" you get >1000 results, with the first 1000 displayed. All this is based on SQL (Structured Query Language) from 1974, and we need better stuff. A technology that 'understands' the content, not only indexing words...

    Agree, the key is "if only you are willing to look for them". I think many have prejudices about science... difficult... boring... etc.

    Of course it has to be more a programming language than a human language. But is this really impossible? Extremely simplified: :smile:

    Human:
    Take one green banana and one yellow banana, and put them in the basket. How many bananas are in the basket now? There are two bananas in the basket.

    Computer:
    GreenBanana = 1
    YellowBanana = 1
    Basket = 0
    Basket = GreenBanana + YellowBanana


    Scientist:
    1 + 1 = 2
     
  13. Jan 26, 2010 #12

    Chalnoth

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    A good fraction of this is down to encouraging better science education, I think.

    Try doing it with a more difficult question such as:

    What is the comoving angular diameter distance to the surface of last scattering (z = 1089) assuming unperturbed FRW and the WMAP 5-year best fit parameters?

    You can state in words what that means, but you couldn't convey how to actually perform the calculation without presenting the mathematics. The most readable computer program would generally just be a simple representation of the mathematics (in this case, it would have to be one that understands how to compute an integral).
     
  14. Jan 26, 2010 #13

    DevilsAvocado

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    :rofl: HAHA!! Oh man oh man!! I’m laughing off my chair!! LOL!! :rofl:
    This for sure proves who the real nut in this forum is... Intellectual seppuku!! Hahahoho! Green banana, yellow banana, I’m going bananas!! :biggrin:

    Absolutely correct! And the right thing for me now is to: "Shut up and calculate!" :surprised

    Nevertheless, this kind of software must be more effective than a slide-rule. Maybe there is a way to improve this software development? (Providing the user has the right skills from the start.)

    600px-WxMaxima_0.7.1_screenshot.png
     
  15. Jan 26, 2010 #14
    Because answers are easy, it's phrasing the question that is hard. It takes months often years to write a piece of software that asks a non-trivial scientific question. Also, trying to get the problem in a form that a computer can deal with it takes *more* math, not less.

    Great!!!! Who is going to program this?

    The usefulness of computer visualization is that it lets you associate a set of symbols with pictures. Once you can touch and feel complex surfaces, then you can better have a sense of what the symbols mean.
     
  16. Jan 26, 2010 #15
    Maybe. But you do have to realize that a lot of the basic ideas of computer programming date from the 1930's.

    It's really not. It turns out that chess computers can beat the best players because chess is a problem that works well if you just do massive numbers of simulations. There is very, very little intelligence in chess playing programs.

    The next step is really to get people to summarize those papers and find the three or four that are worth reading.

    Or a technology that makes it easy for humans to comment on the content. If I hand yoiu a thousand papers on string theory, it's going to be totally useless to you. What you need is someone to go into those papers, add commentary, filter out the dross, put together summaries, cross reference them to other sources. We can call them teachers.

    I don't see the point in getting a computer to do what a human is good at doing. If you want to query a topic, instead of an automated search, it would be better to have a place where you can type in a question like "I'm looking for a good introduction to deRham co-homologies, where can I find one" and then have some group of human beings answer the question.
     
  17. Jan 27, 2010 #16

    Chalnoth

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    The point is that computers are merely tools. Extremely useful and capable tools, this is true. But they cannot replace genuine understanding of the mathematics and concepts being used.
     
  18. Jan 27, 2010 #17

    DevilsAvocado

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    Agree, but if Max Tegmark is right, it’s going to be quite powerful tools in the far future, since you then will be able to simulate complete worlds...
     
  19. Jan 27, 2010 #18

    Chalnoth

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    I don't think so. The number of degrees of freedom for an entire universe is just too vast.
     
  20. Jan 27, 2010 #19

    DevilsAvocado

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    That’s true. Just my wild speculation: If we solve the IA problem in the future – what if it then would be possible to construct a 'mathematical internet' that is 'aware' of what has been tried out, what works, and what’s going in on at moment? Just as you today go to Google or Wiki and type word or a phrase to get information – this system would 'assist' you in the mathematical world...

    Again, it's wild speculations... but of if you don’t have any visions about the future... probably less happens in the future...

    :smile: Maybe I can put a team together... can you provide the bucks...? :smile:

    Exactly! Let us move one level above pen & paper, and make things that move in 3D/4D, to move in 3D/4D!
     
    Last edited: Jan 27, 2010
  21. Jan 27, 2010 #20

    DevilsAvocado

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    Or, maybe 200 BC? When an Indian writer presented the first known description of a binary numeral system!? :wink:

    It’s all about 1 and 0, but the thing that changes is ability to process data and calculate faster and faster. Also the tools for developing software have gone from punch card to graphical RAD (Rapid Application Development), which speeds up everything by many factors.

    Personally I think we need better/smarter software to make a leap into the future...

    Agree, basically what the program does (when leaving the opening book database) is testing every possible move (while the opponent speculate what’s for dinner :smile:), save the evaluation, and then select the best move.

    Maybe there is no possibility to translate real intelligence to 1/0... Maybe one way is to find out what real intelligence is, and how it 'works'... first...

    Yes, another thing one could do tomorrow is to extend the arguments for SQL:
    * How many have required the paper (last month, year, etc)?
    * What’s the score (usefulness)?
    * What’s the average author score (usefulness)?
    * How many references to this paper on internet?
    etc ...

    Comments yes, and 'scores' etc.

    Human interaction is always good. But if you apply this reasoning on Google it becomes a 'little' hard to justify... "I don’t want any stupid Google! I want to call my professor in the middle of the night so he can recommend some really cool webpage to me! God damnit!" :wink:
     
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