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At PBS: Puzzle of mathematics is more complex than we sometimes think

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Astrophysicist Mario Livio shares some thoughts: Math: Discovered, Invented, or Both?

The puzzle of the power of mathematics is in fact even more complex than the above examples from electromagnetism might suggest. There are actually two facets to the “unreasonable effectiveness,” one that I call active and another that I dub passive. The active facet refers to the fact that when scientists attempt to light their way through the labyrinth of natural phenomena, they use mathematics as their torch. In other words, at least some of the laws of nature are formulated in directly applicable mathematical terms. The mathematical entities, relations, and equations used in those laws were developed for a specific application. Newton, for instance, formulated the branch of mathematics known as calculus because he needed this tool for capturing motion and change, breaking them up into tiny frame-by-frame sequences. Similarly, string theorists today often develop the mathematical machinery they need.

Passive effectiveness, on the other hand, refers to cases in which mathematicians developed abstract branches of mathematics with absolutely no applications in mind; yet decades, or sometimes centuries later, physicists discovered that those theories provided necessary mathematical underpinnings for physical phenomena. Examples of passive effectiveness abound. Mathematician Bernhard Riemann, for example, discussed in the 1850s new types of geometries that you would encounter on surfaces curved like a sphere or a saddle (instead of the flat plane geometry that we learn in school). Then, when Einstein formulated his theory of General Relativity (in 1915), Riemann’s geometries turned out to be precisely the tool he needed! More.

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Comments
Hi tb.Querius
April 26, 2015
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Hi everyone!truthbringer
April 24, 2015
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Q, thanks. Though I suspect that someone who tried to take direct action against the latest targetted branch of my extended family would come off very badly indeed in the resulting rather direct confrontation. KF PS: The fact that this seems to be what they have left itself speaks volumes on the merits. And the kind of neo-fascism that now stalks our civilisation is suicidally foolish.kairosfocus
April 23, 2015
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kairosfocus, I'm truly sorry to hear about all this. The behavior you describe exposes both the concession of rational argument and the underlying murderous motivation of certain individuals. People who launch such destructive campaigns are arrogantly self-righteous. Tolerance extends only to their views and those they consider compatible. They can then safely lash out as judge, jury, and executioner from their personal fortress of Victimhood. They apparently see their barbaric actions as wholly acceptable and fully justified. As a result, they can vent their rage, frustration, and hatred without limit against all who dare to challenge their self-indulgence. Their “cause” collectively absolves them of any and all criticism. They are perishing. -QQuerius
April 23, 2015
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UP, I actually have long had little choice in the matter. As an academic requirement I had to submit my full name with documents subsequently published by my uni. I didn't even know about it until abusers were triumphantly trumpeting details. Subsequently they have gone after my residential address (hitting that of some in laws), my wife and children, and now more remote relatives and their activities. Some of that points to on the ground stalking, not just web trolling. It seems there are attempts to join a local political malice motivated slander campaign that seized on parliamentary immunity to get away with what would have been "take a fat checque book to High Court" otherwise; actually no sane lawyer would have tried to defend it. All of this is patent stalking and harassment, which is implicitly threatening not only to me but to others who are even remotely connected. And of course for years participants in and enablers of the stalking and abuse have continued their delight in wrongdoing. All of which speak volumes on the attitudes and tendencies of too many objectors. But it is not just me by any means, just about any person who has stood up in public with any significant background to say that there is something substantial in the design inference, has been targetted for a ruthless or even nihilistic and in some regards outright sadistic or at minimum deeply spiteful witch hunt that is wide and deep, a very bad sign for our civilisation; thus my little poem above. I don't know if it is too late, but you will be able to see the warning I have clipped from Cicero and put up as FTR: https://uncommondescent.com/atheism/fyi-ftr-ciceros-warning-on-the-destructive-power-of-rhetoric/ I must thank you for taking courage to unlurk and speak up. KFkairosfocus
April 23, 2015
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Jerad has joined stenosemellaBarry Arrington
April 23, 2015
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REC: These are people who know the situation and are trying to use my name in connexion with a stalking campaign. What is on the table is not innocent use of a name, which would respond to polite request not to unduly expose to spamming and stalking etc. The insistence we see is directly connected to a stalking campaign motivated by obvious malice and utter want of common civility. When uninvolved people at three degrees of remove from me are being spattered with the mud slinging, that speaks volumes. Jerad: Namecalling. I will just say that TWO independent sets of editors have had to act in the context of patent defamation by the unhinged and obviously deeply malicious. I have spoken for record, for reference, and given the sort of stalking . . . now likely on the ground . . . outing and smearing of uninvolved people and their affairs that has now been resorted to (for the "crime" of being connected to me in some remote degree), I would advise you to cease and desist if you care one least bit about common decency. And if you cannot find in yourself the decency and good sense to realise the sort of lines that have been crossed and what it reveals about the tone and attitudes too long harboured and enabled by the attack sites, I am confident that a great many people will. If what you have left is harbouring and enabling the malicious and unhinged in order to distract from issues on the merits and poison the atmosphere, then crying censorship and the like in the face of actions in response to outright tort and stalking, that speaks volumes. G'day. KF PS: More from the author above as food for thought on what is going on: https://bradrtorgersen.wordpress.com/2015/04/20/ringing-the-bell/ >>Because I wanted to talk specifically about a recurrent kind of “broken” I am seeing in arguments all over the place — beyond the tiny halls of the Peoples Republic of Science Fiction. This “broken” is most commonly manifested among well-meaning straight Caucasian folk, but is often fostered and preached about by non-straight and/or non-Caucasians of a particularly aggressive “progressive” persuasion. The “broken” goes like this: ? Any member of the majority group is always guilty of ism no matter what. ? The ism is a fatal character and moral flaw, from which the afflicted cannot fully recover. ? Members of the minority group can never be guilty of ism; because the minority group lacks power. ? Members of the majority group must be “shown” their ism and/or be made to confess their inherent flaw; en route to being reformed. ? Reformed members of the majority group will actively assist in pointing out the ism of unreformed people. ? Proof (of ism) is not required; guilt will always be assumed. ? The more a target denies or resists charges of ism, the greater the obvious culpability. ? The unreformed are “fair game” for all manner of actions designed to be personally destructive to the target(s). ? Lying (and other unethical behavior) on the part of the plaintiff(s) — against the target(s) — is forgivable, because the ends justify the means. Folks, it doesn’t take a genius to figure out that this is Witch Trials 101. There’s nothing new about any of it. All we’ve done is wrap the witch trials up in trendy 21st century politics. When people are automatically guilty of a crime, for which no evidence is required, and the accusers are permitted a kind of political immunity while the protestations of the innocent are merely used as “proof” that the innocent were guilty all along . . . that’s witch trials. Burning at the stake. Except, these days the stake and the village square are located on the internet, and the villagers — with digital pitch forks and torches — are anyone with access to Twitter, a blog, Facebook, or some other form of social media. >>kairosfocus
April 23, 2015
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I must agree with KairosFocus on his desire for anonymity. If my family had been threatened, as his obviously has, I would demand anonymity as well. The fact that he makes it easy to identify him is beside the point.unwilling participant
April 23, 2015
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UDEditors: stenosemella has been shown the exit. You are a coward. Clearly. And kairosfocus has two new post with comment closed from the start.Jerad
April 23, 2015
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KF, I respect your effort to remain anonymous. However, when your links from your name or documents posted here contain your real name, I'm not sure you can fault people for calling you by that name. Also, where we you when the owner of this blog posted full names and work information of individuals who made him angry?REC
April 23, 2015
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I see. Thanks, the last link, dealing with the model theory connected to mathematical logic, looks especially useful.daveS
April 23, 2015
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DS, Modelling and Simulation body of knowledge as compiled by US DoD. I think you will find it useful, though the tabulation for edu/training purposes may be a little off-putting. KF PS: This too may help: http://www.site.uottawa.ca/~oren/y/2012/-08-MS-BOK.pdf and this on b/gd Math: http://www.math.toronto.edu/weiss/model_theory.pdf (That one is very broadly applicable, note how they deal with strings for instance.)kairosfocus
April 23, 2015
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of necessity, headlined: https://uncommondescent.com/atheism/fyi-ftr-a-headlined-noticeresponse-to-abusive-new-atheists-and-their-enablers/kairosfocus
April 23, 2015
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Eh? What's this pdf in #105 about?daveS
April 23, 2015
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F/N: let me link on modelling & sim body of knowledge, what I have followed up on what has been positive above, overnight: https://www.csiac.org/sites/default/files/DoD%20M&S%20BOK%20%28M&SCO%29%202008_0.pdf KFkairosfocus
April 23, 2015
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sparc: FTR, the extent of outing and slander seems to get worse -- more and more unhinged -- on each drearily predictable willful cycle of playing the distract distort demonise poison discussion stratagem too often used or enabled by objectors to design theory. I suggest you and ilk ponder 102 above before further enabling inexcusable willful wrongdoing: https://uncommondescent.com/mathematics/at-pbs-puzzle-of-mathematics-is-more-complex-than-we-sometimes-think/#comment-560570 KFkairosfocus
April 23, 2015
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96 stenosemella April 22, 2015 at 3:50 pm Gordon: ” And, I have seen people more than willing to indulge in ugly threats against uninvolved family…” You have claimed this repeatedly but when asked to provide details you run away. Please stop pretending to be the victim. You claim victimization and act like a drama queen every time someone uses your real name. And then in the same thread you link to a document with your name on it. Have you ever heard about the boy who cried wolf?
97 Barry Arrington April 22, 2015 at 4:07 pm UDEditors: stenosemella has been shown the exit.
Haven't we been through this before?sparc
April 23, 2015
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F/N: It seems there is a settling down of this thread. The deep unities highlighted by the Euler eqn that also bridge so much of Mathematics, Physics and engineering are there. One's response to same will both be shaped by and will shape one's worldview. This definitely puts on the table at that level the issue that in relevant domains of Mathematics, one is confronted by the possibility that the astonishing power of mathematical considerations in the physical science may reflect that the cosmos itself reflects not just fine tuning but framing by a highly mathematical mind. KF PS: On a less happy note, a few words need to be said after taking time to ponder how to speak to truly difficult to address issues without further giving currency to slander, outing and implicitly menacing intimidation. As in: we know you, where you are, those you care for, their homes or places of business etc. including things not readily found on the Internet that suggest on the ground casing of the joint. Ah, but we are not stalking or threatening you and those you care about, see. Mafioso style tactics that should not fool any decent person above five years of age, as has been going on for years in a penumbra of attack sites: a: Immediate context. Across yesterday and going back some time, I have had to deal with further word snipping, twisting and false accusation tactics emanating from circles that operate such sites or are harboured by them. And no, I will not give salacious details. b: It seems, the theory used by such rage-fueled unhinged attackers is that if one cannot cogently address a matter fairly on substance, then public false accusation, twisting words and circumstances into falsehood, raising undue suspicion and/or harming reputations through snide suggestions and making implicitly menacing references to uninvolved family can intimidate into silence. Or at least hopelessly polarise, poison, cloud and confuse the atmosphere as part of cynical divide, poison and rule tactics. c: I must also note, again, that it is highly reasonable to request that the privacy of one's name, email address, uninvolved relatives etc be respected in high traffic, contentious contexts on the Internet where spam crawlers and identity thieves etc as well as cyberbulies are likely to lurk in one form or another, whilst in much lower traffic corners of the net academic papers etc will give information per legitimate requirements of publication. d: The deliberate and willful exposure of personal information in the context of cyberstalking and defamation, is cyber harrassment and worse, tort. Also the extension of such in contexts of attempting to undermine livelihood, falsely accuse of family abuse, consorting with criminals [as opposed to supporting the rehabilitation of former criminals], outing of uninvolved family etc is multiply and implicitly threatening behaviour. e: Likewise, there is a reason why certain classes of cases protect the victim from public humiliation and forced further spreading of accusations. The former practice of trying to publicly humiliate and discredit rape victims in court is a thankfully now finished case in point. That is, there are good reasons to refuse to further engage details of hostile attack and abusive behaviour in public. Let us just say here that the relevant authorities with editorial power do know enough detail to base their actions. And so do the civil authorities. f: Further to this, let the proverbial frog speak to the boy approaching, stone in hand: "fun fe yuh, is death to me." In that vein, I note to the jack-booted bully-boy radicals of today who are playing at mob rule tactics and discrediting and smearing targets to seemingly justify attacks on freedom of expression, association and conscience:
He who would rob me of my means of daily bread, would rob me of my life; He who would rob me of my children, would rob me of my posterity; He who would rob me of my free voice and good name, would rob me of my means of defending myself; He who would rob me of my conscience, would rob me of my soul.
g: Those who harbour, cosset or enable such behaviour and those who indulge in such should ponder what they are letting loose in our civilisation. For, as Solomon so aptly warned, life and death are in the power of the tongue and those who love it will eat the fruit thereof. I note too, as follows, from an author recently subjected to a slander attack, and forced to reply to false accusation of racism, by revealing his (inter-racial) family photo:
. . . a blog “journalist” . . . working beneath the banner of Entertainment Weekly — penned a short, error-laden article titled, “Hugo award nominations fall victim to misogynistic, racist voting.” The mistakes in the article could have been easily avoided if [X] had done some research into the issue she was reporting on. Near as I can tell, [X] was spoon-fed some links and a very rushed and sloppy narrative about Sad Puppies 3 being racist and woman-hating, and she posted all of this without stopping to consider whether or not anything she was disseminating into the wider world was true, and accurate. The error-laden article quickly went viral — especially among opponents of Sad Puppies 3. Twitter (which I generally avoid and ignore) lit up like a Christmas tree, and quickly I had friends and other authors contacting me to say, “Entertainment Weekly has run a hatchet piece on you! Better jump on it!” So I read the piece. I noted the errors. I also noted that the piece made an explicitly inductive link between Sad Puppies 3 and last year’s great nerd controversy: GamerGate. The reasons for this were pretty obvious. Words like “racist” and “misogynist” are presently code for “not part of the human equation” thus any man or woman who can be successfully labeled these things, is cut off from polite circles, perhaps even driven out of the workplace, or worse. These words tend to be used as general-purpose ideological grenades, when the thrower of said grenades lacks sufficiently real evidence of wrong-doing — but wants to see the target squirm and suffer anyway. An unadulterated version of the . . . article can be found here. The presently “corrected” version of the article — Entertainment Weekly made several alterations to the article, including its root URL, after myself and many others noted that the article was a) grossly in error and could also b) serve as grounds for libel litigation — can be viewed here. But of course, by then, the damage had been done. Both myself and my colleague Larry Correia — who typed up a very good piece here — had been dragged through the digital mud. I count no less than a dozen different links which all picked up the error-laden . . . piece, and ran with it sight-unseen; because of the blaring headline. Again, the spoon-fed in turn spoon-feed others. And whatever hope there might have been that facts could trump a narrative, was lost in the white noise of a not-so-subtle smear job. I can’t say which individuals decided to launch the smear job. The internet moves at the speed of light and the 24 hour news cycle is forever hungry for new material; regardless of how bogus it might be. I suspect some of the insider SF/F people who dislike Sad Puppies 3 decided that the best way to “win” the insider baseball argument, was to stage a broader media flare-up for the sake of fatally discrediting the “poster people” of Sad Puppies 3. Namely, myself, and Larry Correia. Now, I am a patient man. I’ve got a long fuse. But this tactic employed today . . . it’s on another level. This isn’t just nerds bickering anymore. Baseless, false allegations of this type can ruin careers as well as lives. We’ve seen this before. The internet has allowed yellow journalism and rumor-mongering to run riot. And I have to be honest. No lie told in the service of a supposedly higher cause, ever does justice to the higher cause. No matter how widely-spread the narrative. If the basis of the narrative is false, then the narrative itself is fatally undermined, and thus the arguments that form the building blocks of the narrative are themselves undermined. Oh, I am sure this will blow over eventually. To Entertainment Weekly’s credit, they did take action — once myself and others explicitly told them that the . . . article was a dreadfully poor piece of research. Frankly, I feel like [X] herself owes myself and Larry Correia a public apology. That was shoddy reporting. And it’s potentially very damaging. I mean, if you’re going to play a role in somebody else’s effort to trash us, at least spend two minutes doing a little googling. I understand that tabloid tactics make money, and that on the internet especially, journalistic integrity has become something of an oxymoron. What disturbs me more is that the field of SF/F is stooping this low. That some of my colleagues — and no, contrary to my impression of the field 20 years ago, not everyone likes or gets along with each other — have decided to make the nerd argument over the Hugos into a decidedly personal grudge match. Where the objective is to not just win the argument, but to destroy the arguer. Professionally. In the marketplace. On the big stage of public opinion. This is the kind of stuff you ordinarily find in cut-throat national political elections, but then it’s been clear for years that cut-throat politics have drifted down into nerd circles of all kinds: comic book circles, movie and television circles, video game circles, etc. There’s simply no escaping it. And there are people for whom winning is more important than ethics, more important than integrity, and more important than the truth . . .
As the Greeks say, a word to the wise . . . and, if one's neighbour's house is afire, wet your roof and help him put out the blaze.kairosfocus
April 23, 2015
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Thanks for the info and link, Querius. As it happens, I'm trying to read about model theory right now and this should be very helpful.daveS
April 22, 2015
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DaveS @ 81
However, it’s clear that you can get interesting and useful mathematics even in a non-Euclidean setting.
Yes. Exactly. The mathematical reasoning and structure transcends artificial geometries. DaveS @ 89
No doubt if you try to merge the axioms for Euclidean and hyperbolic geometry, you will get an inconsistent system, so the two systems are incompatible in that sense, and similarly for fuzzy logic.
You might already know this, but your observation touches on Kurt Gödel's incompleteness theorums. Here's a good description of a paradigm shift in mathematics and logic: http://plato.stanford.edu/entries/goedel-incompleteness/ So, if there is a unifying pragmatic system of mathematics, it's apparently inaccessible to us in this universe. Together with Chaos theory, this pretty much explodes scientific determinism. It should be noted that Gödel's application for a paid position at the University of Vienna was turned down by people that history has now forgotten. -QQuerius
April 22, 2015
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Kairosfocus @ 80 Regarding paradigm change, I was reminded of how precisely Ptolmaic astronomers were able to predict celestial events such as eclipses and planetary motion with ever more complicated epicycles, and then came the Copernican revolution, which didn't actually produce better results . . . Macroeconomics fascinates me, although I've only ever taken one class in the general subject, which I found disappointing (yes, Samuelson). I've heard that economists have conducted experiments on the economies of MMORP games, which I understand tend to crash despite the god-like control of the moderators and programmers. Lately, I've been thinking about consumer spending, how it does matter what people purchase, which molds the supply side, and perhaps (I'm totally speculating here) cheapens (inflates) the currency if consumer spending is foolish. Thus, I suspect that there's a significant connection between economic health and moral health. Regarding your third link on education, I'd encourage you to look into the education system in Finland as compared to that in California, where over half the state budget is spent on “education” with dismal results for the children (education bureaucrats are paid embarrassingly high salaries). I'd also recommend John Sweller's Cognitive Load Theory since it's data driven with profoundly better results rather than ideologically driven theories (B.F. Skinner comes to mind). Thanks for your links on economics and industrial production in Jamaica. -QQuerius
April 22, 2015
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Kairosfocus @ 76 Yes, and Sophie has been extremely patient with me. Often her insights cut deep, because she doesn't want to change my thinking as much as who I am, which can be a little scary. But I wouldn't want to sit anywhere else! -QQuerius
April 22, 2015
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UDEditors: stenosemella has been shown the exit.Barry Arrington
April 22, 2015
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Gordon: " And, I have seen people more than willing to indulge in ugly threats against uninvolved family..." You have claimed this repeatedly but when asked to provide details you run away. Please stop pretending to be the victim. You claim victimization and act like a drama queen every time someone uses your real name. And then in the same thread you link to a document with your name on it. Have you ever heard about the boy who cried wolf?stenosemella
April 22, 2015
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Well, not being particularly well-versed in philosophy or biology, I don't have much to say about materialism or evolution.daveS
April 22, 2015
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DS, I have pointed out that here at UD we have dealt with many cases of evolutionary materialist atheists and fellow travellers who not only cling to a self-referentially incoherent ideology but are perfectly willing to burn down logic starting with first principles of reason. Far many more, are so locked into ideology that they become just that, locked in. KFkairosfocus
April 22, 2015
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Rest assured that I'm not in favor of burning down any temples. I like mathematics in part because I'm interested in the acquisition of knowledge, not its destruction.daveS
April 22, 2015
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DS, I do not expect it to. I have had to deal with people willing to burn down the temple of reason to maintain their evolutionary materialist ideology. And, I have seen people more than willing to indulge in ugly threats against uninvolved family and those who pretend that all is well and act as though such web thugs are normal people in their behaviour; thus enabling it. Above in this thread there is a shadow of this. KFkairosfocus
April 22, 2015
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KF,
All I am saying is that that sort of neatly fitting jigsaw puzzle that comes together all at once then goes out again and conquers the physical world for Mathematics, is saying something, something powerful about an inner logical-mathematical coherence to reality.
I do agree with this.
And that sort of coherence invites reflection on unifying mind.
Reflection, sure, but I don't find that it sways me one way or the other on whether such a unifying mind exists.daveS
April 22, 2015
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DS, If you look at the OP, you will see that it is raising the issue of the effectiveness of math and asking about discovery vs invention. I have pointed out on a relevant case, signs of the sort of unexpected coherence and convergence then flowing back out again with awesome power that should seriously raise the issue of deep coherence and undesigned coincidences because of underlying unifying mind at work. Such, that we find it a very reasonable point to ask, are we here for these things thinking God's thoughts after him? The side tracks and side points are essentially irrelevant to this point. I have shown that some things have the sort of coherence that we normally associate with unifying mind, rather than massive coincidence of inventions. For sure, pi was identified for utterly distinct reasons in a different time and culture than both i and e. Area under 1/x beyond x = 1, such that A = 1 to become the base of a natural log system, is not particularly deliberately tied to the value of pi. The proposing of a sqrt of -1 to make all polynomials have solutions, and the identifying of series expressions for sin and cos and e^x are not particularly initially connected either. Euler noticed the resemblances in the series and injected i into the sin series and lo and behold, cos theta plus i sin theta equals e ^i*theta. Then substitute theta is pi and bang. It turns out e, i and pi are connected down to the very end of the infinite series to construct each. Then, bang, bring on Fourier and Laplace analysis and this naturally extends into a vast range of domains that are deeply significant in the sciences and in reality as we understand it. All this has been pointed out, explained, discussed in your presence. All I am saying is that that sort of neatly fitting jigsaw puzzle that comes together all at once then goes out again and conquers the physical world for Mathematics, is saying something, something powerful about an inner logical-mathematical coherence to reality. And that sort of coherence invites reflection on unifying mind. For, this is not like car parts that though cars have similar architecture, constantly show themselves mutually incompatible. That, is what things that are micro-designed usually are like, exapting something new from the parts is generally very hard due to lack of standardisation. But, I know, this is probably very hard for you to begin to acknowledge as even being remotely significant; it obviously potentially points just where you would not go. KFkairosfocus
April 22, 2015
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