# A question about renormalization **URL:** \ **Category:** Factual Questions\ **Created:** [February 15, 2020, 11:29pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997 "2020-02-15T23:29:43Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [February 19, 2020, 4:01am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/21 "2020-02-19T04:01:28Z")
That is obviously true, but you have still neither explained nor suggested why defining spacetime over a field other than the real numbers would gain you anything as concerns the non-renormalizability of gravity or any other problems in physics. There are (at least in some toy examples…) potential applications of (eg) non-commutative geometry to QFT, but all these questions about elementary limits (which have all been answered long since) have nothing to do with physics, at least not the way you keep asking them. ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 20, 2020, 2:16am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/22 "2020-02-20T02:16:20Z")
I am intrigued by lim x=\> 1 of 1/(x - 1) and lim x=\> infinity of 1/x. Neither seem to describe the real world. I’ll read up on limits and non-commutative geometry and try to ask a better question. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [February 20, 2020, 2:29am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/23 "2020-02-20T02:29:16Z")
> [@EastUmpqua](#): > > Neither seem to describe the real world. Is there a reason why you think they _should_ describe the real world? There’s all sorts of things in mathematics that have no relationship to reality. Math exists only in our minds. We can use some tools from mathematics to make models of the real world - that’s what physics is - but that does not mean all mathematics has a particular meaning with regard to physicality. Most of it doesn’t. One of the very first mathematical things we all learn are the names of shapes like square and circle. But you’ve never seen an actual square or circle anywhere, and neither has anybody else. Circles are useful as _models_ of things that are vaguely circle-like, such as manhole cover. By using the mathematics of circles, we can predict how much material we will need to cast a manhole cover, how much it will weigh, and so on. That’s what makes mathematics useful. If you start with the premise that anything we can write down mathematically must have some relation to the real world, you will be sorely disappointed. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 20, 2020, 3:26am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/24 "2020-02-20T03:26:18Z")
Lim x-\> 1 of 1/(1-x) doesn’t describe anything, because it doesn’t exist. Lim x-\> inf of 1/x = 0, which just means that the more people you share your snacks with, the less snacks everyone gets, which describes the real world just fine. ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 22, 2020, 12:31am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/25 "2020-02-22T00:31:33Z")
Ok so let p = Planck Length without units = 1.616(10)^-35 Let e = lim n -\> (1/p) of (1- 1/n)^n. Would this be close to the actual value? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 22, 2020, 1:40pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/26 "2020-02-22T13:40:23Z")
No, Planck length without units = 1. And even if you for some reason include a silly number like p=1.6e-35 into your equations, it doesn’t matter. Yes, (1-p)^(1/p) is very, very close to e. But the whole point of limits is, you can get even closer than that. ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 22, 2020, 8:30pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/27 "2020-02-22T20:30:56Z")
According to Wikipedia, the Plank Length “is the smallest distance about which current, experimentally corroborated, models of physics can make meaningful statements.[2]”. So why is it necessary to get even closer than that? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 22, 2020, 8:42pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/28 "2020-02-22T20:42:41Z")
Wikipedia, in that case, is wrong. The limit for which we have experimentally corroborated results is _much_ larger than that. As for “necessary to get even closer than that”, necessary for what? It’s often good enough to approximate pi as 3.14. Heck, it’s often good enough to approximate pi as 3. But that doesn’t mean that it’s not possible to calculate it out to ten decimal places, or 20, or a billion. ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [February 22, 2020, 9:06pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/29 "2020-02-22T21:06:21Z")
> [@Exapno\_Mapcase](#): > > Physicists can use math to understand and calculate properties of things, even basic things (matter, energy, time, information, etc.) But math doesn’t define physics or set any boundaries per se any more than English defines biology. You cannot change a human by redefining the word “body.” Mathematical limits do not imply anything about the existence or non-existence of physical objects. That’s a non-starter. Indeed. This is very reminiscent of what Russell said: > [@Bertrand Russell](#): > > Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover.\* (\*an old sig from [RM Mentock](https://boards.straightdope.com/sdmb/member.php)) ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 22, 2020, 10:09pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/30 "2020-02-22T22:09:04Z")
I looked up the source for the Wiki article I referenced above. It states “If two particles were separated by the Planck length, or anything less, then it is impossible to actually tell their positions apart. Moreover, any effects of quantum gravity at this scale (if there are any) are entirely unknown as space itself is not properly defined. In a sense, you could say that, even if we were to develop methods of measurements that took us down to these scales, we would never be able to measure anything smaller despite any sort of improvements to our equipment or methods.“ This source doesn’t cite any peer-reviewed publications. Does anyone know a better source? ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 22, 2020, 10:28pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/31 "2020-02-22T22:28:40Z")
Maybe we can discover more about the physical world if we adjust mathematics to better describe it. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 22, 2020, 11:04pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/32 "2020-02-22T23:04:23Z")
> [@EastUmpqua](#): > > Maybe we can discover more about the physical world if we adjust mathematics to better describe it. If that is so, then why don’t actual physicists advocate doing it? ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [February 22, 2020, 11:10pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/33 "2020-02-22T23:10:49Z")
> [@EastUmpqua](#): > > Maybe we can discover more about the physical world if we adjust mathematics to better describe it. You have described theoretical physics. > [@Exapno\_Mapcase](#): > > If that is so, then why don’t actual physicists advocate doing it? Doing what, is the question. There are many theoretical ideas. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 22, 2020, 11:41pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/34 "2020-02-22T23:41:59Z")
> [@DPRK](#): > > You have described theoretical physics. > > Doing what, is the question. There are many theoretical ideas. Physicists do look for mathematical tools they have not used before. They do not at any time try to “adjust mathematics” to create those tools. Nothing in this thread represents actual theoretical physics. ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [February 22, 2020, 11:47pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/35 "2020-02-22T23:47:54Z")
> [@Exapno\_Mapcase](#): > > Physicists do look for mathematical tools they have not used before. They do not at any time try to “adjust mathematics” to create those tools. Nothing in this thread represents actual theoretical physics. Still, physicists can ‘create’ new mathematics to do theoretical physics a la Fields medallist [Ed Witten](https://en.wikipedia.org/wiki/Edward_Witten#Fields_medal_work). ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 23, 2020, 12:41am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/36 "2020-02-23T00:41:32Z")
> [@KarlGauss](#): > > Still, physicists can ‘create’ new mathematics to do theoretical physics a la Fields medallist [Ed Witten](https://en.wikipedia.org/wiki/Edward_Witten#Fields_medal_work). Yeah? If he’s so smart why hasn’t redefined zero? (For those who aren’t familiar with the name, Witten is today’s Einstein. When discussions of who’s the smartest take place, his name is sure to come up. If redefining zero was a good idea, he’d already have thought of it. He hasn’t. Ergo, it’s not a workable idea.) ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [February 23, 2020, 2:45am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/37 "2020-02-23T02:45:57Z")
> [@Exapno\_Mapcase](#): > > … > Witten is today’s Einstein. I can find you a lot of eminent physicists who would disagree with that characterisation. Not that he isn’t very smart. But he is yet to have a miracle year, let alone come up with any physics that is testable. He certainly is the epitome of physicists that create new mathematics in the search for ways of modelling reality. ---
**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\ **Post date:** [February 23, 2020, 2:52am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/38 "2020-02-23T02:52:30Z")
> [@Exapno\_Mapcase](#): > > Yeah? If he’s so smart why hasn’t redefined zero? In the early '70s, there was a rather successful effort to redefine Zero. They simply used [Topol](https://www.imdb.com/title/tt0067093/trivia?item=tr0671301)-ogy, and I seem to recall no dearth of division involved. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 23, 2020, 3:39am UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/39 "2020-02-23T03:39:24Z")
> [@eschereal](#): > > In the early '70s, there was a rather successful effort to redefine Zero. They simply used [Topol](https://www.imdb.com/title/tt0067093/trivia?item=tr0671301)-ogy, and I seem to recall no dearth of division involved. _WARNING_ eschereal is not being serious. _WARNING_ ---
**Author:** ![74westy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/74westy/32/3950_2.png) [@74westy](https://boards.straightdope.com/u/74westy)\ **Post date:** [February 25, 2020, 7:59pm UTC](https://boards.straightdope.com/t/a-question-about-renormalization/847997/40 "2020-02-25T19:59:37Z")
For eschereal, that’s a tradition. [Previous page](https://boards.straightdope.com/t/a-question-about-renormalization/847997.md?page=1) [Next page](https://boards.straightdope.com/t/a-question-about-renormalization/847997.md?page=3)