I guess I'd call that an infinitely understandable clarification of infinities.

@frun

3 жыл бұрын

I think you will like this -> kzread.info/dash/bejne/h55nwa2qm6yfitI.html

@youliantroyanov2941

3 жыл бұрын

So true 🤓

@myfriendbro

3 жыл бұрын

Teachers pet/ asss kisser

@mrwideboy

3 жыл бұрын

I come for the physics, but i stay for the dresses

@richmiller2804

3 жыл бұрын

Nice presentation, well beyond my math understanding. A question, maybe you can do a presentation on the coriolis effect. Does it affect the planets in orbit, how about star systems orbiting in galaxies? How about dimensions?

"I hope there are no mathematicians watching this." Theoretical physics in a nutshell ;P

@brianbuch1

3 жыл бұрын

Something, something...for support, not illumination.

@knipping

3 жыл бұрын

Being a mathematician, I truly flinched in the moment she showed the equation. And I felt so much relieved when she gave the disclaimer for mathematicians. :-)

@David_T

3 жыл бұрын

Remember the battle between physicists and mathematicians over the Dirac Delta Function?

@albertohernandeza5661

2 жыл бұрын

I just started and I defenitly feel you.

@bumbleWeaver

2 жыл бұрын

"I hope there are no electrical engineers watching this." Classical Physics in a nutshell...

Aleph‎-null bottles of beer on the wall Aleph-null bottles of beer Take one down Pass it around Aleph-null bottles of beer on the wall

@frechjo

3 жыл бұрын

Great song for when that car trip takes forever.

@drrtfm

3 жыл бұрын

@@frechjo Well it certainly beats "Are we there yet? Are we there yet? Are we there yet? ....." :)

@meesalikeu

3 жыл бұрын

thats how you catch the covid

@nistornicolaevici2965

3 жыл бұрын

The first beer goes to Mr. Hilbert.

@skilz8098

3 жыл бұрын

Nope, Aleph broke because of Zeta!

I find it easiest to think of infinity as a process rather than a number. Its a process that discribes a neverending chain of numbers or events or whatever you wanna plug into it. This works with how some infitities are "larger" than others.

Great video. I recently noticed an example of infinity (or division by zero) arising in an everyday mathematical formula. When I am driving my car, the dashboard displays the current fuel efficiency that the car is getting in litres per 100 km. It shows it as a bar that gets longer or shorter as the car consumes more fuel or less fuel per unit distance. When I bring the car to a stop (to stop at a traffic light, for example), the bar becomes as long as the display will allow, and then suddenly disappears. This is just how the indicator handles the division by zero issue, since when your car is stopped but the engine is still running, it is consuming fuel but not travelling any distance, and therefore has a momentary fuel efficiency of "infinity" litres per 100 km.

@ethanholshouser5648

2 жыл бұрын

That's one instance where "km per liter" would be a better metric, since it would just be "0" in that case.

@daarom3472

2 жыл бұрын

I'd say its simply an invalid measure, it doesn't make sense to measure X to Y when Y doesn't exist.

@tinkeringtim7999

Жыл бұрын

@@daarom3472 it's not that simple, as pointed out above the inverse relation exists and is well defined therefore both relations must exist.

@daarom3472

Жыл бұрын

@@tinkeringtim7999 how much milk do you have if you have 0 liters of milk? How fast do you go when you go 0 km/hour? When the value reaches 0, the property stops existing other than that we can talk about it.

@tinkeringtim7999

Жыл бұрын

@@daarom3472 If you are using existence in a colloquial sense, please explain in what sense. If you mean existence as in predicate logic, I can't see a way to express that consistently so perhaps write what you mean by that in a concrete unambiguous way. I suspect you will struggle to, because the whole point is these things are incredibly difficult (maybe impossible) to pin down from the perspective of numbers. We've been trying to figure it out since Euler looked at the primes through sequences and polynomials. If it's just simple and self evident in your view, then all you're telling me is you don't actually know what is going on when one litre of milk is "added" to another and the result shown to be consistent with our counting system. In other words, if you think you know what numbers mean/do and you haven't studied number theory from the perspectives algebra/topology/analysis then you have only proved you can fool yourself. I don't see how anyone who has studied even one of those perspectives to a significant degree of apprehension could've entertained such a facile thought for long enough to type it but I'm open to the idea it's possible.

I’m infinitely grateful for this video. Fin.

@red-baitingswine8816

2 жыл бұрын

I have zero disagreements with this.

Me: *about to type "Technically, you would need a limit for those divisions to be true."* Dr. Hossenfelder: "I hope there are no Mathematicians watching..." Me: :)

@yyeeeyyyey8802

3 жыл бұрын

to be fair there surely are some algebraic definitions where that would make sense haha

@martinshoosterman

3 жыл бұрын

@@yyeeeyyyey8802 the thing you are looking for is called a wheel

@lindsay.newman

3 жыл бұрын

I got a laugh at that too

@shoopinc

3 жыл бұрын

Nonstandard analysis in my opinion is superior to Cauchy's limit idea. It allows you to do this arithmetic with the transfinite and infinitesimal.

@martinshoosterman

3 жыл бұрын

@@shoopinc once you get the ball rolling with non standard analysis, it can be extremely intuitive, however, to make it rigorous requires a ton of heavy machinery to be developed. Whereas using the standard real numbers, a close to fully rigorous treatment can be done in first year.

No one else explains these concepts so clearly like you do

That really blows my mind away, what a masterpiece of didactics! Sabine is the absolutely best teacher, I've ever met. Read a whole book (by John Barrow) about this, but didn't understand half of what she explains in ten minutes. I'm so thankful for this

If you've ever waited at the DMV here in the states, you know infinity is real.

@homomorphic

3 жыл бұрын

Especially when you are trying to register your new infinity. Those infinities are different types though.

@ReasonableForseeability

3 жыл бұрын

The fact that you can report on it means it wasn't infinite. It's over.

@charleswoods2996

3 жыл бұрын

I swear I would've said similar, upon being a disabled person and waiting on the g-d damned government to getting around the agree to the obvious while you're sitting in homeless shelter waiting on subsidized housing shoulder to shoulder with convicted murderers that are completely oblivious to the idea that upon finding out their names that you can check their criminal convictions on a damn smartphone. The DMV? Yeah. Even just renewing a state ID; time slows down and yet somehow you age faster!

@saulgoodman7858

3 жыл бұрын

When you get a number and they skip your number and you have to get a new number but they say you just didn't hear your number. No lady you all skipped like 10 numbers.

@allenjenkins7947

3 жыл бұрын

Not just in the States. Vehicle registration and driving licences work the same way in Australia too. And don't even start on social security.

Thank you for a useful discussion of infinity. I have been tangled up in this for a while, and this clear summary of the mathematical and scientific interpretations was just what I needed to get past my current block! I am really enjoying your channel.

One of the most valuable educative and well-made videos in the whole KZread and maybe to infinity and beyond... 👌

I love your videos because you explain things and I immediately have questions but then, like you're reading my mind, the question gets answered.

4:41 I think there’s a correction necessary. Shouldn’t x tend to infinity? Something like this: lim x → ∞

@uhbayhue

3 жыл бұрын

I noticed that too, thanks for pointing it out!

@ecranmagique

3 жыл бұрын

Yes, lim x → ∞ makes sense and Sabine says ∞ at 4:42.

@SabineHossenfelder

3 жыл бұрын

Yes, sorry. I have put a note on this in the information below the video. Thanks for being so observant!

@azzinny

3 жыл бұрын

@@SabineHossenfelder limit_{x -> \infty} x^2/e^x: the limit OF ex squared over ee to the ex squared AS ex approaches infinity

@mathrixe9

3 жыл бұрын

The limit as written is still equal to 0).

Thank you for adding much clarity to this topic!

Thanks Sabine, you made me see the difference between mathematical reality and physical reality. 🙏🏻

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..

@alexleibovici4834

Жыл бұрын

> the difference between mathematical reality and physical reality That is between concepts and objects

@YT8699

Жыл бұрын

@@alexleibovici4834 Perhaps we can consider that "objects" are really just "concepts" that we use to gather together various observations about "something" and talk about it....

@alexleibovici4834

Жыл бұрын

@@YT8699 > Perhaps we can consider that "objects" are really just "concepts" that we use to gather together various observations No. There are objects out there and the concepts are the representations in our brains of those objects out there.

@YT8699

Жыл бұрын

@@alexleibovici4834 I am also a realist who believes in the existence of stuff out there. However, our entire knowledge or understanding of any particular "object" is contained within our "concept", and it appears that our attempts to form coherent concepts from our observations of objects almost always involves the use of "mathematical realities". If fact our attempts to "prove" (another loaded word...) that any particular object actually exists also depends upon the usage of these mathematical realities. So when the distinction between "mathematical realities" and "physical realities" (or objects and concepts) is reduced to the notion that only "physical realities" exist....then we're faced with admitting that our knowledge of that which "exists" is dependent upon that which "does not exist". Of course, some consistent naturalists identify "concepts" as nothing more than a particular set of chemical reactions among the organized elements of the human brain. Thus making concepts into objects...

What great topic ! Thanks Sabine. The standard cosmological model includes a spatially infinite universe, and it seems to attract little attention how strange indeed it would be! I've only found an obscure paper by Ellis. Thanks also for mentioning others in physics are concerned by this or related issues. It's a shame you didn't mention Hilbert's Hotel. That really drove the point home for me and carries the weight of a great mathematician.

Thanks Sabine, that was immeasurably informative.

@4:42: There is a mistake in the formulat. Under the limit the formula should have x->∞, not x->0.

The videos on this channel consistently progress from stuff I know comfortably to stuff I *don't* know, usually at about the 75% mark. It's a rare and wonderful thing. Thank you.

Brilliant exposition, Sabine. 👌

As usual, I don't really understand, but my lack of understanding is less infinite than it was before. Thank You.

@Maciej-Komosinski

3 жыл бұрын

​@Goran Vukovic Oh no, the aleph number of Grok Effer's lack of understanding decreased.

@RussellMWebb

3 жыл бұрын

What Grok Effer said!

@Aurinkohirvi

3 жыл бұрын

Well, if she/he took away 1, it may still be infinte, but less so. Because, 1 still was removed.

@oceanlawnlove8109

3 жыл бұрын

@@Aurinkohirvi nope

@tTtt-ho3tq

3 жыл бұрын

@Goran Vukovic but but but, was it the story of Socrates or Aristotle that he's the most smart person? He heard people were saying he's the smartest person in the city. So he thought he'd go out to see if that's true. He went out and ask many smart people questions after questions. At first they answered the questions but then in end they ran out of answers. At the end of the day he had found out nobody really didn't know. But he already knew that that he didn't know. And everybody thinks they knew when they didn't know but he knew he didn't know. That means he said he is the most smart person in the city. Then was he wrong?

Thank you Sabine, i’m gonna sound like a broken record but all,you vids are great and much appreciated. 😍

@SabineHossenfelder

3 жыл бұрын

Thanks, I appreciate the feedback. Keeps me going :)

@Honestandtruth

3 жыл бұрын

@@SabineHossenfelder Hello Sabine , From All your knowledge and intelligent, What are you Stand for Atheism or God's follower.... ????????

@bmoneybby

3 жыл бұрын

Well, this went south quickly..

@PicaMula

3 жыл бұрын

@@bmoneybby well it sure did 😂

@augustinemmuogbana3382

2 жыл бұрын

@@Honestandtruth From her scientific presentations, and body language. She is likely agnostic.

“Is it just something that we get when we divide something by zero” Careful there, thats fighting talk.

Thanks Sabine, you give very clear explanations.

I really enjoy your videos.. you explain models and theory's in a way I can follow..your videos give me food for thought..thank you Sabine.

There's another infinity - Sabine's variety of cool clothes

@anderstopansson

3 жыл бұрын

The perfect gay comment...

@andyiswonderful

3 жыл бұрын

Also, her nail polish matches her outfit. An even more perfect gay comment.

@DheerajBhaskar

3 жыл бұрын

She's likely using a clothes rental biz. That seems like a smart move for anyone

@anderstopansson

3 жыл бұрын

@@DheerajBhaskar Ha-ha-ha, this happens when I think there´s nothing gayest than what we already had... Well I opened a comment (see the last), just for gay comments.

@bazoo513

3 жыл бұрын

But this dress does not look to be topologically impossible, unlike some others we have seen...

3:10: "I hope there are no mathematicians watching this" Me: Too late muahahaha

thanks fore the educative video sabine Respect and greetings from Holland 🙏

Ah a new Sabine video, just what I needed. THANK YOU!

Great video. Thank you. From my point of view I can understand reticence to ditch convenient tools for the sake of some that are unable to make the distinction between the tool and reality.

Great vid. A MUCH more detailed version of what I just recently told my son about the topic.

u know ure a genius when u explain highly complex subjects without animation, just speech without any flashy video editing and effects. ure a genius and i love ur videos u are a scientist and a writer sabine

Your voice is very enjoyable!

I am at the end of my physics bachelor (actually I'm doing QFT now, so that was a fun shout out), and there was a lot of new stuff for me in this video. I'm surprised by the amount of material you managed to get in her, because I would think it is also possible to grasp most of what you say with much less of a mathematical background. You inspire me as an educator!

@daarom3472

2 жыл бұрын

Just wondering, since some physicists want to practice physics without using infinities, would this mean that Pi and e would no longer be usable?

@chickenfrend

Жыл бұрын

@@daarom3472 No, because pi and e are not infinite in magnitude. Pi is less than 4 but more than 3, that's not infinite. It just has infinite digits in it's decimal representation

@chickenfrend

Жыл бұрын

So do other numbers depending on how you represent them by the way. 1/3 is 0.33333... on and on forever when represented in it's base 10 decimal form for example. Pi just doesn't have a nice pattern like that, it's irrational

Totally agree with this. When I was an undergraduate physics student, I always felt that assumptions were being made whenever I saw a limit as a variable tended to infinity or 0 - fine as an approximation, but it shouldn't be taken as a final model.

@Loots1

Жыл бұрын

There are always assumptions and there is no such thing as a final model

Thanks for clarifying the distinction between the existence of infinity in the mathematical and scientific sense! It helped me understand the concept of "infinity" better.

Thank you. Great description ...

I did economics at uni, no infinity there, everything is scarce!

@zubstep

3 жыл бұрын

Hyperinflation on the other hand... :P

@goyonman9655

3 жыл бұрын

lol

@GregoryTheGr8ster

3 жыл бұрын

I'm a Democrat and a Socialist. We don't let the laws of economics get in the way of progress and doing what's right for the common good of society. I'm just sayin'

@Mosern1977

3 жыл бұрын

@@GregoryTheGr8ster - the "common good" - used to excuse infinite human suffering throughout the ages.

@alcalaino1486

3 жыл бұрын

@@GregoryTheGr8ster A Democrat and a Socialist? Sorry Greg, they're mutually exclusive

I binge watch your videos because I love your demeanor. You are so cool!

Sabine, you are a great lecturer !!!! Five Stars.

Her first “examples” definitely raised my eyebrows but when she hit her groove the examples turned out to be “bait” for the grand finale. Her completely approachable explanation of the epistemological difference between physics and mathematics is just brilliant. Entire college courses don’t do any better.

@miguelandrade5964

3 жыл бұрын

Ok, I stopped watching and I as was about to call bullshit and leave, now I have to watch that part.

@miguelandrade5964

3 жыл бұрын

Unfortunately not. More bullshit. Physics with infinity are just mathematical abstractions to try to approximate the observable. There are theories to state even time in not infinite divisible. At this time, there is no concluding evidence that infinite is real. It sure exists in math, in our minds, but not in the observable universe.

@dirktween244

3 жыл бұрын

@@miguelandrade5964 Actually ? Do NOT exist, in math ! Must use them, to express them ! Each, is an "infinite Limit" ! X^Infiity = Infinity 1/X as X aproaches infinity, aproached 00 ! 00 +/- Any/Every possible number, is NOT 00 ! IF can add any number to Infinity: then previous number IS NOT Infinity !

@dirktween244

3 жыл бұрын

@@miguelandrade5964 Our minds, can understand the concept of always. Our minds, can not understand what is an Infinite amount. (One of definitions, of infinity)

@miguelandrade5964

3 жыл бұрын

@@dirktween244 In math (and in our minds), for something to exist all it needs is to be defined. If you like math a little, you maybe want to search some stuff from Cantor. It's fascinating and a bit funny.

The different types of infinities had always confused me. Thank you for the great explanation!

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion

Professor, i thank you so much!

Really concise summation of the gap between mathematics and phenomenology. You cannot measure infinity because its value will always be greater by at least one unit than what you have measured.

It would take me an infinite amount of time to fully grasp your explanations, but I am finitely better informed by each of them. Thank you!

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..

@brianarbenz7206

Жыл бұрын

@@fluentpiffle I was using those metaphorically.

I recently learned some of the Haskell programming language... it is a language deeply concerned with repeating processes and "types"... the idea that Infinity is a 'type' and not a value just makes so much sense to me right now. Thankyou for the awesome video :)

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature..

Fascinating stuff Sabine! The conclusion I come to is that no matter how large the magnitude of a number that we can compute, there must logically always remain an infinity of numbers of greater magnitude which are un-computable. The set of un-computable numbers is necessarily infinitely larger than the set of computable numbers.

@23jackleeder

2 жыл бұрын

Further to this - A perfect circle is infinitely round, however no examples of perfect circles exist in the universe. One of the roundest object available - a neutron star is close but not perfectly round. Perfect circles only exist in the human imagination. So computing numbers with idealized functions such as pi and infinity does not reflect the universe as it actually is.

I absolutely trust what you tell me. I can’t think of any other channel that I do that for

Great video! I always nitpick whenever people talk about black holes and singularities and their infinite densities; I just could never believe in Infinities in nature. I submitted a question about this to some subreddit, and someone wisely replied to me that they agreed that the densities of the singularities at the hearts of black holes were not infinite... they were just COLOSSAL.

@red-baitingswine8816

2 жыл бұрын

Yes e.g. while reading Hawking I've been thinking the same thing, & he never seems to mention the issue. This is the first time I've seen it mentioned at all (much like the bogus characterizations of fusion achievements).

@purpleglitter9596

2 жыл бұрын

But she didn't say they don't exist in nature. She said they don't exist in science.

@red-baitingswine8816

2 жыл бұрын

@@purpleglitter9596 . "Do not exist in science" means [omit 3/11: "not known to exist", ie.] "not known to exist in nature". . Imo, strictly speaking, infinity doesn't exist in math either.

@purpleglitter9596

2 жыл бұрын

@@red-baitingswine8816 Science is not nature. Its an attempt to explain nature. But nature is nature. Otherwise why would she need to specify that it doesn't exist in science if she meant nature. Infinity does exist in math. Mathematics is pattern identification. Infinity is a pattern. If it didn't exist in mathematics they wouldn't have to keep finding ways to avoid it.

@red-baitingswine8816

2 жыл бұрын

@@purpleglitter9596 . Straw man I didn't say science is nature. . (but please see my revision of my previous comment)

Wow. So refreshing listen to a scientist which dares to say what needs to be said. Carry on, people like you are your weight worth in gold. Sincerely respect Klaus

I appreciate your commitment to the proper use of mathematics in physics. Can you make a video, about some examples of improper use of mathematics in mainstream science?

A typo. At 4:44 there should be lim_{x->+inf}, not lim_{x->0}

@SabineHossenfelder

3 жыл бұрын

You are right, of course. Sorry about that.

@LimitedWard

3 жыл бұрын

The physicist would say infinity is roughly zero anyways

@KRYPTOS_K5

3 жыл бұрын

It doesn't matter! It is zero any way.

@johnnicholson8811

3 жыл бұрын

@@SabineHossenfelder You might want to make this go to the top so everyone sees it.

"In science, we can always replace infinity with a very large number, we don't do this, but we could." -- We do it all the time in numerical simulations, by replacing the infinite dt's in any integral with a large number of delta t's.

Thank you for your videos, Sabine. I would like to hear your opinion of the mass equation of special relativity. I assume that the singularity at the speed of light indicates that the Special Theory of Relativity is incomplete in the same way that the singularity at the centre of a black hole indicates that the General Theory is incomplete. What does the Standard Model of particle physics have to say about this?

Can you next time talk about complex numbers and it's physical meaning, please..

@SabineHossenfelder

3 жыл бұрын

Thanks for the suggestion, I will keep this in mind!

@2072

3 жыл бұрын

Personally, i see complex numbers as 2 dimensional numbers, so they are useful to describe or model things that need 2 dimensions instead of one.

@2072

3 жыл бұрын

​@@SeanPeckham-xe2gt Yes this also reminds me that I used to call complex numbers "circular numbers", I don't know where this "complex" or "imaginary" comes from but this is really sad. A bit like Pi which should have been 2Pi (the ratio circumference/radius instead of circumference/diameter), That's what the Tau Initiative is about. If you replace Pi by Tau in equations, everything becomes way more intuitive. With Tau, the Euler's identity is even more interesting because instead of tracing a half circle and landing on -1 you make a full circle and come back to 1... tauday.com/tau-manifesto#sec-euler_s_identity Unfortunately I didn't get a proper education in maths so I'm in the process of relearning the base concepts such as the one you described: turn concepts into a physical representation involving the senses (visual, kinesthetic, etc...) and develop an intuitive "feel" instead of applying rules and hoping for the best... This is the kind of thing that you either develop by chance when you are a child and then you become "good at math" or that you don't and then, since school doesn't teach you how to conceptualize and create mental models, you become stuck with the wrong/impractical models in your brain until you decide to take the mater into your own hands... With that in mind I'd be interested if you could share your mental model of the natural logarithm or exponentiation!

@meesalikeu

3 жыл бұрын

@@2072 a proper education in maths ok nigel

@sohlbergk

3 жыл бұрын

Very good discussion of that may be seen here: kzread.info/dash/bejne/hmpomaWAo9i1hrg.html (Disclaimer, I have no association with Welch Labs, the producer of the video.)

I am mathematician and I enjoyed watching this video. In optimization we consider extended valued functions and make up such rules for playing with the infinite.

@SabineHossenfelder

3 жыл бұрын

Glad I didn't commit any major blunder! It's been a while since my math classes.

@espaciohexadimencionalsern3668

3 жыл бұрын

Just take your right frame.

@hyperduality2838

3 жыл бұрын

Infinity is a Platonic or mathematical concept! Platonic forms are dual to to particulates -- Plato. Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant. Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein. Synthetic a priori knowledge == space/time -- Immanuel Kant. Concepts are dual to percepts -- the mind duality of Immanuel Kant. Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality. The future is dual to the past, we remember the past and predict the future -- Time duality. My absolute time is your relative time and your absolute time is my relative time -- Time duality. Length, distance or space is defined by two dual points -- space duality. Absolute space is dual to relative space -- space duality. Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality. Space duality is dual to time duality. "Always two there are" -- Yoda.

@hyperduality2838

3 жыл бұрын

@TheAbstraction The big bang is a Janus point (two faces) = duality! The future is dual to the past -- time duality. Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Apples fall to the ground because they are conserving duality. Potential energy is dual to kinetic energy. The force of gravity is scientific or empirical proof of duality!

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion

Serendipity. I was just thinking, a month or two ago, that mathematicians should not be using infinity because it's not real, it's not understandable, and makes for possible misunderstandings in the calculations. Now I see this. Did the universe give me you because it thought I was ready? I have not studied maths or physics, but I think about these things. I thought I was really smart. You guys have already worked all this out. Well, I'm glad to have found you, at last. Too late, but I can die in some peace!! Thanks again! 🙂

Why is it that Ms. Hossenfelder is the only KZreadr that forms her words so perfectly that I never miss one? The slight German accent doesn't hurt, it may even help. Subscribed!

@jpt3640

3 жыл бұрын

It's because they speak like they learned from the book. No slang, no dialect. My first spanish teacher was German. She almost never talked german to us, but we understood everything. Years later, when I wasn't a beginner any more I had a teacher from Bolivia. We just didn't understand a word, so he tried to explain in German. We still didn't understand anything.

Awesome video, thank you Sabine. I just report a little typo at 4:41 with the limit.

@SabineHossenfelder

3 жыл бұрын

Thanks, you are right. Sorry for the blunder!

@anderstopansson

3 жыл бұрын

How could you pay attention to that and notice it, while Sabine was on the screen?

@CosmosMarinerDU

3 жыл бұрын

Nonsense. It was completely correct. Sabine was leaving it as an exercise to the viewer to determine what the limit would be if x tended to infinity! Pure magnificent pedagogy!

@KRYPTOS_K5

3 жыл бұрын

No no no. It is right in both senses! Zero or infinite. Sabine never mistakes! LoL

Sabine explains difficult concepts with such ease :)

@v3le

3 жыл бұрын

"If you can't explain it simply, you don't understand it well enough" - A.E.

@vikraal6974

3 жыл бұрын

@@v3le Einstein never said it btw

@v3le

3 жыл бұрын

@@vikraal6974 from the memes

@v3le

3 жыл бұрын

It must be R.F.!

@SevenDeMagnus

3 жыл бұрын

I too love, Dr. Sabine, though I counter some of her videos (the flaw is always on assumptions). I hope there'll be a debunking between nuclear physicist Thunderfoot (is that the same as particle physicist?) and theoretical physicist Dr. Sabine, not coz' of dislike but because the exchange between minds who are experts in their fields, is an inspiration and a great example for everybody. God bless, Revelation 21:4

Paul Dirac also had similar thoughts about infinities in physics representing problem areas with theoretical models.

The moving dot reminds me the first time i read the "writing speed" spec of a CRT oscilloscope (70's). It was way above the speed of light. I had to double check my math before i realized i had not discovered something earth shattering. It took a little while i calmed down internally.

The laser dot explanation blew my cats tiny mind 😻💥 Thank you

@ThermalWorld_

3 жыл бұрын

Yes, but in that explanation we forgot the finite speed of light, so it can't move infinitely fast. For that in reality infinity in the real world is not infinite. 😁

At 4:50 it should be the lim as x goes to infinity. This was a nice explanation of dealing with infinity

@Wallach_a

3 жыл бұрын

Noticed that too.

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion

Infinities in mathematics are defined by unbounded sequences and mappings using induction, thus any mathematics that relies on infinities also implicitly relies on those sequences and mappings. This applies to transcendental numbers and numbers with infinite precision as well. When I consider a transcendental number like "pi", I think about how it's like a sort of placeholder for a process that produces it, similar to how the square-root of '-1' is a placeholder in complex analysis. When we think about all numbers as placeholders in this way -- even the integers -- we start to move away from numbers as the final results of computations and move towards functions and operators as the final results. How numbers are defined and the relationships between these definitions is more important than the numbers themselves.

I have a question about the beam of light reflected by the wall. When the wall is far far away, as the light source turns to one side, the distance the beam of light needs to travel in order to reach the wall increases very fast and so does the time it takes to reach the wall. Wouldn't the light point on the wall then always move to the side at a speed below the speed of light?

I Always waiting for your new ones ..

How she blitzed in the ad was definitely infinitely German. 😂 God, I love her videos. Please don't ever stop. 😊

The interval (-∞, ∞) is homemorphic with the the open interval (0,1) , i.e there is a continuous bijection with a continuous inverse function that sends one of them to the other one supported by the usual metric topology and its inherited one on the interval (0,1). Howevers we can't find such a function between the Real line and the compact interval [0,1] and this opens the gate to the idea of the set [-∞,∞] with infenity numbers included and this set is compact and thus homeomorphic to [0, 1] . Similar discussion can be made concerning the complex field C wich can have an extension homeomorphic to the disc D= {z , |z|≤1} .

Ein sehr interessantes Video über ein sehr interessantes Thema 😀! Es ist wichtig, dass wir uns im Klaren sind, was wir mit dem Zeichen „∞” eigentlich meinen, wie es in diesem Video auch gesagt worden ist. Wenn wir damit ein unendliches Element u in einem nichtarchimedischen angeordneten Körper wie demjenigen der rationalen Funktionen über IR oder IQ meinen, dann kann man mit diesem Element wie mit jeder anderen Zahl rechnen. Insbesondere gilt u+1=1+u>u, u*2=2*u>u, und 1/u>0. Das ist z.B. der Fall, wenn man die rationalen Funktionen alphabetisch so angeordnet hat, dass nichtkonstante Polynome größer als alle konstanten Polynome (d.h. alle Elemente des zu Grunde liegenden angeordneten Körpers, was stets alle natürlichen Zahlen einschließt) sind, und u etwa das Monom T ist. Der hypothetische Kehrwert der 0 wäre dann immer noch größer als alle Elemente des nichtarchimedischen Körpers. Besonders interessant ist der angeordete Körper der Surrealzahlen, da dieser der größte aller angeordneten Körper ist und alle Ordinalzahlen beinhalten. Damit sind wir bei den Ordinalzahlen (Ordnungszahlen) und dem Unterschied zwischen diesen und den Kardinalzahlen (Mächtigkeitszahlen). Wenn mit „∞” eine unendliche Kardinalzahl K (wie etwa aleph0) gemeint ist, dann gelten die Gleichungen K+1=K+1=K und K*2=2*K=K. Wenn mit „∞” jedoch eine unendliche Ordinalzahl O gemeint ist, dann gilt 1+O = O < O+1 und, falls O eine Grenzzahl wie omega0 ist, 2*O=O

@Kah7654

3 жыл бұрын

Allerdings gibt es den Unterschied zwischen Mathematik und Physik. Konzeptuell existiert "unendlich" natürlich, angewandt auf die Physik ist aber die Frage, ob zB der Abstand zwischen zwei Teilchen beliebig klein oder beliebig gross werden kann. Und das ist keine mathematische Fragestellung sondern eine physikalische, die letztlich nur ein Experiment beantworten kann. Analog ist es ja zB einfach, sich vorzustellen mit 10-facher Lichtgeschwindigkeit zu reisen, selbst wenn das in der Realität evtl. nicht möglich ist. Daher sind Mathematik und Physik auch nicht dasselbe und jedes mathematische Konzept muss mit Vorsicht betrachtet werden, wenn man es in der Physik anwendet. Sonst ist man schnell "Lost in math".

@TristanLaguz

3 жыл бұрын

@@Kah7654 Es stimmt natürlich, dass Physik und Mathematik nicht dasselbe sind. Wenn es aber in der physikalischen Welt nichts unendliches gäbe, könnten wir auch unsere Gehirne nicht dazu einsetzen, über die Unendlichkeit und das Unendliche nachzudenken, nicht wahr? Diese Fähigkeit müssten wir dann ganz unseren Seelen zuschreiben. Nun geht die Seele freilich über das Gehirn hinaus, aber ich glaube wirklich nicht, dass beim Denken über das Unendliche das Gehirn nicht beteiligt ist, und ich glaube, dass man diese meine Meinung auch versuchlich nachprüfen kann. Könnte also diese Diskussion da sein, wenn es in der physischen Welt nichts Unendliches gäbe?

Excellent Programme

This is helpful & interesting. I'm going to watch it again. I watched Are We Made of Math? What type infinity is in the speed of light or the EMF? I have an abstract art, metaphysics use of infinity in the speed of light. I like this talk & this topic. Everyone can find a place in infinity. You have a pleasant speaking voice Sabine.

@dalitshiv834

2 жыл бұрын

😊

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion

Dear, Excellent, CONGRATULATIONS !

I hope you do a video on normalization of infinities in physics as a followup.

0:04 Instantly upsets all the mathematicians. I'm an engineer, so I don't mind XD

@Inujasa88

3 жыл бұрын

Yep, we do this all the time, no big deal 😂

@theobolt250

3 жыл бұрын

@Shadman Shahriar: You should talk to Sheldon Cooper (Tv series "The Big Bang" NBC if I'm not mistaken).

@NoMoreForeignWars

3 жыл бұрын

Infinity is untestable and unobservable ergo its not scientific.

@Inujasa88

3 жыл бұрын

@@theobolt250 Sheldon despites experimental physicists, so i wouldn't start a debate with him xD

@jellyfishjelly1941

3 жыл бұрын

I'll gladly take that infinity, divide 3V by it, call the result -90dBm and point thermal camera at a colleague who just entered the room.

I just asked this question! Thank you!!!!!!

Thank you, Professor.

3:10 Thanks for this. The math side of my brain was getting a bit squeamish a few seconds earlier.

I love how whenever there is a conversation about an expression of 0 becoming solution everyone freaks out because they think somewhere in the world they’ve just given a mathematician a aneurysm lol

@didack1419

Жыл бұрын

I did cringe a little

Deep, wow. Loving this content m'lady, you rock.

I waited soooooo hard for a Video which has infinty as topic in this "direction" thank you Mrs Hossenfelder great inspiration.🙏

@ZeroOskul

3 жыл бұрын

Hey, buddy, you call her DOCTOR Hossenfelder! (see: "hey lady you call him DOCTOR Jones +Temple of Doom" to see humor)

Wait, we do know Chuck Norris counted to infinity. Twice.

@andreasarnoalthofsobottka2928

Жыл бұрын

While doing so he discovered - the last digit of Pi. - that e is periodic. - a numerical value for i .

The ideas of infinity and an end came into my head when I was 8 years old and lying in my bed going to sleep. In the form of trying to imagine it in space, not in the form of mathematical equations. It was so unimaginable that I finally started crying. It just blew my mind. So here I am over 50 years later thinking maybe I will be able to get 2 hours sleep and this pops- up. Great.

@mathfincoding

Жыл бұрын

Had a similar experience. I ended up puking because it was just overwhelming.

@vickiezaccardo1711

Жыл бұрын

@@mathfincoding It really is. How anyone can accept ' the soup' as an ultimate answer to origins is beyond me. Or that mathematical equations are equivalent to comprehending eternity, an end, or nothingness.

Excelent presentation.

Another great video, Sabine. That is a very nice outfit you are wearing today!

Are there also different types of zeroes? Like 1/(countable infinity) compared to 1/(uncountable infinity)?

@clmasse

3 жыл бұрын

Yes, there are also the zeros of a polynomial.

@Aurinkohirvi

3 жыл бұрын

My zeroes are fatter than in these computer fonts.

@NikolajKuntner

3 жыл бұрын

If you have an operation "·" defined on a set X (i.e. if you have what's called a magma), then there is at most one element "0" characterized by the property that "0 · x = 0" as well as "x · 0 = 0" for any x in X (a magma has at most one absorbing zero element).

@NikolajKuntner

3 жыл бұрын

@@clmasse A "zero" of a polynomial is merely a value where the polynomial value is zero. The number 2 is a zero of the polynomial p(x) := x^2-4. I mean just because someone is a "bookworm", doesn't mean she's a worm. A bookworm is not a special kind of worm :)

@clmasse

3 жыл бұрын

@@NikolajKuntner The zero of a polynomial is like a zero of a multiplicative group, or the zero of an additive group, a purely abstract concept. A whole mathematical theory can be build from a fundamental polynomial, and have several zeros. It can even be formalised so that the fundamental polynomial never shows up explicitly.

This is one of your best videos

A very nice presentation. It reminds of my first calculus class given by a Bell Labs instructor at a remote University of Hawaii location. His introduction paraphased: .." the most difficult concepts to grasp are the terms infinity and infinitesimal. His explanation of infinity was similar to yours. His explanation of iinfinitesimal, was; you can describe you walking towards a point, dividing the distance in half continually. The infinitesimal is that moment you cross that point." Probably, as you explained zero and may be has a real meaning in the universe. It's amazing how infinity applies to mathematics, but not anything real in the universe. Or perhaps the universe is infinite, but I even find that difficult to believe. If it's an everlasting expanding and contracting universe, I contend the universe is finite of particles/energy. If it's infinte in particles/energy, who knows what to think. In either case, we will only be able to explain those two terms mathematically. Thanks so much for the details in your presentation.

Chuck Norris counted to infinity, twice.

@waynedarronwalls6468

3 жыл бұрын

He didn’t though, did he?

@markthebldr6834

3 жыл бұрын

He also started the sun.

@Z-Diode

3 жыл бұрын

@@markthebldr6834 And he‘s also going to stop and finish the 🌞.

I was going crazy before she mentioned the technicality at 3:16 ...😅 Thanks . Great video 👏

I love these videos but it goes right over my head!

I actually understood this one - thanks!

"There are infinitely many types of infinity" - Terrific. Are there countably infinitely many types or are there even more infinitely many types of infinity?

@tamptus3479

3 жыл бұрын

look at wikipedia: Cardinal number, large Cardinal number, huge Cardinal number, List of large cardinal properties Other infinity concept is : Surreal number also kown as Convay numbers. an other concept is: Hyperreal number. Adding one point to a space to make the space kompakt is called Alexandroff extension .Example for Alexandroff extension is adding infinity to the the complex numbers equals a sphere. All thess can be done in Settheory called ZFC, ZFC is defined by using FOL (first order Language). Every Theory in FOL has a countable Model. Looking from outside we have only countable many set, but looking from inside we see uncountable sets. This is not a contradiction, because the map which makes a set countable is not a Member of the Model.

@sobeeaton5693

2 жыл бұрын

According to the continuum hypothesis, the answer is either yes or no.

@NoName-gp2dt

2 жыл бұрын

infinte types of infinity

@fluentpiffle

Жыл бұрын

People generally have a very poor understanding of what the word 'infinite' actually means.. This is not any kind of 'fault', but just that we have evolved within the confines of what appears to be a finite environment, and we thus try to look at things in finite ways, also justifying those 'finite' thoughts. When I first approached the 'problem' I had the same difficulties, so it takes our minds a lot of effort to reach another perspective of understanding, but it IS achievable.. Firstly, there cannot be more than one 'instance' of infinitude, otherwise a secondary 'thing' would render them both 'finite'. So we are describing a 'oneness'.. Also, it can have no 'beginning' nor 'ending' as these would also necessitate a secondary 'thing' (or the utter nonsense of a 'nothing'!), so we are describing 'eternity' when we apply 'time' concepts. Then, we have to admit that it can only be the one thing that interconnects all other 'things', and we deduce this to be 'Space', necessarily.. All references to 'size' or 'direction' do not apply to the nature of infinitude, and thus have no relevance to our understanding of the true nature of existence. 'Measurement' has limitations.. When we point to any position in Space, we effectively create a 'beginning' to any subsequent forms of measurement, which only has relevance to the entity desiring to understand said 'measurement'. Measuring things does not make them a main-feature of the nature of reality, only a desire of 'measurement' from a purely Human perspective. Within infinitude everything appears to be at the 'centre' of that which it finds detectable ('observable').. So, the moment you create the perspective of a 'centre', you become that centre..Here we can find the real problem with using 'mathematics' as a tool for understanding infinite nature. We have to firstly posit the 'points' to be 'measured' in order for the measurement to take place.. And this is why we end up inventing 'things' that do not exist in reality from mathematical constructs that do not describe the truth about nature.. 'Math' is another finite aspect, and so has limited usage. It helps us to describe specific positions and calculate certain desirable measurements to ourselves, so that we may use finite reference points, but it breaks down at the level of describing a necessarily infinite reality. Thus, as it is with our 'senses', we need various different kinds of understanding, all working in tandem with each other to produce the 'bigger picture', and we have philosophy and psychology, arts and 'mysticism'/intuition, among others, evolved for this task. However, because we live in an 'expert' driven society, all the 'senses/methods' are at war with each other, jostling for control, when the only true understanding occurs if we emulate nature itself, and work from a foundation of wholeness.. "Commendation from NASA for research work at Massachusetts Institute of Technology on the Earth's atmosphere and the Moon's surface for navigation of the Apollo spacecraft to the Moon.. Dr. Milo Wolff has found the structure of the electron consisting of two spherical quantum waves, one moving radially outward and another moving radially inward. The center of the waves is the nominal location of the electron 'particle'. These waves extend infinitely, like charge force. All 'particle' waves mix and contribute to each other, thus all matter of the universe is interrelated by this intimate connection between the fundamental 'particles' and the universe. The natural laws are a direct consequence of this Wave Structure of Matter (WSM), thus WSM underlies all of science." spaceandmotion

That shirt is amazing!

infinity is like a shorthand for "as big as you want". Like saying something equals infinity is just saying that it keeps going, like you'll never run out no matter what you do, unless you use the infinity to destroy the infinity. And putting infinity inside an expression is like saying you're interested in what happens as you keep going, and if things ever stop happening, or if they all would hypothetically cancel out. so saying infinity+1=infinity for example is just saying something like, "if I will never run out of apples, and you give me an apple, I will never run out of apples" or "if I started counting my apples I would not be able to finish (this is not the same as uncountable infinity), and if you gave me another one, I still wouldn't be able to finish counting them" 2*infinity = infinity is like "I'm never gonna run out of apples, and you're never gonna run out of apples, and if you gave me your apples I would still never run out of apples" infinity^2/2^infinity = 0 means like if my friends start cloning themselves, and I buy square grid of apples each time all my friends (including their clones, and their clones' clones, etc.) have had a turn in the cloning machine with a side length equal to the number of times they've been cloned, and split them between everyone, as time goes on each person will get less and less, and in fact if you pick a really tiny (positive) number, at some point each friend/clone will get less than that amount ok that actually probably made it sound more complicated than it is, so dropping the apple analogy, if you start squaring really big numbers, and raising 2 to the same really big numbers, the numbers in the second group will be many times bigger, and in fact, with a big enough number, bigger by an amount bigger than any (finite) amount you want. the last bit of that is sort of the crucial part. Because things that approach 0.0001 or a gazillion without going any smaller/bigger respectively exist, which are in many ways similar to being 0 or infinity, but are crucially distinct. Like you can count a gazillion apples, and see that it is distinct from having a gazillion and one apples.

Best comment ever, by Dirac, about renormalization - "One should ignore a quantity because it is small, not because it is infinite." :) There is also geometric infinity, as the ideal domain in projective geometry. And as a thing in the complex plane, where one adjoins infinity to the ordinary complex numbers and so puts it into 1-1 correspondence with a sphere.

True story: I was a high school physics student and our course had progressed on to the general topic of electromagnetism... One morning our lecturer began with some basic principles of electromagnetic field theory, starting with, "OK, let's suppose we take a piece of super-conducting wire of infinite length..." I raised my hand. "Yes?" ... "Doc, if you had a piece of wire of infinite length and you cut it in half, what would you get?" ... "Get out..." In the subsequent detention period that is the only just outcome for being a smart-ass in class, we had a really excellent discussion about the principles and problems of infinity. Looking back, it's probably fair to say that the one hour of detention completely turned around my appreciation of physics, from something that I "took to complement the chemistry and math", turning it in to a field that still delights me, 40 years later. Thanks, infinity...

In my student days, some 50 years ago, we learnt that mathematical constructs could be equally proven with or without the assumption of infinity. Has this now moved on?

@kerr354

3 жыл бұрын

Do you mean some form of mathematical finitism?

@onecowstampede9140

3 жыл бұрын

Go get some Kurt Gödel from your library, mathematics itself is either unprovable or incomplete.

@espaciohexadimencionalsern3668

3 жыл бұрын

@@onecowstampede9140 or is not the right frame.

@guribuza2007

3 жыл бұрын

Wow, was that statement ever standard?

@hyperduality2838

3 жыл бұрын

Infinity is a Platonic or mathematical concept! Platonic forms are dual to to particulates -- Plato. Universals (Noumenal, A priori) are dual to finite localized forms (Phenomenal, A posteriori) -- Immanuel Kant. Space & time are both noumenal objects or objects of the mind "A priori" -- Immanuel Kant, The critique of pure reason. Space is dual to time -- Einstein. Synthetic a priori knowledge == space/time -- Immanuel Kant. Concepts are dual to percepts -- the mind duality of Immanuel Kant. Absolute time (Galileo) is dual to relative time (Einstein) -- Time duality. The future is dual to the past, we remember the past and predict the future -- Time duality. My absolute time is your relative time and your absolute time is my relative time -- Time duality. Length, distance or space is defined by two dual points -- space duality. Absolute space is dual to relative space -- space duality. Up is dual to down, left is dual to right, in is dual to out (x,y,z) -- space duality. Space duality is dual to time duality. "Always two there are" -- Yoda.

Some information on immortals. I always await your videos as they are so useful and informative. Creating a mathematical equation to express the potential number of dance steps surpassing the age of the universe is quite abstract and challenging. However, as a creative metaphor, you might express this idea poetically rather than with a precise equation. The concept could convey the infinite possibilities of dance steps, transcending the boundaries of time and cycles in a poetic or metaphorical sense. Indeed, the comparison of dance steps to the digits of pi, both being infinite and forwardly enumerated without knowing everything, adds a poetic and abstract dimension. This metaphor suggests an immortal dance, echoing the limitless and unpredictable nature of both the mathematical constant pi and the potential choreography of dance steps. An immortal being might find more fulfillment in embracing new creative endeavors, as sticking solely to the old and familiar could eventually lead to boredom. Exploring new perspectives and engaging with fresh, creative experiences adds excitement and meaning to an eternal existence, providing continuous growth and enrichment. Developing an abundance mindset can be beneficial. It involves focusing on opportunities, possibilities, and the belief that there are enough resources and success to go around. This mindset often leads to positive thinking, resilience, and a willingness to explore new possibilities. It contrasts with a scarcity mindset, which is rooted in fear and the belief that resources are limited. Embracing an abundance mindset can contribute to personal growth and a more positive outlook on life. ChatGPT 🌹