9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927:2293] (1 Viewer)

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

psikeyhackr's recent post falls into the first category, "equal and opposite destruction."

Yeah, yeah, yeah.

Newton's 3rd Law of Motion went on vacation that day.

Newton's Third Law

If the top LEVEL of the stationary portion was crushed, then the bottom LEVEL of the falling portion had to be crushed.

When I go to the link above, I see:

For every action, there is an equal and opposite reaction.

I don't see the words "destruction" or "crush" in there anywhere.

What it says is that the force exerted by one body on another is matched by a reaction force equal in magnitude and opposite in direction which is exerted on the first body by the second. It can be extended to other quantities besides force via scaling or integration over time or distance. Based on that principle, which surely holds here, we can reason about the mechanics and infer what sort of destruction there might be. The twin fallacy of argument #1 is

- the unspoken assumption of equivalence between force/action and the destruction which would result from application of that force
- the failure to recognize that distribution of stress and associated strain is the cause of damage, which is derived from the internal force at any given point in the structure

To be continued.


BTW, I wrote this post before going to the link to copy the quote on N3. Regardless of the variations in wording when the law is quoted, I was 100% confident the notion of crush up/crush down wasn't in there anywhere. Makes you wonder why this argument is allowed to fly as often as it is.

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

There are crucial mechanical constraints imposed on this problem. It is a self-supporting structure. The motion is in the vertical dimension, with gravity applied. Let us consider a single "block", in this case at rest on the ground under the influence of gravity. While the object could be thought of a bar or rod or sheet (etc), it's really an abstract 1D line of some arbitrary material. The 2D graphics I'm going to be using here and going forward are just for purposes of illustration and do not actually reflect the situation for 2D/3D because 1D models cannot account for edge effects in stress distribution (although it does make a decent first approximation).


A block of ideal isotropic solid material of uniform density in static equilibrium will have a stress distribution like so, with red representing maximum stress and green being minimum:

The smooth gradient is precisely what intuition expects. The bottom experiences the greatest, the top the least, and the linearity of the gradient is the result of the linearly decreasing load imposed at each point going up the "structure". Because the object is at rest, the sum of all forces acting on the block must be zero. If the mass of the block is m, the weight is mg and, in order to satisy N3, the downward force of the block on the ground must be matched by a force of the same magnitude directed upwards. Therefore we can say the equal and opposite forces at ground level are each of magnitude mg.

But, move an infinitesimal displacement upwards from that point, and those forces are NOT mg, they are infinitesimally less. At half-height, they are mg/2 and, at the top, zero. Obviously the very top edge has no load applied from above. What happened to Newton's third law? It is satisfied at EVERY point in the structure, BY DEFINITION. We worked forward from first principles USING N3 to determine the expectation for stress in this simple system. How could it be any other way?

Bazant states this explicitly, and conforms to the law throughout his treatment. To be continued.

 

[ozeco41]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

No way. Stellar job, as usual. And complementary, as usual.

[edited for brevity]

If the claims of violation of physical law are false in light of more realistic mechanisms for the tower collapses, could they be true for blocks world? No. That's what I'm going to attempt to address.

Thank you - all understood and agreed.

@nooByzarC - First note that the 8th word is "complementary" - it is important to understand that and where Kat and I are coming from.

Simply stated I tend to focus on qualitative explanations of "real event 9/11" - Kat tends to go for full legitimacy in a broader context. At risk of 'verbaling' Kat my focus is on simplicity of explanation in WTC real event discussions. Kat prefers rigour of physics and argument in a more generic context. And, yes, we have a long history of discussing these matters from those complementary positions. And occasionally we are complimentary.

Psikey's statements tend to be ambiguous[SUP]#[/SUP] - there are several misinterpretations in the claim that started this bit of discussion. I slightly disagree with Kat - this is what I think is the situation:

You're correct that most of the misinterpretations are not really related to blocks.

...but the one ozeco identified is.

I see Kat has started his explanation - I'll leave him to it.



# That should rank as "Understatement of the Year" :roll:

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Now, divide the block into a bunch of equal blocks... say 110 of them... and zoom in to blocks 96-100, as numbered from the bottom going up:

The first thing I want to point out is that I've rescaled the stress color map from the previous graphic; the colors still reflect maxima and minima for the portion visible, but it is not nearly so steep a gradient as before. If the same scale were retained, it would be a nearly uniform dull green for just these five blocks. All the same there is a stress gradient (easily discerned with the rescaling) and we see the lower blocks bear more load than the upper. Also, and more importantly, we can see how the stress concentrations are divvied up amongst the blocks.

Once again, the lowest experiences the greatest load/stress, the highest the least. N3 satisfied at every point in the structure, but opposing forces at different vertical locations ALL different, as N3 dictates they must be.

If it were a matter of a homogenous material - uniform density and modulus, etc - then we'd be done with the N3 aspect of this entirely. Obviously, there is a vertical asymmetry or bias in this problem - the red block is under greater compressive stress than the green block. Make the block large enough, theoretically, and it will crush under its own self weight. Where will that happen? At the bottom, clearly.

To be continued.

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

This truly is a useless model of a skyscraper, but it was good enough to get the initial N3 part across. To make this block more closely conform to a building, two primary constraints can be introduced:

1) the ratio of load to modulus at equilibrium is a constant everywhere
2) the density increases going down the structure

NOTE: by adding these constraints, the block can no longer be considered bulk material, for the most part. It may be possible to create a bulk material which satisfies these properties, but it would be advanced beyond the discussion here, and irrelevant. By adding these constraints, the subject has shifted to structures. But we can still call it a block or a collection of blocks when we rightly consider the properties of the structure or portions of it.

The first constraint is an idealization; it's an architectural objective to assure a minimum factor of safety (FOS) over the entire structure so, while never achieved in practice, it is a good first approximation to call demand to capacity (DCR, equivalent to the ratio in [1]) constant. Technically, FOS is not the reciprocal of DCR, but it is close and good enough for this.

The second constraint is simply a practical consequence of the first: in order to maintain a constant FOS/DCR, the structure must have greater capacity at the bottom than the top, and it takes more of the (same) material to accomplish this. This is one of psikeyhacker's most commonly made points. Yawn. Of course a tall building is stronger and therefore heavier at the bottom.

This changes nothing with respect to N3 or whether or not the internal forces in a body in static equilbrium sum to zero. N3 automatically applies to the structure as defined; again, called out explicitly by Bazant.

Yes, to be continued.

 

[Sunzi]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

... I was not a "truther" but someone who wanted to UNDERSTAND in some level of specificity how the structures failed. I saw no reason to believe there were taken down by CD. CD was apparently Gage's meme. I really didn't know when I signed their petition and didn't look at their online materials.

By 2009 and with every anniversary of 9/11... ...

Not a truther. Was the date for your PNAC NPH kind of timing?

December 7th 2009 SanderO, Why the Truth Matters? "Using the scientific method, AE911Truth along with scientific investigators have determined that the buildings were not destroyed as a result of fires leading to a “progressive collapse” and global structural failure. AE911Truth has found that all three towers were destroyed as the result of explosives placed within the towers before September 11, 2001 detonated after the first plane struck the north tower. In the case of WTC 7, it was seven hours after the first plan struck before the demolition was initiated. The three towers did not collapse, they were destroyed by explosions."

Which scientific method did you guys at AE911 use when you were "not a truther"?

"The three towers did not collapse, they were destroyed by explosions."

Not a truther? Ever?

The evidence of explosive that is undisputed as far as I am concerned is that the building could not fall as quickly as they did UNLESS explosives destroyed the lower parts so the parts above could descend so fast and un impeded. - SanderO, 2009

I believe you. The real research at 911FF?, real research and technical people. LOL, that is rich, and more BS, or does Major Tom's book have a conclusion now? I think the "book" sums up all the real research at 911FF.

This is a lot of extra credit for what is solved by a stopwatch.

 

[SanderO]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Not a truther. Was the date for your PNAC NPH kind of timing?

Which scientific method did you guys at AE911 use when you were "not a truther"?
Not a truther? Ever?




I believe you. The real research at 911FF?, real research and technical people. LOL, that is rich, and more BS, or does Major Tom's book have a conclusion now? I think the "book" sums up all the real research at 911FF.

This is a lot of extra credit for what is solved by a stopwatch.

Sunzi,

If not has yet, let me be the first to tell you that you're a snotty condescending jerk.

What makes you think you are some sort of expert? An expert that everyone has to kow tow to?

I can always recognize a creep when they mine quotes from 5 years ago and play gotcha. If you don't care for my explanation it doesn't bother me one iota.

I don't care how intelligent or educated you are, your manners have rendered you a persona non grata.

 

[ozeco41]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

If you don't care for my explanation it doesn't bother me one iota.

For what it is worth Sander I admire your honesty in explaining the journey you travelled.

I don't understand the obsession with past events from which you have clearly moved on.

There are many things you now accept that I fully agree with. There are some areas where we disagree. Those are the areas I enjoy discussing with you.

The past is gone.

 

[SanderO]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

For what it is worth Sander I admire your honesty in explaining the journey you travelled.

I don't understand the obsession with past events from which you have clearly moved on.

There are many things you now accept that I fully agree with. There are some areas where we disagree. Those are the areas I enjoy discussing with you.

The past is gone.

Precisely... Discussion with you is not something of personal insults but a challenge to get an idea accepted. It forces me to find better ways to present and even to clarify my own understanding of... my own understanding.

When others constantly, such as Sunzi, drag up this nonsense... tfk, Beachy seem to love to do this as well... for me it's like turning off the volume and I won't pay attention to anything they say, right, wrong or indifferent.

Nothing wrong with being wrong and realizing it and leveraging it to learn. I've been taking criticism for what I do all my life... it's part of the process. But the tacky insults are really childish and creepy.

So a big intellect turns themselves in my mind into a mental midget for the pettiness and obsessing over trivial nonsense.

I am always moving on...

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

The first type of claim:

the unspoken assumption of equivalence between force/action and the destruction which would result from application of that force

is missing the mark as far as "destruction" goes because N3 is satisfied everywhere in a structure whether or not any part of it is intact, crushing, static, dynamic or whatever. That's the way the law rolls. Things like motion come about because of unbalanced forces, and this is the simple fact which escapes every whiner I've seen grousing about violations of N3. Destruction of a material or structure is a more complex notion than motion, though it does involve motion, but it has nothing to do with N3.

Newton's OTHER laws of motion govern this problem!

Those laboring under misunderstandings of the application of N3 should review the cart and horse problem.

-------------------

To determine what gets damaged, crush, or generically failed, an entirely different criteria distinct from those implied N3 must be introduced. It is necessary to consider strain in the materials, which is expresses the change in length of the material under stress (force applied over material extent). At a particular strain, real world materials yield. Break, crush, deform, etc.

Now the model has moved to a continuum of non-uniform material with two additional properties which can be considered structural. How does change the diagrams I've posted? The diagrams were meant to represent stress which, in a uniform material in the circumstances described, is proportional to strain. If the new property constraint given by #2 above were assumed to be a linear density decreasing with increasing height, then the stress gradient would be even steeper. But now the strain is constant throughout. Diagrammatically:

Pretty boring. Gray because any color will do. Now it's no more likely to self-crush at the bottom, or anywhere in particular. Assuming any part is self-supporting, the entirety of the structure is self-supporting. It will not fail or self-crush unless something new is introduced, namely a defect which reduces the capacity (locally) so as to allow the structure to move away from static equilibrium. That will be covered next.

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

The Bazantian defect?

Removing a story? Yes, no, maybe so?

NO. Bazant did NOT remove a story, he arbitrarily decreed it to be zero capacity. All the mass is still there. This is extremely important with respect to the great one-way crush down controversy. Everything, in fact. If the story were "disappeared", that would be an interesting separate problem, one I've studied quite a bit, as well as others. I'm going to take a moment to talk about it since I'm certain this is most people's conception of the model - two blocks smashing into each other.

When you set up a model with the conditions and constraints mentioned so far, with just about any variation of that you can imagine (continuum vs discrete, uniform versus nonuniform, etc), the results differ from Bazant. Markedly. Without doing a formal sampling, I will tell you anecdotally that most scenarios will crush both directions. If there is only one crush direction, it is predominantly crush up. In cases of exclusive crush up, the end result is arrest when crush up is complete - what I call the "dumpster in the sky" result. A dense pile of rubble atop a fully intact lower section.

This should give you all a pretty good feel for how applicable this sort of model is to the collapses. Not very!

These types of results are in line with most intuitive expectations, despite the vertical bias and so on. Crush in both directions. This intuitive expectation is correct. How, then, does Bazant come up with one-way crush down? I mean, besides by decree in declaring the upper section to be rigid until crush down was done. He did a more rigorous two degree of freedom analysis in the Bazant and Le discussion and was able to justify the assumption of upper block rigidity at first impact. Given the propensity for the "smaller, weaker" upper section to crush, this seems impossible.

He missed mixed crush direction by skin of a rat's ass. It's the mass of the defect story that makes all of the difference. When it fails, it compresses. As it compresses, it acquires momentum. At so-called first impact, the failed story has compressed to some finite height given by the maximum compaction and effectively "re-hardened". It is this full compaction state which actually comprised the impact, NOT the collision of two disconnected bodies.

As the failed story compresses, the top part is moving at the same speed as the upper section, dropping at freefall. The bottom part is stationary. On average it has a velocity between zero and upper block velocity. Bazant takes the velocity of the mass of the failed story just prior to impact to be one-half the upper block velocity. It is the momentum of this failed story which nudges the result into exclusive crush down.

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

The real research at 911FF?, real research and technical people. LOL, that is rich, and more BS...

I recommend you abandon this tack. One warning and one only. Stop right now.

 

[booNyzarC]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Not a truther. Was the date for your PNAC NPH kind of timing?

Which scientific method did you guys at AE911 use when you were "not a truther"?
Not a truther? Ever?




I believe you. The real research at 911FF?, real research and technical people. LOL, that is rich, and more BS, or does Major Tom's book have a conclusion now? I think the "book" sums up all the real research at 911FF.

This is a lot of extra credit for what is solved by a stopwatch.

You know, there really is no need to create another target simply because the preferred one is at present unavailable. Recognize an ally and do not make him an enemy.

 

[booNyzarC]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Please don't get distracted Kat, I want to see this finished.

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Please don't get distracted Kat, I want to see this finished.

Thanks. I'm trying to do this and yet tend to some things simultaneously, it'll be a bit before the conclusion. (One, two more posts; hopefully not too dry - promise I'll say ****, piss or **** somewhere in there).

Edit: ooh, "piss" got through. Piss licker? Piss monger?
Edit2: awesome.

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Sometimes a picture is worth a thousand words, so is cutting to the chase. The graphs below are from B&L, with my annotation in red:

The slight difference in displacement indicated between end of crush up and the mg line is the difference between the intuitive expectations of most of the world (from scholarly to profane) and Bazant's results. Had the displacement in the numerical solution reached the mg line, crush up would've continued.

The result is fully justified, given the assumptions and trappings. It's actually great stuff. It is, however, purely academic. Change the input parameters a bit in most realistic directions and the result is mixed crush direction. In no case does it bear a resemblance to the actual collapse mechanism.

Actually, I think that about covers it as far as factual examination. I have some opinions to throw on that, but it can wait.

 

[ozeco41]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

I must be getting old - had to read this three times AND put brain in gear before I got it:

It is this full compaction state which actually comprised the impact, NOT the collision of two disconnected bodies.

Somehow I spotted this bit jumping off the screen at me.

This should give you all a pretty good feel for how applicable this sort of model is to the collapses. Not very!

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

I must be getting old - had to read this three times AND put brain in gear before I got it:

It is this full compaction state which actually comprised the impact, NOT the collision of two disconnected bodies.

Don't feel bad. It took me forever to recognize what I'd already read a dozen times in B&L. The answer was always right there in plain English and not complicated maths. I'm embarrassed to say I puzzled over this and related aspects for years. I'm less embarrassed when I take note that I'm the only one providing the explanation when faced with the conundrum. I've seen people try to explain it - now that can be embarrassing! - but no success and mostly they just avoid it.

Turns out it's ridiculously simple, once you get it. Conveying the idea is not as easy as it seems.

Somehow I spotted this bit jumping off the screen at me.

Uh huh!

 

[ozeco41]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Don't feel bad.

Who me!!

Turns out it's ridiculously simple, once you get it. Conveying the idea is not as easy as it seems.

Don't I know it. Getting the limits of Bazant even recognised was hard work back in 2010 - with me and M_T singing off the same sheet of music. There was little room for finesse which is one reason I never even looked hard at the details of papers later then B&Z.

But my latest partial frustration is at the initiation <>progression interface. The Eureka point for me a year or two back was seeing the "anachronism" (wrong word but it is the one I've been using.) underpinning "Missing Jolt" and all the "tilt v axial contact" stuff. Too late - it has already passed. even femr doubts my sanity over that one. And "initiating ROOSD" does not rely solely on accumulated floor debris is very closely related. But those still count as two separate "newish" concepts I suppose.

And, total diversion, the one I don't see ever progressing is the twin hypotheses "truthers cannot think" and "that's why they became truthers" - both stated more rigorously naturally. Behavioural psych is not the stuff for 9/11 forums with technocrats. Even tho' it explains so much.



[/EndWandering]

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

All of the allegations of Newton's third law violation and failure to observe momentum conservation on the part of Bazant (aka THE official story on progression (only half-serious)) are nonsense and a complete waste of time. Bazant is not the be-all and end-all of analytical approaches to collapse, he was simply the first and best for a long time. The accusations of violations of physics are unfounded but, even if they were, it wouldn't change the fact that his models are not a narrative of mechanism - even though he apparently thinks so. The false claims are therefore distractions upon distraction, and only serve to clog forums with ANYTHING BUT interesting discussion on real mechanisms or even improved analytical approaches.

99.9999% of discussion about the collapses is psychosocial in foundation, having little or nothing to do with engineering mechanics or forensics. A faith-based divide, if you will. A whole lot to say, a whole lot of nothin' to say....

 

[booNyzarC]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

So really you're talking about the compacted layer which acts as a shield for the upper block/upper portion of the building, being the defining factor in terms of why crush up does not occur at the same rate as crush down? I'm being called to dinner, but wanted to pose that question before heading off, just so that I was clear (or corrected if I'm unclear).

Excellent description by the way, and I'll have to go back over it a few times to make sure I'm not missing anything.

 

[ozeco41]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

All of the allegations of Newton's third law violation and failure to observe momentum conservation on the part of Bazant (aka THE official story on progression (only half-serious)) are nonsense and a complete waste of time. Bazant is not the be-all and end-all of analytical approaches to collapse, he was simply the first and best for a long time.[SUP]1[/SUP] The accusations of violations of physics are unfounded but, even if they were, it wouldn't change the fact that his models are not a narrative of mechanism - even though he apparently thinks so.[SUP]2[/SUP] The false claims are therefore distractions upon distraction, and only serve to clog forums with ANYTHING BUT interesting discussion [SUP]3[/SUP] on real mechanisms or even improved analytical approaches.[SUP]4[/SUP]

1 The big advantage for "Number 1" academic - first to publish in the world of "Publish or Perish"
2 The saddest aspect from my perspective - coz' I think he is seriously off course.
3 Yes - my reference several posts back - the 1D modelling has distorted forum discussions for years and still does.
4 Jointly or severally.

...99.9999% of discussion about the collapses is psychosocial in foundation, having little or nothing to do with engineering mechanics or forensics. A faith-based divide, if you will. A whole lot to say, a whole lot of nothin' to say....

Agreed but don't overbid. 95%?

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

So really you're talking about the compacted layer which acts as a shield for the upper block/upper portion of the building, being the defining factor in terms of why crush up does not occur at the same rate as crush down? I'm being called to dinner, but wanted to pose that question before heading off, just so that I was clear (or corrected if I'm unclear).

Yes, you've got it exactly. That's a lot easier way of explaining it, haha! And I'm sure you've heard that very thing before, many times, going right back to the earliest of times. How do I get off saying I'm the only one explaining it? Because what happens when you say the debris acted as shield for the upper block? People say it's BS. Then what do you say?

Because it is BS. Kinda hard to say it isn't. But there is the model description and the reason for the result, all positive and negative aside. It can be judged objectively as it is and not conflated with incompatible scenarios or misrepresented. Hence my comment about distraction upon distraction. Most people want to talk about official story, right or wrong, and do NOT wish to actually discuss the mechanics of collapse. Bazant is the de facto whipping boy, with some justification IMO. Problem is, it does little or nothing to elucidate actual mechanisms of collapse.

A shield? Really? Really. Specifically, a moving shield, just not moving as fast as the upper section until impact.

I do not believe the ongoing discussions have been served by overanalyzing Bazant. This is a textbook treatment. It's up to the reader to find the gold. I think it would be at least roughly applicable to the types of structures demolished by verinage. Potentially of great value. It's way off the mark for the towers. Ironically, the towers spurred development of the model. No one really cared before.

 

[Kat Dorman]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

1 The big advantage for "Number 1" academic - first to publish in the world of "Publish or Perish"
2 The saddest aspect from my perspective - coz' I think he is seriously off course.
3 Yes - my reference several posts back - the 1D modelling has distorted forum discussions for years and still does.
4 Jointly or severally.

Excellent points all.

Agreed but don't overbid. 95%?

You know I was originally going to write 98%, but then I thought of the vast universe of dedicated forums and threads, and how every time a news story comes out about 9/11 or anything which could be construed as related to fire/demolition/etc it spawns hundreds of comments... and what that usually amounts to... then I just stood on the '9' key for a while.

 

[booNyzarC]

Re: 9/11 - Did the Towers Fall At Free-Fall Speeds? [W:912, 927]

Not just a moving shield, but a moving and constantly growing shield with each additional compacted layer.

Still not the reality of what actually happened, but for the limiting case presented by Bazant, most definitely applicable and valid from a conceptual standpoint in my opinion.

Really great description Kat, and thank you for taking the time to lay it all out.

Hopefully others can take this to heart and truly understand it from what you've provided. I spent a lot of energy trying to convince someone of this very same thing and they simply refused to accept it because it didn't match with what really happened, and they seemed incapable of separating thought model from reality. Personally, I think it was just because they wanted to be right no matter what, and in the effort they intentionally, or subconsciously, confused, or inappropriately converged, the two when attempting to argue against it.

I kind of miss you Q24. I really do. <---- Memory lane

Cheers